| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Copilot.Zephyr
Description
Programming embedded systems with Copilot, in functional reactive style.
This module can be used with any board supported by the Zephyr project. https://zephyrproject.org/
See Copilot.Zephyr.Board.* for board specific modules.
Synopsis
- zephyr :: Sketch () -> IO ()
- type Sketch = GenSketch Zephyr
- data Pin t
- data Zephyr
- type Behavior t = Stream t
- data TypedBehavior (p :: k) t = TypedBehavior (Behavior t)
- data Event (p :: k) v
- (@:) :: IsBehavior behavior => behavior -> Behavior Bool -> BehaviorToEvent behavior
- class Input ctx o t
- input :: Input ctx o t => o -> GenSketch ctx (Behavior t)
- input' :: Input ctx o t => o -> [t] -> GenSketch ctx (Behavior t)
- pullup :: IsDigitalIOPin t => Pin t -> Sketch ()
- class Output ctx o t
- (=:) :: Output ctx o t => o -> t -> GenSketch ctx ()
- delay :: Delay
- data MilliSeconds = MilliSeconds (Stream Word32)
- data MicroSeconds = MicroSeconds (Stream Word32)
- type family IsDigitalIOPin (t :: [PinCapabilities]) where ...
- type family IsAnalogInputPin (t :: [PinCapabilities]) where ...
- type family IsPWMPin (t :: [PinCapabilities]) where ...
- blinking :: Behavior Bool
- firstIteration :: Behavior Bool
- frequency :: Integer -> Behavior Bool
- sketchSpec :: Context ctx => GenSketch ctx a -> Spec
- liftB :: (Behavior a -> Behavior r) -> TypedBehavior t a -> Behavior r
- liftB2 :: (Behavior a -> Behavior b -> Behavior r) -> TypedBehavior t a -> TypedBehavior t b -> Behavior r
- whenB :: Context ctx => Behavior Bool -> GenSketch ctx t -> GenSketch ctx t
- scheduleB :: (Typed t, Eq t, Context ctx) => Behavior t -> [(t, GenSketch ctx ())] -> GenSketch ctx ()
- ifThenElse :: IfThenElse t a => Behavior Bool -> t a -> t a -> t a
- class IfThenElse (t :: Type -> Type) a
- data Stream a
- data Bool
- data Char
- data Double
- data Float
- data Int
- data Word
- data Ordering
- data Maybe a
- class a ~# b => (a :: k) ~ (b :: k)
- data Integer
- data IO a
- data Type a where
- Bool :: Type Bool
- Int8 :: Type Int8
- Int16 :: Type Int16
- Int32 :: Type Int32
- Int64 :: Type Int64
- Word8 :: Type Word8
- Word16 :: Type Word16
- Word32 :: Type Word32
- Word64 :: Type Word64
- Float :: Type Float
- Double :: Type Double
- Array :: forall (n :: Nat) t. (KnownNat n, Typed t) => Type t -> Type (Array n t)
- Struct :: forall a. (Typed a, Struct a) => a -> Type a
- class Applicative m => Monad (m :: Type -> Type) where
- class Functor (f :: Type -> Type) where
- data Either a b
- class Semigroup a => Monoid a where
- class Semigroup a where
- (<>) :: a -> a -> a
- class Functor f => Applicative (f :: Type -> Type) where
- type String = [Char]
- data Array (n :: Nat) t
- data Word8
- data Word64
- data Word32
- data Word16
- class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
- sequenceA :: Applicative f => t (f a) -> f (t a)
- mapM :: Monad m => (a -> m b) -> t a -> m (t b)
- sequence :: Monad m => t (m a) -> m (t a)
- class Foldable (t :: Type -> Type) where
- foldMap :: Monoid m => (a -> m) -> t a -> m
- foldr :: (a -> b -> b) -> b -> t a -> b
- foldl :: (b -> a -> b) -> b -> t a -> b
- foldr1 :: (a -> a -> a) -> t a -> a
- foldl1 :: (a -> a -> a) -> t a -> a
- null :: t a -> Bool
- length :: t a -> Int
- elem :: Eq a => a -> t a -> Bool
- maximum :: Ord a => t a -> a
- minimum :: Ord a => t a -> a
- product :: Num a => t a -> a
- class Eq a
- class Monad m => MonadFail (m :: Type -> Type) where
- class Eq a => Ord a where
- class (Real a, Enum a) => Integral a where
- type Rational = Ratio Integer
- class Read a where
- class Show a where
- data Int8
- data Int16
- data Int32
- data Int64
- type IOError = IOException
- class Bounded a where
- class Enum a where
- succ :: a -> a
- pred :: a -> a
- toEnum :: Int -> a
- fromEnum :: a -> Int
- enumFrom :: a -> [a]
- enumFromThen :: a -> a -> [a]
- enumFromTo :: a -> a -> [a]
- enumFromThenTo :: a -> a -> a -> [a]
- class Fractional a => Floating a where
- class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a
- class Num a where
- class (Num a, Ord a) => Real a where
- toRational :: a -> Rational
- class (RealFrac a, Floating a) => RealFloat a where
- floatRadix :: a -> Integer
- floatDigits :: a -> Int
- floatRange :: a -> (Int, Int)
- decodeFloat :: a -> (Integer, Int)
- encodeFloat :: Integer -> Int -> a
- exponent :: a -> Int
- significand :: a -> a
- scaleFloat :: Int -> a -> a
- isNaN :: a -> Bool
- isInfinite :: a -> Bool
- isDenormalized :: a -> Bool
- isNegativeZero :: a -> Bool
- isIEEE :: a -> Bool
- atan2 :: a -> a -> a
- class (Real a, Fractional a) => RealFrac a where
- type ShowS = String -> String
- class Eq a => Bits a where
- (.&.) :: a -> a -> a
- (.|.) :: a -> a -> a
- complement :: a -> a
- type ReadS a = String -> [(a, String)]
- type FilePath = String
- type Name = String
- data Value a = (Typeable t, KnownSymbol s, Show t) => Value (Type t) (Field s t)
- class Struct a where
- type Spec = Writer [SpecItem] ()
- data UType = Typeable a => UType {}
- class (Show a, Typeable a) => Typed a where
- typeOf :: Type a
- simpleType :: Type a -> SimpleType
- data SimpleType where
- SBool :: SimpleType
- SInt8 :: SimpleType
- SInt16 :: SimpleType
- SInt32 :: SimpleType
- SInt64 :: SimpleType
- SWord8 :: SimpleType
- SWord16 :: SimpleType
- SWord32 :: SimpleType
- SWord64 :: SimpleType
- SFloat :: SimpleType
- SDouble :: SimpleType
- SArray :: forall t. Type t -> SimpleType
- SStruct :: SimpleType
- data Field (s :: Symbol) t = Field t
- class Cast a b where
- class UnsafeCast a b where
- unsafeCast :: Stream a -> Stream b
- array :: forall (n :: Nat) t. KnownNat n => [t] -> Array n t
- (==>) :: Stream Bool -> Stream Bool -> Stream Bool
- local :: (Typed a, Typed b) => Stream a -> (Stream a -> Stream b) -> Stream b
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- id :: a -> a
- fst :: (a, b) -> a
- snd :: (a, b) -> b
- ($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
- otherwise :: Bool
- (++) :: Typed a => [a] -> Stream a -> Stream a
- map :: (a -> b) -> [a] -> [b]
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- takeWhile :: (a -> Bool) -> [a] -> [a]
- take :: (Integral a, Typed b) => a -> Stream b -> [Stream b]
- read :: Read a => String -> a
- (==) :: (Eq a, Typed a) => Stream a -> Stream a -> Stream Bool
- (>=) :: (Ord a, Typed a) => Stream a -> Stream a -> Stream Bool
- error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- even :: Integral a => a -> Bool
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- uncurry :: (a -> b -> c) -> (a, b) -> c
- head :: HasCallStack => [a] -> a
- writeFile :: FilePath -> String -> IO ()
- getLine :: IO String
- putStrLn :: String -> IO ()
- filter :: (a -> Bool) -> [a] -> [a]
- cycle :: Typed a => [a] -> Stream a
- seq :: forall {r :: RuntimeRep} a (b :: TYPE r). a -> b -> b
- concat :: Foldable t => t [a] -> [a]
- zip :: [a] -> [b] -> [(a, b)]
- print :: Show a => a -> IO ()
- fromIntegral :: (Integral a, Num b) => a -> b
- realToFrac :: (Real a, Fractional b) => a -> b
- (^) :: (Typed a, Typed b, Num a, Bits a, Integral b) => Stream a -> Stream b -> Stream a
- (<) :: (Ord a, Typed a) => Stream a -> Stream a -> Stream Bool
- (<=) :: (Ord a, Typed a) => Stream a -> Stream a -> Stream Bool
- (>) :: (Ord a, Typed a) => Stream a -> Stream a -> Stream Bool
- max :: (Typed a, Ord a) => Int -> Stream a -> Stream a
- min :: (Typed a, Ord a) => Int -> Stream a -> Stream a
- (/=) :: (Eq a, Typed a) => Stream a -> Stream a -> Stream Bool
- (&&) :: Stream Bool -> Stream Bool -> Stream Bool
- (||) :: Stream Bool -> Stream Bool -> Stream Bool
- not :: Stream Bool -> Stream Bool
- errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a
- undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- (.) :: (b -> c) -> (a -> b) -> a -> c
- flip :: (a -> b -> c) -> b -> a -> c
- ($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
- until :: Integral a => a -> Stream Bool -> Stream Bool -> Stream Bool
- asTypeOf :: a -> a -> a
- subtract :: Num a => a -> a -> a
- maybe :: b -> (a -> b) -> Maybe a -> b
- tail :: HasCallStack => [a] -> [a]
- last :: HasCallStack => [a] -> a
- init :: HasCallStack => [a] -> [a]
- sum :: (Typed a, Num a, Eq a) => Int -> Stream a -> Stream a
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- iterate :: (a -> a) -> a -> [a]
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- drop :: Typed a => Int -> Stream a -> Stream a
- splitAt :: Int -> [a] -> ([a], [a])
- span :: (a -> Bool) -> [a] -> ([a], [a])
- break :: (a -> Bool) -> [a] -> ([a], [a])
- reverse :: [a] -> [a]
- and :: Foldable t => t Bool -> Bool
- or :: Foldable t => t Bool -> Bool
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- (!!) :: (Typed a, Eq b, Num b, Typed b) => [Stream a] -> Stream b -> Stream a
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- unzip :: [(a, b)] -> ([a], [b])
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- shows :: Show a => a -> ShowS
- showChar :: Char -> ShowS
- showString :: String -> ShowS
- showParen :: Bool -> ShowS -> ShowS
- div :: (Typed a, Integral a) => Stream a -> Stream a -> Stream a
- mod :: (Typed a, Integral a) => Stream a -> Stream a -> Stream a
- odd :: Integral a => a -> Bool
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- gcd :: Integral a => a -> a -> a
- lcm :: Integral a => a -> a -> a
- xor :: Stream Bool -> Stream Bool -> Stream Bool
- byteSwap16 :: Word16 -> Word16
- byteSwap32 :: Word32 -> Word32
- byteSwap64 :: Word64 -> Word64
- bitReverse8 :: Word8 -> Word8
- bitReverse16 :: Word16 -> Word16
- bitReverse32 :: Word32 -> Word32
- bitReverse64 :: Word64 -> Word64
- curry :: ((a, b) -> c) -> a -> b -> c
- lex :: ReadS String
- readParen :: Bool -> ReadS a -> ReadS a
- reads :: Read a => ReadS a
- (.^.) :: Bits a => a -> a -> a
- (.>>.) :: (Bits a, Typed a, Typed b, Integral b) => Stream a -> Stream b -> Stream a
- (.<<.) :: (Bits a, Typed a, Typed b, Integral b) => Stream a -> Stream b -> Stream a
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- tails :: Typed a => Stream a -> [Stream a]
- lines :: String -> [String]
- unlines :: [String] -> String
- words :: String -> [String]
- unwords :: [String] -> String
- userError :: String -> IOError
- ioError :: IOError -> IO a
- release :: Integral a => a -> Stream Bool -> Stream Bool -> Stream Bool
- putChar :: Char -> IO ()
- putStr :: String -> IO ()
- getChar :: IO Char
- getContents :: IO String
- interact :: (String -> String) -> IO ()
- readFile :: FilePath -> IO String
- appendFile :: FilePath -> String -> IO ()
- readLn :: Read a => IO a
- readIO :: Read a => String -> IO a
- phase :: Integral a => a -> Phase a
- label :: Typed a => String -> Stream a -> Stream a
- false :: Stream Bool
- true :: Stream Bool
- copilotMain :: Interpreter -> Printer -> Compiler -> Spec -> IO ()
- defaultMain :: Compiler -> Spec -> IO ()
- impossible :: String -> String -> a
- arrayElems :: forall (n :: Nat) a. Array n a -> [a]
- arrayelems :: forall (n :: Nat) a. Array n a -> [a]
- fieldName :: forall (s :: Symbol) t. KnownSymbol s => Field s t -> String
- fieldname :: forall (s :: Symbol) t. KnownSymbol s => Field s t -> String
- accessorName :: forall a (s :: Symbol) t. (Struct a, KnownSymbol s) => (a -> Field s t) -> String
- accessorname :: forall a (s :: Symbol) t. (Struct a, KnownSymbol s) => (a -> Field s t) -> String
- typeLength :: forall (n :: Nat) t. KnownNat n => Type (Array n t) -> Int
- tylength :: forall (n :: Nat) t. KnownNat n => Type (Array n t) -> Int
- typeSize :: forall (n :: Nat) t. KnownNat n => Type (Array n t) -> Int
- tysize :: forall (n :: Nat) t. KnownNat n => Type (Array n t) -> Int
- interpret :: Integer -> Spec -> IO ()
- badUsage :: String -> a
- observer :: Typed a => String -> Stream a -> Spec
- trigger :: String -> Stream Bool -> [Arg] -> Spec
- forAll :: Stream Bool -> Prop Universal
- forall :: Stream Bool -> Prop Universal
- exists :: Stream Bool -> Prop Existential
- prop :: String -> Prop a -> Writer [SpecItem] (PropRef a)
- theorem :: String -> Prop a -> Proof a -> Writer [SpecItem] (PropRef a)
- arg :: Typed a => Stream a -> Arg
- (#) :: forall (s :: Symbol) t a. (KnownSymbol s, Typed t, Typed a, Struct a) => Stream a -> (a -> Field s t) -> Stream t
- mux :: Typed a => Stream Bool -> Stream a -> Stream a -> Stream a
- extern :: Typed a => String -> Maybe [a] -> Stream a
- externB :: String -> Maybe [Bool] -> Stream Bool
- externW8 :: String -> Maybe [Word8] -> Stream Word8
- externW16 :: String -> Maybe [Word16] -> Stream Word16
- externW32 :: String -> Maybe [Word32] -> Stream Word32
- externW64 :: String -> Maybe [Word64] -> Stream Word64
- externI8 :: String -> Maybe [Int8] -> Stream Int8
- externI16 :: String -> Maybe [Int16] -> Stream Int16
- externI32 :: String -> Maybe [Int32] -> Stream Int32
- externI64 :: String -> Maybe [Int64] -> Stream Int64
- externF :: String -> Maybe [Float] -> Stream Float
- externD :: String -> Maybe [Double] -> Stream Double
- constant :: Typed a => a -> Stream a
- constB :: Bool -> Stream Bool
- constW8 :: Word8 -> Stream Word8
- constW16 :: Word16 -> Stream Word16
- constW32 :: Word32 -> Stream Word32
- constW64 :: Word64 -> Stream Word64
- constI8 :: Int8 -> Stream Int8
- constI16 :: Int16 -> Stream Int16
- constI32 :: Int32 -> Stream Int32
- constI64 :: Int64 -> Stream Int64
- constF :: Float -> Stream Float
- constD :: Double -> Stream Double
- (.!!) :: forall (n :: Nat) t. (KnownNat n, Typed t) => Stream (Array n t) -> Stream Word32 -> Stream t
- csv :: Integer -> Spec -> IO ()
- reify :: Spec' a -> IO Spec
- period :: Integral a => a -> Period a
- clk :: Integral a => Period a -> Phase a -> Stream Bool
- clk1 :: (Integral a, Typed a) => Period a -> Phase a -> Stream Bool
- previous :: Stream Bool -> Stream Bool
- alwaysBeen :: Stream Bool -> Stream Bool
- eventuallyPrev :: Stream Bool -> Stream Bool
- since :: Stream Bool -> Stream Bool -> Stream Bool
- copilotRegexp :: (Typed t, SymbolParser t, Eq t) => Stream t -> SourceName -> Stream Bool -> Stream Bool
- copilotRegexpB :: SourceName -> [(StreamName, Stream Bool)] -> Stream Bool -> Stream Bool
- stack :: (Integral a, Typed b) => a -> b -> Stream Bool -> Stream Bool -> Stream b -> Stream b
- stack' :: (Integral a, Typed b) => a -> b -> Stream Bool -> Stream Bool -> Stream b -> Stream b
- nfoldl :: (Typed a, Typed b) => Int -> (Stream a -> Stream b -> Stream a) -> Stream a -> Stream b -> Stream a
- nfoldl1 :: Typed a => Int -> (Stream a -> Stream a -> Stream a) -> Stream a -> Stream a
- nfoldr :: (Typed a, Typed b) => Int -> (Stream a -> Stream b -> Stream b) -> Stream b -> Stream a -> Stream b
- nfoldr1 :: Typed a => Int -> (Stream a -> Stream a -> Stream a) -> Stream a -> Stream a
- nscanl :: (Typed a, Typed b) => Int -> (Stream a -> Stream b -> Stream a) -> Stream a -> Stream b -> [Stream a]
- nscanr :: Typed a => Int -> (Stream a -> Stream b -> Stream b) -> Stream b -> Stream a -> [Stream b]
- nscanl1 :: Typed a => Int -> (Stream a -> Stream a -> Stream a) -> Stream a -> [Stream a]
- nscanr1 :: Typed a => Int -> (Stream a -> Stream a -> Stream a) -> Stream a -> [Stream a]
- case' :: Typed a => [Stream Bool] -> [Stream a] -> Stream a
- mean :: (Typed a, Eq a, Fractional a) => Int -> Stream a -> Stream a
- meanNow :: (Typed a, Integral a) => [Stream a] -> Stream a
- eventually :: Integral a => a -> Stream Bool -> Stream Bool
- always :: Integral a => a -> Stream Bool -> Stream Bool
- next :: Stream Bool -> Stream Bool
- majority :: (Eq a, Typed a) => [Stream a] -> Stream a
- aMajority :: (Eq a, Typed a) => [Stream a] -> Stream a -> Stream Bool
Sketch generation
zephyr :: Sketch () -> IO () Source #
Typically your program's main will be implemented using this. For example:
{-# LANGUAGE RebindableSyntax #-}
import Copilot.Zephyr.Board.Generic
main = zephyr $ do
led0 =: flashing
delay =: MilliSeconds (constant 100)Running this program compiles the Sketch into C code using copilot
and generates a Zephyr app in the directory "generated". That app
can be built and uploaded to your board using Zephyr, the same as any
other Zephyr app. See Zephyr's documentation for details.
This also supports interpreting a Sketch, without loading it onto a
board. Run the program with parameters "-i 4" to display what it
would do on the first 4 iterations. The output will look something like
this:
gpio_pin_set_led0: k_msleep: (false) (100) (true) (100) (false) (100) (true) (100)
type Sketch = GenSketch Zephyr Source #
A sketch, implemented using Copilot.
It's best to think of the Sketch as a description of the state of the
board at any point in time.
Under the hood, the Sketch is run in a loop. On each iteration, it first
reads inputs and then updates outputs as needed.
While it is a monad, a Sketch's outputs are not updated in any particular order, because Copilot does not guarantee any order.
A pin on the board.
For definitions of specific pins, load a module which provides the pins of a particular board.
A type-level list indicates how a Pin can be used, so the haskell compiler will detect impossible uses of pins.
Instances
| IsAnalogInputPin t => Input Zephyr (Pin t) ADC Source # | |
| IsDigitalIOPin t => Input Zephyr (Pin t) Bool Source # | |
| IsPWMPin t => Output Zephyr (Pin t) (Event 'PWM (Stream Word8)) Source # | |
| IsDigitalIOPin t => Output Zephyr (Pin t) (Event () (Stream Bool)) Source # | |
| Show (Pin t) Source # | |
| Eq (Pin t) Source # | |
| Ord (Pin t) Source # | |
Indicates that you're programming a board with Zephyr. The similar library arduino-copilot allows programming Arduinos in a very similar style to this one.
Instances
| Show Zephyr Source # | |
| Eq Zephyr Source # | |
| Ord Zephyr Source # | |
| Context Zephyr Source # | |
Defined in Copilot.Zephyr.Internals | |
| Output Zephyr Delay MicroSeconds Source # | |
Defined in Copilot.Zephyr.Internals | |
| Output Zephyr Delay MilliSeconds Source # | |
Defined in Copilot.Zephyr.Internals | |
| IsAnalogInputPin t => Input Zephyr (Pin t) ADC Source # | |
| IsDigitalIOPin t => Input Zephyr (Pin t) Bool Source # | |
| IsPWMPin t => Output Zephyr (Pin t) (Event 'PWM (Stream Word8)) Source # | |
| IsDigitalIOPin t => Output Zephyr (Pin t) (Event () (Stream Bool)) Source # | |
Functional reactive programming
A value that changes over time.
This is implemented as a Stream in the Copilot DSL.
Copilot provides many operations on streams, for example
&& to combine two streams of Bools.
For documentation on using the Copilot DSL, see https://copilot-language.github.io/
data TypedBehavior (p :: k) t #
A Behavior with an additional phantom type p.
The Compilot DSL only lets a Stream contain basic C types,
a limitation that Behavior also has. When more type safely
is needed, this can be used.
Constructors
| TypedBehavior (Behavior t) |
Instances
| Output ctx o (Event p (Stream v)) => Output ctx o (TypedBehavior p v) | |
Defined in Sketch.FRP.Copilot.Types Methods (=:) :: o -> TypedBehavior p v -> GenSketch ctx () # | |
| Typed a => IfThenElse (TypedBehavior p) a | |
Defined in Sketch.FRP.Copilot Methods ifThenElse :: Behavior Bool -> TypedBehavior p a -> TypedBehavior p a -> TypedBehavior p a # | |
| IsBehavior (TypedBehavior p v) | |
Defined in Sketch.FRP.Copilot.Types Methods (@:) :: TypedBehavior p v -> Behavior Bool -> BehaviorToEvent (TypedBehavior p v) # | |
| type BehaviorToEvent (TypedBehavior p v) | |
Defined in Sketch.FRP.Copilot.Types | |
A discrete event, that occurs at particular points in time.
(@:) :: IsBehavior behavior => behavior -> Behavior Bool -> BehaviorToEvent behavior #
Generate an Event, from some type of behavior,
that only occurs when the Behavior Bool is True.
Inputs
Minimal complete definition
input :: Input ctx o t => o -> GenSketch ctx (Behavior t) #
Use this to read a value from a component of the board.
For example, to read a digital value from pin12 and turn on the led when the pin is high:
buttonpressed <- input pin12 led =: buttonpressed
Some pins support multiple types of reads, for example a pin may
support a digital read (Type), and an analog to digital converter
read (ADC). In such cases you may need to specify the type of
data to read:
v <- input a0 :: Sketch (Behavior ADC)
input' :: Input ctx o t => o -> [t] -> GenSketch ctx (Behavior t) #
The list is input to use when simulating the Sketch.
pullup :: IsDigitalIOPin t => Pin t -> Sketch () Source #
Normally when a digital value is read from a Pin, it is configured
without the internal pullup resistor being enabled. Use this to enable
the pullup register for all reads from the Pin. When the board does not
have an internal pullup resistor, this will have no effect.
Bear in mind that enabling the pullup resistor inverts the value that will be read from the pin.
pullup pin12
Outputs
Minimal complete definition
Instances
| Output Zephyr Delay MicroSeconds Source # | |
Defined in Copilot.Zephyr.Internals | |
| Output Zephyr Delay MilliSeconds Source # | |
Defined in Copilot.Zephyr.Internals | |
| Output ctx o (Event () (Stream v)) => Output ctx o (Behavior v) | |
Defined in Sketch.FRP.Copilot.Types | |
| Output ctx o (Event p (Stream v)) => Output ctx o (TypedBehavior p v) | |
Defined in Sketch.FRP.Copilot.Types Methods (=:) :: o -> TypedBehavior p v -> GenSketch ctx () # | |
| IsPWMPin t => Output Zephyr (Pin t) (Event 'PWM (Stream Word8)) Source # | |
| IsDigitalIOPin t => Output Zephyr (Pin t) (Event () (Stream Bool)) Source # | |
(=:) :: Output ctx o t => o -> t -> GenSketch ctx () infixr 1 #
Connect a Behavior or Event to an Output
led =: blinking
When a Behavior is used, its current value is written on each
iteration of the Sketch.
For example, this constantly turns on the LED, even though it will
already be on after the first iteration, because true
is a Behavior (that is always True).
led =: true
To avoid unncessary work being done, you can use an Event
instead. Then the write only happens at the points in time
when the Event occurs. To turn a Behavior into an Event,
use @:
So to make the LED only be turned on in the first iteration, and allow it to remain on thereafter without doing extra work:
led =: true @: firstIteration
Use this to add a delay between each iteration of the Sketch.
A Sketch with no delay will run as fast as the hardware can run it.
delay := MilliSeconds (constant 100)
Other types
data MilliSeconds #
A stream of milliseconds.
Constructors
| MilliSeconds (Stream Word32) |
Instances
| Output Zephyr Delay MilliSeconds Source # | |
Defined in Copilot.Zephyr.Internals | |
data MicroSeconds #
A stream of microseconds.
Constructors
| MicroSeconds (Stream Word32) |
Instances
| Output Zephyr Delay MicroSeconds Source # | |
Defined in Copilot.Zephyr.Internals | |
type family IsDigitalIOPin (t :: [PinCapabilities]) where ... #
Equations
| IsDigitalIOPin t = 'True ~ If (HasPinCapability 'DigitalIO t) 'True (TypeError ('Text "This Pin does not support digital IO") :: Bool) |
type family IsAnalogInputPin (t :: [PinCapabilities]) where ... #
Equations
| IsAnalogInputPin t = 'True ~ If (HasPinCapability 'AnalogInput t) 'True (TypeError ('Text "This Pin does not support analog input") :: Bool) |
type family IsPWMPin (t :: [PinCapabilities]) where ... #
Utilities
firstIteration :: Behavior Bool #
True on the first iteration of the Sketch, and False thereafter.
frequency :: Integer -> Behavior Bool #
Use this to make an event occur 1 time out of n.
This is implemented using Copilot's clk:
frequency = clk (period n) (phase 1)
sketchSpec :: Context ctx => GenSketch ctx a -> Spec #
Extracts a copilot Spec from a Sketch.
This can be useful to intergrate with other libraries such as copilot-theorem.
Combinators
liftB :: (Behavior a -> Behavior r) -> TypedBehavior t a -> Behavior r #
Apply a Copilot DSL function to a TypedBehavior.
liftB2 :: (Behavior a -> Behavior b -> Behavior r) -> TypedBehavior t a -> TypedBehavior t b -> Behavior r #
Apply a Copilot DSL function to two TypedBehaviors.
whenB :: Context ctx => Behavior Bool -> GenSketch ctx t -> GenSketch ctx t #
Limit the effects of a Sketch to times when a Behavior Type is True.
When applied to =:, this does the same thing as @: but without
the FRP style conversion the input Behavior into an Event. So @:
is generally better to use than this.
But, this can also be applied to input, to limit how often input
gets read. Useful to avoid performing slow input operations on every
iteration of a Sketch.
v <- whenB (frequency 10) $ input pin12
(It's best to think of the value returned by that as an Event, but it's currently represented as a Behavior, since the Copilot DSL cannot operate on Events.)
scheduleB :: (Typed t, Eq t, Context ctx) => Behavior t -> [(t, GenSketch ctx ())] -> GenSketch ctx () #
Schedule when to perform different Sketches.
ifThenElse :: IfThenElse t a => Behavior Bool -> t a -> t a -> t a #
This allows "if then else" expressions to be written that choose between two Streams, or Behaviors, or TypedBehaviors, or Sketches, when the RebindableSyntax language extension is enabled.
{-# LANGUAGE RebindableSyntax #-}
buttonpressed <- input pin3
if buttonpressed then ... else ...class IfThenElse (t :: Type -> Type) a #
Minimal complete definition
Instances
| Typed a => IfThenElse Stream a | |
Defined in Sketch.FRP.Copilot | |
| Context ctx => IfThenElse (GenSketch ctx) () | |
Defined in Sketch.FRP.Copilot | |
| (Context ctx, Typed a) => IfThenElse (GenSketch ctx) (Behavior a) | |
| Typed a => IfThenElse (TypedBehavior p) a | |
Defined in Sketch.FRP.Copilot Methods ifThenElse :: Behavior Bool -> TypedBehavior p a -> TypedBehavior p a -> TypedBehavior p a # | |
Copilot DSL
Most of the Copilot.Language module is re-exported here, including a version of the Prelude modified for it. You should enable the RebindableSyntax language extension in your program to use the Copilot DSL.
