praglude-0.4.1.0: A pragmatic Prelude

Safe HaskellNone
LanguageHaskell2010

Praglude

Contents

Synopsis

The Original Prelude

module Prelude

Monoids

class Monoid a where #

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:

  • mappend mempty x = x
  • mappend x mempty = x
  • mappend x (mappend y z) = mappend (mappend x y) z
  • mconcat = foldr mappend mempty

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product.

Minimal complete definition

mempty, mappend

Methods

mempty :: a #

Identity of mappend

mappend :: a -> a -> a #

An associative operation

mconcat :: [a] -> a #

Fold a list using the monoid. For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

Instances

Monoid Ordering 
Monoid () 

Methods

mempty :: () #

mappend :: () -> () -> () #

mconcat :: [()] -> () #

Monoid ByteString 
Monoid ByteString 
Monoid Encoding 
Monoid Series 
Monoid Buffer 

Methods

mempty :: Buffer #

mappend :: Buffer -> Buffer -> Buffer #

mconcat :: [Buffer] -> Buffer #

Monoid Buffer 

Methods

mempty :: Buffer #

mappend :: Buffer -> Buffer -> Buffer #

mconcat :: [Buffer] -> Buffer #

Monoid More 

Methods

mempty :: More #

mappend :: More -> More -> More #

mconcat :: [More] -> More #

Monoid All 

Methods

mempty :: All #

mappend :: All -> All -> All #

mconcat :: [All] -> All #

Monoid Any 

Methods

mempty :: Any #

mappend :: Any -> Any -> Any #

mconcat :: [Any] -> Any #

Monoid ShortByteString 
Monoid [a] 

Methods

mempty :: [a] #

mappend :: [a] -> [a] -> [a] #

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

Monoid a => Monoid (Maybe a)

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S." Since there is no "Semigroup" typeclass providing just mappend, we use Monoid instead.

Methods

mempty :: Maybe a #

mappend :: Maybe a -> Maybe a -> Maybe a #

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

Monoid a => Monoid (IO a) 

Methods

mempty :: IO a #

mappend :: IO a -> IO a -> IO a #

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

Monoid (IResult a) 

Methods

mempty :: IResult a #

mappend :: IResult a -> IResult a -> IResult a #

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

Monoid (Result a) 

Methods

mempty :: Result a #

mappend :: Result a -> Result a -> Result a #

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

Monoid (Parser a) 

Methods

mempty :: Parser a #

mappend :: Parser a -> Parser a -> Parser a #

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

Ord a => Monoid (Max a) 

Methods

mempty :: Max a #

mappend :: Max a -> Max a -> Max a #

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

Ord a => Monoid (Min a) 

Methods

mempty :: Min a #

mappend :: Min a -> Min a -> Min a #

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

Monoid a => Monoid (Identity a) 

Methods

mempty :: Identity a #

mappend :: Identity a -> Identity a -> Identity a #

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

(Ord a, Bounded a) => Monoid (Min a) 

Methods

mempty :: Min a #

mappend :: Min a -> Min a -> Min a #

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

(Ord a, Bounded a) => Monoid (Max a) 

Methods

mempty :: Max a #

mappend :: Max a -> Max a -> Max a #

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

Monoid m => Monoid (WrappedMonoid m) 
Semigroup a => Monoid (Option a) 

Methods

mempty :: Option a #

mappend :: Option a -> Option a -> Option a #

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

Monoid a => Monoid (Dual a) 

Methods

mempty :: Dual a #

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

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

Monoid (Endo a) 

Methods

mempty :: Endo a #

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

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

Num a => Monoid (Sum a) 

Methods

mempty :: Sum a #

mappend :: Sum a -> Sum a -> Sum a #

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

Num a => Monoid (Product a) 

Methods

mempty :: Product a #

mappend :: Product a -> Product a -> Product a #

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

Monoid (First a) 

Methods

mempty :: First a #

mappend :: First a -> First a -> First a #

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

Monoid (Last a) 

Methods

mempty :: Last a #

mappend :: Last a -> Last a -> Last a #

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

Monoid (Seq a) 

Methods

mempty :: Seq a #

mappend :: Seq a -> Seq a -> Seq a #

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

Ord a => Monoid (Set a) 

Methods

mempty :: Set a #

mappend :: Set a -> Set a -> Set a #

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

Monoid (Comparison a) 
Monoid (Equivalence a) 
Monoid (DList a) 

Methods

mempty :: DList a #

mappend :: DList a -> DList a -> DList a #

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

Monoid (Vector a) 

Methods

mempty :: Vector a #

mappend :: Vector a -> Vector a -> Vector a #

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

(Hashable a, Eq a) => Monoid (HashSet a) 

Methods

mempty :: HashSet a #

mappend :: HashSet a -> HashSet a -> HashSet a #

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

Ord a => Monoid (Min a) 

Methods

mempty :: Min a #

mappend :: Min a -> Min a -> Min a #

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

Ord a => Monoid (Max a) 

Methods

mempty :: Max a #

mappend :: Max a -> Max a -> Max a #

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

Monoid (Leftmost a) 

Methods

mempty :: Leftmost a #

mappend :: Leftmost a -> Leftmost a -> Leftmost a #

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

Monoid (Rightmost a) 
Monoid b => Monoid (a -> b) 

Methods

mempty :: a -> b #

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

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

(Monoid a, Monoid b) => Monoid (a, b) 

Methods

mempty :: (a, b) #

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

mconcat :: [(a, b)] -> (a, b) #

Monoid a => Monoid (Op a b) 

Methods

mempty :: Op a b #

mappend :: Op a b -> Op a b -> Op a b #

mconcat :: [Op a b] -> Op a b #

(Eq k, Hashable k) => Monoid (HashMap k v) 

Methods

mempty :: HashMap k v #

mappend :: HashMap k v -> HashMap k v -> HashMap k v #

mconcat :: [HashMap k v] -> HashMap k v #

Ord k => Monoid (Map k v) 

Methods

mempty :: Map k v #

mappend :: Map k v -> Map k v -> Map k v #

mconcat :: [Map k v] -> Map k v #

Monoid (Parser i a) 

Methods

mempty :: Parser i a #

mappend :: Parser i a -> Parser i a -> Parser i a #

mconcat :: [Parser i a] -> Parser i a #

Monoid (Proxy k s) 

Methods

mempty :: Proxy k s #

mappend :: Proxy k s -> Proxy k s -> Proxy k s #

mconcat :: [Proxy k s] -> Proxy k s #

Monoid (ReifiedFold s a) 

Methods

mempty :: ReifiedFold s a #

mappend :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a #

mconcat :: [ReifiedFold s a] -> ReifiedFold s a #

(Contravariant f, Applicative f) => Monoid (Folding f a) 

Methods

mempty :: Folding f a #

mappend :: Folding f a -> Folding f a -> Folding f a #

mconcat :: [Folding f a] -> Folding f a #

Applicative f => Monoid (Traversed a f) 

Methods

mempty :: Traversed a f #

mappend :: Traversed a f -> Traversed a f -> Traversed a f #

mconcat :: [Traversed a f] -> Traversed a f #

Monad m => Monoid (Sequenced a m) 

Methods

mempty :: Sequenced a m #

mappend :: Sequenced a m -> Sequenced a m -> Sequenced a m #

mconcat :: [Sequenced a m] -> Sequenced a m #

Monoid (Deepening i a)

This is an illegal Monoid.

Methods

mempty :: Deepening i a #

mappend :: Deepening i a -> Deepening i a -> Deepening i a #

mconcat :: [Deepening i a] -> Deepening i a #

(Hashable k, Eq k) => Monoid (LHashMap k v) # 

Methods

mempty :: LHashMap k v #

mappend :: LHashMap k v -> LHashMap k v -> LHashMap k v #

mconcat :: [LHashMap k v] -> LHashMap k v #

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

Methods

mempty :: (a, b, c) #

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

mconcat :: [(a, b, c)] -> (a, b, c) #

Monoid a => Monoid (Const k a b) 

Methods

mempty :: Const k a b #

mappend :: Const k a b -> Const k a b -> Const k a b #

mconcat :: [Const k a b] -> Const k a b #

Alternative f => Monoid (Alt * f a) 

Methods

mempty :: Alt * f a #

mappend :: Alt * f a -> Alt * f a -> Alt * f a #

mconcat :: [Alt * f a] -> Alt * f a #

Monoid (ReifiedIndexedFold i s a) 
ArrowPlus p => Monoid (Tambara p a b) 

Methods

mempty :: Tambara p a b #

mappend :: Tambara p a b -> Tambara p a b -> Tambara p a b #

mconcat :: [Tambara p a b] -> Tambara p a b #

Reifies k s (ReifiedMonoid a) => Monoid (ReflectedMonoid k a s) 
(Semigroup a, Monoid a) => Monoid (Tagged k s a) 

Methods

mempty :: Tagged k s a #

mappend :: Tagged k s a -> Tagged k s a -> Tagged k s a #

mconcat :: [Tagged k s a] -> Tagged k s a #

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

Methods

mempty :: (a, b, c, d) #

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

mconcat :: [(a, b, c, d)] -> (a, b, c, d) #

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

Methods

mempty :: (a, b, c, d, e) #

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

mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) #

Contravariant g => Monoid (BazaarT p g a b t) 

Methods

mempty :: BazaarT p g a b t #

mappend :: BazaarT p g a b t -> BazaarT p g a b t -> BazaarT p g a b t #

mconcat :: [BazaarT p g a b t] -> BazaarT p g a b t #

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

An associative operation.

(a <> b) <> c = a <> (b <> c)

If a is also a Monoid we further require

(<>) = mappend

newtype Dual a :: * -> * #

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

Constructors

Dual 

Fields

Instances

Monad Dual 

Methods

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

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

return :: a -> Dual a #

fail :: String -> Dual a #

Functor Dual 

Methods

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

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

Applicative Dual 

Methods

pure :: a -> Dual a #

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

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

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

Foldable Dual 

Methods

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

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

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

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

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

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

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

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

toList :: Dual a -> [a] #

null :: Dual a -> Bool #

length :: Dual a -> Int #

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

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

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

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

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

Traversable Dual 

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) #

Generic1 Dual 

Associated Types

type Rep1 (Dual :: * -> *) :: * -> * #

Methods

from1 :: Dual a -> Rep1 Dual a #

to1 :: Rep1 Dual a -> Dual a #

Representable Dual 

Associated Types

type Rep (Dual :: * -> *) :: * #

Methods

tabulate :: (Rep Dual -> a) -> Dual a #

index :: Dual a -> Rep Dual -> a #

Bounded a => Bounded (Dual a) 

Methods

minBound :: Dual a #

maxBound :: Dual a #

Eq a => Eq (Dual a) 

Methods

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

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

Data a => Data (Dual a) 

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 :: (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) #

Ord a => Ord (Dual a) 

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 #

Read a => Read (Dual a) 
Show a => Show (Dual a) 

Methods

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

show :: Dual a -> String #

showList :: [Dual a] -> ShowS #

Generic (Dual a) 

Associated Types

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

Methods

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

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

Semigroup a => Semigroup (Dual a) 

Methods

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

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

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

Monoid a => Monoid (Dual a) 

Methods

mempty :: Dual a #

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

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

Default a => Default (Dual a) 

Methods

def :: Dual a #

NFData a => NFData (Dual a)

Since: 1.4.0.0

Methods

rnf :: Dual a -> () #

AsEmpty a => AsEmpty (Dual a) 

Methods

_Empty :: Prism' (Dual a) () #

Wrapped (Dual a) 

Associated Types

type Unwrapped (Dual a) :: * #

Methods

_Wrapped' :: Iso' (Dual a) (Unwrapped (Dual a)) #

(~) * t (Dual b) => Rewrapped (Dual a) t 
type Rep1 Dual 
type Rep1 Dual = D1 (MetaData "Dual" "Data.Monoid" "base" True) (C1 (MetaCons "Dual" PrefixI True) (S1 (MetaSel (Just Symbol "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep Dual 
type Rep Dual = ()
type Rep (Dual a) 
type Rep (Dual a) = D1 (MetaData "Dual" "Data.Monoid" "base" True) (C1 (MetaCons "Dual" PrefixI True) (S1 (MetaSel (Just Symbol "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Dual a) 
type Unwrapped (Dual a) = a

newtype Endo a :: * -> * #

The monoid of endomorphisms under composition.

