numhask-0.12.0.2: A numeric class hierarchy.
Safe HaskellSafe-Inferred
LanguageGHC2021

NumHask.Prelude

Description

A prelude composed by overlaying numhask on Prelude, together with a few minor tweaks needed for RebindableSyntax.

Synopsis

numhask exports

rebindables

Using different types for numbers requires RebindableSyntax. This then removes base-level stuff that has to be put back in.

ifThenElse :: Bool -> a -> a -> a Source #

RebindableSyntax splats this, and I'm not sure where it exists in GHC land

fromList :: IsList l => [Item l] -> l #

The fromList function constructs the structure l from the given list of Item l

fromListN :: IsList l => Int -> [Item l] -> l #

The fromListN function takes the input list's length and potentially uses it to construct the structure l more efficiently compared to fromList. If the given number does not equal to the input list's length the behaviour of fromListN is not specified.

fromListN (length xs) xs == fromList xs

data Natural where #

Natural number

Invariant: numbers <= 0xffffffffffffffff use the NS constructor

Bundled Patterns

pattern NatJ# :: BigNat -> Natural 
pattern NatS# :: Word# -> Natural 

Instances

Instances details
Data Natural

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Natural -> c Natural #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Natural #

toConstr :: Natural -> Constr #

dataTypeOf :: Natural -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Natural) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Natural) #

gmapT :: (forall b. Data b => b -> b) -> Natural -> Natural #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r #

gmapQ :: (forall d. Data d => d -> u) -> Natural -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Natural -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Natural -> m Natural #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural #

Enum Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Enum

Num Natural

Note that Natural's Num instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though.

Since: base-4.8.0.0

Instance details

Defined in GHC.Num

Read Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Read

Integral Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Real

Real Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Real

Show Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Show

Eq Natural 
Instance details

Defined in GHC.Num.Natural

Methods

(==) :: Natural -> Natural -> Bool #

(/=) :: Natural -> Natural -> Bool #

Ord Natural 
Instance details

Defined in GHC.Num.Natural

Additive Natural Source # 
Instance details

Defined in NumHask.Algebra.Additive

Subtractive Natural Source # 
Instance details

Defined in NumHask.Algebra.Additive

BoundedJoinSemiLattice Natural Source # 
Instance details

Defined in NumHask.Algebra.Lattice

JoinSemiLattice Natural Source # 
Instance details

Defined in NumHask.Algebra.Lattice

MeetSemiLattice Natural Source # 
Instance details

Defined in NumHask.Algebra.Lattice

Basis Natural Source # 
Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Natural Source #

type Base Natural Source #

Multiplicative Natural Source # 
Instance details

Defined in NumHask.Algebra.Multiplicative

InvolutiveRing Natural Source # 
Instance details

Defined in NumHask.Algebra.Ring

Methods

adj :: Natural -> Natural Source #

FromInteger Natural Source # 
Instance details

Defined in NumHask.Data.Integral

Integral Natural Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Natural Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Natural Natural Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Natural Int Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Natural Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Natural Natural Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Natural Int Source # 
Instance details

Defined in NumHask.Data.Integral

ToRatio Natural Integer Source # 
Instance details

Defined in NumHask.Data.Rational

type Base Natural Source # 
Instance details

Defined in NumHask.Algebra.Metric

type Mag Natural Source # 
Instance details

Defined in NumHask.Algebra.Metric

type Compare (a :: Natural) (b :: Natural) 
Instance details

Defined in Data.Type.Ord

type Compare (a :: Natural) (b :: Natural) = CmpNat a b

Modules you can't live without

module Data.Bool

module Data.Kind

newtype Any #

Boolean monoid under disjunction (||).

>>> getAny (Any True <> mempty <> Any False)
True
>>> getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))
True

Constructors

Any 

Fields

Instances

Instances details
Data Any

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any #

toConstr :: Any -> Constr #

dataTypeOf :: Any -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Any) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) #

gmapT :: (forall b. Data b => b -> b) -> Any -> Any #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r #

gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any #

Monoid Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Any #

mappend :: Any -> Any -> Any #

mconcat :: [Any] -> Any #

Semigroup Any

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any #

sconcat :: NonEmpty Any -> Any #

stimes :: Integral b => b -> Any -> Any #

Bounded Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Any #

maxBound :: Any #

Generic Any 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep Any :: Type -> Type #

Methods

from :: Any -> Rep Any x #

to :: Rep Any x -> Any #

Read Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Any -> ShowS #

show :: Any -> String #

showList :: [Any] -> ShowS #

Eq Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: Any -> Any -> Bool #

(/=) :: Any -> Any -> Bool #

Ord Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Any -> Any -> Ordering #

(<) :: Any -> Any -> Bool #

(<=) :: Any -> Any -> Bool #

(>) :: Any -> Any -> Bool #

(>=) :: Any -> Any -> Bool #

max :: Any -> Any -> Any #

min :: Any -> Any -> Any #

type Rep Any

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep Any = D1 ('MetaData "Any" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Any" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAny") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

class Semigroup a where #

The class of semigroups (types with an associative binary operation).

Instances should satisfy the following:

Associativity
x <> (y <> z) = (x <> y) <> z

You can alternatively define sconcat instead of (<>), in which case the laws are:

Unit
sconcat (pure x) = x
Multiplication
sconcat (join xss) = sconcat (fmap sconcat xss)

Since: base-4.9.0.0

Minimal complete definition

(<>) | sconcat

Methods

(<>) :: a -> a -> a infixr 6 #

An associative operation.

>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]

sconcat :: NonEmpty a -> a #

Reduce a non-empty list with <>

The default definition should be sufficient, but this can be overridden for efficiency.

>>> import Data.List.NonEmpty (NonEmpty (..))
>>> sconcat $ "Hello" :| [" ", "Haskell", "!"]
"Hello Haskell!"

stimes :: Integral b => b -> a -> a #

Repeat a value n times.

Given that this works on a Semigroup it is allowed to fail if you request 0 or fewer repetitions, and the default definition will do so.

By making this a member of the class, idempotent semigroups and monoids can upgrade this to execute in \(\mathcal{O}(1)\) by picking stimes = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

>>> stimes 4 [1]
[1,1,1,1]

Instances

Instances details
Semigroup All

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All #

sconcat :: NonEmpty All -> All #

stimes :: Integral b => b -> All -> All #

Semigroup Any

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any #

sconcat :: NonEmpty Any -> Any #

stimes :: Integral b => b -> Any -> Any #

Semigroup Void

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: Void -> Void -> Void #

sconcat :: NonEmpty Void -> Void #

stimes :: Integral b => b -> Void -> Void #

Semigroup Ordering

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Semigroup ()

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: () -> () -> () #

sconcat :: NonEmpty () -> () #

stimes :: Integral b => b -> () -> () #

Semigroup a => Semigroup (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Methods

(<>) :: Identity a -> Identity a -> Identity a #

sconcat :: NonEmpty (Identity a) -> Identity a #

stimes :: Integral b => b -> Identity a -> Identity a #

Semigroup (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Monoid

Methods

(<>) :: First a -> First a -> First a #

sconcat :: NonEmpty (First a) -> First a #

stimes :: Integral b => b -> First a -> First a #

Semigroup (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Monoid

Methods

(<>) :: Last a -> Last a -> Last a #

sconcat :: NonEmpty (Last a) -> Last a #

stimes :: Integral b => b -> Last a -> Last a #

Semigroup a => Semigroup (Down a)

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

(<>) :: Down a -> Down a -> Down a #

sconcat :: NonEmpty (Down a) -> Down a #

stimes :: Integral b => b -> Down a -> Down a #

Semigroup (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: First a -> First a -> First a #

sconcat :: NonEmpty (First a) -> First a #

stimes :: Integral b => b -> First a -> First a #

Semigroup (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: Last a -> Last a -> Last a #

sconcat :: NonEmpty (Last a) -> Last a #

stimes :: Integral b => b -> Last a -> Last a #

Ord a => Semigroup (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: Max a -> Max a -> Max a #

sconcat :: NonEmpty (Max a) -> Max a #

stimes :: Integral b => b -> Max a -> Max a #

Ord a => Semigroup (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: Min a -> Min a -> Min a #

sconcat :: NonEmpty (Min a) -> Min a #

stimes :: Integral b => b -> Min a -> Min a #

Monoid m => Semigroup (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Semigroup a => Semigroup (Dual a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Dual a -> Dual a -> Dual a #

sconcat :: NonEmpty (Dual a) -> Dual a #

stimes :: Integral b => b -> Dual a -> Dual a #

Semigroup (Endo a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Endo a -> Endo a -> Endo a #

sconcat :: NonEmpty (Endo a) -> Endo a #

stimes :: Integral b => b -> Endo a -> Endo a #

Num a => Semigroup (Product a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Product a -> Product a -> Product a #

sconcat :: NonEmpty (Product a) -> Product a #

stimes :: Integral b => b -> Product a -> Product a #

Num a => Semigroup (Sum a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Sum a -> Sum a -> Sum a #

sconcat :: NonEmpty (Sum a) -> Sum a #

stimes :: Integral b => b -> Sum a -> Sum a #

Semigroup (NonEmpty a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a #

sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a #

stimes :: Integral b => b -> NonEmpty a -> NonEmpty a #

(Generic a, Semigroup (Rep a ())) => Semigroup (Generically a)

Since: base-4.17.0.0

Instance details

Defined in GHC.Generics

Semigroup p => Semigroup (Par1 p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: Par1 p -> Par1 p -> Par1 p #

sconcat :: NonEmpty (Par1 p) -> Par1 p #

stimes :: Integral b => b -> Par1 p -> Par1 p #

Semigroup a => Semigroup (IO a)

Since: base-4.10.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: IO a -> IO a -> IO a #

sconcat :: NonEmpty (IO a) -> IO a #

stimes :: Integral b => b -> IO a -> IO a #

Additive a => Semigroup (Sum a) Source # 
Instance details

Defined in NumHask.Algebra.Additive

Methods

(<>) :: Sum a -> Sum a -> Sum a #

sconcat :: NonEmpty (Sum a) -> Sum a #

stimes :: Integral b => b -> Sum a -> Sum a #

Multiplicative a => Semigroup (Product a) Source # 
Instance details

Defined in NumHask.Algebra.Multiplicative

Methods

(<>) :: Product a -> Product a -> Product a #

sconcat :: NonEmpty (Product a) -> Product a #

stimes :: Integral b => b -> Product a -> Product a #

Semigroup a => Semigroup (Maybe a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: Maybe a -> Maybe a -> Maybe a #

sconcat :: NonEmpty (Maybe a) -> Maybe a #

stimes :: Integral b => b -> Maybe a -> Maybe a #

Semigroup a => Semigroup (a)

Since: base-4.15

Instance details

Defined in GHC.Base

Methods

(<>) :: (a) -> (a) -> (a) #

sconcat :: NonEmpty (a) -> (a) #

stimes :: Integral b => b -> (a) -> (a) #

Semigroup [a]

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: [a] -> [a] -> [a] #

sconcat :: NonEmpty [a] -> [a] #

stimes :: Integral b => b -> [a] -> [a] #

Semigroup (Either a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Either

Methods

(<>) :: Either a b -> Either a b -> Either a b #

sconcat :: NonEmpty (Either a b) -> Either a b #

stimes :: Integral b0 => b0 -> Either a b -> Either a b #

Semigroup (U1 p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: U1 p -> U1 p -> U1 p #

sconcat :: NonEmpty (U1 p) -> U1 p #

stimes :: Integral b => b -> U1 p -> U1 p #

Semigroup (V1 p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: V1 p -> V1 p -> V1 p #

sconcat :: NonEmpty (V1 p) -> V1 p #

stimes :: Integral b => b -> V1 p -> V1 p #

(Semigroup a, Semigroup b) => Semigroup (a, b)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: (a, b) -> (a, b) -> (a, b) #

sconcat :: NonEmpty (a, b) -> (a, b) #

stimes :: Integral b0 => b0 -> (a, b) -> (a, b) #

Semigroup b => Semigroup (a -> b)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: (a -> b) -> (a -> b) -> a -> b #

sconcat :: NonEmpty (a -> b) -> a -> b #

stimes :: Integral b0 => b0 -> (a -> b) -> a -> b #

Semigroup a => Semigroup (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

(<>) :: Const a b -> Const a b -> Const a b #

sconcat :: NonEmpty (Const a b) -> Const a b #

stimes :: Integral b0 => b0 -> Const a b -> Const a b #

(Applicative f, Semigroup a) => Semigroup (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