{-# LANGUAGE RebindableSyntax #-}For documentation on using the Copilot DSL, see https://copilot-language.github.io/
A stream in Copilot is an infinite succession of values of the same type.
Streams can be built using simple primities (e.g., Const), by applying
step-wise (e.g., Op1) or temporal transformations (e.g., Append, Drop)
to streams, or by combining existing streams to form new streams (e.g.,
Op2, Op3).
Instances
| Typed a => IfThenElse Stream a | |
Defined in Sketch.FRP.Copilot | |
| Output ctx o (Event () (Stream v)) => Output ctx o (Behavior v) | |
Defined in Sketch.FRP.Copilot.Types | |
| IsPWMPin t => Output Zephyr (Pin t) (Event 'PWM (Stream Word8)) Source # | |
| IsDigitalIOPin t => Output Zephyr (Pin t) (Event () (Stream Bool)) Source # | |
| (Typed a, Eq a, Floating a) => Floating (Stream a) | Streams carrying floating point numbers are instances of |
Defined in Copilot.Language.Stream Methods sqrt :: Stream a -> Stream a # (**) :: Stream a -> Stream a -> Stream a # logBase :: Stream a -> Stream a -> Stream a # asin :: Stream a -> Stream a # acos :: Stream a -> Stream a # atan :: Stream a -> Stream a # sinh :: Stream a -> Stream a # cosh :: Stream a -> Stream a # tanh :: Stream a -> Stream a # asinh :: Stream a -> Stream a # acosh :: Stream a -> Stream a # atanh :: Stream a -> Stream a # log1p :: Stream a -> Stream a # expm1 :: Stream a -> Stream a # | |
| (Typed a, Eq a, Num a) => Num (Stream a) | Streams carrying numbers are instances of |
| (Typed a, Eq a, Fractional a) => Fractional (Stream a) | Streams carrying fractional numbers are instances of |
| Show (Stream a) | |
| Eq (Stream a) | |
| IsBehavior (Behavior v) | |
Defined in Sketch.FRP.Copilot.Types | |
| (Context ctx, Typed a) => IfThenElse (GenSketch ctx) (Behavior a) | |
| type BehaviorToEvent (Behavior v) | |
Defined in Sketch.FRP.Copilot.Types | |
Instances
| Bits Bool | Interpret Since: base-4.7.0.0 |
Defined in GHC.Bits Methods (.&.) :: Bool -> Bool -> Bool # (.|.) :: Bool -> Bool -> Bool # complement :: Bool -> Bool # shift :: Bool -> Int -> Bool # rotate :: Bool -> Int -> Bool # setBit :: Bool -> Int -> Bool # clearBit :: Bool -> Int -> Bool # complementBit :: Bool -> Int -> Bool # testBit :: Bool -> Int -> Bool # bitSizeMaybe :: Bool -> Maybe Int # shiftL :: Bool -> Int -> Bool # unsafeShiftL :: Bool -> Int -> Bool # shiftR :: Bool -> Int -> Bool # unsafeShiftR :: Bool -> Int -> Bool # rotateL :: Bool -> Int -> Bool # | |
| FiniteBits Bool | Since: base-4.7.0.0 |
Defined in GHC.Bits Methods finiteBitSize :: Bool -> Int # countLeadingZeros :: Bool -> Int # countTrailingZeros :: Bool -> Int # | |
| Bounded Bool | Since: base-2.1 |
| Enum Bool | Since: base-2.1 |
| Generic Bool | |
| SingKind Bool | Since: base-4.9.0.0 |
Defined in GHC.Generics Associated Types type DemoteRep Bool | |
| Read Bool | Since: base-2.1 |
| Show Bool | Since: base-2.1 |
| Typed Bool | |
Defined in Copilot.Core.Type | |
| SymbolParser Bool | |
Defined in Copilot.Library.RegExp | |
| Eq Bool | |
| Ord Bool | |
| Pretty Bool |
|
Defined in Prettyprinter.Internal | |
| Uniform Bool | |
Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Bool # | |
| UniformRange Bool | |
Defined in System.Random.Internal | |
| SingI 'False | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| SingI 'True | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Cast Bool Int16 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Int32 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Int64 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Int8 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Word16 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Word32 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Word64 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Word8 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Bool | Identity casting. |
| IsDigitalIOPin t => Input Zephyr (Pin t) Bool Source # | |
| IsDigitalIOPin t => Output Zephyr (Pin t) (Event () (Stream Bool)) Source # | |
| type DemoteRep Bool | |
Defined in GHC.Generics | |
| type Rep Bool | Since: base-4.6.0.0 |
| data Sing (a :: Bool) | |
The character type Char is an enumeration whose values represent
Unicode (or equivalently ISO/IEC 10646) code points (i.e. characters, see
http://www.unicode.org/ for details). This set extends the ISO 8859-1
(Latin-1) character set (the first 256 characters), which is itself an extension
of the ASCII character set (the first 128 characters). A character literal in
Haskell has type Char.
To convert a Char to or from the corresponding Int value defined
by Unicode, use toEnum and fromEnum from the
Enum class respectively (or equivalently ord and
chr).
Instances
| Bounded Char | Since: base-2.1 |
| Enum Char | Since: base-2.1 |
| Read Char | Since: base-2.1 |
| Show Char | Since: base-2.1 |
| Eq Char | |
| Ord Char | |
| Pretty Char | Instead of
|
Defined in Prettyprinter.Internal | |
| Uniform Char | |
Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Char # | |
| UniformRange Char | |
Defined in System.Random.Internal | |
| TestCoercion SChar | Since: base-4.18.0.0 |
Defined in GHC.TypeLits | |
| TestEquality SChar | Since: base-4.18.0.0 |
Defined in GHC.TypeLits | |
| Generic1 (URec Char :: k -> Type) | |
| Foldable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UChar m -> m # foldMap :: Monoid m => (a -> m) -> UChar a -> m # foldMap' :: Monoid m => (a -> m) -> UChar a -> m # foldr :: (a -> b -> b) -> b -> UChar a -> b # foldr' :: (a -> b -> b) -> b -> UChar a -> b # foldl :: (b -> a -> b) -> b -> UChar a -> b # foldl' :: (b -> a -> b) -> b -> UChar a -> b # foldr1 :: (a -> a -> a) -> UChar a -> a # foldl1 :: (a -> a -> a) -> UChar a -> a # elem :: Eq a => a -> UChar a -> Bool # maximum :: Ord a => UChar a -> a # minimum :: Ord a => UChar a -> a # | |
| Traversable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
| Generic (URec Char p) | |
| Show (URec Char p) | Since: base-4.9.0.0 |
| Eq (URec Char p) | Since: base-4.9.0.0 |
| Ord (URec Char p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| data URec Char (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
| type Rep1 (URec Char :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| type Rep (URec Char p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.
Instances
| Floating Double | Since: base-2.1 |
| RealFloat Double | Since: base-2.1 |
Defined in GHC.Float Methods floatRadix :: Double -> Integer # floatDigits :: Double -> Int # floatRange :: Double -> (Int, Int) # decodeFloat :: Double -> (Integer, Int) # encodeFloat :: Integer -> Int -> Double # significand :: Double -> Double # scaleFloat :: Int -> Double -> Double # isInfinite :: Double -> Bool # isDenormalized :: Double -> Bool # isNegativeZero :: Double -> Bool # | |
| Read Double | Since: base-2.1 |
| Typed Double | |
Defined in Copilot.Core.Type | |
| Eq Double | Note that due to the presence of
Also note that
|
| Ord Double | Note that due to the presence of
Also note that, due to the same,
|
| Pretty Double |
|
Defined in Prettyprinter.Internal | |
| UniformRange Double | |
Defined in System.Random.Internal | |
| UnsafeCast Int16 Double | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int32 Double | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Double | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int8 Double | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word16 Double | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word32 Double | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word64 Double | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word8 Double | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| Generic1 (URec Double :: k -> Type) | |
| Foldable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UDouble m -> m # foldMap :: Monoid m => (a -> m) -> UDouble a -> m # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m # foldr :: (a -> b -> b) -> b -> UDouble a -> b # foldr' :: (a -> b -> b) -> b -> UDouble a -> b # foldl :: (b -> a -> b) -> b -> UDouble a -> b # foldl' :: (b -> a -> b) -> b -> UDouble a -> b # foldr1 :: (a -> a -> a) -> UDouble a -> a # foldl1 :: (a -> a -> a) -> UDouble a -> a # elem :: Eq a => a -> UDouble a -> Bool # maximum :: Ord a => UDouble a -> a # minimum :: Ord a => UDouble a -> a # | |
| Traversable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
| Generic (URec Double p) | |
| Show (URec Double p) | Since: base-4.9.0.0 |
| Eq (URec Double p) | Since: base-4.9.0.0 |
| Ord (URec Double p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods compare :: URec Double p -> URec Double p -> Ordering # (<) :: URec Double p -> URec Double p -> Bool # (<=) :: URec Double p -> URec Double p -> Bool # (>) :: URec Double p -> URec Double p -> Bool # (>=) :: URec Double p -> URec Double p -> Bool # | |
| data URec Double (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
| type Rep1 (URec Double :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| type Rep (URec Double p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.
Instances
| Floating Float | Since: base-2.1 |
| RealFloat Float | Since: base-2.1 |
Defined in GHC.Float Methods floatRadix :: Float -> Integer # floatDigits :: Float -> Int # floatRange :: Float -> (Int, Int) # decodeFloat :: Float -> (Integer, Int) # encodeFloat :: Integer -> Int -> Float # significand :: Float -> Float # scaleFloat :: Int -> Float -> Float # isInfinite :: Float -> Bool # isDenormalized :: Float -> Bool # isNegativeZero :: Float -> Bool # | |
| Read Float | Since: base-2.1 |
| Typed Float | |
Defined in Copilot.Core.Type | |
| Eq Float | Note that due to the presence of
Also note that
|
| Ord Float | Note that due to the presence of
Also note that, due to the same,
|
| Pretty Float |
|
Defined in Prettyprinter.Internal | |
| UniformRange Float | |
Defined in System.Random.Internal | |
| UnsafeCast Int16 Float | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int32 Float | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Float | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int8 Float | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word16 Float | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word32 Float | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word64 Float | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word8 Float | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| Generic1 (URec Float :: k -> Type) | |
| Foldable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m # foldMap :: Monoid m => (a -> m) -> UFloat a -> m # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m # foldr :: (a -> b -> b) -> b -> UFloat a -> b # foldr' :: (a -> b -> b) -> b -> UFloat a -> b # foldl :: (b -> a -> b) -> b -> UFloat a -> b # foldl' :: (b -> a -> b) -> b -> UFloat a -> b # foldr1 :: (a -> a -> a) -> UFloat a -> a # foldl1 :: (a -> a -> a) -> UFloat a -> a # elem :: Eq a => a -> UFloat a -> Bool # maximum :: Ord a => UFloat a -> a # minimum :: Ord a => UFloat a -> a # | |
| Traversable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
| Generic (URec Float p) | |
| Show (URec Float p) | |
| Eq (URec Float p) | |
| Ord (URec Float p) | |
Defined in GHC.Generics | |
| data URec Float (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
| type Rep1 (URec Float :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| type Rep (URec Float p) | |
Defined in GHC.Generics | |
A fixed-precision integer type with at least the range [-2^29 .. 2^29-1].
The exact range for a given implementation can be determined by using
minBound and maxBound from the Bounded class.
Instances
| Bits Int | Since: base-2.1 |
Defined in GHC.Bits | |
| FiniteBits Int | Since: base-4.6.0.0 |
Defined in GHC.Bits Methods finiteBitSize :: Int -> Int # countLeadingZeros :: Int -> Int # countTrailingZeros :: Int -> Int # | |
| Bounded Int | Since: base-2.1 |
| Enum Int | Since: base-2.1 |
| Num Int | Since: base-2.1 |
| Read Int | Since: base-2.1 |
| Integral Int | Since: base-2.0.1 |
| Real Int | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Int -> Rational # | |
| Show Int | Since: base-2.1 |
| Eq Int | |
| Ord Int | |
| Pretty Int |
|
Defined in Prettyprinter.Internal | |
| Uniform Int | |
Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Int # | |
| UniformRange Int | |
Defined in System.Random.Internal | |
| Generic1 (URec Int :: k -> Type) | |
| Foldable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UInt m -> m # foldMap :: Monoid m => (a -> m) -> UInt a -> m # foldMap' :: Monoid m => (a -> m) -> UInt a -> m # foldr :: (a -> b -> b) -> b -> UInt a -> b # foldr' :: (a -> b -> b) -> b -> UInt a -> b # foldl :: (b -> a -> b) -> b -> UInt a -> b # foldl' :: (b -> a -> b) -> b -> UInt a -> b # foldr1 :: (a -> a -> a) -> UInt a -> a # foldl1 :: (a -> a -> a) -> UInt a -> a # elem :: Eq a => a -> UInt a -> Bool # maximum :: Ord a => UInt a -> a # | |
| Traversable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
| Generic (URec Int p) | |
| Show (URec Int p) | Since: base-4.9.0.0 |
| Eq (URec Int p) | Since: base-4.9.0.0 |
| Ord (URec Int p) | Since: base-4.9.0.0 |
| data URec Int (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
| type Rep1 (URec Int :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| type Rep (URec Int p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Instances
| Bits Word | Since: base-2.1 |
Defined in GHC.Bits Methods (.&.) :: Word -> Word -> Word # (.|.) :: Word -> Word -> Word # complement :: Word -> Word # shift :: Word -> Int -> Word # rotate :: Word -> Int -> Word # setBit :: Word -> Int -> Word # clearBit :: Word -> Int -> Word # complementBit :: Word -> Int -> Word # testBit :: Word -> Int -> Bool # bitSizeMaybe :: Word -> Maybe Int # shiftL :: Word -> Int -> Word # unsafeShiftL :: Word -> Int -> Word # shiftR :: Word -> Int -> Word # unsafeShiftR :: Word -> Int -> Word # rotateL :: Word -> Int -> Word # | |
| FiniteBits Word | Since: base-4.6.0.0 |
Defined in GHC.Bits Methods finiteBitSize :: Word -> Int # countLeadingZeros :: Word -> Int # countTrailingZeros :: Word -> Int # | |
| Bounded Word | Since: base-2.1 |
| Enum Word | Since: base-2.1 |
| Num Word | Since: base-2.1 |
| Read Word | Since: base-4.5.0.0 |
| Integral Word | Since: base-2.1 |
| Real Word | Since: base-2.1 |
Defined in GHC.Real Methods toRational :: Word -> Rational # | |
| Show Word | Since: base-2.1 |
| Eq Word | |
| Ord Word | |
| Pretty Word | |
Defined in Prettyprinter.Internal | |
| Uniform Word | |
Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Word # | |
| UniformRange Word | |
Defined in System.Random.Internal | |
| Generic1 (URec Word :: k -> Type) | |
| Foldable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UWord m -> m # foldMap :: Monoid m => (a -> m) -> UWord a -> m # foldMap' :: Monoid m => (a -> m) -> UWord a -> m # foldr :: (a -> b -> b) -> b -> UWord a -> b # foldr' :: (a -> b -> b) -> b -> UWord a -> b # foldl :: (b -> a -> b) -> b -> UWord a -> b # foldl' :: (b -> a -> b) -> b -> UWord a -> b # foldr1 :: (a -> a -> a) -> UWord a -> a # foldl1 :: (a -> a -> a) -> UWord a -> a # elem :: Eq a => a -> UWord a -> Bool # maximum :: Ord a => UWord a -> a # minimum :: Ord a => UWord a -> a # | |
| Traversable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
| Generic (URec Word p) | |
| Show (URec Word p) | Since: base-4.9.0.0 |
| Eq (URec Word p) | Since: base-4.9.0.0 |
| Ord (URec Word p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| data URec Word (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
| type Rep1 (URec Word :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| type Rep (URec Word p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Instances
| Monoid Ordering | Since: base-2.1 |
| Semigroup Ordering | Since: base-4.9.0.0 |
| Bounded Ordering | Since: base-2.1 |
| Enum Ordering | Since: base-2.1 |
| Generic Ordering | |
| Read Ordering | Since: base-2.1 |
| Show Ordering | Since: base-2.1 |
| Eq Ordering | |
| Ord Ordering | |
Defined in GHC.Classes | |
| type Rep Ordering | Since: base-4.6.0.0 |
The Maybe type encapsulates an optional value. A value of type
Maybe aa (represented as Just aNothing). Using Maybe is a good way to
deal with errors or exceptional cases without resorting to drastic
measures such as error.
The Maybe type is also a monad. It is a simple kind of error
monad, where all errors are represented by Nothing. A richer
error monad can be built using the Either type.
Instances
| MonadFail Maybe | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
| Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # | |
| Traversable Maybe | Since: base-2.1 |
| Alternative Maybe | Picks the leftmost Since: base-2.1 |
| Applicative Maybe | Since: base-2.1 |
| Functor Maybe | Since: base-2.1 |
| Monad Maybe | Since: base-2.1 |
| MonadPlus Maybe | Picks the leftmost Since: base-2.1 |
| MonadThrow Maybe | |
Defined in Control.Monad.Catch Methods throwM :: (HasCallStack, Exception e) => e -> Maybe a # | |
| Generic1 Maybe | |
| Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
| Generic (Maybe a) | |
| SingKind a => SingKind (Maybe a) | Since: base-4.9.0.0 |
Defined in GHC.Generics Associated Types type DemoteRep (Maybe a) | |
| Read a => Read (Maybe a) | Since: base-2.1 |
| Show a => Show (Maybe a) | Since: base-2.1 |
| Eq a => Eq (Maybe a) | Since: base-2.1 |
| Ord a => Ord (Maybe a) | Since: base-2.1 |
| Pretty a => Pretty (Maybe a) | Ignore
|
Defined in Prettyprinter.Internal | |
| SingI ('Nothing :: Maybe a) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| SingI a2 => SingI ('Just a2 :: Maybe a1) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| type Rep1 Maybe | Since: base-4.6.0.0 |
| type DemoteRep (Maybe a) | |
Defined in GHC.Generics | |
| type Rep (Maybe a) | Since: base-4.6.0.0 |
Defined in GHC.Generics | |
| data Sing (b :: Maybe a) | |
class a ~# b => (a :: k) ~ (b :: k) infix 4 #
Lifted, homogeneous equality. By lifted, we mean that it
can be bogus (deferred type error). By homogeneous, the two
types a and b must have the same kinds.
Arbitrary precision integers. In contrast with fixed-size integral types
such as Int, the Integer type represents the entire infinite range of
integers.
Integers are stored in a kind of sign-magnitude form, hence do not expect two's complement form when using bit operations.
If the value is small (fit into an Int), IS constructor is used.
Otherwise Integer and IN constructors are used to store a BigNat
representing respectively the positive or the negative value magnitude.
Invariant: Integer and IN are used iff value doesn't fit in IS
Instances
A value of type IO aa.
There is really only one way to "perform" an I/O action: bind it to
Main.main in your program. When your program is run, the I/O will
be performed. It isn't possible to perform I/O from an arbitrary
function, unless that function is itself in the IO monad and called
at some point, directly or indirectly, from Main.main.
IO is a monad, so IO actions can be combined using either the do-notation
or the >> and >>= operations from the Monad
class.
Instances
| MonadFail IO | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
| MonadIO IO | Since: base-4.9.0.0 |
Defined in Control.Monad.IO.Class | |
| Alternative IO | Takes the first non-throwing Since: base-4.9.0.0 |
| Applicative IO | Since: base-2.1 |
| Functor IO | Since: base-2.1 |
| Monad IO | Since: base-2.1 |
| MonadPlus IO | Takes the first non-throwing Since: base-4.9.0.0 |
| MonadCatch IO | |
Defined in Control.Monad.Catch | |
| MonadMask IO | |
Defined in Control.Monad.Catch Methods mask :: HasCallStack => ((forall a. IO a -> IO a) -> IO b) -> IO b # uninterruptibleMask :: HasCallStack => ((forall a. IO a -> IO a) -> IO b) -> IO b # generalBracket :: HasCallStack => IO a -> (a -> ExitCase b -> IO c) -> (a -> IO b) -> IO (b, c) # | |
| MonadThrow IO | |
Defined in Control.Monad.Catch Methods throwM :: (HasCallStack, Exception e) => e -> IO a # | |
| Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0 |
A Type representing the types of expressions or values handled by Copilot Core.
Note that both arrays and structs use dependently typed features. In the former, the length of the array is part of the type. In the latter, the names of the fields are part of the type.
Constructors
| Bool :: Type Bool | |
| Int8 :: Type Int8 | |
| Int16 :: Type Int16 | |
| Int32 :: Type Int32 | |
| Int64 :: Type Int64 | |
| Word8 :: Type Word8 | |
| Word16 :: Type Word16 | |
| Word32 :: Type Word32 | |
| Word64 :: Type Word64 | |
| Float :: Type Float | |
| Double :: Type Double | |
| Array :: forall (n :: Nat) t. (KnownNat n, Typed t) => Type t -> Type (Array n t) | |
| Struct :: forall a. (Typed a, Struct a) => a -> Type a |
Instances
| TestEquality Type | |
Defined in Copilot.Core.Type | |
class Applicative m => Monad (m :: Type -> Type) where #
The Monad class defines the basic operations over a monad,
a concept from a branch of mathematics known as category theory.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an abstract datatype of actions.
Haskell's do expressions provide a convenient syntax for writing
monadic expressions.
Instances of Monad should satisfy the following:
- Left identity
returna>>=k = k a- Right identity
m>>=return= m- Associativity
m>>=(\x -> k x>>=h) = (m>>=k)>>=h
Furthermore, the Monad and Applicative operations should relate as follows:
The above laws imply:
and that pure and (<*>) satisfy the applicative functor laws.
The instances of Monad for lists, Maybe and IO
defined in the Prelude satisfy these laws.
Minimal complete definition
Methods
(>>=) :: m a -> (a -> m b) -> m b infixl 1 #
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
'as ' can be understood as the >>= bsdo expression
do a <- as bs a
(>>) :: m a -> m b -> m b infixl 1 #
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
'as ' can be understood as the >> bsdo expression
do as bs
Inject a value into the monadic type.
Instances
| Monad Identity | Since: base-4.8.0.0 |
| Monad NonEmpty | Since: base-4.9.0.0 |
| Monad Par1 | Since: base-4.9.0.0 |
| Monad P | Since: base-2.1 |
| Monad ReadP | Since: base-2.1 |
| Monad Seq | |
| Monad Tree | |
| Monad IO | Since: base-2.1 |
| Monad ParserM | |
| Monad ParserResult | |
Defined in Options.Applicative.Types Methods (>>=) :: ParserResult a -> (a -> ParserResult b) -> ParserResult b # (>>) :: ParserResult a -> ParserResult b -> ParserResult b # return :: a -> ParserResult a # | |
| Monad ReadM | |
| Monad Maybe | Since: base-2.1 |
| Monad Solo | Since: base-4.15 |
| Monad List | Since: base-2.1 |
| Monad m => Monad (WrappedMonad m) | Since: base-4.7.0.0 |
Defined in Control.Applicative Methods (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # return :: a -> WrappedMonad m a # | |
| Monad (Either e) | Since: base-4.4.0.0 |
| Monad (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Monad (ProofScheme a) | |
Defined in Copilot.Theorem.Prove Methods (>>=) :: ProofScheme a a0 -> (a0 -> ProofScheme a b) -> ProofScheme a b # (>>) :: ProofScheme a a0 -> ProofScheme a b -> ProofScheme a b # return :: a0 -> ProofScheme a a0 # | |
| Monad (GenSketch ctx) | |
| Monoid a => Monad ((,) a) | Since: base-4.9.0.0 |
| Monad f => Monad (Rec1 f) | Since: base-4.9.0.0 |
| (Applicative f, Monad f) => Monad (WhenMissing f x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods (>>=) :: WhenMissing f x a -> (a -> WhenMissing f x b) -> WhenMissing f x b # (>>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # return :: a -> WhenMissing f x a # | |
| (Monoid w, Monad m) => Monad (WriterT w m) | |
| (Monoid a, Monoid b) => Monad ((,,) a b) | Since: base-4.14.0.0 |
| (Monad f, Monad g) => Monad (f :*: g) | Since: base-4.9.0.0 |
| (Monad f, Applicative f) => Monad (WhenMatched f x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods (>>=) :: WhenMatched f x y a -> (a -> WhenMatched f x y b) -> WhenMatched f x y b # (>>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # return :: a -> WhenMatched f x y a # | |
| (Applicative f, Monad f) => Monad (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods (>>=) :: WhenMissing f k x a -> (a -> WhenMissing f k x b) -> WhenMissing f k x b # (>>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # return :: a -> WhenMissing f k x a # | |
| (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | Since: base-4.14.0.0 |
| Monad ((->) r) | Since: base-2.1 |
| Monad f => Monad (M1 i c f) | Since: base-4.9.0.0 |
| (Monad f, Applicative f) => Monad (WhenMatched f k x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods (>>=) :: WhenMatched f k x y a -> (a -> WhenMatched f k x y b) -> WhenMatched f k x y b # (>>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # return :: a -> WhenMatched f k x y a # | |
class Functor (f :: Type -> Type) where #
A type f is a Functor if it provides a function fmap which, given any types a and b
lets you apply any function from (a -> b) to turn an f a into an f b, preserving the
structure of f. Furthermore f needs to adhere to the following:
Note, that the second law follows from the free theorem of the type fmap and
the first law, so you need only check that the former condition holds.
See https://www.schoolofhaskell.com/user/edwardk/snippets/fmap or
https://github.com/quchen/articles/blob/master/second_functor_law.md
for an explanation.
Minimal complete definition
Methods
fmap :: (a -> b) -> f a -> f b #
fmap is used to apply a function of type (a -> b) to a value of type f a,
where f is a functor, to produce a value of type f b.
Note that for any type constructor with more than one parameter (e.g., Either),
only the last type parameter can be modified with fmap (e.g., b in `Either a b`).
Some type constructors with two parameters or more have a Bifunctor
Examples
Convert from a Maybe IntMaybe String
using show:
>>>fmap show NothingNothing>>>fmap show (Just 3)Just "3"
Convert from an Either Int IntEither Int String using show:
>>>fmap show (Left 17)Left 17>>>fmap show (Right 17)Right "17"
Double each element of a list:
>>>fmap (*2) [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>fmap even (2,2)(2,True)
It may seem surprising that the function is only applied to the last element of the tuple
compared to the list example above which applies it to every element in the list.
To understand, remember that tuples are type constructors with multiple type parameters:
a tuple of 3 elements (a,b,c) can also be written (,,) a b c and its Functor instance
is defined for Functor ((,,) a b) (i.e., only the third parameter is free to be mapped over
with fmap).
