Safe Haskell	Trustworthy
Language	Haskell2010

Data.Universe.Instances.Extended

Contents

Orphan instances

Synopsis

class Universe a where
- universe :: [a]
class Universe a => Finite a where
- universeF :: [a]
- cardinality :: Tagged a Natural

Documentation

Instances for Universe and Finite for function-like functors and the empty type.

class Universe a where #

Creating an instance of this class is a declaration that your type is recursively enumerable (and that universe is that enumeration). In particular, you promise that any finite inhabitant has a finite index in universe, and that no inhabitant appears at two different finite indices.

Well-behaved instance should produce elements lazily.

Laws:

elem x universe                    -- any inhabitant has a finite index
let pfx = take n universe          -- any finite prefix of universe has unique elements
in length pfx = length (nub pfx)

Minimal complete definition

Nothing

Methods

universe :: [a] #

Instances

Instances details

Universe Bool
Instance details Defined in Data.Universe.Class Methods universe :: [Bool] #
Universe Char
Instance details Defined in Data.Universe.Class Methods universe :: [Char] #
Universe Int
Instance details Defined in Data.Universe.Class Methods universe :: [Int] #
Universe Int8
Instance details Defined in Data.Universe.Class Methods universe :: [Int8] #
Universe Int16
Instance details Defined in Data.Universe.Class Methods universe :: [Int16] #
Universe Int32
Instance details Defined in Data.Universe.Class Methods universe :: [Int32] #
Universe Int64
Instance details Defined in Data.Universe.Class Methods universe :: [Int64] #
Universe Integer
Instance details Defined in Data.Universe.Class Methods universe :: [Integer] #
Universe Natural
Instance details Defined in Data.Universe.Class Methods universe :: [Natural] #
Universe Ordering
Instance details Defined in Data.Universe.Class Methods universe :: [Ordering] #
Universe Word
Instance details Defined in Data.Universe.Class Methods universe :: [Word] #
Universe Word8
Instance details Defined in Data.Universe.Class Methods universe :: [Word8] #
Universe Word16
Instance details Defined in Data.Universe.Class Methods universe :: [Word16] #
Universe Word32
Instance details Defined in Data.Universe.Class Methods universe :: [Word32] #
Universe Word64
Instance details Defined in Data.Universe.Class Methods universe :: [Word64] #
Universe ()
Instance details Defined in Data.Universe.Class Methods universe :: [()] #
Universe Void
Instance details Defined in Data.Universe.Class Methods universe :: [Void] #
Universe All
Instance details Defined in Data.Universe.Class Methods universe :: [All] #
Universe Any
Instance details Defined in Data.Universe.Class Methods universe :: [Any] #
Universe a => Universe [a]
Instance details Defined in Data.Universe.Class Methods universe :: [[a]] #
Universe a => Universe (Maybe a)
Instance details Defined in Data.Universe.Class Methods universe :: [Maybe a] #
RationalUniverse a => Universe (Ratio a)
Instance details Defined in Data.Universe.Class Methods universe :: [Ratio a] #
(Finite a, Ord a) => Universe (Predicate a) Source #
Instance details Defined in Data.Universe.Instances.Extended Methods universe :: [Predicate a] #
Universe a => Universe (Min a)
Instance details Defined in Data.Universe.Class Methods universe :: [Min a] #
Universe a => Universe (Max a)
Instance details Defined in Data.Universe.Class Methods universe :: [Max a] #
Universe a => Universe (First a)
Instance details Defined in Data.Universe.Class Methods universe :: [First a] #
Universe a => Universe (Last a)
Instance details Defined in Data.Universe.Class Methods universe :: [Last a] #
Universe a => Universe (Identity a)
Instance details Defined in Data.Universe.Class Methods universe :: [Identity a] #
Universe a => Universe (First a)
Instance details Defined in Data.Universe.Class Methods universe :: [First a] #
Universe a => Universe (Last a)
Instance details Defined in Data.Universe.Class Methods universe :: [Last a] #
Universe a => Universe (Dual a)
Instance details Defined in Data.Universe.Class Methods universe :: [Dual a] #
Universe a => Universe (Sum a)
Instance details Defined in Data.Universe.Class Methods universe :: [Sum a] #