(<>) :: Ap f a -> Ap f a -> Ap f a #

sconcat :: NonEmpty (Ap f a) -> Ap f a #

stimes :: Integral b => b -> Ap f a -> Ap f a #

Alternative f => Semigroup (Alt f a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Alt f a -> Alt f a -> Alt f a #

sconcat :: NonEmpty (Alt f a) -> Alt f a #

stimes :: Integral b => b -> Alt f a -> Alt f a #

Semigroup (f p) => Semigroup (Rec1 f p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p #

sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p #

stimes :: Integral b => b -> Rec1 f p -> Rec1 f p #

(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) #

sconcat :: NonEmpty (a, b, c) -> (a, b, c) #

stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) #

(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p #

sconcat :: NonEmpty ((f :*: g) p) -> (f :*: g) p #

stimes :: Integral b => b -> (f :*: g) p -> (f :*: g) p #

Semigroup c => Semigroup (K1 i c p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: K1 i c p -> K1 i c p -> K1 i c p #

sconcat :: NonEmpty (K1 i c p) -> K1 i c p #

stimes :: Integral b => b -> K1 i c p -> K1 i c p #

(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #

sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) #

stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) #

Semigroup (f (g p)) => Semigroup ((f :.: g) p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p #

sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p #

stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p #

Semigroup (f p) => Semigroup (M1 i c f p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p #

sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p #

stimes :: Integral b => b -> M1 i c f p -> M1 i c f p #

(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) #

sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) #

stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) #

newtype Last a #

Beware that Data.Semigroup.Last is different from Data.Monoid.Last. The former simply returns the last value, so x <> Data.Semigroup.Last Nothing = Data.Semigroup.Last Nothing. The latter returns the last non-Nothing, thus x <> Data.Monoid.Last Nothing = x.

Constructors

Last 

Fields

Instances

Instances details
MonadFix Last

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mfix :: (a -> Last a) -> Last a #

Foldable Last

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => Last m -> m #

foldMap :: Monoid m => (a -> m) -> Last a -> m #

foldMap' :: Monoid m => (a -> m) -> Last a -> m #

foldr :: (a -> b -> b) -> b -> Last a -> b #

foldr' :: (a -> b -> b) -> b -> Last a -> b #

foldl :: (b -> a -> b) -> b -> Last a -> b #

foldl' :: (b -> a -> b) -> b -> Last a -> b #

foldr1 :: (a -> a -> a) -> Last a -> a #

foldl1 :: (a -> a -> a) -> Last a -> a #

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 #

Traversable Last

Since: base-4.9.0.0

Instance details

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) #

Applicative Last

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Last a #

(<*>) :: Last (a -> b) -> Last a -> Last b #

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c #

(*>) :: Last a -> Last b -> Last b #

(<*) :: Last a -> Last b -> Last a #

Functor Last

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Last a -> Last b #

(<$) :: a -> Last b -> Last a #

Monad Last

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b #

(>>) :: Last a -> Last b -> Last b #

return :: a -> Last a #

Generic1 Last 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 Last :: k -> Type #

Methods

from1 :: forall (a :: k). Last a -> Rep1 Last a #

to1 :: forall (a :: k). Rep1 Last a -> Last a #

Data a => Data (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) #

toConstr :: Last a -> Constr #

dataTypeOf :: Last a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) #

gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) #

Semigroup (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: Last a -> Last a -> Last a #

sconcat :: NonEmpty (Last a) -> Last a #

stimes :: Integral b => b -> Last a -> Last a #

Bounded a => Bounded (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: Last a #

maxBound :: Last a #

Enum a => Enum (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: Last a -> Last a #

pred :: Last a -> Last a #

toEnum :: Int -> Last a #

fromEnum :: Last a -> Int #

enumFrom :: Last a -> [Last a] #

enumFromThen :: Last a -> Last a -> [Last a] #

enumFromTo :: Last a -> Last a -> [Last a] #

enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] #

Generic (Last a) 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep (Last a) :: Type -> Type #

Methods

from :: Last a -> Rep (Last a) x #

to :: Rep (Last a) x -> Last a #

Read a => Read (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Show a => Show (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Last a -> ShowS #

show :: Last a -> String #

showList :: [Last a] -> ShowS #

Eq a => Eq (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Last a -> Last a -> Bool #

(/=) :: Last a -> Last a -> Bool #

Ord a => Ord (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: Last a -> Last a -> Ordering #

(<) :: Last a -> Last a -> Bool #

(<=) :: Last a -> Last a -> Bool #

(>) :: Last a -> Last a -> Bool #

(>=) :: Last a -> Last a -> Bool #

max :: Last a -> Last a -> Last a #

min :: Last a -> Last a -> Last a #

type Rep1 Last

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep1 Last = D1 ('MetaData "Last" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (Last a) = D1 ('MetaData "Last" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype First a #

Beware that Data.Semigroup.First is different from Data.Monoid.First. The former simply returns the first value, so Data.Semigroup.First Nothing <> x = Data.Semigroup.First Nothing. The latter returns the first non-Nothing, thus Data.Monoid.First Nothing <> x = x.

Constructors

First 

Fields

Instances

Instances details
MonadFix First

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mfix :: (a -> First a) -> First a #

Foldable First

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => First m -> m #

foldMap :: Monoid m => (a -> m) -> First a -> m #

foldMap' :: Monoid m => (a -> m) -> First a -> m #

foldr :: (a -> b -> b) -> b -> First a -> b #

foldr' :: (a -> b -> b) -> b -> First a -> b #

foldl :: (b -> a -> b) -> b -> First a -> b #

foldl' :: (b -> a -> b) -> b -> First a -> b #

foldr1 :: (a -> a -> a) -> First a -> a #

foldl1 :: (a -> a -> a) -> First a -> a #

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 #

Traversable First

Since: base-4.9.0.0

Instance details

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) #

Applicative First

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> First a #

(<*>) :: First (a -> b) -> First a -> First b #

liftA2 :: (a -> b -> c) -> First a -> First b -> First c #

(*>) :: First a -> First b -> First b #

(<*) :: First a -> First b -> First a #

Functor First

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> First a -> First b #

(<$) :: a -> First b -> First a #

Monad First

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(>>=) :: First a -> (a -> First b) -> First b #

(>>) :: First a -> First b -> First b #

return :: a -> First a #

Generic1 First 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 First :: k -> Type #

Methods

from1 :: forall (a :: k). First a -> Rep1 First a #

to1 :: forall (a :: k). Rep1 First a -> First a #

Data a => Data (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) #

toConstr :: First a -> Constr #

dataTypeOf :: First a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) #

gmapT :: (forall b. Data b => b -> b) -> First a -> First a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r #

gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) #

Semigroup (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: First a -> First a -> First a #

sconcat :: NonEmpty (First a) -> First a #

stimes :: Integral b => b -> First a -> First a #

Bounded a => Bounded (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: First a #

maxBound :: First a #

Enum a => Enum (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: First a -> First a #

pred :: First a -> First a #

toEnum :: Int -> First a #

fromEnum :: First a -> Int #

enumFrom :: First a -> [First a] #

enumFromThen :: First a -> First a -> [First a] #

enumFromTo :: First a -> First a -> [First a] #

enumFromThenTo :: First a -> First a -> First a -> [First a] #

Generic (First a) 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep (First a) :: Type -> Type #

Methods

from :: First a -> Rep (First a) x #

to :: Rep (First a) x -> First a #

Read a => Read (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Show a => Show (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> First a -> ShowS #

show :: First a -> String #

showList :: [First a] -> ShowS #

Eq a => Eq (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: First a -> First a -> Bool #

(/=) :: First a -> First a -> Bool #

Ord a => Ord (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: First a -> First a -> Ordering #

(<) :: First a -> First a -> Bool #

(<=) :: First a -> First a -> Bool #

(>) :: First a -> First a -> Bool #

(>=) :: First a -> First a -> Bool #

max :: First a -> First a -> First a #

min :: First a -> First a -> First a #

type Rep1 First

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep1 First = D1 ('MetaData "First" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (First a) = D1 ('MetaData "First" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype All #

Boolean monoid under conjunction (&&).

>>> getAll (All True <> mempty <> All False)
False
>>> getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))
False

Constructors

All 

Fields

Instances

Instances details
Data All

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All #

toConstr :: All -> Constr #

dataTypeOf :: All -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c All) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) #

gmapT :: (forall b. Data b => b -> b) -> All -> All #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r #

gmapQ :: (forall d. Data d => d -> u) -> All -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All #

Monoid All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: All #

mappend :: All -> All -> All #

mconcat :: [All] -> All #

Semigroup All

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All #

sconcat :: NonEmpty All -> All #

stimes :: Integral b => b -> All -> All #

Bounded All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: All #

maxBound :: All #

Generic All 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep All :: Type -> Type #

Methods

from :: All -> Rep All x #

to :: Rep All x -> All #

Read All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> All -> ShowS #

show :: All -> String #

showList :: [All] -> ShowS #

Eq All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: All -> All -> Bool #

(/=) :: All -> All -> Bool #

Ord All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: All -> All -> Ordering #

(<) :: All -> All -> Bool #

(<=) :: All -> All -> Bool #

(>) :: All -> All -> Bool #

(>=) :: All -> All -> Bool #

max :: All -> All -> All #

min :: All -> All -> All #

type Rep All

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep All = D1 ('MetaData "All" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "All" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAll") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

newtype Endo a #

The monoid of endomorphisms under composition.

>>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>> appEndo computation "Haskell"
"Hello, Haskell!"

Constructors

Endo 

Fields

Instances

Instances details
Monoid (Endo a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Endo a #

mappend :: Endo a -> Endo a -> Endo a #

mconcat :: [Endo a] -> Endo a #

Semigroup (Endo a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Endo a -> Endo a -> Endo a #

sconcat :: NonEmpty (Endo a) -> Endo a #

stimes :: Integral b => b -> Endo a -> Endo a #

Generic (Endo a) 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Endo a) :: Type -> Type #

Methods

from :: Endo a -> Rep (Endo a) x #

to :: Rep (Endo a) x -> Endo a #

type Rep (Endo a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep (Endo a) = D1 ('MetaData "Endo" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Endo" 'PrefixI 'True) (S1 ('MetaSel ('Just "appEndo") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a -> a))))

newtype Dual a #

The dual of a Monoid, obtained by swapping the arguments of mappend.