It explains why fmap can be used with tuples containing values of different types as in the
following example:
>>>fmap even ("hello", 1.0, 4)("hello",1.0,True)
Instances
| Functor ZipList | Since: base-2.1 |
| Functor Identity | Since: base-4.8.0.0 |
| Functor NonEmpty | Since: base-4.9.0.0 |
| Functor Par1 | Since: base-4.9.0.0 |
| Functor P | Since: base-4.8.0.0 |
Defined in Text.ParserCombinators.ReadP | |
| Functor ReadP | Since: base-2.1 |
| Functor IntMap | |
| Functor Digit | |
| Functor Elem | |
| Functor FingerTree | |
Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> FingerTree a -> FingerTree b # (<$) :: a -> FingerTree b -> FingerTree a # | |
| Functor Node | |
| Functor Seq | |
| Functor ViewL | |
| Functor ViewR | |
| Functor Tree | |
| Functor IO | Since: base-2.1 |
| Functor CReader | |
| Functor OptReader | |
| Functor Option | |
| Functor Parser | |
| Functor ParserFailure | |
Defined in Options.Applicative.Types Methods fmap :: (a -> b) -> ParserFailure a -> ParserFailure b # (<$) :: a -> ParserFailure b -> ParserFailure a # | |
| Functor ParserInfo | |
Defined in Options.Applicative.Types Methods fmap :: (a -> b) -> ParserInfo a -> ParserInfo b # (<$) :: a -> ParserInfo b -> ParserInfo a # | |
| Functor ParserM | |
| Functor ParserResult | |
Defined in Options.Applicative.Types Methods fmap :: (a -> b) -> ParserResult a -> ParserResult b # (<$) :: a -> ParserResult b -> ParserResult a # | |
| Functor ReadM | |
| Functor AnnotDetails | |
Defined in Text.PrettyPrint.Annotated.HughesPJ Methods fmap :: (a -> b) -> AnnotDetails a -> AnnotDetails b # (<$) :: a -> AnnotDetails b -> AnnotDetails a # | |
| Functor Doc | |
| Functor Span | |
| Functor Doc | Alter the document’s annotations. This instance makes |
| Functor FlattenResult | |
Defined in Prettyprinter.Internal | |
| Functor SimpleDocStream | Alter the document’s annotations. This instance makes |
Defined in Prettyprinter.Internal Methods fmap :: (a -> b) -> SimpleDocStream a -> SimpleDocStream b # (<$) :: a -> SimpleDocStream b -> SimpleDocStream a # | |
| Functor Maybe | Since: base-2.1 |
| Functor Solo | Since: base-4.15 |
| Functor List | Since: base-2.1 |
| Monad m => Functor (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a # | |
| Functor (Either a) | Since: base-3.0 |
| Functor (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (V1 :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (Map k) | |
| Functor (ProofScheme a) | |
Defined in Copilot.Theorem.Prove Methods fmap :: (a0 -> b) -> ProofScheme a a0 -> ProofScheme a b # (<$) :: a0 -> ProofScheme a b -> ProofScheme a a0 # | |
| Monad m => Functor (Handler m) | |
| Functor (GenSketch ctx) | |
| Functor ((,) a) | Since: base-2.1 |
| Arrow a => Functor (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
| Functor (Const m :: Type -> Type) | Since: base-2.1 |
| (Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) | Since: base-4.17.0.0 |
Defined in GHC.Generics Methods fmap :: (a -> b) -> Generically1 f a -> Generically1 f b # (<$) :: a -> Generically1 f b -> Generically1 f a # | |
| Functor f => Functor (Rec1 f) | Since: base-4.9.0.0 |
| Functor (URec (Ptr ()) :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
| (Applicative f, Monad f) => Functor (WhenMissing f x) | Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMissing f x a -> WhenMissing f x b # (<$) :: a -> WhenMissing f x b -> WhenMissing f x a # | |
| Functor m => Functor (WriterT w m) | |
| Functor ((,,) a b) | Since: base-4.14.0.0 |
| (Functor f, Functor g) => Functor (f :*: g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :+: g) | Since: base-4.9.0.0 |
| Functor (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
| Functor f => Functor (WhenMatched f x y) | Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # (<$) :: a -> WhenMatched f x y b -> WhenMatched f x y a # | |
| (Applicative f, Monad f) => Functor (WhenMissing f k x) | Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # (<$) :: a -> WhenMissing f k x b -> WhenMissing f k x a # | |
| Functor ((,,,) a b c) | Since: base-4.14.0.0 |
| Functor ((->) r) | Since: base-2.1 |
| (Functor f, Functor g) => Functor (f :.: g) | Since: base-4.9.0.0 |
| Functor f => Functor (M1 i c f) | Since: base-4.9.0.0 |
| Functor f => Functor (WhenMatched f k x y) | Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # (<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y a # | |
| Functor ((,,,,) a b c d) | Since: base-4.18.0.0 |
| Functor ((,,,,,) a b c d e) | Since: base-4.18.0.0 |
| Functor ((,,,,,,) a b c d e f) | Since: base-4.18.0.0 |
The Either type represents values with two possibilities: a value of
type Either a bLeft aRight b
The Either type is sometimes used to represent a value which is
either correct or an error; by convention, the Left constructor is
used to hold an error value and the Right constructor is used to
hold a correct value (mnemonic: "right" also means "correct").
Examples
The type Either String IntString or an Int. The Left constructor can be used only on
Strings, and the Right constructor can be used only on Ints:
>>>let s = Left "foo" :: Either String Int>>>sLeft "foo">>>let n = Right 3 :: Either String Int>>>nRight 3>>>:type ss :: Either String Int>>>:type nn :: Either String Int
The fmap from our Functor instance will ignore Left values, but
will apply the supplied function to values contained in a Right:
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>fmap (*2) sLeft "foo">>>fmap (*2) nRight 6
The Monad instance for Either allows us to chain together multiple
actions which may fail, and fail overall if any of the individual
steps failed. First we'll write a function that can either parse an
Int from a Char, or fail.
>>>import Data.Char ( digitToInt, isDigit )>>>:{let parseEither :: Char -> Either String Int parseEither c | isDigit c = Right (digitToInt c) | otherwise = Left "parse error">>>:}
The following should work, since both '1' and '2' can be
parsed as Ints.
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither '1' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleRight 3
But the following should fail overall, since the first operation where
we attempt to parse 'm' as an Int will fail:
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither 'm' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleLeft "parse error"
Instances
| Generic1 (Either a :: Type -> Type) | |
| Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # length :: Either a a0 -> Int # elem :: Eq a0 => a0 -> Either a a0 -> Bool # maximum :: Ord a0 => Either a a0 -> a0 # minimum :: Ord a0 => Either a a0 -> a0 # | |
| Traversable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Traversable | |
| Applicative (Either e) | Since: base-3.0 |
| Functor (Either a) | Since: base-3.0 |
| Monad (Either e) | Since: base-4.4.0.0 |
| e ~ SomeException => MonadCatch (Either e) | Since: exceptions-0.8.3 |
Defined in Control.Monad.Catch | |
| e ~ SomeException => MonadMask (Either e) | Since: exceptions-0.8.3 |
Defined in Control.Monad.Catch Methods mask :: HasCallStack => ((forall a. Either e a -> Either e a) -> Either e b) -> Either e b # uninterruptibleMask :: HasCallStack => ((forall a. Either e a -> Either e a) -> Either e b) -> Either e b # generalBracket :: HasCallStack => Either e a -> (a -> ExitCase b -> Either e c) -> (a -> Either e b) -> Either e (b, c) # | |
| e ~ SomeException => MonadThrow (Either e) | |
Defined in Control.Monad.Catch Methods throwM :: (HasCallStack, Exception e0) => e0 -> Either e a # | |
| Semigroup (Either a b) | Since: base-4.9.0.0 |
| Generic (Either a b) | |
| (Read a, Read b) => Read (Either a b) | Since: base-3.0 |
| (Show a, Show b) => Show (Either a b) | Since: base-3.0 |
| (Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
| (Ord a, Ord b) => Ord (Either a b) | Since: base-2.1 |
| type Rep1 (Either a :: Type -> Type) | Since: base-4.6.0.0 |
Defined in GHC.Generics type Rep1 (Either a :: Type -> Type) = D1 ('MetaData "Either" "Data.Either" "base" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) | |
| type Rep (Either a b) | Since: base-4.6.0.0 |
Defined in GHC.Generics type Rep (Either a b) = D1 ('MetaData "Either" "Data.Either" "base" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b))) | |
class Semigroup a => Monoid a where #
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:
- Right identity
x<>mempty= x- Left identity
mempty<>x = x- Associativity
x(<>(y<>z) = (x<>y)<>zSemigrouplaw)- Concatenation
mconcat=foldr(<>)mempty
You can alternatively define mconcat instead of mempty, in which case the
laws are:
- Unit
mconcat(purex) = x- Multiplication
mconcat(joinxss) =mconcat(fmapmconcatxss)- Subclass
mconcat(toListxs) =sconcatxs
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define newtypes and make those instances
of Monoid, e.g. Sum and Product.
NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.
Methods
Identity of mappend
>>>"Hello world" <> mempty"Hello world"
An associative operation
NOTE: This method is redundant and has the default
implementation mappend = (<>)mappend is a synonym for
(<>), it is expected that the two functions are defined the same
way. In a future GHC release mappend will be removed from Monoid.
Fold a list using the monoid.
For most types, the default definition for mconcat will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.
>>>mconcat ["Hello", " ", "Haskell", "!"]"Hello Haskell!"
Instances
| Monoid ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods mappend :: ShortByteString -> ShortByteString -> ShortByteString # mconcat :: [ShortByteString] -> ShortByteString # | |
| Monoid IntSet | |
| Monoid OsString | "String-Concatenation" for |
| Monoid PosixString | |
Defined in System.OsString.Internal.Types Methods mempty :: PosixString # mappend :: PosixString -> PosixString -> PosixString # mconcat :: [PosixString] -> PosixString # | |
| Monoid WindowsString | |
Defined in System.OsString.Internal.Types Methods mempty :: WindowsString # mappend :: WindowsString -> WindowsString -> WindowsString # mconcat :: [WindowsString] -> WindowsString # | |
| Monoid Ordering | Since: base-2.1 |
| Monoid PrefsMod | |
| Monoid ParserHelp | |
Defined in Options.Applicative.Help.Types Methods mempty :: ParserHelp # mappend :: ParserHelp -> ParserHelp -> ParserHelp # mconcat :: [ParserHelp] -> ParserHelp # | |
| Monoid Completer | |
| Monoid ParseError | |
Defined in Options.Applicative.Types Methods mempty :: ParseError # mappend :: ParseError -> ParseError -> ParseError # mconcat :: [ParseError] -> ParseError # | |
| Monoid Doc | |
| Monoid CChunk | |
| Monoid TriggerLimit | |
Defined in Sketch.FRP.Copilot.Types Methods mempty :: TriggerLimit # mappend :: TriggerLimit -> TriggerLimit -> TriggerLimit # mconcat :: [TriggerLimit] -> TriggerLimit # | |
| Monoid () | Since: base-2.1 |
| FiniteBits a => Monoid (And a) | This constraint is arguably too strong. However,
as some types (such as Since: base-4.16 |
| FiniteBits a => Monoid (Iff a) | This constraint is arguably
too strong. However, as some types (such as Since: base-4.16 |
| Bits a => Monoid (Ior a) | Since: base-4.16 |
| Bits a => Monoid (Xor a) | Since: base-4.16 |
| Monoid a => Monoid (Identity a) | Since: base-4.9.0.0 |
| (Generic a, Monoid (Rep a ())) => Monoid (Generically a) | Since: base-4.17.0.0 |
Defined in GHC.Generics Methods mempty :: Generically a # mappend :: Generically a -> Generically a -> Generically a # mconcat :: [Generically a] -> Generically a # | |
| Monoid p => Monoid (Par1 p) | Since: base-4.12.0.0 |
| Monoid (IntMap a) | |
| Monoid (Seq a) | |
| Monoid (MergeSet a) | |
| Ord a => Monoid (Set a) | |
| Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
| Monoid (InfoMod a) | |
| Monoid (DefaultProp a) | |
Defined in Options.Applicative.Builder.Internal Methods mempty :: DefaultProp a # mappend :: DefaultProp a -> DefaultProp a -> DefaultProp a # mconcat :: [DefaultProp a] -> DefaultProp a # | |
| Monoid (Doc a) | |
| Monoid (Doc ann) |
|
| Context ctx => Monoid (GenFramework ctx) | |
Defined in Sketch.FRP.Copilot.Types Methods mempty :: GenFramework ctx # mappend :: GenFramework ctx -> GenFramework ctx -> GenFramework ctx # mconcat :: [GenFramework ctx] -> GenFramework ctx # | |
| Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Monoid a => Monoid (a) | Since: base-4.15 |
| Monoid [a] | Since: base-2.1 |
| Monoid (U1 p) | Since: base-4.12.0.0 |
| Ord k => Monoid (Map k v) | |
| Monoid (Mod f a) | |
| Monoid (GenSketch ctx ()) | |
| (Monoid a, Monoid b) => Monoid (a, b) | Since: base-2.1 |
| Monoid b => Monoid (a -> b) | Since: base-2.1 |
| Monoid a => Monoid (Const a b) | Since: base-4.9.0.0 |
| Monoid (f p) => Monoid (Rec1 f p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | Since: base-2.1 |
| (Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) | Since: base-4.12.0.0 |
| Monoid c => Monoid (K1 i c p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | Since: base-2.1 |
| Monoid (f (g p)) => Monoid ((f :.: g) p) | Since: base-4.12.0.0 |
| Monoid (f p) => Monoid (M1 i c f p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | Since: base-2.1 |
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
You can alternatively define sconcat instead of (<>), in which case the
laws are:
Since: base-4.9.0.0
Instances
class Functor f => Applicative (f :: Type -> Type) where #
A functor with application, providing operations to
A minimal complete definition must include implementations of pure
and of either <*> or liftA2. If it defines both, then they must behave
the same as their default definitions:
(<*>) =liftA2id
liftA2f x y = f<$>x<*>y
Further, any definition must satisfy the following:
- Identity
pureid<*>v = v- Composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- Homomorphism
puref<*>purex =pure(f x)- Interchange
u
<*>purey =pure($y)<*>u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor instance for f will satisfy
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2p (liftA2q u v) =liftA2f u .liftA2g v
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Methods
Lift a value.
(<*>) :: f (a -> b) -> f a -> f b infixl 4 #
Sequential application.
A few functors support an implementation of <*> that is more
efficient than the default one.
Example
Used in combination with (, <$>)( can be used to build a record.<*>)
>>>data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}
>>>produceFoo :: Applicative f => f Foo
>>>produceBar :: Applicative f => f Bar>>>produceBaz :: Applicative f => f Baz
>>>mkState :: Applicative f => f MyState>>>mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz
liftA2 :: (a -> b -> c) -> f a -> f b -> f c #
Lift a binary function to actions.
Some functors support an implementation of liftA2 that is more
efficient than the default one. In particular, if fmap is an
expensive operation, it is likely better to use liftA2 than to
fmap over the structure and then use <*>.
This became a typeclass method in 4.10.0.0. Prior to that, it was
a function defined in terms of <*> and fmap.
Example
>>>liftA2 (,) (Just 3) (Just 5)Just (3,5)
(*>) :: f a -> f b -> f b infixl 4 #
Sequence actions, discarding the value of the first argument.
Examples
If used in conjunction with the Applicative instance for Maybe,
you can chain Maybe computations, with a possible "early return"
in case of Nothing.
>>>Just 2 *> Just 3Just 3
>>>Nothing *> Just 3Nothing
Of course a more interesting use case would be to have effectful computations instead of just returning pure values.
>>>import Data.Char>>>import Text.ParserCombinators.ReadP>>>let p = string "my name is " *> munch1 isAlpha <* eof>>>readP_to_S p "my name is Simon"[("Simon","")]
(<*) :: f a -> f b -> f a infixl 4 #
Sequence actions, discarding the value of the second argument.
Instances
| Applicative ZipList | f <$> ZipList xs1 <*> ... <*> ZipList xsN
= ZipList (zipWithN f xs1 ... xsN)where (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
= ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
= ZipList {getZipList = ["a5","b6b6","c7c7c7"]}Since: base-2.1 |
| Applicative Identity | Since: base-4.8.0.0 |
| Applicative NonEmpty | Since: base-4.9.0.0 |
| Applicative Par1 | Since: base-4.9.0.0 |
| Applicative P | Since: base-4.5.0.0 |
| Applicative ReadP | Since: base-4.6.0.0 |
| Applicative Seq | Since: containers-0.5.4 |
| Applicative Tree | |
| Applicative IO | Since: base-2.1 |
| Applicative Parser | |
| Applicative ParserM | |
| Applicative ParserResult | |
Defined in Options.Applicative.Types Methods pure :: a -> ParserResult a # (<*>) :: ParserResult (a -> b) -> ParserResult a -> ParserResult b # liftA2 :: (a -> b -> c) -> ParserResult a -> ParserResult b -> ParserResult c # (*>) :: ParserResult a -> ParserResult b -> ParserResult b # (<*) :: ParserResult a -> ParserResult b -> ParserResult a # | |
| Applicative ReadM | |
| Applicative Maybe | Since: base-2.1 |
| Applicative Solo | Since: base-4.15 |
| Applicative List | Since: base-2.1 |
| Monad m => Applicative (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a # (<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c # (*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a # | |
| Applicative (Either e) | Since: base-3.0 |
| Applicative (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Applicative (ProofScheme a) | |
Defined in Copilot.Theorem.Prove Methods pure :: a0 -> ProofScheme a a0 # (<*>) :: ProofScheme a (a0 -> b) -> ProofScheme a a0 -> ProofScheme a b # liftA2 :: (a0 -> b -> c) -> ProofScheme a a0 -> ProofScheme a b -> ProofScheme a c # (*>) :: ProofScheme a a0 -> ProofScheme a b -> ProofScheme a b # (<*) :: ProofScheme a a0 -> ProofScheme a b -> ProofScheme a a0 # | |
| Applicative (GenSketch ctx) | |
Defined in Sketch.FRP.Copilot.Types Methods pure :: a -> GenSketch ctx a # (<*>) :: GenSketch ctx (a -> b) -> GenSketch ctx a -> GenSketch ctx b # liftA2 :: (a -> b -> c) -> GenSketch ctx a -> GenSketch ctx b -> GenSketch ctx c # (*>) :: GenSketch ctx a -> GenSketch ctx b -> GenSketch ctx b # (<*) :: GenSketch ctx a -> GenSketch ctx b -> GenSketch ctx a # | |
| Monoid a => Applicative ((,) a) | For tuples, the ("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)Since: base-2.1 |
| Arrow a => Applicative (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
| Monoid m => Applicative (Const m :: Type -> Type) | Since: base-2.0.1 |
| (Generic1 f, Applicative (Rep1 f)) => Applicative (Generically1 f) | Since: base-4.17.0.0 |
Defined in GHC.Generics Methods pure :: a -> Generically1 f a # (<*>) :: Generically1 f (a -> b) -> Generically1 f a -> Generically1 f b # liftA2 :: (a -> b -> c) -> Generically1 f a -> Generically1 f b -> Generically1 f c # (*>) :: Generically1 f a -> Generically1 f b -> Generically1 f b # (<*) :: Generically1 f a -> Generically1 f b -> Generically1 f a # | |
| Applicative f => Applicative (Rec1 f) | Since: base-4.9.0.0 |
| (Applicative f, Monad f) => Applicative (WhenMissing f x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods pure :: a -> WhenMissing f x a # (<*>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b # liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c # (*>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a # | |
| (Monoid w, Applicative m) => Applicative (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.Lazy | |
| (Monoid a, Monoid b) => Applicative ((,,) a b) | Since: base-4.14.0.0 |
| (Applicative f, Applicative g) => Applicative (f :*: g) | Since: base-4.9.0.0 |
| Monoid c => Applicative (K1 i c :: Type -> Type) | Since: base-4.12.0.0 |
| (Monad f, Applicative f) => Applicative (WhenMatched f x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods pure :: a -> WhenMatched f x y a # (<*>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c # (*>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # (<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a # | |
| (Applicative f, Monad f) => Applicative (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods pure :: a -> WhenMissing f k x a # (<*>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c # (*>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a # | |
| (Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) | Since: base-4.14.0.0 |
Defined in GHC.Base | |
| Applicative ((->) r) | Since: base-2.1 |
| (Applicative f, Applicative g) => Applicative (f :.: g) | Since: base-4.9.0.0 |
| Applicative f => Applicative (M1 i c f) | Since: base-4.9.0.0 |
| (Monad f, Applicative f) => Applicative (WhenMatched f k x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods pure :: a -> WhenMatched f k x y a # (<*>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c # (*>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a # | |
Implementation of an array that uses type literals to store length.
8-bit unsigned integer type
Instances
| Bits Word8 | Since: base-2.1 |
Defined in GHC.Word Methods (.&.) :: Word8 -> Word8 -> Word8 # (.|.) :: Word8 -> Word8 -> Word8 # xor :: Word8 -> Word8 -> Word8 # complement :: Word8 -> Word8 # shift :: Word8 -> Int -> Word8 # rotate :: Word8 -> Int -> Word8 # setBit :: Word8 -> Int -> Word8 # clearBit :: Word8 -> Int -> Word8 # complementBit :: Word8 -> Int -> Word8 # testBit :: Word8 -> Int -> Bool # bitSizeMaybe :: Word8 -> Maybe Int # shiftL :: Word8 -> Int -> Word8 # unsafeShiftL :: Word8 -> Int -> Word8 # shiftR :: Word8 -> Int -> Word8 # unsafeShiftR :: Word8 -> Int -> Word8 # rotateL :: Word8 -> Int -> Word8 # | |
| FiniteBits Word8 | Since: base-4.6.0.0 |
Defined in GHC.Word Methods finiteBitSize :: Word8 -> Int # countLeadingZeros :: Word8 -> Int # countTrailingZeros :: Word8 -> Int # | |
| Bounded Word8 | Since: base-2.1 |
| Enum Word8 | Since: base-2.1 |
| Ix Word8 | Since: base-2.1 |
| Num Word8 | Since: base-2.1 |
| Read Word8 | Since: base-2.1 |
| Integral Word8 | Since: base-2.1 |
| Real Word8 | Since: base-2.1 |
Defined in GHC.Word Methods toRational :: Word8 -> Rational # | |
| Show Word8 | Since: base-2.1 |
| Typed Word8 | |
Defined in Copilot.Core.Type | |
| SymbolParser Word8 | |
Defined in Copilot.Library.RegExp | |
| Eq Word8 | Since: base-2.1 |
| Ord Word8 | Since: base-2.1 |
| Pretty Word8 | |
Defined in Prettyprinter.Internal | |
| Uniform Word8 | |
Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Word8 # | |
| UniformRange Word8 | |
Defined in System.Random.Internal | |
| Cast Word8 Int16 | Cast number to bigger type. |
| Cast Word8 Int32 | Cast number to bigger type. |
| Cast Word8 Int64 | Cast number to bigger type. |
| Cast Word8 Word16 | Cast number to bigger type. |
| Cast Word8 Word32 | Cast number to bigger type. |
| Cast Word8 Word64 | Cast number to bigger type. |
| Cast Word8 Word8 | Identity casting. |
| Cast Bool Word8 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| UnsafeCast Int8 Word8 | Signed to unsigned casting. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word16 Word8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word32 Word8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word64 Word8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word8 Int8 | Cast from unsigned numbers to signed numbers. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word8 Double | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word8 Float | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| IsPWMPin t => Output Zephyr (Pin t) (Event 'PWM (Stream Word8)) Source # | |
64-bit unsigned integer type
Instances
32-bit unsigned integer type
Instances
16-bit unsigned integer type
Instances
class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where #
Functors representing data structures that can be transformed to
structures of the same shape by performing an Applicative (or,
therefore, Monad) action on each element from left to right.
A more detailed description of what same shape means, the various methods, how traversals are constructed, and example advanced use-cases can be found in the Overview section of Data.Traversable.
For the class laws see the Laws section of Data.Traversable.
Methods
traverse :: Applicative f => (a -> f b) -> t a -> f (t b) #
Map each element of a structure to an action, evaluate these actions
from left to right, and collect the results. For a version that ignores
the results see traverse_.
Examples
Basic usage:
In the first two examples we show each evaluated action mapping to the output structure.
>>>traverse Just [1,2,3,4]Just [1,2,3,4]
>>>traverse id [Right 1, Right 2, Right 3, Right 4]Right [1,2,3,4]
In the next examples, we show that Nothing and Left values short
circuit the created structure.
>>>traverse (const Nothing) [1,2,3,4]Nothing
>>>traverse (\x -> if odd x then Just x else Nothing) [1,2,3,4]Nothing
>>>traverse id [Right 1, Right 2, Right 3, Right 4, Left 0]Left 0
sequenceA :: Applicative f => t (f a) -> f (t a) #
Evaluate each action in the structure from left to right, and
collect the results. For a version that ignores the results
see sequenceA_.
Examples
Basic usage:
For the first two examples we show sequenceA fully evaluating a a structure and collecting the results.
>>>sequenceA [Just 1, Just 2, Just 3]Just [1,2,3]
>>>sequenceA [Right 1, Right 2, Right 3]Right [1,2,3]
The next two example show Nothing and Just will short circuit
the resulting structure if present in the input. For more context,
check the Traversable instances for Either and Maybe.
>>>sequenceA [Just 1, Just 2, Just 3, Nothing]Nothing
>>>sequenceA [Right 1, Right 2, Right 3, Left 4]Left 4
mapM :: Monad m => (a -> m b) -> t a -> m (t b) #
Map each element of a structure to a monadic action, evaluate
these actions from left to right, and collect the results. For
a version that ignores the results see mapM_.
Examples
sequence :: Monad m => t (m a) -> m (t a) #
Evaluate each monadic action in the structure from left to
right, and collect the results. For a version that ignores the
results see sequence_.
Examples
Basic usage:
The first two examples are instances where the input and
and output of sequence are isomorphic.
>>>sequence $ Right [1,2,3,4][Right 1,Right 2,Right 3,Right 4]
>>>sequence $ [Right 1,Right 2,Right 3,Right 4]Right [1,2,3,4]
The following examples demonstrate short circuit behavior
for sequence.
>>>sequence $ Left [1,2,3,4]Left [1,2,3,4]
>>>sequence $ [Left 0, Right 1,Right 2,Right 3,Right 4]Left 0
Instances
| Traversable ZipList | Since: base-4.9.0.0 |
| Traversable Identity | Since: base-4.9.0.0 |
| Traversable First | Since: base-4.8.0.0 |
| Traversable Last | Since: base-4.8.0.0 |
| Traversable Down | Since: base-4.12.0.0 |
| Traversable Dual | Since: base-4.8.0.0 |
| Traversable Product | Since: base-4.8.0.0 |
| Traversable Sum | Since: base-4.8.0.0 |
| Traversable NonEmpty | Since: base-4.9.0.0 |
| Traversable Par1 | Since: base-4.9.0.0 |
| Traversable IntMap | Traverses in order of increasing key. |
| Traversable Digit | |
| Traversable Elem | |
| Traversable FingerTree | |
Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> FingerTree a -> f (FingerTree b) # sequenceA :: Applicative f => FingerTree (f a) -> f (FingerTree a) # mapM :: Monad m => (a -> m b) -> FingerTree a -> m (FingerTree b) # sequence :: Monad m => FingerTree (m a) -> m (FingerTree a) # | |
| Traversable Node | |
| Traversable Seq | |
| Traversable ViewL | |
| Traversable ViewR | |
| Traversable Tree | |
| Traversable SimpleDocStream | Transform a document based on its annotations, possibly leveraging
|
Defined in Prettyprinter.Internal Methods traverse :: Applicative f => (a -> f b) -> SimpleDocStream a -> f (SimpleDocStream b) # sequenceA :: Applicative f => SimpleDocStream (f a) -> f (SimpleDocStream a) # mapM :: Monad m => (a -> m b) -> SimpleDocStream a -> m (SimpleDocStream b) # sequence :: Monad m => SimpleDocStream (m a) -> m (SimpleDocStream a) # | |
| Traversable Maybe | Since: base-2.1 |
| Traversable Solo | Since: base-4.15 |
| Traversable List | Since: base-2.1 |
Defined in Data.Traversable | |
| Traversable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Traversable | |
| Traversable (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Ix i => Traversable (Array i) | Since: base-2.1 |
| Traversable (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (UAddr :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (V1 :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (Map k) | Traverses in order of increasing key. |
| Traversable ((,) a) | Since: base-4.7.0.0 |
Defined in Data.Traversable | |
| Traversable (Const m :: Type -> Type) | Since: base-4.7.0.0 |
| Traversable f => Traversable (Ap f) | Since: base-4.12.0.0 |
| Traversable f => Traversable (Alt f) | Since: base-4.12.0.0 |
| Traversable f => Traversable (Rec1 f) | Since: base-4.9.0.0 |
| Traversable f => Traversable (WriterT w f) | |
Defined in Control.Monad.Trans.Writer.Lazy | |
| (Traversable f, Traversable g) => Traversable (f :*: g) | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| (Traversable f, Traversable g) => Traversable (f :+: g) | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| Traversable (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
| (Traversable f, Traversable g) => Traversable (f :.: g) | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| Traversable f => Traversable (M1 i c f) | Since: base-4.9.0.0 |
class Foldable (t :: Type -> Type) where #
The Foldable class represents data structures that can be reduced to a summary value one element at a time. Strict left-associative folds are a good fit for space-efficient reduction, while lazy right-associative folds are a good fit for corecursive iteration, or for folds that short-circuit after processing an initial subsequence of the structure's elements.
Instances can be derived automatically by enabling the DeriveFoldable
extension. For example, a derived instance for a binary tree might be:
{-# LANGUAGE DeriveFoldable #-}
data Tree a = Empty
| Leaf a
| Node (Tree a) a (Tree a)
deriving FoldableA more detailed description can be found in the Overview section of Data.Foldable.
For the class laws see the Laws section of Data.Foldable.
Methods
foldMap :: Monoid m => (a -> m) -> t a -> m #
Map each element of the structure into a monoid, and combine the
results with (. This fold is right-associative and lazy in the
accumulator. For strict left-associative folds consider <>)foldMap'
instead.
Examples
Basic usage:
>>>foldMap Sum [1, 3, 5]Sum {getSum = 9}
>>>foldMap Product [1, 3, 5]Product {getProduct = 15}
>>>foldMap (replicate 3) [1, 2, 3][1,1,1,2,2,2,3,3,3]
When a Monoid's ( is lazy in its second argument, <>)foldMap can
return a result even from an unbounded structure. For example, lazy
accumulation enables Data.ByteString.Builder to efficiently serialise
large data structures and produce the output incrementally:
>>>import qualified Data.ByteString.Lazy as L>>>import qualified Data.ByteString.Builder as B>>>let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20>>>let lbs = B.toLazyByteString $ foldMap bld [0..]>>>L.take 64 lbs"0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"
foldr :: (a -> b -> b) -> b -> t a -> b #
Right-associative fold of a structure, lazy in the accumulator.