Universe a => Universe (Product a)
Instance details Defined in Data.Universe.Class Methods universe :: [Product a] #
Universe a => Universe (NonEmpty a)
Instance details Defined in Data.Universe.Class Methods universe :: [NonEmpty a] #
(Ord a, Universe a) => Universe (Set a)	`>>>` `import qualified Data.Set as Set``>>>` `mapM_ print (universe :: [Set.Set Bool])`fromList [] fromList [False] fromList [True] fromList [False,True]
Instance details Defined in Data.Universe.Class Methods universe :: [Set a] #
(Finite a, Ord a, Universe b) => Universe (a -> b)	`>>>` `mapM_ print (universe :: [Bool -> Bool])`[(False,False),(True,False)] [(False,False),(True,True)] [(False,True),(True,False)] [(False,True),(True,True)]
Instance details Defined in Data.Universe.Class Methods universe :: [a -> b] #
(Universe a, Universe b) => Universe (Either a b)
Instance details Defined in Data.Universe.Class Methods universe :: [Either a b] #
(Universe a, Universe b) => Universe (a, b)
Instance details Defined in Data.Universe.Class Methods universe :: [(a, b)] #
(Universe a, Finite b, Ord b) => Universe (Op a b) Source #
Instance details Defined in Data.Universe.Instances.Extended Methods universe :: [Op a b] #
(Representable f, Finite (Rep f), Ord (Rep f), Universe a) => Universe (Co f a) Source #	We could do this: instance Universe (f a) => Universe (Co f a) where universe = map Rep universe However, since you probably only apply Rep to functors when you want to think of them as being representable, I think it makes sense to use an instance based on the representable-ness rather than the inherent universe-ness. Please complain if you disagree!
Instance details Defined in Data.Universe.Instances.Extended Methods universe :: [Co f a] #
Universe (Proxy a)
Instance details Defined in Data.Universe.Class Methods universe :: [Proxy a] #
(Ord k, Finite k, Universe v) => Universe (Map k v)	`>>>` `import qualified Data.Map as Map``>>>` `mapM_ print (universe :: [Map.Map Bool Bool])`fromList [] fromList [(True,False)] fromList [(False,False)] fromList [(True,True)] fromList [(False,False),(True,False)] fromList [(False,True)] fromList [(False,False),(True,True)] fromList [(False,True),(True,False)] fromList [(False,True),(True,True)]
Instance details Defined in Data.Universe.Class Methods universe :: [Map k v] #
(Universe a, Universe b, Universe c) => Universe (a, b, c)
Instance details Defined in Data.Universe.Class Methods universe :: [(a, b, c)] #
Universe a => Universe (Const a b)
Instance details Defined in Data.Universe.Class Methods universe :: [Const a b] #
(Representable f, Finite s, Ord s, Finite (Rep f), Ord (Rep f), Universe a) => Universe (TracedT s f a) Source #
Instance details Defined in Data.Universe.Instances.Extended Methods universe :: [TracedT s f a] #
Universe (f a) => Universe (IdentityT f a)
Instance details Defined in Data.Universe.Class Methods universe :: [IdentityT f a] #
(Finite e, Ord e, Universe (m a)) => Universe (ReaderT e m a)
Instance details Defined in Data.Universe.Class Methods universe :: [ReaderT e m a] #
Universe a => Universe (Tagged b a)
Instance details Defined in Data.Universe.Class Methods universe :: [Tagged b a] #
(Universe a, Universe b, Universe c, Universe d) => Universe (a, b, c, d)
Instance details Defined in Data.Universe.Class Methods universe :: [(a, b, c, d)] #
(Universe (f a), Universe (g a)) => Universe (Product f g a)
Instance details Defined in Data.Universe.Class Methods universe :: [Product f g a] #
(Universe (f a), Universe (g a)) => Universe (Sum f g a)
Instance details Defined in Data.Universe.Class Methods universe :: [Sum f g a] #
(Universe a, Universe b, Universe c, Universe d, Universe e) => Universe (a, b, c, d, e)
Instance details Defined in Data.Universe.Class Methods universe :: [(a, b, c, d, e)] #
Universe (f (g a)) => Universe (Compose f g a)
Instance details Defined in Data.Universe.Class Methods universe :: [Compose f g a] #

class Universe a => Finite a where #

Creating an instance of this class is a declaration that your universe eventually ends. Minimal definition: no methods defined. By default, universeF = universe, but for some types (like Either) the universeF method may have a more intuitive ordering.