Constructors

Endo 

Fields

Instances

Generic (Endo a) 

Associated Types

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

Methods

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

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

Semigroup (Endo a) 

Methods

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

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

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

Monoid (Endo a) 

Methods

mempty :: Endo a #

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

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

Default (Endo a) 

Methods

def :: Endo a #

Wrapped (Endo a) 

Associated Types

type Unwrapped (Endo a) :: * #

Methods

_Wrapped' :: Iso' (Endo a) (Unwrapped (Endo a)) #

(~) * t (Endo b) => Rewrapped (Endo b) t 
type Rep (Endo a) 
type Rep (Endo a) = D1 (MetaData "Endo" "Data.Monoid" "base" True) (C1 (MetaCons "Endo" PrefixI True) (S1 (MetaSel (Just Symbol "appEndo") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a -> a))))
type Unwrapped (Endo a) 
type Unwrapped (Endo a) = a -> a

newtype All :: * #

Boolean monoid under conjunction (&&).

Constructors

All 

Fields

Instances

Bounded All 

Methods

minBound :: All #

maxBound :: All #

Eq All 

Methods

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

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

Data All 

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 :: (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 #

Ord All 

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 #

Read All 
Show All 

Methods

showsPrec :: Int -> All -> ShowS #

show :: All -> String #

showList :: [All] -> ShowS #

Generic All 

Associated Types

type Rep All :: * -> * #

Methods

from :: All -> Rep All x #

to :: Rep All x -> All #

Semigroup All 

Methods

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

sconcat :: NonEmpty All -> All #

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

Monoid All 

Methods

mempty :: All #

mappend :: All -> All -> All #

mconcat :: [All] -> All #

Default All 

Methods

def :: All #

NFData All

Since: 1.4.0.0

Methods

rnf :: All -> () #

AsEmpty All 

Methods

_Empty :: Prism' All () #

Wrapped All 

Associated Types

type Unwrapped All :: * #

(~) * t All => Rewrapped All t 
type Rep All 
type Rep All = D1 (MetaData "All" "Data.Monoid" "base" True) (C1 (MetaCons "All" PrefixI True) (S1 (MetaSel (Just Symbol "getAll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool)))
type Unwrapped All 

newtype Any :: * #

Boolean monoid under disjunction (||).

Constructors

Any 

Fields

Instances

Bounded Any 

Methods

minBound :: Any #

maxBound :: Any #

Eq Any 

Methods

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

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

Data Any 

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 :: (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 #

Ord Any 

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 #

Read Any 
Show Any 

Methods

showsPrec :: Int -> Any -> ShowS #

show :: Any -> String #

showList :: [Any] -> ShowS #

Generic Any 

Associated Types

type Rep Any :: * -> * #

Methods

from :: Any -> Rep Any x #

to :: Rep Any x -> Any #

Semigroup Any 

Methods

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

sconcat :: NonEmpty Any -> Any #

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

Monoid Any 

Methods

mempty :: Any #

mappend :: Any -> Any -> Any #

mconcat :: [Any] -> Any #

Default Any 

Methods

def :: Any #

NFData Any

Since: 1.4.0.0

Methods

rnf :: Any -> () #

AsEmpty Any 

Methods

_Empty :: Prism' Any () #

Wrapped Any 

Associated Types

type Unwrapped Any :: * #

(~) * t Any => Rewrapped Any t 
type Rep Any 
type Rep Any = D1 (MetaData "Any" "Data.Monoid" "base" True) (C1 (MetaCons "Any" PrefixI True) (S1 (MetaSel (Just Symbol "getAny") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool)))
type Unwrapped Any 

newtype Sum a :: * -> * #

Monoid under addition.

Constructors

Sum 

Fields

Instances

Monad Sum 

Methods

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

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

return :: a -> Sum a #

fail :: String -> Sum a #

Functor Sum 

Methods

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

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

Applicative Sum 

Methods

pure :: a -> Sum a #

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

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

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

Foldable Sum 

Methods

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

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

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

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

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

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

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

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

toList :: Sum a -> [a] #

null :: Sum a -> Bool #

length :: Sum a -> Int #

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

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

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

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

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

Traversable Sum 

Methods

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

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

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

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

Generic1 Sum 

Associated Types

type Rep1 (Sum :: * -> *) :: * -> * #

Methods

from1 :: Sum a -> Rep1 Sum a #

to1 :: Rep1 Sum a -> Sum a #

Representable Sum 

Associated Types

type Rep (Sum :: * -> *) :: * #

Methods

tabulate :: (Rep Sum -> a) -> Sum a #

index :: Sum a -> Rep Sum -> a #

Bounded a => Bounded (Sum a) 

Methods

minBound :: Sum a #

maxBound :: Sum a #

Eq a => Eq (Sum a) 

Methods

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

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

Data a => Data (Sum a) 

Methods

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

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

toConstr :: Sum a -> Constr #

dataTypeOf :: Sum a -> DataType #

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

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

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

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

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

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

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

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

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

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

Num a => Num (Sum a) 

Methods

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

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

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

negate :: Sum a -> Sum a #

abs :: Sum a -> Sum a #

signum :: Sum a -> Sum a #

fromInteger :: Integer -> Sum a #

Ord a => Ord (Sum a) 

Methods

compare :: Sum a -> Sum a -> Ordering #

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

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

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

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

max :: Sum a -> Sum a -> Sum a #

min :: Sum a -> Sum a -> Sum a #

Read a => Read (Sum a) 
Show a => Show (Sum a) 

Methods

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

show :: Sum a -> String #

showList :: [Sum a] -> ShowS #

Generic (Sum a) 

Associated Types

type Rep (Sum a) :: * -> * #

Methods

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

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

Num a => Semigroup (Sum a) 

Methods

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

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

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

Num a => Monoid (Sum a) 

Methods

mempty :: Sum a #

mappend :: Sum a -> Sum a -> Sum a #

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

Num a => Default (Sum a) 

Methods

def :: Sum a #

NFData a => NFData (Sum a)

Since: 1.4.0.0

Methods

rnf :: Sum a -> () #

(Eq a, Num a) => AsEmpty (Sum a) 

Methods

_Empty :: Prism' (Sum a) () #

Wrapped (Sum a) 

Associated Types

type Unwrapped (Sum a) :: * #

Methods

_Wrapped' :: Iso' (Sum a) (Unwrapped (Sum a)) #

(~) * t (Sum b) => Rewrapped (Sum a) t 
type Rep1 Sum 
type Rep1 Sum = D1 (MetaData "Sum" "Data.Monoid" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep Sum 
type Rep Sum = ()
type Rep (Sum a) 
type Rep (Sum a) = D1 (MetaData "Sum" "Data.Monoid" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Sum a) 
type Unwrapped (Sum a) = a

newtype Product a :: * -> * #

Monoid under multiplication.

Constructors

Product 

Fields

Instances

Monad Product 

Methods

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

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

return :: a -> Product a #

fail :: String -> Product a #

Functor Product 

Methods

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

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

Applicative Product 

Methods

pure :: a -> Product a #

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

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

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

Foldable Product 

Methods

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

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

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

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

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

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

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

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

toList :: Product a -> [a] #

null :: Product a -> Bool #

length :: Product a -> Int #

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

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

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

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

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

Traversable Product 

Methods

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

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

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

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

Generic1 Product 

Associated Types

type Rep1 (Product :: * -> *) :: * -> * #

Methods

from1 :: Product a -> Rep1 Product a #

to1 :: Rep1 Product a -> Product a #

Representable Product 

Associated Types

type Rep (Product :: * -> *) :: * #

Methods

tabulate :: (Rep Product -> a) -> Product a #

index :: Product a -> Rep Product -> a #

Bounded a => Bounded (Product a) 
Eq a => Eq (Product a) 

Methods

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

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

Data a => Data (Product a) 

Methods

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

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

toConstr :: Product a -> Constr #

dataTypeOf :: Product a -> DataType #

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

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

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

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

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

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

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

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

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

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

Num a => Num (Product a) 

Methods

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

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

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

negate :: Product a -> Product a #

abs :: Product a -> Product a #

signum :: Product a -> Product a #

fromInteger :: Integer -> Product a #

Ord a => Ord (Product a) 

Methods

compare :: Product a -> Product a -> Ordering #

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

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

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

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

max :: Product a -> Product a -> Product a #

min :: Product a -> Product a -> Product a #

Read a => Read (Product a) 
Show a => Show (Product a) 

Methods

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

show :: Product a -> String #

showList :: [Product a] -> ShowS #

Generic (Product a) 

Associated Types

type Rep (Product a) :: * -> * #

Methods

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

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

Num a => Semigroup (Product a) 

Methods

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

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

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

Num a => Monoid (Product a) 

Methods

mempty :: Product a #

mappend :: Product a -> Product a -> Product a #

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

Num a => Default (Product a) 

Methods

def :: Product a #

NFData a => NFData (Product a)

Since: 1.4.0.0

Methods

rnf :: Product a -> () #

(Eq a, Num a) => AsEmpty (Product a) 

Methods

_Empty :: Prism' (Product a) () #

Wrapped (Product a) 

Associated Types

type Unwrapped (Product a) :: * #

Methods

_Wrapped' :: Iso' (Product a) (Unwrapped (Product a)) #

(~) * t (Product b) => Rewrapped (Product a) t 
type Rep1 Product 
type Rep1 Product = D1 (MetaData "Product" "Data.Monoid" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep Product 
type Rep Product = ()
type Rep (Product a) 
type Rep (Product a) = D1 (MetaData "Product" "Data.Monoid" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Product a) 
type Unwrapped (Product a) = a

newtype First a :: * -> * #

Use Option (First a) to get the behavior of First from Data.Monoid.

