| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Test.Feat.Enumerate
Description
Basic combinators for building enumerations most users will want to use the type class based combinators in Test.Feat.Class instead.
Synopsis
- type Index = Integer
- data Enumerate a = Enumerate {}
- parts :: Enumerate a -> [Finite a]
- fromParts :: [Finite a] -> Enumerate a
- data RevList a = RevList {}
- toRev :: [a] -> RevList a
- data Finite a = Finite {}
- fromFinite :: Finite a -> (Index, [a])
- class Semigroup a => Monoid a where
- newtype First a = First {}
- newtype Last a = Last {}
- newtype Ap (f :: k -> Type) (a :: k) = Ap {
- getAp :: f a
- newtype Dual a = Dual {
- getDual :: a
- newtype Endo a = Endo {
- appEndo :: a -> a
- newtype All = All {}
- newtype Any = Any {}
- newtype Sum a = Sum {
- getSum :: a
- newtype Product a = Product {
- getProduct :: a
- newtype Alt (f :: k -> Type) (a :: k) = Alt {
- getAlt :: f a
- union :: Enumerate a -> Enumerate a -> Enumerate a
- module Control.Applicative
- cartesian :: Enumerate a -> Enumerate b -> Enumerate (a, b)
- singleton :: a -> Enumerate a
- pay :: Sized f => f a -> f a
Documentation
A functional enumeration of type t is a partition of
t into finite numbered sets. Each part contains values
of a certain cost (typically the size of the value).
Instances
| Functor Enumerate Source # | Only use fmap with bijective functions (e.g. data constructors) |
| Applicative Enumerate Source # | Pure is |
| Alternative Enumerate Source # | |
| Sized Enumerate Source # | |
| Semigroup (Enumerate a) Source # | |
| Monoid (Enumerate a) Source # | |
Reversed lists
A data structure that contains a list and the reversals of all initial segments of the list. Intuitively
reversals xs !! n = reverse (take (n+1) (fromRev xs))
Any operation on a RevList typically discards the reversals and constructs
new reversals on demand.
toRev :: [a] -> RevList a Source #
Constructs a "Reverse list" variant of a given list. In a sensible
Haskell implementation evaluating any inital segment of
reversals (toRev xs)
Finite ordered sets
fromFinite :: Finite a -> (Index, [a]) Source #
Combinators for building enumerations
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
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.
Minimal complete definition
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 Ordering | Since: base-2.1 |
| Monoid () | Since: base-2.1 |
| Monoid All | Since: base-2.1 |
| Monoid Any | Since: base-2.1 |
| Monoid [a] | Since: base-2.1 |
| Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
| (Ord a, Bounded a) => Monoid (Min a) | Since: base-4.9.0.0 |
| (Ord a, Bounded a) => Monoid (Max a) | Since: base-4.9.0.0 |
| Monoid m => Monoid (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m # | |
| Semigroup a => Monoid (Option a) | Since: base-4.9.0.0 |
| Monoid (First a) | Since: base-2.1 |
| Monoid (Last a) | Since: base-2.1 |
| Monoid a => Monoid (Dual a) | Since: base-2.1 |
| Monoid (Endo a) | Since: base-2.1 |
| Num a => Monoid (Sum a) | Since: base-2.1 |
| Num a => Monoid (Product a) | Since: base-2.1 |
| Monoid (Finite a) Source # | |
| Semigroup a => Monoid (RevList a) Source # | Padded zip |
| Monoid (Enumerate a) Source # | |
| Monoid b => Monoid (a -> b) | Since: base-2.1 |
| (Monoid a, Monoid b) => Monoid (a, b) | Since: base-2.1 |
| Monoid (Proxy s) | Since: base-4.7.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | Since: base-2.1 |
| Monoid a => Monoid (Const a b) | Since: base-4.9.0.0 |
| (Applicative f, Monoid a) => Monoid (Ap f a) | Since: base-4.12.0.0 |
| Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | Since: base-2.1 |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | Since: base-2.1 |
Maybe monoid returning the leftmost non-Nothing value.
First aAlt Maybe a
>>>getFirst (First (Just "hello") <> First Nothing <> First (Just "world"))Just "hello"
Use of this type is discouraged. Note the following equivalence:
Data.Monoid.First x === Maybe (Data.Semigroup.First x)
In addition to being equivalent in the structural sense, the two
also have Monoid instances that behave the same. This type will
be marked deprecated in GHC 8.8, and removed in GHC 8.10.
Users are advised to use the variant from Data.Semigroup and wrap
it in Maybe.
