Data.Comp.Derive

This module contains functionality for automatically deriving boilerplate code using Template Haskell. Examples include instances of Functor, Foldable, and Traversable.

Documentation

derive :: [Name -> Q [Dec]] -> [Name] -> Q [Dec]

Helper function for generating a list of instances for a list of named signatures. For example, in order to derive instances Functor and ShowF for a signature Exp, use derive as follows (requires Template Haskell):

$(derive [makeFunctor, makeShowF] [''Exp])

Derive boilerplate instances for compositional data type signatures.

ShowF

class ShowF f where

Signature printing. An instance ShowF f gives rise to an instance Show (Term f).

Minimal complete definition

showF

Methods

showF :: f String -> String

Instances

ShowF []

Defined in Data.Comp.Show

Methods

showF :: [String] -> String

ShowF Maybe

Defined in Data.Comp.Show

Methods

showF :: Maybe String -> String

Show a => ShowF ((,) a)

Defined in Data.Comp.Show

Methods

showF :: (a, String) -> String

(Functor f, ShowF f) => ShowF (Cxt h f)

Defined in Data.Comp.Show

Methods

showF :: Cxt h f String -> String

(ShowF f, Show p) => ShowF (f :&: p)

Defined in Data.Comp.Show

Methods

showF :: (f :&: p) String -> String

(ShowF f, ShowF g) => ShowF (f :+: g)

Defined in Data.Comp.Show

Methods

showF :: (f :+: g) String -> String

makeShowF :: Name -> Q [Dec]

Derive an instance of ShowF for a type constructor of any first-order kind taking at least one argument.

class ShowConstr f where

Constructor printing.

Minimal complete definition

showConstr

Methods

showConstr :: f a -> String

Instances

(ShowConstr f, Show p) => ShowConstr (f :&: p)

Defined in Data.Comp.Show

Methods

showConstr :: (f :&: p) a -> String

(ShowConstr f, ShowConstr g) => ShowConstr (f :+: g)

Defined in Data.Comp.Show

Methods

showConstr :: (f :+: g) a -> String

makeShowConstr :: Name -> Q [Dec]

Derive an instance of showConstr for a type constructor of any first-order kind taking at least one argument.

EqF

class EqF f where

Signature equality. An instance EqF f gives rise to an instance Eq (Term f).

Minimal complete definition

eqF

Methods

eqF :: Eq a => f a -> f a -> Bool

Instances

EqF []

Defined in Data.Comp.Equality

Methods

eqF :: Eq a => [a] -> [a] -> Bool

EqF Maybe

Defined in Data.Comp.Equality

Methods

eqF :: Eq a => Maybe a -> Maybe a -> Bool

Eq a => EqF ((,) a)

Defined in Data.Comp.Equality

Methods

eqF :: Eq a0 => (a, a0) -> (a, a0) -> Bool

(Eq a, Eq b) => EqF ((,,) a b)

Defined in Data.Comp.Equality

Methods

eqF :: Eq a0 => (a, b, a0) -> (a, b, a0) -> Bool

EqF f => EqF (Cxt h f)

Defined in Data.Comp.Equality

Methods

eqF :: Eq a => Cxt h f a -> Cxt h f a -> Bool

(Eq a, Eq b, Eq c) => EqF ((,,,) a b c)

Defined in Data.Comp.Equality

Methods

eqF :: Eq a0 => (a, b, c, a0) -> (a, b, c, a0) -> Bool

(EqF f, EqF g) => EqF (f :+: g)

EqF is propagated through sums.

Defined in Data.Comp.Equality

Methods

eqF :: Eq a => (f :+: g) a -> (f :+: g) a -> Bool

(Eq a, Eq b, Eq c, Eq d) => EqF ((,,,,) a b c d)

Defined in Data.Comp.Equality

Methods

eqF :: Eq a0 => (a, b, c, d, a0) -> (a, b, c, d, a0) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e) => EqF ((,,,,,) a b c d e)

Defined in Data.Comp.Equality

Methods

eqF :: Eq a0 => (a, b, c, d, e, a0) -> (a, b, c, d, e, a0) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => EqF ((,,,,,,) a b c d e f)

Defined in Data.Comp.Equality

Methods

eqF :: Eq a0 => (a, b, c, d, e, f, a0) -> (a, b, c, d, e, f, a0) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => EqF ((,,,,,,,) a b c d e f g)

Defined in Data.Comp.Equality

Methods

eqF :: Eq a0 => (a, b, c, d, e, f, g, a0) -> (a, b, c, d, e, f, g, a0) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => EqF ((,,,,,,,,) a b c d e f g h)

Defined in Data.Comp.Equality

Methods

eqF :: Eq a0 => (a, b, c, d, e, f, g, h, a0) -> (a, b, c, d, e, f, g, h, a0) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => EqF ((,,,,,,,,,) a b c d e f g h i)

Defined in Data.Comp.Equality

Methods

eqF :: Eq a0 => (a, b, c, d, e, f, g, h, i, a0) -> (a, b, c, d, e, f, g, h, i, a0) -> Bool

makeEqF :: Name -> Q [Dec]

Derive an instance of EqF for a type constructor of any first-order kind taking at least one argument.

OrdF

class EqF f => OrdF f where

Signature ordering. An instance OrdF f gives rise to an instance Ord (Term f).

Minimal complete definition

compareF

Methods

compareF :: Ord a => f a -> f a -> Ordering

Instances

OrdF []

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a => [a] -> [a] -> Ordering

OrdF Maybe

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a => Maybe a -> Maybe a -> Ordering

Ord a => OrdF ((,) a)

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a0 => (a, a0) -> (a, a0) -> Ordering

(Ord a, Ord b) => OrdF ((,,) a b)

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a0 => (a, b, a0) -> (a, b, a0) -> Ordering

OrdF f => OrdF (Cxt h f)

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a => Cxt h f a -> Cxt h f a -> Ordering

(Ord a, Ord b, Ord c) => OrdF ((,,,) a b c)

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a0 => (a, b, c, a0) -> (a, b, c, a0) -> Ordering

(OrdF f, OrdF g) => OrdF (f :+: g)

OrdF is propagated through sums.

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a => (f :+: g) a -> (f :+: g) a -> Ordering

(Ord a, Ord b, Ord c, Ord d) => OrdF ((,,,,) a b c d)

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a0 => (a, b, c, d, a0) -> (a, b, c, d, a0) -> Ordering

(Ord a, Ord b, Ord c, Ord d, Ord e) => OrdF ((,,,,,) a b c d e)

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a0 => (a, b, c, d, e, a0) -> (a, b, c, d, e, a0) -> Ordering

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => OrdF ((,,,,,,) a b c d e f)

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a0 => (a, b, c, d, e, f, a0) -> (a, b, c, d, e, f, a0) -> Ordering

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => OrdF ((,,,,,,,) a b c d e f g)

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a0 => (a, b, c, d, e, f, g, a0) -> (a, b, c, d, e, f, g, a0) -> Ordering

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => OrdF ((,,,,,,,,) a b c d e f g h)

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a0 => (a, b, c, d, e, f, g, h, a0) -> (a, b, c, d, e, f, g, h, a0) -> Ordering

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => OrdF ((,,,,,,,,,) a b c d e f g h i)

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a0 => (a, b, c, d, e, f, g, h, i, a0) -> (a, b, c, d, e, f, g, h, i, a0) -> Ordering

makeOrdF :: Name -> Q [Dec]

Derive an instance of OrdF for a type constructor of any first-order kind taking at least one argument.

Foldable

class Foldable (t :: * -> *)

Data structures that can be folded.

For example, given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Foldable Tree where
   foldMap f Empty = mempty
   foldMap f (Leaf x) = f x
   foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r

This is suitable even for abstract types, as the monoid is assumed to satisfy the monoid laws. Alternatively, one could define foldr:

instance Foldable Tree where
   foldr f z Empty = z
   foldr f z (Leaf x) = f x z
   foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l

Foldable instances are expected to satisfy the following laws:

foldr f z t = appEndo (foldMap (Endo . f) t ) z

foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z

fold = foldMap id

length = getSum . foldMap (Sum . const  1)

sum, product, maximum, and minimum should all be essentially equivalent to foldMap forms, such as

sum = getSum . foldMap Sum

but may be less defined.

If the type is also a Functor instance, it should satisfy

foldMap f = fold . fmap f

which implies that

foldMap f . fmap g = foldMap (f . g)

Minimal complete definition

foldMap | foldr

Instances

Foldable []

Since: base-2.1

Defined in Data.Foldable

Methods

fold :: Monoid m => [m] -> 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

toList :: [a] -> [a]

null :: [a] -> Bool

length :: [a] -> Int

elem :: Eq a => a -> [a] -> Bool

maximum :: Ord a => [a] -> a

minimum :: Ord a => [a] -> a

sum :: Num a => [a] -> a

product :: Num a => [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

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

toList :: Maybe a -> [a]

null :: Maybe a -> Bool

length :: Maybe a -> Int

elem :: Eq a => a -> Maybe a -> Bool

maximum :: Ord a => Maybe a -> a

minimum :: Ord a => Maybe a -> a

sum :: Num a => Maybe a -> a

product :: Num a => Maybe a -> a

Foldable Par1

Defined in Data.Foldable

Methods

fold :: Monoid m => Par1 m -> 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

toList :: Par1 a -> [a]

null :: Par1 a -> Bool

length :: Par1 a -> Int

elem :: Eq a => a -> Par1 a -> Bool

maximum :: Ord a => Par1 a -> a

minimum :: Ord a => Par1 a -> a

sum :: Num a => Par1 a -> a

product :: Num a => Par1 a -> a

Foldable Complex

Defined in Data.Complex

Methods

fold :: Monoid m => Complex m -> m

foldMap :: Monoid m => (a -> m) -> Complex a -> m

foldr :: (a -> b -> b) -> b -> Complex a -> b

foldr' :: (a -> b -> b) -> b -> Complex a -> b

foldl :: (b -> a -> b) -> b -> Complex a -> b

foldl' :: (b -> a -> b) -> b -> Complex a -> b

foldr1 :: (a -> a -> a) -> Complex a -> a

foldl1 :: (a -> a -> a) -> Complex a -> a

toList :: Complex a -> [a]

null :: Complex a -> Bool

length :: Complex a -> Int

elem :: Eq a => a -> Complex a -> Bool

maximum :: Ord a => Complex a -> a

minimum :: Ord a => Complex a -> a

sum :: Num a => Complex a -> a

product :: Num a => Complex a -> a

Foldable Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fold :: Monoid m => Min m -> m

foldMap :: Monoid m => (a -> m) -> Min a -> m

foldr :: (a -> b -> b) -> b -> Min a -> b

foldr' :: (a -> b -> b) -> b -> Min a -> b

foldl :: (b -> a -> b) -> b -> Min a -> b

foldl' :: (b -> a -> b) -> b -> Min a -> b

foldr1 :: (a -> a -> a) -> Min a -> a

foldl1 :: (a -> a -> a) -> Min a -> a

toList :: Min a -> [a]

null :: Min a -> Bool

length :: Min a -> Int

elem :: Eq a => a -> Min a -> Bool

maximum :: Ord a => Min a -> a

minimum :: Ord a => Min a -> a

sum :: Num a => Min a -> a

product :: Num a => Min a -> a

Foldable Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fold :: Monoid m => Max m -> m

foldMap :: Monoid m => (a -> m) -> Max a -> m

foldr :: (a -> b -> b) -> b -> Max a -> b

foldr' :: (a -> b -> b) -> b -> Max a -> b

foldl :: (b -> a -> b) -> b -> Max a -> b

foldl' :: (b -> a -> b) -> b -> Max a -> b

foldr1 :: (a -> a -> a) -> Max a -> a

foldl1 :: (a -> a -> a) -> Max a -> a

toList :: Max a -> [a]

null :: Max a -> Bool

length :: Max a -> Int

elem :: Eq a => a -> Max a -> Bool

maximum :: Ord a => Max a -> a

minimum :: Ord a => Max a -> a

sum :: Num a => Max a -> a

product :: Num a => Max a -> a

Foldable First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fold :: Monoid m => First m -> 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

toList :: First a -> [a]

null :: First a -> Bool

length :: First a -> Int

elem :: Eq a => a -> First a -> Bool

maximum :: Ord a => First a -> a

minimum :: Ord a => First a -> a

sum :: Num a => First a -> a

product :: Num a => First a -> a

Foldable Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fold :: Monoid m => Last m -> 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

toList :: Last a -> [a]

null :: Last a -> Bool

length :: Last a -> Int

elem :: Eq a => a -> Last a -> Bool

maximum :: Ord a => Last a -> a

minimum :: Ord a => Last a -> a

sum :: Num a => Last a -> a

product :: Num a => Last a -> a

Foldable Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fold :: Monoid m => Option m -> m

