Safe Haskell | None |
---|---|
Language | Haskell2010 |
Synopsis
- ($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
- class IsList l where
- class Eq a where
- class Applicative m => Monad (m :: Type -> Type) where
- (>>=) :: m a -> (a -> m b) -> m b
- class Functor (f :: Type -> Type) where
- fmap :: (a -> b) -> f a -> f b
- class Eq a => Ord a where
- class Show a
- class Functor f => Applicative (f :: Type -> Type) where
- class Foldable (t :: Type -> Type)
- class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
- class Generic a
- class Semigroup a where
- (<>) :: a -> a -> a
- class Semigroup a => Monoid a where
- mempty :: a
- data Bool
- data Maybe a
- data Ordering = EQ
- data Either a b
- type Type = Type
- type family Item l
- newtype Identity a = Identity {
- runIdentity :: a
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- mapMaybe :: (a -> Maybe b) -> [a] -> [b]
- fromMaybe :: a -> Maybe a -> a
- maybe :: b -> (a -> b) -> Maybe a -> b
- on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
- (<&>) :: Functor f => f a -> (a -> b) -> f b
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- (.) :: (b -> c) -> (a -> b) -> a -> c
- const :: a -> b -> a
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- (<|>) :: Alternative f => f a -> f a -> f a
- (&&) :: Bool -> Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
- data Map k a
- data Seq a
- data Set a
- class NFData a
- class Eq a => Hashable a
- _1 :: Field1 s t a b => Lens s t a b
- _2 :: Field2 s t a b => Lens s t a b
- adjoin :: forall k l (is :: IxList) s a (js :: IxList). (Is k A_Traversal, Is l A_Traversal) => Optic' k is s a -> Optic' l js s a -> Traversal' s a
- traversed :: Traversable t => Traversal (t a) (t b) a b
- traverseOf :: forall k f (is :: IxList) s t a b. (Is k A_Traversal, Applicative f) => Optic k is s t a b -> (a -> f b) -> s -> f t
- traversalVL :: TraversalVL s t a b -> Traversal s t a b
- type Traversal s t a b = Optic A_Traversal NoIx s t a b
- type Traversal' s a = Optic' A_Traversal NoIx s a
- set :: forall k (is :: IxList) s t a b. Is k A_Setter => Optic k is s t a b -> b -> s -> t
- over :: forall k (is :: IxList) s t a b. Is k A_Setter => Optic k is s t a b -> (a -> b) -> s -> t
- pattern Empty :: AsEmpty a => a
- _Empty :: AsEmpty a => Prism' a ()
- coerced :: (Coercible s a, Coercible t b) => Iso s t a b
- simple :: Iso' a a
- equality :: (s ~ a, t ~ b) => Iso s t a b
- iso :: (s -> a) -> (b -> t) -> Iso s t a b
- type Iso s t a b = Optic An_Iso NoIx s t a b
- type Iso' s a = Optic' An_Iso NoIx s a
- review :: forall k (is :: IxList) t b. Is k A_Review => Optic' k is t b -> b -> t
- re :: forall (is :: IxList) s t a b. (ReversibleOptic k, AcceptsEmptyIndices "re" is) => Optic k is s t a b -> Optic (ReversedOptic k) is b a t s
- _Right :: Prism (Either a b) (Either a c) b c
- _Left :: Prism (Either a b) (Either c b) a c
- _Just :: Prism (Maybe a) (Maybe b) a b
- prism' :: (b -> s) -> (s -> Maybe a) -> Prism s s a b
- type Prism' s a = Optic' A_Prism NoIx s a
- lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b
- type Lens s t a b = Optic A_Lens NoIx s t a b
- type Lens' s a = Optic' A_Lens NoIx s a
- afailing :: forall k l (is :: IxList) s a (js :: IxList). (Is k An_AffineFold, Is l An_AffineFold) => Optic' k is s a -> Optic' l js s a -> AffineFold s a
- afolding :: (s -> Maybe a) -> AffineFold s a
- preview :: forall k (is :: IxList) s a. Is k An_AffineFold => Optic' k is s a -> s -> Maybe a
- type AffineFold s a = Optic' An_AffineFold NoIx s a
- matching :: forall k (is :: IxList) s t a b. Is k An_AffineTraversal => Optic k is s t a b -> s -> Either t a
- atraversal :: (s -> Either t a) -> (s -> b -> t) -> AffineTraversal s t a b
- type AffineTraversal s t a b = Optic An_AffineTraversal NoIx s t a b
- type AffineTraversal' s a = Optic' An_AffineTraversal NoIx s a
- to :: (s -> a) -> Getter s a
- view :: forall k (is :: IxList) s a. Is k A_Getter => Optic' k is s a -> s -> a
- type Getter s a = Optic' A_Getter NoIx s a
- (%) :: forall k l m (is :: IxList) (js :: IxList) (ks :: IxList) s t u v a b. (JoinKinds k l m, AppendIndices is js ks) => Optic k is s t u v -> Optic l js u v a b -> Optic m ks s t a b
- castOptic :: forall destKind srcKind (is :: IxList) s t a b. Is srcKind destKind => Optic srcKind is s t a b -> Optic destKind is s t a b
- data Optic k (is :: IxList) s t a b
- type Optic' k (is :: IxList) s a = Optic k is s s a a
- class Is k l
- class JoinKinds k l m | k l -> m
- type OpticKind = Type
- data An_Iso
- data A_Lens
- data An_AffineTraversal
- data A_Traversal
- data A_Getter
- data An_AffineFold
- data A_Fold
- type NoIx = '[] :: [Type]
- data Text
- mapLookup :: Ord k => k -> Map k a -> Maybe a
- mapDelete :: Ord k => k -> Map k a -> Map k a
- mapInsert :: Ord k => k -> a -> Map k a -> Map k a
- mapFromSet :: (k -> a) -> Set k -> Map k a
- mapMapEither :: (a -> Either b c) -> Map k a -> (Map k b, Map k c)
- mapMapMaybe :: (a -> Maybe b) -> Map k a -> Map k b
- mapKeysSet :: Map k a -> Set k
- mapUnionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a
- mapFilter :: (a -> Bool) -> Map k a -> Map k a
- mapToList :: Map k a -> [(k, a)]
- mapFoldMapWithKey :: Monoid m => (k -> a -> m) -> Map k a -> m
- setMember :: Ord a => a -> Set a -> Bool
- setInsert :: Ord a => a -> Set a -> Set a
- setDelete :: Ord a => a -> Set a -> Set a
- seqWither :: Applicative f => (a -> f (Maybe b)) -> Seq a -> f (Seq b)
- seqReduceR :: b -> (a -> Seq a -> b) -> Seq a -> b
- seqConsMaybe :: Maybe a -> Seq a -> Seq a
- seqFromMaybe :: Maybe a -> Seq a
- seqSingleton :: Prism' (Seq a) a
- seqAtMostOne :: Prism' (Seq a) (Maybe a)
- seqToList :: Seq a -> [a]
- seqConcat :: Seq (Seq a) -> Seq a
- textEmpty :: Text
- textConcat :: Foldable t => t Text -> Text
- seqAppendAndConcat :: Semigroup a => Seq a -> Seq a -> Seq a
- seqAppendAndConcatWith :: (a -> a -> Maybe a) -> Seq a -> Seq a -> Seq a
Documentation
($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 #
Application operator. This operator is redundant, since ordinary
application (f x)
means the same as (f
. However, $
x)$
has
low, right-associative binding precedence, so it sometimes allows
parentheses to be omitted; for example:
f $ g $ h x = f (g (h x))
It is also useful in higher-order situations, such as
,
or map
($
0) xs
.zipWith
($
) fs xs
Note that (
is levity-polymorphic in its result type, so that
$
)foo
where $
Truefoo :: Bool -> Int#
is well-typed.
The IsList
class and its methods are intended to be used in
conjunction with the OverloadedLists extension.
Since: base-4.7.0.0
The fromList
function constructs the structure l
from the given
list of Item l
fromListN :: Int -> [Item l] -> l #
The fromListN
function takes the input list's length as a hint. Its
behaviour should be equivalent to fromList
. The hint can be used to
construct the structure l
more efficiently compared to fromList
. If
the given hint does not equal to the input list's length the behaviour of
fromListN
is not specified.
The toList
function extracts a list of Item l
from the structure l
.
It should satisfy fromList . toList = id.
Instances
IsList CallStack | Be aware that 'fromList . toList = id' only for unfrozen Since: base-4.9.0.0 |
IsList Version | Since: base-4.8.0.0 |
IsList [a] | Since: base-4.7.0.0 |
IsList (ZipList a) | Since: base-4.15.0.0 |
IsList (NonEmpty a) | Since: base-4.9.0.0 |
IsList (Seq a) | |
Ord a => IsList (Set a) | Since: containers-0.5.6.2 |
Ord k => IsList (Map k v) | Since: containers-0.5.6.2 |
The Eq
class defines equality (==
) and inequality (/=
).
All the basic datatypes exported by the Prelude are instances of Eq
,
and Eq
may be derived for any datatype whose constituents are also
instances of Eq
.
The Haskell Report defines no laws for Eq
. However, ==
is customarily
expected to implement an equivalence relationship where two values comparing
equal are indistinguishable by "public" functions, with a "public" function
being one not allowing to see implementation details. For example, for a
type representing non-normalised natural numbers modulo 100, a "public"
function doesn't make the difference between 1 and 201. It is expected to
have the following properties:
Instances
Eq Bool | |
Eq Char | |
Eq Double | Note that due to the presence of
Also note that
|
Eq Float | Note that due to the presence of
Also note that
|
Eq Int | |
Eq Integer | |
Eq Ordering | |
Eq Word | |
Eq Exp | |
Eq Match | |
Eq Clause | |
Eq Pat | |
Eq Type | |
Eq Dec | |
Eq Name | |
Eq FunDep | |
Eq InjectivityAnn | |
Defined in Language.Haskell.TH.Syntax (==) :: InjectivityAnn -> InjectivityAnn -> Bool # (/=) :: InjectivityAnn -> InjectivityAnn -> Bool # | |
Eq Overlap | |
Eq () | |
Eq TyCon | |
Eq Module | |
Eq TrName | |
Eq SpecConstrAnnotation | Since: base-4.3.0.0 |
Defined in GHC.Exts (==) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool # (/=) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool # | |
Eq Fixity | Since: base-4.6.0.0 |
Eq Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics (==) :: Associativity -> Associativity -> Bool # (/=) :: Associativity -> Associativity -> Bool # | |
Eq SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # | |
Eq SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics (==) :: SourceStrictness -> SourceStrictness -> Bool # (/=) :: SourceStrictness -> SourceStrictness -> Bool # | |
Eq DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics (==) :: DecidedStrictness -> DecidedStrictness -> Bool # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool # | |
Eq Extension | |
Eq ForeignSrcLang | |
Defined in GHC.ForeignSrcLang.Type (==) :: ForeignSrcLang -> ForeignSrcLang -> Bool # (/=) :: ForeignSrcLang -> ForeignSrcLang -> Bool # | |
Eq BigNat | |
Eq ModName | |
Eq PkgName | |
Eq Module | |
Eq OccName | |
Eq NameFlavour | |
Defined in Language.Haskell.TH.Syntax (==) :: NameFlavour -> NameFlavour -> Bool # (/=) :: NameFlavour -> NameFlavour -> Bool # | |
Eq NameSpace | |
Eq Loc | |
Eq Info | |
Eq ModuleInfo | |
Defined in Language.Haskell.TH.Syntax (==) :: ModuleInfo -> ModuleInfo -> Bool # (/=) :: ModuleInfo -> ModuleInfo -> Bool # | |
Eq Fixity | |
Eq FixityDirection | |
Defined in Language.Haskell.TH.Syntax (==) :: FixityDirection -> FixityDirection -> Bool # (/=) :: FixityDirection -> FixityDirection -> Bool # | |
Eq Lit | |
Eq Bytes | |
Eq Body | |
Eq Guard | |
Eq Stmt | |
Eq Range | |
Eq DerivClause | |
Defined in Language.Haskell.TH.Syntax (==) :: DerivClause -> DerivClause -> Bool # (/=) :: DerivClause -> DerivClause -> Bool # | |
Eq DerivStrategy | |
Defined in Language.Haskell.TH.Syntax (==) :: DerivStrategy -> DerivStrategy -> Bool # (/=) :: DerivStrategy -> DerivStrategy -> Bool # | |
Eq TypeFamilyHead | |
Defined in Language.Haskell.TH.Syntax (==) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (/=) :: TypeFamilyHead -> TypeFamilyHead -> Bool # | |
Eq TySynEqn | |
Eq Foreign | |
Eq Callconv | |
Eq Safety | |
Eq Pragma | |
Eq Inline | |
Eq RuleMatch | |
Eq Phases | |
Eq RuleBndr | |
Eq AnnTarget | |
Eq SourceUnpackedness | |
Defined in Language.Haskell.TH.Syntax (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # | |
Eq SourceStrictness | |
Defined in Language.Haskell.TH.Syntax (==) :: SourceStrictness -> SourceStrictness -> Bool # (/=) :: SourceStrictness -> SourceStrictness -> Bool # | |
Eq DecidedStrictness | |
Defined in Language.Haskell.TH.Syntax (==) :: DecidedStrictness -> DecidedStrictness -> Bool # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool # | |
Eq Con | |
Eq Bang | |
Eq PatSynDir | |
Eq PatSynArgs | |
Defined in Language.Haskell.TH.Syntax (==) :: PatSynArgs -> PatSynArgs -> Bool # (/=) :: PatSynArgs -> PatSynArgs -> Bool # | |
Eq TyVarBndr | |
Eq FamilyResultSig | |
Defined in Language.Haskell.TH.Syntax (==) :: FamilyResultSig -> FamilyResultSig -> Bool # (/=) :: FamilyResultSig -> FamilyResultSig -> Bool # | |
Eq TyLit | |
Eq Role | |
Eq AnnLookup | |
Eq a => Eq [a] | |
Eq a => Eq (Maybe a) | Since: base-2.1 |
Eq p => Eq (Par1 p) | Since: base-4.7.0.0 |
Eq a => Eq (ZipList a) | Since: base-4.7.0.0 |
Eq a => Eq (Identity a) | Since: base-4.8.0.0 |
Eq a => Eq (NonEmpty a) | Since: base-4.9.0.0 |
Eq a => Eq (Seq a) | |
Eq a => Eq (ViewL a) | |
Eq a => Eq (ViewR a) | |
Eq a => Eq (Set a) | |
Eq a => Eq (Hashed a) | Uses precomputed hash to detect inequality faster |
(Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
Eq (V1 p) | Since: base-4.9.0.0 |
Eq (U1 p) | Since: base-4.9.0.0 |
(Eq a, Eq b) => Eq (a, b) | |
(Eq k, Eq a) => Eq (Map k a) | |
Eq (f p) => Eq (Rec1 f p) | Since: base-4.7.0.0 |
Eq (URec (Ptr ()) p) | Since: base-4.9.0.0 |
Eq (URec Char p) | Since: base-4.9.0.0 |
Eq (URec Double p) | Since: base-4.9.0.0 |
Eq (URec Float p) | |
Eq (URec Int p) | Since: base-4.9.0.0 |
Eq (URec Word p) | Since: base-4.9.0.0 |
(Eq a, Eq b, Eq c) => Eq (a, b, c) | |
Eq a => Eq (Const a b) | Since: base-4.9.0.0 |
Eq c => Eq (K1 i c p) | Since: base-4.7.0.0 |
(Eq (f p), Eq (g p)) => Eq ((f :+: g) p) | Since: base-4.7.0.0 |
(Eq (f p), Eq (g p)) => Eq ((f :*: g) p) | Since: base-4.7.0.0 |
(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
Eq (f p) => Eq (M1 i c f p) | Since: base-4.7.0.0 |
Eq (f (g p)) => Eq ((f :.: g) p) | Since: base-4.7.0.0 |
(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
class Applicative m => Monad (m :: Type -> Type) 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:
- Left identity
return
a>>=
k = k a- Right identity
m
>>=
return
= m- Associativity
m
>>=
(\x -> k x>>=
h) = (m>>=
k)>>=
h
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.
