Safe Haskell | None |
---|---|
Language | Haskell2010 |
Prologue.Data.Foldable
Synopsis
- type family Foldables (lst :: [Type -> Type]) :: Constraint where ...
- sequence_ :: (Foldable t, Applicative f) => t (f a) -> f ()
- bisequence_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f ()
- traverse2_ :: (Applicative m, Foldables '[t1, t2]) => (a -> m b) -> t1 (t2 a) -> m ()
- traverse3_ :: (Applicative m, Foldables '[t1, t2, t3]) => (a -> m b) -> t1 (t2 (t3 a)) -> m ()
- traverse4_ :: (Applicative m, Foldables '[t1, t2, t3, t4]) => (a -> m b) -> t1 (t2 (t3 (t4 a))) -> m ()
- traverse5_ :: (Applicative m, Foldables '[t1, t2, t3, t4, t5]) => (a -> m b) -> t1 (t2 (t3 (t4 (t5 a)))) -> m ()
- unsafeMinimum :: Ord a => [a] -> a
- unsafeMaximum :: Ord a => [a] -> a
- minimum :: MonadPlus m => Ord a => [a] -> m a
- maximum :: MonadPlus m => Ord a => [a] -> m a
- minimumDef :: Ord a => a -> [a] -> a
- maximumDef :: Ord a => a -> [a] -> a
- mapM_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()
- bimapM_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f ()
- forM_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()
- class Foldable (t :: Type -> Type) where
- fold :: Monoid m => t m -> m
- foldMap :: Monoid m => (a -> m) -> t a -> m
- foldr :: (a -> b -> b) -> b -> t a -> b
- foldr' :: (a -> b -> b) -> b -> t a -> b
- foldl :: (b -> a -> b) -> b -> t a -> b
- foldl' :: (b -> a -> b) -> b -> t a -> b
- elem :: Eq a => a -> t a -> Bool
- sum :: Num a => t a -> a
- product :: Num a => t a -> a
- biall :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool
- biany :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool
- bior :: Bifoldable t => t Bool Bool -> Bool
- biand :: Bifoldable t => t Bool Bool -> Bool
- biconcatMap :: Bifoldable t => (a -> [c]) -> (b -> [c]) -> t a b -> [c]
- biproduct :: (Bifoldable t, Num a) => t a a -> a
- bisum :: (Bifoldable t, Num a) => t a a -> a
- biconcat :: Bifoldable t => t [a] [a] -> [a]
- bielem :: (Bifoldable t, Eq a) => a -> t a a -> Bool
- biasum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a
- bifor_ :: (Bifoldable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f ()
- bitraverse_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f ()
- bifoldlM :: (Bifoldable t, Monad m) => (a -> b -> m a) -> (a -> c -> m a) -> a -> t b c -> m a
- bifoldl' :: Bifoldable t => (a -> b -> a) -> (a -> c -> a) -> a -> t b c -> a
- bifoldrM :: (Bifoldable t, Monad m) => (a -> c -> m c) -> (b -> c -> m c) -> c -> t a b -> m c
- bifoldr' :: Bifoldable t => (a -> c -> c) -> (b -> c -> c) -> c -> t a b -> c
- class Bifoldable (p :: Type -> Type -> Type) where
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- or :: Foldable t => t Bool -> Bool
- and :: Foldable t => t Bool -> Bool
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- concat :: Foldable t => t [a] -> [a]
- asum :: (Foldable t, Alternative f) => t (f a) -> f a
- for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()
- traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()
- foldlM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
- foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b
- class Foldable t => Foldable1 (t :: Type -> Type) where
Documentation
sequence_ :: (Foldable t, Applicative f) => t (f a) -> f () Source #
bisequence_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f () Source #
traverse2_ :: (Applicative m, Foldables '[t1, t2]) => (a -> m b) -> t1 (t2 a) -> m () Source #
traverse3_ :: (Applicative m, Foldables '[t1, t2, t3]) => (a -> m b) -> t1 (t2 (t3 a)) -> m () Source #
traverse4_ :: (Applicative m, Foldables '[t1, t2, t3, t4]) => (a -> m b) -> t1 (t2 (t3 (t4 a))) -> m () Source #
traverse5_ :: (Applicative m, Foldables '[t1, t2, t3, t4, t5]) => (a -> m b) -> t1 (t2 (t3 (t4 (t5 a)))) -> m () Source #
unsafeMinimum :: Ord a => [a] -> a Source #
unsafeMaximum :: Ord a => [a] -> a Source #
minimumDef :: Ord a => a -> [a] -> a Source #
maximumDef :: Ord a => a -> [a] -> a Source #
mapM_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f () Source #
bimapM_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f () Source #
forM_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f () Source #
Deprecated: Use for_
instead
class Foldable (t :: Type -> Type) where #
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)
Methods
fold :: Monoid m => t m -> m #
Combine the elements of a structure using a monoid.