Laws:

elem x universeF                       -- any inhabitant has a finite index
length (filter (== x) universeF) == 1  -- should terminate
(xs -> cardinality xs == genericLength xs) universeF

Note: elemIndex x universe == elemIndex x universeF may not hold for all types, though the laws imply that universe is a permutation of universeF.

>>> elemIndex (Left True :: Either Bool Bool) universe
Just 2

>>> elemIndex (Left True :: Either Bool Bool) universeF
Just 1

Minimal complete definition

Nothing

Methods

universeF :: [a] #

cardinality :: Tagged a Natural #

Instances

Instances details

Finite Bool
Instance details Defined in Data.Universe.Class Methods universeF :: [Bool] # cardinality :: Tagged Bool Natural #
Finite Char
Instance details Defined in Data.Universe.Class Methods universeF :: [Char] # cardinality :: Tagged Char Natural #
Finite Int
Instance details Defined in Data.Universe.Class Methods universeF :: [Int] # cardinality :: Tagged Int Natural #
Finite Int8
Instance details Defined in Data.Universe.Class Methods universeF :: [Int8] # cardinality :: Tagged Int8 Natural #
Finite Int16
Instance details Defined in Data.Universe.Class Methods universeF :: [Int16] # cardinality :: Tagged Int16 Natural #
Finite Int32
Instance details Defined in Data.Universe.Class Methods universeF :: [Int32] # cardinality :: Tagged Int32 Natural #
Finite Int64
Instance details Defined in Data.Universe.Class Methods universeF :: [Int64] # cardinality :: Tagged Int64 Natural #
Finite Ordering
Instance details Defined in Data.Universe.Class Methods universeF :: [Ordering] # cardinality :: Tagged Ordering Natural #
Finite Word
Instance details Defined in Data.Universe.Class Methods universeF :: [Word] # cardinality :: Tagged Word Natural #
Finite Word8
Instance details Defined in Data.Universe.Class Methods universeF :: [Word8] # cardinality :: Tagged Word8 Natural #
Finite Word16
Instance details Defined in Data.Universe.Class Methods universeF :: [Word16] # cardinality :: Tagged Word16 Natural #
Finite Word32
Instance details Defined in Data.Universe.Class Methods universeF :: [Word32] # cardinality :: Tagged Word32 Natural #
Finite Word64
Instance details Defined in Data.Universe.Class Methods universeF :: [Word64] # cardinality :: Tagged Word64 Natural #
Finite ()
Instance details Defined in Data.Universe.Class Methods universeF :: [()] # cardinality :: Tagged () Natural #
Finite Void
Instance details Defined in Data.Universe.Class Methods universeF :: [Void] # cardinality :: Tagged Void Natural #
Finite All
Instance details Defined in Data.Universe.Class Methods universeF :: [All] # cardinality :: Tagged All Natural #
Finite Any
Instance details Defined in Data.Universe.Class Methods universeF :: [Any] # cardinality :: Tagged Any Natural #
Finite a => Finite (Maybe a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Maybe a] # cardinality :: Tagged (Maybe a) Natural #
(Finite a, Ord a) => Finite (Predicate a) Source #	`>>>` `mapM_ print (universe :: [Predicate Ordering])`Predicate {getPredicate = [(LT,False),(EQ,False),(GT,False)]} Predicate {getPredicate = [(LT,True),(EQ,False),(GT,False)]} Predicate {getPredicate = [(LT,False),(EQ,True),(GT,False)]} Predicate {getPredicate = [(LT,True),(EQ,True),(GT,False)]} Predicate {getPredicate = [(LT,False),(EQ,False),(GT,True)]} Predicate {getPredicate = [(LT,True),(EQ,False),(GT,True)]} Predicate {getPredicate = [(LT,False),(EQ,True),(GT,True)]} Predicate {getPredicate = [(LT,True),(EQ,True),(GT,True)]} Beware, function type universes are large... `>>>` `cardinality :: Tagged (Predicate Int8) Natural`Tagged 115792089237316195423570985008687907853269984665640564039457584007913129639936 ... but thanks to laziness, you can expect at least few: `>>>` `let Predicate f : _ = universe :: [Predicate Int8]``>>>` `f 0`False
Instance details Defined in Data.Universe.Instances.Extended Methods universeF :: [Predicate a] # cardinality :: Tagged (Predicate a) Natural #
Finite a => Finite (Min a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Min a] # cardinality :: Tagged (Min a) Natural #
Finite a => Finite (Max a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Max a] # cardinality :: Tagged (Max a) Natural #
Finite a => Finite (First a)
Instance details Defined in Data.Universe.Class Methods universeF :: [First a] # cardinality :: Tagged (First a) Natural #
Finite a => Finite (Last a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Last a] # cardinality :: Tagged (Last a) Natural #