(>>=) :: 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.
'as
' can be understood as the >>=
bsdo
expression
do a <- as bs a
Instances
Monad [] | Since: base-2.1 |
Monad Maybe | Since: base-2.1 |
Monad IO | Since: base-2.1 |
Monad Par1 | Since: base-4.9.0.0 |
Monad Q | |
Monad Identity | Since: base-4.8.0.0 |
Monad NonEmpty | Since: base-4.9.0.0 |
Monad Seq | |
Monad (Either e) | Since: base-4.4.0.0 |
Monad (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Monoid a => Monad ((,) a) | Since: base-4.9.0.0 |
Monad m => Monad (WrappedMonad m) | Since: base-4.7.0.0 |
Defined in Control.Applicative (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # return :: a -> WrappedMonad m a # | |
ArrowApply a => Monad (ArrowMonad a) | Since: base-2.1 |
Defined in Control.Arrow (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # return :: a0 -> ArrowMonad a a0 # | |
Monad f => Monad (Rec1 f) | Since: base-4.9.0.0 |
(Monoid a, Monoid b) => Monad ((,,) a b) | Since: base-4.14.0.0 |
Monad m => Monad (Kleisli m a) | Since: base-4.14.0.0 |
Monad ((->) r :: Type -> Type) | Since: base-2.1 |
(Monad f, Monad g) => Monad (f :*: g) | Since: base-4.9.0.0 |
(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | Since: base-4.14.0.0 |
(Applicative f, Monad f) => Monad (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal (>>=) :: WhenMissing f k x a -> (a -> WhenMissing f k x b) -> WhenMissing f k x b # (>>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # return :: a -> WhenMissing f k x a # | |
Monad f => Monad (M1 i c f) | Since: base-4.9.0.0 |
(Monad f, Applicative f) => Monad (WhenMatched f k x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal (>>=) :: WhenMatched f k x y a -> (a -> WhenMatched f k x y b) -> WhenMatched f k x y b # (>>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # return :: a -> WhenMatched f k x y a # |
class Functor (f :: Type -> Type) where #
A type f
is a Functor if it provides a function fmap
which, given any types a
and b
lets you apply any function from (a -> b)
to turn an f a
into an f b
, preserving the
structure of f
. Furthermore f
needs to adhere to the following:
Note, that the second law follows from the free theorem of the type fmap
and
the first law, so you need only check that the former condition holds.
fmap :: (a -> b) -> f a -> f b #
Using ApplicativeDo
: '
' can be understood as
the fmap
f asdo
expression
do a <- as pure (f a)
with an inferred Functor
constraint.
Instances
Functor [] | Since: base-2.1 |
Functor Maybe | Since: base-2.1 |
Functor IO | Since: base-2.1 |
Functor Par1 | Since: base-4.9.0.0 |
Functor Q | |
Functor ZipList | Since: base-2.1 |
Functor Identity | Since: base-4.8.0.0 |
Functor NonEmpty | Since: base-4.9.0.0 |
Functor Seq | |
Functor FingerTree | |
Defined in Data.Sequence.Internal fmap :: (a -> b) -> FingerTree a -> FingerTree b # (<$) :: a -> FingerTree b -> FingerTree a # | |
Functor Digit | |
Functor Node | |
Functor Elem | |
Functor ViewL | |
Functor ViewR | |
Functor (Either a) | Since: base-3.0 |
Functor (V1 :: Type -> Type) | Since: base-4.9.0.0 |
Functor (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Functor ((,) a) | Since: base-2.1 |
Monad m => Functor (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a # | |
Arrow a => Functor (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 # | |
Functor (Map k) | |
Functor f => Functor (Rec1 f) | Since: base-4.9.0.0 |
Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec (Ptr ()) :: Type -> Type) | Since: base-4.9.0.0 |
Functor ((,,) a b) | Since: base-4.14.0.0 |
Arrow a => Functor (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
Functor m => Functor (Kleisli m a) | Since: base-4.14.0.0 |
Functor (Const m :: Type -> Type) | Since: base-2.1 |
Functor ((->) r :: Type -> Type) | Since: base-2.1 |
Functor (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :+: g) | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :*: g) | Since: base-4.9.0.0 |
Functor ((,,,) a b c) | Since: base-4.14.0.0 |
(Applicative f, Monad f) => Functor (WhenMissing f k x) | Since: containers-0.5.9 |
Defined in Data.Map.Internal fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # (<$) :: a -> WhenMissing f k x b -> WhenMissing f k x a # | |
Functor f => Functor (M1 i c f) | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :.: g) | Since: base-4.9.0.0 |
Functor f => Functor (WhenMatched f k x y) | Since: containers-0.5.9 |
Defined in Data.Map.Internal fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # (<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y a # |
The Ord
class is used for totally ordered datatypes.
Instances of Ord
can be derived for any user-defined datatype whose
constituent types are in Ord
. The declared order of the constructors in
the data declaration determines the ordering in derived Ord
instances. The
Ordering
datatype allows a single comparison to determine the precise
ordering of two objects.
The Haskell Report defines no laws for Ord
. However, <=
is customarily
expected to implement a non-strict partial order and have the following
properties:
- Transitivity
- if
x <= y && y <= z
=True
, thenx <= z
=True
- Reflexivity
x <= x
=True
- Antisymmetry
- if
x <= y && y <= x
=True
, thenx == y
=True
Note that the following operator interactions are expected to hold:
x >= y
=y <= x
x < y
=x <= y && x /= y
x > y
=y < x
x < y
=compare x y == LT
x > y
=compare x y == GT
x == y
=compare x y == EQ
min x y == if x <= y then x else y
=True
max x y == if x >= y then x else y
=True
Note that (7.) and (8.) do not require min
and max
to return either of
their arguments. The result is merely required to equal one of the
arguments in terms of (==)
.
Minimal complete definition: either compare
or <=
.
Using compare
can be more efficient for complex types.
Instances
Ord Bool | |
Ord Char | |
Ord Double | Note that due to the presence of
Also note that, due to the same,
|
Ord Float | Note that due to the presence of
Also note that, due to the same,
|
Ord Int | |
Ord Integer | |
Ord Ordering | |
Defined in GHC.Classes | |
Ord Word | |
Ord Exp | |
Ord Match | |
Ord Clause | |
Ord Pat | |
Ord Type | |
Ord Dec | |
Ord Name | |
Ord FunDep | |
Ord InjectivityAnn | |
Defined in Language.Haskell.TH.Syntax compare :: InjectivityAnn -> InjectivityAnn -> Ordering # (<) :: InjectivityAnn -> InjectivityAnn -> Bool # (<=) :: InjectivityAnn -> InjectivityAnn -> Bool # (>) :: InjectivityAnn -> InjectivityAnn -> Bool # (>=) :: InjectivityAnn -> InjectivityAnn -> Bool # max :: InjectivityAnn -> InjectivityAnn -> InjectivityAnn # min :: InjectivityAnn -> InjectivityAnn -> InjectivityAnn # | |
Ord Overlap | |
Ord () | |
Ord TyCon | |
Ord Fixity | Since: base-4.6.0.0 |
Ord Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics compare :: Associativity -> Associativity -> Ordering # (<) :: Associativity -> Associativity -> Bool # (<=) :: Associativity -> Associativity -> Bool # (>) :: Associativity -> Associativity -> Bool # (>=) :: Associativity -> Associativity -> Bool # max :: Associativity -> Associativity -> Associativity # min :: Associativity -> Associativity -> Associativity # | |
Ord SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics compare :: SourceUnpackedness -> SourceUnpackedness -> Ordering # (<) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (<=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # max :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness # min :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness # | |
Ord SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics compare :: SourceStrictness -> SourceStrictness -> Ordering # (<) :: SourceStrictness -> SourceStrictness -> Bool # (<=) :: SourceStrictness -> SourceStrictness -> Bool # (>) :: SourceStrictness -> SourceStrictness -> Bool # (>=) :: SourceStrictness -> SourceStrictness -> Bool # max :: SourceStrictness -> SourceStrictness -> SourceStrictness # min :: SourceStrictness -> SourceStrictness -> SourceStrictness # | |
Ord DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics compare :: DecidedStrictness -> DecidedStrictness -> Ordering # (<) :: DecidedStrictness -> DecidedStrictness -> Bool # (<=) :: DecidedStrictness -> DecidedStrictness -> Bool # (>) :: DecidedStrictness -> DecidedStrictness -> Bool # (>=) :: DecidedStrictness -> DecidedStrictness -> Bool # max :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness # min :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness # | |
Ord BigNat | |
Ord ModName | |
Ord PkgName | |
Ord Module | |
Ord OccName | |
Ord NameFlavour | |
Defined in Language.Haskell.TH.Syntax compare :: NameFlavour -> NameFlavour -> Ordering # (<) :: NameFlavour -> NameFlavour -> Bool # (<=) :: NameFlavour -> NameFlavour -> Bool # (>) :: NameFlavour -> NameFlavour -> Bool # (>=) :: NameFlavour -> NameFlavour -> Bool # max :: NameFlavour -> NameFlavour -> NameFlavour # min :: NameFlavour -> NameFlavour -> NameFlavour # | |
Ord NameSpace | |
Defined in Language.Haskell.TH.Syntax | |
Ord Loc | |
Ord Info | |
Ord ModuleInfo | |
Defined in Language.Haskell.TH.Syntax compare :: ModuleInfo -> ModuleInfo -> Ordering # (<) :: ModuleInfo -> ModuleInfo -> Bool # (<=) :: ModuleInfo -> ModuleInfo -> Bool # (>) :: ModuleInfo -> ModuleInfo -> Bool # (>=) :: ModuleInfo -> ModuleInfo -> Bool # max :: ModuleInfo -> ModuleInfo -> ModuleInfo # min :: ModuleInfo -> ModuleInfo -> ModuleInfo # | |
Ord Fixity | |
Ord FixityDirection | |
Defined in Language.Haskell.TH.Syntax compare :: FixityDirection -> FixityDirection -> Ordering # (<) :: FixityDirection -> FixityDirection -> Bool # (<=) :: FixityDirection -> FixityDirection -> Bool # (>) :: FixityDirection -> FixityDirection -> Bool # (>=) :: FixityDirection -> FixityDirection -> Bool # max :: FixityDirection -> FixityDirection -> FixityDirection # min :: FixityDirection -> FixityDirection -> FixityDirection # | |
Ord Lit | |
Ord Bytes | |
Ord Body | |
Ord Guard | |
Ord Stmt | |
Ord Range | |
Ord DerivClause | |
Defined in Language.Haskell.TH.Syntax compare :: DerivClause -> DerivClause -> Ordering # (<) :: DerivClause -> DerivClause -> Bool # (<=) :: DerivClause -> DerivClause -> Bool # (>) :: DerivClause -> DerivClause -> Bool # (>=) :: DerivClause -> DerivClause -> Bool # max :: DerivClause -> DerivClause -> DerivClause # min :: DerivClause -> DerivClause -> DerivClause # | |
Ord DerivStrategy | |
Defined in Language.Haskell.TH.Syntax compare :: DerivStrategy -> DerivStrategy -> Ordering # (<) :: DerivStrategy -> DerivStrategy -> Bool # (<=) :: DerivStrategy -> DerivStrategy -> Bool # (>) :: DerivStrategy -> DerivStrategy -> Bool # (>=) :: DerivStrategy -> DerivStrategy -> Bool # max :: DerivStrategy -> DerivStrategy -> DerivStrategy # min :: DerivStrategy -> DerivStrategy -> DerivStrategy # | |
Ord TypeFamilyHead | |
Defined in Language.Haskell.TH.Syntax compare :: TypeFamilyHead -> TypeFamilyHead -> Ordering # (<) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (<=) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (>) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (>=) :: TypeFamilyHead -> TypeFamilyHead -> Bool # max :: TypeFamilyHead -> TypeFamilyHead -> TypeFamilyHead # min :: TypeFamilyHead -> TypeFamilyHead -> TypeFamilyHead # | |
Ord TySynEqn | |
Defined in Language.Haskell.TH.Syntax | |
Ord Foreign | |
Ord Callconv | |
Defined in Language.Haskell.TH.Syntax | |
Ord Safety | |
Ord Pragma | |
Ord Inline | |
Ord RuleMatch | |
Defined in Language.Haskell.TH.Syntax | |
Ord Phases | |
Ord RuleBndr | |
Defined in Language.Haskell.TH.Syntax | |
Ord AnnTarget | |
Defined in Language.Haskell.TH.Syntax | |
Ord SourceUnpackedness | |