foldMap :: Monoid m => (a -> m) -> Option a -> m

foldr :: (a -> b -> b) -> b -> Option a -> b

foldr' :: (a -> b -> b) -> b -> Option a -> b

foldl :: (b -> a -> b) -> b -> Option a -> b

foldl' :: (b -> a -> b) -> b -> Option a -> b

foldr1 :: (a -> a -> a) -> Option a -> a

foldl1 :: (a -> a -> a) -> Option a -> a

toList :: Option a -> [a]

null :: Option a -> Bool

length :: Option a -> Int

elem :: Eq a => a -> Option a -> Bool

maximum :: Ord a => Option a -> a

minimum :: Ord a => Option a -> a

sum :: Num a => Option a -> a

product :: Num a => Option a -> a

Foldable ZipList

Defined in Control.Applicative

Methods

fold :: Monoid m => ZipList m -> 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

toList :: ZipList a -> [a]

null :: ZipList a -> Bool

length :: ZipList a -> Int

elem :: Eq a => a -> ZipList a -> Bool

maximum :: Ord a => ZipList a -> a

minimum :: Ord a => ZipList a -> a

sum :: Num a => ZipList a -> a

product :: Num 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

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

toList :: Identity a -> [a]

null :: Identity a -> Bool

length :: Identity a -> Int

elem :: Eq a => a -> Identity a -> Bool

maximum :: Ord a => Identity a -> a

minimum :: Ord a => Identity a -> a

sum :: Num a => Identity a -> a

product :: Num 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

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

toList :: First a -> [a]

null :: First a -> Bool

length :: First a -> Int

elem :: Eq a => a -> First a -> Bool

maximum :: Ord a => First a -> a

minimum :: Ord a => First a -> a

sum :: Num a => First a -> a

product :: Num 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

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

toList :: Last a -> [a]

null :: Last a -> Bool

length :: Last a -> Int

elem :: Eq a => a -> Last a -> Bool

maximum :: Ord a => Last a -> a

minimum :: Ord a => Last a -> a

sum :: Num a => Last a -> a

product :: Num a => Last 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

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

toList :: Dual a -> [a]

null :: Dual a -> Bool

length :: Dual a -> Int

elem :: Eq a => a -> Dual a -> Bool

maximum :: Ord a => Dual a -> a

minimum :: Ord a => Dual a -> a

sum :: Num a => Dual a -> a

product :: Num a => Dual 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

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

toList :: Sum a -> [a]

null :: Sum a -> Bool

length :: Sum a -> Int

elem :: Eq a => a -> Sum a -> Bool

maximum :: Ord a => Sum a -> a

minimum :: Ord a => Sum a -> a

sum :: Num a => Sum a -> a

product :: Num a => Sum 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

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

toList :: Product a -> [a]

null :: Product a -> Bool

length :: Product a -> Int

elem :: Eq a => a -> Product a -> Bool

maximum :: Ord a => Product a -> a

minimum :: Ord a => Product a -> a

sum :: Num a => Product a -> a

product :: Num a => Product 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

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

toList :: NonEmpty a -> [a]

null :: NonEmpty a -> Bool

length :: NonEmpty a -> Int

elem :: Eq a => a -> NonEmpty a -> Bool

maximum :: Ord a => NonEmpty a -> a

minimum :: Ord a => NonEmpty a -> a

sum :: Num a => NonEmpty a -> a

product :: Num a => NonEmpty a -> a

Foldable IntMap

Defined in Data.IntMap.Internal

Methods

fold :: Monoid m => IntMap m -> 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

toList :: IntMap a -> [a]

null :: IntMap a -> Bool

length :: IntMap a -> Int

elem :: Eq a => a -> IntMap a -> Bool

maximum :: Ord a => IntMap a -> a

minimum :: Ord a => IntMap a -> a

sum :: Num a => IntMap a -> a

product :: Num a => IntMap a -> a

Foldable Tree

Defined in Data.Tree

Methods

fold :: Monoid m => Tree m -> 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

toList :: Tree a -> [a]

null :: Tree a -> Bool

length :: Tree a -> Int

elem :: Eq a => a -> Tree a -> Bool

maximum :: Ord a => Tree a -> a

minimum :: Ord a => Tree a -> a

sum :: Num a => Tree a -> a

product :: Num a => Tree a -> a

Foldable Seq

Defined in Data.Sequence.Internal

Methods

fold :: Monoid m => Seq m -> 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

toList :: Seq a -> [a]

null :: Seq a -> Bool

length :: Seq a -> Int

elem :: Eq a => a -> Seq a -> Bool

maximum :: Ord a => Seq a -> a

minimum :: Ord a => Seq a -> a

sum :: Num a => Seq a -> a

product :: Num a => Seq a -> a

Foldable FingerTree

Defined in Data.Sequence.Internal

Methods

fold :: Monoid m => FingerTree m -> 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 Digit

Defined in Data.Sequence.Internal

Methods

fold :: Monoid m => Digit m -> 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

toList :: Digit a -> [a]

null :: Digit a -> Bool

length :: Digit a -> Int

elem :: Eq a => a -> Digit a -> Bool

maximum :: Ord a => Digit a -> a

minimum :: Ord a => Digit a -> a

sum :: Num a => Digit a -> a

product :: Num a => Digit a -> a

Foldable Node

Defined in Data.Sequence.Internal

Methods

fold :: Monoid m => Node m -> 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

toList :: Node a -> [a]

null :: Node a -> Bool

length :: Node a -> Int

elem :: Eq a => a -> Node a -> Bool

maximum :: Ord a => Node a -> a

minimum :: Ord a => Node a -> a

sum :: Num a => Node a -> a

product :: Num a => Node a -> a

Foldable Elem

Defined in Data.Sequence.Internal

Methods

fold :: Monoid m => Elem m -> 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

toList :: Elem a -> [a]

null :: Elem a -> Bool

length :: Elem a -> Int

elem :: Eq a => a -> Elem a -> Bool

maximum :: Ord a => Elem a -> a

minimum :: Ord a => Elem a -> a

sum :: Num a => Elem a -> a

product :: Num a => Elem a -> a

Foldable ViewL

Defined in Data.Sequence.Internal

Methods

fold :: Monoid m => ViewL m -> 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

toList :: ViewL a -> [a]

null :: ViewL a -> Bool

length :: ViewL a -> Int

elem :: Eq a => a -> ViewL a -> Bool

maximum :: Ord a => ViewL a -> a

minimum :: Ord a => ViewL a -> a

sum :: Num a => ViewL a -> a

product :: Num 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

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

toList :: ViewR a -> [a]

null :: ViewR a -> Bool

length :: ViewR a -> Int

elem :: Eq a => a -> ViewR a -> Bool

maximum :: Ord a => ViewR a -> a

minimum :: Ord a => ViewR a -> a

sum :: Num a => ViewR a -> a

product :: Num a => ViewR a -> a

Foldable Set

Defined in Data.Set.Internal

Methods

fold :: Monoid m => Set m -> 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

toList :: Set a -> [a]

null :: Set a -> Bool

length :: Set a -> Int

elem :: Eq a => a -> Set a -> Bool

maximum :: Ord a => Set a -> a

minimum :: Ord a => Set a -> a

sum :: Num a => Set a -> a

product :: Num a => Set a -> a

Foldable I

Defined in Data.Comp.Multi.HFunctor

Methods

fold :: Monoid m => I m -> m

foldMap :: Monoid m => (a -> m) -> I a -> m

foldr :: (a -> b -> b) -> b -> I a -> b

foldr' :: (a -> b -> b) -> b -> I a -> b

foldl :: (b -> a -> b) -> b -> I a -> b

foldl' :: (b -> a -> b) -> b -> I a -> b

foldr1 :: (a -> a -> a) -> I a -> a

foldl1 :: (a -> a -> a) -> I a -> a

toList :: I a -> [a]

null :: I a -> Bool

length :: I a -> Int

elem :: Eq a => a -> I a -> Bool

maximum :: Ord a => I a -> a

minimum :: Ord a => I a -> a

sum :: Num a => I a -> a

product :: Num a => I 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

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]

null :: Either a a0 -> Bool

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

sum :: Num a0 => Either a a0 -> a0

product :: Num a0 => Either a a0 -> a0

Foldable (V1 :: * -> *)

Defined in Data.Foldable

Methods

fold :: Monoid m => V1 m -> 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

toList :: V1 a -> [a]

null :: V1 a -> Bool

length :: V1 a -> Int

elem :: Eq a => a -> V1 a -> Bool

maximum :: Ord a => V1 a -> a

minimum :: Ord a => V1 a -> a

sum :: Num a => V1 a -> a

product :: Num a => V1 a -> a

Foldable (U1 :: * -> *)

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

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

toList :: U1 a -> [a]

null :: U1 a -> Bool

length :: U1 a -> Int

elem :: Eq a => a -> U1 a -> Bool

maximum :: Ord a => U1 a -> a

minimum :: Ord a => U1 a -> a

sum :: Num a => U1 a -> a

product :: Num a => U1 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

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

toList :: (a, a0) -> [a0]

null :: (a, a0) -> Bool

length :: (a, a0) -> Int

elem :: Eq a0 => a0 -> (a, a0) -> Bool

maximum :: Ord a0 => (a, a0) -> a0

minimum :: Ord a0 => (a, a0) -> a0

sum :: Num a0 => (a, a0) -> a0

product :: Num a0 => (a, a0) -> a0

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

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

toList :: Array i a -> [a]

null :: Array i a -> Bool

length :: Array i a -> Int

elem :: Eq a => a -> Array i a -> Bool

maximum :: Ord a => Array i a -> a

minimum :: Ord a => Array i a -> a

sum :: Num a => Array i a -> a

product :: Num a => Array i a -> a

Foldable (Arg a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fold :: Monoid m => Arg a m -> m

foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m

foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b

foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0

toList :: Arg a a0 -> [a0]

null :: Arg a a0 -> Bool

length :: Arg a a0 -> Int

elem :: Eq a0 => a0 -> Arg a a0 -> Bool

maximum :: Ord a0 => Arg a a0 -> a0

minimum :: Ord a0 => Arg a a0 -> a0

sum :: Num a0 => Arg a a0 -> a0

product :: Num a0 => Arg a a0 -> a0

Foldable (Proxy :: * -> *)

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

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

toList :: Proxy a -> [a]

null :: Proxy a -> Bool

length :: Proxy a -> Int

elem :: Eq a => a -> Proxy a -> Bool

maximum :: Ord a => Proxy a -> a

minimum :: Ord a => Proxy a -> a

sum :: Num a => Proxy a -> a

product :: Num a => Proxy a -> a

Foldable (Map k)

Defined in Data.Map.Internal

Methods

fold :: Monoid m => Map k m -> 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

toList :: Map k a -> [a]

null :: Map k a -> Bool

length :: Map k a -> Int

elem :: Eq a => a -> Map k a -> Bool

maximum :: Ord a => Map k a -> a

minimum :: Ord a => Map k a -> a

sum :: Num a => Map k a -> a

product :: Num a => Map k a -> a

Foldable f => Foldable (ListT f)

Defined in Control.Monad.Trans.List

Methods

fold :: Monoid m => ListT f m -> m

foldMap :: Monoid m => (a -> m) -> ListT f a -> m

foldr :: (a -> b -> b) -> b -> ListT f a -> b

foldr' :: (a -> b -> b) -> b -> ListT f a -> b

foldl :: (b -> a -> b) -> b -> ListT f a -> b

foldl' :: (b -> a -> b) -> b -> ListT f a -> b

foldr1 :: (a -> a -> a) -> ListT f a -> a

foldl1 :: (a -> a -> a) -> ListT f a -> a

toList :: ListT f a -> [a]

null :: ListT f a -> Bool

length :: ListT f a -> Int

elem :: Eq a => a -> ListT f a -> Bool

maximum :: Ord a => ListT f a -> a

minimum :: Ord a => ListT f a -> a

sum :: Num a => ListT f a -> a

product :: Num a => ListT f a -> a

Foldable f => Foldable (MaybeT f)

Defined in Control.Monad.Trans.Maybe

Methods

fold :: Monoid m => MaybeT f m -> m

foldMap :: Monoid m => (a -> m) -> MaybeT f a -> m

foldr :: (a -> b -> b) -> b -> MaybeT f a -> b

foldr' :: (a -> b -> b) -> b -> MaybeT f a -> b

foldl :: (b -> a -> b) -> b -> MaybeT f a -> b

foldl' :: (b -> a -> b) -> b -> MaybeT f a -> b

foldr1 :: (a -> a -> a) -> MaybeT f a -> a

foldl1 :: (a -> a -> a) -> MaybeT f a -> a

toList :: MaybeT f a -> [a]

null :: MaybeT f a -> Bool

length :: MaybeT f a -> Int

elem :: Eq a => a -> MaybeT f a -> Bool

maximum :: Ord a => MaybeT f a -> a

minimum :: Ord a => MaybeT f a -> a

sum :: Num a => MaybeT f a -> a

product :: Num a => MaybeT f a -> a

Foldable (NumMap k)