In the case of lists, foldr, when applied to a binary operator, a
starting value (typically the right-identity of the operator), and a
list, reduces the list using the binary operator, from right to left:
foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
Note that since the head of the resulting expression is produced by an
application of the operator to the first element of the list, given an
operator lazy in its right argument, foldr can produce a terminating
expression from an unbounded list.
For a general Foldable structure this should be semantically identical
to,
foldr f z =foldrf z .toList
Examples
Basic usage:
>>>foldr (||) False [False, True, False]True
>>>foldr (||) False []False
>>>foldr (\c acc -> acc ++ [c]) "foo" ['a', 'b', 'c', 'd']"foodcba"
Infinite structures
⚠️ Applying foldr to infinite structures usually doesn't terminate.
It may still terminate under one of the following conditions:
- the folding function is short-circuiting
- the folding function is lazy on its second argument
Short-circuiting
( short-circuits on ||)True values, so the following terminates
because there is a True value finitely far from the left side:
>>>foldr (||) False (True : repeat False)True
But the following doesn't terminate:
>>>foldr (||) False (repeat False ++ [True])* Hangs forever *
Laziness in the second argument
Applying foldr to infinite structures terminates when the operator is
lazy in its second argument (the initial accumulator is never used in
this case, and so could be left undefined, but [] is more clear):
>>>take 5 $ foldr (\i acc -> i : fmap (+3) acc) [] (repeat 1)[1,4,7,10,13]
foldl :: (b -> a -> b) -> b -> t a -> b #
Left-associative fold of a structure, lazy in the accumulator. This is rarely what you want, but can work well for structures with efficient right-to-left sequencing and an operator that is lazy in its left argument.
In the case of lists, foldl, when applied to a binary operator, a
starting value (typically the left-identity of the operator), and a
list, reduces the list using the binary operator, from left to right:
foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
Note that to produce the outermost application of the operator the
entire input list must be traversed. Like all left-associative folds,
foldl will diverge if given an infinite list.
If you want an efficient strict left-fold, you probably want to use
foldl' instead of foldl. The reason for this is that the latter
does not force the inner results (e.g. z `f` x1 in the above
example) before applying them to the operator (e.g. to (`f` x2)).
This results in a thunk chain O(n) elements long, which then must be
evaluated from the outside-in.
For a general Foldable structure this should be semantically identical
to:
foldl f z =foldlf z .toList
Examples
The first example is a strict fold, which in practice is best performed
with foldl'.
>>>foldl (+) 42 [1,2,3,4]52
Though the result below is lazy, the input is reversed before prepending it to the initial accumulator, so corecursion begins only after traversing the entire input string.
>>>foldl (\acc c -> c : acc) "abcd" "efgh""hgfeabcd"
A left fold of a structure that is infinite on the right cannot terminate, even when for any finite input the fold just returns the initial accumulator:
>>>foldl (\a _ -> a) 0 $ repeat 1* Hangs forever *
WARNING: When it comes to lists, you always want to use either foldl' or foldr instead.
foldr1 :: (a -> a -> a) -> t a -> a #
A variant of foldr that has no base case,
and thus may only be applied to non-empty structures.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
Examples
Basic usage:
>>>foldr1 (+) [1..4]10
>>>foldr1 (+) []Exception: Prelude.foldr1: empty list
>>>foldr1 (+) Nothing*** Exception: foldr1: empty structure
>>>foldr1 (-) [1..4]-2
>>>foldr1 (&&) [True, False, True, True]False
>>>foldr1 (||) [False, False, True, True]True
>>>foldr1 (+) [1..]* Hangs forever *
foldl1 :: (a -> a -> a) -> t a -> a #
A variant of foldl that has no base case,
and thus may only be applied to non-empty structures.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
foldl1f =foldl1f .toList
Examples
Basic usage:
>>>foldl1 (+) [1..4]10
>>>foldl1 (+) []*** Exception: Prelude.foldl1: empty list
>>>foldl1 (+) Nothing*** Exception: foldl1: empty structure
>>>foldl1 (-) [1..4]-8
>>>foldl1 (&&) [True, False, True, True]False
>>>foldl1 (||) [False, False, True, True]True
>>>foldl1 (+) [1..]* Hangs forever *
Test whether the structure is empty. The default implementation is Left-associative and lazy in both the initial element and the accumulator. Thus optimised for structures where the first element can be accessed in constant time. Structures where this is not the case should have a non-default implementation.
Examples
Basic usage:
>>>null []True
>>>null [1]False
null is expected to terminate even for infinite structures.
The default implementation terminates provided the structure
is bounded on the left (there is a leftmost element).
>>>null [1..]False
Since: base-4.8.0.0
Returns the size/length of a finite structure as an Int. The
default implementation just counts elements starting with the leftmost.
Instances for structures that can compute the element count faster
than via element-by-element counting, should provide a specialised
implementation.
Examples
Basic usage:
>>>length []0
>>>length ['a', 'b', 'c']3>>>length [1..]* Hangs forever *
Since: base-4.8.0.0
elem :: Eq a => a -> t a -> Bool infix 4 #
Does the element occur in the structure?
Note: elem is often used in infix form.
Examples
Basic usage:
>>>3 `elem` []False
>>>3 `elem` [1,2]False
>>>3 `elem` [1,2,3,4,5]True
For infinite structures, the default implementation of elem
terminates if the sought-after value exists at a finite distance
from the left side of the structure:
>>>3 `elem` [1..]True
>>>3 `elem` ([4..] ++ [3])* Hangs forever *
Since: base-4.8.0.0
maximum :: Ord a => t a -> a #
The largest element of a non-empty structure.
This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the maximum in faster than linear time.
Examples
Basic usage:
>>>maximum [1..10]10
>>>maximum []*** Exception: Prelude.maximum: empty list
>>>maximum Nothing*** Exception: maximum: empty structure
WARNING: This function is partial for possibly-empty structures like lists.
Since: base-4.8.0.0
minimum :: Ord a => t a -> a #
The least element of a non-empty structure.
This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the minimum in faster than linear time.
Examples
Basic usage:
>>>minimum [1..10]1
>>>minimum []*** Exception: Prelude.minimum: empty list
>>>minimum Nothing*** Exception: minimum: empty structure
WARNING: This function is partial for possibly-empty structures like lists.
Since: base-4.8.0.0
product :: Num a => t a -> a #
The product function computes the product of the numbers of a
structure.
Examples
Basic usage:
>>>product []1
>>>product [42]42
>>>product [1..10]3628800
>>>product [4.1, 2.0, 1.7]13.939999999999998
>>>product [1..]* Hangs forever *
Since: base-4.8.0.0
Instances
| Foldable ZipList | Since: base-4.9.0.0 |
Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m # foldMap :: Monoid m => (a -> m) -> ZipList a -> m # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m # foldr :: (a -> b -> b) -> b -> ZipList a -> b # foldr' :: (a -> b -> b) -> b -> ZipList a -> b # foldl :: (b -> a -> b) -> b -> ZipList a -> b # foldl' :: (b -> a -> b) -> b -> ZipList a -> b # foldr1 :: (a -> a -> a) -> ZipList a -> a # foldl1 :: (a -> a -> a) -> ZipList a -> a # elem :: Eq a => a -> ZipList a -> Bool # maximum :: Ord a => ZipList a -> a # minimum :: Ord a => ZipList a -> a # | |
| Foldable Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldMap' :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # | |
| Foldable First | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
| Foldable Last | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
| Foldable Down | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Down m -> m # foldMap :: Monoid m => (a -> m) -> Down a -> m # foldMap' :: Monoid m => (a -> m) -> Down a -> m # foldr :: (a -> b -> b) -> b -> Down a -> b # foldr' :: (a -> b -> b) -> b -> Down a -> b # foldl :: (b -> a -> b) -> b -> Down a -> b # foldl' :: (b -> a -> b) -> b -> Down a -> b # foldr1 :: (a -> a -> a) -> Down a -> a # foldl1 :: (a -> a -> a) -> Down a -> a # elem :: Eq a => a -> Down a -> Bool # maximum :: Ord a => Down a -> a # | |
| Foldable Dual | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldMap' :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # | |
| Foldable Product | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldMap' :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # | |
| Foldable Sum | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldMap' :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # | |
| Foldable NonEmpty | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b # foldr1 :: (a -> a -> a) -> NonEmpty a -> a # foldl1 :: (a -> a -> a) -> NonEmpty a -> a # elem :: Eq a => a -> NonEmpty a -> Bool # maximum :: Ord a => NonEmpty a -> a # minimum :: Ord a => NonEmpty a -> a # | |
| Foldable Par1 | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Par1 m -> m # foldMap :: Monoid m => (a -> m) -> Par1 a -> m # foldMap' :: Monoid m => (a -> m) -> Par1 a -> m # foldr :: (a -> b -> b) -> b -> Par1 a -> b # foldr' :: (a -> b -> b) -> b -> Par1 a -> b # foldl :: (b -> a -> b) -> b -> Par1 a -> b # foldl' :: (b -> a -> b) -> b -> Par1 a -> b # foldr1 :: (a -> a -> a) -> Par1 a -> a # foldl1 :: (a -> a -> a) -> Par1 a -> a # elem :: Eq a => a -> Par1 a -> Bool # maximum :: Ord a => Par1 a -> a # | |
| Foldable IntMap | Folds in order of increasing key. |
Defined in Data.IntMap.Internal Methods fold :: Monoid m => IntMap m -> m # foldMap :: Monoid m => (a -> m) -> IntMap a -> m # foldMap' :: Monoid m => (a -> m) -> IntMap a -> m # foldr :: (a -> b -> b) -> b -> IntMap a -> b # foldr' :: (a -> b -> b) -> b -> IntMap a -> b # foldl :: (b -> a -> b) -> b -> IntMap a -> b # foldl' :: (b -> a -> b) -> b -> IntMap a -> b # foldr1 :: (a -> a -> a) -> IntMap a -> a # foldl1 :: (a -> a -> a) -> IntMap a -> a # elem :: Eq a => a -> IntMap a -> Bool # maximum :: Ord a => IntMap a -> a # minimum :: Ord a => IntMap a -> a # | |
| Foldable Digit | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Digit m -> m # foldMap :: Monoid m => (a -> m) -> Digit a -> m # foldMap' :: Monoid m => (a -> m) -> Digit a -> m # foldr :: (a -> b -> b) -> b -> Digit a -> b # foldr' :: (a -> b -> b) -> b -> Digit a -> b # foldl :: (b -> a -> b) -> b -> Digit a -> b # foldl' :: (b -> a -> b) -> b -> Digit a -> b # foldr1 :: (a -> a -> a) -> Digit a -> a # foldl1 :: (a -> a -> a) -> Digit a -> a # elem :: Eq a => a -> Digit a -> Bool # maximum :: Ord a => Digit a -> a # minimum :: Ord a => Digit a -> a # | |
| Foldable Elem | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Elem m -> m # foldMap :: Monoid m => (a -> m) -> Elem a -> m # foldMap' :: Monoid m => (a -> m) -> Elem a -> m # foldr :: (a -> b -> b) -> b -> Elem a -> b # foldr' :: (a -> b -> b) -> b -> Elem a -> b # foldl :: (b -> a -> b) -> b -> Elem a -> b # foldl' :: (b -> a -> b) -> b -> Elem a -> b # foldr1 :: (a -> a -> a) -> Elem a -> a # foldl1 :: (a -> a -> a) -> Elem a -> a # elem :: Eq a => a -> Elem a -> Bool # maximum :: Ord a => Elem a -> a # | |
| Foldable FingerTree | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => FingerTree m -> m # foldMap :: Monoid m => (a -> m) -> FingerTree a -> m # foldMap' :: Monoid m => (a -> m) -> FingerTree a -> m # foldr :: (a -> b -> b) -> b -> FingerTree a -> b # foldr' :: (a -> b -> b) -> b -> FingerTree a -> b # foldl :: (b -> a -> b) -> b -> FingerTree a -> b # foldl' :: (b -> a -> b) -> b -> FingerTree a -> b # foldr1 :: (a -> a -> a) -> FingerTree a -> a # foldl1 :: (a -> a -> a) -> FingerTree a -> a # toList :: FingerTree a -> [a] # null :: FingerTree a -> Bool # length :: FingerTree a -> Int # elem :: Eq a => a -> FingerTree a -> Bool # maximum :: Ord a => FingerTree a -> a # minimum :: Ord a => FingerTree a -> a # sum :: Num a => FingerTree a -> a # product :: Num a => FingerTree a -> a # | |
| Foldable Node | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Node m -> m # foldMap :: Monoid m => (a -> m) -> Node a -> m # foldMap' :: Monoid m => (a -> m) -> Node a -> m # foldr :: (a -> b -> b) -> b -> Node a -> b # foldr' :: (a -> b -> b) -> b -> Node a -> b # foldl :: (b -> a -> b) -> b -> Node a -> b # foldl' :: (b -> a -> b) -> b -> Node a -> b # foldr1 :: (a -> a -> a) -> Node a -> a # foldl1 :: (a -> a -> a) -> Node a -> a # elem :: Eq a => a -> Node a -> Bool # maximum :: Ord a => Node a -> a # | |
| Foldable Seq | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Seq m -> m # foldMap :: Monoid m => (a -> m) -> Seq a -> m # foldMap' :: Monoid m => (a -> m) -> Seq a -> m # foldr :: (a -> b -> b) -> b -> Seq a -> b # foldr' :: (a -> b -> b) -> b -> Seq a -> b # foldl :: (b -> a -> b) -> b -> Seq a -> b # foldl' :: (b -> a -> b) -> b -> Seq a -> b # foldr1 :: (a -> a -> a) -> Seq a -> a # foldl1 :: (a -> a -> a) -> Seq a -> a # elem :: Eq a => a -> Seq a -> Bool # maximum :: Ord a => Seq a -> a # | |
| Foldable ViewL | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewL m -> m # foldMap :: Monoid m => (a -> m) -> ViewL a -> m # foldMap' :: Monoid m => (a -> m) -> ViewL a -> m # foldr :: (a -> b -> b) -> b -> ViewL a -> b # foldr' :: (a -> b -> b) -> b -> ViewL a -> b # foldl :: (b -> a -> b) -> b -> ViewL a -> b # foldl' :: (b -> a -> b) -> b -> ViewL a -> b # foldr1 :: (a -> a -> a) -> ViewL a -> a # foldl1 :: (a -> a -> a) -> ViewL a -> a # elem :: Eq a => a -> ViewL a -> Bool # maximum :: Ord a => ViewL a -> a # minimum :: Ord a => ViewL a -> a # | |
| Foldable ViewR | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewR m -> m # foldMap :: Monoid m => (a -> m) -> ViewR a -> m # foldMap' :: Monoid m => (a -> m) -> ViewR a -> m # foldr :: (a -> b -> b) -> b -> ViewR a -> b # foldr' :: (a -> b -> b) -> b -> ViewR a -> b # foldl :: (b -> a -> b) -> b -> ViewR a -> b # foldl' :: (b -> a -> b) -> b -> ViewR a -> b # foldr1 :: (a -> a -> a) -> ViewR a -> a # foldl1 :: (a -> a -> a) -> ViewR a -> a # elem :: Eq a => a -> ViewR a -> Bool # maximum :: Ord a => ViewR a -> a # minimum :: Ord a => ViewR a -> a # | |
| Foldable Set | Folds in order of increasing key. |
Defined in Data.Set.Internal Methods fold :: Monoid m => Set m -> m # foldMap :: Monoid m => (a -> m) -> Set a -> m # foldMap' :: Monoid m => (a -> m) -> Set a -> m # foldr :: (a -> b -> b) -> b -> Set a -> b # foldr' :: (a -> b -> b) -> b -> Set a -> b # foldl :: (b -> a -> b) -> b -> Set a -> b # foldl' :: (b -> a -> b) -> b -> Set a -> b # foldr1 :: (a -> a -> a) -> Set a -> a # foldl1 :: (a -> a -> a) -> Set a -> a # elem :: Eq a => a -> Set a -> Bool # maximum :: Ord a => Set a -> a # | |
| Foldable Tree | Folds in preorder |
Defined in Data.Tree Methods fold :: Monoid m => Tree m -> m # foldMap :: Monoid m => (a -> m) -> Tree a -> m # foldMap' :: Monoid m => (a -> m) -> Tree a -> m # foldr :: (a -> b -> b) -> b -> Tree a -> b # foldr' :: (a -> b -> b) -> b -> Tree a -> b # foldl :: (b -> a -> b) -> b -> Tree a -> b # foldl' :: (b -> a -> b) -> b -> Tree a -> b # foldr1 :: (a -> a -> a) -> Tree a -> a # foldl1 :: (a -> a -> a) -> Tree a -> a # elem :: Eq a => a -> Tree a -> Bool # maximum :: Ord a => Tree a -> a # | |
| Foldable SimpleDocStream | Collect all annotations from a document. |
Defined in Prettyprinter.Internal Methods fold :: Monoid m => SimpleDocStream m -> m # foldMap :: Monoid m => (a -> m) -> SimpleDocStream a -> m # foldMap' :: Monoid m => (a -> m) -> SimpleDocStream a -> m # foldr :: (a -> b -> b) -> b -> SimpleDocStream a -> b # foldr' :: (a -> b -> b) -> b -> SimpleDocStream a -> b # foldl :: (b -> a -> b) -> b -> SimpleDocStream a -> b # foldl' :: (b -> a -> b) -> b -> SimpleDocStream a -> b # foldr1 :: (a -> a -> a) -> SimpleDocStream a -> a # foldl1 :: (a -> a -> a) -> SimpleDocStream a -> a # toList :: SimpleDocStream a -> [a] # null :: SimpleDocStream a -> Bool # length :: SimpleDocStream a -> Int # elem :: Eq a => a -> SimpleDocStream a -> Bool # maximum :: Ord a => SimpleDocStream a -> a # minimum :: Ord a => SimpleDocStream a -> a # sum :: Num a => SimpleDocStream a -> a # product :: Num a => SimpleDocStream a -> a # | |
| Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # | |
| Foldable Solo | Since: base-4.15 |
Defined in Data.Foldable Methods fold :: Monoid m => Solo m -> m # foldMap :: Monoid m => (a -> m) -> Solo a -> m # foldMap' :: Monoid m => (a -> m) -> Solo a -> m # foldr :: (a -> b -> b) -> b -> Solo a -> b # foldr' :: (a -> b -> b) -> b -> Solo a -> b # foldl :: (b -> a -> b) -> b -> Solo a -> b # foldl' :: (b -> a -> b) -> b -> Solo a -> b # foldr1 :: (a -> a -> a) -> Solo a -> a # foldl1 :: (a -> a -> a) -> Solo a -> a # elem :: Eq a => a -> Solo a -> Bool # maximum :: Ord a => Solo a -> a # | |
| Foldable List | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => [m] -> m # foldMap :: Monoid m => (a -> m) -> [a] -> m # foldMap' :: Monoid m => (a -> m) -> [a] -> m # foldr :: (a -> b -> b) -> b -> [a] -> b # foldr' :: (a -> b -> b) -> b -> [a] -> b # foldl :: (b -> a -> b) -> b -> [a] -> b # foldl' :: (b -> a -> b) -> b -> [a] -> b # foldr1 :: (a -> a -> a) -> [a] -> a # foldl1 :: (a -> a -> a) -> [a] -> a # elem :: Eq a => a -> [a] -> Bool # maximum :: Ord a => [a] -> a # | |
| Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # length :: Either a a0 -> Int # elem :: Eq a0 => a0 -> Either a a0 -> Bool # maximum :: Ord a0 => Either a a0 -> a0 # minimum :: Ord a0 => Either a a0 -> a0 # | |
| Foldable (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m # foldMap :: Monoid m => (a -> m) -> Proxy a -> m # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m # foldr :: (a -> b -> b) -> b -> Proxy a -> b # foldr' :: (a -> b -> b) -> b -> Proxy a -> b # foldl :: (b -> a -> b) -> b -> Proxy a -> b # foldl' :: (b -> a -> b) -> b -> Proxy a -> b # foldr1 :: (a -> a -> a) -> Proxy a -> a # foldl1 :: (a -> a -> a) -> Proxy a -> a # elem :: Eq a => a -> Proxy a -> Bool # maximum :: Ord a => Proxy a -> a # minimum :: Ord a => Proxy a -> a # | |
| Foldable (Array i) | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Array i m -> m # foldMap :: Monoid m => (a -> m) -> Array i a -> m # foldMap' :: Monoid m => (a -> m) -> Array i a -> m # foldr :: (a -> b -> b) -> b -> Array i a -> b # foldr' :: (a -> b -> b) -> b -> Array i a -> b # foldl :: (b -> a -> b) -> b -> Array i a -> b # foldl' :: (b -> a -> b) -> b -> Array i a -> b # foldr1 :: (a -> a -> a) -> Array i a -> a # foldl1 :: (a -> a -> a) -> Array i a -> a # elem :: Eq a => a -> Array i a -> Bool # maximum :: Ord a => Array i a -> a # minimum :: Ord a => Array i a -> a # | |
| Foldable (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => U1 m -> m # foldMap :: Monoid m => (a -> m) -> U1 a -> m # foldMap' :: Monoid m => (a -> m) -> U1 a -> m # foldr :: (a -> b -> b) -> b -> U1 a -> b # foldr' :: (a -> b -> b) -> b -> U1 a -> b # foldl :: (b -> a -> b) -> b -> U1 a -> b # foldl' :: (b -> a -> b) -> b -> U1 a -> b # foldr1 :: (a -> a -> a) -> U1 a -> a # foldl1 :: (a -> a -> a) -> U1 a -> a # elem :: Eq a => a -> U1 a -> Bool # maximum :: Ord a => U1 a -> a # | |
| Foldable (UAddr :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UAddr m -> m # foldMap :: Monoid m => (a -> m) -> UAddr a -> m # foldMap' :: Monoid m => (a -> m) -> UAddr a -> m # foldr :: (a -> b -> b) -> b -> UAddr a -> b # foldr' :: (a -> b -> b) -> b -> UAddr a -> b # foldl :: (b -> a -> b) -> b -> UAddr a -> b # foldl' :: (b -> a -> b) -> b -> UAddr a -> b # foldr1 :: (a -> a -> a) -> UAddr a -> a # foldl1 :: (a -> a -> a) -> UAddr a -> a # elem :: Eq a => a -> UAddr a -> Bool # maximum :: Ord a => UAddr a -> a # minimum :: Ord a => UAddr a -> a # | |
| Foldable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UChar m -> m # foldMap :: Monoid m => (a -> m) -> UChar a -> m # foldMap' :: Monoid m => (a -> m) -> UChar a -> m # foldr :: (a -> b -> b) -> b -> UChar a -> b # foldr' :: (a -> b -> b) -> b -> UChar a -> b # foldl :: (b -> a -> b) -> b -> UChar a -> b # foldl' :: (b -> a -> b) -> b -> UChar a -> b # foldr1 :: (a -> a -> a) -> UChar a -> a # foldl1 :: (a -> a -> a) -> UChar a -> a # elem :: Eq a => a -> UChar a -> Bool # maximum :: Ord a => UChar a -> a # minimum :: Ord a => UChar a -> a # | |
| Foldable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UDouble m -> m # foldMap :: Monoid m => (a -> m) -> UDouble a -> m # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m # foldr :: (a -> b -> b) -> b -> UDouble a -> b # foldr' :: (a -> b -> b) -> b -> UDouble a -> b # foldl :: (b -> a -> b) -> b -> UDouble a -> b # foldl' :: (b -> a -> b) -> b -> UDouble a -> b # foldr1 :: (a -> a -> a) -> UDouble a -> a # foldl1 :: (a -> a -> a) -> UDouble a -> a # elem :: Eq a => a -> UDouble a -> Bool # maximum :: Ord a => UDouble a -> a # minimum :: Ord a => UDouble a -> a # | |
| Foldable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m # foldMap :: Monoid m => (a -> m) -> UFloat a -> m # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m # foldr :: (a -> b -> b) -> b -> UFloat a -> b # foldr' :: (a -> b -> b) -> b -> UFloat a -> b # foldl :: (b -> a -> b) -> b -> UFloat a -> b # foldl' :: (b -> a -> b) -> b -> UFloat a -> b # foldr1 :: (a -> a -> a) -> UFloat a -> a # foldl1 :: (a -> a -> a) -> UFloat a -> a # elem :: Eq a => a -> UFloat a -> Bool # maximum :: Ord a => UFloat a -> a # minimum :: Ord a => UFloat a -> a # | |
| Foldable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UInt m -> m # foldMap :: Monoid m => (a -> m) -> UInt a -> m # foldMap' :: Monoid m => (a -> m) -> UInt a -> m # foldr :: (a -> b -> b) -> b -> UInt a -> b # foldr' :: (a -> b -> b) -> b -> UInt a -> b # foldl :: (b -> a -> b) -> b -> UInt a -> b # foldl' :: (b -> a -> b) -> b -> UInt a -> b # foldr1 :: (a -> a -> a) -> UInt a -> a # foldl1 :: (a -> a -> a) -> UInt a -> a # elem :: Eq a => a -> UInt a -> Bool # maximum :: Ord a => UInt a -> a # | |
| Foldable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UWord m -> m # foldMap :: Monoid m => (a -> m) -> UWord a -> m # foldMap' :: Monoid m => (a -> m) -> UWord a -> m # foldr :: (a -> b -> b) -> b -> UWord a -> b # foldr' :: (a -> b -> b) -> b -> UWord a -> b # foldl :: (b -> a -> b) -> b -> UWord a -> b # foldl' :: (b -> a -> b) -> b -> UWord a -> b # foldr1 :: (a -> a -> a) -> UWord a -> a # foldl1 :: (a -> a -> a) -> UWord a -> a # elem :: Eq a => a -> UWord a -> Bool # maximum :: Ord a => UWord a -> a # minimum :: Ord a => UWord a -> a # | |
| Foldable (V1 :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> m # foldMap' :: Monoid m => (a -> m) -> V1 a -> m # foldr :: (a -> b -> b) -> b -> V1 a -> b # foldr' :: (a -> b -> b) -> b -> V1 a -> b # foldl :: (b -> a -> b) -> b -> V1 a -> b # foldl' :: (b -> a -> b) -> b -> V1 a -> b # foldr1 :: (a -> a -> a) -> V1 a -> a # foldl1 :: (a -> a -> a) -> V1 a -> a # elem :: Eq a => a -> V1 a -> Bool # maximum :: Ord a => V1 a -> a # | |
| Foldable (Map k) | Folds in order of increasing key. |
Defined in Data.Map.Internal Methods fold :: Monoid m => Map k m -> m # foldMap :: Monoid m => (a -> m) -> Map k a -> m # foldMap' :: Monoid m => (a -> m) -> Map k a -> m # foldr :: (a -> b -> b) -> b -> Map k a -> b # foldr' :: (a -> b -> b) -> b -> Map k a -> b # foldl :: (b -> a -> b) -> b -> Map k a -> b # foldl' :: (b -> a -> b) -> b -> Map k a -> b # foldr1 :: (a -> a -> a) -> Map k a -> a # foldl1 :: (a -> a -> a) -> Map k a -> a # elem :: Eq a => a -> Map k a -> Bool # maximum :: Ord a => Map k a -> a # minimum :: Ord a => Map k a -> a # | |
| Foldable ((,) a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (a, m) -> m # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # elem :: Eq a0 => a0 -> (a, a0) -> Bool # maximum :: Ord a0 => (a, a0) -> a0 # minimum :: Ord a0 => (a, a0) -> a0 # | |
| Foldable (Const m :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # | |
| Foldable f => Foldable (Ap f) | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Ap f m -> m # foldMap :: Monoid m => (a -> m) -> Ap f a -> m # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m # foldr :: (a -> b -> b) -> b -> Ap f a -> b # foldr' :: (a -> b -> b) -> b -> Ap f a -> b # foldl :: (b -> a -> b) -> b -> Ap f a -> b # foldl' :: (b -> a -> b) -> b -> Ap f a -> b # foldr1 :: (a -> a -> a) -> Ap f a -> a # foldl1 :: (a -> a -> a) -> Ap f a -> a # elem :: Eq a => a -> Ap f a -> Bool # maximum :: Ord a => Ap f a -> a # | |
| Foldable f => Foldable (Alt f) | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Alt f m -> m # foldMap :: Monoid m => (a -> m) -> Alt f a -> m # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m # foldr :: (a -> b -> b) -> b -> Alt f a -> b # foldr' :: (a -> b -> b) -> b -> Alt f a -> b # foldl :: (b -> a -> b) -> b -> Alt f a -> b # foldl' :: (b -> a -> b) -> b -> Alt f a -> b # foldr1 :: (a -> a -> a) -> Alt f a -> a # foldl1 :: (a -> a -> a) -> Alt f a -> a # elem :: Eq a => a -> Alt f a -> Bool # maximum :: Ord a => Alt f a -> a # minimum :: Ord a => Alt f a -> a # | |
| Foldable f => Foldable (Rec1 f) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Rec1 f m -> m # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m # foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b # foldr1 :: (a -> a -> a) -> Rec1 f a -> a # foldl1 :: (a -> a -> a) -> Rec1 f a -> a # elem :: Eq a => a -> Rec1 f a -> Bool # maximum :: Ord a => Rec1 f a -> a # minimum :: Ord a => Rec1 f a -> a # | |
| Foldable f => Foldable (WriterT w f) | |
Defined in Control.Monad.Trans.Writer.Lazy Methods fold :: Monoid m => WriterT w f m -> m # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m # foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b # foldr1 :: (a -> a -> a) -> WriterT w f a -> a # foldl1 :: (a -> a -> a) -> WriterT w f a -> a # toList :: WriterT w f a -> [a] # null :: WriterT w f a -> Bool # length :: WriterT w f a -> Int # elem :: Eq a => a -> WriterT w f a -> Bool # maximum :: Ord a => WriterT w f a -> a # minimum :: Ord a => WriterT w f a -> a # | |
| (Foldable f, Foldable g) => Foldable (f :*: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :*: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :*: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b # foldr1 :: (a -> a -> a) -> (f :*: g) a -> a # foldl1 :: (a -> a -> a) -> (f :*: g) a -> a # toList :: (f :*: g) a -> [a] # length :: (f :*: g) a -> Int # elem :: Eq a => a -> (f :*: g) a -> Bool # maximum :: Ord a => (f :*: g) a -> a # minimum :: Ord a => (f :*: g) a -> a # | |
| (Foldable f, Foldable g) => Foldable (f :+: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a # toList :: (f :+: g) a -> [a] # length :: (f :+: g) a -> Int # elem :: Eq a => a -> (f :+: g) a -> Bool # maximum :: Ord a => (f :+: g) a -> a # minimum :: Ord a => (f :+: g) a -> a # | |
| Foldable (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => K1 i c m -> m # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m # foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m # foldr :: (a -> b -> b) -> b -> K1 i c a -> b # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b # foldl :: (b -> a -> b) -> b -> K1 i c a -> b # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b # foldr1 :: (a -> a -> a) -> K1 i c a -> a # foldl1 :: (a -> a -> a) -> K1 i c a -> a # elem :: Eq a => a -> K1 i c a -> Bool # maximum :: Ord a => K1 i c a -> a # minimum :: Ord a => K1 i c a -> a # | |
| (Foldable f, Foldable g) => Foldable (f :.: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :.: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a # toList :: (f :.: g) a -> [a] # length :: (f :.: g) a -> Int # elem :: Eq a => a -> (f :.: g) a -> Bool # maximum :: Ord a => (f :.: g) a -> a # minimum :: Ord a => (f :.: g) a -> a # | |
| Foldable f => Foldable (M1 i c f) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => M1 i c f m -> m # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m # foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b # foldr1 :: (a -> a -> a) -> M1 i c f a -> a # foldl1 :: (a -> a -> a) -> M1 i c f a -> a # elem :: Eq a => a -> M1 i c f a -> Bool # maximum :: Ord a => M1 i c f a -> a # minimum :: Ord a => M1 i c f a -> a # | |
The Eq class defines equality (==) and inequality (/=).