Constructors

First 

Fields

Instances

Monad First 

Methods

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

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

return :: a -> First a #

fail :: String -> First a #

Functor First 

Methods

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

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

MonadFix First 

Methods

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

Applicative First 

Methods

pure :: a -> First a #

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

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

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

Foldable First 

Methods

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

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

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

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

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

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

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

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

toList :: First a -> [a] #

null :: First a -> Bool #

length :: First a -> Int #

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

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

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

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

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

Traversable First 

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) #

Generic1 First 

Associated Types

type Rep1 (First :: * -> *) :: * -> * #

Methods

from1 :: First a -> Rep1 First a #

to1 :: Rep1 First a -> First a #

Bounded a => Bounded (First a) 

Methods

minBound :: First a #

maxBound :: First a #

Enum a => Enum (First a) 

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] #

Eq a => Eq (First a) 

Methods

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

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

Data a => Data (First a) 

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 :: (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) #

Ord a => Ord (First a) 

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 #

Read a => Read (First a) 
Show a => Show (First a) 

Methods

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

show :: First a -> String #

showList :: [First a] -> ShowS #

Generic (First a) 

Associated Types

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

Methods

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

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

Semigroup (First a) 

Methods

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

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

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

NFData a => NFData (First a)

Since: 1.4.2.0

Methods

rnf :: First a -> () #

Hashable a => Hashable (First a) 

Methods

hashWithSalt :: Int -> First a -> Int #

hash :: First a -> Int #

Wrapped (First a) 

Associated Types

type Unwrapped (First a) :: * #

Methods

_Wrapped' :: Iso' (First a) (Unwrapped (First a)) #

(~) * t (First b) => Rewrapped (First a) t 
type Rep1 First 
type Rep1 First = D1 (MetaData "First" "Data.Semigroup" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep (First a) 
type Rep (First a) = D1 (MetaData "First" "Data.Semigroup" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (First a) 
type Unwrapped (First a) = a

newtype Alt k f a :: forall k. (k -> *) -> k -> * #

Monoid under <|>.

Since: 4.8.0.0

Constructors

Alt 

Fields

Instances

Monad f => Monad (Alt * f) 

Methods

(>>=) :: Alt * f a -> (a -> Alt * f b) -> Alt * f b #

(>>) :: Alt * f a -> Alt * f b -> Alt * f b #

return :: a -> Alt * f a #

fail :: String -> Alt * f a #

Functor f => Functor (Alt * f) 

Methods

fmap :: (a -> b) -> Alt * f a -> Alt * f b #

(<$) :: a -> Alt * f b -> Alt * f a #

Applicative f => Applicative (Alt * f) 

Methods

pure :: a -> Alt * f a #

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

(*>) :: Alt * f a -> Alt * f b -> Alt * f b #

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

Generic1 (Alt * f) 

Associated Types

type Rep1 (Alt * f :: * -> *) :: * -> * #

Methods

from1 :: Alt * f a -> Rep1 (Alt * f) a #

to1 :: Rep1 (Alt * f) a -> Alt * f a #

Contravariant f => Contravariant (Alt * f) 

Methods

contramap :: (a -> b) -> Alt * f b -> Alt * f a #

(>$) :: b -> Alt * f b -> Alt * f a #

Alternative f => Alternative (Alt * f) 

Methods

empty :: Alt * f a #

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

some :: Alt * f a -> Alt * f [a] #

many :: Alt * f a -> Alt * f [a] #

MonadPlus f => MonadPlus (Alt * f) 

Methods

mzero :: Alt * f a #

mplus :: Alt * f a -> Alt * f a -> Alt * f a #

Enum (f a) => Enum (Alt k f a) 

Methods

succ :: Alt k f a -> Alt k f a #

pred :: Alt k f a -> Alt k f a #

toEnum :: Int -> Alt k f a #

fromEnum :: Alt k f a -> Int #

enumFrom :: Alt k f a -> [Alt k f a] #

enumFromThen :: Alt k f a -> Alt k f a -> [Alt k f a] #

enumFromTo :: Alt k f a -> Alt k f a -> [Alt k f a] #

enumFromThenTo :: Alt k f a -> Alt k f a -> Alt k f a -> [Alt k f a] #

Eq (f a) => Eq (Alt k f a) 

Methods

(==) :: Alt k f a -> Alt k f a -> Bool #

(/=) :: Alt k f a -> Alt k f a -> Bool #

(Data (f a), Data a, Typeable (* -> *) f) => Data (Alt * f a) 

Methods

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

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

toConstr :: Alt * f a -> Constr #

dataTypeOf :: Alt * f a -> DataType #

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

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

gmapT :: (forall b. Data b => b -> b) -> Alt * f a -> Alt * f a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Alt * f a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Alt * f a -> r #

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

gmapQi :: Int -> (forall d. Data d => d -> u) -> Alt * f a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Alt * f a -> m (Alt * f a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt * f a -> m (Alt * f a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt * f a -> m (Alt * f a) #

Num (f a) => Num (Alt k f a) 

Methods

(+) :: Alt k f a -> Alt k f a -> Alt k f a #

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

(*) :: Alt k f a -> Alt k f a -> Alt k f a #

negate :: Alt k f a -> Alt k f a #

abs :: Alt k f a -> Alt k f a #

signum :: Alt k f a -> Alt k f a #

fromInteger :: Integer -> Alt k f a #

Ord (f a) => Ord (Alt k f a) 

Methods

compare :: Alt k f a -> Alt k f a -> Ordering #

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

(<=) :: Alt k f a -> Alt k f a -> Bool #

(>) :: Alt k f a -> Alt k f a -> Bool #

(>=) :: Alt k f a -> Alt k f a -> Bool #

max :: Alt k f a -> Alt k f a -> Alt k f a #

min :: Alt k f a -> Alt k f a -> Alt k f a #

Read (f a) => Read (Alt k f a) 

Methods

readsPrec :: Int -> ReadS (Alt k f a) #

readList :: ReadS [Alt k f a] #

readPrec :: ReadPrec (Alt k f a) #

readListPrec :: ReadPrec [Alt k f a] #

Show (f a) => Show (Alt k f a) 

Methods

showsPrec :: Int -> Alt k f a -> ShowS #

show :: Alt k f a -> String #

showList :: [Alt k f a] -> ShowS #

Generic (Alt k f a) 

Associated Types

type Rep (Alt k f a) :: * -> * #

Methods

from :: Alt k f a -> Rep (Alt k f a) x #

to :: Rep (Alt k f a) x -> Alt k f a #

Alternative f => Semigroup (Alt * f a) 

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 #

Alternative f => Monoid (Alt * f a) 

Methods

mempty :: Alt * f a #

mappend :: Alt * f a -> Alt * f a -> Alt * f a #

mconcat :: [Alt * f a] -> Alt * f a #

Wrapped (Alt k f a) 

Associated Types

type Unwrapped (Alt k f a) :: * #

Methods

_Wrapped' :: Iso' (Alt k f a) (Unwrapped (Alt k f a)) #

(~) * t (Alt k1 g b) => Rewrapped (Alt k f a) t 
type Rep1 (Alt * f) 
type Rep1 (Alt * f) = D1 (MetaData "Alt" "Data.Monoid" "base" True) (C1 (MetaCons "Alt" PrefixI True) (S1 (MetaSel (Just Symbol "getAlt") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f)))
type Rep (Alt k f a) 
type Rep (Alt k f a) = D1 (MetaData "Alt" "Data.Monoid" "base" True) (C1 (MetaCons "Alt" PrefixI True) (S1 (MetaSel (Just Symbol "getAlt") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a))))
type Unwrapped (Alt k f a) 
type Unwrapped (Alt k f a) = f a

concat :: Monoid a => [a] -> a Source #

append :: Monoid a => a -> a -> a Source #

empty :: Monoid a => a Source #

Maybe

data Maybe a :: * -> * #

The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing). Using Maybe is a good way to deal with errors or exceptional cases without resorting to drastic measures such as error.

The Maybe type is also a monad. It is a simple kind of error monad, where all errors are represented by Nothing. A richer error monad can be built using the Either type.

Constructors

Nothing 
Just a 

Instances

Monad Maybe 

Methods

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

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

return :: a -> Maybe a #

fail :: String -> Maybe a #

Functor Maybe 

Methods

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

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

Applicative Maybe 

Methods

pure :: a -> Maybe a #

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

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

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

Foldable Maybe 

Methods

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

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

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

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

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

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

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

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

toList :: Maybe a -> [a] #

null :: Maybe a -> Bool #

length :: Maybe a -> Int #

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

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

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

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

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

Traversable Maybe 

Methods

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

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

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

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

Generic1 Maybe 

Associated Types

type Rep1 (Maybe :: * -> *) :: * -> * #

Methods

from1 :: Maybe a -> Rep1 Maybe a #

to1 :: Rep1 Maybe a -> Maybe a #

Alternative Maybe 

Methods

empty :: Maybe a #

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

some :: Maybe a -> Maybe [a] #

many :: Maybe a -> Maybe [a] #

MonadPlus Maybe 

Methods

mzero :: Maybe a #

mplus :: Maybe a -> Maybe a -> Maybe a #

Eq1 Maybe 

Methods

liftEq :: (a -> b -> Bool) -> Maybe a -> Maybe b -> Bool #

Ord1 Maybe 

Methods

liftCompare :: (a -> b -> Ordering) -> Maybe a -> Maybe b -> Ordering #

Read1 Maybe 

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Maybe a) #

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Maybe a] #

Show1 Maybe 

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Maybe a -> ShowS #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Maybe a] -> ShowS #

Hashable1 Maybe 

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Maybe a -> Int #

Apply Maybe 

Methods

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

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

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

Bind Maybe 

Methods

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

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

FunctorWithIndex () Maybe 

Methods

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

imapped :: (Indexable () p, Settable f) => p a (f b) -> Maybe a -> f (Maybe b) #

FoldableWithIndex () Maybe 

Methods

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

ifolded :: (Indexable () p, Contravariant f, Applicative f) => p a (f a) -> Maybe a -> f (Maybe a) #

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

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

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

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

TraversableWithIndex () Maybe 

Methods

itraverse :: Applicative f => (() -> a -> f b) -> Maybe a -> f (Maybe b) #

itraversed :: (Indexable () p, Applicative f) => p a (f b) -> Maybe a -> f (Maybe b) #

Eq a => Eq (Maybe a) 

Methods

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

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

Data a => Data (Maybe a) 

Methods

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

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

toConstr :: Maybe a -> Constr #

dataTypeOf :: Maybe a -> DataType #

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (Maybe a) 

Methods

compare :: Maybe a -> Maybe a -> Ordering #

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

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

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

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

max :: Maybe a -> Maybe a -> Maybe a #

min :: Maybe a -> Maybe a -> Maybe a #

Read a => Read (Maybe a) 
Show a => Show (Maybe a) 

Methods

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

show :: Maybe a -> String #

showList :: [Maybe a] -> ShowS #

Generic (Maybe a) 

Associated Types

type Rep (Maybe a) :: * -> * #

Methods

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

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

Semigroup a => Semigroup (Maybe a) 

Methods

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

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

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

Monoid a => Monoid (Maybe a)

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S." Since there is no "Semigroup" typeclass providing just mappend, we use Monoid instead.