Defined in Data.Comp.Mapping

Methods

fold :: Monoid m => NumMap k m -> m

foldMap :: Monoid m => (a -> m) -> NumMap k a -> m

foldr :: (a -> b -> b) -> b -> NumMap k a -> b

foldr' :: (a -> b -> b) -> b -> NumMap k a -> b

foldl :: (b -> a -> b) -> b -> NumMap k a -> b

foldl' :: (b -> a -> b) -> b -> NumMap k a -> b

foldr1 :: (a -> a -> a) -> NumMap k a -> a

foldl1 :: (a -> a -> a) -> NumMap k a -> a

toList :: NumMap k a -> [a]

null :: NumMap k a -> Bool

length :: NumMap k a -> Int

elem :: Eq a => a -> NumMap k a -> Bool

maximum :: Ord a => NumMap k a -> a

minimum :: Ord a => NumMap k a -> a

sum :: Num a => NumMap k a -> a

product :: Num a => NumMap k a -> a

Foldable (K a)

Defined in Data.Comp.Multi.HFunctor

Methods

fold :: Monoid m => K a m -> m

foldMap :: Monoid m => (a0 -> m) -> K a a0 -> m

foldr :: (a0 -> b -> b) -> b -> K a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> K a a0 -> b

foldl :: (b -> a0 -> b) -> b -> K a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> K a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> K a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> K a a0 -> a0

toList :: K a a0 -> [a0]

null :: K a a0 -> Bool

length :: K a a0 -> Int

elem :: Eq a0 => a0 -> K a a0 -> Bool

maximum :: Ord a0 => K a a0 -> a0

minimum :: Ord a0 => K a a0 -> a0

sum :: Num a0 => K a a0 -> a0

product :: Num a0 => K a a0 -> a0

Foldable f => Foldable (Rec1 f)

Defined in Data.Foldable

Methods

fold :: Monoid m => Rec1 f m -> 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

toList :: Rec1 f a -> [a]

null :: Rec1 f a -> Bool

length :: Rec1 f a -> Int

elem :: Eq a => a -> Rec1 f a -> Bool

maximum :: Ord a => Rec1 f a -> a

minimum :: Ord a => Rec1 f a -> a

sum :: Num a => Rec1 f a -> a

product :: Num a => Rec1 f a -> a

Foldable (URec Char :: * -> *)

Defined in Data.Foldable

Methods

fold :: Monoid m => URec Char m -> m

foldMap :: Monoid m => (a -> m) -> URec Char a -> m

foldr :: (a -> b -> b) -> b -> URec Char a -> b

foldr' :: (a -> b -> b) -> b -> URec Char a -> b

foldl :: (b -> a -> b) -> b -> URec Char a -> b

foldl' :: (b -> a -> b) -> b -> URec Char a -> b

foldr1 :: (a -> a -> a) -> URec Char a -> a

foldl1 :: (a -> a -> a) -> URec Char a -> a

toList :: URec Char a -> [a]

null :: URec Char a -> Bool

length :: URec Char a -> Int

elem :: Eq a => a -> URec Char a -> Bool

maximum :: Ord a => URec Char a -> a

minimum :: Ord a => URec Char a -> a

sum :: Num a => URec Char a -> a

product :: Num a => URec Char a -> a

Foldable (URec Double :: * -> *)

Defined in Data.Foldable

Methods

fold :: Monoid m => URec Double m -> m

foldMap :: Monoid m => (a -> m) -> URec Double a -> m

foldr :: (a -> b -> b) -> b -> URec Double a -> b

foldr' :: (a -> b -> b) -> b -> URec Double a -> b

foldl :: (b -> a -> b) -> b -> URec Double a -> b

foldl' :: (b -> a -> b) -> b -> URec Double a -> b

foldr1 :: (a -> a -> a) -> URec Double a -> a

foldl1 :: (a -> a -> a) -> URec Double a -> a

toList :: URec Double a -> [a]

null :: URec Double a -> Bool

length :: URec Double a -> Int

elem :: Eq a => a -> URec Double a -> Bool

maximum :: Ord a => URec Double a -> a

minimum :: Ord a => URec Double a -> a

sum :: Num a => URec Double a -> a

product :: Num a => URec Double a -> a

Foldable (URec Float :: * -> *)

Defined in Data.Foldable

Methods

fold :: Monoid m => URec Float m -> m

foldMap :: Monoid m => (a -> m) -> URec Float a -> m

foldr :: (a -> b -> b) -> b -> URec Float a -> b

foldr' :: (a -> b -> b) -> b -> URec Float a -> b

foldl :: (b -> a -> b) -> b -> URec Float a -> b

foldl' :: (b -> a -> b) -> b -> URec Float a -> b

foldr1 :: (a -> a -> a) -> URec Float a -> a

foldl1 :: (a -> a -> a) -> URec Float a -> a

toList :: URec Float a -> [a]

null :: URec Float a -> Bool

length :: URec Float a -> Int

elem :: Eq a => a -> URec Float a -> Bool

maximum :: Ord a => URec Float a -> a

minimum :: Ord a => URec Float a -> a

sum :: Num a => URec Float a -> a

product :: Num a => URec Float a -> a

Foldable (URec Int :: * -> *)

Defined in Data.Foldable

Methods

fold :: Monoid m => URec Int m -> m

foldMap :: Monoid m => (a -> m) -> URec Int a -> m

foldr :: (a -> b -> b) -> b -> URec Int a -> b

foldr' :: (a -> b -> b) -> b -> URec Int a -> b

foldl :: (b -> a -> b) -> b -> URec Int a -> b

foldl' :: (b -> a -> b) -> b -> URec Int a -> b

foldr1 :: (a -> a -> a) -> URec Int a -> a

foldl1 :: (a -> a -> a) -> URec Int a -> a

toList :: URec Int a -> [a]

null :: URec Int a -> Bool

length :: URec Int a -> Int

elem :: Eq a => a -> URec Int a -> Bool

maximum :: Ord a => URec Int a -> a

minimum :: Ord a => URec Int a -> a

sum :: Num a => URec Int a -> a

product :: Num a => URec Int a -> a

Foldable (URec Word :: * -> *)

Defined in Data.Foldable

Methods

fold :: Monoid m => URec Word m -> m

foldMap :: Monoid m => (a -> m) -> URec Word a -> m

foldr :: (a -> b -> b) -> b -> URec Word a -> b

foldr' :: (a -> b -> b) -> b -> URec Word a -> b

foldl :: (b -> a -> b) -> b -> URec Word a -> b

foldl' :: (b -> a -> b) -> b -> URec Word a -> b

foldr1 :: (a -> a -> a) -> URec Word a -> a

foldl1 :: (a -> a -> a) -> URec Word a -> a

toList :: URec Word a -> [a]

null :: URec Word a -> Bool

length :: URec Word a -> Int

elem :: Eq a => a -> URec Word a -> Bool

maximum :: Ord a => URec Word a -> a

minimum :: Ord a => URec Word a -> a

sum :: Num a => URec Word a -> a

product :: Num a => URec Word a -> a

Foldable (URec (Ptr ()) :: * -> *)

Defined in Data.Foldable

Methods

fold :: Monoid m => URec (Ptr ()) m -> m

foldMap :: Monoid m => (a -> m) -> URec (Ptr ()) a -> m

foldr :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b

foldr' :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b

foldl :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b

foldl' :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b

foldr1 :: (a -> a -> a) -> URec (Ptr ()) a -> a

foldl1 :: (a -> a -> a) -> URec (Ptr ()) a -> a

toList :: URec (Ptr ()) a -> [a]

null :: URec (Ptr ()) a -> Bool

length :: URec (Ptr ()) a -> Int

elem :: Eq a => a -> URec (Ptr ()) a -> Bool

maximum :: Ord a => URec (Ptr ()) a -> a

minimum :: Ord a => URec (Ptr ()) a -> a

sum :: Num a => URec (Ptr ()) a -> a

product :: Num a => URec (Ptr ()) a -> a

Foldable (Const m :: * -> *)

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

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

toList :: Const m a -> [a]

null :: Const m a -> Bool

length :: Const m a -> Int

elem :: Eq a => a -> Const m a -> Bool

maximum :: Ord a => Const m a -> a

minimum :: Ord a => Const m a -> a

sum :: Num a => Const m a -> a

product :: Num a => Const m a -> a

Foldable f => Foldable (IdentityT f)

Defined in Control.Monad.Trans.Identity

Methods

fold :: Monoid m => IdentityT f m -> m

foldMap :: Monoid m => (a -> m) -> IdentityT f a -> m

foldr :: (a -> b -> b) -> b -> IdentityT f a -> b

foldr' :: (a -> b -> b) -> b -> IdentityT f a -> b

foldl :: (b -> a -> b) -> b -> IdentityT f a -> b

foldl' :: (b -> a -> b) -> b -> IdentityT f a -> b

foldr1 :: (a -> a -> a) -> IdentityT f a -> a

foldl1 :: (a -> a -> a) -> IdentityT f a -> a

toList :: IdentityT f a -> [a]

null :: IdentityT f a -> Bool

length :: IdentityT f a -> Int

elem :: Eq a => a -> IdentityT f a -> Bool

maximum :: Ord a => IdentityT f a -> a

minimum :: Ord a => IdentityT f a -> a

sum :: Num a => IdentityT f a -> a

product :: Num a => IdentityT f a -> a

Foldable f => Foldable (ErrorT e f)

Defined in Control.Monad.Trans.Error

Methods

fold :: Monoid m => ErrorT e f m -> m

foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m

foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b

foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b

foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b

foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b

foldr1 :: (a -> a -> a) -> ErrorT e f a -> a

foldl1 :: (a -> a -> a) -> ErrorT e f a -> a

toList :: ErrorT e f a -> [a]

null :: ErrorT e f a -> Bool

length :: ErrorT e f a -> Int

elem :: Eq a => a -> ErrorT e f a -> Bool

maximum :: Ord a => ErrorT e f a -> a

minimum :: Ord a => ErrorT e f a -> a

sum :: Num a => ErrorT e f a -> a

product :: Num a => ErrorT e f a -> a

Foldable f => Foldable (ExceptT e f)

Defined in Control.Monad.Trans.Except

Methods

fold :: Monoid m => ExceptT e f m -> m

foldMap :: Monoid m => (a -> m) -> ExceptT e f a -> m

foldr :: (a -> b -> b) -> b -> ExceptT e f a -> b

foldr' :: (a -> b -> b) -> b -> ExceptT e f a -> b

foldl :: (b -> a -> b) -> b -> ExceptT e f a -> b

foldl' :: (b -> a -> b) -> b -> ExceptT e f a -> b

foldr1 :: (a -> a -> a) -> ExceptT e f a -> a

foldl1 :: (a -> a -> a) -> ExceptT e f a -> a

toList :: ExceptT e f a -> [a]

null :: ExceptT e f a -> Bool

length :: ExceptT e f a -> Int

elem :: Eq a => a -> ExceptT e f a -> Bool

maximum :: Ord a => ExceptT e f a -> a

minimum :: Ord a => ExceptT e f a -> a

sum :: Num a => ExceptT e f a -> a

product :: Num a => ExceptT e 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

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

sum :: Num a => WriterT w f a -> a

product :: Num a => WriterT w f a -> a

Foldable f => Foldable (WriterT w f)

Defined in Control.Monad.Trans.Writer.Strict

Methods

fold :: Monoid m => WriterT w f m -> 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

sum :: Num a => WriterT w f a -> a

product :: Num a => WriterT w f a -> a

Foldable (Constant a :: * -> *)

Defined in Data.Functor.Constant

Methods

fold :: Monoid m => Constant a m -> m

foldMap :: Monoid m => (a0 -> m) -> Constant a a0 -> m

foldr :: (a0 -> b -> b) -> b -> Constant a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> Constant a a0 -> b

foldl :: (b -> a0 -> b) -> b -> Constant a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> Constant a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> Constant a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> Constant a a0 -> a0

toList :: Constant a a0 -> [a0]

null :: Constant a a0 -> Bool

length :: Constant a a0 -> Int

elem :: Eq a0 => a0 -> Constant a a0 -> Bool

maximum :: Ord a0 => Constant a a0 -> a0

minimum :: Ord a0 => Constant a a0 -> a0

sum :: Num a0 => Constant a a0 -> a0

product :: Num a0 => Constant a a0 -> a0

Foldable f => Foldable (Cxt h f)