All the basic datatypes exported by the Prelude are instances of Eq,
and Eq may be derived for any datatype whose constituents are also
instances of Eq.
The Haskell Report defines no laws for Eq. However, instances are
encouraged to follow these properties:
Instances
| Eq SomeTypeRep | |
Defined in Data.Typeable.Internal | |
| Eq Void | Since: base-4.8.0.0 |
| Eq Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics Methods (==) :: Associativity -> Associativity -> Bool # (/=) :: Associativity -> Associativity -> Bool # | |
| Eq DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool # | |
| Eq Fixity | Since: base-4.6.0.0 |
| Eq SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: SourceStrictness -> SourceStrictness -> Bool # (/=) :: SourceStrictness -> SourceStrictness -> Bool # | |
| Eq SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # | |
| Eq MaskingState | Since: base-4.3.0.0 |
Defined in GHC.IO | |
| Eq IODeviceType | Since: base-4.2.0.0 |
Defined in GHC.IO.Device | |
| Eq SeekMode | Since: base-4.2.0.0 |
| Eq CodingProgress | Since: base-4.4.0.0 |
Defined in GHC.IO.Encoding.Types Methods (==) :: CodingProgress -> CodingProgress -> Bool # (/=) :: CodingProgress -> CodingProgress -> Bool # | |
| Eq ArrayException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods (==) :: ArrayException -> ArrayException -> Bool # (/=) :: ArrayException -> ArrayException -> Bool # | |
| Eq AsyncException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods (==) :: AsyncException -> AsyncException -> Bool # (/=) :: AsyncException -> AsyncException -> Bool # | |
| Eq ExitCode | |
| Eq IOErrorType | Since: base-4.1.0.0 |
Defined in GHC.IO.Exception | |
| Eq IOException | Since: base-4.1.0.0 |
Defined in GHC.IO.Exception | |
| Eq HandlePosn | Since: base-4.1.0.0 |
Defined in GHC.IO.Handle | |
| Eq BufferMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types | |
| Eq Handle | Since: base-4.1.0.0 |
| Eq Newline | Since: base-4.2.0.0 |
| Eq NewlineMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types | |
| Eq IOMode | Since: base-4.2.0.0 |
| Eq Int16 | Since: base-2.1 |
| Eq Int32 | Since: base-2.1 |
| Eq Int64 | Since: base-2.1 |
| Eq Int8 | Since: base-2.1 |
| Eq SrcLoc | Since: base-4.9.0.0 |
| Eq SomeChar | |
| Eq SomeSymbol | Since: base-4.7.0.0 |
Defined in GHC.TypeLits | |
| Eq SomeNat | Since: base-4.7.0.0 |
| Eq GeneralCategory | Since: base-2.1 |
Defined in GHC.Unicode Methods (==) :: GeneralCategory -> GeneralCategory -> Bool # (/=) :: GeneralCategory -> GeneralCategory -> Bool # | |
| Eq Word16 | Since: base-2.1 |
| Eq Word32 | Since: base-2.1 |
| Eq Word64 | Since: base-2.1 |
| Eq Word8 | Since: base-2.1 |
| Eq ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods (==) :: ShortByteString -> ShortByteString -> Bool # (/=) :: ShortByteString -> ShortByteString -> Bool # | |
| Eq IntSet | |
| Eq SimpleType | Type equality, used to help type inference. |
Defined in Copilot.Core.Type | |
| Eq UType | |
| Eq P | |
| Eq FileType | |
| Eq Permissions | |
Defined in System.Directory.Internal.Common | |
| Eq XdgDirectory | |
Defined in System.Directory.Internal.Common | |
| Eq XdgDirectoryList | |
Defined in System.Directory.Internal.Common Methods (==) :: XdgDirectoryList -> XdgDirectoryList -> Bool # (/=) :: XdgDirectoryList -> XdgDirectoryList -> Bool # | |
| Eq OsChar | Byte equality of the internal representation. |
| Eq OsString | Byte equality of the internal representation. |
| Eq PosixChar | |
| Eq PosixString | |
Defined in System.OsString.Internal.Types | |
| Eq WindowsChar | |
Defined in System.OsString.Internal.Types | |
| Eq WindowsString | |
Defined in System.OsString.Internal.Types Methods (==) :: WindowsString -> WindowsString -> Bool # (/=) :: WindowsString -> WindowsString -> Bool # | |
| Eq Module | |
| Eq Ordering | |
| Eq TrName | |
| Eq TyCon | |
| Eq AltNodeType | |
Defined in Options.Applicative.Types | |
| Eq ArgPolicy | |
| Eq ArgumentReachability | |
Defined in Options.Applicative.Types Methods (==) :: ArgumentReachability -> ArgumentReachability -> Bool # (/=) :: ArgumentReachability -> ArgumentReachability -> Bool # | |
| Eq Backtracking | |
Defined in Options.Applicative.Types | |
| Eq OptName | |
| Eq OptVisibility | |
Defined in Options.Applicative.Types Methods (==) :: OptVisibility -> OptVisibility -> Bool # (/=) :: OptVisibility -> OptVisibility -> Bool # | |
| Eq ParserPrefs | |
Defined in Options.Applicative.Types | |
| Eq SourcePos | |
| Eq Mode | |
| Eq Style | |
| Eq TextDetails | |
Defined in Text.PrettyPrint.Annotated.HughesPJ | |
| Eq Doc | |
| Eq FusionDepth | |
Defined in Prettyprinter.Internal | |
| Eq LayoutOptions | |
Defined in Prettyprinter.Internal Methods (==) :: LayoutOptions -> LayoutOptions -> Bool # (/=) :: LayoutOptions -> LayoutOptions -> Bool # | |
| Eq PageWidth | |
| Eq StdGen | |
| Eq CChunk | |
| Eq CLine | |
| Eq PinCapabilities | |
Defined in Sketch.FRP.Copilot.Types Methods (==) :: PinCapabilities -> PinCapabilities -> Bool # (/=) :: PinCapabilities -> PinCapabilities -> Bool # | |
| Eq PinMode | |
| Eq LocalTime | |
| Eq GPIOAddress Source # | |
Defined in Copilot.Zephyr.Internals | |
| Eq GPIOAlias Source # | |
| Eq Zephyr Source # | |
| Eq Integer | |
| Eq () | |
| Eq Bool | |
| Eq Char | |
| Eq Double | Note that due to the presence of
Also note that
|
| Eq Float | Note that due to the presence of
Also note that
|
| Eq Int | |
| Eq Word | |
| Eq a => Eq (ZipList a) | Since: base-4.7.0.0 |
| Eq a => Eq (And a) | Since: base-4.16 |
| Eq a => Eq (Iff a) | Since: base-4.16 |
| Eq a => Eq (Ior a) | Since: base-4.16 |
| Eq a => Eq (Xor a) | Since: base-4.16 |
| Eq a => Eq (Identity a) | Since: base-4.8.0.0 |
| Eq a => Eq (NonEmpty a) | Since: base-4.9.0.0 |
| Eq p => Eq (Par1 p) | Since: base-4.7.0.0 |
| Eq a => Eq (Ratio a) | Since: base-2.1 |
| Eq a => Eq (IntMap a) | |
| Eq a => Eq (Seq a) | |
| Eq a => Eq (ViewL a) | |
| Eq a => Eq (ViewR a) | |
| Eq a => Eq (Intersection a) | |
Defined in Data.Set.Internal Methods (==) :: Intersection a -> Intersection a -> Bool # (/=) :: Intersection a -> Intersection a -> Bool # | |
| Eq a => Eq (Set a) | |
| Eq a => Eq (Tree a) | |
| Eq (Stream a) | |
| Eq t => Eq (NumSym t) | |
| Eq t => Eq (Sym t) | |
| Eq a => Eq (AnnotDetails a) | |
Defined in Text.PrettyPrint.Annotated.HughesPJ Methods (==) :: AnnotDetails a -> AnnotDetails a -> Bool # (/=) :: AnnotDetails a -> AnnotDetails a -> Bool # | |
| Eq (Doc a) | |
| Eq a => Eq (Span a) | |
| Eq ann => Eq (SimpleDocStream ann) | |
Defined in Prettyprinter.Internal Methods (==) :: SimpleDocStream ann -> SimpleDocStream ann -> Bool # (/=) :: SimpleDocStream ann -> SimpleDocStream ann -> Bool # | |
| Eq g => Eq (StateGen g) | |
| Eq a => Eq (Maybe a) | Since: base-2.1 |
| Eq a => Eq (a) | |
| Eq a => Eq [a] | |
| (Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
| Eq (TypeRep a) | Since: base-2.1 |
| Eq (U1 p) | Since: base-4.9.0.0 |
| Eq (V1 p) | Since: base-4.9.0.0 |
| (Eq k, Eq a) => Eq (Map k a) | |
| Eq (Pin t) Source # | |
| (Eq a, Eq b) => Eq (a, b) | |
| Eq a => Eq (Const a b) | Since: base-4.9.0.0 |
| (Generic1 f, Eq (Rep1 f a)) => Eq (Generically1 f a) | Since: base-4.18.0.0 |
Defined in GHC.Generics Methods (==) :: Generically1 f a -> Generically1 f a -> Bool # (/=) :: Generically1 f a -> Generically1 f a -> Bool # | |
| Eq (f p) => Eq (Rec1 f p) | Since: base-4.7.0.0 |
| Eq (URec (Ptr ()) p) | Since: base-4.9.0.0 |
| Eq (URec Char p) | Since: base-4.9.0.0 |
| Eq (URec Double p) | Since: base-4.9.0.0 |
| Eq (URec Float p) | |
| Eq (URec Int p) | Since: base-4.9.0.0 |
| Eq (URec Word p) | Since: base-4.9.0.0 |
| (Eq w, Eq1 m, Eq a) => Eq (WriterT w m a) | |
| (Eq a, Eq b, Eq c) => Eq (a, b, c) | |
| (Eq (f p), Eq (g p)) => Eq ((f :*: g) p) | Since: base-4.7.0.0 |
| (Eq (f p), Eq (g p)) => Eq ((f :+: g) p) | Since: base-4.7.0.0 |
| Eq c => Eq (K1 i c p) | Since: base-4.7.0.0 |
| (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
| Eq (f (g p)) => Eq ((f :.: g) p) | Since: base-4.7.0.0 |
| Eq (f p) => Eq (M1 i c f p) | Since: base-4.7.0.0 |
| (Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
class Monad m => MonadFail (m :: Type -> Type) where #
When a value is bound in do-notation, the pattern on the left
hand side of <- might not match. In this case, this class
provides a function to recover.
A Monad without a MonadFail instance may only be used in conjunction
with pattern that always match, such as newtypes, tuples, data types with
only a single data constructor, and irrefutable patterns (~pat).
Instances of MonadFail should satisfy the following law: fail s should
be a left zero for >>=,
fail s >>= f = fail s
If your Monad is also MonadPlus, a popular definition is
fail _ = mzero
fail s should be an action that runs in the monad itself, not an
exception (except in instances of MonadIO). In particular,
fail should not be implemented in terms of error.
Since: base-4.9.0.0
Instances
| MonadFail P | Since: base-4.9.0.0 |
Defined in Text.ParserCombinators.ReadP | |
| MonadFail ReadP | Since: base-4.9.0.0 |
Defined in Text.ParserCombinators.ReadP | |
| MonadFail IO | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
| MonadFail ReadM | |
Defined in Options.Applicative.Types | |
| MonadFail Maybe | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
| MonadFail List | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
| (Monoid w, MonadFail m) => MonadFail (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.Lazy | |
The Ord class is used for totally ordered datatypes.
Instances of Ord can be derived for any user-defined datatype whose
constituent types are in Ord. The declared order of the constructors in
the data declaration determines the ordering in derived Ord instances. The
Ordering datatype allows a single comparison to determine the precise
ordering of two objects.
Ord, as defined by the Haskell report, implements a total order and has the
following properties:
- Comparability
x <= y || y <= x=True- Transitivity
- if
x <= y && y <= z=True, thenx <= z=True - Reflexivity
x <= x=True- Antisymmetry
- if
x <= y && y <= x=True, thenx == y=True
The following operator interactions are expected to hold:
x >= y=y <= xx < y=x <= y && x /= yx > y=y < xx < y=compare x y == LTx > y=compare x y == GTx == y=compare x y == EQmin x y == if x <= y then x else y=Truemax x y == if x >= y then x else y=True
Note that (7.) and (8.) do not require min and max to return either of
their arguments. The result is merely required to equal one of the
arguments in terms of (==).
Minimal complete definition: either compare or <=.
Using compare can be more efficient for complex types.
Instances
| Ord SomeTypeRep | |
Defined in Data.Typeable.Internal Methods compare :: SomeTypeRep -> SomeTypeRep -> Ordering # (<) :: SomeTypeRep -> SomeTypeRep -> Bool # (<=) :: SomeTypeRep -> SomeTypeRep -> Bool # (>) :: SomeTypeRep -> SomeTypeRep -> Bool # (>=) :: SomeTypeRep -> SomeTypeRep -> Bool # max :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep # min :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep # | |
| Ord Void | Since: base-4.8.0.0 |
| Ord Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics Methods compare :: Associativity -> Associativity -> Ordering # (<) :: Associativity -> Associativity -> Bool # (<=) :: Associativity -> Associativity -> Bool # (>) :: Associativity -> Associativity -> Bool # (>=) :: Associativity -> Associativity -> Bool # max :: Associativity -> Associativity -> Associativity # min :: Associativity -> Associativity -> Associativity # | |
| Ord DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods compare :: DecidedStrictness -> DecidedStrictness -> Ordering # (<) :: DecidedStrictness -> DecidedStrictness -> Bool # (<=) :: DecidedStrictness -> DecidedStrictness -> Bool # (>) :: DecidedStrictness -> DecidedStrictness -> Bool # (>=) :: DecidedStrictness -> DecidedStrictness -> Bool # max :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness # min :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness # | |
| Ord Fixity | Since: base-4.6.0.0 |
| Ord SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods compare :: SourceStrictness -> SourceStrictness -> Ordering # (<) :: SourceStrictness -> SourceStrictness -> Bool # (<=) :: SourceStrictness -> SourceStrictness -> Bool # (>) :: SourceStrictness -> SourceStrictness -> Bool # (>=) :: SourceStrictness -> SourceStrictness -> Bool # max :: SourceStrictness -> SourceStrictness -> SourceStrictness # min :: SourceStrictness -> SourceStrictness -> SourceStrictness # | |
| Ord SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods compare :: SourceUnpackedness -> SourceUnpackedness -> Ordering # (<) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (<=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # max :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness # min :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness # | |
| Ord SeekMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Device | |
| Ord ArrayException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods compare :: ArrayException -> ArrayException -> Ordering # (<) :: ArrayException -> ArrayException -> Bool # (<=) :: ArrayException -> ArrayException -> Bool # (>) :: ArrayException -> ArrayException -> Bool # (>=) :: ArrayException -> ArrayException -> Bool # max :: ArrayException -> ArrayException -> ArrayException # min :: ArrayException -> ArrayException -> ArrayException # | |
| Ord AsyncException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods compare :: AsyncException -> AsyncException -> Ordering # (<) :: AsyncException -> AsyncException -> Bool # (<=) :: AsyncException -> AsyncException -> Bool # (>) :: AsyncException -> AsyncException -> Bool # (>=) :: AsyncException -> AsyncException -> Bool # max :: AsyncException -> AsyncException -> AsyncException # min :: AsyncException -> AsyncException -> AsyncException # | |
| Ord ExitCode | |
Defined in GHC.IO.Exception | |
| Ord BufferMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types Methods compare :: BufferMode -> BufferMode -> Ordering # (<) :: BufferMode -> BufferMode -> Bool # (<=) :: BufferMode -> BufferMode -> Bool # (>) :: BufferMode -> BufferMode -> Bool # (>=) :: BufferMode -> BufferMode -> Bool # max :: BufferMode -> BufferMode -> BufferMode # min :: BufferMode -> BufferMode -> BufferMode # | |
| Ord Newline | Since: base-4.3.0.0 |
| Ord NewlineMode | Since: base-4.3.0.0 |
Defined in GHC.IO.Handle.Types Methods compare :: NewlineMode -> NewlineMode -> Ordering # (<) :: NewlineMode -> NewlineMode -> Bool # (<=) :: NewlineMode -> NewlineMode -> Bool # (>) :: NewlineMode -> NewlineMode -> Bool # (>=) :: NewlineMode -> NewlineMode -> Bool # max :: NewlineMode -> NewlineMode -> NewlineMode # min :: NewlineMode -> NewlineMode -> NewlineMode # | |
| Ord IOMode | Since: base-4.2.0.0 |
| Ord Int16 | Since: base-2.1 |
| Ord Int32 | Since: base-2.1 |
| Ord Int64 | Since: base-2.1 |
| Ord Int8 | Since: base-2.1 |
| Ord SomeChar | |
Defined in GHC.TypeLits | |
| Ord SomeSymbol | Since: base-4.7.0.0 |
Defined in GHC.TypeLits Methods compare :: SomeSymbol -> SomeSymbol -> Ordering # (<) :: SomeSymbol -> SomeSymbol -> Bool # (<=) :: SomeSymbol -> SomeSymbol -> Bool # (>) :: SomeSymbol -> SomeSymbol -> Bool # (>=) :: SomeSymbol -> SomeSymbol -> Bool # max :: SomeSymbol -> SomeSymbol -> SomeSymbol # min :: SomeSymbol -> SomeSymbol -> SomeSymbol # | |
| Ord SomeNat | Since: base-4.7.0.0 |
| Ord GeneralCategory | Since: base-2.1 |
Defined in GHC.Unicode Methods compare :: GeneralCategory -> GeneralCategory -> Ordering # (<) :: GeneralCategory -> GeneralCategory -> Bool # (<=) :: GeneralCategory -> GeneralCategory -> Bool # (>) :: GeneralCategory -> GeneralCategory -> Bool # (>=) :: GeneralCategory -> GeneralCategory -> Bool # max :: GeneralCategory -> GeneralCategory -> GeneralCategory # min :: GeneralCategory -> GeneralCategory -> GeneralCategory # | |
| Ord Word16 | Since: base-2.1 |
| Ord Word32 | Since: base-2.1 |
| Ord Word64 | Since: base-2.1 |
| Ord Word8 | Since: base-2.1 |
| Ord ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods compare :: ShortByteString -> ShortByteString -> Ordering # (<) :: ShortByteString -> ShortByteString -> Bool # (<=) :: ShortByteString -> ShortByteString -> Bool # (>) :: ShortByteString -> ShortByteString -> Bool # (>=) :: ShortByteString -> ShortByteString -> Bool # max :: ShortByteString -> ShortByteString -> ShortByteString # min :: ShortByteString -> ShortByteString -> ShortByteString # | |
| Ord IntSet | |
| Ord FileType | |
Defined in System.Directory.Internal.Common | |
| Ord Permissions | |
Defined in System.Directory.Internal.Common Methods compare :: Permissions -> Permissions -> Ordering # (<) :: Permissions -> Permissions -> Bool # (<=) :: Permissions -> Permissions -> Bool # (>) :: Permissions -> Permissions -> Bool # (>=) :: Permissions -> Permissions -> Bool # max :: Permissions -> Permissions -> Permissions # min :: Permissions -> Permissions -> Permissions # | |
| Ord XdgDirectory | |
Defined in System.Directory.Internal.Common Methods compare :: XdgDirectory -> XdgDirectory -> Ordering # (<) :: XdgDirectory -> XdgDirectory -> Bool # (<=) :: XdgDirectory -> XdgDirectory -> Bool # (>) :: XdgDirectory -> XdgDirectory -> Bool # (>=) :: XdgDirectory -> XdgDirectory -> Bool # max :: XdgDirectory -> XdgDirectory -> XdgDirectory # min :: XdgDirectory -> XdgDirectory -> XdgDirectory # | |
| Ord XdgDirectoryList | |
Defined in System.Directory.Internal.Common Methods compare :: XdgDirectoryList -> XdgDirectoryList -> Ordering # (<) :: XdgDirectoryList -> XdgDirectoryList -> Bool # (<=) :: XdgDirectoryList -> XdgDirectoryList -> Bool # (>) :: XdgDirectoryList -> XdgDirectoryList -> Bool # (>=) :: XdgDirectoryList -> XdgDirectoryList -> Bool # max :: XdgDirectoryList -> XdgDirectoryList -> XdgDirectoryList # min :: XdgDirectoryList -> XdgDirectoryList -> XdgDirectoryList # | |
| Ord OsChar | Byte ordering of the internal representation. |
| Ord OsString | Byte ordering of the internal representation. |
Defined in System.OsString.Internal.Types | |
| Ord PosixChar | |
| Ord PosixString | |
Defined in System.OsString.Internal.Types Methods compare :: PosixString -> PosixString -> Ordering # (<) :: PosixString -> PosixString -> Bool # (<=) :: PosixString -> PosixString -> Bool # (>) :: PosixString -> PosixString -> Bool # (>=) :: PosixString -> PosixString -> Bool # max :: PosixString -> PosixString -> PosixString # min :: PosixString -> PosixString -> PosixString # | |
| Ord WindowsChar | |
Defined in System.OsString.Internal.Types Methods compare :: WindowsChar -> WindowsChar -> Ordering # (<) :: WindowsChar -> WindowsChar -> Bool # (<=) :: WindowsChar -> WindowsChar -> Bool # (>) :: WindowsChar -> WindowsChar -> Bool # (>=) :: WindowsChar -> WindowsChar -> Bool # max :: WindowsChar -> WindowsChar -> WindowsChar # min :: WindowsChar -> WindowsChar -> WindowsChar # | |
| Ord WindowsString | |
Defined in System.OsString.Internal.Types Methods compare :: WindowsString -> WindowsString -> Ordering # (<) :: WindowsString -> WindowsString -> Bool # (<=) :: WindowsString -> WindowsString -> Bool # (>) :: WindowsString -> WindowsString -> Bool # (>=) :: WindowsString -> WindowsString -> Bool # max :: WindowsString -> WindowsString -> WindowsString # min :: WindowsString -> WindowsString -> WindowsString # | |
| Ord Ordering | |
Defined in GHC.Classes | |
| Ord TyCon | |
| Ord ArgPolicy | |
| Ord OptName | |
Defined in Options.Applicative.Types | |
| Ord OptVisibility | |
Defined in Options.Applicative.Types Methods compare :: OptVisibility -> OptVisibility -> Ordering # (<) :: OptVisibility -> OptVisibility -> Bool # (<=) :: OptVisibility -> OptVisibility -> Bool # (>) :: OptVisibility -> OptVisibility -> Bool # (>=) :: OptVisibility -> OptVisibility -> Bool # max :: OptVisibility -> OptVisibility -> OptVisibility # min :: OptVisibility -> OptVisibility -> OptVisibility # | |
| Ord SourcePos | |
| Ord FusionDepth | |
Defined in Prettyprinter.Internal Methods compare :: FusionDepth -> FusionDepth -> Ordering # (<) :: FusionDepth -> FusionDepth -> Bool # (<=) :: FusionDepth -> FusionDepth -> Bool # (>) :: FusionDepth -> FusionDepth -> Bool # (>=) :: FusionDepth -> FusionDepth -> Bool # max :: FusionDepth -> FusionDepth -> FusionDepth # min :: FusionDepth -> FusionDepth -> FusionDepth # | |
| Ord LayoutOptions | |
Defined in Prettyprinter.Internal Methods compare :: LayoutOptions -> LayoutOptions -> Ordering # (<) :: LayoutOptions -> LayoutOptions -> Bool # (<=) :: LayoutOptions -> LayoutOptions -> Bool # (>) :: LayoutOptions -> LayoutOptions -> Bool # (>=) :: LayoutOptions -> LayoutOptions -> Bool # max :: LayoutOptions -> LayoutOptions -> LayoutOptions # min :: LayoutOptions -> LayoutOptions -> LayoutOptions # | |
| Ord PageWidth | |
| Ord CChunk | |
| Ord CLine | |
| Ord PinCapabilities | |
Defined in Sketch.FRP.Copilot.Types Methods compare :: PinCapabilities -> PinCapabilities -> Ordering # (<) :: PinCapabilities -> PinCapabilities -> Bool # (<=) :: PinCapabilities -> PinCapabilities -> Bool # (>) :: PinCapabilities -> PinCapabilities -> Bool # (>=) :: PinCapabilities -> PinCapabilities -> Bool # max :: PinCapabilities -> PinCapabilities -> PinCapabilities # min :: PinCapabilities -> PinCapabilities -> PinCapabilities # | |
| Ord PinMode | |
Defined in Sketch.FRP.Copilot.Types | |
| Ord LocalTime | |
Defined in Data.Time.LocalTime.Internal.LocalTime | |
| Ord GPIOAddress Source # | |
Defined in Copilot.Zephyr.Internals Methods compare :: GPIOAddress -> GPIOAddress -> Ordering # (<) :: GPIOAddress -> GPIOAddress -> Bool # (<=) :: GPIOAddress -> GPIOAddress -> Bool # (>) :: GPIOAddress -> GPIOAddress -> Bool # (>=) :: GPIOAddress -> GPIOAddress -> Bool # max :: GPIOAddress -> GPIOAddress -> GPIOAddress # min :: GPIOAddress -> GPIOAddress -> GPIOAddress # | |
| Ord GPIOAlias Source # | |
| Ord Zephyr Source # | |
| Ord Integer | |
| Ord () | |
| Ord Bool | |
| Ord Char | |
| Ord Double | Note that due to the presence of
Also note that, due to the same,
|
| Ord Float | Note that due to the presence of
Also note that, due to the same,
|
| Ord Int | |
| Ord Word | |
| Ord a => Ord (ZipList a) | Since: base-4.7.0.0 |
| Ord a => Ord (Identity a) | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity | |
| Ord a => Ord (NonEmpty a) | Since: base-4.9.0.0 |
| Ord p => Ord (Par1 p) | Since: base-4.7.0.0 |
| Integral a => Ord (Ratio a) | Since: base-2.0.1 |
| Ord a => Ord (IntMap a) | |
Defined in Data.IntMap.Internal | |
| Ord a => Ord (Seq a) | |
| Ord a => Ord (ViewL a) | |
Defined in Data.Sequence.Internal | |
| Ord a => Ord (ViewR a) | |
Defined in Data.Sequence.Internal | |
| Ord a => Ord (Intersection a) | |
Defined in Data.Set.Internal Methods compare :: Intersection a -> Intersection a -> Ordering # (<) :: Intersection a -> Intersection a -> Bool # (<=) :: Intersection a -> Intersection a -> Bool # (>) :: Intersection a -> Intersection a -> Bool # (>=) :: Intersection a -> Intersection a -> Bool # max :: Intersection a -> Intersection a -> Intersection a # min :: Intersection a -> Intersection a -> Intersection a # | |
| Ord a => Ord (Set a) | |
| Ord a => Ord (Tree a) | Since: containers-0.6.5 |
| Ord t => Ord (Sym t) | |
| Ord ann => Ord (SimpleDocStream ann) | |
Defined in Prettyprinter.Internal Methods compare :: SimpleDocStream ann -> SimpleDocStream ann -> Ordering # (<) :: SimpleDocStream ann -> SimpleDocStream ann -> Bool # (<=) :: SimpleDocStream ann -> SimpleDocStream ann -> Bool # (>) :: SimpleDocStream ann -> SimpleDocStream ann -> Bool # (>=) :: SimpleDocStream ann -> SimpleDocStream ann -> Bool # max :: SimpleDocStream ann -> SimpleDocStream ann -> SimpleDocStream ann # min :: SimpleDocStream ann -> SimpleDocStream ann -> SimpleDocStream ann # | |
| Ord g => Ord (StateGen g) | |
Defined in System.Random.Internal | |
| Ord a => Ord (Maybe a) | Since: base-2.1 |
| Ord a => Ord (a) | |
| Ord a => Ord [a] | |
| (Ord a, Ord b) => Ord (Either a b) | Since: base-2.1 |
| Ord (TypeRep a) | Since: base-4.4.0.0 |
| Ord (U1 p) | Since: base-4.7.0.0 |
| Ord (V1 p) | Since: base-4.9.0.0 |
| (Ord k, Ord v) => Ord (Map k v) | |
| Ord (Pin t) Source # | |
| (Ord a, Ord b) => Ord (a, b) | |
| Ord a => Ord (Const a b) | Since: base-4.9.0.0 |
| (Generic1 f, Ord (Rep1 f a)) => Ord (Generically1 f a) | Since: base-4.18.0.0 |
Defined in GHC.Generics Methods compare :: Generically1 f a -> Generically1 f a -> Ordering # (<) :: Generically1 f a -> Generically1 f a -> Bool # (<=) :: Generically1 f a -> Generically1 f a -> Bool # (>) :: Generically1 f a -> Generically1 f a -> Bool # (>=) :: Generically1 f a -> Generically1 f a -> Bool # max :: Generically1 f a -> Generically1 f a -> Generically1 f a # min :: Generically1 f a -> Generically1 f a -> Generically1 f a # | |
| Ord (f p) => Ord (Rec1 f p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
| Ord (URec (Ptr ()) p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods compare :: URec (Ptr ()) p -> URec (Ptr ()) p -> Ordering # (<) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (<=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (>) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (>=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # max :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p # min :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p # | |
| Ord (URec Char p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Ord (URec Double p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods compare :: URec Double p -> URec Double p -> Ordering # (<) :: URec Double p -> URec Double p -> Bool # (<=) :: URec Double p -> URec Double p -> Bool # (>) :: URec Double p -> URec Double p -> Bool # (>=) :: URec Double p -> URec Double p -> Bool # | |
| Ord (URec Float p) | |
Defined in GHC.Generics | |
| Ord (URec Int p) | Since: base-4.9.0.0 |
| Ord (URec Word p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| (Ord w, Ord1 m, Ord a) => Ord (WriterT w m a) | |
Defined in Control.Monad.Trans.Writer.Lazy Methods compare :: WriterT w m a -> WriterT w m a -> Ordering # (<) :: WriterT w m a -> WriterT w m a -> Bool # (<=) :: WriterT w m a -> WriterT w m a -> Bool # (>) :: WriterT w m a -> WriterT w m a -> Bool # (>=) :: WriterT w m a -> WriterT w m a -> Bool # | |
| (Ord a, Ord b, Ord c) => Ord (a, b, c) | |
| (Ord (f p), Ord (g p)) => Ord ((f :*: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
| (Ord (f p), Ord (g p)) => Ord ((f :+: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
| Ord c => Ord (K1 i c p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
| (Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) | |
Defined in GHC.Classes | |
| Ord (f (g p)) => Ord ((f :.: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
| Ord (f p) => Ord (M1 i c f p) | Since: base-4.7.0.0 |
| (Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering # (<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering # (<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) # min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering # (<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) # min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering # (<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # max :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) # min :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # max :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) # min :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) # min :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) # min :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) # min :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # | |
class (Real a, Enum a) => Integral a where #
Integral numbers, supporting integer division.