Defined in Language.Haskell.TH.Syntax compare :: SourceUnpackedness -> SourceUnpackedness -> Ordering # (<) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (<=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # max :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness # min :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness # | |
Ord SourceStrictness | |
Defined in Language.Haskell.TH.Syntax compare :: SourceStrictness -> SourceStrictness -> Ordering # (<) :: SourceStrictness -> SourceStrictness -> Bool # (<=) :: SourceStrictness -> SourceStrictness -> Bool # (>) :: SourceStrictness -> SourceStrictness -> Bool # (>=) :: SourceStrictness -> SourceStrictness -> Bool # max :: SourceStrictness -> SourceStrictness -> SourceStrictness # min :: SourceStrictness -> SourceStrictness -> SourceStrictness # | |
Ord DecidedStrictness | |
Defined in Language.Haskell.TH.Syntax compare :: DecidedStrictness -> DecidedStrictness -> Ordering # (<) :: DecidedStrictness -> DecidedStrictness -> Bool # (<=) :: DecidedStrictness -> DecidedStrictness -> Bool # (>) :: DecidedStrictness -> DecidedStrictness -> Bool # (>=) :: DecidedStrictness -> DecidedStrictness -> Bool # max :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness # min :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness # | |
Ord Con | |
Ord Bang | |
Ord PatSynDir | |
Defined in Language.Haskell.TH.Syntax | |
Ord PatSynArgs | |
Defined in Language.Haskell.TH.Syntax compare :: PatSynArgs -> PatSynArgs -> Ordering # (<) :: PatSynArgs -> PatSynArgs -> Bool # (<=) :: PatSynArgs -> PatSynArgs -> Bool # (>) :: PatSynArgs -> PatSynArgs -> Bool # (>=) :: PatSynArgs -> PatSynArgs -> Bool # max :: PatSynArgs -> PatSynArgs -> PatSynArgs # min :: PatSynArgs -> PatSynArgs -> PatSynArgs # | |
Ord TyVarBndr | |
Defined in Language.Haskell.TH.Syntax | |
Ord FamilyResultSig | |
Defined in Language.Haskell.TH.Syntax compare :: FamilyResultSig -> FamilyResultSig -> Ordering # (<) :: FamilyResultSig -> FamilyResultSig -> Bool # (<=) :: FamilyResultSig -> FamilyResultSig -> Bool # (>) :: FamilyResultSig -> FamilyResultSig -> Bool # (>=) :: FamilyResultSig -> FamilyResultSig -> Bool # max :: FamilyResultSig -> FamilyResultSig -> FamilyResultSig # min :: FamilyResultSig -> FamilyResultSig -> FamilyResultSig # | |
Ord TyLit | |
Ord Role | |
Ord AnnLookup | |
Defined in Language.Haskell.TH.Syntax | |
Ord a => Ord [a] | |
Ord a => Ord (Maybe a) | Since: base-2.1 |
Ord p => Ord (Par1 p) | Since: base-4.7.0.0 |
Ord a => Ord (ZipList a) | Since: base-4.7.0.0 |
Defined in Control.Applicative | |
Ord a => Ord (Identity a) | Since: base-4.8.0.0 |
Ord a => Ord (NonEmpty a) | Since: base-4.9.0.0 |
Ord a => Ord (Seq a) | |
Ord a => Ord (ViewL a) | |
Ord a => Ord (ViewR a) | |
Ord a => Ord (Set a) | |
Ord a => Ord (Hashed a) | |
Defined in Data.Hashable.Class | |
(Ord a, Ord b) => Ord (Either a b) | Since: base-2.1 |
Ord (V1 p) | Since: base-4.9.0.0 |
Ord (U1 p) | Since: base-4.7.0.0 |
(Ord a, Ord b) => Ord (a, b) | |
(Ord k, Ord v) => Ord (Map k v) | |
Ord (f p) => Ord (Rec1 f p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
Ord (URec (Ptr ()) p) | Since: base-4.9.0.0 |
Defined in GHC.Generics compare :: URec (Ptr ()) p -> URec (Ptr ()) p -> Ordering # (<) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (<=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (>) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (>=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # max :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p # min :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p # | |
Ord (URec Char p) | Since: base-4.9.0.0 |
Ord (URec Double p) | Since: base-4.9.0.0 |
Defined in GHC.Generics compare :: URec Double p -> URec Double p -> Ordering # (<) :: URec Double p -> URec Double p -> Bool # (<=) :: URec Double p -> URec Double p -> Bool # (>) :: URec Double p -> URec Double p -> Bool # (>=) :: URec Double p -> URec Double p -> Bool # | |
Ord (URec Float p) | |
Defined in GHC.Generics | |
Ord (URec Int p) | Since: base-4.9.0.0 |
Ord (URec Word p) | Since: base-4.9.0.0 |
(Ord a, Ord b, Ord c) => Ord (a, b, c) | |
Defined in GHC.Classes | |
Ord a => Ord (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
Ord c => Ord (K1 i c p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
(Ord (f p), Ord (g p)) => Ord ((f :+: g) p) | Since: base-4.7.0.0 |
(Ord (f p), Ord (g p)) => Ord ((f :*: g) p) | Since: base-4.7.0.0 |
(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) | |
Defined in GHC.Classes | |
Ord (f p) => Ord (M1 i c f p) | Since: base-4.7.0.0 |
Ord (f (g p)) => Ord ((f :.: g) p) | Since: base-4.7.0.0 |
(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) | |
Defined in GHC.Classes compare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering # (<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) | |
Defined in GHC.Classes compare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering # (<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) # min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) | |
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering # (<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) # min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) | |
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering # (<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # max :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) # min :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) | |
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # max :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) # min :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) | |
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) # min :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) | |
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) # min :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) | |
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) # min :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # |
Conversion of values to readable String
s.
Derived instances of Show
have the following properties, which
are compatible with derived instances of Read
:
- The result of
show
is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. - If the constructor is defined to be an infix operator, then
showsPrec
will produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
x
is less thand
(associativity is ignored). Thus, ifd
is0
then the result is never surrounded in parentheses; ifd
is11
it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
show
will produce the record-syntax form, with the fields given in the same order as the original declaration.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Show
is equivalent to
instance (Show a) => Show (Tree a) where showsPrec d (Leaf m) = showParen (d > app_prec) $ showString "Leaf " . showsPrec (app_prec+1) m where app_prec = 10 showsPrec d (u :^: v) = showParen (d > up_prec) $ showsPrec (up_prec+1) u . showString " :^: " . showsPrec (up_prec+1) v where up_prec = 5
Note that right-associativity of :^:
is ignored. For example,
produces the stringshow
(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)"
.
Instances
class Functor f => Applicative (f :: Type -> Type) where #
A functor with application, providing operations to
A minimal complete definition must include implementations of pure
and of either <*>
or liftA2
. If it defines both, then they must behave
the same as their default definitions:
(<*>
) =liftA2
id
liftA2
f x y = f<$>
x<*>
y
Further, any definition must satisfy the following:
- Identity
pure
id
<*>
v = v- Composition
pure
(.)<*>
u<*>
v<*>
w = u<*>
(v<*>
w)- Homomorphism
pure
f<*>
pure
x =pure
(f x)- Interchange
u
<*>
pure
y =pure
($
y)<*>
u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor
instance for f
will satisfy
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2
p (liftA2
q u v) =liftA2
f u .liftA2
g v
If f
is also a Monad
, it should satisfy
(which implies that pure
and <*>
satisfy the applicative functor laws).
Lift a value.
Instances
Applicative [] | Since: base-2.1 |
Applicative Maybe | Since: base-2.1 |
Applicative IO | Since: base-2.1 |
Applicative Par1 | Since: base-4.9.0.0 |
Applicative Q | |
Applicative ZipList | f <$> ZipList xs1 <*> ... <*> ZipList xsN = ZipList (zipWithN f xs1 ... xsN) where (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: base-2.1 |
Applicative Identity | Since: base-4.8.0.0 |
Applicative NonEmpty | Since: base-4.9.0.0 |
Applicative Seq | Since: containers-0.5.4 |
Applicative (Either e) | Since: base-3.0 |
Applicative (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Monoid a => Applicative ((,) a) | For tuples, the ("hello ", (+15)) <*> ("world!", 2002) ("hello world!",2017) Since: base-2.1 |
Monad m => Applicative (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative pure :: a -> WrappedMonad m a # (<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c # (*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a # | |
Arrow a => Applicative (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow pure :: a0 -> ArrowMonad a a0 # (<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c # (*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 # | |
Applicative f => Applicative (Rec1 f) | Since: base-4.9.0.0 |
(Monoid a, Monoid b) => Applicative ((,,) a b) | Since: base-4.14.0.0 |
Arrow a => Applicative (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative pure :: a0 -> WrappedArrow a b a0 # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
Applicative m => Applicative (Kleisli m a) | Since: base-4.14.0.0 |
Defined in Control.Arrow | |
Monoid m => Applicative (Const m :: Type -> Type) | Since: base-2.0.1 |
Applicative ((->) r :: Type -> Type) | Since: base-2.1 |
Monoid c => Applicative (K1 i c :: Type -> Type) | Since: base-4.12.0.0 |
(Applicative f, Applicative g) => Applicative (f :*: g) | Since: base-4.9.0.0 |
(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) | Since: base-4.14.0.0 |
Defined in GHC.Base | |
(Applicative f, Monad f) => Applicative (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal pure :: a -> WhenMissing f k x a # (<*>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c # (*>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a # | |
Applicative f => Applicative (M1 i c f) | Since: base-4.9.0.0 |
(Applicative f, Applicative g) => Applicative (f :.: g) | Since: base-4.9.0.0 |
(Monad f, Applicative f) => Applicative (WhenMatched f k x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal pure :: a -> WhenMatched f k x y a # (<*>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c # (*>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a # |
class Foldable (t :: Type -> Type) #
Data structures that can be folded.
For example, given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Foldable Tree where foldMap f Empty = mempty foldMap f (Leaf x) = f x foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
This is suitable even for abstract types, as the monoid is assumed
to satisfy the monoid laws. Alternatively, one could define foldr
:
instance Foldable Tree where foldr f z Empty = z foldr f z (Leaf x) = f x z foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l
Foldable
instances are expected to satisfy the following laws:
foldr f z t = appEndo (foldMap (Endo . f) t ) z
foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
fold = foldMap id
length = getSum . foldMap (Sum . const 1)
sum
, product
, maximum
, and minimum
should all be essentially
equivalent to foldMap
forms, such as
sum = getSum . foldMap Sum
but may be less defined.