Defined in Data.Comp.Term

Methods

fold :: Monoid m => Cxt h f m -> m

foldMap :: Monoid m => (a -> m) -> Cxt h f a -> m

foldr :: (a -> b -> b) -> b -> Cxt h f a -> b

foldr' :: (a -> b -> b) -> b -> Cxt h f a -> b

foldl :: (b -> a -> b) -> b -> Cxt h f a -> b

foldl' :: (b -> a -> b) -> b -> Cxt h f a -> b

foldr1 :: (a -> a -> a) -> Cxt h f a -> a

foldl1 :: (a -> a -> a) -> Cxt h f a -> a

toList :: Cxt h f a -> [a]

null :: Cxt h f a -> Bool

length :: Cxt h f a -> Int

elem :: Eq a => a -> Cxt h f a -> Bool

maximum :: Ord a => Cxt h f a -> a

minimum :: Ord a => Cxt h f a -> a

sum :: Num a => Cxt h f a -> a

product :: Num a => Cxt h f a -> a

Foldable (K1 i c :: * -> *)

Defined in Data.Foldable

Methods

fold :: Monoid m => K1 i c m -> 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

toList :: K1 i c a -> [a]

null :: K1 i c a -> Bool

length :: K1 i c a -> Int

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

sum :: Num a => K1 i c a -> a

product :: Num a => K1 i c a -> a

(Foldable f, Foldable g) => Foldable (f :+: g)

Defined in Data.Foldable

Methods

fold :: Monoid m => (f :+: g) m -> 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]

null :: (f :+: g) a -> Bool

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

sum :: Num a => (f :+: g) a -> a

product :: Num a => (f :+: g) a -> a

(Foldable f, Foldable g) => Foldable (f :*: g)

Defined in Data.Foldable

Methods

fold :: Monoid m => (f :*: g) m -> 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]

null :: (f :*: g) a -> Bool

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

sum :: Num a => (f :*: g) a -> a

product :: Num a => (f :*: g) a -> a

(Foldable f, Foldable g) => Foldable (Product f g)

Since: base-4.9.0.0

Defined in Data.Functor.Product

Methods

fold :: Monoid m => Product f g m -> m

foldMap :: Monoid m => (a -> m) -> Product f g a -> m

foldr :: (a -> b -> b) -> b -> Product f g a -> b

foldr' :: (a -> b -> b) -> b -> Product f g a -> b

foldl :: (b -> a -> b) -> b -> Product f g a -> b

foldl' :: (b -> a -> b) -> b -> Product f g a -> b

foldr1 :: (a -> a -> a) -> Product f g a -> a

foldl1 :: (a -> a -> a) -> Product f g a -> a

toList :: Product f g a -> [a]

null :: Product f g a -> Bool

length :: Product f g a -> Int

elem :: Eq a => a -> Product f g a -> Bool

maximum :: Ord a => Product f g a -> a

minimum :: Ord a => Product f g a -> a

sum :: Num a => Product f g a -> a

product :: Num a => Product f g a -> a

(Foldable f, Foldable g) => Foldable (Sum f g)

Since: base-4.9.0.0

Defined in Data.Functor.Sum

Methods

fold :: Monoid m => Sum f g m -> m

foldMap :: Monoid m => (a -> m) -> Sum f g a -> m

foldr :: (a -> b -> b) -> b -> Sum f g a -> b

foldr' :: (a -> b -> b) -> b -> Sum f g a -> b

foldl :: (b -> a -> b) -> b -> Sum f g a -> b

foldl' :: (b -> a -> b) -> b -> Sum f g a -> b

foldr1 :: (a -> a -> a) -> Sum f g a -> a

foldl1 :: (a -> a -> a) -> Sum f g a -> a

toList :: Sum f g a -> [a]

null :: Sum f g a -> Bool

length :: Sum f g a -> Int

elem :: Eq a => a -> Sum f g a -> Bool

maximum :: Ord a => Sum f g a -> a

minimum :: Ord a => Sum f g a -> a

sum :: Num a => Sum f g a -> a

product :: Num a => Sum f g a -> a

Foldable f => Foldable (f :&: a)

Defined in Data.Comp.Ops

Methods

fold :: Monoid m => (f :&: a) m -> m

foldMap :: Monoid m => (a0 -> m) -> (f :&: a) a0 -> m

foldr :: (a0 -> b -> b) -> b -> (f :&: a) a0 -> b

foldr' :: (a0 -> b -> b) -> b -> (f :&: a) a0 -> b

foldl :: (b -> a0 -> b) -> b -> (f :&: a) a0 -> b

foldl' :: (b -> a0 -> b) -> b -> (f :&: a) a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> (f :&: a) a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> (f :&: a) a0 -> a0

toList :: (f :&: a) a0 -> [a0]

null :: (f :&: a) a0 -> Bool

length :: (f :&: a) a0 -> Int

elem :: Eq a0 => a0 -> (f :&: a) a0 -> Bool

maximum :: Ord a0 => (f :&: a) a0 -> a0

minimum :: Ord a0 => (f :&: a) a0 -> a0

sum :: Num a0 => (f :&: a) a0 -> a0

product :: Num a0 => (f :&: a) a0 -> a0

(Foldable f, Foldable g) => Foldable (f :*: g)

Defined in Data.Comp.Ops

Methods

fold :: Monoid m => (f :*: g) m -> 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]

null :: (f :*: g) a -> Bool

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

sum :: Num a => (f :*: g) a -> a

product :: Num a => (f :*: g) a -> a

(Foldable f, Foldable g) => Foldable (f :+: g)

Defined in Data.Comp.Ops

Methods

fold :: Monoid m => (f :+: g) m -> 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]

null :: (f :+: g) a -> Bool

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

sum :: Num a => (f :+: g) a -> a

product :: Num a => (f :+: g) a -> a

Foldable f => Foldable (M1 i c f)

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

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

toList :: M1 i c f a -> [a]

null :: M1 i c f a -> Bool

length :: M1 i c f a -> Int

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

sum :: Num a => M1 i c f a -> a

product :: Num a => M1 i c f a -> a

(Foldable f, Foldable g) => Foldable (f :.: g)

Defined in Data.Foldable

Methods

fold :: Monoid m => (f :.: g) m -> 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]

null :: (f :.: g) a -> Bool

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

sum :: Num a => (f :.: g) a -> a

product :: Num a => (f :.: g) a -> a

(Foldable f, Foldable g) => Foldable (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

fold :: Monoid m => Compose f g m -> m

foldMap :: Monoid m => (a -> m) -> Compose f g a -> m

foldr :: (a -> b -> b) -> b -> Compose f g a -> b

foldr' :: (a -> b -> b) -> b -> Compose f g a -> b

foldl :: (b -> a -> b) -> b -> Compose f g a -> b

foldl' :: (b -> a -> b) -> b -> Compose f g a -> b

foldr1 :: (a -> a -> a) -> Compose f g a -> a

foldl1 :: (a -> a -> a) -> Compose f g a -> a

toList :: Compose f g a -> [a]

null :: Compose f g a -> Bool

length :: Compose f g a -> Int

elem :: Eq a => a -> Compose f g a -> Bool

maximum :: Ord a => Compose f g a -> a

minimum :: Ord a => Compose f g a -> a

sum :: Num a => Compose f g a -> a

product :: Num a => Compose f g a -> a

makeFoldable :: Name -> Q [Dec]

Derive an instance of Foldable for a type constructor of any first-order kind taking at least one argument.

Traversable

class (Functor t, Foldable t) => Traversable (t :: * -> *)

Functors representing data structures that can be traversed from left to right.

A definition of traverse must satisfy the following laws:

naturality

t . traverse f = traverse (t . f) for every applicative transformation t

identity

traverse Identity = Identity

composition

traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f

A definition of sequenceA must satisfy the following laws:

naturality

t . sequenceA = sequenceA . fmap t for every applicative transformation t

identity

sequenceA . fmap Identity = Identity

composition

sequenceA . fmap Compose = Compose . fmap sequenceA . sequenceA

where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations, i.e.

• t (pure x) = pure x

• t (x <*> y) = t x <*> t y

and the identity functor Identity and composition of functors Compose are defined as

  newtype Identity a = Identity a

  instance Functor Identity where
    fmap f (Identity x) = Identity (f x)

  instance Applicative Identity where
    pure x = Identity x
    Identity f <*> Identity x = Identity (f x)

  newtype Compose f g a = Compose (f (g a))

  instance (Functor f, Functor g) => Functor (Compose f g) where
    fmap f (Compose x) = Compose (fmap (fmap f) x)

  instance (Applicative f, Applicative g) => Applicative (Compose f g) where
    pure x = Compose (pure (pure x))
    Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)

(The naturality law is implied by parametricity.)

Instances are similar to Functor, e.g. given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Traversable Tree where
   traverse f Empty = pure Empty
   traverse f (Leaf x) = Leaf <$> f x
   traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r

This is suitable even for abstract types, as the laws for <*> imply a form of associativity.

The superclass instances should satisfy the following:

• In the Functor instance, fmap should be equivalent to traversal with the identity applicative functor (fmapDefault).
• In the Foldable instance, foldMap should be equivalent to traversal with a constant applicative functor (foldMapDefault).

Minimal complete definition

traverse | sequenceA

Instances

Traversable []

Since: base-2.1

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> [a] -> f [b]

sequenceA :: Applicative f => [f a] -> f [a]

mapM :: Monad m => (a -> m b) -> [a] -> m [b]

sequence :: Monad m => [m a] -> m [a]

Traversable Maybe

Since: base-2.1

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b)

sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a)

mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b)

sequence :: Monad m => Maybe (m a) -> m (Maybe a)

Traversable Par1

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Par1 a -> f (Par1 b)

sequenceA :: Applicative f => Par1 (f a) -> f (Par1 a)

mapM :: Monad m => (a -> m b) -> Par1 a -> m (Par1 b)

sequence :: Monad m => Par1 (m a) -> m (Par1 a)

Traversable Complex

Defined in Data.Complex

Methods

traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b)

sequenceA :: Applicative f => Complex (f a) -> f (Complex a)

mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b)

sequence :: Monad m => Complex (m a) -> m (Complex a)

Traversable Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b)

sequenceA :: Applicative f => Min (f a) -> f (Min a)

mapM :: Monad m => (a -> m b) -> Min a -> m (Min b)

sequence :: Monad m => Min (m a) -> m (Min a)

Traversable Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b)

sequenceA :: Applicative f => Max (f a) -> f (Max a)

mapM :: Monad m => (a -> m b) -> Max a -> m (Max b)

sequence :: Monad m => Max (m a) -> m (Max a)

Traversable First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

traverse :: Applicative f => (a -> f b) -> First a -> f (First b)

sequenceA :: Applicative f => First (f a) -> f (First a)

mapM :: Monad m => (a -> m b) -> First a -> m (First b)

sequence :: Monad m => First (m a) -> m (First a)

Traversable Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b)

sequenceA :: Applicative f => Last (f a) -> f (Last a)

mapM :: Monad m => (a -> m b) -> Last a -> m (Last b)

sequence :: Monad m => Last (m a) -> m (Last a)

Traversable Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b)

sequenceA :: Applicative f => Option (f a) -> f (Option a)

mapM :: Monad m => (a -> m b) -> Option a -> m (Option b)

sequence :: Monad m => Option (m a) -> m (Option a)

Traversable ZipList

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b)

sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a)

mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b)

sequence :: Monad m => ZipList (m a) -> m (ZipList a)

Traversable Identity

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b)

sequenceA :: Applicative f => Identity (f a) -> f (Identity a)

mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b)

sequence :: Monad m => Identity (m a) -> m (Identity a)

Traversable First

Since: base-4.8.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> First a -> f (First b)

sequenceA :: Applicative f => First (f a) -> f (First a)

mapM :: Monad m => (a -> m b) -> First a -> m (First b)

sequence :: Monad m => First (m a) -> m (First a)

Traversable Last

Since: base-4.8.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b)

sequenceA :: Applicative f => Last (f a) -> f (Last a)

mapM :: Monad m => (a -> m b) -> Last a -> m (Last b)

sequence :: Monad m => Last (m a) -> m (Last a)

Traversable Dual

Since: base-4.8.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b)

sequenceA :: Applicative f => Dual (f a) -> f (Dual a)

mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b)

sequence :: Monad m => Dual (m a) -> m (Dual a)

Traversable Sum

Since: base-4.8.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b)

sequenceA :: Applicative f => Sum (f a) -> f (Sum a)

mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b)

sequence :: Monad m => Sum (m a) -> m (Sum a)