The Haskell Report defines no laws for Integral. However, Integral
instances are customarily expected to define a Euclidean domain and have the
following properties for the div/mod and quot/rem pairs, given
suitable Euclidean functions f and g:
x=y * quot x y + rem x ywithrem x y=fromInteger 0org (rem x y)<g yx=y * div x y + mod x ywithmod x y=fromInteger 0orf (mod x y)<f y
An example of a suitable Euclidean function, for Integer's instance, is
abs.
In addition, toInteger should be total, and fromInteger should be a left
inverse for it, i.e. fromInteger (toInteger i) = i.
Methods
quot :: a -> a -> a infixl 7 #
integer division truncated toward zero
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base.
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base.
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base.
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base.
conversion to Integer
Instances
| Integral Int16 | Since: base-2.1 |
| Integral Int32 | Since: base-2.1 |
| Integral Int64 | Since: base-2.1 |
| Integral Int8 | Since: base-2.1 |
| Integral Word16 | Since: base-2.1 |
| Integral Word32 | Since: base-2.1 |
| Integral Word64 | Since: base-2.1 |
| Integral Word8 | Since: base-2.1 |
| Integral Integer | Since: base-2.0.1 |
Defined in GHC.Real | |
| Integral Natural | Since: base-4.8.0.0 |
Defined in GHC.Real | |
| Integral Int | Since: base-2.0.1 |
| Integral Word | Since: base-2.1 |
| Integral a => Integral (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity Methods quot :: Identity a -> Identity a -> Identity a # rem :: Identity a -> Identity a -> Identity a # div :: Identity a -> Identity a -> Identity a # mod :: Identity a -> Identity a -> Identity a # quotRem :: Identity a -> Identity a -> (Identity a, Identity a) # divMod :: Identity a -> Identity a -> (Identity a, Identity a) # | |
| Integral a => Integral (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b # rem :: Const a b -> Const a b -> Const a b # div :: Const a b -> Const a b -> Const a b # mod :: Const a b -> Const a b -> Const a b # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) # divMod :: Const a b -> Const a b -> (Const a b, Const a b) # | |
Parsing of Strings, producing values.
Derived instances of Read make the following assumptions, which
derived instances of Show obey:
- If the constructor is defined to be an infix operator, then the
derived
Readinstance will parse only infix applications of the constructor (not the prefix form). - Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
- If the constructor is defined using record syntax, the derived
Readwill parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. - The derived
Readinstance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Read in Haskell 2010 is equivalent to
instance (Read a) => Read (Tree a) where
readsPrec d r = readParen (d > app_prec)
(\r -> [(Leaf m,t) |
("Leaf",s) <- lex r,
(m,t) <- readsPrec (app_prec+1) s]) r
++ readParen (d > up_prec)
(\r -> [(u:^:v,w) |
(u,s) <- readsPrec (up_prec+1) r,
(":^:",t) <- lex s,
(v,w) <- readsPrec (up_prec+1) t]) r
where app_prec = 10
up_prec = 5Note that right-associativity of :^: is unused.
The derived instance in GHC is equivalent to
instance (Read a) => Read (Tree a) where
readPrec = parens $ (prec app_prec $ do
Ident "Leaf" <- lexP
m <- step readPrec
return (Leaf m))
+++ (prec up_prec $ do
u <- step readPrec
Symbol ":^:" <- lexP
v <- step readPrec
return (u :^: v))
where app_prec = 10
up_prec = 5
readListPrec = readListPrecDefaultWhy do both readsPrec and readPrec exist, and why does GHC opt to
implement readPrec in derived Read instances instead of readsPrec?
The reason is that readsPrec is based on the ReadS type, and although
ReadS is mentioned in the Haskell 2010 Report, it is not a very efficient
parser data structure.
readPrec, on the other hand, is based on a much more efficient ReadPrec
datatype (a.k.a "new-style parsers"), but its definition relies on the use
of the RankNTypes language extension. Therefore, readPrec (and its
cousin, readListPrec) are marked as GHC-only. Nevertheless, it is
recommended to use readPrec instead of readsPrec whenever possible
for the efficiency improvements it brings.
As mentioned above, derived Read instances in GHC will implement
readPrec instead of readsPrec. The default implementations of
readsPrec (and its cousin, readList) will simply use readPrec under
the hood. If you are writing a Read instance by hand, it is recommended
to write it like so:
instanceReadT wherereadPrec= ...readListPrec=readListPrecDefault
Methods
Arguments
| :: Int | the operator precedence of the enclosing
context (a number from |
| -> ReadS a |
attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.
Derived instances of Read and Show satisfy the following:
That is, readsPrec parses the string produced by
showsPrec, and delivers the value that
showsPrec started with.
Instances
| Read Void | Reading a Since: base-4.8.0.0 |
| Read Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS Associativity # readList :: ReadS [Associativity] # | |
| Read DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS DecidedStrictness # readList :: ReadS [DecidedStrictness] # | |
| Read Fixity | Since: base-4.6.0.0 |
| Read SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceStrictness # readList :: ReadS [SourceStrictness] # | |
| Read SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceUnpackedness # readList :: ReadS [SourceUnpackedness] # | |
| Read SeekMode | Since: base-4.2.0.0 |
| Read ExitCode | |
| Read BufferMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS BufferMode # readList :: ReadS [BufferMode] # readPrec :: ReadPrec BufferMode # readListPrec :: ReadPrec [BufferMode] # | |
| Read Newline | Since: base-4.3.0.0 |
| Read NewlineMode | Since: base-4.3.0.0 |
Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS NewlineMode # readList :: ReadS [NewlineMode] # readPrec :: ReadPrec NewlineMode # readListPrec :: ReadPrec [NewlineMode] # | |
| Read IOMode | Since: base-4.2.0.0 |
| Read Int16 | Since: base-2.1 |
| Read Int32 | Since: base-2.1 |
| Read Int64 | Since: base-2.1 |
| Read Int8 | Since: base-2.1 |
| Read SomeChar | |
| Read SomeSymbol | Since: base-4.7.0.0 |
Defined in GHC.TypeLits Methods readsPrec :: Int -> ReadS SomeSymbol # readList :: ReadS [SomeSymbol] # readPrec :: ReadPrec SomeSymbol # readListPrec :: ReadPrec [SomeSymbol] # | |
| Read SomeNat | Since: base-4.7.0.0 |
| Read GeneralCategory | Since: base-2.1 |
Defined in GHC.Read Methods readsPrec :: Int -> ReadS GeneralCategory # readList :: ReadS [GeneralCategory] # | |
| Read Word16 | Since: base-2.1 |
| Read Word32 | Since: base-2.1 |
| Read Word64 | Since: base-2.1 |
| Read Word8 | Since: base-2.1 |
| Read Lexeme | Since: base-2.1 |
| Read ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods readsPrec :: Int -> ReadS ShortByteString # readList :: ReadS [ShortByteString] # | |
| Read IntSet | |
| Read FileType | |
| Read Permissions | |
Defined in System.Directory.Internal.Common Methods readsPrec :: Int -> ReadS Permissions # readList :: ReadS [Permissions] # readPrec :: ReadPrec Permissions # readListPrec :: ReadPrec [Permissions] # | |
| Read XdgDirectory | |
Defined in System.Directory.Internal.Common Methods readsPrec :: Int -> ReadS XdgDirectory # readList :: ReadS [XdgDirectory] # | |
| Read XdgDirectoryList | |
Defined in System.Directory.Internal.Common Methods readsPrec :: Int -> ReadS XdgDirectoryList # readList :: ReadS [XdgDirectoryList] # | |
| Read Ordering | Since: base-2.1 |
| Read Integer | Since: base-2.1 |
| Read Natural | Since: base-4.8.0.0 |
| Read () | Since: base-2.1 |
| Read Bool | Since: base-2.1 |
| Read Char | Since: base-2.1 |
| Read Double | Since: base-2.1 |
| Read Float | Since: base-2.1 |
| Read Int | Since: base-2.1 |
| Read Word | Since: base-4.5.0.0 |
| Read a => Read (ZipList a) | Since: base-4.7.0.0 |
| Read a => Read (And a) | Since: base-4.16 |
| Read a => Read (Iff a) | Since: base-4.16 |
| Read a => Read (Ior a) | Since: base-4.16 |
| Read a => Read (Xor a) | Since: base-4.16 |
| Read a => Read (Identity a) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Read a => Read (NonEmpty a) | Since: base-4.11.0.0 |
| Read p => Read (Par1 p) | Since: base-4.7.0.0 |
| (Integral a, Read a) => Read (Ratio a) | Since: base-2.1 |
| Read e => Read (IntMap e) | |
| Read a => Read (Seq a) | |
| Read a => Read (ViewL a) | |
| Read a => Read (ViewR a) | |
| (Read a, Ord a) => Read (Set a) | |
| Read a => Read (Tree a) | |
| Read a => Read (Maybe a) | Since: base-2.1 |
| Read a => Read (a) | Since: base-4.15 |
| Read a => Read [a] | Since: base-2.1 |
| (Read a, Read b) => Read (Either a b) | Since: base-3.0 |
| (Ix a, Read a, Read b) => Read (Array a b) | Since: base-2.1 |
| Read (U1 p) | Since: base-4.9.0.0 |
| Read (V1 p) | Since: base-4.9.0.0 |
| (Ord k, Read k, Read e) => Read (Map k e) | |
| (Read a, Read b) => Read (a, b) | Since: base-2.1 |
| Read a => Read (Const a b) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Read (f p) => Read (Rec1 f p) | Since: base-4.7.0.0 |
| (Read w, Read1 m, Read a) => Read (WriterT w m a) | |
| (Read a, Read b, Read c) => Read (a, b, c) | Since: base-2.1 |
| (Read (f p), Read (g p)) => Read ((f :*: g) p) | Since: base-4.7.0.0 |
| (Read (f p), Read (g p)) => Read ((f :+: g) p) | Since: base-4.7.0.0 |
| Read c => Read (K1 i c p) | Since: base-4.7.0.0 |
| (Read a, Read b, Read c, Read d) => Read (a, b, c, d) | Since: base-2.1 |
| Read (f (g p)) => Read ((f :.: g) p) | Since: base-4.7.0.0 |
| Read (f p) => Read (M1 i c f p) | Since: base-4.7.0.0 |
| (Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1 |
Defined in GHC.Read | |
Conversion of values to readable Strings.
Derived instances of Show have the following properties, which
are compatible with derived instances of Read:
- The result of
showis a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. - If the constructor is defined to be an infix operator, then
showsPrecwill produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
xis less thand(associativity is ignored). Thus, ifdis0then the result is never surrounded in parentheses; ifdis11it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
showwill produce the record-syntax form, with the fields given in the same order as the original declaration.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Show is equivalent to
instance (Show a) => Show (Tree a) where
showsPrec d (Leaf m) = showParen (d > app_prec) $
showString "Leaf " . showsPrec (app_prec+1) m
where app_prec = 10
showsPrec d (u :^: v) = showParen (d > up_prec) $
showsPrec (up_prec+1) u .
showString " :^: " .
showsPrec (up_prec+1) v
where up_prec = 5Note that right-associativity of :^: is ignored. For example,
show(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)".
Methods
Arguments
| :: Int | the operator precedence of the enclosing
context (a number from |
| -> a | the value to be converted to a |
| -> ShowS |
Convert a value to a readable String.
showsPrec should satisfy the law
showsPrec d x r ++ s == showsPrec d x (r ++ s)
Derived instances of Read and Show satisfy the following:
That is, readsPrec parses the string produced by
showsPrec, and delivers the value that showsPrec started with.
Instances
8-bit signed integer type
Instances
| Bits Int8 | Since: base-2.1 |
Defined in GHC.Int Methods (.&.) :: Int8 -> Int8 -> Int8 # (.|.) :: Int8 -> Int8 -> Int8 # complement :: Int8 -> Int8 # shift :: Int8 -> Int -> Int8 # rotate :: Int8 -> Int -> Int8 # setBit :: Int8 -> Int -> Int8 # clearBit :: Int8 -> Int -> Int8 # complementBit :: Int8 -> Int -> Int8 # testBit :: Int8 -> Int -> Bool # bitSizeMaybe :: Int8 -> Maybe Int # shiftL :: Int8 -> Int -> Int8 # unsafeShiftL :: Int8 -> Int -> Int8 # shiftR :: Int8 -> Int -> Int8 # unsafeShiftR :: Int8 -> Int -> Int8 # rotateL :: Int8 -> Int -> Int8 # | |
| FiniteBits Int8 | Since: base-4.6.0.0 |
Defined in GHC.Int Methods finiteBitSize :: Int8 -> Int # countLeadingZeros :: Int8 -> Int # countTrailingZeros :: Int8 -> Int # | |
| Bounded Int8 | Since: base-2.1 |
| Enum Int8 | Since: base-2.1 |
| Ix Int8 | Since: base-2.1 |
| Num Int8 | Since: base-2.1 |
| Read Int8 | Since: base-2.1 |
| Integral Int8 | Since: base-2.1 |
| Real Int8 | Since: base-2.1 |
Defined in GHC.Int Methods toRational :: Int8 -> Rational # | |
| Show Int8 | Since: base-2.1 |
| Typed Int8 | |
Defined in Copilot.Core.Type | |
| SymbolParser Int8 | |
Defined in Copilot.Library.RegExp | |
| Eq Int8 | Since: base-2.1 |
| Ord Int8 | Since: base-2.1 |
| Pretty Int8 | |
Defined in Prettyprinter.Internal | |
| Uniform Int8 | |
Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Int8 # | |
| UniformRange Int8 | |
Defined in System.Random.Internal | |
| Cast Int8 Int16 | Cast number to bigger type. |
| Cast Int8 Int32 | Cast number to bigger type. |
| Cast Int8 Int64 | Cast number to bigger type. |
| Cast Int8 Int8 | Identity casting. |
| Cast Bool Int8 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| UnsafeCast Int16 Int8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int32 Int8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Int8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int8 Word8 | Signed to unsigned casting. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int8 Double | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int8 Float | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word8 Int8 | Cast from unsigned numbers to signed numbers. |
Defined in Copilot.Language.Operators.Cast | |
16-bit signed integer type
Instances
| Bits Int16 | Since: base-2.1 |
Defined in GHC.Int Methods (.&.) :: Int16 -> Int16 -> Int16 # (.|.) :: Int16 -> Int16 -> Int16 # xor :: Int16 -> Int16 -> Int16 # complement :: Int16 -> Int16 # shift :: Int16 -> Int -> Int16 # rotate :: Int16 -> Int -> Int16 # setBit :: Int16 -> Int -> Int16 # clearBit :: Int16 -> Int -> Int16 # complementBit :: Int16 -> Int -> Int16 # testBit :: Int16 -> Int -> Bool # bitSizeMaybe :: Int16 -> Maybe Int # shiftL :: Int16 -> Int -> Int16 # unsafeShiftL :: Int16 -> Int -> Int16 # shiftR :: Int16 -> Int -> Int16 # unsafeShiftR :: Int16 -> Int -> Int16 # rotateL :: Int16 -> Int -> Int16 # | |
| FiniteBits Int16 | Since: base-4.6.0.0 |
Defined in GHC.Int Methods finiteBitSize :: Int16 -> Int # countLeadingZeros :: Int16 -> Int # countTrailingZeros :: Int16 -> Int # | |
| Bounded Int16 | Since: base-2.1 |
| Enum Int16 | Since: base-2.1 |
| Ix Int16 | Since: base-2.1 |
| Num Int16 | Since: base-2.1 |
| Read Int16 | Since: base-2.1 |
| Integral Int16 | Since: base-2.1 |
| Real Int16 | Since: base-2.1 |
Defined in GHC.Int Methods toRational :: Int16 -> Rational # | |
| Show Int16 | Since: base-2.1 |
| Typed Int16 | |
Defined in Copilot.Core.Type | |
| SymbolParser Int16 | |
Defined in Copilot.Library.RegExp | |
| Eq Int16 | Since: base-2.1 |
| Ord Int16 | Since: base-2.1 |
| Pretty Int16 | |
Defined in Prettyprinter.Internal | |
| Uniform Int16 | |
Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Int16 # | |
| UniformRange Int16 | |
Defined in System.Random.Internal | |
| Cast Int16 Int16 | Identity casting. |
| Cast Int16 Int32 | Cast number to bigger type. |
| Cast Int16 Int64 | Cast number to bigger type. |
| Cast Int8 Int16 | Cast number to bigger type. |
| Cast Word8 Int16 | Cast number to bigger type. |
| Cast Bool Int16 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| UnsafeCast Int16 Int8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int16 Word16 | Signed to unsigned casting. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int16 Double | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int16 Float | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int32 Int16 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Int16 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word16 Int16 | Cast from unsigned numbers to signed numbers. |
Defined in Copilot.Language.Operators.Cast | |
| IsAnalogInputPin t => Input Zephyr (Pin t) ADC Source # | |
32-bit signed integer type
Instances
| Bits Int32 | Since: base-2.1 |
Defined in GHC.Int Methods (.&.) :: Int32 -> Int32 -> Int32 # (.|.) :: Int32 -> Int32 -> Int32 # xor :: Int32 -> Int32 -> Int32 # complement :: Int32 -> Int32 # shift :: Int32 -> Int -> Int32 # rotate :: Int32 -> Int -> Int32 # setBit :: Int32 -> Int -> Int32 # clearBit :: Int32 -> Int -> Int32 # complementBit :: Int32 -> Int -> Int32 # testBit :: Int32 -> Int -> Bool # bitSizeMaybe :: Int32 -> Maybe Int # shiftL :: Int32 -> Int -> Int32 # unsafeShiftL :: Int32 -> Int -> Int32 # shiftR :: Int32 -> Int -> Int32 # unsafeShiftR :: Int32 -> Int -> Int32 # rotateL :: Int32 -> Int -> Int32 # | |
| FiniteBits Int32 | Since: base-4.6.0.0 |
Defined in GHC.Int Methods finiteBitSize :: Int32 -> Int # countLeadingZeros :: Int32 -> Int # countTrailingZeros :: Int32 -> Int # | |
| Bounded Int32 | Since: base-2.1 |
| Enum Int32 | Since: base-2.1 |
| Ix Int32 | Since: base-2.1 |
| Num Int32 | Since: base-2.1 |
| Read Int32 | Since: base-2.1 |
| Integral Int32 | Since: base-2.1 |
| Real Int32 | Since: base-2.1 |
Defined in GHC.Int Methods toRational :: Int32 -> Rational # | |
| Show Int32 | Since: base-2.1 |
| Typed Int32 | |
Defined in Copilot.Core.Type | |
| SymbolParser Int32 | |
Defined in Copilot.Library.RegExp | |
| Eq Int32 | Since: base-2.1 |
| Ord Int32 | Since: base-2.1 |
| Pretty Int32 | |
Defined in Prettyprinter.Internal | |
| Uniform Int32 | |
Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Int32 # | |
| UniformRange Int32 | |
Defined in System.Random.Internal | |
| Cast Int16 Int32 | Cast number to bigger type. |
| Cast Int32 Int32 | Identity casting. |
| Cast Int32 Int64 | Cast number to bigger type. |
| Cast Int8 Int32 | Cast number to bigger type. |
| Cast Word16 Int32 | Cast number to bigger type. |
| Cast Word8 Int32 | Cast number to bigger type. |
| Cast Bool Int32 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| UnsafeCast Int32 Int16 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int32 Int8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int32 Word32 | Signed to unsigned casting. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int32 Double | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int32 Float | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Int32 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word32 Int32 | Cast from unsigned numbers to signed numbers. |
Defined in Copilot.Language.Operators.Cast | |
64-bit signed integer type
Instances
| Bits Int64 | Since: base-2.1 |
Defined in GHC.Int Methods (.&.) :: Int64 -> Int64 -> Int64 # (.|.) :: Int64 -> Int64 -> Int64 # xor :: Int64 -> Int64 -> Int64 # complement :: Int64 -> Int64 # shift :: Int64 -> Int -> Int64 # rotate :: Int64 -> Int -> Int64 # setBit :: Int64 -> Int -> Int64 # clearBit :: Int64 -> Int -> Int64 # complementBit :: Int64 -> Int -> Int64 # testBit :: Int64 -> Int -> Bool # bitSizeMaybe :: Int64 -> Maybe Int # shiftL :: Int64 -> Int -> Int64 # unsafeShiftL :: Int64 -> Int -> Int64 # shiftR :: Int64 -> Int -> Int64 # unsafeShiftR :: Int64 -> Int -> Int64 # rotateL :: Int64 -> Int -> Int64 # | |
| FiniteBits Int64 | Since: base-4.6.0.0 |
Defined in GHC.Int Methods finiteBitSize :: Int64 -> Int # countLeadingZeros :: Int64 -> Int # countTrailingZeros :: Int64 -> Int # | |
| Bounded Int64 | Since: base-2.1 |
| Enum Int64 | Since: base-2.1 |
| Ix Int64 | Since: base-2.1 |
| Num Int64 | Since: base-2.1 |
| Read Int64 | Since: base-2.1 |
| Integral Int64 | Since: base-2.1 |
| Real Int64 | Since: base-2.1 |
Defined in GHC.Int Methods toRational :: Int64 -> Rational # | |
| Show Int64 | Since: base-2.1 |
| Typed Int64 | |
Defined in Copilot.Core.Type | |
| SymbolParser Int64 | |
Defined in Copilot.Library.RegExp | |
| Eq Int64 | Since: base-2.1 |
| Ord Int64 | Since: base-2.1 |
| Pretty Int64 | |
Defined in Prettyprinter.Internal | |
| Uniform Int64 | |
Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Int64 # | |
| UniformRange Int64 | |
Defined in System.Random.Internal | |
| Cast Int16 Int64 | Cast number to bigger type. |
| Cast Int32 Int64 | Cast number to bigger type. |
| Cast Int64 Int64 | Identity casting. |
| Cast Int8 Int64 | Cast number to bigger type. |
| Cast Word16 Int64 | Cast number to bigger type. |
| Cast Word32 Int64 | Cast number to bigger type. |
| Cast Word8 Int64 | Cast number to bigger type. |
| Cast Bool Int64 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| UnsafeCast Int64 Int16 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Int32 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Int8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Word64 | Signed to unsigned casting. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Double | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Float | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word64 Int64 | Cast from unsigned numbers to signed numbers. |
Defined in Copilot.Language.Operators.Cast | |
type IOError = IOException #
The Haskell 2010 type for exceptions in the IO monad.
Any I/O operation may raise an IOException instead of returning a result.
For a more general type of exception, including also those that arise
in pure code, see Exception.
In Haskell 2010, this is an opaque type.
The Bounded class is used to name the upper and lower limits of a
type. Ord is not a superclass of Bounded since types that are not
totally ordered may also have upper and lower bounds.
The Bounded class may be derived for any enumeration type;
minBound is the first constructor listed in the data declaration
and maxBound is the last.
Bounded may also be derived for single-constructor datatypes whose
constituent types are in Bounded.
Instances
| Bounded Associativity | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded Int16 | Since: base-2.1 |
| Bounded Int32 | Since: base-2.1 |
| Bounded Int64 | Since: base-2.1 |
| Bounded Int8 | Since: base-2.1 |
| Bounded GeneralCategory | Since: base-2.1 |
Defined in GHC.Unicode | |
| Bounded Word16 | Since: base-2.1 |
| Bounded Word32 | Since: base-2.1 |
| Bounded Word64 | Since: base-2.1 |
| Bounded Word8 | Since: base-2.1 |
| Bounded FileType | |
| Bounded XdgDirectory | |
Defined in System.Directory.Internal.Common | |
| Bounded XdgDirectoryList | |
Defined in System.Directory.Internal.Common | |
| Bounded Ordering | Since: base-2.1 |
| Bounded () | Since: base-2.1 |
| Bounded Bool | Since: base-2.1 |
| Bounded Char | Since: base-2.1 |
| Bounded Int | Since: base-2.1 |
| Bounded Levity | Since: base-4.16.0.0 |
| Bounded VecCount | Since: base-4.10.0.0 |
| Bounded VecElem | Since: base-4.10.0.0 |
| Bounded Word | Since: base-2.1 |
| Bounded a => Bounded (And a) | Since: base-4.16 |
| Bounded a => Bounded (Iff a) | Since: base-4.16 |
| Bounded a => Bounded (Ior a) | Since: base-4.16 |
| Bounded a => Bounded (Xor a) | Since: base-4.16 |
| Bounded a => Bounded (Identity a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (a) | |
| (Bounded a, Bounded b) => Bounded (a, b) | Since: base-2.1 |
| Bounded a => Bounded (Const a b) | Since: base-4.9.0.0 |
| (Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1 |
Class Enum defines operations on sequentially ordered types.