If the type is also a Functor
instance, it should satisfy
foldMap f = fold . fmap f
which implies that
foldMap f . fmap g = foldMap (f . g)
Instances
Foldable [] | Since: base-2.1 |
Defined in Data.Foldable fold :: Monoid m => [m] -> m # foldMap :: Monoid m => (a -> m) -> [a] -> m # foldMap' :: Monoid m => (a -> m) -> [a] -> m # foldr :: (a -> b -> b) -> b -> [a] -> b # foldr' :: (a -> b -> b) -> b -> [a] -> b # foldl :: (b -> a -> b) -> b -> [a] -> b # foldl' :: (b -> a -> b) -> b -> [a] -> b # foldr1 :: (a -> a -> a) -> [a] -> a # foldl1 :: (a -> a -> a) -> [a] -> a # elem :: Eq a => a -> [a] -> Bool # maximum :: Ord a => [a] -> a # | |
Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # | |
Foldable Par1 | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => Par1 m -> m # foldMap :: Monoid m => (a -> m) -> Par1 a -> m # foldMap' :: Monoid m => (a -> m) -> Par1 a -> m # foldr :: (a -> b -> b) -> b -> Par1 a -> b # foldr' :: (a -> b -> b) -> b -> Par1 a -> b # foldl :: (b -> a -> b) -> b -> Par1 a -> b # foldl' :: (b -> a -> b) -> b -> Par1 a -> b # foldr1 :: (a -> a -> a) -> Par1 a -> a # foldl1 :: (a -> a -> a) -> Par1 a -> a # elem :: Eq a => a -> Par1 a -> Bool # maximum :: Ord a => Par1 a -> a # | |
Foldable ZipList | Since: base-4.9.0.0 |
Defined in Control.Applicative fold :: Monoid m => ZipList m -> m # foldMap :: Monoid m => (a -> m) -> ZipList a -> m # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m # foldr :: (a -> b -> b) -> b -> ZipList a -> b # foldr' :: (a -> b -> b) -> b -> ZipList a -> b # foldl :: (b -> a -> b) -> b -> ZipList a -> b # foldl' :: (b -> a -> b) -> b -> ZipList a -> b # foldr1 :: (a -> a -> a) -> ZipList a -> a # foldl1 :: (a -> a -> a) -> ZipList a -> a # elem :: Eq a => a -> ZipList a -> Bool # maximum :: Ord a => ZipList a -> a # minimum :: Ord a => ZipList a -> a # | |
Foldable Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldMap' :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # | |
Foldable First | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
Foldable Last | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
Foldable Dual | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldMap' :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # | |
Foldable Sum | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldMap' :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # | |
Foldable Product | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldMap' :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # | |
Foldable Down | Since: base-4.12.0.0 |
Defined in Data.Foldable fold :: Monoid m => Down m -> m # foldMap :: Monoid m => (a -> m) -> Down a -> m # foldMap' :: Monoid m => (a -> m) -> Down a -> m # foldr :: (a -> b -> b) -> b -> Down a -> b # foldr' :: (a -> b -> b) -> b -> Down a -> b # foldl :: (b -> a -> b) -> b -> Down a -> b # foldl' :: (b -> a -> b) -> b -> Down a -> b # foldr1 :: (a -> a -> a) -> Down a -> a # foldl1 :: (a -> a -> a) -> Down a -> a # elem :: Eq a => a -> Down a -> Bool # maximum :: Ord a => Down a -> a # | |
Foldable NonEmpty | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => NonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b # foldr1 :: (a -> a -> a) -> NonEmpty a -> a # foldl1 :: (a -> a -> a) -> NonEmpty a -> a # elem :: Eq a => a -> NonEmpty a -> Bool # maximum :: Ord a => NonEmpty a -> a # minimum :: Ord a => NonEmpty a -> a # | |
Foldable Seq | |
Defined in Data.Sequence.Internal fold :: Monoid m => Seq m -> m # foldMap :: Monoid m => (a -> m) -> Seq a -> m # foldMap' :: Monoid m => (a -> m) -> Seq a -> m # foldr :: (a -> b -> b) -> b -> Seq a -> b # foldr' :: (a -> b -> b) -> b -> Seq a -> b # foldl :: (b -> a -> b) -> b -> Seq a -> b # foldl' :: (b -> a -> b) -> b -> Seq a -> b # foldr1 :: (a -> a -> a) -> Seq a -> a # foldl1 :: (a -> a -> a) -> Seq a -> a # elem :: Eq a => a -> Seq a -> Bool # maximum :: Ord a => Seq a -> a # | |
Foldable FingerTree | |
Defined in Data.Sequence.Internal fold :: Monoid m => FingerTree m -> m # foldMap :: Monoid m => (a -> m) -> FingerTree a -> m # foldMap' :: Monoid m => (a -> m) -> FingerTree a -> m # foldr :: (a -> b -> b) -> b -> FingerTree a -> b # foldr' :: (a -> b -> b) -> b -> FingerTree a -> b # foldl :: (b -> a -> b) -> b -> FingerTree a -> b # foldl' :: (b -> a -> b) -> b -> FingerTree a -> b # foldr1 :: (a -> a -> a) -> FingerTree a -> a # foldl1 :: (a -> a -> a) -> FingerTree a -> a # toList :: FingerTree a -> [a] # null :: FingerTree a -> Bool # length :: FingerTree a -> Int # elem :: Eq a => a -> FingerTree a -> Bool # maximum :: Ord a => FingerTree a -> a # minimum :: Ord a => FingerTree a -> a # sum :: Num a => FingerTree a -> a # product :: Num a => FingerTree a -> a # | |
Foldable Digit | |
Defined in Data.Sequence.Internal fold :: Monoid m => Digit m -> m # foldMap :: Monoid m => (a -> m) -> Digit a -> m # foldMap' :: Monoid m => (a -> m) -> Digit a -> m # foldr :: (a -> b -> b) -> b -> Digit a -> b # foldr' :: (a -> b -> b) -> b -> Digit a -> b # foldl :: (b -> a -> b) -> b -> Digit a -> b # foldl' :: (b -> a -> b) -> b -> Digit a -> b # foldr1 :: (a -> a -> a) -> Digit a -> a # foldl1 :: (a -> a -> a) -> Digit a -> a # elem :: Eq a => a -> Digit a -> Bool # maximum :: Ord a => Digit a -> a # minimum :: Ord a => Digit a -> a # | |
Foldable Node | |
Defined in Data.Sequence.Internal fold :: Monoid m => Node m -> m # foldMap :: Monoid m => (a -> m) -> Node a -> m # foldMap' :: Monoid m => (a -> m) -> Node a -> m # foldr :: (a -> b -> b) -> b -> Node a -> b # foldr' :: (a -> b -> b) -> b -> Node a -> b # foldl :: (b -> a -> b) -> b -> Node a -> b # foldl' :: (b -> a -> b) -> b -> Node a -> b # foldr1 :: (a -> a -> a) -> Node a -> a # foldl1 :: (a -> a -> a) -> Node a -> a # elem :: Eq a => a -> Node a -> Bool # maximum :: Ord a => Node a -> a # | |
Foldable Elem | |
Defined in Data.Sequence.Internal fold :: Monoid m => Elem m -> m # foldMap :: Monoid m => (a -> m) -> Elem a -> m # foldMap' :: Monoid m => (a -> m) -> Elem a -> m # foldr :: (a -> b -> b) -> b -> Elem a -> b # foldr' :: (a -> b -> b) -> b -> Elem a -> b # foldl :: (b -> a -> b) -> b -> Elem a -> b # foldl' :: (b -> a -> b) -> b -> Elem a -> b # foldr1 :: (a -> a -> a) -> Elem a -> a # foldl1 :: (a -> a -> a) -> Elem a -> a # elem :: Eq a => a -> Elem a -> Bool # maximum :: Ord a => Elem a -> a # | |
Foldable ViewL | |
Defined in Data.Sequence.Internal fold :: Monoid m => ViewL m -> m # foldMap :: Monoid m => (a -> m) -> ViewL a -> m # foldMap' :: Monoid m => (a -> m) -> ViewL a -> m # foldr :: (a -> b -> b) -> b -> ViewL a -> b # foldr' :: (a -> b -> b) -> b -> ViewL a -> b # foldl :: (b -> a -> b) -> b -> ViewL a -> b # foldl' :: (b -> a -> b) -> b -> ViewL a -> b # foldr1 :: (a -> a -> a) -> ViewL a -> a # foldl1 :: (a -> a -> a) -> ViewL a -> a # elem :: Eq a => a -> ViewL a -> Bool # maximum :: Ord a => ViewL a -> a # minimum :: Ord a => ViewL a -> a # | |
Foldable ViewR | |
Defined in Data.Sequence.Internal fold :: Monoid m => ViewR m -> m # foldMap :: Monoid m => (a -> m) -> ViewR a -> m # foldMap' :: Monoid m => (a -> m) -> ViewR a -> m # foldr :: (a -> b -> b) -> b -> ViewR a -> b # foldr' :: (a -> b -> b) -> b -> ViewR a -> b # foldl :: (b -> a -> b) -> b -> ViewR a -> b # foldl' :: (b -> a -> b) -> b -> ViewR a -> b # foldr1 :: (a -> a -> a) -> ViewR a -> a # foldl1 :: (a -> a -> a) -> ViewR a -> a # elem :: Eq a => a -> ViewR a -> Bool # maximum :: Ord a => ViewR a -> a # minimum :: Ord a => ViewR a -> a # | |
Foldable Set | Folds in order of increasing key. |
Defined in Data.Set.Internal fold :: Monoid m => Set m -> m # foldMap :: Monoid m => (a -> m) -> Set a -> m # foldMap' :: Monoid m => (a -> m) -> Set a -> m # foldr :: (a -> b -> b) -> b -> Set a -> b # foldr' :: (a -> b -> b) -> b -> Set a -> b # foldl :: (b -> a -> b) -> b -> Set a -> b # foldl' :: (b -> a -> b) -> b -> Set a -> b # foldr1 :: (a -> a -> a) -> Set a -> a # foldl1 :: (a -> a -> a) -> Set a -> a # elem :: Eq a => a -> Set a -> Bool # maximum :: Ord a => Set a -> a # | |
Foldable Hashed | |
Defined in Data.Hashable.Class fold :: Monoid m => Hashed m -> m # foldMap :: Monoid m => (a -> m) -> Hashed a -> m # foldMap' :: Monoid m => (a -> m) -> Hashed a -> m # foldr :: (a -> b -> b) -> b -> Hashed a -> b # foldr' :: (a -> b -> b) -> b -> Hashed a -> b # foldl :: (b -> a -> b) -> b -> Hashed a -> b # foldl' :: (b -> a -> b) -> b -> Hashed a -> b # foldr1 :: (a -> a -> a) -> Hashed a -> a # foldl1 :: (a -> a -> a) -> Hashed a -> a # elem :: Eq a => a -> Hashed a -> Bool # maximum :: Ord a => Hashed a -> a # minimum :: Ord a => Hashed a -> a # | |
Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # length :: Either a a0 -> Int # elem :: Eq a0 => a0 -> Either a a0 -> Bool # maximum :: Ord a0 => Either a a0 -> a0 # minimum :: Ord a0 => Either a a0 -> a0 # | |
Foldable (V1 :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> m # foldMap' :: Monoid m => (a -> m) -> V1 a -> m # foldr :: (a -> b -> b) -> b -> V1 a -> b # foldr' :: (a -> b -> b) -> b -> V1 a -> b # foldl :: (b -> a -> b) -> b -> V1 a -> b # foldl' :: (b -> a -> b) -> b -> V1 a -> b # foldr1 :: (a -> a -> a) -> V1 a -> a # foldl1 :: (a -> a -> a) -> V1 a -> a # elem :: Eq a => a -> V1 a -> Bool # maximum :: Ord a => V1 a -> a # | |
Foldable (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => U1 m -> m # foldMap :: Monoid m => (a -> m) -> U1 a -> m # foldMap' :: Monoid m => (a -> m) -> U1 a -> m # foldr :: (a -> b -> b) -> b -> U1 a -> b # foldr' :: (a -> b -> b) -> b -> U1 a -> b # foldl :: (b -> a -> b) -> b -> U1 a -> b # foldl' :: (b -> a -> b) -> b -> U1 a -> b # foldr1 :: (a -> a -> a) -> U1 a -> a # foldl1 :: (a -> a -> a) -> U1 a -> a # elem :: Eq a => a -> U1 a -> Bool # maximum :: Ord a => U1 a -> a # | |
Foldable (UAddr :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => UAddr m -> m # foldMap :: Monoid m => (a -> m) -> UAddr a -> m # foldMap' :: Monoid m => (a -> m) -> UAddr a -> m # foldr :: (a -> b -> b) -> b -> UAddr a -> b # foldr' :: (a -> b -> b) -> b -> UAddr a -> b # foldl :: (b -> a -> b) -> b -> UAddr a -> b # foldl' :: (b -> a -> b) -> b -> UAddr a -> b # foldr1 :: (a -> a -> a) -> UAddr a -> a # foldl1 :: (a -> a -> a) -> UAddr a -> a # elem :: Eq a => a -> UAddr a -> Bool # maximum :: Ord a => UAddr a -> a # minimum :: Ord a => UAddr a -> a # | |
Foldable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => UChar m -> m # foldMap :: Monoid m => (a -> m) -> UChar a -> m # foldMap' :: Monoid m => (a -> m) -> UChar a -> m # foldr :: (a -> b -> b) -> b -> UChar a -> b # foldr' :: (a -> b -> b) -> b -> UChar a -> b # foldl :: (b -> a -> b) -> b -> UChar a -> b # foldl' :: (b -> a -> b) -> b -> UChar a -> b # foldr1 :: (a -> a -> a) -> UChar a -> a # foldl1 :: (a -> a -> a) -> UChar a -> a # elem :: Eq a => a -> UChar a -> Bool # maximum :: Ord a => UChar a -> a # minimum :: Ord a => UChar a -> a # | |