Finite a => Finite (Identity a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Identity a] # cardinality :: Tagged (Identity a) Natural #
Finite a => Finite (First a)
Instance details Defined in Data.Universe.Class Methods universeF :: [First a] # cardinality :: Tagged (First a) Natural #
Finite a => Finite (Last a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Last a] # cardinality :: Tagged (Last a) Natural #
Finite a => Finite (Dual a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Dual a] # cardinality :: Tagged (Dual a) Natural #
Finite a => Finite (Sum a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Sum a] # cardinality :: Tagged (Sum a) Natural #
Finite a => Finite (Product a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Product a] # cardinality :: Tagged (Product a) Natural #
(Ord a, Finite a) => Finite (Set a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Set a] # cardinality :: Tagged (Set a) Natural #
(Ord a, Finite a, Finite b) => Finite (a -> b)	`>>>` `mapM_ print (universeF :: [Bool -> Bool])`[(False,False),(True,False)] [(False,False),(True,True)] [(False,True),(True,False)] [(False,True),(True,True)] `>>>` `cardinality :: Tagged (Bool -> Ordering) Natural`Tagged 9 `>>>` `cardinality :: Tagged (Ordering -> Bool) Natural`Tagged 8
Instance details Defined in Data.Universe.Class Methods universeF :: [a -> b] # cardinality :: Tagged (a -> b) Natural #
(Finite a, Finite b) => Finite (Either a b)
Instance details Defined in Data.Universe.Class Methods universeF :: [Either a b] # cardinality :: Tagged (Either a b) Natural #
(Finite a, Finite b) => Finite (a, b)
Instance details Defined in Data.Universe.Class Methods universeF :: [(a, b)] # cardinality :: Tagged (a, b) Natural #
(Finite a, Finite b, Ord b) => Finite (Op a b) Source #
Instance details Defined in Data.Universe.Instances.Extended Methods universeF :: [Op a b] # cardinality :: Tagged (Op a b) Natural #
(Representable f, Finite (Rep f), Ord (Rep f), Finite a) => Finite (Co f a) Source #
Instance details Defined in Data.Universe.Instances.Extended Methods universeF :: [Co f a] # cardinality :: Tagged (Co f a) Natural #
Finite (Proxy a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Proxy a] # cardinality :: Tagged (Proxy a) Natural #
(Ord k, Finite k, Finite v) => Finite (Map k v)
Instance details Defined in Data.Universe.Class Methods universeF :: [Map k v] # cardinality :: Tagged (Map k v) Natural #
(Finite a, Finite b, Finite c) => Finite (a, b, c)
Instance details Defined in Data.Universe.Class Methods universeF :: [(a, b, c)] # cardinality :: Tagged (a, b, c) Natural #
Finite a => Finite (Const a b)
Instance details Defined in Data.Universe.Class Methods universeF :: [Const a b] # cardinality :: Tagged (Const a b) Natural #
(Representable f, Finite s, Ord s, Finite (Rep f), Ord (Rep f), Finite a) => Finite (TracedT s f a) Source #
Instance details Defined in Data.Universe.Instances.Extended Methods universeF :: [TracedT s f a] # cardinality :: Tagged (TracedT s f a) Natural #
Finite (f a) => Finite (IdentityT f a)
Instance details Defined in Data.Universe.Class Methods universeF :: [IdentityT f a] # cardinality :: Tagged (IdentityT f a) Natural #
(Finite e, Ord e, Finite (m a)) => Finite (ReaderT e m a)
Instance details Defined in Data.Universe.Class Methods universeF :: [ReaderT e m a] # cardinality :: Tagged (ReaderT e m a) Natural #
Finite a => Finite (Tagged b a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Tagged b a] # cardinality :: Tagged (Tagged b a) Natural #
(Finite a, Finite b, Finite c, Finite d) => Finite (a, b, c, d)
Instance details Defined in Data.Universe.Class Methods universeF :: [(a, b, c, d)] # cardinality :: Tagged (a, b, c, d) Natural #
(Finite (f a), Finite (g a)) => Finite (Product f g a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Product f g a] # cardinality :: Tagged (Product f g a) Natural #
(Finite (f a), Finite (g a)) => Finite (Sum f g a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Sum f g a] # cardinality :: Tagged (Sum f g a) Natural #
(Finite a, Finite b, Finite c, Finite d, Finite e) => Finite (a, b, c, d, e)
Instance details Defined in Data.Universe.Class Methods universeF :: [(a, b, c, d, e)] # cardinality :: Tagged (a, b, c, d, e) Natural #
Finite (f (g a)) => Finite (Compose f g a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Compose f g a] # cardinality :: Tagged (Compose f g a) Natural #