The enumFrom... methods are used in Haskell's translation of
arithmetic sequences.
Instances of Enum may be derived for any enumeration type (types
whose constructors have no fields). The nullary constructors are
assumed to be numbered left-to-right by fromEnum from 0 through n-1.
See Chapter 10 of the Haskell Report for more details.
For any type that is an instance of class Bounded as well as Enum,
the following should hold:
- The calls
succmaxBoundpredminBound fromEnumandtoEnumshould give a runtime error if the result value is not representable in the result type. For example,toEnum7 ::BoolenumFromandenumFromThenshould be defined with an implicit bound, thus:
enumFrom x = enumFromTo x maxBound
enumFromThen x y = enumFromThenTo x y bound
where
bound | fromEnum y >= fromEnum x = maxBound
| otherwise = minBoundMethods
the successor of a value. For numeric types, succ adds 1.
the predecessor of a value. For numeric types, pred subtracts 1.
Convert from an Int.
Convert to an Int.
It is implementation-dependent what fromEnum returns when
applied to a value that is too large to fit in an Int.
Used in Haskell's translation of [n..] with [n..] = enumFrom n,
a possible implementation being enumFrom n = n : enumFrom (succ n).
For example:
enumFrom 4 :: [Integer] = [4,5,6,7,...]
enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]
enumFromThen :: a -> a -> [a] #
Used in Haskell's translation of [n,n'..]
with [n,n'..] = enumFromThen n n', a possible implementation being
enumFromThen n n' = n : n' : worker (f x) (f x n'),
worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y
For example:
enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]
enumFromTo :: a -> a -> [a] #
Used in Haskell's translation of [n..m] with
[n..m] = enumFromTo n m, a possible implementation being
enumFromTo n m
| n <= m = n : enumFromTo (succ n) m
| otherwise = [].
For example:
enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
enumFromTo 42 1 :: [Integer] = []
enumFromThenTo :: a -> a -> a -> [a] #
Used in Haskell's translation of [n,n'..m] with
[n,n'..m] = enumFromThenTo n n' m, a possible implementation
being enumFromThenTo n n' m = worker (f x) (c x) n m,
x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0)
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y and
worker s c v m
| c v m = v : worker s c (s v) m
| otherwise = []
For example:
enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
enumFromThenTo 6 8 2 :: [Int] = []
Instances
class Fractional a => Floating a where #
Trigonometric and hyperbolic functions and related functions.
The Haskell Report defines no laws for Floating. However, (, +)(
and *)exp are customarily expected to define an exponential field and have
the following properties:
exp (a + b)=exp a * exp bexp (fromInteger 0)=fromInteger 1
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
Instances
class Num a => Fractional a where #
Fractional numbers, supporting real division.
The Haskell Report defines no laws for Fractional. However, ( and
+)( are customarily expected to define a division ring and have the
following properties:*)
recipgives the multiplicative inversex * recip x=recip x * x=fromInteger 1- Totality of
toRational toRationalis total- Coherence with
toRational - if the type also implements
Real, thenfromRationalis a left inverse fortoRational, i.e.fromRational (toRational i) = i
Note that it isn't customarily expected that a type instance of
Fractional implement a field. However, all instances in base do.
Minimal complete definition
fromRational, (recip | (/))
Methods
Fractional division.
Reciprocal fraction.
fromRational :: Rational -> a #
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
Instances
| Fractional a => Fractional (Identity a) | Since: base-4.9.0.0 |
| Integral a => Fractional (Ratio a) | Since: base-2.0.1 |
| (Typed a, Eq a, Fractional a) => Fractional (Stream a) | Streams carrying fractional numbers are instances of |
| Fractional a => Fractional (Const a b) | Since: base-4.9.0.0 |
Basic numeric class.
The Haskell Report defines no laws for Num. However, ( and +)( are
customarily expected to define a ring and have the following properties:*)
- Associativity of
(+) (x + y) + z=x + (y + z)- Commutativity of
(+) x + y=y + xfromInteger0x + fromInteger 0=xnegategives the additive inversex + negate x=fromInteger 0- Associativity of
(*) (x * y) * z=x * (y * z)fromInteger1x * fromInteger 1=xandfromInteger 1 * x=x- Distributivity of
(with respect to*)(+) a * (b + c)=(a * b) + (a * c)and(b + c) * a=(b * a) + (c * a)- Coherence with
toInteger - if the type also implements
Integral, thenfromIntegeris a left inverse fortoInteger, i.e.fromInteger (toInteger i) == i
Note that it isn't customarily expected that a type instance of both Num
and Ord implement an ordered ring. Indeed, in base only Integer and
Rational do.
Methods
Unary negation.
Absolute value.
Sign of a number.
The functions abs and signum should satisfy the law:
abs x * signum x == x
For real numbers, the signum is either -1 (negative), 0 (zero)
or 1 (positive).
fromInteger :: Integer -> a #
Conversion from an Integer.
An integer literal represents the application of the function
fromInteger to the appropriate value of type Integer,
so such literals have type (.Num a) => a
Instances
| Num Int16 | Since: base-2.1 |
| Num Int32 | Since: base-2.1 |
| Num Int64 | Since: base-2.1 |
| Num Int8 | Since: base-2.1 |
| Num Word16 | Since: base-2.1 |
| Num Word32 | Since: base-2.1 |
| Num Word64 | Since: base-2.1 |
| Num Word8 | Since: base-2.1 |
| Num Integer | Since: base-2.1 |
| Num Natural | Note that Since: base-4.8.0.0 |
| Num Int | Since: base-2.1 |
| Num Word | Since: base-2.1 |
| Num a => Num (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity | |
| Integral a => Num (Ratio a) | Since: base-2.0.1 |
| (Typed a, Eq a, Num a) => Num (Stream a) | Streams carrying numbers are instances of |
| Num a => Num (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
class (Num a, Ord a) => Real a where #
Real numbers.
The Haskell report defines no laws for Real, however Real instances
are customarily expected to adhere to the following law:
- Coherence with
fromRational - if the type also implements
Fractional, thenfromRationalis a left inverse fortoRational, i.e.fromRational (toRational i) = i
Methods
toRational :: a -> Rational #
the rational equivalent of its real argument with full precision
Instances
| Real Int16 | Since: base-2.1 |
Defined in GHC.Int Methods toRational :: Int16 -> Rational # | |
| Real Int32 | Since: base-2.1 |
Defined in GHC.Int Methods toRational :: Int32 -> Rational # | |
| Real Int64 | Since: base-2.1 |
Defined in GHC.Int Methods toRational :: Int64 -> Rational # | |
| Real Int8 | Since: base-2.1 |
Defined in GHC.Int Methods toRational :: Int8 -> Rational # | |
| Real Word16 | Since: base-2.1 |
Defined in GHC.Word Methods toRational :: Word16 -> Rational # | |
| Real Word32 | Since: base-2.1 |
Defined in GHC.Word Methods toRational :: Word32 -> Rational # | |
| Real Word64 | Since: base-2.1 |
Defined in GHC.Word Methods toRational :: Word64 -> Rational # | |
| Real Word8 | Since: base-2.1 |
Defined in GHC.Word Methods toRational :: Word8 -> Rational # | |
| Real Integer | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Integer -> Rational # | |
| Real Natural | Since: base-4.8.0.0 |
Defined in GHC.Real Methods toRational :: Natural -> Rational # | |
| Real Int | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Int -> Rational # | |
| Real Word | Since: base-2.1 |
Defined in GHC.Real Methods toRational :: Word -> Rational # | |
| Real a => Real (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity Methods toRational :: Identity a -> Rational # | |
| Integral a => Real (Ratio a) | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Ratio a -> Rational # | |
| Real a => Real (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods toRational :: Const a b -> Rational # | |
class (RealFrac a, Floating a) => RealFloat a where #
Efficient, machine-independent access to the components of a floating-point number.
Minimal complete definition
floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
Methods
floatRadix :: a -> Integer #
a constant function, returning the radix of the representation
(often 2)
floatDigits :: a -> Int #
a constant function, returning the number of digits of
floatRadix in the significand
floatRange :: a -> (Int, Int) #
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a -> (Integer, Int) #
The function decodeFloat applied to a real floating-point
number returns the significand expressed as an Integer and an
appropriately scaled exponent (an Int). If decodeFloat x(m,n), then x is equal in value to m*b^^n, where b
is the floating-point radix, and furthermore, either m and n
are both zero or else b^(d-1) <= , where abs m < b^dd is
the value of floatDigits xdecodeFloat 0 = (0,0)decodeFloat (-0.0) = (0,0)decodeFloat xisNaN xisInfinite xTrue.
encodeFloat :: Integer -> Int -> a #
encodeFloat performs the inverse of decodeFloat in the
sense that for finite x with the exception of -0.0,
uncurry encodeFloat (decodeFloat x) = xencodeFloat m nm*b^^n (or ±Infinity if overflow
occurs); usually the closer, but if m contains too many bits,
the result may be rounded in the wrong direction.
exponent corresponds to the second component of decodeFloat.
exponent 0 = 0x,
exponent x = snd (decodeFloat x) + floatDigits xx is a finite floating-point number, it is equal in value to
significand x * b ^^ exponent xb is the
floating-point radix.
The behaviour is unspecified on infinite or NaN values.
significand :: a -> a #
The first component of decodeFloat, scaled to lie in the open
interval (-1,1), either 0.0 or of absolute value >= 1/b,
where b is the floating-point radix.
The behaviour is unspecified on infinite or NaN values.
scaleFloat :: Int -> a -> a #
multiplies a floating-point number by an integer power of the radix
True if the argument is an IEEE "not-a-number" (NaN) value
isInfinite :: a -> Bool #
True if the argument is an IEEE infinity or negative infinity
isDenormalized :: a -> Bool #
True if the argument is too small to be represented in
normalized format
isNegativeZero :: a -> Bool #
True if the argument is an IEEE negative zero
True if the argument is an IEEE floating point number
a version of arctangent taking two real floating-point arguments.
For real floating x and y, atan2 y x(x,y). atan2 y x-pi,
pi]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported. atan2 y 1y in a type
that is RealFloat, should return the same value as atan yatan2 is provided, but implementors
can provide a more accurate implementation.
Instances
class (Real a, Fractional a) => RealFrac a where #
Extracting components of fractions.
Minimal complete definition
Methods
properFraction :: Integral b => a -> (b, a) #
The function properFraction takes a real fractional number x
and returns a pair (n,f) such that x = n+f, and:
nis an integral number with the same sign asx; andfis a fraction with the same type and sign asx, and with absolute value less than1.
The default definitions of the ceiling, floor, truncate
and round functions are in terms of properFraction.
truncate :: Integral b => a -> b #
truncate xx between zero and x
round :: Integral b => a -> b #
round xx;
the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> b #
ceiling xx
floor :: Integral b => a -> b #
floor xx
The Bits class defines bitwise operations over integral types.
- Bits are numbered from 0 with bit 0 being the least significant bit.
Minimal complete definition
(.&.), (.|.), xor, complement, (shift | shiftL, shiftR), (rotate | rotateL, rotateR), bitSize, bitSizeMaybe, isSigned, testBit, bit, popCount
Methods
(.&.) :: a -> a -> a infixl 7 #
Bitwise "and"
(.|.) :: a -> a -> a infixl 5 #
Bitwise "or"
complement :: a -> a #
Reverse all the bits in the argument
Instances
File and directory names are values of type String, whose precise
meaning is operating system dependent. Files can be opened, yielding a
handle which can then be used to operate on the contents of that file.
The field of a struct, together with a representation of its type.
The value of that is a product or struct, defined as a constructor with several fields.
Minimal complete definition
type Spec = Writer [SpecItem] () #
A specification is a list of declarations of triggers, observers, properties and theorems.
Specifications are normally declared in monadic style, for example:
monitor1 :: Stream Bool monitor1 = [False] ++ not monitor1 counter :: Stream Int32 counter = [0] ++ not counter spec :: Spec spec = do trigger "handler_1" monitor1 [] trigger "handler_2" (counter > 10) [arg counter]
A untyped type (no phantom type).
class (Show a, Typeable a) => Typed a where #
A typed expression, from which we can obtain the two type representations
used by Copilot: Type and SimpleType.
Minimal complete definition
Instances
| Typed Int16 | |
Defined in Copilot.Core.Type | |
| Typed Int32 | |
Defined in Copilot.Core.Type | |
| Typed Int64 | |
Defined in Copilot.Core.Type | |
| Typed Int8 | |
Defined in Copilot.Core.Type | |
| Typed Word16 | |
Defined in Copilot.Core.Type | |
| Typed Word32 | |
Defined in Copilot.Core.Type | |
| Typed Word64 | |
Defined in Copilot.Core.Type | |
| Typed Word8 | |
Defined in Copilot.Core.Type | |
| Typed Bool | |
Defined in Copilot.Core.Type | |
| Typed Double | |
Defined in Copilot.Core.Type | |
| Typed Float | |
Defined in Copilot.Core.Type | |
| (Typeable t, Typed t, KnownNat n) => Typed (Array n t) | |
Defined in Copilot.Core.Type | |
data SimpleType where #
A simple, monomorphic representation of types that facilitates putting variables in heterogeneous lists and environments in spite of their types being different.
Constructors
| SBool :: SimpleType | |
| SInt8 :: SimpleType | |
| SInt16 :: SimpleType | |
| SInt32 :: SimpleType | |
| SInt64 :: SimpleType | |
| SWord8 :: SimpleType | |
| SWord16 :: SimpleType | |
| SWord32 :: SimpleType | |
| SWord64 :: SimpleType | |
| SFloat :: SimpleType | |
| SDouble :: SimpleType | |
| SArray :: forall t. Type t -> SimpleType | |
| SStruct :: SimpleType |
Instances
| Eq SimpleType | Type equality, used to help type inference. |
Defined in Copilot.Core.Type | |
A field in a struct. The name of the field is a literal at the type level.
Constructors
| Field t |
Class to capture casting between types for which it can be performed safely.
Instances
| Cast Int16 Int16 | Identity casting. |
| Cast Int16 Int32 | Cast number to bigger type. |
| Cast Int16 Int64 | Cast number to bigger type. |
| Cast Int32 Int32 | Identity casting. |
| Cast Int32 Int64 | Cast number to bigger type. |
| Cast Int64 Int64 | Identity casting. |
| Cast Int8 Int16 | Cast number to bigger type. |
| Cast Int8 Int32 | Cast number to bigger type. |
| Cast Int8 Int64 | Cast number to bigger type. |
| Cast Int8 Int8 | Identity casting. |
| Cast Word16 Int32 | Cast number to bigger type. |
| Cast Word16 Int64 | Cast number to bigger type. |
| Cast Word16 Word16 | Identity casting. |
| Cast Word16 Word32 | Cast number to bigger type. |
| Cast Word16 Word64 | Cast number to bigger type. |
| Cast Word32 Int64 | Cast number to bigger type. |
| Cast Word32 Word32 | Identity casting. |
| Cast Word32 Word64 | Cast number to bigger type. |
| Cast Word64 Word64 | Identity casting. |
| Cast Word8 Int16 | Cast number to bigger type. |
| Cast Word8 Int32 | Cast number to bigger type. |
| Cast Word8 Int64 | Cast number to bigger type. |
| Cast Word8 Word16 | Cast number to bigger type. |
| Cast Word8 Word32 | Cast number to bigger type. |
| Cast Word8 Word64 | Cast number to bigger type. |
| Cast Word8 Word8 | Identity casting. |
| Cast Bool Int16 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Int32 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Int64 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Int8 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Word16 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Word32 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Word64 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Word8 | Cast a boolean stream to a stream of numbers, producing 1 if the
value at a point in time is |
| Cast Bool Bool | Identity casting. |
class UnsafeCast a b where #
Class to capture casting between types for which casting may be unsafe and/or result in a loss of precision or information.
Instances
| UnsafeCast Int16 Int8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int16 Word16 | Signed to unsigned casting. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int16 Double | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int16 Float | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int32 Int16 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int32 Int8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int32 Word32 | Signed to unsigned casting. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int32 Double | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int32 Float | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Int16 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Int32 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Int8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Word64 | Signed to unsigned casting. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Double | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int64 Float | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int8 Word8 | Signed to unsigned casting. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int8 Double | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Int8 Float | Unsafe signed integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word16 Int16 | Cast from unsigned numbers to signed numbers. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word16 Word8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word16 Double | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word16 Float | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word32 Int32 | Cast from unsigned numbers to signed numbers. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word32 Word16 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word32 Word8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word32 Double | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word32 Float | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word64 Int64 | Cast from unsigned numbers to signed numbers. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word64 Word16 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word64 Word32 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word64 Word8 | Unsafe downcasting to smaller sizes. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word64 Double | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word64 Float | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word8 Int8 | Cast from unsigned numbers to signed numbers. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word8 Double | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
| UnsafeCast Word8 Float | Unsafe unsigned integer promotion to floating point values. |
Defined in Copilot.Language.Operators.Cast | |
array :: forall (n :: Nat) t. KnownNat n => [t] -> Array n t #
Smart array constructor that only type checks if the length of the given list matches the length of the array at type level.
(==>) :: Stream Bool -> Stream Bool -> Stream Bool #
Apply the implication (==>) operator to two boolean streams, point-wise.
local :: (Typed a, Typed b) => Stream a -> (Stream a -> Stream b) -> Stream b #
Let expressions.
Create a stream that results from applying a stream to a function on
streams. Standard usage would be similar to Haskell's let. See the
following example, where stream1, stream2 and s are all streams
carrying values of some numeric type:
expression = local (stream1 + stream2) $ \s ->
(s >= 0 && s <= 10)
either :: (a -> c) -> (b -> c) -> Either a b -> c #
Case analysis for the Either type.
If the value is Left aa;
if it is Right bb.
Examples
We create two values of type Either String IntLeft constructor and another using the Right constructor. Then
we apply "either" the length function (if we have a String)
or the "times-two" function (if we have an Int):
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>either length (*2) s3>>>either length (*2) n6
($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 #
Application operator. This operator is redundant, since ordinary
application (f x) means the same as (f . However, $ x)$ has
low, right-associative binding precedence, so it sometimes allows
parentheses to be omitted; for example:
f $ g $ h x = f (g (h x))
It is also useful in higher-order situations, such as map ($ 0) xszipWith ($) fs xs
Note that ( is representation-polymorphic in its result type, so that
$)foo where $ Truefoo :: Bool -> Int# is well-typed.
(++) :: Typed a => [a] -> Stream a -> Stream a infixr 1 #
Prepend a fixed number of samples to a stream.
The elements to be appended at the beginning of the stream must be limited, that is, the list must have finite length.
Prepending elements to a stream may increase the memory requirements of the generated programs (which now must hold the same number of elements in memory for future processing).
map :: (a -> b) -> [a] -> [b] #
\(\mathcal{O}(n)\). map f xs is the list obtained by applying f to
each element of xs, i.e.,
map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]
>>>map (+1) [1, 2, 3][2,3,4]
takeWhile :: (a -> Bool) -> [a] -> [a] #
takeWhile, applied to a predicate p and a list xs, returns the
longest prefix (possibly empty) of xs of elements that satisfy p.
>>>takeWhile (< 3) [1,2,3,4,1,2,3,4][1,2]>>>takeWhile (< 9) [1,2,3][1,2,3]>>>takeWhile (< 0) [1,2,3][]
take :: (Integral a, Typed b) => a -> Stream b -> [Stream b] #
Given a stream and a number, produce a finite list of streams dropping an
increasing number of elements of the given stream, up to that number. For
example, for a given stream s, the expression take 2 s is equal to
[ drop 0 s, drop 1 s].
read :: Read a => String -> a #
The read function reads input from a string, which must be
completely consumed by the input process. read fails with an error if the
parse is unsuccessful, and it is therefore discouraged from being used in
real applications. Use readMaybe or readEither for safe alternatives.
>>>read "123" :: Int123
>>>read "hello" :: Int*** Exception: Prelude.read: no parse
(==) :: (Eq a, Typed a) => Stream a -> Stream a -> Stream Bool #
Compare two streams point-wise for equality.
The output stream contains the value True at a point in time if both argument streams contain the same value at that point in time.
(>=) :: (Ord a, Typed a) => Stream a -> Stream a -> Stream Bool #
Compare two streams point-wise for order.
The output stream contains the value True at a point in time if the element in the first stream is greater or equal than the element in the second stream at that point in time, and False otherwise.
error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a #
error stops execution and displays an error message.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] #
\(\mathcal{O}(\min(m,n))\). zipWith generalises zip by zipping with the
function given as the first argument, instead of a tupling function.
zipWith (,) xs ys == zip xs ys zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]
For example, zipWith (+)
>>>zipWith (+) [1, 2, 3] [4, 5, 6][5,7,9]
zipWith is right-lazy:
>>>let f = undefined>>>zipWith f [] undefined[]
zipWith is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #
An infix synonym for fmap.
The name of this operator is an allusion to $.
Note the similarities between their types:
($) :: (a -> b) -> a -> b (<$>) :: Functor f => (a -> b) -> f a -> f b
Whereas $ is function application, <$> is function
application lifted over a Functor.
Examples
Convert from a Maybe IntMaybe
Stringshow:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> Left 17Left 17>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>even <$> (2,2)(2,True)
uncurry :: (a -> b -> c) -> (a, b) -> c #
uncurry converts a curried function to a function on pairs.
Examples
>>>uncurry (+) (1,2)3
>>>uncurry ($) (show, 1)"1"
>>>map (uncurry max) [(1,2), (3,4), (6,8)][2,4,8]
head :: HasCallStack => [a] -> a #
\(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty.
>>>head [1, 2, 3]1>>>head [1..]1>>>head []*** Exception: Prelude.head: empty list
WARNING: This function is partial. You can use case-matching, uncons or
listToMaybe instead.
writeFile :: FilePath -> String -> IO () #
The computation writeFile file str function writes the string str,
to the file file.
filter :: (a -> Bool) -> [a] -> [a] #
\(\mathcal{O}(n)\). filter, applied to a predicate and a list, returns
the list of those elements that satisfy the predicate; i.e.,
filter p xs = [ x | x <- xs, p x]
>>>filter odd [1, 2, 3][1,3]
seq :: forall {r :: RuntimeRep} a (b :: TYPE r). a -> b -> b infixr 0 #
The value of seq a ba is bottom, and
otherwise equal to b. In other words, it evaluates the first
argument a to weak head normal form (WHNF). seq is usually
introduced to improve performance by avoiding unneeded laziness.
A note on evaluation order: the expression seq a ba will be evaluated before b.
The only guarantee given by seq is that the both a
and b will be evaluated before seq returns a value.
In particular, this means that b may be evaluated before
a. If you need to guarantee a specific order of evaluation,
you must use the function pseq from the "parallel" package.
concat :: Foldable t => t [a] -> [a] #
The concatenation of all the elements of a container of lists.
Examples
Basic usage:
>>>concat (Just [1, 2, 3])[1,2,3]
>>>concat (Left 42)[]
>>>concat [[1, 2, 3], [4, 5], [6], []][1,2,3,4,5,6]
zip :: [a] -> [b] -> [(a, b)] #
\(\mathcal{O}(\min(m,n))\). zip takes two lists and returns a list of
corresponding pairs.
>>>zip [1, 2] ['a', 'b'][(1,'a'),(2,'b')]
If one input list is shorter than the other, excess elements of the longer list are discarded, even if one of the lists is infinite:
>>>zip [1] ['a', 'b'][(1,'a')]>>>zip [1, 2] ['a'][(1,'a')]>>>zip [] [1..][]>>>zip [1..] [][]
zip is right-lazy:
>>>zip [] undefined[]>>>zip undefined []*** Exception: Prelude.undefined ...
zip is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
print :: Show a => a -> IO () #
The print function outputs a value of any printable type to the
standard output device.
Printable types are those that are instances of class Show; print
converts values to strings for output using the show operation and
adds a newline.
For example, a program to print the first 20 integers and their powers of 2 could be written as:
main = print ([(n, 2^n) | n <- [0..19]])
fromIntegral :: (Integral a, Num b) => a -> b #
General coercion from Integral types.
WARNING: This function performs silent truncation if the result type is not at least as big as the argument's type.
realToFrac :: (Real a, Fractional b) => a -> b #
General coercion to Fractional types.
WARNING: This function goes through the Rational type, which does not have values for NaN for example.
This means it does not round-trip.
For Double it also behaves differently with or without -O0:
Prelude> realToFrac nan -- With -O0 -Infinity Prelude> realToFrac nan NaN
(^) :: (Typed a, Typed b, Num a, Bits a, Integral b) => Stream a -> Stream b -> Stream a #
Apply a limited form of exponentiation (^) to two streams, point-wise.
Either the first stream must be the constant 2, or the second must be a constant stream.
(<) :: (Ord a, Typed a) => Stream a -> Stream a -> Stream Bool #
Compare two streams point-wise for order.
The output stream contains the value True at a point in time if the element in the first stream is smaller than the element in the second stream at that point in time, and False otherwise.
(<=) :: (Ord a, Typed a) => Stream a -> Stream a -> Stream Bool #
Compare two streams point-wise for order.
The output stream contains the value True at a point in time if the element in the first stream is smaller or equal than the element in the second stream at that point in time, and False otherwise.
(>) :: (Ord a, Typed a) => Stream a -> Stream a -> Stream Bool #
Compare two streams point-wise for order.
The output stream contains the value True at a point in time if the element in the first stream is greater than the element in the second stream at that point in time, and False otherwise.
(/=) :: (Eq a, Typed a) => Stream a -> Stream a -> Stream Bool #
Compare two streams point-wise for inequality.
The output stream contains the value True at a point in time if both argument streams contain different values at that point in time.
(&&) :: Stream Bool -> Stream Bool -> Stream Bool infixr 4 #
Apply the and (&&) operator to two boolean streams, point-wise.
(||) :: Stream Bool -> Stream Bool -> Stream Bool infixr 4 #
Apply the or (||) operator to two boolean streams, point-wise.
errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a #
A variant of error that does not produce a stack trace.
Since: base-4.9.0.0
undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a #
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #
Same as >>=, but with the arguments interchanged.
flip :: (a -> b -> c) -> b -> a -> c #
flip ff.
>>>flip (++) "hello" "world""worldhello"
($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 #
Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.
until :: Integral a => a -> Stream Bool -> Stream Bool -> Stream Bool #
until n s0 s1 means that eventually n s1, and up until at least the
period before s1 holds, s0 continuously holds.
Note: Both argument streams must have sufficient history to drop n
values from them.
maybe :: b -> (a -> b) -> Maybe a -> b #
The maybe function takes a default value, a function, and a Maybe
value. If the Maybe value is Nothing, the function returns the
default value. Otherwise, it applies the function to the value inside
the Just and returns the result.
Examples
Basic usage:
>>>maybe False odd (Just 3)True
>>>maybe False odd NothingFalse
Read an integer from a string using readMaybe. If we succeed,
return twice the integer; that is, apply (*2) to it. If instead
we fail to parse an integer, return 0 by default:
>>>import Text.Read ( readMaybe )>>>maybe 0 (*2) (readMaybe "5")10>>>maybe 0 (*2) (readMaybe "")0
Apply show to a Maybe Int. If we have Just n, we want to show
the underlying Int n. But if we have Nothing, we return the
empty string instead of (for example) "Nothing":
>>>maybe "" show (Just 5)"5">>>maybe "" show Nothing""
tail :: HasCallStack => [a] -> [a] #
\(\mathcal{O}(1)\). Extract the elements after the head of a list, which must be non-empty.
>>>tail [1, 2, 3][2,3]>>>tail [1][]>>>tail []*** Exception: Prelude.tail: empty list
WARNING: This function is partial. You can use case-matching or uncons
instead.
last :: HasCallStack => [a] -> a #
\(\mathcal{O}(n)\). Extract the last element of a list, which must be finite and non-empty.