foldMap :: Monoid m => (a -> m) -> t a -> m #
Map each element of the structure to a monoid, and combine the results.
foldr :: (a -> b -> b) -> b -> t a -> b #
Right-associative fold of a structure.
In the case of lists, foldr
, when applied to a binary operator, a
starting value (typically the right-identity of the operator), and a
list, reduces the list using the binary operator, from right to left:
foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
Note that, since the head of the resulting expression is produced by
an application of the operator to the first element of the list,
foldr
can produce a terminating expression from an infinite list.
For a general Foldable
structure this should be semantically identical
to,
foldr f z =foldr
f z .toList
foldr' :: (a -> b -> b) -> b -> t a -> b #
Right-associative fold of a structure, but with strict application of the operator.
foldl :: (b -> a -> b) -> b -> t a -> b #
Left-associative fold of a structure.
In the case of lists, foldl
, when applied to a binary
operator, a starting value (typically the left-identity of the operator),
and a list, reduces the list using the binary operator, from left to
right:
foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
Note that to produce the outermost application of the operator the
entire input list must be traversed. This means that foldl'
will
diverge if given an infinite list.
Also note that if you want an efficient left-fold, you probably want to
use foldl'
instead of foldl
. The reason for this is that latter does
not force the "inner" results (e.g. z
in the above example)
before applying them to the operator (e.g. to f
x1(
). This results
in a thunk chain f
x2)O(n)
elements long, which then must be evaluated from
the outside-in.
For a general Foldable
structure this should be semantically identical
to,
foldl f z =foldl
f z .toList
foldl' :: (b -> a -> b) -> b -> t a -> b #
Left-associative fold of a structure but with strict application of the operator.
This ensures that each step of the fold is forced to weak head normal
form before being applied, avoiding the collection of thunks that would
otherwise occur. This is often what you want to strictly reduce a finite
list to a single, monolithic result (e.g. length
).
For a general Foldable
structure this should be semantically identical
to,
foldl f z =foldl'
f z .toList
elem :: Eq a => a -> t a -> Bool infix 4 #
Does the element occur in the structure?
The sum
function computes the sum of the numbers of a structure.
product :: Num a => t a -> a #
The product
function computes the product of the numbers of a
structure.