Methods

mempty :: Maybe a #

mappend :: Maybe a -> Maybe a -> Maybe a #

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

Lift a => Lift (Maybe a) 

Methods

lift :: Maybe a -> Q Exp #

FromJSON a => LookupField (Maybe a) 

Methods

lookupField :: String -> String -> Object -> Text -> Parser (Maybe a)

Default (Maybe a) 

Methods

def :: Maybe a #

NFData a => NFData (Maybe a) 

Methods

rnf :: Maybe a -> () #

Hashable a => Hashable (Maybe a) 

Methods

hashWithSalt :: Int -> Maybe a -> Int #

hash :: Maybe a -> Int #

Ixed (Maybe a) 

Methods

ix :: Index (Maybe a) -> Traversal' (Maybe a) (IxValue (Maybe a)) #

At (Maybe a) 

Methods

at :: Index (Maybe a) -> Lens' (Maybe a) (Maybe (IxValue (Maybe a))) #

AsEmpty (Maybe a) 

Methods

_Empty :: Prism' (Maybe a) () #

SingI (Maybe a) (Nothing a) 

Methods

sing :: Sing (Nothing a) a

SingKind a (KProxy a) => SingKind (Maybe a) (KProxy (Maybe a)) 

Associated Types

type DemoteRep (KProxy (Maybe a)) (kparam :: KProxy (KProxy (Maybe a))) :: *

Methods

fromSing :: Sing (KProxy (Maybe a)) a -> DemoteRep (KProxy (Maybe a)) kparam

Each (Maybe a) (Maybe b) a b
each :: Traversal (Maybe a) (Maybe b) a b

Methods

each :: Traversal (Maybe a) (Maybe b) a b #

SingI a a1 => SingI (Maybe a) (Just a a1) 

Methods

sing :: Sing (Just a a1) a

(Selector Meta s, ToJSON a) => RecordToPairs (S1 s (K1 i (Maybe a))) 

Methods

recordToPairs :: Options -> S1 s (K1 i (Maybe a)) a -> DList Pair

(Selector Meta s, ToJSON a) => RecordToEncoding (S1 s (K1 i (Maybe a))) 

Methods

recordToEncoding :: Options -> S1 s (K1 i (Maybe a)) a -> Builder

(Selector Meta s, FromJSON a) => FromRecord (S1 s (K1 i (Maybe a))) 

Methods

parseRecord :: Options -> Maybe Text -> Object -> Parser (S1 s (K1 i (Maybe a)) a)

type Rep1 Maybe 
type Rep (Maybe a) 
data Sing (Maybe a) 
data Sing (Maybe a) where
type Index (Maybe a) 
type Index (Maybe a) = ()
type IxValue (Maybe a) 
type IxValue (Maybe a) = a
type (==) (Maybe k) a b 
type (==) (Maybe k) a b = EqMaybe k a b
type DemoteRep (Maybe a) (KProxy (Maybe a)) 
type DemoteRep (Maybe a) (KProxy (Maybe a)) = Maybe (DemoteRep a (KProxy a))

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

The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result.

Examples

Basic usage:

>>> maybe False odd (Just 3)
True
>>> maybe False odd Nothing
False

Read an integer from a string using readMaybe. If we succeed, return twice the integer; that is, apply (*2) to it. If instead we fail to parse an integer, return 0 by default:

>>> import Text.Read ( readMaybe )
>>> maybe 0 (*2) (readMaybe "5")
10
>>> maybe 0 (*2) (readMaybe "")
0

Apply show to a Maybe Int. If we have Just n, we want to show the underlying Int n. But if we have Nothing, we return the empty string instead of (for example) "Nothing":

>>> maybe "" show (Just 5)
"5"
>>> maybe "" show Nothing
""

isJust :: Maybe a -> Bool #

The isJust function returns True iff its argument is of the form Just _.

Examples

Basic usage:

>>> isJust (Just 3)
True
>>> isJust (Just ())
True
>>> isJust Nothing
False

Only the outer constructor is taken into consideration:

>>> isJust (Just Nothing)
True

isNothing :: Maybe a -> Bool #

The isNothing function returns True iff its argument is Nothing.

Examples

Basic usage:

>>> isNothing (Just 3)
False
>>> isNothing (Just ())
False
>>> isNothing Nothing
True

Only the outer constructor is taken into consideration:

>>> isNothing (Just Nothing)
False

fromJust :: Maybe a -> a #

The fromJust function extracts the element out of a Just and throws an error if its argument is Nothing.

Examples

Basic usage:

>>> fromJust (Just 1)
1
>>> 2 * (fromJust (Just 10))
20
>>> 2 * (fromJust Nothing)
*** Exception: Maybe.fromJust: Nothing

fromMaybe :: a -> Maybe a -> a #

The fromMaybe function takes a default value and and Maybe value. If the Maybe is Nothing, it returns the default values; otherwise, it returns the value contained in the Maybe.

Examples

Basic usage:

>>> fromMaybe "" (Just "Hello, World!")
"Hello, World!"
>>> fromMaybe "" Nothing
""

Read an integer from a string using readMaybe. If we fail to parse an integer, we want to return 0 by default:

>>> import Text.Read ( readMaybe )
>>> fromMaybe 0 (readMaybe "5")
5
>>> fromMaybe 0 (readMaybe "")
0

listToMaybe :: [a] -> Maybe a #

The listToMaybe function returns Nothing on an empty list or Just a where a is the first element of the list.

Examples

Basic usage:

>>> listToMaybe []
Nothing
>>> listToMaybe [9]
Just 9
>>> listToMaybe [1,2,3]
Just 1

Composing maybeToList with listToMaybe should be the identity on singleton/empty lists:

>>> maybeToList $ listToMaybe [5]
[5]
>>> maybeToList $ listToMaybe []
[]

But not on lists with more than one element:

>>> maybeToList $ listToMaybe [1,2,3]
[1]

maybeToList :: Maybe a -> [a] #

The maybeToList function returns an empty list when given Nothing or a singleton list when not given Nothing.

Examples

Basic usage:

>>> maybeToList (Just 7)
[7]
>>> maybeToList Nothing
[]

One can use maybeToList to avoid pattern matching when combined with a function that (safely) works on lists:

>>> import Text.Read ( readMaybe )
>>> sum $ maybeToList (readMaybe "3")
3
>>> sum $ maybeToList (readMaybe "")
0

catMaybes :: [Maybe a] -> [a] #

The catMaybes function takes a list of Maybes and returns a list of all the Just values.

Examples

Basic usage:

>>> catMaybes [Just 1, Nothing, Just 3]
[1,3]

When constructing a list of Maybe values, catMaybes can be used to return all of the "success" results (if the list is the result of a map, then mapMaybe would be more appropriate):

>>> import Text.Read ( readMaybe )
>>> [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[Just 1,Nothing,Just 3]
>>> catMaybes $ [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[1,3]

mapMaybe :: (a -> Maybe b) -> [a] -> [b] #

The mapMaybe function is a version of map which can throw out elements. In particular, the functional argument returns something of type Maybe b. If this is Nothing, no element is added on to the result list. If it is Just b, then b is included in the result list.

Examples

Using mapMaybe f x is a shortcut for catMaybes $ map f x in most cases:

>>> import Text.Read ( readMaybe )
>>> let readMaybeInt = readMaybe :: String -> Maybe Int
>>> mapMaybe readMaybeInt ["1", "Foo", "3"]
[1,3]
>>> catMaybes $ map readMaybeInt ["1", "Foo", "3"]
[1,3]

If we map the Just constructor, the entire list should be returned:

>>> mapMaybe Just [1,2,3]
[1,2,3]

Applicative

(<|>) :: Alternative f => forall a. f a -> f a -> f a #

An associative binary operation

Monads

class Applicative m => Monad m where #

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following laws:

Furthermore, the Monad and Applicative operations should relate as follows:

The above laws imply:

and that pure and (<*>) satisfy the applicative functor laws.

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: m a -> (a -> m b) -> m b infixl 1 #

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

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

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

return :: a -> m a #

Inject a value into the monadic type.

fail :: String -> m a #

Fail with a message. This operation is not part of the mathematical definition of a monad, but is invoked on pattern-match failure in a do expression.

As part of the MonadFail proposal (MFP), this function is moved to its own class MonadFail (see Control.Monad.Fail for more details). The definition here will be removed in a future release.

Instances

Monad [] 

Methods

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

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

return :: a -> [a] #

fail :: String -> [a] #

Monad Maybe 

Methods

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

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

return :: a -> Maybe a #

fail :: String -> Maybe a #

Monad IO 

Methods

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

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

return :: a -> IO a #

fail :: String -> IO a #

Monad U1 

Methods

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

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

return :: a -> U1 a #

fail :: String -> U1 a #

Monad Par1 

Methods

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

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

return :: a -> Par1 a #

fail :: String -> Par1 a #

Monad Q 

Methods

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

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

return :: a -> Q a #

fail :: String -> Q a #

Monad IResult 

Methods

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

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

return :: a -> IResult a #

fail :: String -> IResult a #

Monad Result 

Methods

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

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

return :: a -> Result a #

fail :: String -> Result a #

Monad Parser 

Methods

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

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

return :: a -> Parser a #

fail :: String -> Parser a #

Monad P 

Methods

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

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

return :: a -> P a #

fail :: String -> P a #

Monad Identity 

Methods

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

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

return :: a -> Identity a #

fail :: String -> Identity a #

Monad Min 

Methods

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

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

return :: a -> Min a #

fail :: String -> Min a #

Monad Max 

Methods

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

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

return :: a -> Max a #

fail :: String -> Max a #

Monad First 

Methods

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

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

return :: a -> First a #

fail :: String -> First a #

Monad Last 

Methods

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

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

return :: a -> Last a #

fail :: String -> Last a #

Monad Option 

Methods

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

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

return :: a -> Option a #

fail :: String -> Option a #

Monad NonEmpty 

Methods

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

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

return :: a -> NonEmpty a #

fail :: String -> NonEmpty a #

Monad Complex 

Methods

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

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

return :: a -> Complex a #

fail :: String -> Complex a #

Monad STM 

Methods

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

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

return :: a -> STM a #

fail :: String -> STM a #

Monad Dual 

Methods

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

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

return :: a -> Dual a #

fail :: String -> Dual a #

Monad Sum 

Methods

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

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

return :: a -> Sum a #

fail :: String -> Sum a #

Monad Product 

Methods

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

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

return :: a -> Product a #

fail :: String -> Product a #

Monad First 

Methods

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

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

return :: a -> First a #

fail :: String -> First a #

Monad Last 

Methods

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

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

return :: a -> Last a #

fail :: String -> Last a #

Monad ReadPrec 

Methods

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

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

return :: a -> ReadPrec a #

fail :: String -> ReadPrec a #

Monad ReadP 

Methods

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

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

return :: a -> ReadP a #

fail :: String -> ReadP a #

Monad Identifier 

Methods

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

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

return :: a -> Identifier a #

fail :: String -> Identifier a #

Monad Tree 

Methods

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

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

return :: a -> Tree a #

fail :: String -> Tree a #

Monad Seq 

Methods

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

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

return :: a -> Seq a #

fail :: String -> Seq a #

Monad DList 

Methods

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

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

return :: a -> DList a #

fail :: String -> DList a #

Monad Vector 

Methods

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

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

return :: a -> Vector a #

fail :: String -> Vector a #

Monad Id 

Methods

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

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

return :: a -> Id a #

fail :: String -> Id a #

Monad Box 

Methods

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

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

return :: a -> Box a #

fail :: String -> Box a #

Monad ((->) r) 