>>> getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"

Constructors

Dual 

Fields

Instances

Instances details
Foldable Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Dual m -> m #

foldMap :: Monoid m => (a -> m) -> Dual a -> m #

foldMap' :: Monoid m => (a -> m) -> Dual a -> m #

foldr :: (a -> b -> b) -> b -> Dual a -> b #

foldr' :: (a -> b -> b) -> b -> Dual a -> b #

foldl :: (b -> a -> b) -> b -> Dual a -> b #

foldl' :: (b -> a -> b) -> b -> Dual a -> b #

foldr1 :: (a -> a -> a) -> Dual a -> a #

foldl1 :: (a -> a -> a) -> Dual a -> a #

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 #

Traversable Dual

Since: base-4.8.0.0

Instance details

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) #

Applicative Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Dual a #

(<*>) :: Dual (a -> b) -> Dual a -> Dual b #

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c #

(*>) :: Dual a -> Dual b -> Dual b #

(<*) :: Dual a -> Dual b -> Dual a #

Functor Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Dual a -> Dual b #

(<$) :: a -> Dual b -> Dual a #

Monad Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Dual a -> (a -> Dual b) -> Dual b #

(>>) :: Dual a -> Dual b -> Dual b #

return :: a -> Dual a #

Generic1 Dual 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Dual :: k -> Type #

Methods

from1 :: forall (a :: k). Dual a -> Rep1 Dual a #

to1 :: forall (a :: k). Rep1 Dual a -> Dual a #

Data a => Data (Dual a)

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dual a -> c (Dual a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) #

toConstr :: Dual a -> Constr #

dataTypeOf :: Dual a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) #

gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) #

Monoid a => Monoid (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Dual a #

mappend :: Dual a -> Dual a -> Dual a #

mconcat :: [Dual a] -> Dual a #

Semigroup a => Semigroup (Dual a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Dual a -> Dual a -> Dual a #

sconcat :: NonEmpty (Dual a) -> Dual a #

stimes :: Integral b => b -> Dual a -> Dual a #

Bounded a => Bounded (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Dual a #

maxBound :: Dual a #

Generic (Dual a) 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Dual a) :: Type -> Type #

Methods

from :: Dual a -> Rep (Dual a) x #

to :: Rep (Dual a) x -> Dual a #

Read a => Read (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show a => Show (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Dual a -> ShowS #

show :: Dual a -> String #

showList :: [Dual a] -> ShowS #

Eq a => Eq (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: Dual a -> Dual a -> Bool #

(/=) :: Dual a -> Dual a -> Bool #

Ord a => Ord (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Dual a -> Dual a -> Ordering #

(<) :: Dual a -> Dual a -> Bool #

(<=) :: Dual a -> Dual a -> Bool #

(>) :: Dual a -> Dual a -> Bool #

(>=) :: Dual a -> Dual a -> Bool #

max :: Dual a -> Dual a -> Dual a #

min :: Dual a -> Dual a -> Dual a #

type Rep1 Dual

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep1 Dual = D1 ('MetaData "Dual" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Dual a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep (Dual a) = D1 ('MetaData "Dual" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype WrappedMonoid m #

Provide a Semigroup for an arbitrary Monoid.

NOTE: This is not needed anymore since Semigroup became a superclass of Monoid in base-4.11 and this newtype be deprecated at some point in the future.

Constructors

WrapMonoid 

Fields

Instances

Instances details
Generic1 WrappedMonoid 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 WrappedMonoid :: k -> Type #

Methods

from1 :: forall (a :: k). WrappedMonoid a -> Rep1 WrappedMonoid a #

to1 :: forall (a :: k). Rep1 WrappedMonoid a -> WrappedMonoid a #

Data m => Data (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WrappedMonoid m -> c (WrappedMonoid m) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonoid m) #

toConstr :: WrappedMonoid m -> Constr #

dataTypeOf :: WrappedMonoid m -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonoid m)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonoid m)) #

gmapT :: (forall b. Data b => b -> b) -> WrappedMonoid m -> WrappedMonoid m #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r #

gmapQ :: (forall d. Data d => d -> u) -> WrappedMonoid m -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonoid m -> u #

gmapM :: Monad m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) #

gmapMp :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) #

gmapMo :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) #

Monoid m => Monoid (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Monoid m => Semigroup (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Bounded m => Bounded (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Enum a => Enum (WrappedMonoid a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Generic (WrappedMonoid m) 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep (WrappedMonoid m) :: Type -> Type #

Read m => Read (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Show m => Show (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Eq m => Eq (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Ord m => Ord (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep1 WrappedMonoid

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep1 WrappedMonoid = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (WrappedMonoid m) = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 m)))

type ArgMax a b = Max (Arg a b) #

>>> Max (Arg 0 ()) <> Max (Arg 1 ())
Max {getMax = Arg 1 ()}

type ArgMin a b = Min (Arg a b) #

>>> Min (Arg 0 ()) <> Min (Arg 1 ())
Min {getMin = Arg 0 ()}

data Arg a b #

Arg isn't itself a Semigroup in its own right, but it can be placed inside Min and Max to compute an arg min or arg max.

>>> minimum [ Arg (x * x) x | x <- [-10 .. 10] ]
Arg 0 0

Constructors

Arg 

Fields

  • a

    The argument used for comparisons in Eq and Ord.

  • b

    The "value" exposed via the Functor, Foldable etc. instances.

Instances

Instances details
Bifoldable Arg

Since: base-4.10.0.0

Instance details

Defined in Data.Semigroup

Methods

bifold :: Monoid m => Arg m m -> m #

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m #

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c #

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c #

Bifunctor Arg

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d #

first :: (a -> b) -> Arg a c -> Arg b c #

second :: (b -> c) -> Arg a b -> Arg a c #

Bitraversable Arg

Since: base-4.10.0.0

Instance details

Defined in Data.Semigroup

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) #

Generic1 (Arg a :: Type -> Type) 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 (Arg a) :: k -> Type #

Methods

from1 :: forall (a0 :: k). Arg a a0 -> Rep1 (Arg a) a0 #

to1 :: forall (a0 :: k). Rep1 (Arg a) a0 -> Arg a a0 #

Foldable (Arg a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Traversable (Arg a)

Since: base-4.9.0.0

Instance details

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) #

Functor (Arg a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a0 -> b) -> Arg a a0 -> Arg a b #

(<$) :: a0 -> Arg a b -> Arg a a0 #

(Data a, Data b) => Data (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b) #

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b) #

toConstr :: Arg a b -> Constr #

dataTypeOf :: Arg a b -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b)) #

gmapT :: (forall b0. Data b0 => b0 -> b0) -> Arg a b -> Arg a b #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r #

gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) #

Generic (Arg a b) 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep (Arg a b) :: Type -> Type #

Methods

from :: Arg a b -> Rep (Arg a b) x #

to :: Rep (Arg a b) x -> Arg a b #

(Read a, Read b) => Read (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (Arg a b) #

readList :: ReadS [Arg a b] #

readPrec :: ReadPrec (Arg a b) #

readListPrec :: ReadPrec [Arg a b] #

(Show a, Show b) => Show (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Arg a b -> ShowS #

show :: Arg a b -> String #

showList :: [Arg a b] -> ShowS #

Eq a => Eq (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Arg a b -> Arg a b -> Bool #

(/=) :: Arg a b -> Arg a b -> Bool #

Ord a => Ord (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: Arg a b -> Arg a b -> Ordering #

(<) :: Arg a b -> Arg a b -> Bool #

(<=) :: Arg a b -> Arg a b -> Bool #

(>) :: Arg a b -> Arg a b -> Bool #

(>=) :: Arg a b -> Arg a b -> Bool #

max :: Arg a b -> Arg a b -> Arg a b #

min :: Arg a b -> Arg a b -> Arg a b #

type Rep1 (Arg a :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

stimesIdempotent :: Integral b => b -> a -> a #

This is a valid definition of stimes for an idempotent Semigroup.

When x <> x = x, this definition should be preferred, because it works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\).

stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a #

This is a valid definition of stimes for an idempotent Monoid.

When mappend x x = x, this definition should be preferred, because it works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\)

stimesMonoid :: (Integral b, Monoid a) => b -> a -> a #

This is a valid definition of stimes for a Monoid.

Unlike the default definition of stimes, it is defined for 0 and so it should be preferred where possible.

cycle1 :: Semigroup m => m -> m #

A generalization of cycle to an arbitrary Semigroup. May fail to terminate for some values in some semigroups.

diff :: Semigroup m => m -> Endo m #

This lets you use a difference list of a Semigroup as a Monoid.

Example:

Expand
>>> let hello = diff "Hello, "
>>> appEndo hello "World!"
"Hello, World!"
>>> appEndo (hello <> mempty) "World!"
"Hello, World!"
>>> appEndo (mempty <> hello) "World!"
"Hello, World!"
>>> let world = diff "World"
>>> let excl = diff "!"
>>> appEndo (hello <> (world <> excl)) mempty
"Hello, World!"
>>> appEndo ((hello <> world) <> excl) mempty
"Hello, World!"

mtimesDefault :: (Integral b, Monoid a) => b -> a -> a #

Repeat a value n times.

mtimesDefault n a = a <> a <> ... <> a  -- using <> (n-1) times

In many cases, `stimes 0 a` for a Monoid will produce mempty. However, there are situations when it cannot do so. In particular, the following situation is fairly common:

data T a = ...

class Constraint1 a
class Constraint1 a => Constraint2 a

instance Constraint1 a => Semigroup (T a) instance Constraint2 a => Monoid (T a) @

Since Constraint1 is insufficient to implement mempty, stimes for T a cannot do so.

When working with such a type, or when working polymorphically with Semigroup instances, mtimesDefault should be used when the multiplier might be zero. It is implemented using stimes when the multiplier is nonzero and mempty when it is zero.

module Data.Maybe

Data.Function

($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 #

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

Note that ($) is representation-polymorphic in its result type, so that foo $ True where foo :: Bool -> Int# is well-typed.

const :: a -> b -> a #

const x y always evaluates to x, ignoring its second argument.

>>> const 42 "hello"
42
>>> map (const 42) [0..3]
[42,42,42,42]

flip :: (a -> b -> c) -> b -> a -> c #

flip f takes its (first) two arguments in the reverse order of f.

>>> flip (++) "hello" "world"
"worldhello"

fix :: (a -> a) -> a #

fix f is the least fixed point of the function f, i.e. the least defined x such that f x = x.

For example, we can write the factorial function using direct recursion as

>>> let fac n = if n <= 1 then 1 else n * fac (n-1) in fac 5
120

This uses the fact that Haskell’s let introduces recursive bindings. We can rewrite this definition using fix,

>>> fix (\rec n -> if n <= 1 then 1 else n * rec (n-1)) 5
120

Instead of making a recursive call, we introduce a dummy parameter rec; when used within fix, this parameter then refers to fix’s argument, hence the recursion is reintroduced.

on :: (b -> b -> c) -> (a -> b) -> a -> a -> c infixl 0 #

on b u x y runs the binary function b on the results of applying unary function u to two arguments x and y. From the opposite perspective, it transforms two inputs and combines the outputs.

((+) `on` f) x y = f x + f y

Typical usage: sortBy (compare `on` fst).

Algebraic properties:

  • (*) `on` id = (*) -- (if (*) ∉ {⊥, const ⊥})
  • ((*) `on` f) `on` g = (*) `on` (f . g)
  • flip on f . flip on g = flip on (g . f)

(&) :: a -> (a -> b) -> b infixl 1 #

& is a reverse application operator. This provides notational convenience. Its precedence is one higher than that of the forward application operator $, which allows & to be nested in $.

>>> 5 & (+1) & show
"6"

Since: base-4.8.0.0

applyWhen :: Bool -> (a -> a) -> a -> a #

applyWhen applies a function to a value if a condition is true, otherwise, it returns the value unchanged.

It is equivalent to flip (bool id).

Algebraic properties:

Since: base-4.18.0.0

Control.Category

Data.Foldable

class Foldable (t :: Type -> Type) where #

The Foldable class represents data structures that can be reduced to a summary value one element at a time. Strict left-associative folds are a good fit for space-efficient reduction, while lazy right-associative folds are a good fit for corecursive iteration, or for folds that short-circuit after processing an initial subsequence of the structure's elements.

Instances can be derived automatically by enabling the DeriveFoldable extension. For example, a derived instance for a binary tree might be:

{-# LANGUAGE DeriveFoldable #-}
data Tree a = Empty
            | Leaf a
            | Node (Tree a) a (Tree a)
    deriving Foldable

A more detailed description can be found in the Overview section of Data.Foldable.

For the class laws see the Laws section of Data.Foldable.

Minimal complete definition

foldMap | foldr

Methods

fold :: Monoid m => t m -> m #

Given a structure with elements whose type is a Monoid, combine them via the monoid's (<>) operator. This fold is right-associative and lazy in the accumulator. When you need a strict left-associative fold, use foldMap' instead, with id as the map.

Examples

Expand

Basic usage:

>>> fold [[1, 2, 3], [4, 5], [6], []]
[1,2,3,4,5,6]
>>> fold $ Node (Leaf (Sum 1)) (Sum 3) (Leaf (Sum 5))
Sum {getSum = 9}

Folds of unbounded structures do not terminate when the monoid's (<>) operator is strict:

>>> fold (repeat Nothing)
* Hangs forever *

Lazy corecursive folds of unbounded structures are fine:

>>> take 12 $ fold $ map (\i -> [i..i+2]) [0..]
[0,1,2,1,2,3,2,3,4,3,4,5]
>>> sum $ take 4000000 $ fold $ map (\i -> [i..i+2]) [0..]
2666668666666

foldMap :: Monoid m => (a -> m) -> t a -> m #

Map each element of the structure into a monoid, and combine the results with (<>). This fold is right-associative and lazy in the accumulator. For strict left-associative folds consider foldMap' instead.