Orphan instances

(Finite a, Ord a) => Universe (Predicate a) Source #
Instance details Methods universe :: [Predicate a] #
(Finite a, Ord a) => Finite (Predicate a) Source #	`>>>` `mapM_ print (universe :: [Predicate Ordering])`Predicate {getPredicate = [(LT,False),(EQ,False),(GT,False)]} Predicate {getPredicate = [(LT,True),(EQ,False),(GT,False)]} Predicate {getPredicate = [(LT,False),(EQ,True),(GT,False)]} Predicate {getPredicate = [(LT,True),(EQ,True),(GT,False)]} Predicate {getPredicate = [(LT,False),(EQ,False),(GT,True)]} Predicate {getPredicate = [(LT,True),(EQ,False),(GT,True)]} Predicate {getPredicate = [(LT,False),(EQ,True),(GT,True)]} Predicate {getPredicate = [(LT,True),(EQ,True),(GT,True)]} Beware, function type universes are large... `>>>` `cardinality :: Tagged (Predicate Int8) Natural`Tagged 115792089237316195423570985008687907853269984665640564039457584007913129639936 ... but thanks to laziness, you can expect at least few: `>>>` `let Predicate f : _ = universe :: [Predicate Int8]``>>>` `f 0`False
Instance details Methods universeF :: [Predicate a] # cardinality :: Tagged (Predicate a) Natural #
(Universe a, Finite b, Ord b) => Universe (Op a b) Source #
Instance details Methods universe :: [Op a b] #
(Representable f, Finite (Rep f), Ord (Rep f), Universe a) => Universe (Co f a) Source #	We could do this: instance Universe (f a) => Universe (Co f a) where universe = map Rep universe However, since you probably only apply Rep to functors when you want to think of them as being representable, I think it makes sense to use an instance based on the representable-ness rather than the inherent universe-ness. Please complain if you disagree!
Instance details Methods universe :: [Co f a] #
(Finite a, Finite b, Ord b) => Finite (Op a b) Source #
Instance details Methods universeF :: [Op a b] # cardinality :: Tagged (Op a b) Natural #
(Representable f, Finite (Rep f), Ord (Rep f), Finite a) => Finite (Co f a) Source #
Instance details Methods universeF :: [Co f a] # cardinality :: Tagged (Co f a) Natural #
(Representable f, Finite s, Ord s, Finite (Rep f), Ord (Rep f), Universe a) => Universe (TracedT s f a) Source #
Instance details Methods universe :: [TracedT s f a] #
(Representable f, Finite s, Ord s, Finite (Rep f), Ord (Rep f), Finite a) => Finite (TracedT s f a) Source #
Instance details Methods universeF :: [TracedT s f a] # cardinality :: Tagged (TracedT s f a) Natural #