Foldable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => UDouble m -> m # foldMap :: Monoid m => (a -> m) -> UDouble a -> m # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m # foldr :: (a -> b -> b) -> b -> UDouble a -> b # foldr' :: (a -> b -> b) -> b -> UDouble a -> b # foldl :: (b -> a -> b) -> b -> UDouble a -> b # foldl' :: (b -> a -> b) -> b -> UDouble a -> b # foldr1 :: (a -> a -> a) -> UDouble a -> a # foldl1 :: (a -> a -> a) -> UDouble a -> a # elem :: Eq a => a -> UDouble a -> Bool # maximum :: Ord a => UDouble a -> a # minimum :: Ord a => UDouble a -> a # | |
Foldable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => UFloat m -> m # foldMap :: Monoid m => (a -> m) -> UFloat a -> m # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m # foldr :: (a -> b -> b) -> b -> UFloat a -> b # foldr' :: (a -> b -> b) -> b -> UFloat a -> b # foldl :: (b -> a -> b) -> b -> UFloat a -> b # foldl' :: (b -> a -> b) -> b -> UFloat a -> b # foldr1 :: (a -> a -> a) -> UFloat a -> a # foldl1 :: (a -> a -> a) -> UFloat a -> a # elem :: Eq a => a -> UFloat a -> Bool # maximum :: Ord a => UFloat a -> a # minimum :: Ord a => UFloat a -> a # | |
Foldable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => UInt m -> m # foldMap :: Monoid m => (a -> m) -> UInt a -> m # foldMap' :: Monoid m => (a -> m) -> UInt a -> m # foldr :: (a -> b -> b) -> b -> UInt a -> b # foldr' :: (a -> b -> b) -> b -> UInt a -> b # foldl :: (b -> a -> b) -> b -> UInt a -> b # foldl' :: (b -> a -> b) -> b -> UInt a -> b # foldr1 :: (a -> a -> a) -> UInt a -> a # foldl1 :: (a -> a -> a) -> UInt a -> a # elem :: Eq a => a -> UInt a -> Bool # maximum :: Ord a => UInt a -> a # | |
Foldable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => UWord m -> m # foldMap :: Monoid m => (a -> m) -> UWord a -> m # foldMap' :: Monoid m => (a -> m) -> UWord a -> m # foldr :: (a -> b -> b) -> b -> UWord a -> b # foldr' :: (a -> b -> b) -> b -> UWord a -> b # foldl :: (b -> a -> b) -> b -> UWord a -> b # foldl' :: (b -> a -> b) -> b -> UWord a -> b # foldr1 :: (a -> a -> a) -> UWord a -> a # foldl1 :: (a -> a -> a) -> UWord a -> a # elem :: Eq a => a -> UWord a -> Bool # maximum :: Ord a => UWord a -> a # minimum :: Ord a => UWord a -> a # | |
Foldable ((,) a) | Since: base-4.7.0.0 |
Defined in Data.Foldable fold :: Monoid m => (a, m) -> m # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # elem :: Eq a0 => a0 -> (a, a0) -> Bool # maximum :: Ord a0 => (a, a0) -> a0 # minimum :: Ord a0 => (a, a0) -> a0 # | |
Foldable (Array i) | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => Array i m -> m # foldMap :: Monoid m => (a -> m) -> Array i a -> m # foldMap' :: Monoid m => (a -> m) -> Array i a -> m # foldr :: (a -> b -> b) -> b -> Array i a -> b # foldr' :: (a -> b -> b) -> b -> Array i a -> b # foldl :: (b -> a -> b) -> b -> Array i a -> b # foldl' :: (b -> a -> b) -> b -> Array i a -> b # foldr1 :: (a -> a -> a) -> Array i a -> a # foldl1 :: (a -> a -> a) -> Array i a -> a # elem :: Eq a => a -> Array i a -> Bool # maximum :: Ord a => Array i a -> a # minimum :: Ord a => Array i a -> a # | |
Foldable (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Data.Foldable fold :: Monoid m => Proxy m -> m # foldMap :: Monoid m => (a -> m) -> Proxy a -> m # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m # foldr :: (a -> b -> b) -> b -> Proxy a -> b # foldr' :: (a -> b -> b) -> b -> Proxy a -> b # foldl :: (b -> a -> b) -> b -> Proxy a -> b # foldl' :: (b -> a -> b) -> b -> Proxy a -> b # foldr1 :: (a -> a -> a) -> Proxy a -> a # foldl1 :: (a -> a -> a) -> Proxy a -> a # elem :: Eq a => a -> Proxy a -> Bool # maximum :: Ord a => Proxy a -> a # minimum :: Ord a => Proxy a -> a # | |
Foldable (Map k) | Folds in order of increasing key. |
Defined in Data.Map.Internal fold :: Monoid m => Map k m -> m # foldMap :: Monoid m => (a -> m) -> Map k a -> m # foldMap' :: Monoid m => (a -> m) -> Map k a -> m # foldr :: (a -> b -> b) -> b -> Map k a -> b # foldr' :: (a -> b -> b) -> b -> Map k a -> b # foldl :: (b -> a -> b) -> b -> Map k a -> b # foldl' :: (b -> a -> b) -> b -> Map k a -> b # foldr1 :: (a -> a -> a) -> Map k a -> a # foldl1 :: (a -> a -> a) -> Map k a -> a # elem :: Eq a => a -> Map k a -> Bool # maximum :: Ord a => Map k a -> a # minimum :: Ord a => Map k a -> a # | |
Foldable f => Foldable (Rec1 f) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => Rec1 f m -> m # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m # foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b # foldr1 :: (a -> a -> a) -> Rec1 f a -> a # foldl1 :: (a -> a -> a) -> Rec1 f a -> a # elem :: Eq a => a -> Rec1 f a -> Bool # maximum :: Ord a => Rec1 f a -> a # minimum :: Ord a => Rec1 f a -> a # | |
Foldable (Const m :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Data.Functor.Const fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # | |
Foldable f => Foldable (Ap f) | Since: base-4.12.0.0 |
Defined in Data.Foldable fold :: Monoid m => Ap f m -> m # foldMap :: Monoid m => (a -> m) -> Ap f a -> m # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m # foldr :: (a -> b -> b) -> b -> Ap f a -> b # foldr' :: (a -> b -> b) -> b -> Ap f a -> b # foldl :: (b -> a -> b) -> b -> Ap f a -> b # foldl' :: (b -> a -> b) -> b -> Ap f a -> b # foldr1 :: (a -> a -> a) -> Ap f a -> a # foldl1 :: (a -> a -> a) -> Ap f a -> a # elem :: Eq a => a -> Ap f a -> Bool # maximum :: Ord a => Ap f a -> a # | |
Foldable f => Foldable (Alt f) | Since: base-4.12.0.0 |
Defined in Data.Foldable fold :: Monoid m => Alt f m -> m # foldMap :: Monoid m => (a -> m) -> Alt f a -> m # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m # foldr :: (a -> b -> b) -> b -> Alt f a -> b # foldr' :: (a -> b -> b) -> b -> Alt f a -> b # foldl :: (b -> a -> b) -> b -> Alt f a -> b # foldl' :: (b -> a -> b) -> b -> Alt f a -> b # foldr1 :: (a -> a -> a) -> Alt f a -> a # foldl1 :: (a -> a -> a) -> Alt f a -> a # elem :: Eq a => a -> Alt f a -> Bool # maximum :: Ord a => Alt f a -> a # minimum :: Ord a => Alt f a -> a # | |
Foldable (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => K1 i c m -> m # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m # foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m # foldr :: (a -> b -> b) -> b -> K1 i c a -> b # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b # foldl :: (b -> a -> b) -> b -> K1 i c a -> b # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b # foldr1 :: (a -> a -> a) -> K1 i c a -> a # foldl1 :: (a -> a -> a) -> K1 i c a -> a # elem :: Eq a => a -> K1 i c a -> Bool # maximum :: Ord a => K1 i c a -> a # minimum :: Ord a => K1 i c a -> a # | |
(Foldable f, Foldable g) => Foldable (f :+: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => (f :+: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a # toList :: (f :+: g) a -> [a] # length :: (f :+: g) a -> Int # elem :: Eq a => a -> (f :+: g) a -> Bool # maximum :: Ord a => (f :+: g) a -> a # minimum :: Ord a => (f :+: g) a -> a # | |
(Foldable f, Foldable g) => Foldable (f :*: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => (f :*: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :*: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b # foldr1 :: (a -> a -> a) -> (f :*: g) a -> a # foldl1 :: (a -> a -> a) -> (f :*: g) a -> a # toList :: (f :*: g) a -> [a] # length :: (f :*: g) a -> Int # elem :: Eq a => a -> (f :*: g) a -> Bool # maximum :: Ord a => (f :*: g) a -> a # minimum :: Ord a => (f :*: g) a -> a # | |
Foldable f => Foldable (M1 i c f) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => M1 i c f m -> m # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m # foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b # foldr1 :: (a -> a -> a) -> M1 i c f a -> a # foldl1 :: (a -> a -> a) -> M1 i c f a -> a # elem :: Eq a => a -> M1 i c f a -> Bool # maximum :: Ord a => M1 i c f a -> a # minimum :: Ord a => M1 i c f a -> a # | |
(Foldable f, Foldable g) => Foldable (f :.: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => (f :.: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a # toList :: (f :.: g) a -> [a] # length :: (f :.: g) a -> Int # elem :: Eq a => a -> (f :.: g) a -> Bool # maximum :: Ord a => (f :.: g) a -> a # minimum :: Ord a => (f :.: g) a -> a # |
class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where #
Functors representing data structures that can be traversed from left to right.
A definition of traverse
must satisfy the following laws:
- Naturality
t .
for every applicative transformationtraverse
f =traverse
(t . f)t
- Identity
traverse
Identity
=Identity
- Composition
traverse
(Compose
.fmap
g . f) =Compose
.fmap
(traverse
g) .traverse
f
A definition of sequenceA
must satisfy the following laws:
- Naturality
t .
for every applicative transformationsequenceA
=sequenceA
.fmap
tt
- Identity
sequenceA
.fmap
Identity
=Identity
- Composition
sequenceA
.fmap
Compose
=Compose
.fmap
sequenceA
.sequenceA
where an applicative transformation is a function
t :: (Applicative f, Applicative g) => f a -> g a
preserving the Applicative
operations, i.e.
t (pure
x) =pure
x t (f<*>
x) = t f<*>
t x
and the identity functor Identity
and composition functors
Compose
are from Data.Functor.Identity and
Data.Functor.Compose.
A result of the naturality law is a purity law for traverse
traverse
pure
=pure
(The naturality law is implied by parametricity and thus so is the purity law [1, p15].)
Instances are similar to Functor
, e.g. given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Traversable Tree where traverse f Empty = pure Empty traverse f (Leaf x) = Leaf <$> f x traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
This is suitable even for abstract types, as the laws for <*>
imply a form of associativity.
The superclass instances should satisfy the following:
- In the
Functor
instance,fmap
should be equivalent to traversal with the identity applicative functor (fmapDefault
). - In the
Foldable
instance,foldMap
should be equivalent to traversal with a constant applicative functor (foldMapDefault
).
References: [1] The Essence of the Iterator Pattern, Jeremy Gibbons and Bruno C. d. S. Oliveira
traverse :: Applicative f => (a -> f b) -> t a -> f (t b) #
Map each element of a structure to an action, evaluate these actions
from left to right, and collect the results. For a version that ignores
the results see traverse_
.