Traversable Product

Since: base-4.8.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b)

sequenceA :: Applicative f => Product (f a) -> f (Product a)

mapM :: Monad m => (a -> m b) -> Product a -> m (Product b)

sequence :: Monad m => Product (m a) -> m (Product a)

Traversable NonEmpty

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b)

sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a)

mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b)

sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a)

Traversable IntMap

Defined in Data.IntMap.Internal

Methods

traverse :: Applicative f => (a -> f b) -> IntMap a -> f (IntMap b)

sequenceA :: Applicative f => IntMap (f a) -> f (IntMap a)

mapM :: Monad m => (a -> m b) -> IntMap a -> m (IntMap b)

sequence :: Monad m => IntMap (m a) -> m (IntMap a)

Traversable Tree

Defined in Data.Tree

Methods

traverse :: Applicative f => (a -> f b) -> Tree a -> f (Tree b)

sequenceA :: Applicative f => Tree (f a) -> f (Tree a)

mapM :: Monad m => (a -> m b) -> Tree a -> m (Tree b)

sequence :: Monad m => Tree (m a) -> m (Tree a)

Traversable Seq

Defined in Data.Sequence.Internal

Methods

traverse :: Applicative f => (a -> f b) -> Seq a -> f (Seq b)

sequenceA :: Applicative f => Seq (f a) -> f (Seq a)

mapM :: Monad m => (a -> m b) -> Seq a -> m (Seq b)

sequence :: Monad m => Seq (m a) -> m (Seq a)

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 Digit

Defined in Data.Sequence.Internal

Methods

traverse :: Applicative f => (a -> f b) -> Digit a -> f (Digit b)

sequenceA :: Applicative f => Digit (f a) -> f (Digit a)

mapM :: Monad m => (a -> m b) -> Digit a -> m (Digit b)

sequence :: Monad m => Digit (m a) -> m (Digit a)

Traversable Node

Defined in Data.Sequence.Internal

Methods

traverse :: Applicative f => (a -> f b) -> Node a -> f (Node b)

sequenceA :: Applicative f => Node (f a) -> f (Node a)

mapM :: Monad m => (a -> m b) -> Node a -> m (Node b)

sequence :: Monad m => Node (m a) -> m (Node a)

Traversable Elem

Defined in Data.Sequence.Internal

Methods

traverse :: Applicative f => (a -> f b) -> Elem a -> f (Elem b)

sequenceA :: Applicative f => Elem (f a) -> f (Elem a)

mapM :: Monad m => (a -> m b) -> Elem a -> m (Elem b)

sequence :: Monad m => Elem (m a) -> m (Elem a)

Traversable ViewL

Defined in Data.Sequence.Internal

Methods

traverse :: Applicative f => (a -> f b) -> ViewL a -> f (ViewL b)

sequenceA :: Applicative f => ViewL (f a) -> f (ViewL a)

mapM :: Monad m => (a -> m b) -> ViewL a -> m (ViewL b)

sequence :: Monad m => ViewL (m a) -> m (ViewL a)

Traversable ViewR

Defined in Data.Sequence.Internal

Methods

traverse :: Applicative f => (a -> f b) -> ViewR a -> f (ViewR b)

sequenceA :: Applicative f => ViewR (f a) -> f (ViewR a)

mapM :: Monad m => (a -> m b) -> ViewR a -> m (ViewR b)

sequence :: Monad m => ViewR (m a) -> m (ViewR a)

Traversable I

Defined in Data.Comp.Multi.HFunctor

Methods

traverse :: Applicative f => (a -> f b) -> I a -> f (I b)

sequenceA :: Applicative f => I (f a) -> f (I a)

mapM :: Monad m => (a -> m b) -> I a -> m (I b)

sequence :: Monad m => I (m a) -> m (I a)

Traversable (Either a)

Since: base-4.7.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b)

sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0)

mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b)

sequence :: Monad m => Either a (m a0) -> m (Either a a0)

Traversable (V1 :: * -> *)

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b)

sequenceA :: Applicative f => V1 (f a) -> f (V1 a)

mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b)

sequence :: Monad m => V1 (m a) -> m (V1 a)

Traversable (U1 :: * -> *)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> U1 a -> f (U1 b)

sequenceA :: Applicative f => U1 (f a) -> f (U1 a)

mapM :: Monad m => (a -> m b) -> U1 a -> m (U1 b)

sequence :: Monad m => U1 (m a) -> m (U1 a)

Traversable ((,) a)

Since: base-4.7.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a0 -> f b) -> (a, a0) -> f (a, b)

sequenceA :: Applicative f => (a, f a0) -> f (a, a0)

mapM :: Monad m => (a0 -> m b) -> (a, a0) -> m (a, b)

sequence :: Monad m => (a, m a0) -> m (a, a0)

Ix i => Traversable (Array i)

Since: base-2.1

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b)

sequenceA :: Applicative f => Array i (f a) -> f (Array i a)

mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b)

sequence :: Monad m => Array i (m a) -> m (Array i a)

Traversable (Arg a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b)

sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0)

mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b)

sequence :: Monad m => Arg a (m a0) -> m (Arg a a0)

Traversable (Proxy :: * -> *)

Since: base-4.7.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b)

sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a)

mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b)

sequence :: Monad m => Proxy (m a) -> m (Proxy a)

Traversable (Map k)

Defined in Data.Map.Internal

Methods

traverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b)

sequenceA :: Applicative f => Map k (f a) -> f (Map k a)

mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b)

sequence :: Monad m => Map k (m a) -> m (Map k a)

Traversable f => Traversable (ListT f)

Defined in Control.Monad.Trans.List

Methods

traverse :: Applicative f0 => (a -> f0 b) -> ListT f a -> f0 (ListT f b)

sequenceA :: Applicative f0 => ListT f (f0 a) -> f0 (ListT f a)

mapM :: Monad m => (a -> m b) -> ListT f a -> m (ListT f b)

sequence :: Monad m => ListT f (m a) -> m (ListT f a)

Traversable f => Traversable (MaybeT f)

Defined in Control.Monad.Trans.Maybe

Methods

traverse :: Applicative f0 => (a -> f0 b) -> MaybeT f a -> f0 (MaybeT f b)

sequenceA :: Applicative f0 => MaybeT f (f0 a) -> f0 (MaybeT f a)

mapM :: Monad m => (a -> m b) -> MaybeT f a -> m (MaybeT f b)

sequence :: Monad m => MaybeT f (m a) -> m (MaybeT f a)

Traversable (NumMap k)

Defined in Data.Comp.Mapping

Methods

traverse :: Applicative f => (a -> f b) -> NumMap k a -> f (NumMap k b)

sequenceA :: Applicative f => NumMap k (f a) -> f (NumMap k a)

mapM :: Monad m => (a -> m b) -> NumMap k a -> m (NumMap k b)

sequence :: Monad m => NumMap k (m a) -> m (NumMap k a)

Traversable (K a)

Defined in Data.Comp.Multi.HFunctor

Methods

traverse :: Applicative f => (a0 -> f b) -> K a a0 -> f (K a b)

sequenceA :: Applicative f => K a (f a0) -> f (K a a0)

mapM :: Monad m => (a0 -> m b) -> K a a0 -> m (K a b)

sequence :: Monad m => K a (m a0) -> m (K a a0)

Traversable f => Traversable (Rec1 f)

Defined in Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b)

sequenceA :: Applicative f0 => Rec1 f (f0 a) -> f0 (Rec1 f a)

mapM :: Monad m => (a -> m b) -> Rec1 f a -> m (Rec1 f b)

sequence :: Monad m => Rec1 f (m a) -> m (Rec1 f a)

Traversable (URec Char :: * -> *)

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> URec Char a -> f (URec Char b)

sequenceA :: Applicative f => URec Char (f a) -> f (URec Char a)

mapM :: Monad m => (a -> m b) -> URec Char a -> m (URec Char b)

sequence :: Monad m => URec Char (m a) -> m (URec Char a)

Traversable (URec Double :: * -> *)

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b)

sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a)

mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b)

sequence :: Monad m => URec Double (m a) -> m (URec Double a)

Traversable (URec Float :: * -> *)

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b)

sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a)

mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b)

sequence :: Monad m => URec Float (m a) -> m (URec Float a)

Traversable (URec Int :: * -> *)

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b)

sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a)

mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b)

sequence :: Monad m => URec Int (m a) -> m (URec Int a)

Traversable (URec Word :: * -> *)

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> URec Word a -> f (URec Word b)

sequenceA :: Applicative f => URec Word (f a) -> f (URec Word a)

mapM :: Monad m => (a -> m b) -> URec Word a -> m (URec Word b)

sequence :: Monad m => URec Word (m a) -> m (URec Word a)

Traversable (URec (Ptr ()) :: * -> *)

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> URec (Ptr ()) a -> f (URec (Ptr ()) b)

sequenceA :: Applicative f => URec (Ptr ()) (f a) -> f (URec (Ptr ()) a)

mapM :: Monad m => (a -> m b) -> URec (Ptr ()) a -> m (URec (Ptr ()) b)

sequence :: Monad m => URec (Ptr ()) (m a) -> m (URec (Ptr ()) a)

Traversable (Const m :: * -> *)

Since: base-4.7.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b)

sequenceA :: Applicative f => Const m (f a) -> f (Const m a)

mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b)

sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a)

Traversable f => Traversable (IdentityT f)

Defined in Control.Monad.Trans.Identity

Methods

traverse :: Applicative f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b)

sequenceA :: Applicative f0 => IdentityT f (f0 a) -> f0 (IdentityT f a)

mapM :: Monad m => (a -> m b) -> IdentityT f a -> m (IdentityT f b)

sequence :: Monad m => IdentityT f (m a) -> m (IdentityT f a)

Traversable f => Traversable (ErrorT e f)

Defined in Control.Monad.Trans.Error

Methods

traverse :: Applicative f0 => (a -> f0 b) -> ErrorT e f a -> f0 (ErrorT e f b)

sequenceA :: Applicative f0 => ErrorT e f (f0 a) -> f0 (ErrorT e f a)

mapM :: Monad m => (a -> m b) -> ErrorT e f a -> m (ErrorT e f b)

sequence :: Monad m => ErrorT e f (m a) -> m (ErrorT e f a)

Traversable f => Traversable (ExceptT e f)

Defined in Control.Monad.Trans.Except

Methods

traverse :: Applicative f0 => (a -> f0 b) -> ExceptT e f a -> f0 (ExceptT e f b)

sequenceA :: Applicative f0 => ExceptT e f (f0 a) -> f0 (ExceptT e f a)

mapM :: Monad m => (a -> m b) -> ExceptT e f a -> m (ExceptT e f b)

sequence :: Monad m => ExceptT e f (m a) -> m (ExceptT e f a)

Traversable f => Traversable (WriterT w f)

Defined in Control.Monad.Trans.Writer.Lazy

Methods

traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b)

sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a)

mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b)

sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a)

Traversable f => Traversable (WriterT w f)

Defined in Control.Monad.Trans.Writer.Strict

Methods

traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b)

sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a)

mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b)

sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a)

Traversable (Constant a :: * -> *)

Defined in Data.Functor.Constant

Methods

traverse :: Applicative f => (a0 -> f b) -> Constant a a0 -> f (Constant a b)

sequenceA :: Applicative f => Constant a (f a0) -> f (Constant a a0)

mapM :: Monad m => (a0 -> m b) -> Constant a a0 -> m (Constant a b)

sequence :: Monad m => Constant a (m a0) -> m (Constant a a0)

Traversable f => Traversable (Cxt h f)

Defined in Data.Comp.Term

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Cxt h f a -> f0 (Cxt h f b)

sequenceA :: Applicative f0 => Cxt h f (f0 a) -> f0 (Cxt h f a)

mapM :: Monad m => (a -> m b) -> Cxt h f a -> m (Cxt h f b)

sequence :: Monad m => Cxt h f (m a) -> m (Cxt h f a)

Traversable (K1 i c :: * -> *)

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> K1 i c a -> f (K1 i c b)

sequenceA :: Applicative f => K1 i c (f a) -> f (K1 i c a)

mapM :: Monad m => (a -> m b) -> K1 i c a -> m (K1 i c b)

sequence :: Monad m => K1 i c (m a) -> m (K1 i c a)

(Traversable f, Traversable g) => Traversable (f :+: g)

Defined in Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b)

sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a)

mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b)

sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a)

(Traversable f, Traversable g) => Traversable (f :*: g)

Defined in Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> (f :*: g) a -> f0 ((f :*: g) b)

sequenceA :: Applicative f0 => (f :*: g) (f0 a) -> f0 ((f :*: g) a)

mapM :: Monad m => (a -> m b) -> (f :*: g) a -> m ((f :*: g) b)

sequence :: Monad m => (f :*: g) (m a) -> m ((f :*: g) a)

(Traversable f, Traversable g) => Traversable (Product f g)