Examples

Expand

Basic usage:

>>> foldMap Sum [1, 3, 5]
Sum {getSum = 9}
>>> foldMap Product [1, 3, 5]
Product {getProduct = 15}
>>> foldMap (replicate 3) [1, 2, 3]
[1,1,1,2,2,2,3,3,3]

When a Monoid's (<>) is lazy in its second argument, foldMap can return a result even from an unbounded structure. For example, lazy accumulation enables Data.ByteString.Builder to efficiently serialise large data structures and produce the output incrementally:

>>> import qualified Data.ByteString.Lazy as L
>>> import qualified Data.ByteString.Builder as B
>>> let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20
>>> let lbs = B.toLazyByteString $ foldMap bld [0..]
>>> L.take 64 lbs
"0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"

foldMap' :: Monoid m => (a -> m) -> t a -> m #

A left-associative variant of foldMap that is strict in the accumulator. Use this method for strict reduction when partial results are merged via (<>).

Examples

Expand

Define a Monoid over finite bit strings under xor. Use it to strictly compute the xor of a list of Int values.

>>> :set -XGeneralizedNewtypeDeriving
>>> import Data.Bits (Bits, FiniteBits, xor, zeroBits)
>>> import Data.Foldable (foldMap')
>>> import Numeric (showHex)
>>> 
>>> newtype X a = X a deriving (Eq, Bounded, Enum, Bits, FiniteBits)
>>> instance Bits a => Semigroup (X a) where X a <> X b = X (a `xor` b)
>>> instance Bits a => Monoid    (X a) where mempty     = X zeroBits
>>> 
>>> let bits :: [Int]; bits = [0xcafe, 0xfeed, 0xdeaf, 0xbeef, 0x5411]
>>> (\ (X a) -> showString "0x" . showHex a $ "") $ foldMap' X bits
"0x42"

Since: base-4.13.0.0

foldr :: (a -> b -> b) -> b -> t a -> b #

Right-associative fold of a structure, lazy in the accumulator.

In the case of lists, foldr, when applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

Note that since the head of the resulting expression is produced by an application of the operator to the first element of the list, given an operator lazy in its right argument, foldr can produce a terminating expression from an unbounded list.

For a general Foldable structure this should be semantically identical to,

foldr f z = foldr f z . toList

Examples

Expand

Basic usage:

>>> foldr (||) False [False, True, False]
True
>>> foldr (||) False []
False
>>> foldr (\c acc -> acc ++ [c]) "foo" ['a', 'b', 'c', 'd']
"foodcba"
Infinite structures

⚠️ Applying foldr to infinite structures usually doesn't terminate.

It may still terminate under one of the following conditions:

  • the folding function is short-circuiting
  • the folding function is lazy on its second argument
Short-circuiting

(||) short-circuits on True values, so the following terminates because there is a True value finitely far from the left side:

>>> foldr (||) False (True : repeat False)
True

But the following doesn't terminate:

>>> foldr (||) False (repeat False ++ [True])
* Hangs forever *
Laziness in the second argument

Applying foldr to infinite structures terminates when the operator is lazy in its second argument (the initial accumulator is never used in this case, and so could be left undefined, but [] is more clear):

>>> take 5 $ foldr (\i acc -> i : fmap (+3) acc) [] (repeat 1)
[1,4,7,10,13]

foldr' :: (a -> b -> b) -> b -> t a -> b #

foldr' is a variant of foldr that performs strict reduction from right to left, i.e. starting with the right-most element. The input structure must be finite, otherwise foldr' runs out of space (diverges).

If you want a strict right fold in constant space, you need a structure that supports faster than O(n) access to the right-most element, such as Seq from the containers package.

This method does not run in constant space for structures such as lists that don't support efficient right-to-left iteration and so require O(n) space to perform right-to-left reduction. Use of this method with such a structure is a hint that the chosen structure may be a poor fit for the task at hand. If the order in which the elements are combined is not important, use foldl' instead.

Since: base-4.6.0.0

foldl :: (b -> a -> b) -> b -> t a -> b #

Left-associative fold of a structure, lazy in the accumulator. This is rarely what you want, but can work well for structures with efficient right-to-left sequencing and an operator that is lazy in its left argument.

In the case of lists, foldl, when applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn

Note that to produce the outermost application of the operator the entire input list must be traversed. Like all left-associative folds, foldl will diverge if given an infinite list.

If you want an efficient strict left-fold, you probably want to use foldl' instead of foldl. The reason for this is that the latter does not force the inner results (e.g. z `f` x1 in the above example) before applying them to the operator (e.g. to (`f` x2)). This results in a thunk chain O(n) elements long, which then must be evaluated from the outside-in.

For a general Foldable structure this should be semantically identical to:

foldl f z = foldl f z . toList

Examples

Expand

The first example is a strict fold, which in practice is best performed with foldl'.

>>> foldl (+) 42 [1,2,3,4]
52

Though the result below is lazy, the input is reversed before prepending it to the initial accumulator, so corecursion begins only after traversing the entire input string.

>>> foldl (\acc c -> c : acc) "abcd" "efgh"
"hgfeabcd"

A left fold of a structure that is infinite on the right cannot terminate, even when for any finite input the fold just returns the initial accumulator:

>>> foldl (\a _ -> a) 0 $ repeat 1
* Hangs forever *

WARNING: When it comes to lists, you always want to use either foldl' or foldr instead.

foldl' :: (b -> a -> b) -> b -> t a -> b #

Left-associative fold of a structure but with strict application of the operator.

This ensures that each step of the fold is forced to Weak Head Normal Form before being applied, avoiding the collection of thunks that would otherwise occur. This is often what you want to strictly reduce a finite structure to a single strict result (e.g. sum).

For a general Foldable structure this should be semantically identical to,

foldl' f z = foldl' f z . toList

Since: base-4.6.0.0

foldr1 :: (a -> a -> a) -> t a -> a #

A variant of foldr that has no base case, and thus may only be applied to non-empty structures.

This function is non-total and will raise a runtime exception if the structure happens to be empty.

Examples

Expand

Basic usage:

>>> foldr1 (+) [1..4]
10
>>> foldr1 (+) []
Exception: Prelude.foldr1: empty list
>>> foldr1 (+) Nothing
*** Exception: foldr1: empty structure
>>> foldr1 (-) [1..4]
-2
>>> foldr1 (&&) [True, False, True, True]
False
>>> foldr1 (||) [False, False, True, True]
True
>>> foldr1 (+) [1..]
* Hangs forever *

foldl1 :: (a -> a -> a) -> t a -> a #

A variant of foldl that has no base case, and thus may only be applied to non-empty structures.

This function is non-total and will raise a runtime exception if the structure happens to be empty.

foldl1 f = foldl1 f . toList

Examples

Expand

Basic usage:

>>> foldl1 (+) [1..4]
10
>>> foldl1 (+) []
*** Exception: Prelude.foldl1: empty list
>>> foldl1 (+) Nothing
*** Exception: foldl1: empty structure
>>> foldl1 (-) [1..4]
-8
>>> foldl1 (&&) [True, False, True, True]
False
>>> foldl1 (||) [False, False, True, True]
True
>>> foldl1 (+) [1..]
* Hangs forever *

toList :: t a -> [a] #

List of elements of a structure, from left to right. If the entire list is intended to be reduced via a fold, just fold the structure directly bypassing the list.

Examples

Expand

Basic usage:

>>> toList Nothing
[]
>>> toList (Just 42)
[42]
>>> toList (Left "foo")
[]
>>> toList (Node (Leaf 5) 17 (Node Empty 12 (Leaf 8)))
[5,17,12,8]

For lists, toList is the identity:

>>> toList [1, 2, 3]
[1,2,3]

Since: base-4.8.0.0

null :: t a -> Bool #

Test whether the structure is empty. The default implementation is Left-associative and lazy in both the initial element and the accumulator. Thus optimised for structures where the first element can be accessed in constant time. Structures where this is not the case should have a non-default implementation.

Examples

Expand

Basic usage:

>>> null []
True
>>> null [1]
False

null is expected to terminate even for infinite structures. The default implementation terminates provided the structure is bounded on the left (there is a leftmost element).

>>> null [1..]
False

Since: base-4.8.0.0

length :: t a -> Int #

Returns the size/length of a finite structure as an Int. The default implementation just counts elements starting with the leftmost. Instances for structures that can compute the element count faster than via element-by-element counting, should provide a specialised implementation.

Examples

Expand

Basic usage:

>>> length []
0
>>> length ['a', 'b', 'c']
3
>>> length [1..]
* Hangs forever *

Since: base-4.8.0.0

elem :: Eq a => a -> t a -> Bool infix 4 #

Does the element occur in the structure?

Note: elem is often used in infix form.

Examples

Expand

Basic usage:

>>> 3 `elem` []
False
>>> 3 `elem` [1,2]
False
>>> 3 `elem` [1,2,3,4,5]
True

For infinite structures, the default implementation of elem terminates if the sought-after value exists at a finite distance from the left side of the structure:

>>> 3 `elem` [1..]
True
>>> 3 `elem` ([4..] ++ [3])
* Hangs forever *

Since: base-4.8.0.0

maximum :: Ord a => t a -> a #

The largest element of a non-empty structure.

This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the maximum in faster than linear time.

Examples

Expand

Basic usage:

>>> maximum [1..10]
10
>>> maximum []
*** Exception: Prelude.maximum: empty list
>>> maximum Nothing
*** Exception: maximum: empty structure

WARNING: This function is partial for possibly-empty structures like lists.

Since: base-4.8.0.0

minimum :: Ord a => t a -> a #

The least element of a non-empty structure.

This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the minimum in faster than linear time.

Examples

Expand

Basic usage:

>>> minimum [1..10]
1
>>> minimum []
*** Exception: Prelude.minimum: empty list
>>> minimum Nothing
*** Exception: minimum: empty structure

WARNING: This function is partial for possibly-empty structures like lists.

Since: base-4.8.0.0

Instances

Instances details
Foldable ZipList

Since: base-4.9.0.0

Instance details

Defined in Control.Applicative

Methods

fold :: Monoid m => ZipList m -> m #

foldMap :: Monoid m => (a -> m) -> ZipList a -> m #

foldMap' :: Monoid m => (a -> m) -> ZipList a -> m #

foldr :: (a -> b -> b) -> b -> ZipList a -> b #

foldr' :: (a -> b -> b) -> b -> ZipList a -> b #

foldl :: (b -> a -> b) -> b -> ZipList a -> b #

foldl' :: (b -> a -> b) -> b -> ZipList a -> b #

foldr1 :: (a -> a -> a) -> ZipList a -> a #

foldl1 :: (a -> a -> a) -> ZipList a -> a #

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

Instance details

Defined in Data.Functor.Identity

Methods

fold :: Monoid m => Identity m -> m #

foldMap :: Monoid m => (a -> m) -> Identity a -> m #

foldMap' :: Monoid m => (a -> m) -> Identity a -> m #

foldr :: (a -> b -> b) -> b -> Identity a -> b #

foldr' :: (a -> b -> b) -> b -> Identity a -> b #

foldl :: (b -> a -> b) -> b -> Identity a -> b #

foldl' :: (b -> a -> b) -> b -> Identity a -> b #

foldr1 :: (a -> a -> a) -> Identity a -> a #

foldl1 :: (a -> a -> a) -> Identity a -> a #

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

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => First m -> m #

foldMap :: Monoid m => (a -> m) -> First a -> m #

foldMap' :: Monoid m => (a -> m) -> First a -> m #

foldr :: (a -> b -> b) -> b -> First a -> b #

foldr' :: (a -> b -> b) -> b -> First a -> b #

foldl :: (b -> a -> b) -> b -> First a -> b #

foldl' :: (b -> a -> b) -> b -> First a -> b #

foldr1 :: (a -> a -> a) -> First a -> a #

foldl1 :: (a -> a -> a) -> First a -> a #

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

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Last m -> m #

foldMap :: Monoid m => (a -> m) -> Last a -> m #

foldMap' :: Monoid m => (a -> m) -> Last a -> m #

foldr :: (a -> b -> b) -> b -> Last a -> b #

foldr' :: (a -> b -> b) -> b -> Last a -> b #

foldl :: (b -> a -> b) -> b -> Last a -> b #

foldl' :: (b -> a -> b) -> b -> Last a -> b #

foldr1 :: (a -> a -> a) -> Last a -> a #

foldl1 :: (a -> a -> a) -> Last a -> a #

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 Down

Since: base-4.12.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Down m -> m #