Methods

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

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

return :: a -> r -> a #

fail :: String -> r -> a #

Monad (Either e) 

Methods

(>>=) :: Either e a -> (a -> Either e b) -> Either e b #

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

return :: a -> Either e a #

fail :: String -> Either e a #

Monad f => Monad (Rec1 f) 

Methods

(>>=) :: Rec1 f a -> (a -> Rec1 f b) -> Rec1 f b #

(>>) :: Rec1 f a -> Rec1 f b -> Rec1 f b #

return :: a -> Rec1 f a #

fail :: String -> Rec1 f a #

Monoid a => Monad ((,) a) 

Methods

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

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

return :: a -> (a, a) #

fail :: String -> (a, a) #

Representable f => Monad (Co f) 

Methods

(>>=) :: Co f a -> (a -> Co f b) -> Co f b #

(>>) :: Co f a -> Co f b -> Co f b #

return :: a -> Co f a #

fail :: String -> Co f a #

Monad (Parser i) 

Methods

(>>=) :: Parser i a -> (a -> Parser i b) -> Parser i b #

(>>) :: Parser i a -> Parser i b -> Parser i b #

return :: a -> Parser i a #

fail :: String -> Parser i a #

Monad m => Monad (WrappedMonad m) 

Methods

(>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b #

(>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b #

return :: a -> WrappedMonad m a #

fail :: String -> WrappedMonad m a #

ArrowApply a => Monad (ArrowMonad a) 

Methods

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

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

return :: a -> ArrowMonad a a #

fail :: String -> ArrowMonad a a #

Monad (Proxy *) 

Methods

(>>=) :: Proxy * a -> (a -> Proxy * b) -> Proxy * b #

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

return :: a -> Proxy * a #

fail :: String -> Proxy * a #

Monad (State s) 

Methods

(>>=) :: State s a -> (a -> State s b) -> State s b #

(>>) :: State s a -> State s b -> State s b #

return :: a -> State s a #

fail :: String -> State s a #

Alternative f => Monad (Cofree f) 

Methods

(>>=) :: Cofree f a -> (a -> Cofree f b) -> Cofree f b #

(>>) :: Cofree f a -> Cofree f b -> Cofree f b #

return :: a -> Cofree f a #

fail :: String -> Cofree f a #

Monad m => Monad (Yoneda m) 

Methods

(>>=) :: Yoneda m a -> (a -> Yoneda m b) -> Yoneda m b #

(>>) :: Yoneda m a -> Yoneda m b -> Yoneda m b #

return :: a -> Yoneda m a #

fail :: String -> Yoneda m a #

Monad (ReifiedGetter s) 

Methods

(>>=) :: ReifiedGetter s a -> (a -> ReifiedGetter s b) -> ReifiedGetter s b #

(>>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b #

return :: a -> ReifiedGetter s a #

fail :: String -> ReifiedGetter s a #

Monad (ReifiedFold s) 

Methods

(>>=) :: ReifiedFold s a -> (a -> ReifiedFold s b) -> ReifiedFold s b #

(>>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b #

return :: a -> ReifiedFold s a #

fail :: String -> ReifiedFold s a #

Monad m => Monad (ListT m) 

Methods

(>>=) :: ListT m a -> (a -> ListT m b) -> ListT m b #

(>>) :: ListT m a -> ListT m b -> ListT m b #

return :: a -> ListT m a #

fail :: String -> ListT m a #

(Monad (Rep p), Representable p) => Monad (Prep p) 

Methods

(>>=) :: Prep p a -> (a -> Prep p b) -> Prep p b #

(>>) :: Prep p a -> Prep p b -> Prep p b #

return :: a -> Prep p a #

fail :: String -> Prep p a #

Monad m => Monad (MaybeT m) 

Methods

(>>=) :: MaybeT m a -> (a -> MaybeT m b) -> MaybeT m b #

(>>) :: MaybeT m a -> MaybeT m b -> MaybeT m b #

return :: a -> MaybeT m a #

fail :: String -> MaybeT m a #

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

Methods

(>>=) :: (f :*: g) a -> (a -> (f :*: g) b) -> (f :*: g) b #

(>>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b #

return :: a -> (f :*: g) a #

fail :: String -> (f :*: g) a #

Monad f => Monad (Alt * f) 

Methods

(>>=) :: Alt * f a -> (a -> Alt * f b) -> Alt * f b #

(>>) :: Alt * f a -> Alt * f b -> Alt * f b #

return :: a -> Alt * f a #

fail :: String -> Alt * f a #

Monad (Cokleisli w a) 

Methods

(>>=) :: Cokleisli w a a -> (a -> Cokleisli w a b) -> Cokleisli w a b #

(>>) :: Cokleisli w a a -> Cokleisli w a b -> Cokleisli w a b #

return :: a -> Cokleisli w a a #

fail :: String -> Cokleisli w a a #

Monad m => Monad (IdentityT * m) 

Methods

(>>=) :: IdentityT * m a -> (a -> IdentityT * m b) -> IdentityT * m b #

(>>) :: IdentityT * m a -> IdentityT * m b -> IdentityT * m b #

return :: a -> IdentityT * m a #

fail :: String -> IdentityT * m a #

(Functor f, Monad m) => Monad (FreeT f m) 

Methods

(>>=) :: FreeT f m a -> (a -> FreeT f m b) -> FreeT f m b #

(>>) :: FreeT f m a -> FreeT f m b -> FreeT f m b #

return :: a -> FreeT f m a #

fail :: String -> FreeT f m a #

(Monad m, Error e) => Monad (ErrorT e m) 

Methods

(>>=) :: ErrorT e m a -> (a -> ErrorT e m b) -> ErrorT e m b #

(>>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b #

return :: a -> ErrorT e m a #

fail :: String -> ErrorT e m a #

Monad (Indexed i a) 

Methods

(>>=) :: Indexed i a a -> (a -> Indexed i a b) -> Indexed i a b #

(>>) :: Indexed i a a -> Indexed i a b -> Indexed i a b #

return :: a -> Indexed i a a #

fail :: String -> Indexed i a a #

Monad m => Monad (ExceptT e m) 

Methods

(>>=) :: ExceptT e m a -> (a -> ExceptT e m b) -> ExceptT e m b #

(>>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b #

return :: a -> ExceptT e m a #

fail :: String -> ExceptT e m a #

Monad m => Monad (StateT s m) 

Methods

(>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b #

(>>) :: StateT s m a -> StateT s m b -> StateT s m b #

return :: a -> StateT s m a #

fail :: String -> StateT s m a #

Monad m => Monad (StateT s m) 

Methods

(>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b #

(>>) :: StateT s m a -> StateT s m b -> StateT s m b #

return :: a -> StateT s m a #

fail :: String -> StateT s m a #

(Monoid w, Monad m) => Monad (WriterT w m) 

Methods

(>>=) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b #

(>>) :: WriterT w m a -> WriterT w m b -> WriterT w m b #

return :: a -> WriterT w m a #

fail :: String -> WriterT w m a #

(Monoid w, Monad m) => Monad (WriterT w m) 

Methods

(>>=) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b #

(>>) :: WriterT w m a -> WriterT w m b -> WriterT w m b #

return :: a -> WriterT w m a #

fail :: String -> WriterT w m a #

Monad f => Monad (Star f a) 

Methods

(>>=) :: Star f a a -> (a -> Star f a b) -> Star f a b #

(>>) :: Star f a a -> Star f a b -> Star f a b #

return :: a -> Star f a a #

fail :: String -> Star f a a #

Monad (Costar f a) 

Methods

(>>=) :: Costar f a a -> (a -> Costar f a b) -> Costar f a b #

(>>) :: Costar f a a -> Costar f a b -> Costar f a b #

return :: a -> Costar f a a #

fail :: String -> Costar f a a #

Monad (Tagged k s) 

Methods

(>>=) :: Tagged k s a -> (a -> Tagged k s b) -> Tagged k s b #

(>>) :: Tagged k s a -> Tagged k s b -> Tagged k s b #

return :: a -> Tagged k s a #

fail :: String -> Tagged k s a #

Monad f => Monad (M1 i c f) 

Methods

(>>=) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b #

(>>) :: M1 i c f a -> M1 i c f b -> M1 i c f b #

return :: a -> M1 i c f a #

fail :: String -> M1 i c f a #

(Monad f, Monad g) => Monad (Product * f g) 

Methods

(>>=) :: Product * f g a -> (a -> Product * f g b) -> Product * f g b #

(>>) :: Product * f g a -> Product * f g b -> Product * f g b #

return :: a -> Product * f g a #

fail :: String -> Product * f g a #

Monad (ContT k r m) 

Methods

(>>=) :: ContT k r m a -> (a -> ContT k r m b) -> ContT k r m b #

(>>) :: ContT k r m a -> ContT k r m b -> ContT k r m b #

return :: a -> ContT k r m a #

fail :: String -> ContT k r m a #

Monad m => Monad (ReaderT * r m) 

Methods

(>>=) :: ReaderT * r m a -> (a -> ReaderT * r m b) -> ReaderT * r m b #

(>>) :: ReaderT * r m a -> ReaderT * r m b -> ReaderT * r m b #

return :: a -> ReaderT * r m a #

fail :: String -> ReaderT * r m a #

(Monoid w, Monad m) => Monad (RWST r w s m) 

Methods

(>>=) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b #

(>>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b #

return :: a -> RWST r w s m a #

fail :: String -> RWST r w s m a #

(Monoid w, Monad m) => Monad (RWST r w s m) 

Methods

(>>=) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b #

(>>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b #

return :: a -> RWST r w s m a #

fail :: String -> RWST r w s m a #

class (Alternative m, Monad m) => MonadPlus m where #

Monads that also support choice and failure.