Since: base-4.9.0.0

Defined in Data.Functor.Product

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b)

sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a)

mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b)

sequence :: Monad m => Product f g (m a) -> m (Product f g a)

(Traversable f, Traversable g) => Traversable (Sum f g)

Since: base-4.9.0.0

Defined in Data.Functor.Sum

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b)

sequenceA :: Applicative f0 => Sum f g (f0 a) -> f0 (Sum f g a)

mapM :: Monad m => (a -> m b) -> Sum f g a -> m (Sum f g b)

sequence :: Monad m => Sum f g (m a) -> m (Sum f g a)

Traversable f => Traversable (f :&: a)

Defined in Data.Comp.Ops

Methods

traverse :: Applicative f0 => (a0 -> f0 b) -> (f :&: a) a0 -> f0 ((f :&: a) b)

sequenceA :: Applicative f0 => (f :&: a) (f0 a0) -> f0 ((f :&: a) a0)

mapM :: Monad m => (a0 -> m b) -> (f :&: a) a0 -> m ((f :&: a) b)

sequence :: Monad m => (f :&: a) (m a0) -> m ((f :&: a) a0)

(Traversable f, Traversable g) => Traversable (f :*: g)

Defined in Data.Comp.Ops

Methods

traverse :: Applicative f0 => (a -> f0 b) -> (f :*: g) a -> f0 ((f :*: g) b)

sequenceA :: Applicative f0 => (f :*: g) (f0 a) -> f0 ((f :*: g) a)

mapM :: Monad m => (a -> m b) -> (f :*: g) a -> m ((f :*: g) b)

sequence :: Monad m => (f :*: g) (m a) -> m ((f :*: g) a)

(Traversable f, Traversable g) => Traversable (f :+: g)

Defined in Data.Comp.Ops

Methods

traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b)

sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a)

mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b)

sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a)

Traversable f => Traversable (M1 i c f)

Defined in Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b)

sequenceA :: Applicative f0 => M1 i c f (f0 a) -> f0 (M1 i c f a)

mapM :: Monad m => (a -> m b) -> M1 i c f a -> m (M1 i c f b)

sequence :: Monad m => M1 i c f (m a) -> m (M1 i c f a)

(Traversable f, Traversable g) => Traversable (f :.: g)

Defined in Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b)

sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a)

mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b)

sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a)

(Traversable f, Traversable g) => Traversable (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b)

sequenceA :: Applicative f0 => Compose f g (f0 a) -> f0 (Compose f g a)

mapM :: Monad m => (a -> m b) -> Compose f g a -> m (Compose f g b)

sequence :: Monad m => Compose f g (m a) -> m (Compose f g a)

makeTraversable :: Name -> Q [Dec]

Derive an instance of Traversable for a type constructor of any first-order kind taking at least one argument.

HaskellStrict

makeHaskellStrict :: Name -> Q [Dec]

Derive an instance of HaskellStrict for a type constructor of any first-order kind taking at least one argument.

haskellStrict :: (Monad m, HaskellStrict f, f :<: (m :+: g)) => f (TermT m g) -> TermT m g

haskellStrict' :: (Monad m, HaskellStrict f, f :<: (m :+: g)) => f (TermT m g) -> TermT m g

Arbitrary

class ArbitraryF f where

Signature arbitration. An instance ArbitraryF f gives rise to an instance Arbitrary (Term f).

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (f v))]

arbitraryF :: Arbitrary v => Gen (f v)

shrinkF :: Arbitrary v => f v -> [f v]

Instances

ArbitraryF []

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen [v])]

arbitraryF :: Arbitrary v => Gen [v]

shrinkF :: Arbitrary v => [v] -> [[v]]

ArbitraryF Maybe

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (Maybe v))]

arbitraryF :: Arbitrary v => Gen (Maybe v)

shrinkF :: Arbitrary v => Maybe v -> [Maybe v]

Arbitrary b => ArbitraryF ((,) b)

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (b, v))]

arbitraryF :: Arbitrary v => Gen (b, v)

shrinkF :: Arbitrary v => (b, v) -> [(b, v)]

ArbitraryF f => ArbitraryF (Context f)

This lifts instances of ArbitraryF to instances of ArbitraryF for the corresponding context functor.

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (Context f v))]

arbitraryF :: Arbitrary v => Gen (Context f v)

shrinkF :: Arbitrary v => Context f v -> [Context f v]

(Arbitrary b, Arbitrary c) => ArbitraryF ((,,) b c)

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (b, c, v))]

arbitraryF :: Arbitrary v => Gen (b, c, v)

shrinkF :: Arbitrary v => (b, c, v) -> [(b, c, v)]

(Arbitrary b, Arbitrary c, Arbitrary d) => ArbitraryF ((,,,) b c d)

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (b, c, d, v))]

arbitraryF :: Arbitrary v => Gen (b, c, d, v)

shrinkF :: Arbitrary v => (b, c, d, v) -> [(b, c, d, v)]

(ArbitraryF f, Arbitrary p) => ArbitraryF (f :&: p)

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen ((f :&: p) v))]

arbitraryF :: Arbitrary v => Gen ((f :&: p) v)

shrinkF :: Arbitrary v => (f :&: p) v -> [(f :&: p) v]

(ArbitraryF f, ArbitraryF g) => ArbitraryF (f :+: g)

Instances of ArbitraryF are closed under forming sums.

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen ((f :+: g) v))]

arbitraryF :: Arbitrary v => Gen ((f :+: g) v)

shrinkF :: Arbitrary v => (f :+: g) v -> [(f :+: g) v]

(Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e) => ArbitraryF ((,,,,) b c d e)

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (b, c, d, e, v))]

arbitraryF :: Arbitrary v => Gen (b, c, d, e, v)

shrinkF :: Arbitrary v => (b, c, d, e, v) -> [(b, c, d, e, v)]

(Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f) => ArbitraryF ((,,,,,) b c d e f)

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (b, c, d, e, f, v))]

arbitraryF :: Arbitrary v => Gen (b, c, d, e, f, v)

shrinkF :: Arbitrary v => (b, c, d, e, f, v) -> [(b, c, d, e, f, v)]

(Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f, Arbitrary g) => ArbitraryF ((,,,,,,) b c d e f g)

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (b, c, d, e, f, g, v))]

arbitraryF :: Arbitrary v => Gen (b, c, d, e, f, g, v)

shrinkF :: Arbitrary v => (b, c, d, e, f, g, v) -> [(b, c, d, e, f, g, v)]

(Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f, Arbitrary g, Arbitrary h) => ArbitraryF ((,,,,,,,) b c d e f g h)

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (b, c, d, e, f, g, h, v))]

arbitraryF :: Arbitrary v => Gen (b, c, d, e, f, g, h, v)

shrinkF :: Arbitrary v => (b, c, d, e, f, g, h, v) -> [(b, c, d, e, f, g, h, v)]

(Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f, Arbitrary g, Arbitrary h, Arbitrary i) => ArbitraryF ((,,,,,,,,) b c d e f g h i)

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (b, c, d, e, f, g, h, i, v))]

arbitraryF :: Arbitrary v => Gen (b, c, d, e, f, g, h, i, v)

shrinkF :: Arbitrary v => (b, c, d, e, f, g, h, i, v) -> [(b, c, d, e, f, g, h, i, v)]

(Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f, Arbitrary g, Arbitrary h, Arbitrary i, Arbitrary j) => ArbitraryF ((,,,,,,,,,) b c d e f g h i j)

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (b, c, d, e, f, g, h, i, j, v))]

arbitraryF :: Arbitrary v => Gen (b, c, d, e, f, g, h, i, j, v)

shrinkF :: Arbitrary v => (b, c, d, e, f, g, h, i, j, v) -> [(b, c, d, e, f, g, h, i, j, v)]

makeArbitraryF :: Name -> Q [Dec]

Derive an instance of ArbitraryF for a type constructor of any first-order kind taking at least one argument. It is necessary that all types that are used by the data type definition are themselves instances of Arbitrary.

class Arbitrary a where

Random generation and shrinking of values.

QuickCheck provides Arbitrary instances for most types in base, except those which incur extra dependencies. For a wider range of Arbitrary instances see the quickcheck-instances package.

Minimal complete definition

arbitrary

Methods

arbitrary :: Gen a

A generator for values of the given type.

It is worth spending time thinking about what sort of test data you want - good generators are often the difference between finding bugs and not finding them. You can use sample, label and classify to check the quality of your test data.

There is no generic arbitrary implementation included because we don't know how to make a high-quality one. If you want one, consider using the testing-feat or generic-random packages.

The QuickCheck manual goes into detail on how to write good generators. Make sure to look at it, especially if your type is recursive!

shrink :: a -> [a]

Produces a (possibly) empty list of all the possible immediate shrinks of the given value.

The default implementation returns the empty list, so will not try to shrink the value. If your data type has no special invariants, you can enable shrinking by defining shrink = genericShrink, but by customising the behaviour of shrink you can often get simpler counterexamples.

Most implementations of shrink should try at least three things:

1. Shrink a term to any of its immediate subterms. You can use subterms to do this.
2. Recursively apply shrink to all immediate subterms. You can use recursivelyShrink to do this.
3. Type-specific shrinkings such as replacing a constructor by a simpler constructor.

For example, suppose we have the following implementation of binary trees:

data Tree a = Nil | Branch a (Tree a) (Tree a)

We can then define shrink as follows:

shrink Nil = []
shrink (Branch x l r) =
  -- shrink Branch to Nil
  [Nil] ++
  -- shrink to subterms
  [l, r] ++
  -- recursively shrink subterms
  [Branch x' l' r' | (x', l', r') <- shrink (x, l, r)]

There are a couple of subtleties here:

• QuickCheck tries the shrinking candidates in the order they appear in the list, so we put more aggressive shrinking steps (such as replacing the whole tree by Nil) before smaller ones (such as recursively shrinking the subtrees).
• It is tempting to write the last line as [Branch x' l' r' | x' <- shrink x, l' <- shrink l, r' <- shrink r] but this is the wrong thing! It will force QuickCheck to shrink x, l and r in tandem, and shrinking will stop once one of the three is fully shrunk.

There is a fair bit of boilerplate in the code above. We can avoid it with the help of some generic functions. The function genericShrink tries shrinking a term to all of its subterms and, failing that, recursively shrinks the subterms. Using it, we can define shrink as:

shrink x = shrinkToNil x ++ genericShrink x
  where
    shrinkToNil Nil = []
    shrinkToNil (Branch _ l r) = [Nil]

genericShrink is a combination of subterms, which shrinks a term to any of its subterms, and recursivelyShrink, which shrinks all subterms of a term. These may be useful if you need a bit more control over shrinking than genericShrink gives you.

A final gotcha: we cannot define shrink as simply shrink x = Nil:genericShrink x as this shrinks Nil to Nil, and shrinking will go into an infinite loop.

If all this leaves you bewildered, you might try shrink = genericShrink to begin with, after deriving Generic for your type. However, if your data type has any special invariants, you will need to check that genericShrink can't break those invariants.