Instances
Traversable [] | Since: base-2.1 |
Defined in Data.Traversable | |
Traversable Maybe | Since: base-2.1 |
Traversable Par1 | Since: base-4.9.0.0 |
Traversable ZipList | Since: base-4.9.0.0 |
Traversable Identity | Since: base-4.9.0.0 |
Traversable First | Since: base-4.8.0.0 |
Traversable Last | Since: base-4.8.0.0 |
Traversable Dual | Since: base-4.8.0.0 |
Traversable Sum | Since: base-4.8.0.0 |
Traversable Product | Since: base-4.8.0.0 |
Traversable Down | Since: base-4.12.0.0 |
Traversable NonEmpty | Since: base-4.9.0.0 |
Traversable Seq | |
Traversable FingerTree | |
Defined in Data.Sequence.Internal traverse :: Applicative f => (a -> f b) -> FingerTree a -> f (FingerTree b) # sequenceA :: Applicative f => FingerTree (f a) -> f (FingerTree a) # mapM :: Monad m => (a -> m b) -> FingerTree a -> m (FingerTree b) # sequence :: Monad m => FingerTree (m a) -> m (FingerTree a) # | |
Traversable Digit | |
Traversable Node | |
Traversable Elem | |
Traversable ViewL | |
Traversable ViewR | |
Traversable (Either a) | Since: base-4.7.0.0 |
Traversable (V1 :: Type -> Type) | Since: base-4.9.0.0 |
Traversable (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Traversable (UAddr :: Type -> Type) | Since: base-4.9.0.0 |
Traversable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
Traversable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Traversable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Traversable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
Traversable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
Traversable ((,) a) | Since: base-4.7.0.0 |
Defined in Data.Traversable | |
Ix i => Traversable (Array i) | Since: base-2.1 |
Traversable (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Traversable (Map k) | Traverses in order of increasing key. |
Traversable f => Traversable (Rec1 f) | Since: base-4.9.0.0 |
Traversable (Const m :: Type -> Type) | Since: base-4.7.0.0 |
Traversable f => Traversable (Ap f) | Since: base-4.12.0.0 |
Traversable f => Traversable (Alt f) | Since: base-4.12.0.0 |
Traversable (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
(Traversable f, Traversable g) => Traversable (f :+: g) | Since: base-4.9.0.0 |
(Traversable f, Traversable g) => Traversable (f :*: g) | Since: base-4.9.0.0 |
Traversable f => Traversable (M1 i c f) | Since: base-4.9.0.0 |
(Traversable f, Traversable g) => Traversable (f :.: g) | Since: base-4.9.0.0 |
Representable types of kind *
.
This class is derivable in GHC with the DeriveGeneric
flag on.
A Generic
instance must satisfy the following laws:
from
.to
≡id
to
.from
≡id
Instances
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
Since: base-4.9.0.0
Instances
Semigroup Ordering | Since: base-4.9.0.0 |
Semigroup () | Since: base-4.9.0.0 |
Semigroup [a] | Since: base-4.9.0.0 |
Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0 |
Semigroup p => Semigroup (Par1 p) | Since: base-4.12.0.0 |
Semigroup a => Semigroup (Identity a) | Since: base-4.9.0.0 |
Semigroup (NonEmpty a) | Since: base-4.9.0.0 |
Semigroup (Seq a) | Since: containers-0.5.7 |
Ord a => Semigroup (Set a) | Since: containers-0.5.7 |
Semigroup (MergeSet a) | |
Semigroup b => Semigroup (a -> b) | Since: base-4.9.0.0 |
Semigroup (Either a b) | Since: base-4.9.0.0 |
Semigroup (V1 p) | Since: base-4.12.0.0 |
Semigroup (U1 p) | Since: base-4.12.0.0 |
(Semigroup a, Semigroup b) => Semigroup (a, b) | Since: base-4.9.0.0 |
Ord k => Semigroup (Map k v) | |
Semigroup (f p) => Semigroup (Rec1 f p) | Since: base-4.12.0.0 |
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (Const a b) | Since: base-4.9.0.0 |
Semigroup c => Semigroup (K1 i c p) | Since: base-4.12.0.0 |
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) | Since: base-4.12.0.0 |
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) | Since: base-4.9.0.0 |
Semigroup (f p) => Semigroup (M1 i c f p) | Since: base-4.12.0.0 |
Semigroup (f (g p)) => Semigroup ((f :.: g) p) | Since: base-4.12.0.0 |
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) | Since: base-4.9.0.0 |
class Semigroup a => Monoid a where #
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:
- Right identity
x
<>
mempty
= x- Left identity
mempty
<>
x = x- Associativity
x
(<>
(y<>
z) = (x<>
y)<>
zSemigroup
law)- Concatenation
mconcat
=foldr
(<>
)mempty
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define newtype
s and make those instances
of Monoid
, e.g. Sum
and Product
.
NOTE: Semigroup
is a superclass of Monoid
since base-4.11.0.0.
Instances
Monoid Ordering | Since: base-2.1 |
Monoid () | Since: base-2.1 |
Monoid [a] | Since: base-2.1 |
Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
Monoid p => Monoid (Par1 p) | Since: base-4.12.0.0 |
Monoid a => Monoid (Identity a) | Since: base-4.9.0.0 |
Monoid (Seq a) | |
Ord a => Monoid (Set a) | |
Monoid (MergeSet a) | |
Monoid b => Monoid (a -> b) | Since: base-2.1 |
Monoid (U1 p) | Since: base-4.12.0.0 |
(Monoid a, Monoid b) => Monoid (a, b) | Since: base-2.1 |
Ord k => Monoid (Map k v) | |
Monoid (f p) => Monoid (Rec1 f p) | Since: base-4.12.0.0 |
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | Since: base-2.1 |
Monoid a => Monoid (Const a b) | Since: base-4.9.0.0 |
Monoid c => Monoid (K1 i c p) | Since: base-4.12.0.0 |
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) | Since: base-4.12.0.0 |
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | Since: base-2.1 |
Monoid (f p) => Monoid (M1 i c f p) | Since: base-4.12.0.0 |
Monoid (f (g p)) => Monoid ((f :.: g) p) | Since: base-4.12.0.0 |
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | Since: base-2.1 |
Instances
Eq Bool | |
Ord Bool | |
Show Bool | Since: base-2.1 |
Generic Bool | Since: base-4.6.0.0 |
NFData Bool | |
Defined in Control.DeepSeq | |
Hashable Bool | |
Defined in Data.Hashable.Class | |
SingKind Bool | Since: base-4.9.0.0 |
Defined in GHC.Generics type DemoteRep Bool | |
Lift Bool | |
SingI 'False | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
SingI 'True | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
type Rep Bool | |
type DemoteRep Bool | |
Defined in GHC.Generics | |
data Sing (a :: Bool) | |
The Maybe
type encapsulates an optional value. A value of type
either contains a value of type Maybe
aa
(represented as
),
or it is empty (represented as Just
aNothing
). 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.
Instances
Monad Maybe | Since: base-2.1 |
Functor Maybe | Since: base-2.1 |
Applicative Maybe | Since: base-2.1 |
Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # | |
Traversable Maybe | Since: base-2.1 |
Alternative Maybe | Since: base-2.1 |
MonadPlus Maybe | Since: base-2.1 |
NFData1 Maybe | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Hashable1 Maybe | |
Defined in Data.Hashable.Class | |
Lift a => Lift (Maybe a :: Type) | |
Eq a => Eq (Maybe a) | Since: base-2.1 |
Ord a => Ord (Maybe a) | Since: base-2.1 |
Show a => Show (Maybe a) | Since: base-2.1 |
Generic (Maybe a) | Since: base-4.6.0.0 |
Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
NFData a => NFData (Maybe a) | |
Defined in Control.DeepSeq | |
Hashable a => Hashable (Maybe a) | |
Defined in Data.Hashable.Class | |
Ixed (Maybe a) | |
At (Maybe a) | |
AsEmpty (Maybe a) | |
Defined in Optics.Empty.Core | |
SingKind a => SingKind (Maybe a) | Since: base-4.9.0.0 |
Defined in GHC.Generics type DemoteRep (Maybe a) | |
Generic1 Maybe | Since: base-4.6.0.0 |
SingI ('Nothing :: Maybe a) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
SingI a2 => SingI ('Just a2 :: Maybe a1) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
type Rep (Maybe a) | |
Defined in GHC.Generics | |
type Index (Maybe a) | |
Defined in Optics.At.Core | |
type IxValue (Maybe a) | |
Defined in Optics.At.Core | |
type IxKind (Maybe a) | |
Defined in Optics.At.Core | |
type DemoteRep (Maybe a) | |
Defined in GHC.Generics | |
data Sing (b :: Maybe a) | |
type Rep1 Maybe | |
Instances
Eq Ordering | |
Ord Ordering | |
Defined in GHC.Classes | |
Show Ordering | Since: base-2.1 |
Generic Ordering | Since: base-4.6.0.0 |
Semigroup Ordering | Since: base-4.9.0.0 |
Monoid Ordering | Since: base-2.1 |
NFData Ordering | |
Defined in Control.DeepSeq | |
Hashable Ordering | |
Defined in Data.Hashable.Class | |
AsEmpty Ordering | |
Defined in Optics.Empty.Core | |
type Rep Ordering | |
The Either
type represents values with two possibilities: a value of
type
is either Either
a b
or Left
a
.Right
b
The Either
type is sometimes used to represent a value which is
either correct or an error; by convention, the Left
constructor is
used to hold an error value and the Right
constructor is used to
hold a correct value (mnemonic: "right" also means "correct").
Examples
The type
is the type of values which can be either
a Either
String
Int
String
or an Int
. The Left
constructor can be used only on
String
s, and the Right
constructor can be used only on Int
s:
>>>
let s = Left "foo" :: Either String Int
>>>
s
Left "foo">>>
let n = Right 3 :: Either String Int
>>>
n
Right 3>>>
:type s
s :: Either String Int>>>
:type n
n :: Either String Int
The fmap
from our Functor
instance will ignore Left
values, but
will apply the supplied function to values contained in a Right
:
>>>
let s = Left "foo" :: Either String Int
>>>
let n = Right 3 :: Either String Int
>>>
fmap (*2) s
Left "foo">>>
fmap (*2) n
Right 6
The Monad
instance for Either
allows us to chain together multiple
actions which may fail, and fail overall if any of the individual
steps failed. First we'll write a function that can either parse an
Int
from a Char
, or fail.
>>>
import Data.Char ( digitToInt, isDigit )
>>>
:{
let parseEither :: Char -> Either String Int parseEither c | isDigit c = Right (digitToInt c) | otherwise = Left "parse error">>>
:}
The following should work, since both '1'
and '2'
can be
parsed as Int
s.
>>>
:{
let parseMultiple :: Either String Int parseMultiple = do x <- parseEither '1' y <- parseEither '2' return (x + y)>>>
:}
>>>
parseMultiple
Right 3
But the following should fail overall, since the first operation where
we attempt to parse 'm'
as an Int
will fail:
>>>
:{
let parseMultiple :: Either String Int parseMultiple = do x <- parseEither 'm' y <- parseEither '2' return (x + y)>>>
:}
>>>
parseMultiple
Left "parse error"
Instances
NFData2 Either | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Hashable2 Either | |
Defined in Data.Hashable.Class | |
Swapped Either | |
(Lift a, Lift b) => Lift (Either a b :: Type) | |
Monad (Either e) | Since: base-4.4.0.0 |
Functor (Either a) | Since: base-3.0 |
Applicative (Either e) | Since: base-3.0 |
Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # length :: Either a a0 -> Int # elem :: Eq a0 => a0 -> Either a a0 -> Bool # maximum :: Ord a0 => Either a a0 -> a0 # minimum :: Ord a0 => Either a a0 -> a0 # | |
Traversable (Either a) | Since: base-4.7.0.0 |
NFData a => NFData1 (Either a) | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Hashable a => Hashable1 (Either a) | |
Defined in Data.Hashable.Class | |
Generic1 (Either a :: Type -> Type) | Since: base-4.6.0.0 |
(Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
(Ord a, Ord b) => Ord (Either a b) | Since: base-2.1 |
(Read a, Read b) => Read (Either a b) | Since: base-3.0 |
(Show a, Show b) => Show (Either a b) | Since: base-3.0 |
Generic (Either a b) | Since: base-4.6.0.0 |
Semigroup (Either a b) | Since: base-4.9.0.0 |
(NFData a, NFData b) => NFData (Either a b) | |
Defined in Control.DeepSeq | |
(Hashable a, Hashable b) => Hashable (Either a b) | |
Defined in Data.Hashable.Class | |
type Rep1 (Either a :: Type -> Type) | |
Defined in GHC.Generics type Rep1 (Either a :: Type -> Type) = D1 ('MetaData "Either" "Data.Either" "base" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) | |
type Rep (Either a b) | |
Defined in GHC.Generics type Rep (Either a b) = D1 ('MetaData "Either" "Data.Either" "base" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b))) |
The Item
type function returns the type of items of the structure
l
.
Instances
type Item CallStack | |
type Item Version | |
type Item Text | |
Defined in Data.Text.Lazy | |
type Item Text | |
type Item [a] | |
type Item (ZipList a) | |
type Item (NonEmpty a) | |
type Item (Seq a) | |
Defined in Data.Sequence.Internal | |
type Item (Set a) | |
Defined in Data.Set.Internal | |
type Item (Map k v) | |
Defined in Data.Map.Internal |
Identity functor and monad. (a non-strict monad)
Since: base-4.8.0.0
Identity | |
|
Instances
either :: (a -> c) -> (b -> c) -> Either a b -> c #
Case analysis for the Either
type.
If the value is
, apply the first function to Left
aa
;
if it is
, apply the second function to Right
bb
.