Methods

mzero :: m a #

the identity of mplus. It should also satisfy the equations

mzero >>= f  =  mzero
v >> mzero   =  mzero

mplus :: m a -> m a -> m a #

an associative operation

Instances

MonadPlus [] 

Methods

mzero :: [a] #

mplus :: [a] -> [a] -> [a] #

MonadPlus Maybe 

Methods

mzero :: Maybe a #

mplus :: Maybe a -> Maybe a -> Maybe a #

MonadPlus IO 

Methods

mzero :: IO a #

mplus :: IO a -> IO a -> IO a #

MonadPlus U1 

Methods

mzero :: U1 a #

mplus :: U1 a -> U1 a -> U1 a #

MonadPlus IResult 

Methods

mzero :: IResult a #

mplus :: IResult a -> IResult a -> IResult a #

MonadPlus Result 

Methods

mzero :: Result a #

mplus :: Result a -> Result a -> Result a #

MonadPlus Parser 

Methods

mzero :: Parser a #

mplus :: Parser a -> Parser a -> Parser a #

MonadPlus P 

Methods

mzero :: P a #

mplus :: P a -> P a -> P a #

MonadPlus Option 

Methods

mzero :: Option a #

mplus :: Option a -> Option a -> Option a #

MonadPlus STM 

Methods

mzero :: STM a #

mplus :: STM a -> STM a -> STM a #

MonadPlus ReadPrec 

Methods

mzero :: ReadPrec a #

mplus :: ReadPrec a -> ReadPrec a -> ReadPrec a #

MonadPlus ReadP 

Methods

mzero :: ReadP a #

mplus :: ReadP a -> ReadP a -> ReadP a #

MonadPlus Seq 

Methods

mzero :: Seq a #

mplus :: Seq a -> Seq a -> Seq a #

MonadPlus DList 

Methods

mzero :: DList a #

mplus :: DList a -> DList a -> DList a #

MonadPlus Vector 

Methods

mzero :: Vector a #

mplus :: Vector a -> Vector a -> Vector a #

MonadPlus f => MonadPlus (Rec1 f) 

Methods

mzero :: Rec1 f a #

mplus :: Rec1 f a -> Rec1 f a -> Rec1 f a #

MonadPlus (Parser i) 

Methods

mzero :: Parser i a #

mplus :: Parser i a -> Parser i a -> Parser i a #

(ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a) 

Methods

mzero :: ArrowMonad a a #

mplus :: ArrowMonad a a -> ArrowMonad a a -> ArrowMonad a a #

MonadPlus (Proxy *) 

Methods

mzero :: Proxy * a #

mplus :: Proxy * a -> Proxy * a -> Proxy * a #

MonadPlus m => MonadPlus (Yoneda m) 

Methods

mzero :: Yoneda m a #

mplus :: Yoneda m a -> Yoneda m a -> Yoneda m a #

MonadPlus (ReifiedFold s) 

Methods

mzero :: ReifiedFold s a #

mplus :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a #

Monad m => MonadPlus (ListT m) 

Methods

mzero :: ListT m a #

mplus :: ListT m a -> ListT m a -> ListT m a #

Monad m => MonadPlus (MaybeT m) 

Methods

mzero :: MaybeT m a #

mplus :: MaybeT m a -> MaybeT m a -> MaybeT m a #

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

Methods

mzero :: (f :*: g) a #

mplus :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a #

MonadPlus f => MonadPlus (Alt * f) 

Methods

mzero :: Alt * f a #

mplus :: Alt * f a -> Alt * f a -> Alt * f a #

MonadPlus m => MonadPlus (IdentityT * m) 

Methods

mzero :: IdentityT * m a #

mplus :: IdentityT * m a -> IdentityT * m a -> IdentityT * m a #

(Functor f, MonadPlus m) => MonadPlus (FreeT f m) 

Methods

mzero :: FreeT f m a #

mplus :: FreeT f m a -> FreeT f m a -> FreeT f m a #

(Monad m, Error e) => MonadPlus (ErrorT e m) 

Methods

mzero :: ErrorT e m a #

mplus :: ErrorT e m a -> ErrorT e m a -> ErrorT e m a #

(Monad m, Monoid e) => MonadPlus (ExceptT e m) 

Methods

mzero :: ExceptT e m a #

mplus :: ExceptT e m a -> ExceptT e m a -> ExceptT e m a #

MonadPlus m => MonadPlus (StateT s m) 

Methods

mzero :: StateT s m a #

mplus :: StateT s m a -> StateT s m a -> StateT s m a #

MonadPlus m => MonadPlus (StateT s m) 

Methods

mzero :: StateT s m a #

mplus :: StateT s m a -> StateT s m a -> StateT s m a #

(Monoid w, MonadPlus m) => MonadPlus (WriterT w m) 

Methods

mzero :: WriterT w m a #

mplus :: WriterT w m a -> WriterT w m a -> WriterT w m a #

(Monoid w, MonadPlus m) => MonadPlus (WriterT w m) 

Methods

mzero :: WriterT w m a #

mplus :: WriterT w m a -> WriterT w m a -> WriterT w m a #

MonadPlus f => MonadPlus (Star f a) 

Methods

mzero :: Star f a a #

mplus :: Star f a a -> Star f a a -> Star f a a #

MonadPlus f => MonadPlus (M1 i c f) 

Methods

mzero :: M1 i c f a #

mplus :: M1 i c f a -> M1 i c f a -> M1 i c f a #

(MonadPlus f, MonadPlus g) => MonadPlus (Product * f g) 

Methods

mzero :: Product * f g a #

mplus :: Product * f g a -> Product * f g a -> Product * f g a #

MonadPlus m => MonadPlus (ReaderT * r m) 

Methods

mzero :: ReaderT * r m a #

mplus :: ReaderT * r m a -> ReaderT * r m a -> ReaderT * r m a #

(Monoid w, MonadPlus m) => MonadPlus (RWST r w s m) 

Methods

mzero :: RWST r w s m a #

mplus :: RWST r w s m a -> RWST r w s m a -> RWST r w s m a #

(Monoid w, MonadPlus m) => MonadPlus (RWST r w s m) 

Methods

mzero :: RWST r w s m a #

mplus :: RWST r w s m a -> RWST r w s m a -> RWST r w s m a #

mapM :: Traversable t => forall m a b. Monad m => (a -> m b) -> t a -> m (t b) #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see mapM_.

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.

As of base 4.8.0.0, mapM_ is just traverse_, specialized to Monad.

forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b) #

forM is mapM with its arguments flipped. For a version that ignores the results see forM_.

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.

As of base 4.8.0.0, forM_ is just for_, specialized to Monad.

sequence :: Traversable t => forall m a. Monad m => t (m a) -> m (t a) #

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see sequence_.

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.

As of base 4.8.0.0, sequence_ is just sequenceA_, specialized to Monad.

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #

Same as >>=, but with the arguments interchanged.

(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1 #

Left-to-right Kleisli composition of monads.

(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c infixr 1 #

Right-to-left Kleisli composition of monads. (>=>), with the arguments flipped.

Note how this operator resembles function composition (.):

(.)   ::            (b ->   c) -> (a ->   b) -> a ->   c
(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c

forever :: Applicative f => f a -> f b #

forever act repeats the action infinitely.

void :: Functor f => f a -> f () #

void value discards or ignores the result of evaluation, such as the return value of an IO action.

Examples

Replace the contents of a Maybe Int with unit:

>>> void Nothing
Nothing
>>> void (Just 3)
Just ()

Replace the contents of an Either Int Int with unit, resulting in an Either Int '()':

>>> void (Left 8675309)
Left 8675309
>>> void (Right 8675309)
Right ()

Replace every element of a list with unit:

>>> void [1,2,3]
[(),(),()]

Replace the second element of a pair with unit:

>>> void (1,2)
(1,())

Discard the result of an IO action:

>>> mapM print [1,2]
1
2
[(),()]
>>> void $ mapM print [1,2]
1
2

join :: Monad m => m (m a) -> m a #

The join function is the conventional monad join operator. It is used to remove one level of monadic structure, projecting its bound argument into the outer level.

msum :: (Foldable t, MonadPlus m) => t (m a) -> m a #

The sum of a collection of actions, generalizing concat. As of base 4.8.0.0, msum is just asum, specialized to MonadPlus.

mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a #

Direct MonadPlus equivalent of filter filter = (mfilter:: (a -> Bool) -> [a] -> [a] applicable to any MonadPlus, for example mfilter odd (Just 1) == Just 1 mfilter odd (Just 2) == Nothing

filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a] #

This generalizes the list-based filter function.

mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c]) #

The mapAndUnzipM function maps its first argument over a list, returning the result as a pair of lists. This function is mainly used with complicated data structures or a state-transforming monad.

zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c] #

The zipWithM function generalizes zipWith to arbitrary applicative functors.

zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m () #

zipWithM_ is the extension of zipWithM which ignores the final result.

foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b #

The foldM function is analogous to foldl, except that its result is encapsulated in a monad. Note that foldM works from left-to-right over the list arguments. This could be an issue where (>>) and the `folded function' are not commutative.

      foldM f a1 [x1, x2, ..., xm]

==

      do
        a2 <- f a1 x1
        a3 <- f a2 x2
        ...
        f am xm

If right-to-left evaluation is required, the input list should be reversed.

Note: foldM is the same as foldlM

foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m () #

Like foldM, but discards the result.

replicateM :: Applicative m => Int -> m a -> m [a] #

replicateM n act performs the action n times, gathering the results.

replicateM_ :: Applicative m => Int -> m a -> m () #

Like replicateM, but discards the result.

guard :: Alternative f => Bool -> f () #

guard b is pure () if b is True, and empty if b is False.

when :: Applicative f => Bool -> f () -> f () #

Conditional execution of Applicative expressions. For example,

when debug (putStrLn "Debugging")

will output the string Debugging if the Boolean value debug is True, and otherwise do nothing.

unless :: Applicative f => Bool -> f () -> f () #

The reverse of when.

liftM :: Monad m => (a1 -> r) -> m a1 -> m r #

Promote a function to a monad.

liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r #

Promote a function to a monad, scanning the monadic arguments from left to right. For example,

   liftM2 (+) [0,1] [0,2] = [0,2,1,3]
   liftM2 (+) (Just 1) Nothing = Nothing

liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r #

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r #

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r #

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

ap :: Monad m => m (a -> b) -> m a -> m b #

In many situations, the liftM operations can be replaced by uses of ap, which promotes function application.

      return f `ap` x1 `ap` ... `ap` xn

is equivalent to

      liftMn f x1 x2 ... xn

(<$!>) :: Monad m => (a -> b) -> m a -> m b infixl 4 #

Strict version of <$>.

Since: 4.8.0.0

Arrows

class Category * a => Arrow a where #

The basic arrow class.

Instances should satisfy the following laws:

where

assoc ((a,b),c) = (a,(b,c))

The other combinators have sensible default definitions, which may be overridden for efficiency.

Minimal complete definition

arr, (first | (***))

Methods

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

Lift a function to an arrow.

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

Send the first component of the input through the argument arrow, and copy the rest unchanged to the output.

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

A mirror image of first.

The default definition may be overridden with a more efficient version if desired.