Instances
Foldable [] | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => [m] -> m # foldMap :: Monoid m => (a -> m) -> [a] -> m # foldr :: (a -> b -> b) -> b -> [a] -> b # foldr' :: (a -> b -> b) -> b -> [a] -> b # foldl :: (b -> a -> b) -> b -> [a] -> b # foldl' :: (b -> a -> b) -> b -> [a] -> b # foldr1 :: (a -> a -> a) -> [a] -> a # foldl1 :: (a -> a -> a) -> [a] -> a # elem :: Eq a => a -> [a] -> Bool # maximum :: Ord a => [a] -> a # | |
Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # 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 Methods fold :: Monoid m => Par1 m -> m # foldMap :: Monoid m => (a -> m) -> Par1 a -> m # foldr :: (a -> b -> b) -> b -> Par1 a -> b # foldr' :: (a -> b -> b) -> b -> Par1 a -> b # foldl :: (b -> a -> b) -> b -> Par1 a -> b # foldl' :: (b -> a -> b) -> b -> Par1 a -> b # foldr1 :: (a -> a -> a) -> Par1 a -> a # foldl1 :: (a -> a -> a) -> Par1 a -> a # elem :: Eq a => a -> Par1 a -> Bool # maximum :: Ord a => Par1 a -> a # | |
Foldable Complex | Since: base-4.9.0.0 |
Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> m # foldr :: (a -> b -> b) -> b -> Complex a -> b # foldr' :: (a -> b -> b) -> b -> Complex a -> b # foldl :: (b -> a -> b) -> b -> Complex a -> b # foldl' :: (b -> a -> b) -> b -> Complex a -> b # foldr1 :: (a -> a -> a) -> Complex a -> a # foldl1 :: (a -> a -> a) -> Complex a -> a # elem :: Eq a => a -> Complex a -> Bool # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # | |
Foldable Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m # foldMap :: Monoid m => (a -> m) -> Min a -> m # foldr :: (a -> b -> b) -> b -> Min a -> b # foldr' :: (a -> b -> b) -> b -> Min a -> b # foldl :: (b -> a -> b) -> b -> Min a -> b # foldl' :: (b -> a -> b) -> b -> Min a -> b # foldr1 :: (a -> a -> a) -> Min a -> a # foldl1 :: (a -> a -> a) -> Min a -> a # elem :: Eq a => a -> Min a -> Bool # maximum :: Ord a => Min a -> a # | |
Foldable Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m # foldMap :: Monoid m => (a -> m) -> Max a -> m # foldr :: (a -> b -> b) -> b -> Max a -> b # foldr' :: (a -> b -> b) -> b -> Max a -> b # foldl :: (b -> a -> b) -> b -> Max a -> b # foldl' :: (b -> a -> b) -> b -> Max a -> b # foldr1 :: (a -> a -> a) -> Max a -> a # foldl1 :: (a -> a -> a) -> Max a -> a # elem :: Eq a => a -> Max a -> Bool # maximum :: Ord a => Max a -> a # | |
Foldable First | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
Foldable Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
Foldable Option | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Option m -> m # foldMap :: Monoid m => (a -> m) -> Option a -> m # foldr :: (a -> b -> b) -> b -> Option a -> b # foldr' :: (a -> b -> b) -> b -> Option a -> b # foldl :: (b -> a -> b) -> b -> Option a -> b # foldl' :: (b -> a -> b) -> b -> Option a -> b # foldr1 :: (a -> a -> a) -> Option a -> a # foldl1 :: (a -> a -> a) -> Option a -> a # elem :: Eq a => a -> Option a -> Bool # maximum :: Ord a => Option a -> a # minimum :: Ord a => Option a -> a # | |
Foldable ZipList | Since: base-4.9.0.0 |
Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m # foldMap :: Monoid m => (a -> m) -> ZipList a -> m # foldr :: (a -> b -> b) -> b -> ZipList a -> b # foldr' :: (a -> b -> b) -> b -> ZipList a -> b # foldl :: (b -> a -> b) -> b -> ZipList a -> b # foldl' :: (b -> a -> b) -> b -> ZipList a -> b # foldr1 :: (a -> a -> a) -> ZipList a -> a # foldl1 :: (a -> a -> a) -> ZipList a -> a # 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 Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # 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 Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # 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 Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # 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 Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # 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 Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # 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 Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # 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 Methods fold :: Monoid m => Down m -> 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 Methods fold :: Monoid m => NonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b # foldr1 :: (a -> a -> a) -> NonEmpty a -> a # foldl1 :: (a -> a -> a) -> NonEmpty a -> a # elem :: Eq a => a -> NonEmpty a -> Bool # maximum :: Ord a => NonEmpty a -> a # minimum :: Ord a => NonEmpty a -> a # | |
Foldable IntMap | |
Defined in Data.IntMap.Internal Methods fold :: Monoid m => IntMap m -> m # foldMap :: Monoid m => (a -> m) -> IntMap a -> m # foldr :: (a -> b -> b) -> b -> IntMap a -> b # foldr' :: (a -> b -> b) -> b -> IntMap a -> b # foldl :: (b -> a -> b) -> b -> IntMap a -> b # foldl' :: (b -> a -> b) -> b -> IntMap a -> b # foldr1 :: (a -> a -> a) -> IntMap a -> a # foldl1 :: (a -> a -> a) -> IntMap a -> a # elem :: Eq a => a -> IntMap a -> Bool # maximum :: Ord a => IntMap a -> a # minimum :: Ord a => IntMap a -> a # | |
Foldable Tree | |
Defined in Data.Tree Methods fold :: Monoid m => Tree m -> m # foldMap :: Monoid m => (a -> m) -> Tree a -> m # foldr :: (a -> b -> b) -> b -> Tree a -> b # foldr' :: (a -> b -> b) -> b -> Tree a -> b # foldl :: (b -> a -> b) -> b -> Tree a -> b # foldl' :: (b -> a -> b) -> b -> Tree a -> b # foldr1 :: (a -> a -> a) -> Tree a -> a # foldl1 :: (a -> a -> a) -> Tree a -> a # elem :: Eq a => a -> Tree a -> Bool # maximum :: Ord a => Tree a -> a # | |
Foldable Seq | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Seq m -> m # foldMap :: Monoid m => (a -> m) -> Seq a -> m # foldr :: (a -> b -> b) -> b -> Seq a -> b # foldr' :: (a -> b -> b) -> b -> Seq a -> b # foldl :: (b -> a -> b) -> b -> Seq a -> b # foldl' :: (b -> a -> b) -> b -> Seq a -> b # foldr1 :: (a -> a -> a) -> Seq a -> a # foldl1 :: (a -> a -> a) -> Seq a -> a # elem :: Eq a => a -> Seq a -> Bool # maximum :: Ord a => Seq a -> a # | |
Foldable FingerTree | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => FingerTree m -> m # foldMap :: Monoid m => (a -> m) -> FingerTree a -> m # foldr :: (a -> b -> b) -> b -> FingerTree a -> b # foldr' :: (a -> b -> b) -> b -> FingerTree a -> b # foldl :: (b -> a -> b) -> b -> FingerTree a -> b # foldl' :: (b -> a -> b) -> b -> FingerTree a -> b # foldr1 :: (a -> a -> a) -> FingerTree a -> a # foldl1 :: (a -> a -> a) -> FingerTree a -> a # toList :: FingerTree a -> [a] # null :: FingerTree a -> Bool # length :: FingerTree a -> Int # elem :: Eq a => a -> FingerTree a -> Bool # maximum :: Ord a => FingerTree a -> a # minimum :: Ord a => FingerTree a -> a # sum :: Num a => FingerTree a -> a # product :: Num a => FingerTree a -> a # | |