>>>last [1, 2, 3]3>>>last [1..]* Hangs forever *>>>last []*** Exception: Prelude.last: empty list
WARNING: This function is partial. You can use reverse with case-matching,
uncons or listToMaybe instead.
init :: HasCallStack => [a] -> [a] #
scanl :: (b -> a -> b) -> b -> [a] -> [b] #
\(\mathcal{O}(n)\). scanl is similar to foldl, but returns a list of
successive reduced values from the left:
scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
Note that
last (scanl f z xs) == foldl f z xs
>>>scanl (+) 0 [1..4][0,1,3,6,10]>>>scanl (+) 42 [][42]>>>scanl (-) 100 [1..4][100,99,97,94,90]>>>scanl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']["foo","afoo","bafoo","cbafoo","dcbafoo"]>>>scanl (+) 0 [1..]* Hangs forever *
scanl1 :: (a -> a -> a) -> [a] -> [a] #
\(\mathcal{O}(n)\). scanl1 is a variant of scanl that has no starting
value argument:
scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
>>>scanl1 (+) [1..4][1,3,6,10]>>>scanl1 (+) [][]>>>scanl1 (-) [1..4][1,-1,-4,-8]>>>scanl1 (&&) [True, False, True, True][True,False,False,False]>>>scanl1 (||) [False, False, True, True][False,False,True,True]>>>scanl1 (+) [1..]* Hangs forever *
scanr :: (a -> b -> b) -> b -> [a] -> [b] #
\(\mathcal{O}(n)\). scanr is the right-to-left dual of scanl. Note that the order of parameters on the accumulating function are reversed compared to scanl.
Also note that
head (scanr f z xs) == foldr f z xs.
>>>scanr (+) 0 [1..4][10,9,7,4,0]>>>scanr (+) 42 [][42]>>>scanr (-) 100 [1..4][98,-97,99,-96,100]>>>scanr (\nextChar reversedString -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']["abcdfoo","bcdfoo","cdfoo","dfoo","foo"]>>>force $ scanr (+) 0 [1..]*** Exception: stack overflow
scanr1 :: (a -> a -> a) -> [a] -> [a] #
\(\mathcal{O}(n)\). scanr1 is a variant of scanr that has no starting
value argument.
>>>scanr1 (+) [1..4][10,9,7,4]>>>scanr1 (+) [][]>>>scanr1 (-) [1..4][-2,3,-1,4]>>>scanr1 (&&) [True, False, True, True][False,False,True,True]>>>scanr1 (||) [True, True, False, False][True,True,False,False]>>>force $ scanr1 (+) [1..]*** Exception: stack overflow
iterate :: (a -> a) -> a -> [a] #
iterate f x returns an infinite list of repeated applications
of f to x:
iterate f x == [x, f x, f (f x), ...]
Note that iterate is lazy, potentially leading to thunk build-up if
the consumer doesn't force each iterate. See iterate' for a strict
variant of this function.
>>>take 10 $ iterate not True[True,False,True,False...>>>take 10 $ iterate (+3) 42[42,45,48,51,54,57,60,63...
repeat x is an infinite list, with x the value of every element.
>>>repeat 17[17,17,17,17,17,17,17,17,17...
replicate :: Int -> a -> [a] #
replicate n x is a list of length n with x the value of
every element.
It is an instance of the more general genericReplicate,
in which n may be of any integral type.
>>>replicate 0 True[]>>>replicate (-1) True[]>>>replicate 4 True[True,True,True,True]
drop :: Typed a => Int -> Stream a -> Stream a #
Drop a number of samples from a stream.
The elements must be realizable at the present time to be able to drop elements. For most kinds of streams, you cannot drop elements without prepending an equal or greater number of elements to them first, as it could result in undefined samples.
splitAt :: Int -> [a] -> ([a], [a]) #
splitAt n xs returns a tuple where first element is xs prefix of
length n and second element is the remainder of the list:
>>>splitAt 6 "Hello World!"("Hello ","World!")>>>splitAt 3 [1,2,3,4,5]([1,2,3],[4,5])>>>splitAt 1 [1,2,3]([1],[2,3])>>>splitAt 3 [1,2,3]([1,2,3],[])>>>splitAt 4 [1,2,3]([1,2,3],[])>>>splitAt 0 [1,2,3]([],[1,2,3])>>>splitAt (-1) [1,2,3]([],[1,2,3])
It is equivalent to ( when take n xs, drop n xs)n is not _|_
(splitAt _|_ xs = _|_).
splitAt is an instance of the more general genericSplitAt,
in which n may be of any integral type.
span :: (a -> Bool) -> [a] -> ([a], [a]) #
span, applied to a predicate p and a list xs, returns a tuple where
first element is longest prefix (possibly empty) of xs of elements that
satisfy p and second element is the remainder of the list:
>>>span (< 3) [1,2,3,4,1,2,3,4]([1,2],[3,4,1,2,3,4])>>>span (< 9) [1,2,3]([1,2,3],[])>>>span (< 0) [1,2,3]([],[1,2,3])
break :: (a -> Bool) -> [a] -> ([a], [a]) #
break, applied to a predicate p and a list xs, returns a tuple where
first element is longest prefix (possibly empty) of xs of elements that
do not satisfy p and second element is the remainder of the list:
>>>break (> 3) [1,2,3,4,1,2,3,4]([1,2,3],[4,1,2,3,4])>>>break (< 9) [1,2,3]([],[1,2,3])>>>break (> 9) [1,2,3]([1,2,3],[])
reverse xs returns the elements of xs in reverse order.
xs must be finite.
>>>reverse [][]>>>reverse [42][42]>>>reverse [2,5,7][7,5,2]>>>reverse [1..]* Hangs forever *
and :: Foldable t => t Bool -> Bool #
and returns the conjunction of a container of Bools. For the
result to be True, the container must be finite; False, however,
results from a False value finitely far from the left end.
Examples
Basic usage:
>>>and []True
>>>and [True]True
>>>and [False]False
>>>and [True, True, False]False
>>>and (False : repeat True) -- Infinite list [False,True,True,True,...False
>>>and (repeat True)* Hangs forever *
or :: Foldable t => t Bool -> Bool #
or returns the disjunction of a container of Bools. For the
result to be False, the container must be finite; True, however,
results from a True value finitely far from the left end.
Examples
Basic usage:
>>>or []False
>>>or [True]True
>>>or [False]False
>>>or [True, True, False]True
>>>or (True : repeat False) -- Infinite list [True,False,False,False,...True
>>>or (repeat False)* Hangs forever *
any :: Foldable t => (a -> Bool) -> t a -> Bool #
Determines whether any element of the structure satisfies the predicate.
Examples
Basic usage:
>>>any (> 3) []False
>>>any (> 3) [1,2]False
>>>any (> 3) [1,2,3,4,5]True
>>>any (> 3) [1..]True
>>>any (> 3) [0, -1..]* Hangs forever *
all :: Foldable t => (a -> Bool) -> t a -> Bool #
Determines whether all elements of the structure satisfy the predicate.
Examples
Basic usage:
>>>all (> 3) []True
>>>all (> 3) [1,2]False
>>>all (> 3) [1,2,3,4,5]False
>>>all (> 3) [1..]False
>>>all (> 3) [4..]* Hangs forever *
notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 #
notElem is the negation of elem.
Examples
Basic usage:
>>>3 `notElem` []True
>>>3 `notElem` [1,2]True
>>>3 `notElem` [1,2,3,4,5]False
For infinite structures, notElem terminates if the value exists at a
finite distance from the left side of the structure:
>>>3 `notElem` [1..]False
>>>3 `notElem` ([4..] ++ [3])* Hangs forever *
concatMap :: Foldable t => (a -> [b]) -> t a -> [b] #
Map a function over all the elements of a container and concatenate the resulting lists.
Examples
Basic usage:
>>>concatMap (take 3) [[1..], [10..], [100..], [1000..]][1,2,3,10,11,12,100,101,102,1000,1001,1002]
>>>concatMap (take 3) (Just [1..])[1,2,3]
(!!) :: (Typed a, Eq b, Num b, Typed b) => [Stream a] -> Stream b -> Stream a #
Index.
WARNING: Very expensive! Consider using this only for very short lists.
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] #
The zipWith3 function takes a function which combines three
elements, as well as three lists and returns a list of the function applied
to corresponding elements, analogous to zipWith.
It is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
zipWith3 (,,) xs ys zs == zip3 xs ys zs zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..]
unzip :: [(a, b)] -> ([a], [b]) #
unzip transforms a list of pairs into a list of first components
and a list of second components.
>>>unzip []([],[])>>>unzip [(1, 'a'), (2, 'b')]([1,2],"ab")
utility function converting a Char to a show function that
simply prepends the character unchanged.
showString :: String -> ShowS #
utility function converting a String to a show function that
simply prepends the string unchanged.
div :: (Typed a, Integral a) => Stream a -> Stream a -> Stream a #
Apply the div operation to two streams, point-wise.
mod :: (Typed a, Integral a) => Stream a -> Stream a -> Stream a #
Apply the mod operation to two streams, point-wise.
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 #
raise a number to an integral power
gcd :: Integral a => a -> a -> a #
gcd x yx and y of which
every common factor of x and y is also a factor; for example
gcd 4 2 = 2gcd (-4) 6 = 2gcd 0 44. gcd 0 00.
(That is, the common divisor that is "greatest" in the divisibility
preordering.)
Note: Since for signed fixed-width integer types, abs minBound < 0minBound0 or minBound
lcm :: Integral a => a -> a -> a #
lcm x yx and y divide.
xor :: Stream Bool -> Stream Bool -> Stream Bool #
Apply the exclusive-or (xor) operator to two boolean streams,
point-wise.
byteSwap16 :: Word16 -> Word16 #
Reverse order of bytes in Word16.
Since: base-4.7.0.0
byteSwap32 :: Word32 -> Word32 #
Reverse order of bytes in Word32.
Since: base-4.7.0.0
byteSwap64 :: Word64 -> Word64 #
Reverse order of bytes in Word64.
Since: base-4.7.0.0
bitReverse8 :: Word8 -> Word8 #
Reverse the order of the bits in a Word8.
Since: base-4.14.0.0
bitReverse16 :: Word16 -> Word16 #
Reverse the order of the bits in a Word16.
Since: base-4.14.0.0
bitReverse32 :: Word32 -> Word32 #
Reverse the order of the bits in a Word32.
Since: base-4.14.0.0
bitReverse64 :: Word64 -> Word64 #
Reverse the order of the bits in a Word64.
Since: base-4.14.0.0
The lex function reads a single lexeme from the input, discarding
initial white space, and returning the characters that constitute the
lexeme. If the input string contains only white space, lex returns a
single successful `lexeme' consisting of the empty string. (Thus
lex "" = [("","")]lex fails (i.e. returns []).
This lexer is not completely faithful to the Haskell lexical syntax in the following respects:
- Qualified names are not handled properly
- Octal and hexadecimal numerics are not recognized as a single token
- Comments are not treated properly
(.>>.) :: (Bits a, Typed a, Typed b, Integral b) => Stream a -> Stream b -> Stream a #
Shifting values of a stream to the right.
(.<<.) :: (Bits a, Typed a, Typed b, Integral b) => Stream a -> Stream b -> Stream a #
Shifting values of a stream to the left.
sequence_ :: (Foldable t, Monad m) => t (m a) -> m () #
Evaluate each monadic action in the structure from left to right,
and ignore the results. For a version that doesn't ignore the
results see sequence.
sequence_ is just like sequenceA_, but specialised to monadic
actions.
tails :: Typed a => Stream a -> [Stream a] #
Given a stream, produce an infinite list of streams dropping an increasing
number of elements of the given stream. For example, for a given stream s,
the expression tails s is equal to [ drop 0 s, drop 1 s, drop 2 s, ...].
Splits the argument into a list of lines stripped of their terminating
\n characters. The \n terminator is optional in a final non-empty
line of the argument string.
For example:
>>>lines "" -- empty input contains no lines[]>>>lines "\n" -- single empty line[""]>>>lines "one" -- single unterminated line["one"]>>>lines "one\n" -- single non-empty line["one"]>>>lines "one\n\n" -- second line is empty["one",""]>>>lines "one\ntwo" -- second line is unterminated["one","two"]>>>lines "one\ntwo\n" -- two non-empty lines["one","two"]
When the argument string is empty, or ends in a \n character, it can be
recovered by passing the result of lines to the unlines function.
Otherwise, unlines appends the missing terminating \n. This makes
unlines . lines idempotent:
(unlines . lines) . (unlines . lines) = (unlines . lines)
userError :: String -> IOError #
Construct an IOException value with a string describing the error.
The fail method of the IO instance of the Monad class raises a
userError, thus:
instance Monad IO where ... fail s = ioError (userError s)
release :: Integral a => a -> Stream Bool -> Stream Bool -> Stream Bool #
release n s0 s1 means that either always n s1, or s1 holds up to and
including the period at which s0 becomes true.
Note: Both argument streams must have sufficient history to drop n
values from them.
getContents :: IO String #
The getContents operation returns all user input as a single string,
which is read lazily as it is needed
(same as hGetContents stdin).
interact :: (String -> String) -> IO () #
The interact function takes a function of type String->String
as its argument. The entire input from the standard input device is
passed to this function as its argument, and the resulting string is
output on the standard output device.
readFile :: FilePath -> IO String #
The readFile function reads a file and
returns the contents of the file as a string.
The file is read lazily, on demand, as with getContents.
appendFile :: FilePath -> String -> IO () #
The computation appendFile file str function appends the string str,
to the file file.
Note that writeFile and appendFile write a literal string
to a file. To write a value of any printable type, as with print,
use the show function to convert the value to a string first.
main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])
phase :: Integral a => a -> Phase a #
Constructor for a Phase. Note that phase must be greater than or equal
to 0, and must be less than the period.
label :: Typed a => String -> Stream a -> Stream a #
This function allows you to label a stream with a tag, which can be used by different backends to provide additional information either in error messages or in the generated code (e.g., for traceability purposes).
Semantically, a labelled stream is just the stream inside it. The use of label should not affect the observable behavior of the monitor, and how it is used in the code generated is a decision specific to each backend.
copilotMain :: Interpreter -> Printer -> Compiler -> Spec -> IO () #
Create a main to either compile or interpret a copilot specification.
This function must be provided an auxiliary function capable of compiling Copilot Core specifications for some target.
The command line program supports four main commands:
--output/-o: use the given compiler to produce C code.--justrun/-c: execute a dry-run, which parses and converts the specification to core but does not produce any output.--print/-p: pretty print the specification.--interpret/-i NUM: interpret the specification for a given number of steps.
defaultMain :: Compiler -> Spec -> IO () #
Create a main function with a default interpreter and pretty printer.
This function must be provided an auxiliary function capable of compiling Copilot Core specifications for some target.
This function relies on copilotMain, please refer to that function for the
command line options.
Arguments
| :: String | Name of the function in which the error was detected. |
| -> String | Name of the package in which the function is located. |
| -> a |
Report an error due to a bug in Copilot.
arrayElems :: forall (n :: Nat) a. Array n a -> [a] #
Return the elements of an array.
arrayelems :: forall (n :: Nat) a. Array n a -> [a] #
Return the elemts of an array.
fieldName :: forall (s :: Symbol) t. KnownSymbol s => Field s t -> String #
Extract the name of a field.
fieldname :: forall (s :: Symbol) t. KnownSymbol s => Field s t -> String #
Extract the name of a field.
accessorName :: forall a (s :: Symbol) t. (Struct a, KnownSymbol s) => (a -> Field s t) -> String #
Extract the name of an accessor (a function that returns a field of a struct).
accessorname :: forall a (s :: Symbol) t. (Struct a, KnownSymbol s) => (a -> Field s t) -> String #
Extract the name of an accessor (a function that returns a field of a struct).
typeLength :: forall (n :: Nat) t. KnownNat n => Type (Array n t) -> Int #
Return the length of an array from its type
tylength :: forall (n :: Nat) t. KnownNat n => Type (Array n t) -> Int #
Return the length of an array from its type
typeSize :: forall (n :: Nat) t. KnownNat n => Type (Array n t) -> Int #
Return the total (nested) size of an array from its type
tysize :: forall (n :: Nat) t. KnownNat n => Type (Array n t) -> Int #
Return the total (nested) size of an array from its type
interpret :: Integer -> Spec -> IO () #
Simulate a number of steps of a given specification, printing the results in a table in readable format.
Compared to csv, this function is slower but the output may be more
readable.
Arguments
| :: String | Description of the error. |
| -> a |
Report an error due to an error detected by Copilot (e.g., user error).
Arguments
| :: Typed a | |
| => String | Name used to identify the stream monitored in the output produced during interpretation. |
| -> Stream a | The stream being monitored. |
| -> Spec |
Define a new observer as part of a specification. This allows someone to print the value at every iteration during interpretation. Observers do not have any functionality outside the interpreter.
Arguments
| :: String | Name of the handler to be called. |
| -> Stream Bool | The stream used as the guard for the trigger. |
| -> [Arg] | List of arguments to the handler. |
| -> Spec |
Define a new trigger as part of a specification. A trigger declares which external function, or handler, will be called when a guard defined by a boolean stream becomes true.
prop :: String -> Prop a -> Writer [SpecItem] (PropRef a) #
A proposition, representing a boolean stream that is existentially or universally quantified over time, as part of a specification.
This function returns, in the monadic context, a reference to the proposition.
theorem :: String -> Prop a -> Proof a -> Writer [SpecItem] (PropRef a) #
A theorem, or proposition together with a proof.
This function returns, in the monadic context, a reference to the proposition.
arg :: Typed a => Stream a -> Arg #
Construct a function argument from a stream.
Args can be used to pass arguments to handlers or trigger functions, to
provide additional information to monitor handlers in order to address
property violations. At any given point (e.g., when the trigger must be
called due to a violation), the arguments passed using arg will contain
the current samples of the given streams.
(#) :: forall (s :: Symbol) t a. (KnownSymbol s, Typed t, Typed a, Struct a) => Stream a -> (a -> Field s t) -> Stream t #
Create a stream that carries a field of a struct in another stream.
This function implements a projection of a field of a struct over time. For
example, if a struct of type T has two fields, t1 of type Int and t2
of type Word8, and s is a stream of type Stream T, then s # t2 has
type Stream Word8 and contains the values of the t2 field of the structs
in s at any point in time.
mux :: Typed a => Stream Bool -> Stream a -> Stream a -> Stream a #
Convenient synonym for ifThenElse.
Arguments
| :: Typed a | |
| => String | Name of the global variable to make accessible. |
| -> Maybe [a] | Values to be used exclusively for testing/simulation. |
| -> Stream a |
Create a stream populated by an external global variable.
The Copilot compiler does not check that the type is correct. If the list given as second argument does not constrain the type of the values carried by the stream, this primitive stream building function will match any stream of any type, which is potentially dangerous if the global variable mentioned has a different type. We rely on the compiler used with the generated code to detect type errors of this kind.
Arguments
| :: String | Name of the global variable to make accessible. |
| -> Maybe [Bool] | Values to be used exclusively for testing/simulation. |
| -> Stream Bool |
Create a stream carrying values of type Bool, populated by an external global variable.
Arguments
| :: String | Name of the global variable to make accessible. |
| -> Maybe [Word8] | Values to be used exclusively for testing/simulation. |
| -> Stream Word8 |
Create a stream carrying values of type Word8, populated by an external global variable.
Arguments
| :: String | Name of the global variable to make accessible. |
| -> Maybe [Word16] | Values to be used exclusively for testing/simulation. |
| -> Stream Word16 |
Create a stream carrying values of type Word16, populated by an external global variable.
Arguments
| :: String | Name of the global variable to make accessible. |
| -> Maybe [Word32] | Values to be used exclusively for testing/simulation. |
| -> Stream Word32 |
Create a stream carrying values of type Word32, populated by an external global variable.
Arguments
| :: String | Name of the global variable to make accessible. |
| -> Maybe [Word64] | Values to be used exclusively for testing/simulation. |
| -> Stream Word64 |
Create a stream carrying values of type Word64, populated by an external global variable.
Arguments
| :: String | Name of the global variable to make accessible. |
| -> Maybe [Int8] | Values to be used exclusively for testing/simulation. |
| -> Stream Int8 |
Create a stream carrying values of type Int8, populated by an external global variable.
Arguments
| :: String | Name of the global variable to make accessible. |
| -> Maybe [Int16] | Values to be used exclusively for testing/simulation. |
| -> Stream Int16 |
Create a stream carrying values of type Int16, populated by an external global variable.
Arguments
| :: String | Name of the global variable to make accessible. |
| -> Maybe [Int32] | Values to be used exclusively for testing/simulation. |
| -> Stream Int32 |
Create a stream carrying values of type Int32, populated by an external global variable.
Arguments
| :: String | Name of the global variable to make accessible. |
| -> Maybe [Int64] | Values to be used exclusively for testing/simulation. |
| -> Stream Int64 |
Create a stream carrying values of type Int64, populated by an external global variable.
Arguments
| :: String | Name of the global variable to make accessible. |
| -> Maybe [Float] | Values to be used exclusively for testing/simulation. |
| -> Stream Float |
Create a stream carrying values of type Float, populated by an external global variable.
Arguments
| :: String | Name of the global variable to make accessible. |
| -> Maybe [Double] | Values to be used exclusively for testing/simulation. |
| -> Stream Double |
Create a stream carrying values of type Double, populated by an external global variable.
constant :: Typed a => a -> Stream a #
Create a constant stream that is equal to the given argument, at any point in time.
constB :: Bool -> Stream Bool #
Create a constant stream carrying values of type Bool that is equal to
the given argument, at any point in time.
constW8 :: Word8 -> Stream Word8 #
Create a constant stream carrying values of type Word8 that is equal to
the given argument, at any point in time.
constW16 :: Word16 -> Stream Word16 #
Create a constant stream carrying values of type Word16 that is equal to
the given argument, at any point in time.
constW32 :: Word32 -> Stream Word32 #
Create a constant stream carrying values of type Word32 that is equal to
the given argument, at any point in time.
constW64 :: Word64 -> Stream Word64 #
Create a constant stream carrying values of type Word64 that is equal to
the given argument, at any point in time.
constI8 :: Int8 -> Stream Int8 #
Create a constant stream carrying values of type Int8 that is equal to
the given argument, at any point in time.
constI16 :: Int16 -> Stream Int16 #
Create a constant stream carrying values of type Int16 that is equal to
the given argument, at any point in time.
constI32 :: Int32 -> Stream Int32 #
Create a constant stream carrying values of type Int32 that is equal to
the given argument, at any point in time.
constI64 :: Int64 -> Stream Int64 #
Create a constant stream carrying values of type Int64 that is equal to
the given argument, at any point in time.
constF :: Float -> Stream Float #
Create a constant stream carrying values of type Float that is equal to
the given argument, at any point in time.
constD :: Double -> Stream Double #
Create a constant stream carrying values of type Double that is equal to
the given argument, at any point in time.
(.!!) :: forall (n :: Nat) t. (KnownNat n, Typed t) => Stream (Array n t) -> Stream Word32 -> Stream t #
Create a stream that carries an element of an array in another stream.
This function implements a projection of the element of an array at a given
position, over time. For example, if s is a stream of type Stream (Array
'5 Word8), then s .!! 3 has type Stream Word8 and contains the 3rd
element (starting from zero) of the arrays in s at any point in time.
csv :: Integer -> Spec -> IO () #
Simulate a number of steps of a given specification, printing the results in a table in comma-separated value (CSV) format.
Transform a Copilot Language specification into a Copilot Core specification.
period :: Integral a => a -> Period a #
Constructor for a Period. Note that period must be greater than 0.
Generate a clock that counts every n ticks, starting at tick m, by
using an array of size n.
Arguments
| :: (Integral a, Typed a) | |
| => Period a | Period |
| -> Phase a | Phase |
| -> Stream Bool |
This follows the same convention as clk, but uses a counter variable of
integral type a rather than an array.
alwaysBeen :: Stream Bool -> Stream Bool #
Has s always held (up to and including the current state)?
eventuallyPrev :: Stream Bool -> Stream Bool #
Did s hold at some time in the past (including the current state)?
since :: Stream Bool -> Stream Bool -> Stream Bool #
Is there a time when s2 holds and after which s1 continuously holds?
Arguments
| :: (Typed t, SymbolParser t, Eq t) | |
| => Stream t | The stream to monitor. |
| -> SourceName | The regular expression. |
| -> Stream Bool | A stream indicating when to reset the monitor. |
| -> Stream Bool |
Regular expression matching over an arbitrary stream
Arguments
| :: SourceName | Regular expression |
| -> [(StreamName, Stream Bool)] | A table with the stream associated to each symbol. |
| -> Stream Bool | A stream indicating when to reset the monitor. |
| -> Stream Bool |
Regular expression matching over a collection of boolean streams.
Regular expressions can contain symbols, which are expanded to match specific streams.
For example, the regular expression:
"<s0>(<s1>)+"
would match if you provide a map (association list) that assigns, to the
symbol "s0", a stream that is true at the first sample, and to "s1", a
stream that is true at every sample after the first sample.
Arguments
| :: (Integral a, Typed b) | |
| => a | Depth |
| -> b | Start value |
| -> Stream Bool | Pop signal |
| -> Stream Bool | Push signal |
| -> Stream b | Push stream |
| -> Stream b | Stack top |
Stack stream in which the pop signal has precedence over the push signal in case both are true in the same tick
Arguments
| :: (Integral a, Typed b) | |
| => a | Depth |
| -> b | Start value |
| -> Stream Bool | Pop signal |
| -> Stream Bool | Push signal |
| -> Stream b | Push stream |
| -> Stream b | Stack top |
Stack stream in which the push signal has precedence over the pop signal in case both are true in the same tick
nfoldl :: (Typed a, Typed b) => Int -> (Stream a -> Stream b -> Stream a) -> Stream a -> Stream b -> Stream a #
Given a number, a function on streams, and two streams, fold from the left the function over the finite list of tails of the second stream (up to the given number).
nfoldl1 :: Typed a => Int -> (Stream a -> Stream a -> Stream a) -> Stream a -> Stream a #
Given a number, a function on streams, and two streams, fold from the left the function over the finite list of tails of the second stream (up to the given number).
This function differs from nfoldl in that it does not require an initial
accumulator and it assumes the argument number n is positive.
nfoldr :: (Typed a, Typed b) => Int -> (Stream a -> Stream b -> Stream b) -> Stream b -> Stream a -> Stream b #
Given a number, a function on streams, and two streams, fold from the right the function over the finite list of tails of the second stream (up to the given number).
nfoldr1 :: Typed a => Int -> (Stream a -> Stream a -> Stream a) -> Stream a -> Stream a #
Given a number, a function on streams, and two streams, fold from the right the function over the finite list of tails of the second stream (up to the given number).
This function differs from nfoldr in that it does not require an initial
accumulator and it assumes the argument number n is positive.
nscanl :: (Typed a, Typed b) => Int -> (Stream a -> Stream b -> Stream a) -> Stream a -> Stream b -> [Stream a] #
Given a number, a function on streams, and two streams, fold from the left the function over the finite list of tails of the second stream (up to the given number).
This function differs from nfoldl in that it returns the intermediate
results as well.
nscanr :: Typed a => Int -> (Stream a -> Stream b -> Stream b) -> Stream b -> Stream a -> [Stream b] #
Given a number, a function on streams, and two streams, fold from the right the function over the finite list of tails of the second stream (up to the given number).
This function differs from nfoldr in that it returns the intermediate
results as well.
nscanl1 :: Typed a => Int -> (Stream a -> Stream a -> Stream a) -> Stream a -> [Stream a] #
Given a number, a function on streams, and two streams, fold from the left the function over the finite list of tails of the second stream (up to the given number).
This function assumes the number of elements to scan is positive, and it also returns the intermediate results.
nscanr1 :: Typed a => Int -> (Stream a -> Stream a -> Stream a) -> Stream a -> [Stream a] #
Given a number, a function on streams, and two streams, fold from the right the function over the finite list of tails of the second stream (up to the given number).
This function assumes the number of elements to scan is positive, and it also returns the intermediate results.
case' :: Typed a => [Stream Bool] -> [Stream a] -> Stream a #
Case-like function: The index of the first predicate that is true in the predicate list selects the stream result. If no predicate is true, the last element is chosen (default element)
mean :: (Typed a, Eq a, Fractional a) => Int -> Stream a -> Stream a #
Mean value. n must not overflow
for word size a for streams over which computation is peformed.
meanNow :: (Typed a, Integral a) => [Stream a] -> Stream a #
Mean value over the current set of streams passed in.
Property s holds at some period in the next n periods. If n == 0,
then s holds in the current period. We require n >= 0. E.g., if p =
eventually 2 s, then we have the following relationship between the streams
generated:
s => F F F T F F F T ... p => F T T T F T T T ...
Note: s must have sufficient history to drop n values from it.
always :: Integral a => a -> Stream Bool -> Stream Bool #
Property s holds for the next n periods. We require n >= 0. If n ==
0, then s holds in the current period, e.g., if p = always 2 s, then we
have the following relationship between the streams generated:
0 1 2 3 4 5 6 7 s => T T T F T T T T ... p => T F F F T T ...
Note: s must have sufficient history to drop n values from it.
next :: Stream Bool -> Stream Bool #
Property s holds at the next period. For example:
0 1 2 3 4 5 6 7 s => F F F T F F T F ... next s => F F T F F T F ...
Note: s must have sufficient history to drop a value from it.
Majority vote first pass: choosing a candidate.