(***) :: a b c -> a b' c' -> a (b, b') (c, c') infixr 3 #

Split the input between the two argument arrows and combine their output. Note that this is in general not a functor.

The default definition may be overridden with a more efficient version if desired.

(&&&) :: a b c -> a b c' -> a b (c, c') infixr 3 #

Fanout: send the input to both argument arrows and combine their output.

The default definition may be overridden with a more efficient version if desired.

Instances

Arrow (->) 

Methods

arr :: (b -> c) -> b -> c #

first :: (b -> c) -> (b, d) -> (c, d) #

second :: (b -> c) -> (d, b) -> (d, c) #

(***) :: (b -> c) -> (b' -> c') -> (b, b') -> (c, c') #

(&&&) :: (b -> c) -> (b -> c') -> b -> (c, c') #

Arrow ReifiedGetter 

Methods

arr :: (b -> c) -> ReifiedGetter b c #

first :: ReifiedGetter b c -> ReifiedGetter (b, d) (c, d) #

second :: ReifiedGetter b c -> ReifiedGetter (d, b) (d, c) #

(***) :: ReifiedGetter b c -> ReifiedGetter b' c' -> ReifiedGetter (b, b') (c, c') #

(&&&) :: ReifiedGetter b c -> ReifiedGetter b c' -> ReifiedGetter b (c, c') #

Arrow ReifiedFold 

Methods

arr :: (b -> c) -> ReifiedFold b c #

first :: ReifiedFold b c -> ReifiedFold (b, d) (c, d) #

second :: ReifiedFold b c -> ReifiedFold (d, b) (d, c) #

(***) :: ReifiedFold b c -> ReifiedFold b' c' -> ReifiedFold (b, b') (c, c') #

(&&&) :: ReifiedFold b c -> ReifiedFold b c' -> ReifiedFold b (c, c') #

Monad m => Arrow (Kleisli m) 

Methods

arr :: (b -> c) -> Kleisli m b c #

first :: Kleisli m b c -> Kleisli m (b, d) (c, d) #

second :: Kleisli m b c -> Kleisli m (d, b) (d, c) #

(***) :: Kleisli m b c -> Kleisli m b' c' -> Kleisli m (b, b') (c, c') #

(&&&) :: Kleisli m b c -> Kleisli m b c' -> Kleisli m b (c, c') #

Comonad w => Arrow (Cokleisli w) 

Methods

arr :: (b -> c) -> Cokleisli w b c #

first :: Cokleisli w b c -> Cokleisli w (b, d) (c, d) #

second :: Cokleisli w b c -> Cokleisli w (d, b) (d, c) #

(***) :: Cokleisli w b c -> Cokleisli w b' c' -> Cokleisli w (b, b') (c, c') #

(&&&) :: Cokleisli w b c -> Cokleisli w b c' -> Cokleisli w b (c, c') #

Arrow (Indexed i) 

Methods

arr :: (b -> c) -> Indexed i b c #

first :: Indexed i b c -> Indexed i (b, d) (c, d) #

second :: Indexed i b c -> Indexed i (d, b) (d, c) #

(***) :: Indexed i b c -> Indexed i b' c' -> Indexed i (b, b') (c, c') #

(&&&) :: Indexed i b c -> Indexed i b c' -> Indexed i b (c, c') #

Arrow p => Arrow (Tambara p) 

Methods

arr :: (b -> c) -> Tambara p b c #

first :: Tambara p b c -> Tambara p (b, d) (c, d) #

second :: Tambara p b c -> Tambara p (d, b) (d, c) #

(***) :: Tambara p b c -> Tambara p b' c' -> Tambara p (b, b') (c, c') #

(&&&) :: Tambara p b c -> Tambara p b c' -> Tambara p b (c, c') #

Arrow p => Arrow (WrappedArrow p) 

Methods

arr :: (b -> c) -> WrappedArrow p b c #

first :: WrappedArrow p b c -> WrappedArrow p (b, d) (c, d) #

second :: WrappedArrow p b c -> WrappedArrow p (d, b) (d, c) #

(***) :: WrappedArrow p b c -> WrappedArrow p b' c' -> WrappedArrow p (b, b') (c, c') #

(&&&) :: WrappedArrow p b c -> WrappedArrow p b c' -> WrappedArrow p b (c, c') #

(Applicative f, Arrow p) => Arrow (Tannen * * * f p) 

Methods

arr :: (b -> c) -> Tannen * * * f p b c #

first :: Tannen * * * f p b c -> Tannen * * * f p (b, d) (c, d) #

second :: Tannen * * * f p b c -> Tannen * * * f p (d, b) (d, c) #

(***) :: Tannen * * * f p b c -> Tannen * * * f p b' c' -> Tannen * * * f p (b, b') (c, c') #

(&&&) :: Tannen * * * f p b c -> Tannen * * * f p b c' -> Tannen * * * f p b (c, c') #

newtype Kleisli m a b :: (* -> *) -> * -> * -> * #

Kleisli arrows of a monad.

Constructors

Kleisli 

Fields

Instances

Monad m => Arrow (Kleisli m) 

Methods

arr :: (b -> c) -> Kleisli m b c #

first :: Kleisli m b c -> Kleisli m (b, d) (c, d) #

second :: Kleisli m b c -> Kleisli m (d, b) (d, c) #

(***) :: Kleisli m b c -> Kleisli m b' c' -> Kleisli m (b, b') (c, c') #

(&&&) :: Kleisli m b c -> Kleisli m b c' -> Kleisli m b (c, c') #

MonadPlus m => ArrowZero (Kleisli m) 

Methods

zeroArrow :: Kleisli m b c #

MonadPlus m => ArrowPlus (Kleisli m) 

Methods

(<+>) :: Kleisli m b c -> Kleisli m b c -> Kleisli m b c #

Monad m => ArrowChoice (Kleisli m) 

Methods

left :: Kleisli m b c -> Kleisli m (Either b d) (Either c d) #

right :: Kleisli m b c -> Kleisli m (Either d b) (Either d c) #

(+++) :: Kleisli m b c -> Kleisli m b' c' -> Kleisli m (Either b b') (Either c c') #

(|||) :: Kleisli m b d -> Kleisli m c d -> Kleisli m (Either b c) d #

Monad m => ArrowApply (Kleisli m) 

Methods

app :: Kleisli m (Kleisli m b c, b) c #

MonadFix m => ArrowLoop (Kleisli m)

Beware that for many monads (those for which the >>= operation is strict) this instance will not satisfy the right-tightening law required by the ArrowLoop class.

Methods

loop :: Kleisli m (b, d) (c, d) -> Kleisli m b c #

(Monad m, Functor m) => Representable (Kleisli m) 

Associated Types

type Rep (Kleisli m :: * -> * -> *) :: * -> * #

Methods

tabulate :: (d -> Rep (Kleisli m) c) -> Kleisli m d c #

Monad m => Profunctor (Kleisli m) 

Methods

dimap :: (a -> b) -> (c -> d) -> Kleisli m b c -> Kleisli m a d #

lmap :: (a -> b) -> Kleisli m b c -> Kleisli m a c #

rmap :: (b -> c) -> Kleisli m a b -> Kleisli m a c #

(#.) :: Coercible * c b => (b -> c) -> Kleisli m a b -> Kleisli m a c #

(.#) :: Coercible * b a => Kleisli m b c -> (a -> b) -> Kleisli m a c #

Monad m => Choice (Kleisli m) 

Methods

left' :: Kleisli m a b -> Kleisli m (Either a c) (Either b c) #

right' :: Kleisli m a b -> Kleisli m (Either c a) (Either c b) #

Monad m => Strong (Kleisli m) 

Methods

first' :: Kleisli m a b -> Kleisli m (a, c) (b, c) #

second' :: Kleisli m a b -> Kleisli m (c, a) (c, b) #

MonadFix m => Costrong (Kleisli m) 

Methods

unfirst :: Kleisli m (a, d) (b, d) -> Kleisli m a b #

unsecond :: Kleisli m (d, a) (d, b) -> Kleisli m a b #

Monad m => Category * (Kleisli m) 

Methods

id :: cat a a #

(.) :: cat b c -> cat a b -> cat a c #

Wrapped (Kleisli m a b) 

Associated Types

type Unwrapped (Kleisli m a b) :: * #

Methods

_Wrapped' :: Iso' (Kleisli m a b) (Unwrapped (Kleisli m a b)) #

(~) * t (Kleisli m' a' b') => Rewrapped (Kleisli m a b) t 
type Rep (Kleisli m) 
type Rep (Kleisli m) = m
type Unwrapped (Kleisli m a b) 
type Unwrapped (Kleisli m a b) = a -> m b

returnA :: Arrow a => a b b #

The identity arrow, which plays the role of return in arrow notation.

(^>>) :: Arrow a => (b -> c) -> a c d -> a b d infixr 1 #

Precomposition with a pure function.

(>>^) :: Arrow a => a b c -> (c -> d) -> a b d infixr 1 #

Postcomposition with a pure function.

(>>>) :: Category k cat => cat a b -> cat b c -> cat a c infixr 1 #

Left-to-right composition

(<<<) :: Category k cat => cat b c -> cat a b -> cat a c infixr 1 #

Right-to-left composition

(<<^) :: Arrow a => a c d -> (b -> c) -> a b d infixr 1 #

Precomposition with a pure function (right-to-left variant).

(^<<) :: Arrow a => (c -> d) -> a b c -> a b d infixr 1 #

Postcomposition with a pure function (right-to-left variant).

class Arrow a => ArrowZero a where #

Minimal complete definition

zeroArrow

Methods

zeroArrow :: a b c #

Instances

MonadPlus m => ArrowZero (Kleisli m) 

Methods

zeroArrow :: Kleisli m b c #

ArrowZero p => ArrowZero (Tambara p) 

Methods

zeroArrow :: Tambara p b c #

ArrowZero p => ArrowZero (WrappedArrow p) 

Methods

zeroArrow :: WrappedArrow p b c #

(Applicative f, ArrowZero p) => ArrowZero (Tannen * * * f p) 

Methods

zeroArrow :: Tannen * * * f p b c #

class ArrowZero a => ArrowPlus a where #

A monoid on arrows.

Minimal complete definition

(<+>)

Methods

(<+>) :: a b c -> a b c -> a b c infixr 5 #

An associative operation with identity zeroArrow.

Instances

MonadPlus m => ArrowPlus (Kleisli m) 

Methods

(<+>) :: Kleisli m b c -> Kleisli m b c -> Kleisli m b c #

ArrowPlus p => ArrowPlus (Tambara p) 

Methods

(<+>) :: Tambara p b c -> Tambara p b c -> Tambara p b c #

(Applicative f, ArrowPlus p) => ArrowPlus (Tannen * * * f p) 

Methods

(<+>) :: Tannen * * * f p b c -> Tannen * * * f p b c -> Tannen * * * f p b c #

class Arrow a => ArrowChoice a where #

Choice, for arrows that support it. This class underlies the if and case constructs in arrow notation.