Examples
We create two values of type
, one using the
Either
String
Int
Left
constructor and another using the Right
constructor. Then
we apply "either" the length
function (if we have a String
)
or the "times-two" function (if we have an Int
):
>>>
let s = Left "foo" :: Either String Int
>>>
let n = Right 3 :: Either String Int
>>>
either length (*2) s
3>>>
either length (*2) n
6
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
. If this is Maybe
bNothing
, no element
is added on to the result list. If it is
, then Just
bb
is
included in the result list.
Examples
Using
is a shortcut for mapMaybe
f x
in most cases:catMaybes
$ map
f x
>>>
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]
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
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
""
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #
An infix synonym for fmap
.
The name of this operator is an allusion to $
.
Note the similarities between their types:
($) :: (a -> b) -> a -> b (<$>) :: Functor f => (a -> b) -> f a -> f b
Whereas $
is function application, <$>
is function
application lifted over a Functor
.
Examples
Convert from a
to a Maybe
Int
using Maybe
String
show
:
>>>
show <$> Nothing
Nothing>>>
show <$> Just 3
Just "3"
Convert from an
to an
Either
Int
Int
Either
Int
String
using show
:
>>>
show <$> Left 17
Left 17>>>
show <$> Right 17
Right "17"
Double each element of a list:
>>>
(*2) <$> [1,2,3]
[2,4,6]
Apply even
to the second element of a pair:
>>>
even <$> (2,2)
(2,True)
const x
is a unary function which evaluates to x
for all inputs.
>>>
const 42 "hello"
42
>>>
map (const 42) [0..3]
[42,42,42,42]
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #
Same as >>=
, but with the arguments interchanged.
(<|>) :: Alternative f => f a -> f a -> f a infixl 3 #
An associative binary operation
A Map from keys k
to values a
.
The Semigroup
operation for Map
is union
, which prefers
values from the left operand. If m1
maps a key k
to a value
a1
, and m2
maps the same key to a different value a2
, then
their union m1 <> m2
maps k
to a1
.
Instances
Eq2 Map | Since: containers-0.5.9 |
Ord2 Map | Since: containers-0.5.9 |
Defined in Data.Map.Internal | |
Show2 Map | Since: containers-0.5.9 |
Hashable2 Map | Since: hashable-1.3.4.0 |
Defined in Data.Hashable.Class | |
Functor (Map k) | |
Foldable (Map k) | Folds in order of increasing key. |
Defined in Data.Map.Internal fold :: Monoid m => Map k m -> m # foldMap :: Monoid m => (a -> m) -> Map k a -> m # foldMap' :: Monoid m => (a -> m) -> Map k a -> m # foldr :: (a -> b -> b) -> b -> Map k a -> b # foldr' :: (a -> b -> b) -> b -> Map k a -> b # foldl :: (b -> a -> b) -> b -> Map k a -> b # foldl' :: (b -> a -> b) -> b -> Map k a -> b # foldr1 :: (a -> a -> a) -> Map k a -> a # foldl1 :: (a -> a -> a) -> Map k a -> a # elem :: Eq a => a -> Map k a -> Bool # maximum :: Ord a => Map k a -> a # minimum :: Ord a => Map k a -> a # | |
Traversable (Map k) | Traverses in order of increasing key. |
Eq k => Eq1 (Map k) | Since: containers-0.5.9 |
Ord k => Ord1 (Map k) | Since: containers-0.5.9 |
Defined in Data.Map.Internal | |
(Ord k, Read k) => Read1 (Map k) | Since: containers-0.5.9 |
Defined in Data.Map.Internal | |
Show k => Show1 (Map k) | Since: containers-0.5.9 |
Hashable k => Hashable1 (Map k) | Since: hashable-1.3.4.0 |
Defined in Data.Hashable.Class | |
Ord k => IsList (Map k v) | Since: containers-0.5.6.2 |
(Eq k, Eq a) => Eq (Map k a) | |
(Data k, Data a, Ord k) => Data (Map k a) | |
Defined in Data.Map.Internal gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Map k a -> c (Map k a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Map k a) # toConstr :: Map k a -> Constr # dataTypeOf :: Map k a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Map k a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Map k a)) # gmapT :: (forall b. Data b => b -> b) -> Map k a -> Map k a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r # gmapQ :: (forall d. Data d => d -> u) -> Map k a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Map k a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) # | |
(Ord k, Ord v) => Ord (Map k v) | |
(Ord k, Read k, Read e) => Read (Map k e) | |
(Show k, Show a) => Show (Map k a) | |
Ord k => Semigroup (Map k v) | |
Ord k => Monoid (Map k v) | |
(NFData k, NFData a) => NFData (Map k a) | |
Defined in Data.Map.Internal | |
(Hashable k, Hashable v) => Hashable (Map k v) | Since: hashable-1.3.4.0 |
Defined in Data.Hashable.Class | |
Ord k => Ixed (Map k a) | |
Ord k => At (Map k a) | |
AsEmpty (Map k a) | |
Defined in Optics.Empty.Core | |
type Item (Map k v) | |
Defined in Data.Map.Internal | |
type Index (Map k a) | |
Defined in Optics.At.Core | |
type IxValue (Map k a) | |
Defined in Optics.At.Core | |
type IxKind (Map k a) | |
Defined in Optics.At.Core |
General-purpose finite sequences.
Instances
Monad Seq | |
Functor Seq | |
MonadFix Seq | Since: containers-0.5.11 |
Defined in Data.Sequence.Internal | |
Applicative Seq | Since: containers-0.5.4 |
Foldable Seq | |
Defined in Data.Sequence.Internal fold :: Monoid m => Seq m -> m # foldMap :: Monoid m => (a -> m) -> Seq a -> m # foldMap' :: Monoid m => (a -> m) -> Seq a -> m # foldr :: (a -> b -> b) -> b -> Seq a -> b # foldr' :: (a -> b -> b) -> b -> Seq a -> b # foldl :: (b -> a -> b) -> b -> Seq a -> b # foldl' :: (b -> a -> b) -> b -> Seq a -> b # foldr1 :: (a -> a -> a) -> Seq a -> a # foldl1 :: (a -> a -> a) -> Seq a -> a # elem :: Eq a => a -> Seq a -> Bool # maximum :: Ord a => Seq a -> a # | |
Traversable Seq | |
Eq1 Seq | Since: containers-0.5.9 |
Ord1 Seq | Since: containers-0.5.9 |
Defined in Data.Sequence.Internal | |
Read1 Seq | Since: containers-0.5.9 |
Defined in Data.Sequence.Internal | |
Show1 Seq | Since: containers-0.5.9 |
MonadZip Seq |
|
Alternative Seq | Since: containers-0.5.4 |
MonadPlus Seq | |
Hashable1 Seq | Since: hashable-1.3.4.0 |
Defined in Data.Hashable.Class | |
UnzipWith Seq | |
Defined in Data.Sequence.Internal unzipWith' :: (x -> (a, b)) -> Seq x -> (Seq a, Seq b) | |
IsList (Seq a) | |
Eq a => Eq (Seq a) | |
Data a => Data (Seq a) | |
Defined in Data.Sequence.Internal gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Seq a -> c (Seq a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Seq a) # dataTypeOf :: Seq a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Seq a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Seq a)) # gmapT :: (forall b. Data b => b -> b) -> Seq a -> Seq a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Seq a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Seq a -> r # gmapQ :: (forall d. Data d => d -> u) -> Seq a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Seq a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) # | |
Ord a => Ord (Seq a) | |
Read a => Read (Seq a) | |
Show a => Show (Seq a) | |
a ~ Char => IsString (Seq a) | Since: containers-0.5.7 |
Defined in Data.Sequence.Internal fromString :: String -> Seq a # | |
Semigroup (Seq a) | Since: containers-0.5.7 |
Monoid (Seq a) | |
NFData a => NFData (Seq a) | |
Defined in Data.Sequence.Internal | |
Hashable v => Hashable (Seq v) | Since: hashable-1.3.4.0 |
Defined in Data.Hashable.Class | |
Ixed (Seq a) | |
AsEmpty (Seq a) | |
Defined in Optics.Empty.Core | |
type Item (Seq a) | |
Defined in Data.Sequence.Internal | |
type Index (Seq a) | |
Defined in Optics.At.Core | |
type IxValue (Seq a) | |
Defined in Optics.At.Core | |
type IxKind (Seq a) | |
Defined in Optics.At.Core |
A set of values a
.
Instances
Foldable Set | Folds in order of increasing key. |
Defined in Data.Set.Internal fold :: Monoid m => Set m -> m # foldMap :: Monoid m => (a -> m) -> Set a -> m # foldMap' :: Monoid m => (a -> m) -> Set a -> m # foldr :: (a -> b -> b) -> b -> Set a -> b # foldr' :: (a -> b -> b) -> b -> Set a -> b # foldl :: (b -> a -> b) -> b -> Set a -> b # foldl' :: (b -> a -> b) -> b -> Set a -> b # foldr1 :: (a -> a -> a) -> Set a -> a # foldl1 :: (a -> a -> a) -> Set a -> a # elem :: Eq a => a -> Set a -> Bool # maximum :: Ord a => Set a -> a # | |
Eq1 Set | Since: containers-0.5.9 |
Ord1 Set | Since: containers-0.5.9 |
Defined in Data.Set.Internal | |
Show1 Set | Since: containers-0.5.9 |
Hashable1 Set | Since: hashable-1.3.4.0 |
Defined in Data.Hashable.Class | |
Ord a => IsList (Set a) | Since: containers-0.5.6.2 |
Eq a => Eq (Set a) | |
(Data a, Ord a) => Data (Set a) | |
Defined in Data.Set.Internal gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Set a -> c (Set a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Set a) # dataTypeOf :: Set a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Set a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Set a)) # gmapT :: (forall b. Data b => b -> b) -> Set a -> Set a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Set a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Set a -> r # gmapQ :: (forall d. Data d => d -> u) -> Set a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Set a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Set a -> m (Set a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Set a -> m (Set a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Set a -> m (Set a) # | |
Ord a => Ord (Set a) | |
(Read a, Ord a) => Read (Set a) | |
Show a => Show (Set a) | |
Ord a => Semigroup (Set a) | Since: containers-0.5.7 |
Ord a => Monoid (Set a) | |
NFData a => NFData (Set a) | |
Defined in Data.Set.Internal | |
Hashable v => Hashable (Set v) | Since: hashable-1.3.4.0 |
Defined in Data.Hashable.Class | |
Ord a => Contains (Set a) | |
Ord k => Ixed (Set k) | |
Ord k => At (Set k) | |
AsEmpty (Set a) | |
Defined in Optics.Empty.Core | |
type Item (Set a) | |
Defined in Data.Set.Internal | |
type Index (Set a) | |
Defined in Optics.At.Core | |
type IxValue (Set k) | |
Defined in Optics.At.Core | |
type IxKind (Set k) | |
Defined in Optics.At.Core |
A class of types that can be fully evaluated.