Foldable Digit | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Digit m -> m # foldMap :: Monoid m => (a -> m) -> Digit a -> m # foldr :: (a -> b -> b) -> b -> Digit a -> b # foldr' :: (a -> b -> b) -> b -> Digit a -> b # foldl :: (b -> a -> b) -> b -> Digit a -> b # foldl' :: (b -> a -> b) -> b -> Digit a -> b # foldr1 :: (a -> a -> a) -> Digit a -> a # foldl1 :: (a -> a -> a) -> Digit a -> a # 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 Methods fold :: Monoid m => Node m -> m # foldMap :: Monoid m => (a -> m) -> Node a -> m # foldr :: (a -> b -> b) -> b -> Node a -> b # foldr' :: (a -> b -> b) -> b -> Node a -> b # foldl :: (b -> a -> b) -> b -> Node a -> b # foldl' :: (b -> a -> b) -> b -> Node a -> b # foldr1 :: (a -> a -> a) -> Node a -> a # foldl1 :: (a -> a -> a) -> Node a -> a # elem :: Eq a => a -> Node a -> Bool # maximum :: Ord a => Node a -> a # | |
Foldable Elem | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Elem m -> m # foldMap :: Monoid m => (a -> m) -> Elem a -> m # foldr :: (a -> b -> b) -> b -> Elem a -> b # foldr' :: (a -> b -> b) -> b -> Elem a -> b # foldl :: (b -> a -> b) -> b -> Elem a -> b # foldl' :: (b -> a -> b) -> b -> Elem a -> b # foldr1 :: (a -> a -> a) -> Elem a -> a # foldl1 :: (a -> a -> a) -> Elem a -> a # elem :: Eq a => a -> Elem a -> Bool # maximum :: Ord a => Elem a -> a # | |
Foldable ViewL | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewL m -> m # foldMap :: Monoid m => (a -> m) -> ViewL a -> m # foldr :: (a -> b -> b) -> b -> ViewL a -> b # foldr' :: (a -> b -> b) -> b -> ViewL a -> b # foldl :: (b -> a -> b) -> b -> ViewL a -> b # foldl' :: (b -> a -> b) -> b -> ViewL a -> b # foldr1 :: (a -> a -> a) -> ViewL a -> a # foldl1 :: (a -> a -> a) -> ViewL a -> a # 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 Methods fold :: Monoid m => ViewR m -> m # foldMap :: Monoid m => (a -> m) -> ViewR a -> m # foldr :: (a -> b -> b) -> b -> ViewR a -> b # foldr' :: (a -> b -> b) -> b -> ViewR a -> b # foldl :: (b -> a -> b) -> b -> ViewR a -> b # foldl' :: (b -> a -> b) -> b -> ViewR a -> b # foldr1 :: (a -> a -> a) -> ViewR a -> a # foldl1 :: (a -> a -> a) -> ViewR a -> a # elem :: Eq a => a -> ViewR a -> Bool # maximum :: Ord a => ViewR a -> a # minimum :: Ord a => ViewR a -> a # | |
Foldable Set | |
Defined in Data.Set.Internal Methods fold :: Monoid m => Set m -> m # foldMap :: Monoid m => (a -> m) -> Set a -> m # foldr :: (a -> b -> b) -> b -> Set a -> b # foldr' :: (a -> b -> b) -> b -> Set a -> b # foldl :: (b -> a -> b) -> b -> Set a -> b # foldl' :: (b -> a -> b) -> b -> Set a -> b # foldr1 :: (a -> a -> a) -> Set a -> a # foldl1 :: (a -> a -> a) -> Set a -> a # elem :: Eq a => a -> Set a -> Bool # maximum :: Ord a => Set a -> a # | |
Foldable DList | |
Defined in Data.DList Methods fold :: Monoid m => DList m -> m # foldMap :: Monoid m => (a -> m) -> DList a -> m # foldr :: (a -> b -> b) -> b -> DList a -> b # foldr' :: (a -> b -> b) -> b -> DList a -> b # foldl :: (b -> a -> b) -> b -> DList a -> b # foldl' :: (b -> a -> b) -> b -> DList a -> b # foldr1 :: (a -> a -> a) -> DList a -> a # foldl1 :: (a -> a -> a) -> DList a -> a # elem :: Eq a => a -> DList a -> Bool # maximum :: Ord a => DList a -> a # minimum :: Ord a => DList a -> a # | |
Foldable Hashed | |
Defined in Data.Hashable.Class Methods fold :: Monoid m => Hashed m -> 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 HashSet | |