Instances
| Monad First | Since: base-4.8.0.0 |
| Functor First | Since: base-4.8.0.0 |
| Applicative First | Since: base-4.8.0.0 |
| 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 # | |
| Traversable First | Since: base-4.8.0.0 |
| Eq a => Eq (First a) | Since: base-2.1 |
| Ord a => Ord (First a) | Since: base-2.1 |
| Read a => Read (First a) | Since: base-2.1 |
| Show a => Show (First a) | Since: base-2.1 |
| Generic (First a) | Since: base-4.7.0.0 |
| Semigroup (First a) | Since: base-4.9.0.0 |
| Monoid (First a) | Since: base-2.1 |
| Generic1 First | Since: base-4.7.0.0 |
| type Rep (First a) | |
Defined in Data.Monoid | |
| type Rep1 First | |
Defined in Data.Monoid | |
Maybe monoid returning the rightmost non-Nothing value.
Last aDual (First a)Dual (Alt Maybe a)
>>>getLast (Last (Just "hello") <> Last Nothing <> Last (Just "world"))Just "world"
Use of this type is discouraged. Note the following equivalence:
Data.Monoid.Last x === Maybe (Data.Semigroup.Last x)
In addition to being equivalent in the structural sense, the two
also have Monoid instances that behave the same. This type will
be marked deprecated in GHC 8.8, and removed in GHC 8.10.
Users are advised to use the variant from Data.Semigroup and wrap
it in Maybe.
Instances
| Monad Last | Since: base-4.8.0.0 |
| Functor Last | Since: base-4.8.0.0 |
| Applicative Last | Since: base-4.8.0.0 |
| 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 # | |
| Traversable Last | Since: base-4.8.0.0 |
| Eq a => Eq (Last a) | Since: base-2.1 |
| Ord a => Ord (Last a) | Since: base-2.1 |
| Read a => Read (Last a) | Since: base-2.1 |
| Show a => Show (Last a) | Since: base-2.1 |
| Generic (Last a) | Since: base-4.7.0.0 |
| Semigroup (Last a) | Since: base-4.9.0.0 |
| Monoid (Last a) | Since: base-2.1 |
| Generic1 Last | Since: base-4.7.0.0 |
| type Rep (Last a) | |
Defined in Data.Monoid | |
| type Rep1 Last | |
Defined in Data.Monoid | |
newtype Ap (f :: k -> Type) (a :: k) #
This data type witnesses the lifting of a Monoid into an
Applicative pointwise.
Since: base-4.12.0.0
Instances
| Generic1 (Ap f :: k -> Type) | Since: base-4.12.0.0 |
| Monad f => Monad (Ap f) | Since: base-4.12.0.0 |
| Functor f => Functor (Ap f) | Since: base-4.12.0.0 |
| MonadFail f => MonadFail (Ap f) | Since: base-4.12.0.0 |
Defined in Data.Monoid | |
| Applicative f => Applicative (Ap f) | Since: base-4.12.0.0 |
| 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 # | |
| Traversable f => Traversable (Ap f) | Since: base-4.12.0.0 |
| Alternative f => Alternative (Ap f) | Since: base-4.12.0.0 |
| MonadPlus f => MonadPlus (Ap f) | Since: base-4.12.0.0 |
| (Applicative f, Bounded a) => Bounded (Ap f a) | Since: base-4.12.0.0 |
| Enum (f a) => Enum (Ap f a) | Since: base-4.12.0.0 |
Defined in Data.Monoid | |
| Eq (f a) => Eq (Ap f a) | Since: base-4.12.0.0 |
| (Applicative f, Num a) => Num (Ap f a) | Since: base-4.12.0.0 |
| Ord (f a) => Ord (Ap f a) | Since: base-4.12.0.0 |
| Read (f a) => Read (Ap f a) | Since: base-4.12.0.0 |
| Show (f a) => Show (Ap f a) | Since: base-4.12.0.0 |
| Generic (Ap f a) | Since: base-4.12.0.0 |
| (Applicative f, Semigroup a) => Semigroup (Ap f a) | Since: base-4.12.0.0 |
| (Applicative f, Monoid a) => Monoid (Ap f a) | Since: base-4.12.0.0 |
| type Rep1 (Ap f :: k -> Type) | |
Defined in Data.Monoid | |
| type Rep (Ap f a) | |
Defined in Data.Monoid | |
The dual of a Monoid, obtained by swapping the arguments of mappend.
>>>getDual (mappend (Dual "Hello") (Dual "World"))"WorldHello"
Instances
| Monad Dual | Since: base-4.8.0.0 |
| Functor Dual | Since: base-4.8.0.0 |
| Applicative Dual | Since: base-4.8.0.0 |
| 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 # | |
| Traversable Dual | Since: base-4.8.0.0 |
| Bounded a => Bounded (Dual a) | Since: base-2.1 |
| Eq a => Eq (Dual a) | Since: base-2.1 |
| Ord a => Ord (Dual a) | Since: base-2.1 |
| Read a => Read (Dual a) | Since: base-2.1 |
| Show a => Show (Dual a) | Since: base-2.1 |
| Generic (Dual a) | Since: base-4.7.0.0 |
| Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 |
| Monoid a => Monoid (Dual a) | Since: base-2.1 |
| Generic1 Dual | Since: base-4.7.0.0 |
| type Rep (Dual a) | |
Defined in Data.Semigroup.Internal | |
| type Rep1 Dual | |
Defined in Data.Semigroup.Internal | |
The monoid of endomorphisms under composition.