Instances should satisfy the following laws:

where

assocsum (Left (Left x)) = Left x
assocsum (Left (Right y)) = Right (Left y)
assocsum (Right z) = Right (Right z)

The other combinators have sensible default definitions, which may be overridden for efficiency.

Minimal complete definition

left | (+++)

Methods

left :: a b c -> a (Either b d) (Either c d) #

Feed marked inputs through the argument arrow, passing the rest through unchanged to the output.

right :: a b c -> a (Either d b) (Either d c) #

A mirror image of left.

The default definition may be overridden with a more efficient version if desired.

(+++) :: a b c -> a b' c' -> a (Either b b') (Either c c') infixr 2 #

Split the input between the two argument arrows, retagging and merging their outputs. Note that this is in general not a functor.

The default definition may be overridden with a more efficient version if desired.

(|||) :: a b d -> a c d -> a (Either b c) d infixr 2 #

Fanin: Split the input between the two argument arrows and merge their outputs.

The default definition may be overridden with a more efficient version if desired.

Instances

ArrowChoice (->) 

Methods

left :: (b -> c) -> Either b d -> Either c d #

right :: (b -> c) -> Either d b -> Either d c #

(+++) :: (b -> c) -> (b' -> c') -> Either b b' -> Either c c' #

(|||) :: (b -> d) -> (c -> d) -> Either b c -> d #

ArrowChoice ReifiedGetter 

Methods

left :: ReifiedGetter b c -> ReifiedGetter (Either b d) (Either c d) #

right :: ReifiedGetter b c -> ReifiedGetter (Either d b) (Either d c) #

(+++) :: ReifiedGetter b c -> ReifiedGetter b' c' -> ReifiedGetter (Either b b') (Either c c') #

(|||) :: ReifiedGetter b d -> ReifiedGetter c d -> ReifiedGetter (Either b c) d #

ArrowChoice ReifiedFold 

Methods

left :: ReifiedFold b c -> ReifiedFold (Either b d) (Either c d) #

right :: ReifiedFold b c -> ReifiedFold (Either d b) (Either d c) #

(+++) :: ReifiedFold b c -> ReifiedFold b' c' -> ReifiedFold (Either b b') (Either c c') #

(|||) :: ReifiedFold b d -> ReifiedFold c d -> ReifiedFold (Either b c) d #

Monad m => ArrowChoice (Kleisli m) 

Methods

left :: Kleisli m b c -> Kleisli m (Either b d) (Either c d) #

right :: Kleisli m b c -> Kleisli m (Either d b) (Either d c) #

(+++) :: Kleisli m b c -> Kleisli m b' c' -> Kleisli m (Either b b') (Either c c') #

(|||) :: Kleisli m b d -> Kleisli m c d -> Kleisli m (Either b c) d #

Comonad w => ArrowChoice (Cokleisli w) 

Methods

left :: Cokleisli w b c -> Cokleisli w (Either b d) (Either c d) #

right :: Cokleisli w b c -> Cokleisli w (Either d b) (Either d c) #

(+++) :: Cokleisli w b c -> Cokleisli w b' c' -> Cokleisli w (Either b b') (Either c c') #

(|||) :: Cokleisli w b d -> Cokleisli w c d -> Cokleisli w (Either b c) d #

ArrowChoice (Indexed i) 

Methods

left :: Indexed i b c -> Indexed i (Either b d) (Either c d) #

right :: Indexed i b c -> Indexed i (Either d b) (Either d c) #

(+++) :: Indexed i b c -> Indexed i b' c' -> Indexed i (Either b b') (Either c c') #

(|||) :: Indexed i b d -> Indexed i c d -> Indexed i (Either b c) d #

ArrowChoice p => ArrowChoice (Tambara p) 

Methods

left :: Tambara p b c -> Tambara p (Either b d) (Either c d) #

right :: Tambara p b c -> Tambara p (Either d b) (Either d c) #

(+++) :: Tambara p b c -> Tambara p b' c' -> Tambara p (Either b b') (Either c c') #

(|||) :: Tambara p b d -> Tambara p c d -> Tambara p (Either b c) d #

ArrowChoice p => ArrowChoice (WrappedArrow p) 

Methods

left :: WrappedArrow p b c -> WrappedArrow p (Either b d) (Either c d) #

right :: WrappedArrow p b c -> WrappedArrow p (Either d b) (Either d c) #

(+++) :: WrappedArrow p b c -> WrappedArrow p b' c' -> WrappedArrow p (Either b b') (Either c c') #

(|||) :: WrappedArrow p b d -> WrappedArrow p c d -> WrappedArrow p (Either b c) d #

(Applicative f, ArrowChoice p) => ArrowChoice (Tannen * * * f p) 

Methods

left :: Tannen * * * f p b c -> Tannen * * * f p (Either b d) (Either c d) #

right :: Tannen * * * f p b c -> Tannen * * * f p (Either d b) (Either d c) #

(+++) :: Tannen * * * f p b c -> Tannen * * * f p b' c' -> Tannen * * * f p (Either b b') (Either c c') #

(|||) :: Tannen * * * f p b d -> Tannen * * * f p c d -> Tannen * * * f p (Either b c) d #

class Arrow a => ArrowApply a where #

Some arrows allow application of arrow inputs to other inputs. Instances should satisfy the following laws:

Such arrows are equivalent to monads (see ArrowMonad).

Minimal complete definition

app

Methods

app :: a (a b c, b) c #

Instances

ArrowApply (->) 

Methods

app :: (b -> c, b) -> c #

ArrowApply ReifiedGetter 

Methods

app :: ReifiedGetter (ReifiedGetter b c, b) c #

ArrowApply ReifiedFold 

Methods

app :: ReifiedFold (ReifiedFold b c, b) c #

Monad m => ArrowApply (Kleisli m) 

Methods

app :: Kleisli m (Kleisli m b c, b) c #

Comonad w => ArrowApply (Cokleisli w) 

Methods

app :: Cokleisli w (Cokleisli w b c, b) c #

ArrowApply (Indexed i) 

Methods

app :: Indexed i (Indexed i b c, b) c #

ArrowApply p => ArrowApply (Tambara p) 

Methods

app :: Tambara p (Tambara p b c, b) c #

ArrowApply p => ArrowApply (WrappedArrow p) 

Methods

app :: WrappedArrow p (WrappedArrow p b c, b) c #

newtype ArrowMonad a b :: (* -> * -> *) -> * -> * #

The ArrowApply class is equivalent to Monad: any monad gives rise to a Kleisli arrow, and any instance of ArrowApply defines a monad.

Constructors

ArrowMonad (a () b) 

Instances

ArrowApply a => Monad (ArrowMonad a) 

Methods

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

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

return :: a -> ArrowMonad a a #

fail :: String -> ArrowMonad a a #

Arrow a => Functor (ArrowMonad a) 

Methods

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

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

Arrow a => Applicative (ArrowMonad a) 

Methods

pure :: a -> ArrowMonad a a #

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

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

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

ArrowPlus a => Alternative (ArrowMonad a) 

Methods

empty :: ArrowMonad a a #

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

some :: ArrowMonad a a -> ArrowMonad a [a] #

many :: ArrowMonad a a -> ArrowMonad a [a] #

(ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a) 

Methods

mzero :: ArrowMonad a a #

mplus :: ArrowMonad a a -> ArrowMonad a a -> ArrowMonad a a #

Wrapped (ArrowMonad m a) 

Associated Types

type Unwrapped (ArrowMonad m a) :: * #

Methods

_Wrapped' :: Iso' (ArrowMonad m a) (Unwrapped (ArrowMonad m a)) #

(~) * t (ArrowMonad m' a') => Rewrapped (ArrowMonad m a) t 
type Unwrapped (ArrowMonad m a) 
type Unwrapped (ArrowMonad m a) = m () a

leftApp :: ArrowApply a => a b c -> a (Either b d) (Either c d) #

Any instance of ArrowApply can be made into an instance of ArrowChoice by defining left = leftApp.

class Arrow a => ArrowLoop a where #

The loop operator expresses computations in which an output value is fed back as input, although the computation occurs only once. It underlies the rec value recursion construct in arrow notation. loop should satisfy the following laws:

extension
loop (arr f) = arr (\ b -> fst (fix (\ (c,d) -> f (b,d))))
left tightening
loop (first h >>> f) = h >>> loop f
right tightening
loop (f >>> first h) = loop f >>> h
sliding
loop (f >>> arr (id *** k)) = loop (arr (id *** k) >>> f)
vanishing
loop (loop f) = loop (arr unassoc >>> f >>> arr assoc)
superposing
second (loop f) = loop (arr assoc >>> second f >>> arr unassoc)

where

assoc ((a,b),c) = (a,(b,c))
unassoc (a,(b,c)) = ((a,b),c)

Minimal complete definition

loop

Methods

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

Instances

ArrowLoop (->) 

Methods

loop :: ((b, d) -> (c, d)) -> b -> c #

ArrowLoop ReifiedGetter 

Methods

loop :: ReifiedGetter (b, d) (c, d) -> ReifiedGetter b c #

MonadFix m => ArrowLoop (Kleisli m)

Beware that for many monads (those for which the >>= operation is strict) this instance will not satisfy the right-tightening law required by the ArrowLoop class.

Methods

loop :: Kleisli m (b, d) (c, d) -> Kleisli m b c #

ComonadApply w => ArrowLoop (Cokleisli w) 

Methods

loop :: Cokleisli w (b, d) (c, d) -> Cokleisli w b c #

ArrowLoop (Indexed i) 

Methods

loop :: Indexed i (b, d) (c, d) -> Indexed i b c #

ArrowLoop p => ArrowLoop (Tambara p) 

Methods

loop :: Tambara p (b, d) (c, d) -> Tambara p b c #

ArrowLoop p => ArrowLoop (WrappedArrow p) 

Methods

loop :: WrappedArrow p (b, d) (c, d) -> WrappedArrow p b c #

(Applicative f, ArrowLoop p) => ArrowLoop (Tannen * * * f p) 

Methods

loop :: Tannen * * * f p (b, d) (c, d) -> Tannen * * * f p b c #

left :: ArrowChoice a => forall b c d. a b c -> a (Either b d) (Either c d) #

Feed marked inputs through the argument arrow, passing the rest through unchanged to the output.

right :: ArrowChoice a => forall b c d. a b c -> a (Either d b) (Either d c) #

A mirror image of left.

The default definition may be overridden with a more efficient version if desired.

(+++) :: ArrowChoice a => forall b c b' c'. a b c -> a b' c' -> a (Either b b') (Either c c') #

Split the input between the two argument arrows, retagging and merging their outputs. Note that this is in general not a functor.

The default definition may be overridden with a more efficient version if desired.

(|||) :: ArrowChoice a => forall b d c. a b d -> a c d -> a (Either b c) d #

Fanin: Split the input between the two argument arrows and merge their outputs.

The default definition may be overridden with a more efficient version if desired.

Mutable Variables In IO

IORef

data IORef a :: * -> * #

A mutable variable in the IO monad

Instances

Eq (IORef a) 

Methods

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