Defined in Data.HashSet Methods fold :: Monoid m => HashSet m -> m # foldMap :: Monoid m => (a -> m) -> HashSet a -> m # foldr :: (a -> b -> b) -> b -> HashSet a -> b # foldr' :: (a -> b -> b) -> b -> HashSet a -> b # foldl :: (b -> a -> b) -> b -> HashSet a -> b # foldl' :: (b -> a -> b) -> b -> HashSet a -> b # foldr1 :: (a -> a -> a) -> HashSet a -> a # foldl1 :: (a -> a -> a) -> HashSet a -> a # elem :: Eq a => a -> HashSet a -> Bool # maximum :: Ord a => HashSet a -> a # minimum :: Ord a => HashSet a -> a # | |
Foldable Vector | |
Defined in Data.Vector Methods fold :: Monoid m => Vector m -> m # foldMap :: Monoid m => (a -> m) -> Vector a -> m # foldr :: (a -> b -> b) -> b -> Vector a -> b # foldr' :: (a -> b -> b) -> b -> Vector a -> b # foldl :: (b -> a -> b) -> b -> Vector a -> b # foldl' :: (b -> a -> b) -> b -> Vector a -> b # foldr1 :: (a -> a -> a) -> Vector a -> a # foldl1 :: (a -> a -> a) -> Vector a -> a # elem :: Eq a => a -> Vector a -> Bool # maximum :: Ord a => Vector a -> a # minimum :: Ord a => Vector a -> a # | |
Foldable SmallArray | |
Defined in Data.Primitive.SmallArray Methods fold :: Monoid m => SmallArray m -> m # foldMap :: Monoid m => (a -> m) -> SmallArray a -> m # foldr :: (a -> b -> b) -> b -> SmallArray a -> b # foldr' :: (a -> b -> b) -> b -> SmallArray a -> b # foldl :: (b -> a -> b) -> b -> SmallArray a -> b # foldl' :: (b -> a -> b) -> b -> SmallArray a -> b # foldr1 :: (a -> a -> a) -> SmallArray a -> a # foldl1 :: (a -> a -> a) -> SmallArray a -> a # toList :: SmallArray a -> [a] # null :: SmallArray a -> Bool # length :: SmallArray a -> Int # elem :: Eq a => a -> SmallArray a -> Bool # maximum :: Ord a => SmallArray a -> a # minimum :: Ord a => SmallArray a -> a # sum :: Num a => SmallArray a -> a # product :: Num a => SmallArray a -> a # | |
Foldable Array | |
Defined in Data.Primitive.Array Methods fold :: Monoid m => Array m -> m # foldMap :: Monoid m => (a -> m) -> Array a -> m # foldr :: (a -> b -> b) -> b -> Array a -> b # foldr' :: (a -> b -> b) -> b -> Array a -> b # foldl :: (b -> a -> b) -> b -> Array a -> b # foldl' :: (b -> a -> b) -> b -> Array a -> b # foldr1 :: (a -> a -> a) -> Array a -> a # foldl1 :: (a -> a -> a) -> Array a -> a # elem :: Eq a => a -> Array a -> Bool # maximum :: Ord a => Array a -> a # minimum :: Ord a => Array a -> a # | |
Foldable OneTuple Source # | |
Defined in Prologue.Data.OneTuple Methods fold :: Monoid m => OneTuple m -> m # foldMap :: Monoid m => (a -> m) -> OneTuple a -> m # foldr :: (a -> b -> b) -> b -> OneTuple a -> b # foldr' :: (a -> b -> b) -> b -> OneTuple a -> b # foldl :: (b -> a -> b) -> b -> OneTuple a -> b # foldl' :: (b -> a -> b) -> b -> OneTuple a -> b # foldr1 :: (a -> a -> a) -> OneTuple a -> a # foldl1 :: (a -> a -> a) -> OneTuple a -> a # elem :: Eq a => a -> OneTuple a -> Bool # maximum :: Ord a => OneTuple a -> a # minimum :: Ord a => OneTuple a -> a # | |
Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # 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 Methods fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> m # foldr :: (a -> b -> b) -> b -> V1 a -> b # foldr' :: (a -> b -> b) -> b -> V1 a -> b # foldl :: (b -> a -> b) -> b -> V1 a -> b # foldl' :: (b -> a -> b) -> b -> V1 a -> b # foldr1 :: (a -> a -> a) -> V1 a -> a # foldl1 :: (a -> a -> a) -> V1 a -> a # 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 Methods fold :: Monoid m => U1 m -> m # foldMap :: Monoid m => (a -> m) -> U1 a -> m # foldr :: (a -> b -> b) -> b -> U1 a -> b # foldr' :: (a -> b -> b) -> b -> U1 a -> b # foldl :: (b -> a -> b) -> b -> U1 a -> b # foldl' :: (b -> a -> b) -> b -> U1 a -> b # foldr1 :: (a -> a -> a) -> U1 a -> a # foldl1 :: (a -> a -> a) -> U1 a -> a # elem :: Eq a => a -> U1 a -> Bool # maximum :: Ord a => U1 a -> a # | |