foldMap :: Monoid m => (a -> m) -> Down a -> m #

foldMap' :: Monoid m => (a -> m) -> Down a -> m #

foldr :: (a -> b -> b) -> b -> Down a -> b #

foldr' :: (a -> b -> b) -> b -> Down a -> b #

foldl :: (b -> a -> b) -> b -> Down a -> b #

foldl' :: (b -> a -> b) -> b -> Down a -> b #

foldr1 :: (a -> a -> a) -> Down a -> a #

foldl1 :: (a -> a -> a) -> Down a -> a #

toList :: Down a -> [a] #

null :: Down a -> Bool #

length :: Down a -> Int #

elem :: Eq a => a -> Down a -> Bool #

maximum :: Ord a => Down a -> a #

minimum :: Ord a => Down a -> a #

sum :: Num a => Down a -> a #

product :: Num a => Down a -> a #

Foldable First

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => First m -> m #

foldMap :: Monoid m => (a -> m) -> First a -> m #

foldMap' :: Monoid m => (a -> m) -> First a -> m #

foldr :: (a -> b -> b) -> b -> First a -> b #

foldr' :: (a -> b -> b) -> b -> First a -> b #

foldl :: (b -> a -> b) -> b -> First a -> b #

foldl' :: (b -> a -> b) -> b -> First a -> b #

foldr1 :: (a -> a -> a) -> First a -> a #

foldl1 :: (a -> a -> a) -> First a -> a #

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

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => Last m -> m #

foldMap :: Monoid m => (a -> m) -> Last a -> m #

foldMap' :: Monoid m => (a -> m) -> Last a -> m #

foldr :: (a -> b -> b) -> b -> Last a -> b #

foldr' :: (a -> b -> b) -> b -> Last a -> b #

foldl :: (b -> a -> b) -> b -> Last a -> b #

foldl' :: (b -> a -> b) -> b -> Last a -> b #

foldr1 :: (a -> a -> a) -> Last a -> a #

foldl1 :: (a -> a -> a) -> Last a -> a #

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 Max

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Dual m -> m #

foldMap :: Monoid m => (a -> m) -> Dual a -> m #

foldMap' :: Monoid m => (a -> m) -> Dual a -> m #

foldr :: (a -> b -> b) -> b -> Dual a -> b #

foldr' :: (a -> b -> b) -> b -> Dual a -> b #

foldl :: (b -> a -> b) -> b -> Dual a -> b #

foldl' :: (b -> a -> b) -> b -> Dual a -> b #

foldr1 :: (a -> a -> a) -> Dual a -> a #

foldl1 :: (a -> a -> a) -> Dual a -> a #

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 Product

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Product m -> m #

foldMap :: Monoid m => (a -> m) -> Product a -> m #

foldMap' :: Monoid m => (a -> m) -> Product a -> m #

foldr :: (a -> b -> b) -> b -> Product a -> b #

foldr' :: (a -> b -> b) -> b -> Product a -> b #

foldl :: (b -> a -> b) -> b -> Product a -> b #

foldl' :: (b -> a -> b) -> b -> Product a -> b #

foldr1 :: (a -> a -> a) -> Product a -> a #

foldl1 :: (a -> a -> a) -> Product a -> a #

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 Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Sum m -> m #

foldMap :: Monoid m => (a -> m) -> Sum a -> m #

foldMap' :: Monoid m => (a -> m) -> Sum a -> m #

foldr :: (a -> b -> b) -> b -> Sum a -> b #

foldr' :: (a -> b -> b) -> b -> Sum a -> b #

foldl :: (b -> a -> b) -> b -> Sum a -> b #

foldl' :: (b -> a -> b) -> b -> Sum a -> b #

foldr1 :: (a -> a -> a) -> Sum a -> a #

foldl1 :: (a -> a -> a) -> Sum a -> a #

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 NonEmpty

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => NonEmpty m -> m #

foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m #

foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m #

foldr :: (a -> b -> b) -> b -> NonEmpty a -> b #

foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b #

foldl :: (b -> a -> b) -> b -> NonEmpty a -> b #

foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b #

foldr1 :: (a -> a -> a) -> NonEmpty a -> a #

foldl1 :: (a -> a -> a) -> NonEmpty a -> a #

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 Par1

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Par1 m -> m #

foldMap :: Monoid m => (a -> m) -> Par1 a -> m #

foldMap' :: Monoid m => (a -> m) -> Par1 a -> m #

foldr :: (a -> b -> b) -> b -> Par1 a -> b #

foldr' :: (a -> b -> b) -> b -> Par1 a -> b #

foldl :: (b -> a -> b) -> b -> Par1 a -> b #

foldl' :: (b -> a -> b) -> b -> Par1 a -> b #

foldr1 :: (a -> a -> a) -> Par1 a -> a #

foldl1 :: (a -> a -> a) -> Par1 a -> a #

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 Maybe

Since: base-2.1

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Maybe m -> m #

foldMap :: Monoid m => (a -> m) -> Maybe a -> m #

foldMap' :: Monoid m => (a -> m) -> Maybe a -> m #

foldr :: (a -> b -> b) -> b -> Maybe a -> b #

foldr' :: (a -> b -> b) -> b -> Maybe a -> b #

foldl :: (b -> a -> b) -> b -> Maybe a -> b #

foldl' :: (b -> a -> b) -> b -> Maybe a -> b #

foldr1 :: (a -> a -> a) -> Maybe a -> a #

foldl1 :: (a -> a -> a) -> Maybe a -> a #

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 Solo

Since: base-4.15

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Solo m -> m #

foldMap :: Monoid m => (a -> m) -> Solo a -> m #

foldMap' :: Monoid m => (a -> m) -> Solo a -> m #

foldr :: (a -> b -> b) -> b -> Solo a -> b #

foldr' :: (a -> b -> b) -> b -> Solo a -> b #

foldl :: (b -> a -> b) -> b -> Solo a -> b #

foldl' :: (b -> a -> b) -> b -> Solo a -> b #

foldr1 :: (a -> a -> a) -> Solo a -> a #

foldl1 :: (a -> a -> a) -> Solo a -> a #

toList :: Solo a -> [a] #

null :: Solo a -> Bool #

length :: Solo a -> Int #

elem :: Eq a => a -> Solo a -> Bool #

maximum :: Ord a => Solo a -> a #

minimum :: Ord a => Solo a -> a #

sum :: Num a => Solo a -> a #

product :: Num a => Solo a -> a #

Foldable List

Since: base-2.1

Instance details

Defined in Data.Foldable

Methods

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

foldMap :: Monoid m => (a -> m) -> [a] -> m #

foldMap' :: Monoid m => (a -> m) -> [a] -> m #

foldr :: (a -> b -> b) -> b -> [a] -> b #

foldr' :: (a -> b -> b) -> b -> [a] -> b #

foldl :: (b -> a -> b) -> b -> [a] -> b #

foldl' :: (b -> a -> b) -> b -> [a] -> b #

foldr1 :: (a -> a -> a) -> [a] -> a #

foldl1 :: (a -> a -> a) -> [a] -> a #

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 (Either a)

Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Either a m -> m #

foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m #

foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m #

foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b #

foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b #

foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b #

foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b #

foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 #

foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 #

toList :: Either a a0 -> [a0] #

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 (Proxy :: Type -> Type)

Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Proxy m -> m #

foldMap :: Monoid m => (a -> m) -> Proxy a -> m #

foldMap' :: Monoid m => (a -> m) -> Proxy a -> m #

foldr :: (a -> b -> b) -> b -> Proxy a -> b #

foldr' :: (a -> b -> b) -> b -> Proxy a -> b #

foldl :: (b -> a -> b) -> b -> Proxy a -> b #

foldl' :: (b -> a -> b) -> b -> Proxy a -> b #

foldr1 :: (a -> a -> a) -> Proxy a -> a #

foldl1 :: (a -> a -> a) -> Proxy a -> a #

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 (Arg a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Array i m -> m #

foldMap :: Monoid m => (a -> m) -> Array i a -> m #

foldMap' :: Monoid m => (a -> m) -> Array i a -> m #

foldr :: (a -> b -> b) -> b -> Array i a -> b #

foldr' :: (a -> b -> b) -> b -> Array i a -> b #

foldl :: (b -> a -> b) -> b -> Array i a -> b #

foldl' :: (b -> a -> b) -> b -> Array i a -> b #

foldr1 :: (a -> a -> a) -> Array i a -> a #

foldl1 :: (a -> a -> a) -> Array i a -> a #

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 (U1 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => U1 m -> m #

foldMap :: Monoid m => (a -> m) -> U1 a -> m #

foldMap' :: Monoid m => (a -> m) -> U1 a -> m #

foldr :: (a -> b -> b) -> b -> U1 a -> b #

foldr' :: (a -> b -> b) -> b -> U1 a -> b #

foldl :: (b -> a -> b) -> b -> U1 a -> b #

foldl' :: (b -> a -> b) -> b -> U1 a -> b #

foldr1 :: (a -> a -> a) -> U1 a -> a #

foldl1 :: (a -> a -> a) -> U1 a -> a #

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 (UAddr :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UAddr m -> m #

foldMap :: Monoid m => (a -> m) -> UAddr a -> m #

foldMap' :: Monoid m => (a -> m) -> UAddr a -> m #

foldr :: (a -> b -> b) -> b -> UAddr a -> b #

foldr' :: (a -> b -> b) -> b -> UAddr a -> b #

foldl :: (b -> a -> b) -> b -> UAddr a -> b #

foldl' :: (b -> a -> b) -> b -> UAddr a -> b #

foldr1 :: (a -> a -> a) -> UAddr a -> a #

foldl1 :: (a -> a -> a) -> UAddr a -> a #

toList :: UAddr a -> [a] #

null :: UAddr a -> Bool #

length :: UAddr a -> Int #

elem :: Eq a => a -> UAddr a -> Bool #

maximum :: Ord a => UAddr a -> a #

minimum :: Ord a => UAddr a -> a #

sum :: Num a => UAddr a -> a #

product :: Num a => UAddr a -> a #

Foldable (UChar :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UChar m -> m #

foldMap :: Monoid m => (a -> m) -> UChar a -> m #

foldMap' :: Monoid m => (a -> m) -> UChar a -> m #

foldr :: (a -> b -> b) -> b -> UChar a -> b #

foldr' :: (a -> b -> b) -> b -> UChar a -> b #

foldl :: (b -> a -> b) -> b -> UChar a -> b #

foldl' :: (b -> a -> b) -> b -> UChar a -> b #

foldr1 :: (a -> a -> a) -> UChar a -> a #

foldl1 :: (a -> a -> a) -> UChar a -> a #

toList :: UChar a -> [a] #

null :: UChar a -> Bool #

length :: UChar a -> Int #

elem :: Eq a => a -> UChar a -> Bool #

maximum :: Ord a => UChar a -> a #

minimum :: Ord a => UChar a -> a #

sum :: Num a => UChar a -> a #

product :: Num a => UChar a -> a #

Foldable (UDouble :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UDouble m -> m #

foldMap :: Monoid m => (a -> m) -> UDouble a -> m #

foldMap' :: Monoid m => (a -> m) -> UDouble a -> m #

foldr :: (a -> b -> b) -> b -> UDouble a -> b #

foldr' :: (a -> b -> b) -> b -> UDouble a -> b #

foldl :: (b -> a -> b) -> b -> UDouble a -> b #

foldl' :: (b -> a -> b) -> b -> UDouble a -> b #

foldr1 :: (a -> a -> a) -> UDouble a -> a #

foldl1 :: (a -> a -> a) -> UDouble a -> a #

toList :: UDouble a -> [a] #

null :: UDouble a -> Bool #

length :: UDouble a -> Int #

elem :: Eq a => a -> UDouble a -> Bool #

maximum :: Ord a => UDouble a -> a #

minimum :: Ord a => UDouble a -> a #

sum :: Num a => UDouble a -> a #

product :: Num a => UDouble a -> a #

Foldable (UFloat :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UFloat m -> m #