Instances

Arbitrary Bool

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Bool

shrink :: Bool -> [Bool]

Arbitrary Char

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Char

shrink :: Char -> [Char]

Arbitrary Double

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Double

shrink :: Double -> [Double]

Arbitrary Float

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Float

shrink :: Float -> [Float]

Arbitrary Int

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Int

shrink :: Int -> [Int]

Arbitrary Int8

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Int8

shrink :: Int8 -> [Int8]

Arbitrary Int16

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Int16

shrink :: Int16 -> [Int16]

Arbitrary Int32

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Int32

shrink :: Int32 -> [Int32]

Arbitrary Int64

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Int64

shrink :: Int64 -> [Int64]

Arbitrary Integer

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Integer

shrink :: Integer -> [Integer]

Arbitrary Ordering

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Ordering

shrink :: Ordering -> [Ordering]

Arbitrary Word

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Word

shrink :: Word -> [Word]

Arbitrary Word8

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Word8

shrink :: Word8 -> [Word8]

Arbitrary Word16

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Word16

shrink :: Word16 -> [Word16]

Arbitrary Word32

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Word32

shrink :: Word32 -> [Word32]

Arbitrary Word64

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Word64

shrink :: Word64 -> [Word64]

Arbitrary ()

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen ()

shrink :: () -> [()]

Arbitrary Version

Generates Version with non-empty non-negative versionBranch, and empty versionTags

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Version

shrink :: Version -> [Version]

Arbitrary QCGen

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen QCGen

shrink :: QCGen -> [QCGen]

Arbitrary ASCIIString

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen ASCIIString

shrink :: ASCIIString -> [ASCIIString]

Arbitrary UnicodeString

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen UnicodeString

shrink :: UnicodeString -> [UnicodeString]

Arbitrary PrintableString

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen PrintableString

shrink :: PrintableString -> [PrintableString]

Arbitrary ExitCode

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen ExitCode

shrink :: ExitCode -> [ExitCode]

Arbitrary All

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen All

shrink :: All -> [All]

Arbitrary Any

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Any

shrink :: Any -> [Any]

Arbitrary CChar

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CChar

shrink :: CChar -> [CChar]

Arbitrary CSChar

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CSChar

shrink :: CSChar -> [CSChar]

Arbitrary CUChar

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CUChar

shrink :: CUChar -> [CUChar]

Arbitrary CShort

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CShort

shrink :: CShort -> [CShort]

Arbitrary CUShort

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CUShort

shrink :: CUShort -> [CUShort]

Arbitrary CInt

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CInt

shrink :: CInt -> [CInt]

Arbitrary CUInt

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CUInt

shrink :: CUInt -> [CUInt]

Arbitrary CLong

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CLong

shrink :: CLong -> [CLong]

Arbitrary CULong

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CULong

shrink :: CULong -> [CULong]

Arbitrary CLLong

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CLLong

shrink :: CLLong -> [CLLong]

Arbitrary CULLong

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CULLong

shrink :: CULLong -> [CULLong]

Arbitrary CFloat

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CFloat

shrink :: CFloat -> [CFloat]

Arbitrary CDouble

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CDouble

shrink :: CDouble -> [CDouble]

Arbitrary CPtrdiff

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CPtrdiff

shrink :: CPtrdiff -> [CPtrdiff]

Arbitrary CSize

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CSize

shrink :: CSize -> [CSize]

Arbitrary CWchar

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CWchar

shrink :: CWchar -> [CWchar]

Arbitrary CSigAtomic

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CSigAtomic

shrink :: CSigAtomic -> [CSigAtomic]

Arbitrary CClock

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CClock

shrink :: CClock -> [CClock]

Arbitrary CTime

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CTime

shrink :: CTime -> [CTime]

Arbitrary CUSeconds

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CUSeconds

shrink :: CUSeconds -> [CUSeconds]

Arbitrary CSUSeconds

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CSUSeconds

shrink :: CSUSeconds -> [CSUSeconds]

Arbitrary CIntPtr

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CIntPtr

shrink :: CIntPtr -> [CIntPtr]

Arbitrary CUIntPtr

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CUIntPtr

shrink :: CUIntPtr -> [CUIntPtr]

Arbitrary CIntMax

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CIntMax

shrink :: CIntMax -> [CIntMax]

Arbitrary CUIntMax

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen CUIntMax

shrink :: CUIntMax -> [CUIntMax]

Arbitrary IntSet

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen IntSet

shrink :: IntSet -> [IntSet]

Arbitrary a => Arbitrary [a]

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen [a]

shrink :: [a] -> [[a]]

Arbitrary a => Arbitrary (Maybe a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Maybe a)

shrink :: Maybe a -> [Maybe a]

Integral a => Arbitrary (Ratio a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Ratio a)

shrink :: Ratio a -> [Ratio a]

Arbitrary a => Arbitrary (Blind a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (Blind a)

shrink :: Blind a -> [Blind a]

Arbitrary a => Arbitrary (Fixed a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (Fixed a)

shrink :: Fixed a -> [Fixed a]

(Ord a, Arbitrary a) => Arbitrary (OrderedList a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (OrderedList a)

shrink :: OrderedList a -> [OrderedList a]

Arbitrary a => Arbitrary (NonEmptyList a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (NonEmptyList a)

shrink :: NonEmptyList a -> [NonEmptyList a]

Arbitrary a => Arbitrary (InfiniteList a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (InfiniteList a)

shrink :: InfiniteList a -> [InfiniteList a]

(Arbitrary a, Ord a) => Arbitrary (SortedList a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (SortedList a)

shrink :: SortedList a -> [SortedList a]

(Num a, Ord a, Arbitrary a) => Arbitrary (Positive a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (Positive a)

shrink :: Positive a -> [Positive a]

(Num a, Eq a, Arbitrary a) => Arbitrary (NonZero a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (NonZero a)

shrink :: NonZero a -> [NonZero a]

(Num a, Ord a, Arbitrary a) => Arbitrary (NonNegative a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (NonNegative a)

shrink :: NonNegative a -> [NonNegative a]

(Integral a, Bounded a) => Arbitrary (Large a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (Large a)

shrink :: Large a -> [Large a]

Integral a => Arbitrary (Small a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (Small a)

shrink :: Small a -> [Small a]

Arbitrary a => Arbitrary (Shrink2 a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (Shrink2 a)

shrink :: Shrink2 a -> [Shrink2 a]

Arbitrary a => Arbitrary (Smart a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (Smart a)

shrink :: Smart a -> [Smart a]

(RealFloat a, Arbitrary a) => Arbitrary (Complex a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Complex a)

shrink :: Complex a -> [Complex a]

HasResolution a => Arbitrary (Fixed a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Fixed a)

shrink :: Fixed a -> [Fixed a]

Arbitrary a => Arbitrary (ZipList a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (ZipList a)

shrink :: ZipList a -> [ZipList a]

Arbitrary a => Arbitrary (Identity a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Identity a)

shrink :: Identity a -> [Identity a]

Arbitrary a => Arbitrary (First a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (First a)

shrink :: First a -> [First a]

Arbitrary a => Arbitrary (Last a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Last a)

shrink :: Last a -> [Last a]

Arbitrary a => Arbitrary (Dual a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Dual a)

shrink :: Dual a -> [Dual a]

(Arbitrary a, CoArbitrary a) => Arbitrary (Endo a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Endo a)

shrink :: Endo a -> [Endo a]

Arbitrary a => Arbitrary (Sum a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Sum a)

shrink :: Sum a -> [Sum a]

Arbitrary a => Arbitrary (Product a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Product a)

shrink :: Product a -> [Product a]

Arbitrary a => Arbitrary (IntMap a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (IntMap a)

shrink :: IntMap a -> [IntMap a]

Arbitrary a => Arbitrary (Seq a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Seq a)

shrink :: Seq a -> [Seq a]

(Ord a, Arbitrary a) => Arbitrary (Set a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Set a)

shrink :: Set a -> [Set a]

ArbitraryF f => Arbitrary (Term f)

This lifts instances of ArbitraryF to instances of Arbitrary for the corresponding term type.

Defined in Data.Comp.Arbitrary

Methods

arbitrary :: Gen (Term f)

shrink :: Term f -> [Term f]

Arbitrary a => Arbitrary (InfiniteListInternalData a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (InfiniteListInternalData a)

shrink :: InfiniteListInternalData a -> [InfiniteListInternalData a]

(CoArbitrary a, Arbitrary b) => Arbitrary (a -> b)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (a -> b)

shrink :: (a -> b) -> [a -> b]

(Arbitrary a, Arbitrary b) => Arbitrary (Either a b)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Either a b)

shrink :: Either a b -> [Either a b]

(Arbitrary a, Arbitrary b) => Arbitrary (a, b)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (a, b)

shrink :: (a, b) -> [(a, b)]

(Function a, CoArbitrary a, Arbitrary b) => Arbitrary (a :-> b)

Defined in Test.QuickCheck.Function

Methods

arbitrary :: Gen (a :-> b)

shrink :: (a :-> b) -> [a :-> b]

(Function a, CoArbitrary a, Arbitrary b) => Arbitrary (Fun a b)

Defined in Test.QuickCheck.Function

Methods

arbitrary :: Gen (Fun a b)

shrink :: Fun a b -> [Fun a b]

(Arbitrary a, ShrinkState s a) => Arbitrary (Shrinking s a)

Defined in Test.QuickCheck.Modifiers

Methods

arbitrary :: Gen (Shrinking s a)

shrink :: Shrinking s a -> [Shrinking s a]

Arbitrary (m a) => Arbitrary (WrappedMonad m a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (WrappedMonad m a)

shrink :: WrappedMonad m a -> [WrappedMonad m a]

(Ord k, Arbitrary k, Arbitrary v) => Arbitrary (Map k v)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Map k v)

shrink :: Map k v -> [Map k v]

(ArbitraryF f, Arbitrary a) => Arbitrary (Context f a)

This lifts instances of ArbitraryF to instances of Arbitrary for the corresponding context type.

Defined in Data.Comp.Arbitrary

Methods

arbitrary :: Gen (Context f a)

shrink :: Context f a -> [Context f a]

(Arbitrary a, Arbitrary b, Arbitrary c) => Arbitrary (a, b, c)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (a, b, c)

shrink :: (a, b, c) -> [(a, b, c)]

Arbitrary (a b c) => Arbitrary (WrappedArrow a b c)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (WrappedArrow a b c)

shrink :: WrappedArrow a b c -> [WrappedArrow a b c]

Arbitrary a => Arbitrary (Const a b)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Const a b)

shrink :: Const a b -> [Const a b]

Arbitrary (f a) => Arbitrary (Alt f a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Alt f a)

shrink :: Alt f a -> [Alt f a]

Arbitrary a => Arbitrary (Constant a b)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Constant a b)

shrink :: Constant a b -> [Constant a b]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d) => Arbitrary (a, b, c, d)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (a, b, c, d)

shrink :: (a, b, c, d) -> [(a, b, c, d)]

(Arbitrary1 f, Arbitrary1 g, Arbitrary a) => Arbitrary (Product f g a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Product f g a)

shrink :: Product f g a -> [Product f g a]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e) => Arbitrary (a, b, c, d, e)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (a, b, c, d, e)

shrink :: (a, b, c, d, e) -> [(a, b, c, d, e)]

(Arbitrary1 f, Arbitrary1 g, Arbitrary a) => Arbitrary (Compose f g a)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Compose f g a)

shrink :: Compose f g a -> [Compose f g a]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f) => Arbitrary (a, b, c, d, e, f)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (a, b, c, d, e, f)

shrink :: (a, b, c, d, e, f) -> [(a, b, c, d, e, f)]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f, Arbitrary g) => Arbitrary (a, b, c, d, e, f, g)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (a, b, c, d, e, f, g)

shrink :: (a, b, c, d, e, f, g) -> [(a, b, c, d, e, f, g)]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f, Arbitrary g, Arbitrary h) => Arbitrary (a, b, c, d, e, f, g, h)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (a, b, c, d, e, f, g, h)

shrink :: (a, b, c, d, e, f, g, h) -> [(a, b, c, d, e, f, g, h)]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f, Arbitrary g, Arbitrary h, Arbitrary i) => Arbitrary (a, b, c, d, e, f, g, h, i)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (a, b, c, d, e, f, g, h, i)

shrink :: (a, b, c, d, e, f, g, h, i) -> [(a, b, c, d, e, f, g, h, i)]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f, Arbitrary g, Arbitrary h, Arbitrary i, Arbitrary j) => Arbitrary (a, b, c, d, e, f, g, h, i, j)

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (a, b, c, d, e, f, g, h, i, j)

shrink :: (a, b, c, d, e, f, g, h, i, j) -> [(a, b, c, d, e, f, g, h, i, j)]

class NFData a where

A class of types that can be fully evaluated.

Since: deepseq-1.1.0.0

Methods

rnf :: a -> ()

rnf should reduce its argument to normal form (that is, fully evaluate all sub-components), and then return '()'.

Generic NFData deriving

Starting with GHC 7.2, you can automatically derive instances for types possessing a Generic instance.