Since: deepseq-1.1.0.0
Instances
NFData Bool | |
Defined in Control.DeepSeq | |
NFData Char | |
Defined in Control.DeepSeq | |
NFData Double | |
Defined in Control.DeepSeq | |
NFData Float | |
Defined in Control.DeepSeq | |
NFData Int | |
Defined in Control.DeepSeq | |
NFData Int8 | |
Defined in Control.DeepSeq | |
NFData Int16 | |
Defined in Control.DeepSeq | |
NFData Int32 | |
Defined in Control.DeepSeq | |
NFData Int64 | |
Defined in Control.DeepSeq | |
NFData Integer | |
Defined in Control.DeepSeq | |
NFData Natural | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData Ordering | |
Defined in Control.DeepSeq | |
NFData Word | |
Defined in Control.DeepSeq | |
NFData Word8 | |
Defined in Control.DeepSeq | |
NFData Word16 | |
Defined in Control.DeepSeq | |
NFData Word32 | |
Defined in Control.DeepSeq | |
NFData Word64 | |
Defined in Control.DeepSeq | |
NFData CallStack | Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData () | |
Defined in Control.DeepSeq | |
NFData TyCon | NOTE: Prior to Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData Void | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData Unique | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData Version | Since: deepseq-1.3.0.0 |
Defined in Control.DeepSeq | |
NFData ThreadId | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData ExitCode | Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData MaskingState | Since: deepseq-1.4.4.0 |
Defined in Control.DeepSeq rnf :: MaskingState -> () # | |
NFData TypeRep | NOTE: Prior to Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData All | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData Any | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CChar | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CSChar | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CUChar | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CShort | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CUShort | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CInt | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CUInt | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CLong | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CULong | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CLLong | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CULLong | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CBool | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
NFData CFloat | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CDouble | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CPtrdiff | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CSize | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CWchar | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CSigAtomic | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq rnf :: CSigAtomic -> () # | |
NFData CClock | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CTime | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CUSeconds | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CSUSeconds | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq rnf :: CSUSeconds -> () # | |
NFData CFile | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CFpos | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CJmpBuf | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CIntPtr | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CUIntPtr | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CIntMax | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData CUIntMax | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData Fingerprint | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq rnf :: Fingerprint -> () # | |
NFData SrcLoc | Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData a => NFData [a] | |
Defined in Control.DeepSeq | |
NFData a => NFData (Maybe a) | |
Defined in Control.DeepSeq | |
NFData a => NFData (Ratio a) | |
Defined in Control.DeepSeq | |
NFData (Ptr a) | Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData (FunPtr a) | Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData a => NFData (Complex a) | |
Defined in Control.DeepSeq | |
NFData a => NFData (Min a) | Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData a => NFData (Max a) | Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData a => NFData (First a) | Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData a => NFData (Last a) | Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData m => NFData (WrappedMonoid m) | Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq rnf :: WrappedMonoid m -> () # | |
NFData a => NFData (Option a) | Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData (StableName a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq rnf :: StableName a -> () # | |
NFData a => NFData (ZipList a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData a => NFData (Identity a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData (IORef a) | NOTE: Only strict in the reference and not the referenced value. Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData a => NFData (First a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData a => NFData (Last a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData a => NFData (Dual a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData a => NFData (Sum a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData a => NFData (Product a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData a => NFData (Down a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData (MVar a) | NOTE: Only strict in the reference and not the referenced value. Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData a => NFData (NonEmpty a) | Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData a => NFData (Seq a) | |
Defined in Data.Sequence.Internal | |
NFData a => NFData (FingerTree a) | |
Defined in Data.Sequence.Internal rnf :: FingerTree a -> () # | |
NFData a => NFData (Digit a) | |
Defined in Data.Sequence.Internal | |
NFData a => NFData (Node a) | |
Defined in Data.Sequence.Internal | |
NFData a => NFData (Elem a) | |
Defined in Data.Sequence.Internal | |
NFData a => NFData (Set a) | |
Defined in Data.Set.Internal | |
NFData a => NFData (Hashed a) | |
Defined in Data.Hashable.Class | |
NFData (a -> b) | This instance is for convenience and consistency with Since: deepseq-1.3.0.0 |
Defined in Control.DeepSeq | |
(NFData a, NFData b) => NFData (Either a b) | |
Defined in Control.DeepSeq | |
(NFData a, NFData b) => NFData (a, b) | |
Defined in Control.DeepSeq | |
(NFData a, NFData b) => NFData (Array a b) | |
Defined in Control.DeepSeq | |
NFData (Fixed a) | Since: deepseq-1.3.0.0 |
Defined in Control.DeepSeq | |
(NFData a, NFData b) => NFData (Arg a b) | Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
NFData (Proxy a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData (STRef s a) | NOTE: Only strict in the reference and not the referenced value. Since: deepseq-1.4.2.0 |
Defined in Control.DeepSeq | |
(NFData k, NFData a) => NFData (Map k a) | |
Defined in Data.Map.Internal | |
(NFData a1, NFData a2, NFData a3) => NFData (a1, a2, a3) | |
Defined in Control.DeepSeq | |
NFData a => NFData (Const a b) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
NFData (a :~: b) | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
(NFData a1, NFData a2, NFData a3, NFData a4) => NFData (a1, a2, a3, a4) | |
Defined in Control.DeepSeq | |
(NFData1 f, NFData1 g, NFData a) => NFData (Product f g a) | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
(NFData1 f, NFData1 g, NFData a) => NFData (Sum f g a) | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
NFData (a :~~: b) | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
(NFData a1, NFData a2, NFData a3, NFData a4, NFData a5) => NFData (a1, a2, a3, a4, a5) | |
Defined in Control.DeepSeq | |
(NFData1 f, NFData1 g, NFData a) => NFData (Compose f g a) | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
(NFData a1, NFData a2, NFData a3, NFData a4, NFData a5, NFData a6) => NFData (a1, a2, a3, a4, a5, a6) | |
Defined in Control.DeepSeq | |
(NFData a1, NFData a2, NFData a3, NFData a4, NFData a5, NFData a6, NFData a7) => NFData (a1, a2, a3, a4, a5, a6, a7) | |
Defined in Control.DeepSeq | |
(NFData a1, NFData a2, NFData a3, NFData a4, NFData a5, NFData a6, NFData a7, NFData a8) => NFData (a1, a2, a3, a4, a5, a6, a7, a8) | |
Defined in Control.DeepSeq | |
(NFData a1, NFData a2, NFData a3, NFData a4, NFData a5, NFData a6, NFData a7, NFData a8, NFData a9) => NFData (a1, a2, a3, a4, a5, a6, a7, a8, a9) | |
Defined in Control.DeepSeq |
The class of types that can be converted to a hash value.
Minimal implementation: hashWithSalt
.
Note: the hash is not guaranteed to be stable across library versions, operating systems or architectures. For stable hashing use named hashes: SHA256, CRC32 etc.
If you are looking for Hashable
instance in time
package,
check time-compat
Instances
_1 :: Field1 s t a b => Lens s t a b #
Access the 1st field of a tuple (and possibly change its type).
>>>
(1,2) ^. _1
1
>>>
(1,2) & _1 .~ "hello"
("hello",2)
>>>
traverseOf _1 putStrLn ("hello","world")
hello ((),"world")
This can also be used on larger tuples as well:
>>>
(1,2,3,4,5) & _1 %~ (+41)
(42,2,3,4,5)
_2 :: Field2 s t a b => Lens s t a b #
Access the 2nd field of a tuple.
>>>
_2 .~ "hello" $ (1,(),3,4)
(1,"hello",3,4)
>>>
(1,2,3,4) & _2 %~ (*3)
(1,6,3,4)
>>>
traverseOf _2 print (1,2)
2 (1,())
adjoin :: forall k l (is :: IxList) s a (js :: IxList). (Is k A_Traversal, Is l A_Traversal) => Optic' k is s a -> Optic' l js s a -> Traversal' s a infixr 6 #
Combine two disjoint traversals into one.
>>>
over (_1 % _Just `adjoin` _2 % _Right) not (Just True, Right False)
(Just False,Right True)
Note: if the argument traversals are not disjoint, the result will not
respect the Traversal
laws, because it will visit the same element multiple
times. See section 7 of
Understanding Idiomatic Traversals Backwards and Forwards
by Bird et al. for why this is illegal.
>>>
view (partsOf (each `adjoin` _1)) ('x','y')
"xyx">>>
set (partsOf (each `adjoin` _1)) "abc" ('x','y')
('c','b')
For the Fold
version see summing
.
Since: optics-core-0.4
traversed :: Traversable t => Traversal (t a) (t b) a b #
Construct a Traversal
via the Traversable
class.
traverseOf
traversed
=traverse
traverseOf :: forall k f (is :: IxList) s t a b. (Is k A_Traversal, Applicative f) => Optic k is s t a b -> (a -> f b) -> s -> f t #
Map each element of a structure targeted by a Traversal
, evaluate these
actions from left to right, and collect the results.
traversalVL :: TraversalVL s t a b -> Traversal s t a b #
Build a traversal from the van Laarhoven representation.
traversalVL
.
traverseOf
≡id
traverseOf
.
traversalVL
≡id
type Traversal s t a b = Optic A_Traversal NoIx s t a b #
Type synonym for a type-modifying traversal.
type Traversal' s a = Optic' A_Traversal NoIx s a #
Type synonym for a type-preserving traversal.
over :: forall k (is :: IxList) s t a b. Is k A_Setter => Optic k is s t a b -> (a -> b) -> s -> t #
Apply a setter as a modifier.
pattern Empty :: AsEmpty a => a #
Pattern synonym for matching on any type with an AsEmpty
instance.
>>>
case Nothing of { Empty -> True; _ -> False }
True
coerced :: (Coercible s a, Coercible t b) => Iso s t a b #
Data types that are representationally equal are isomorphic.
>>>
view coerced 'x' :: Identity Char
Identity 'x'
equality :: (s ~ a, t ~ b) => Iso s t a b #
Capture type constraints as an isomorphism.
Note: This is the identity optic:
>>>
:t view equality
view equality :: a -> a
iso :: (s -> a) -> (b -> t) -> Iso s t a b #
Build an iso from a pair of inverse functions.
If you want to build an Iso
from the van Laarhoven representation, use
isoVL
from the optics-vl
package.
review :: forall k (is :: IxList) t b. Is k A_Review => Optic' k is t b -> b -> t #
Retrieve the value targeted by a Review
.
>>>
review _Left "hi"
Left "hi"
re :: forall (is :: IxList) s t a b. (ReversibleOptic k, AcceptsEmptyIndices "re" is) => Optic k is s t a b -> Optic (ReversedOptic k) is b a t s #
Reverses optics, turning around Iso
into Iso
,
Prism
into ReversedPrism
(and
back), Lens
into ReversedLens
(and back)
and Getter
into Review
(and back).
afailing :: forall k l (is :: IxList) s a (js :: IxList). (Is k An_AffineFold, Is l An_AffineFold) => Optic' k is s a -> Optic' l js s a -> AffineFold s a infixl 3 #
Try the first AffineFold
. If it returns no entry, try the second one.
>>>
preview (ix 1 % re _Left `afailing` ix 2 % re _Right) [0,1,2,3]
Just (Left 1)
>>>
preview (ix 42 % re _Left `afailing` ix 2 % re _Right) [0,1,2,3]
Just (Right 2)
afolding :: (s -> Maybe a) -> AffineFold s a #
Create an AffineFold
from a partial function.
>>>
preview (afolding listToMaybe) "foo"
Just 'f'
preview :: forall k (is :: IxList) s a. Is k An_AffineFold => Optic' k is s a -> s -> Maybe a #
Retrieve the value targeted by an AffineFold
.
>>>
let _Right = prism Right $ either (Left . Left) Right
>>>
preview _Right (Right 'x')
Just 'x'
>>>
preview _Right (Left 'y')
Nothing
type AffineFold s a = Optic' An_AffineFold NoIx s a #
Type synonym for an affine fold.
matching :: forall k (is :: IxList) s t a b. Is k An_AffineTraversal => Optic k is s t a b -> s -> Either t a #
atraversal :: (s -> Either t a) -> (s -> b -> t) -> AffineTraversal s t a b #
Build an affine traversal from a matcher and an updater.
If you want to build an AffineTraversal
from the van Laarhoven
representation, use atraversalVL
.
type AffineTraversal s t a b = Optic An_AffineTraversal NoIx s t a b #
Type synonym for a type-modifying affine traversal.
type AffineTraversal' s a = Optic' An_AffineTraversal NoIx s a #
Type synonym for a type-preserving affine traversal.
(%) :: forall k l m (is :: IxList) (js :: IxList) (ks :: IxList) s t u v a b. (JoinKinds k l m, AppendIndices is js ks) => Optic k is s t u v -> Optic l js u v a b -> Optic m ks s t a b infixl 9 #
Compose two optics of compatible flavours.
Returns an optic of the appropriate supertype. If either or both optics are indexed, the composition preserves all the indices.
castOptic :: forall destKind srcKind (is :: IxList) s t a b. Is srcKind destKind => Optic srcKind is s t a b -> Optic destKind is s t a b #
data Optic k (is :: IxList) s t a b #
Wrapper newtype for the whole family of optics.
The first parameter k
identifies the particular optic kind (e.g. A_Lens
or A_Traversal
).
The parameter is
is a list of types available as indices. This will
typically be NoIx
for unindexed optics, or WithIx
for optics with a
single index. See the "Indexed optics" section of the overview documentation
in the Optics
module of the main optics
package for more details.
The parameters s
and t
represent the "big" structure,
whereas a
and b
represent the "small" structure.
type Optic' k (is :: IxList) s a = Optic k is s s a a #
Common special case of Optic
where source and target types are equal.
Here, we need only one "big" and one "small" type. For lenses, this means that in the restricted form we cannot do type-changing updates.
Subtyping relationship between kinds of optics.
An instance of
means that any Is
k l
can be used
as an Optic
k
. For example, we have an Optic
l
instance, but not Is
A_Lens
A_Traversal
.Is
A_Traversal
A_Lens
This class needs instances for all possible combinations of tags.
Instances
class JoinKinds k l m | k l -> m #
Computes the least upper bound of two optics kinds.
In presence of a JoinKinds k l m
constraint Optic m
represents the least
upper bound of an Optic k
and an Optic l
. This means in particular that
composition of an Optic k
and an Optic k
will yield an Optic m
.
Since: optics-core-0.4
Instances
Tag for an iso.
Instances
Tag for a lens.
Instances
data An_AffineTraversal #
Tag for an affine traversal.
Instances
data A_Traversal #
Tag for a traversal.
Instances
Tag for a getter.
Instances
data An_AffineFold #
Tag for an affine fold.
Instances
Tag for a fold.
Instances
A space efficient, packed, unboxed Unicode text type.
mapFromSet :: (k -> a) -> Set k -> Map k a Source #
mapKeysSet :: Map k a -> Set k Source #
mapFoldMapWithKey :: Monoid m => (k -> a -> m) -> Map k a -> m Source #
seqReduceR :: b -> (a -> Seq a -> b) -> Seq a -> b Source #
seqFromMaybe :: Maybe a -> Seq a Source #
seqSingleton :: Prism' (Seq a) a Source #