foldMap :: Monoid m => (a -> m) -> UFloat a -> m #

foldMap' :: Monoid m => (a -> m) -> UFloat a -> m #

foldr :: (a -> b -> b) -> b -> UFloat a -> b #

foldr' :: (a -> b -> b) -> b -> UFloat a -> b #

foldl :: (b -> a -> b) -> b -> UFloat a -> b #

foldl' :: (b -> a -> b) -> b -> UFloat a -> b #

foldr1 :: (a -> a -> a) -> UFloat a -> a #

foldl1 :: (a -> a -> a) -> UFloat a -> a #

toList :: UFloat a -> [a] #

null :: UFloat a -> Bool #

length :: UFloat a -> Int #

elem :: Eq a => a -> UFloat a -> Bool #

maximum :: Ord a => UFloat a -> a #

minimum :: Ord a => UFloat a -> a #

sum :: Num a => UFloat a -> a #

product :: Num a => UFloat a -> a #

Foldable (UInt :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UInt m -> m #

foldMap :: Monoid m => (a -> m) -> UInt a -> m #

foldMap' :: Monoid m => (a -> m) -> UInt a -> m #

foldr :: (a -> b -> b) -> b -> UInt a -> b #

foldr' :: (a -> b -> b) -> b -> UInt a -> b #

foldl :: (b -> a -> b) -> b -> UInt a -> b #

foldl' :: (b -> a -> b) -> b -> UInt a -> b #

foldr1 :: (a -> a -> a) -> UInt a -> a #

foldl1 :: (a -> a -> a) -> UInt a -> a #

toList :: UInt a -> [a] #

null :: UInt a -> Bool #

length :: UInt a -> Int #

elem :: Eq a => a -> UInt a -> Bool #

maximum :: Ord a => UInt a -> a #

minimum :: Ord a => UInt a -> a #

sum :: Num a => UInt a -> a #

product :: Num a => UInt a -> a #

Foldable (UWord :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UWord m -> m #

foldMap :: Monoid m => (a -> m) -> UWord a -> m #

foldMap' :: Monoid m => (a -> m) -> UWord a -> m #

foldr :: (a -> b -> b) -> b -> UWord a -> b #

foldr' :: (a -> b -> b) -> b -> UWord a -> b #

foldl :: (b -> a -> b) -> b -> UWord a -> b #

foldl' :: (b -> a -> b) -> b -> UWord a -> b #

foldr1 :: (a -> a -> a) -> UWord a -> a #

foldl1 :: (a -> a -> a) -> UWord a -> a #

toList :: UWord a -> [a] #

null :: UWord a -> Bool #

length :: UWord a -> Int #

elem :: Eq a => a -> UWord a -> Bool #

maximum :: Ord a => UWord a -> a #

minimum :: Ord a => UWord a -> a #

sum :: Num a => UWord a -> a #

product :: Num a => UWord a -> a #

Foldable (V1 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => V1 m -> m #

foldMap :: Monoid m => (a -> m) -> V1 a -> m #

foldMap' :: Monoid m => (a -> m) -> V1 a -> m #

foldr :: (a -> b -> b) -> b -> V1 a -> b #

foldr' :: (a -> b -> b) -> b -> V1 a -> b #

foldl :: (b -> a -> b) -> b -> V1 a -> b #

foldl' :: (b -> a -> b) -> b -> V1 a -> b #

foldr1 :: (a -> a -> a) -> V1 a -> a #

foldl1 :: (a -> a -> a) -> V1 a -> a #

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 ((,) a)

Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => (a, m) -> m #

foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m #

foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m #

foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b #

foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b #

foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b #

foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b #

foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 #

foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 #

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 (Const m :: Type -> Type)

Since: base-4.7.0.0

Instance details

Defined in Data.Functor.Const

Methods

fold :: Monoid m0 => Const m m0 -> m0 #

foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 #

foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 #

foldr :: (a -> b -> b) -> b -> Const m a -> b #

foldr' :: (a -> b -> b) -> b -> Const m a -> b #

foldl :: (b -> a -> b) -> b -> Const m a -> b #

foldl' :: (b -> a -> b) -> b -> Const m a -> b #

foldr1 :: (a -> a -> a) -> Const m a -> a #

foldl1 :: (a -> a -> a) -> Const m a -> a #

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 (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Ap f m -> m #

foldMap :: Monoid m => (a -> m) -> Ap f a -> m #

foldMap' :: Monoid m => (a -> m) -> Ap f a -> m #

foldr :: (a -> b -> b) -> b -> Ap f a -> b #

foldr' :: (a -> b -> b) -> b -> Ap f a -> b #

foldl :: (b -> a -> b) -> b -> Ap f a -> b #

foldl' :: (b -> a -> b) -> b -> Ap f a -> b #

foldr1 :: (a -> a -> a) -> Ap f a -> a #

foldl1 :: (a -> a -> a) -> Ap f a -> a #

toList :: Ap f a -> [a] #

null :: Ap f a -> Bool #

length :: Ap f a -> Int #

elem :: Eq a => a -> Ap f a -> Bool #

maximum :: Ord a => Ap f a -> a #

minimum :: Ord a => Ap f a -> a #

sum :: Num a => Ap f a -> a #

product :: Num a => Ap f a -> a #

Foldable f => Foldable (Alt f)

Since: base-4.12.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Alt f m -> m #

foldMap :: Monoid m => (a -> m) -> Alt f a -> m #

foldMap' :: Monoid m => (a -> m) -> Alt f a -> m #

foldr :: (a -> b -> b) -> b -> Alt f a -> b #

foldr' :: (a -> b -> b) -> b -> Alt f a -> b #

foldl :: (b -> a -> b) -> b -> Alt f a -> b #

foldl' :: (b -> a -> b) -> b -> Alt f a -> b #

foldr1 :: (a -> a -> a) -> Alt f a -> a #

foldl1 :: (a -> a -> a) -> Alt f a -> a #

toList :: Alt f a -> [a] #

null :: Alt f a -> Bool #

length :: Alt f a -> Int #

elem :: Eq a => a -> Alt f a -> Bool #

maximum :: Ord a => Alt f a -> a #

minimum :: Ord a => Alt f a -> a #

sum :: Num a => Alt f a -> a #

product :: Num a => Alt f a -> a #

Foldable f => Foldable (Rec1 f)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

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

foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m #

foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m #

foldr :: (a -> b -> b) -> b -> Rec1 f a -> b #

foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b #

foldl :: (b -> a -> b) -> b -> Rec1 f a -> b #

foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b #

foldr1 :: (a -> a -> a) -> Rec1 f a -> a #

foldl1 :: (a -> a -> a) -> Rec1 f a -> a #

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

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

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

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

foldMap' :: Monoid m => (a -> m) -> (f :*: g) a -> m #

foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b #

foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b #

foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b #

foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b #

foldr1 :: (a -> a -> a) -> (f :*: g) a -> a #

foldl1 :: (a -> a -> a) -> (f :*: g) a -> a #

toList :: (f :*: g) a -> [a] #

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)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

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

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

foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m #

foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b #

foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b #

foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b #

foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b #

foldr1 :: (a -> a -> a) -> (f :+: g) a -> a #

foldl1 :: (a -> a -> a) -> (f :+: g) a -> a #

toList :: (f :+: g) a -> [a] #

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 (K1 i c :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

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

foldMap :: Monoid m => (a -> m) -> K1 i c a -> m #

foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m #

foldr :: (a -> b -> b) -> b -> K1 i c a -> b #

foldr' :: (a -> b -> b) -> b -> K1 i c a -> b #

foldl :: (b -> a -> b) -> b -> K1 i c a -> b #

foldl' :: (b -> a -> b) -> b -> K1 i c a -> b #

foldr1 :: (a -> a -> a) -> K1 i c a -> a #

foldl1 :: (a -> a -> a) -> K1 i c a -> a #

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)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

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

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

foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m #

foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b #

foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b #

foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b #

foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b #

foldr1 :: (a -> a -> a) -> (f :.: g) a -> a #

foldl1 :: (a -> a -> a) -> (f :.: g) a -> a #

toList :: (f :.: g) a -> [a] #

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)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => M1 i c f m -> m #

foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m #

foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m #

foldr :: (a -> b -> b) -> b -> M1 i c f a -> b #

foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b #

foldl :: (b -> a -> b) -> b -> M1 i c f a -> b #

foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b #

foldr1 :: (a -> a -> a) -> M1 i c f a -> a #

foldl1 :: (a -> a -> a) -> M1 i c f a -> a #

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 #

maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a #

The largest element of a non-empty structure with respect to the given comparison function.

Examples

Expand

Basic usage:

>>> maximumBy (compare `on` length) ["Hello", "World", "!", "Longest", "bar"]
"Longest"

WARNING: This function is partial for possibly-empty structures like lists.

minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a #

The least element of a non-empty structure with respect to the given comparison function.

Examples

Expand

Basic usage:

>>> minimumBy (compare `on` length) ["Hello", "World", "!", "Longest", "bar"]
"!"

WARNING: This function is partial for possibly-empty structures like lists.

concat :: Foldable t => t [a] -> [a] #

The concatenation of all the elements of a container of lists.

Examples

Expand

Basic usage:

>>> concat (Just [1, 2, 3])
[1,2,3]
>>> concat (Left 42)
[]
>>> concat [[1, 2, 3], [4, 5], [6], []]
[1,2,3,4,5,6]

and :: Foldable t => t Bool -> Bool #

and returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.

Examples

Expand

Basic usage:

>>> and []
True
>>> and [True]
True
>>> and [False]
False
>>> and [True, True, False]
False
>>> and (False : repeat True) -- Infinite list [False,True,True,True,...
False
>>> and (repeat True)
* Hangs forever *

or :: Foldable t => t Bool -> Bool #

or returns the disjunction of a container of Bools. For the result to be False, the container must be finite; True, however, results from a True value finitely far from the left end.

Examples

Expand

Basic usage:

>>> or []
False
>>> or [True]
True
>>> or [False]
False
>>> or [True, True, False]
True
>>> or (True : repeat False) -- Infinite list [True,False,False,False,...
True
>>> or (repeat False)
* Hangs forever *

any :: Foldable t => (a -> Bool) -> t a -> Bool #

Determines whether any element of the structure satisfies the predicate.

Examples

Expand

Basic usage:

>>> any (> 3) []
False
>>> any (> 3) [1,2]
False
>>> any (> 3) [1,2,3,4,5]
True
>>> any (> 3) [1..]
True
>>> any (> 3) [0, -1..]
* Hangs forever *

all :: Foldable t => (a -> Bool) -> t a -> Bool #

Determines whether all elements of the structure satisfy the predicate.

Examples

Expand

Basic usage:

>>> all (> 3) []
True
>>> all (> 3) [1,2]
False
>>> all (> 3) [1,2,3,4,5]
False
>>> all (> 3) [1..]
False
>>> all (> 3) [4..]
* Hangs forever *

notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 #

notElem is the negation of elem.

Examples

Expand

Basic usage:

>>> 3 `notElem` []
True
>>> 3 `notElem` [1,2]
True
>>> 3 `notElem` [1,2,3,4,5]
False

For infinite structures, notElem terminates if the value exists at a finite distance from the left side of the structure:

>>> 3 `notElem` [1..]
False
>>> 3 `notElem` ([4..] ++ [3])
* Hangs forever *

concatMap :: Foldable t => (a -> [b]) -> t a -> [b] #

Map a function over all the elements of a container and concatenate the resulting lists.

Examples

Expand

Basic usage:

>>> concatMap (take 3) [[1..], [10..], [100..], [1000..]]
[1,2,3,10,11,12,100,101,102,1000,1001,1002]
>>> concatMap (take 3) (Just [1..])
[1,2,3]

foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b #

Right-to-left monadic fold over the elements of a structure.