>>>let computation = Endo ("Hello, " ++) <> Endo (++ "!")>>>appEndo computation "Haskell""Hello, Haskell!"
Boolean monoid under conjunction (&&).
>>>getAll (All True <> mempty <> All False)False
>>>getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))False
Boolean monoid under disjunction (||).
>>>getAny (Any True <> mempty <> Any False)True
>>>getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))True
Monoid under addition.
>>>getSum (Sum 1 <> Sum 2 <> mempty)3
Instances
| Monad Sum | Since: base-4.8.0.0 |
| Functor Sum | Since: base-4.8.0.0 |
| Applicative Sum | Since: base-4.8.0.0 |
| 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 # | |
| Traversable Sum | Since: base-4.8.0.0 |
| Bounded a => Bounded (Sum a) | Since: base-2.1 |
| Eq a => Eq (Sum a) | Since: base-2.1 |
| Num a => Num (Sum a) | Since: base-4.7.0.0 |
| Ord a => Ord (Sum a) | Since: base-2.1 |
| Read a => Read (Sum a) | Since: base-2.1 |
| Show a => Show (Sum a) | Since: base-2.1 |
| Generic (Sum a) | Since: base-4.7.0.0 |
| Num a => Semigroup (Sum a) | Since: base-4.9.0.0 |
| Num a => Monoid (Sum a) | Since: base-2.1 |
| Generic1 Sum | Since: base-4.7.0.0 |
| type Rep (Sum a) | |
Defined in Data.Semigroup.Internal | |
| type Rep1 Sum | |
Defined in Data.Semigroup.Internal | |
Monoid under multiplication.
>>>getProduct (Product 3 <> Product 4 <> mempty)12
Constructors
| Product | |
Fields
| |
Instances
| Monad Product | Since: base-4.8.0.0 |
| Functor Product | Since: base-4.8.0.0 |
| Applicative Product | Since: base-4.8.0.0 |
| 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 # | |
| Traversable Product | Since: base-4.8.0.0 |
| Bounded a => Bounded (Product a) | Since: base-2.1 |
| Eq a => Eq (Product a) | Since: base-2.1 |
| Num a => Num (Product a) | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
| Ord a => Ord (Product a) | Since: base-2.1 |
| Read a => Read (Product a) | Since: base-2.1 |
| Show a => Show (Product a) | Since: base-2.1 |
| Generic (Product a) | Since: base-4.7.0.0 |
| Num a => Semigroup (Product a) | Since: base-4.9.0.0 |
| Num a => Monoid (Product a) | Since: base-2.1 |
| Generic1 Product | Since: base-4.7.0.0 |
| type Rep (Product a) | |
Defined in Data.Semigroup.Internal | |
| type Rep1 Product | |
Defined in Data.Semigroup.Internal | |
newtype Alt (f :: k -> Type) (a :: k) #
Monoid under <|>.
>>>getAlt (Alt (Just 12) <> Alt (Just 24))Just 12
>>>getAlt $ Alt Nothing <> Alt (Just 24)Just 24
Since: base-4.8.0.0
Instances
| Generic1 (Alt f :: k -> Type) | Since: base-4.8.0.0 |
| Monad f => Monad (Alt f) | Since: base-4.8.0.0 |
| Functor f => Functor (Alt f) | Since: base-4.8.0.0 |
| Applicative f => Applicative (Alt f) | Since: base-4.8.0.0 |
| 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 # | |
| Traversable f => Traversable (Alt f) | Since: base-4.12.0.0 |
| Alternative f => Alternative (Alt f) | Since: base-4.8.0.0 |
| MonadPlus f => MonadPlus (Alt f) | Since: base-4.8.0.0 |
| Enum (f a) => Enum (Alt f a) | Since: base-4.8.0.0 |
| Eq (f a) => Eq (Alt f a) | Since: base-4.8.0.0 |
| Num (f a) => Num (Alt f a) | Since: base-4.8.0.0 |
| Ord (f a) => Ord (Alt f a) | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal | |
| Read (f a) => Read (Alt f a) | Since: base-4.8.0.0 |
| Show (f a) => Show (Alt f a) | Since: base-4.8.0.0 |
| Generic (Alt f a) | Since: base-4.8.0.0 |
| Alternative f => Semigroup (Alt f a) | Since: base-4.9.0.0 |
| Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0 |
| type Rep1 (Alt f :: k -> Type) | |
Defined in Data.Semigroup.Internal | |
| type Rep (Alt f a) | |
Defined in Data.Semigroup.Internal | |
module Control.Applicative