Note: Generic1 can be auto-derived starting with GHC 7.4

{-# LANGUAGE DeriveGeneric #-}

import GHC.Generics (Generic, Generic1)
import Control.DeepSeq

data Foo a = Foo a String
             deriving (Eq, Generic, Generic1)

instance NFData a => NFData (Foo a)
instance NFData1 Foo

data Colour = Red | Green | Blue
              deriving Generic

instance NFData Colour

Starting with GHC 7.10, the example above can be written more concisely by enabling the new DeriveAnyClass extension:

{-# LANGUAGE DeriveGeneric, DeriveAnyClass #-}

import GHC.Generics (Generic)
import Control.DeepSeq

data Foo a = Foo a String
             deriving (Eq, Generic, Generic1, NFData, NFData1)

data Colour = Red | Green | Blue
              deriving (Generic, NFData)

Compatibility with previous deepseq versions

Prior to version 1.4.0.0, the default implementation of the rnf method was defined as

rnf a = seq a ()

However, starting with deepseq-1.4.0.0, the default implementation is based on DefaultSignatures allowing for more accurate auto-derived NFData instances. If you need the previously used exact default rnf method implementation semantics, use

instance NFData Colour where rnf x = seq x ()

or alternatively

instance NFData Colour where rnf = rwhnf

or

{-# LANGUAGE BangPatterns #-}
instance NFData Colour where rnf !_ = ()

Instances

NFData Bool

Defined in Control.DeepSeq

Methods

rnf :: Bool -> ()

NFData Char

Defined in Control.DeepSeq

Methods

rnf :: Char -> ()

NFData Double

Defined in Control.DeepSeq

Methods

rnf :: Double -> ()

NFData Float

Defined in Control.DeepSeq

Methods

rnf :: Float -> ()

NFData Int

Defined in Control.DeepSeq

Methods

rnf :: Int -> ()

NFData Int8

Defined in Control.DeepSeq

Methods

rnf :: Int8 -> ()

NFData Int16

Defined in Control.DeepSeq

Methods

rnf :: Int16 -> ()

NFData Int32

Defined in Control.DeepSeq

Methods

rnf :: Int32 -> ()

NFData Int64

Defined in Control.DeepSeq

Methods

rnf :: Int64 -> ()

NFData Integer

Defined in Control.DeepSeq

Methods

rnf :: Integer -> ()

NFData Natural

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Natural -> ()

NFData Ordering

Defined in Control.DeepSeq

Methods

rnf :: Ordering -> ()

NFData Word

Defined in Control.DeepSeq

Methods

rnf :: Word -> ()

NFData Word8

Defined in Control.DeepSeq

Methods

rnf :: Word8 -> ()

NFData Word16

Defined in Control.DeepSeq

Methods

rnf :: Word16 -> ()

NFData Word32

Defined in Control.DeepSeq

Methods

rnf :: Word32 -> ()

NFData Word64

Defined in Control.DeepSeq

Methods

rnf :: Word64 -> ()

NFData CallStack

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: CallStack -> ()

NFData ()

Defined in Control.DeepSeq

Methods

rnf :: () -> ()

NFData TyCon

NOTE: Only defined for base-4.8.0.0 and later

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: TyCon -> ()

NFData Version

Since: deepseq-1.3.0.0

Defined in Control.DeepSeq

Methods

rnf :: Version -> ()

NFData Void

Defined as rnf = absurd.

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Void -> ()

NFData Unique

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Unique -> ()

NFData ThreadId

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: ThreadId -> ()

NFData ExitCode

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: ExitCode -> ()

NFData TypeRep

NOTE: Only defined for base-4.8.0.0 and later

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: TypeRep -> ()

NFData All

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: All -> ()

NFData Any

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Any -> ()

NFData CChar

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CChar -> ()

NFData CSChar

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CSChar -> ()

NFData CUChar

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CUChar -> ()

NFData CShort

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CShort -> ()

NFData CUShort

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CUShort -> ()

NFData CInt

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CInt -> ()

NFData CUInt

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CUInt -> ()

NFData CLong

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CLong -> ()

NFData CULong

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CULong -> ()

NFData CLLong

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CLLong -> ()

NFData CULLong

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CULLong -> ()

NFData CBool

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

rnf :: CBool -> ()

NFData CFloat

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CFloat -> ()

NFData CDouble

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CDouble -> ()

NFData CPtrdiff

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CPtrdiff -> ()

NFData CSize

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CSize -> ()

NFData CWchar

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CWchar -> ()

NFData CSigAtomic

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CSigAtomic -> ()

NFData CClock

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CClock -> ()

NFData CTime

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CTime -> ()

NFData CUSeconds

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CUSeconds -> ()

NFData CSUSeconds

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CSUSeconds -> ()

NFData CFile

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CFile -> ()

NFData CFpos

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CFpos -> ()

NFData CJmpBuf

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CJmpBuf -> ()

NFData CIntPtr

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CIntPtr -> ()

NFData CUIntPtr

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CUIntPtr -> ()

NFData CIntMax

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CIntMax -> ()

NFData CUIntMax

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: CUIntMax -> ()

NFData Fingerprint

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Fingerprint -> ()

NFData SrcLoc

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: SrcLoc -> ()

NFData IntSet

Defined in Data.IntSet.Internal

Methods

rnf :: IntSet -> ()

NFData Doc

Defined in Text.PrettyPrint.HughesPJ

Methods

rnf :: Doc -> ()

NFData TextDetails

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

rnf :: TextDetails -> ()

NFData ZonedTime

Defined in Data.Time.LocalTime.Internal.ZonedTime

Methods

rnf :: ZonedTime -> ()

NFData LocalTime

Defined in Data.Time.LocalTime.Internal.LocalTime

Methods

rnf :: LocalTime -> ()

NFData a => NFData [a]

Defined in Control.DeepSeq

Methods

rnf :: [a] -> ()

NFData a => NFData (Maybe a)

Defined in Control.DeepSeq

Methods

rnf :: Maybe a -> ()

NFData a => NFData (Ratio a)

Defined in Control.DeepSeq

Methods

rnf :: Ratio a -> ()

NFData (Ptr a)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: Ptr a -> ()

NFData (FunPtr a)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: FunPtr a -> ()

NFData a => NFData (Complex a)

Defined in Control.DeepSeq

Methods

rnf :: Complex a -> ()

NFData (Fixed a)

Since: deepseq-1.3.0.0

Defined in Control.DeepSeq

Methods

rnf :: Fixed a -> ()

NFData a => NFData (Min a)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: Min a -> ()

NFData a => NFData (Max a)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: Max a -> ()

NFData a => NFData (First a)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: First a -> ()

NFData a => NFData (Last a)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: Last a -> ()

NFData m => NFData (WrappedMonoid m)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: WrappedMonoid m -> ()

NFData a => NFData (Option a)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: Option a -> ()

NFData (StableName a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: StableName a -> ()

NFData a => NFData (ZipList a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: ZipList a -> ()

NFData a => NFData (Identity a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Identity a -> ()

NFData (IORef a)

NOTE: Only strict in the reference and not the referenced value.

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: IORef a -> ()

NFData a => NFData (First a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: First a -> ()

NFData a => NFData (Last a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Last a -> ()

NFData a => NFData (Dual a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Dual a -> ()

NFData a => NFData (Sum a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Sum a -> ()

NFData a => NFData (Product a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Product a -> ()

NFData a => NFData (Down a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Down a -> ()

NFData (MVar a)

NOTE: Only strict in the reference and not the referenced value.

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: MVar a -> ()

NFData a => NFData (NonEmpty a)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: NonEmpty a -> ()

NFData a => NFData (IntMap a)

Defined in Data.IntMap.Internal

Methods

rnf :: IntMap a -> ()

NFData a => NFData (Tree a)

Defined in Data.Tree

Methods

rnf :: Tree a -> ()

NFData a => NFData (Seq a)

Defined in Data.Sequence.Internal

Methods

rnf :: Seq a -> ()

NFData a => NFData (FingerTree a)

Defined in Data.Sequence.Internal

Methods

rnf :: FingerTree a -> ()

NFData a => NFData (Digit a)

Defined in Data.Sequence.Internal

Methods

rnf :: Digit a -> ()

NFData a => NFData (Node a)

Defined in Data.Sequence.Internal

Methods

rnf :: Node a -> ()

NFData a => NFData (Elem a)

Defined in Data.Sequence.Internal

Methods

rnf :: Elem a -> ()

NFData a => NFData (Set a)

Defined in Data.Set.Internal

Methods

rnf :: Set a -> ()

NFData a => NFData (Doc a)

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

rnf :: Doc a -> ()

NFData a => NFData (AnnotDetails a)

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

rnf :: AnnotDetails a -> ()

NFData (a -> b)

This instance is for convenience and consistency with seq. This assumes that WHNF is equivalent to NF for functions.

Since: deepseq-1.3.0.0

Defined in Control.DeepSeq

Methods

rnf :: (a -> b) -> ()

(NFData a, NFData b) => NFData (Either a b)

Defined in Control.DeepSeq

Methods

rnf :: Either a b -> ()

(NFData a, NFData b) => NFData (a, b)

Defined in Control.DeepSeq

Methods

rnf :: (a, b) -> ()

(NFData a, NFData b) => NFData (Array a b)

Defined in Control.DeepSeq

Methods

rnf :: Array a b -> ()

(NFData a, NFData b) => NFData (Arg a b)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: Arg a b -> ()

NFData (Proxy a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Proxy a -> ()

NFData (STRef s a)

NOTE: Only strict in the reference and not the referenced value.

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: STRef s a -> ()

(NFData k, NFData a) => NFData (Map k a)

Defined in Data.Map.Internal

Methods

rnf :: Map k a -> ()

(NFData a1, NFData a2, NFData a3) => NFData (a1, a2, a3)

Defined in Control.DeepSeq

Methods

rnf :: (a1, a2, a3) -> ()

NFData a => NFData (Const a b)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Const a b -> ()

NFData (a :~: b)

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

rnf :: (a :~: b) -> ()

(NFDataF f, NFData a) => NFData (Cxt h f a)

Defined in Data.Comp.DeepSeq

Methods

rnf :: Cxt h f a -> ()

(NFData a1, NFData a2, NFData a3, NFData a4) => NFData (a1, a2, a3, a4)

Defined in Control.DeepSeq

Methods

rnf :: (a1, a2, a3, a4) -> ()

(NFData1 f, NFData1 g, NFData a) => NFData (Product f g a)

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

rnf :: Product f g a -> ()

(NFData1 f, NFData1 g, NFData a) => NFData (Sum f g a)

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

rnf :: Sum f g a -> ()

NFData (a :~~: b)

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

rnf :: (a :~~: b) -> ()

(NFData a1, NFData a2, NFData a3, NFData a4, NFData a5) => NFData (a1, a2, a3, a4, a5)

Defined in Control.DeepSeq

Methods

rnf :: (a1, a2, a3, a4, a5) -> ()

(NFData1 f, NFData1 g, NFData a) => NFData (Compose f g a)

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

rnf :: Compose f g a -> ()

(NFData a1, NFData a2, NFData a3, NFData a4, NFData a5, NFData a6) => NFData (a1, a2, a3, a4, a5, a6)

Defined in Control.DeepSeq

Methods

rnf :: (a1, a2, a3, a4, a5, a6) -> ()

(NFData a1, NFData a2, NFData a3, NFData a4, NFData a5, NFData a6, NFData a7) => NFData (a1, a2, a3, a4, a5, a6, a7)

Defined in Control.DeepSeq

Methods

rnf :: (a1, a2, a3, a4, a5, a6, a7) -> ()

(NFData a1, NFData a2, NFData a3, NFData a4, NFData a5, NFData a6, NFData a7, NFData a8) => NFData (a1, a2, a3, a4, a5, a6, a7, a8)

Defined in Control.DeepSeq

Methods

rnf :: (a1, a2, a3, a4, a5, a6, a7, a8) -> ()

(NFData a1, NFData a2, NFData a3, NFData a4, NFData a5, NFData a6, NFData a7, NFData a8, NFData a9) => NFData (a1, a2, a3, a4, a5, a6, a7, a8, a9)

Defined in Control.DeepSeq

Methods

rnf :: (a1, a2, a3, a4, a5, a6, a7, a8, a9) -> ()

DeepSeq

class NFDataF f where

Signature normal form. An instance NFDataF f gives rise to an instance NFData (Term f).

Minimal complete definition

rnfF

Methods

rnfF :: NFData a => f a -> ()

Instances

NFDataF []

Defined in Data.Comp.DeepSeq

Methods

rnfF :: NFData a => [a] -> ()

NFDataF Maybe

Defined in Data.Comp.DeepSeq

Methods

rnfF :: NFData a => Maybe a -> ()

NFData a => NFDataF ((,) a)

Defined in Data.Comp.DeepSeq

Methods

rnfF :: NFData a0 => (a, a0) -> ()

(NFDataF f, NFData a) => NFDataF (f :&: a)

Defined in Data.Comp.DeepSeq

Methods

rnfF :: NFData a0 => (f :&: a) a0 -> ()

(NFDataF f, NFDataF g) => NFDataF (f :+: g)

Defined in Data.Comp.DeepSeq

Methods

rnfF :: NFData a => (f :+: g) a -> ()

makeNFDataF :: Name -> Q [Dec]

Derive an instance of NFDataF for a type constructor of any first-order kind taking at least one argument.

Smart Constructors

smartConstructors :: Name -> Q [Dec]

Derive smart constructors for a type constructor of any first-order kind taking at least one argument. The smart constructors are similar to the ordinary constructors, but an inject is automatically inserted.

Smart Constructors w/ Annotations

smartAConstructors :: Name -> Q [Dec]

Derive smart constructors with products for a type constructor of any parametric kind taking at least one argument. The smart constructors are similar to the ordinary constructors, but an injectA is automatically inserted.

Lifting to Sums

liftSum :: Name -> Q [Dec]

Given the name of a type class, where the first parameter is a functor, lift it to sums of functors. Example: class ShowF f where ... is lifted as instance (ShowF f, ShowF g) => ShowF (f :+: g) where ... .