Given a structure t with elements (a, b, c, ..., x, y), the result of a fold with an operator function f is equivalent to:

foldrM f z t = do
    yy <- f y z
    xx <- f x yy
    ...
    bb <- f b cc
    aa <- f a bb
    return aa -- Just @return z@ when the structure is empty

For a Monad m, given two functions f1 :: a -> m b and f2 :: b -> m c, their Kleisli composition (f1 >=> f2) :: a -> m c is defined by:

(f1 >=> f2) a = f1 a >>= f2

Another way of thinking about foldrM is that it amounts to an application to z of a Kleisli composition:

foldrM f z t = f y >=> f x >=> ... >=> f b >=> f a $ z

The monadic effects of foldrM are sequenced from right to left, and e.g. folds of infinite lists will diverge.

If at some step the bind operator (>>=) short-circuits (as with, e.g., mzero in a MonadPlus), the evaluated effects will be from a tail of the element sequence. If you want to evaluate the monadic effects in left-to-right order, or perhaps be able to short-circuit after an initial sequence of elements, you'll need to use foldlM instead.

If the monadic effects don't short-circuit, the outermost application of f is to the leftmost element a, so that, ignoring effects, the result looks like a right fold:

a `f` (b `f` (c `f` (... (x `f` (y `f` z))))).

Examples

Expand

Basic usage:

>>> let f i acc = do { print i ; return $ i : acc }
>>> foldrM f [] [0..3]
3
2
1
0
[0,1,2,3]

foldlM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b #

Left-to-right monadic fold over the elements of a structure.

Given a structure t with elements (a, b, ..., w, x, y), the result of a fold with an operator function f is equivalent to:

foldlM f z t = do
    aa <- f z a
    bb <- f aa b
    ...
    xx <- f ww x
    yy <- f xx y
    return yy -- Just @return z@ when the structure is empty

For a Monad m, given two functions f1 :: a -> m b and f2 :: b -> m c, their Kleisli composition (f1 >=> f2) :: a -> m c is defined by:

(f1 >=> f2) a = f1 a >>= f2

Another way of thinking about foldlM is that it amounts to an application to z of a Kleisli composition:

foldlM f z t =
    flip f a >=> flip f b >=> ... >=> flip f x >=> flip f y $ z

The monadic effects of foldlM are sequenced from left to right.

If at some step the bind operator (>>=) short-circuits (as with, e.g., mzero in a MonadPlus), the evaluated effects will be from an initial segment of the element sequence. If you want to evaluate the monadic effects in right-to-left order, or perhaps be able to short-circuit after processing a tail of the sequence of elements, you'll need to use foldrM instead.

If the monadic effects don't short-circuit, the outermost application of f is to the rightmost element y, so that, ignoring effects, the result looks like a left fold:

((((z `f` a) `f` b) ... `f` w) `f` x) `f` y

Examples

Expand

Basic usage:

>>> let f a e = do { print e ; return $ e : a }
>>> foldlM f [] [0..3]
0
1
2
3
[3,2,1,0]

traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f () #

Map each element of a structure to an Applicative action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see traverse.

traverse_ is just like mapM_, but generalised to Applicative actions.

Examples

Expand

Basic usage:

>>> traverse_ print ["Hello", "world", "!"]
"Hello"
"world"
"!"

for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f () #

for_ is traverse_ with its arguments flipped. For a version that doesn't ignore the results see for. This is forM_ generalised to Applicative actions.

for_ is just like forM_, but generalised to Applicative actions.

Examples

Expand

Basic usage:

>>> for_ [1..4] print
1
2
3
4

mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m () #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see mapM.

mapM_ is just like traverse_, but specialised to monadic actions.

forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m () #

forM_ is mapM_ with its arguments flipped. For a version that doesn't ignore the results see forM.

forM_ is just like for_, but specialised to monadic actions.

sequenceA_ :: (Foldable t, Applicative f) => t (f a) -> f () #

Evaluate each action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequenceA.

sequenceA_ is just like sequence_, but generalised to Applicative actions.

Examples

Expand

Basic usage:

>>> sequenceA_ [print "Hello", print "world", print "!"]
"Hello"
"world"
"!"

sequence_ :: (Foldable t, Monad m) => t (m a) -> m () #

Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequence.

sequence_ is just like sequenceA_, but specialised to monadic actions.

asum :: (Foldable t, Alternative f) => t (f a) -> f a #

The sum of a collection of actions using (<|>), generalizing concat.

asum is just like msum, but generalised to Alternative.

Examples

Expand

Basic usage:

>>> asum [Just "Hello", Nothing, Just "World"]
Just "Hello"

msum :: (Foldable t, MonadPlus m) => t (m a) -> m a #

The sum of a collection of actions using (<|>), generalizing concat.

msum is just like asum, but specialised to MonadPlus.

Examples

Expand

Basic usage, using the MonadPlus instance for Maybe:

>>> msum [Just "Hello", Nothing, Just "World"]
Just "Hello"

find :: Foldable t => (a -> Bool) -> t a -> Maybe a #

The find function takes a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

Examples

Expand

Basic usage:

>>> find (> 42) [0, 5..]
Just 45
>>> find (> 12) [1..7]
Nothing

The Prelude

data Int #

A fixed-precision integer type with at least the range [-2^29 .. 2^29-1]. The exact range for a given implementation can be determined by using minBound and maxBound from the Bounded class.

Instances

Instances details
Data Int

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Int -> c Int #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Int #

toConstr :: Int -> Constr #

dataTypeOf :: Int -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Int) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Int) #

gmapT :: (forall b. Data b => b -> b) -> Int -> Int #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r #

gmapQ :: (forall d. Data d => d -> u) -> Int -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Int -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Int -> m Int #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int #

Bounded Int

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: Int #

maxBound :: Int #

Enum Int

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Int -> Int #

pred :: Int -> Int #

toEnum :: Int -> Int #

fromEnum :: Int -> Int #

enumFrom :: Int -> [Int] #

enumFromThen :: Int -> Int -> [Int] #

enumFromTo :: Int -> Int -> [Int] #

enumFromThenTo :: Int -> Int -> Int -> [Int] #

Num Int

Since: base-2.1

Instance details

Defined in GHC.Num

Methods

(+) :: Int -> Int -> Int #

(-) :: Int -> Int -> Int #

(*) :: Int -> Int -> Int #

negate :: Int -> Int #

abs :: Int -> Int #

signum :: Int -> Int #

fromInteger :: Integer -> Int #

Read Int

Since: base-2.1

Instance details

Defined in GHC.Read

Integral Int

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

quot :: Int -> Int -> Int #

rem :: Int -> Int -> Int #

div :: Int -> Int -> Int #

mod :: Int -> Int -> Int #

quotRem :: Int -> Int -> (Int, Int) #

divMod :: Int -> Int -> (Int, Int) #

toInteger :: Int -> Integer #

Real Int

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

toRational :: Int -> Rational #

Show Int

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Int -> ShowS #

show :: Int -> String #

showList :: [Int] -> ShowS #

Eq Int 
Instance details

Defined in GHC.Classes

Methods

(==) :: Int -> Int -> Bool #

(/=) :: Int -> Int -> Bool #

Ord Int 
Instance details

Defined in GHC.Classes

Methods

compare :: Int -> Int -> Ordering #

(<) :: Int -> Int -> Bool #

(<=) :: Int -> Int -> Bool #

(>) :: Int -> Int -> Bool #

(>=) :: Int -> Int -> Bool #

max :: Int -> Int -> Int #

min :: Int -> Int -> Int #

Additive Int Source # 
Instance details

Defined in NumHask.Algebra.Additive

Methods

(+) :: Int -> Int -> Int Source #

zero :: Int Source #

Subtractive Int Source # 
Instance details

Defined in NumHask.Algebra.Additive

Methods

negate :: Int -> Int Source #

(-) :: Int -> Int -> Int Source #

BoundedJoinSemiLattice Int Source # 
Instance details

Defined in NumHask.Algebra.Lattice

Methods

bottom :: Int Source #

BoundedMeetSemiLattice Int Source # 
Instance details

Defined in NumHask.Algebra.Lattice

Methods

top :: Int Source #

JoinSemiLattice Int Source # 
Instance details

Defined in NumHask.Algebra.Lattice

Methods

(\/) :: Int -> Int -> Int Source #

MeetSemiLattice Int Source # 
Instance details

Defined in NumHask.Algebra.Lattice

Methods

(/\) :: Int -> Int -> Int Source #

Basis Int Source # 
Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Int Source #

type Base Int Source #

Epsilon Int Source #

0

Instance details

Defined in NumHask.Algebra.Metric

Methods

epsilon :: Int Source #

Multiplicative Int Source # 
Instance details

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Int -> Int -> Int Source #

one :: Int Source #

InvolutiveRing Int Source # 
Instance details

Defined in NumHask.Algebra.Ring

Methods

adj :: Int -> Int Source #

FromInteger Int Source # 
Instance details

Defined in NumHask.Data.Integral

Integral Int Source # 
Instance details

Defined in NumHask.Data.Integral

Methods

div :: Int -> Int -> Int Source #

mod :: Int -> Int -> Int Source #

divMod :: Int -> Int -> (Int, Int) Source #

quot :: Int -> Int -> Int Source #

rem :: Int -> Int -> Int Source #

quotRem :: Int -> Int -> (Int, Int) Source #

FromIntegral Int16 Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Int32 Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Int64 Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Int8 Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Word16 Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Word32 Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Word64 Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Word8 Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Integer Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Natural Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Double Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Float Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Int Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Int Int Source # 
Instance details

Defined in NumHask.Data.Integral

Methods

fromIntegral :: Int -> Int Source #

FromIntegral Word Int Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Int16 Int Source # 
Instance details

Defined in NumHask.Data.Integral

Methods

toIntegral :: Int16 -> Int Source #

ToIntegral Int32 Int Source # 
Instance details

Defined in NumHask.Data.Integral

Methods

toIntegral :: Int32 -> Int Source #

ToIntegral Int64 Int Source # 
Instance details

Defined in NumHask.Data.Integral

Methods

toIntegral :: Int64 -> Int Source #

ToIntegral Int8 Int Source # 
Instance details

Defined in NumHask.Data.Integral

Methods

toIntegral :: Int8 -> Int Source #

ToIntegral Word16 Int Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Word32 Int Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Word64 Int Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Word8 Int Source # 
Instance details

Defined in NumHask.Data.Integral

Methods

toIntegral :: Word8 -> Int Source #

ToIntegral Integer Int Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Natural Int Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Int Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Int Int Source # 
Instance details

Defined in NumHask.Data.Integral

Methods

toIntegral :: Int -> Int Source #

ToIntegral Word Int Source # 
Instance details

Defined in NumHask.Data.Integral

Methods

toIntegral :: Word -> Int Source #

ToRatio Int Integer Source # 
Instance details

Defined in NumHask.Data.Rational

Generic1 (URec Int :: k -> Type) 
Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec Int) :: k -> Type #

Methods

from1 :: forall (a :: k0). URec Int a -> Rep1 (URec Int) a #

to1 :: forall (a :: k0). Rep1 (URec Int) a -> URec Int a #

Foldable (UInt :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UInt m -> m #

foldMap :: Monoid m => (a -> m) -> UInt a -> m #

foldMap' :: Monoid m => (a -> m) -> UInt a -> m #

foldr :: (a -> b -> b) -> b -> UInt a -> b #

foldr' :: (a -> b -> b) -> b -> UInt a -> b #

foldl :: (b -> a -> b) -> b -> UInt a -> b #

foldl' :: (b -> a -> b) -> b -> UInt a -> b #

foldr1 :: (a -> a -> a) -> UInt a -> a #

foldl1 :: (a -> a -> a) -> UInt a -> a #

toList :: UInt a -> [a] #

null :: UInt a -> Bool #

length :: UInt a -> Int #

elem :: Eq a => a -> UInt a -> Bool #

maximum :: Ord a => UInt a -> a #

minimum :: Ord a => UInt a -> a #

sum :: Num a => UInt a -> a #

product :: Num a => UInt a -> a #

Traversable (UInt :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UInt a -> f (UInt b) #

sequenceA :: Applicative f => UInt (f a) -> f (UInt a) #

mapM :: Monad m => (a -> m b) -> UInt a -> m (UInt b) #

sequence :: Monad m => UInt (m a) -> m (UInt a) #

Functor (URec Int :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Int a -> URec Int b #

(<$) :: a -> URec Int b -> URec Int a #

Generic (URec Int p) 
Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Int p) :: Type -> Type #

Methods

from :: URec Int p -> Rep (URec Int p) x #

to :: Rep (URec Int p) x -> URec Int p #

Show (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Int p -> ShowS #

show :: URec Int p -> String #

showList :: [URec Int p] -> ShowS #

Eq (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Int p -> URec Int p -> Bool #

(/=) :: URec Int p -> URec Int p -> Bool #

Ord (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec Int p -> URec Int p -> Ordering #

(<) :: URec Int p -> URec Int p -> Bool #

(<=) :: URec Int p -> URec Int p -> Bool #

(>) :: URec Int p -> URec Int p -> Bool #

(>=) :: URec Int p -> URec Int p -> Bool #

max :: URec Int p -> URec Int p -> URec Int p #

min :: URec Int p -> URec Int p -> URec Int p #

type Base Int Source # 
Instance details

Defined in NumHask.Algebra.Metric

type Base Int = Int
type Mag Int Source # 
Instance details

Defined in NumHask.Algebra.Metric

type Mag Int = Int
data URec Int (p :: k)

Used for marking occurrences of Int#

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

data URec Int (p :: k) = UInt {}
type Rep1 (URec Int :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

type Rep1 (URec Int :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: k -> Type)))
type Rep (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

type Rep (URec Int p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: Type -> Type)))

data Integer #

Arbitrary precision integers. In contrast with fixed-size integral types such as Int, the Integer type represents the entire infinite range of integers.

Integers are stored in a kind of sign-magnitude form, hence do not expect two's complement form when using bit operations.

If the value is small (fit into an Int), IS constructor is used. Otherwise Integer and IN constructors are used to store a BigNat representing respectively the positive or the negative value magnitude.

Invariant: Integer and IN are used iff value doesn't fit in IS

Instances

Instances details
Data Integer

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Integer -> c Integer #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Integer #

toConstr :: Integer -> Constr #

dataTypeOf :: Integer -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Integer) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Integer) #

gmapT :: (forall b. Data b => b -> b) -> Integer -> Integer #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r #

gmapQ :: (forall d. Data d => d -> u) -> Integer -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Integer -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Integer -> m Integer #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer #

Enum Integer

Since: base-2.1

Instance details

Defined in GHC.Enum

Num Integer

Since: base-2.1

Instance details

Defined in GHC.Num

Read Integer

Since: base-2.1

Instance details

Defined in GHC.Read

Integral Integer

Since: base-2.0.1

Instance details

Defined in GHC.Real

Real Integer

Since: base-2.0.1

Instance details

Defined in GHC.Real

Show Integer

Since: base-2.1

Instance details

Defined in GHC.Show

Eq Integer 
Instance details

Defined in GHC.Num.Integer

Methods

(==) :: Integer -> Integer -> Bool #

(/=) :: Integer -> Integer -> Bool #

Ord Integer 
Instance details

Defined in GHC.Num.Integer

Additive Integer Source # 
Instance details

Defined in NumHask.Algebra.Additive

Subtractive Integer Source # 
Instance details

Defined in NumHask.Algebra.Additive

JoinSemiLattice Integer Source # 
Instance details

Defined in NumHask.Algebra.Lattice

MeetSemiLattice Integer Source # 
Instance details

Defined in NumHask.Algebra.Lattice

Basis Integer Source # 
Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Integer Source #

type Base Integer Source #

Epsilon Integer Source # 
Instance details

Defined in NumHask.Algebra.Metric

Multiplicative Integer Source # 
Instance details

Defined in NumHask.Algebra.Multiplicative

InvolutiveRing Integer Source # 
Instance details

Defined in NumHask.Algebra.Ring

Methods

adj :: Integer -> Integer Source #

FromInteger Integer Source # 
Instance details

Defined in NumHask.Data.Integral

Integral Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Int16 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Int32 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Int64 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Int8 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Word16 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Word32 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Word64 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Word8 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Integer Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Integer Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Natural Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Double Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Float Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Int Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Word Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Int16 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Int32 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Int64 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Int8 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Word16 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Word32 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Word64 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Word8 Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Integer Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Integer Int Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Natural Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Int Integer Source # 
Instance details

Defined in NumHask.Data.Integral

ToIntegral Word Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromRatio Rational Integer Source # 
Instance details

Defined in NumHask.Data.Rational

FromRatio Double Integer Source # 
Instance details

Defined in NumHask.Data.Rational

FromRatio Float Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Int16 Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Int32 Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Int64 Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Int8 Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Word16 Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Word32 Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Word64 Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Word8 Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Integer Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Natural Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Double Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Float Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Int Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Word Integer Source # 
Instance details

Defined in NumHask.Data.Rational

FromRational (Ratio Integer) Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio (Ratio Integer) Integer Source # 
Instance details

Defined in NumHask.Data.Rational

type Base Integer Source # 
Instance details

Defined in NumHask.Algebra.Metric

type Mag Integer Source # 
Instance details

Defined in NumHask.Algebra.Metric

data Double #

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

Instances

Instances details
Data Double

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Double -> c Double #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Double #

toConstr :: Double -> Constr #

dataTypeOf :: Double -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Double) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Double) #

gmapT :: (forall b. Data b => b -> b) -> Double -> Double #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r #

gmapQ :: (forall d. Data d => d -> u) -> Double -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Double -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Double -> m Double #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double #

Floating Double

Since: base-2.1

Instance details

Defined in GHC.Float

RealFloat Double

Since: base-2.1

Instance details

Defined in GHC.Float

Read Double

Since: base-2.1

Instance details

Defined in GHC.Read

Eq Double

Note that due to the presence of NaN, Double's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Double)
False

Also note that Double's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Double)
True
>>> recip 0 == recip (-0 :: Double)
False
Instance details

Defined in GHC.Classes

Methods

(==) :: Double -> Double -> Bool #

(/=) :: Double -> Double -> Bool #

Ord Double

Note that due to the presence of NaN, Double's Ord instance does not satisfy reflexivity.

>>> 0/0 <= (0/0 :: Double)
False

Also note that, due to the same, Ord's operator interactions are not respected by Double's instance:

>>> (0/0 :: Double) > 1
False
>>> compare (0/0 :: Double) 1
GT
Instance details

Defined in GHC.Classes

Additive Double Source # 
Instance details

Defined in NumHask.Algebra.Additive

Subtractive Double Source # 
Instance details

Defined in NumHask.Algebra.Additive

ExpField Double Source # 
Instance details

Defined in NumHask.Algebra.Field

QuotientField Double Source # 
Instance details

Defined in NumHask.Algebra.Field

Associated Types

type Whole Double Source #

TrigField Double Source # 
Instance details

Defined in NumHask.Algebra.Field

BoundedJoinSemiLattice Double Source # 
Instance details

Defined in NumHask.Algebra.Lattice

Methods

bottom :: Double Source #

BoundedMeetSemiLattice Double Source # 
Instance details

Defined in NumHask.Algebra.Lattice

Methods

top :: Double Source #

JoinSemiLattice Double Source # 
Instance details

Defined in NumHask.Algebra.Lattice

Methods

(\/) :: Double -> Double -> Double Source #

MeetSemiLattice Double Source # 
Instance details

Defined in NumHask.Algebra.Lattice

Methods

(/\) :: Double -> Double -> Double Source #

Basis Double Source # 
Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Double Source #

type Base Double Source #

Epsilon Double Source #

1e-14

Instance details

Defined in NumHask.Algebra.Metric

Divisive Double Source # 
Instance details

Defined in NumHask.Algebra.Multiplicative

Multiplicative Double Source # 
Instance details

Defined in NumHask.Algebra.Multiplicative

InvolutiveRing Double Source # 
Instance details

Defined in NumHask.Algebra.Ring

Methods

adj :: Double -> Double Source #

FromInteger Double Source # 
Instance details

Defined in NumHask.Data.Integral

FromRational Double Source # 
Instance details

Defined in NumHask.Data.Rational

FromIntegral Double Integer Source # 
Instance details

Defined in NumHask.Data.Integral

FromIntegral Double Int Source # 
Instance details

Defined in NumHask.Data.Integral

FromRatio Double Integer Source # 
Instance details

Defined in NumHask.Data.Rational

ToRatio Double Integer Source # 
Instance details

Defined in NumHask.Data.Rational

Generic1 (URec Double :: k -> Type) 
Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec Double) :: k -> Type #

Methods

from1 :: forall (a :: k0). URec Double a -> Rep1 (URec Double) a #

to1 :: forall (a :: k0). Rep1 (URec Double) a -> URec Double a #

Foldable (UDouble :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UDouble m -> m #

foldMap :: Monoid m => (a -> m) -> UDouble a -> m #

foldMap' :: Monoid m => (a -> m) -> UDouble a -> m #

foldr :: (a -> b -> b) -> b -> UDouble a -> b #

foldr' :: (a -> b -> b) -> b -> UDouble a -> b #

foldl :: (b -> a -> b) -> b -> UDouble a -> b #

foldl' :: (b -> a -> b) -> b -> UDouble a -> b #

foldr1 :: (a -> a -> a) -> UDouble a -> a #

foldl1 :: (a -> a -> a) -> UDouble a -> a #

toList :: UDouble a -> [a] #

null :: UDouble a -> Bool #

length :: UDouble a -> Int #

elem :: Eq a => a -> UDouble a -> Bool #

maximum :: Ord a => UDouble a -> a #

minimum :: Ord a => UDouble a -> a #

sum :: Num a => UDouble a -> a #

product :: Num a => UDouble a -> a #

Traversable (UDouble :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UDouble a -> f (UDouble b) #

sequenceA :: Applicative f => UDouble (f a) -> f (UDouble a) #

mapM :: Monad m => (a -> m b) -> UDouble a -> m (UDouble b) #

sequence :: Monad m => UDouble (m a) -> m (UDouble a) #

QuotientField (Positive Double) Source # 
Instance details

Defined in NumHask.Data.Positive

Associated Types

type Whole (Positive Double) Source #

Functor (URec Double :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Double a -> URec Double b #

(<$) :: a -> URec Double b -> URec Double a #

Generic (URec Double p) 
Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Double p) :: Type -> Type #

Methods

from :: URec Double p -> Rep (URec Double p) x #

to :: Rep (URec Double p) x -> URec Double p #

Show (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Double p -> ShowS #

show :: URec Double p -> String #

showList :: [URec Double p] -> ShowS #

Eq (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Double p -> URec Double p -> Bool #

(/=) :: URec Double p -> URec Double p -> Bool #

Ord (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec Double p -> URec Double p -> Ordering #

(<) :: URec Double p -> URec Double p -> Bool #

(<=) :: URec Double p -> URec Double p -> Bool #

(>) :: URec Double p -> URec Double p -> Bool #

(>=) :: URec Double p -> URec Double p -> Bool #

max :: URec Double p -> URec Double p -> URec Double p #

min :: URec Double p -> URec Double p -> URec Double p #

type Whole Double Source # 
Instance details

Defined in NumHask.Algebra.Field

type Base Double Source # 
Instance details

Defined in NumHask.Algebra.Metric

type Mag Double Source # 
Instance details

Defined in NumHask.Algebra.Metric

data URec Double (p :: k)

Used for marking occurrences of Double#

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

data URec Double (p :: k) = UDouble {}
type Rep1 (URec Double :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

type Rep1 (URec Double :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: k -> Type)))
type Whole (Positive Double) Source # 
Instance details

Defined in NumHask.Data.Positive

type Rep (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

type Rep (URec Double p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: Type -> Type)))

data Float #

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

Instances

Instances details
Data Float

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Float -> c Float #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Float #

toConstr :: Float -> Constr #

dataTypeOf :: Float -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Float) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Float) #

gmapT :: (forall b. Data b => b -> b) -> Float -> Float #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r #

gmapQ :: (forall d. Data d => d -> u) -> Float -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Float -> u #

gmapM :: Monad m => (forall d.