Foldable ((,) a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (a, m) -> m # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # elem :: Eq a0 => a0 -> (a, a0) -> Bool # maximum :: Ord a0 => (a, a0) -> a0 # minimum :: Ord a0 => (a, a0) -> a0 # | |
Foldable (HashMap k) | |
Defined in Data.HashMap.Base Methods fold :: Monoid m => HashMap k m -> m # foldMap :: Monoid m => (a -> m) -> HashMap k a -> m # foldr :: (a -> b -> b) -> b -> HashMap k a -> b # foldr' :: (a -> b -> b) -> b -> HashMap k a -> b # foldl :: (b -> a -> b) -> b -> HashMap k a -> b # foldl' :: (b -> a -> b) -> b -> HashMap k a -> b # foldr1 :: (a -> a -> a) -> HashMap k a -> a # foldl1 :: (a -> a -> a) -> HashMap k a -> a # toList :: HashMap k a -> [a] # length :: HashMap k a -> Int # elem :: Eq a => a -> HashMap k a -> Bool # maximum :: Ord a => HashMap k a -> a # minimum :: Ord a => HashMap k a -> a # | |
Foldable (Map k) | |
Defined in Data.Map.Internal Methods fold :: Monoid m => Map k m -> m # foldMap :: Monoid m => (a -> m) -> Map k a -> m # foldr :: (a -> b -> b) -> b -> Map k a -> b # foldr' :: (a -> b -> b) -> b -> Map k a -> b # foldl :: (b -> a -> b) -> b -> Map k a -> b # foldl' :: (b -> a -> b) -> b -> Map k a -> b # foldr1 :: (a -> a -> a) -> Map k a -> a # foldl1 :: (a -> a -> a) -> Map k a -> a # elem :: Eq a => a -> Map k a -> Bool # maximum :: Ord a => Map k a -> a # minimum :: Ord a => Map k a -> a # | |
Foldable (Array i) | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Array i m -> m # foldMap :: Monoid m => (a -> m) -> Array i a -> m # foldr :: (a -> b -> b) -> b -> Array i a -> b # foldr' :: (a -> b -> b) -> b -> Array i a -> b # foldl :: (b -> a -> b) -> b -> Array i a -> b # foldl' :: (b -> a -> b) -> b -> Array i a -> b # foldr1 :: (a -> a -> a) -> Array i a -> a # foldl1 :: (a -> a -> a) -> Array i a -> a # elem :: Eq a => a -> Array i a -> Bool # maximum :: Ord a => Array i a -> a # minimum :: Ord a => Array i a -> a # | |
Foldable (Arg a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # elem :: Eq a0 => a0 -> Arg a a0 -> Bool # maximum :: Ord a0 => Arg a a0 -> a0 # minimum :: Ord a0 => Arg a a0 -> a0 # | |
Foldable (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m # foldMap :: Monoid m => (a -> m) -> Proxy a -> m # foldr :: (a -> b -> b) -> b -> Proxy a -> b # foldr' :: (a -> b -> b) -> b -> Proxy a -> b # foldl :: (b -> a -> b) -> b -> Proxy a -> b # foldl' :: (b -> a -> b) -> b -> Proxy a -> b # foldr1 :: (a -> a -> a) -> Proxy a -> a # foldl1 :: (a -> a -> a) -> Proxy a -> a # elem :: Eq a => a -> Proxy a -> Bool # maximum :: Ord a => Proxy a -> a # minimum :: Ord a => Proxy a -> a # | |
Foldable f => Foldable (MaybeT f) | |
Defined in Control.Monad.Trans.Maybe Methods fold :: Monoid m => MaybeT f m -> m # foldMap :: Monoid m => (a -> m) -> MaybeT f a -> m # foldr :: (a -> b -> b) -> b -> MaybeT f a -> b # foldr' :: (a -> b -> b) -> b -> MaybeT f a -> b # foldl :: (b -> a -> b) -> b -> MaybeT f a -> b # foldl' :: (b -> a -> b) -> b -> MaybeT f a -> b # foldr1 :: (a -> a -> a) -> MaybeT f a -> a # foldl1 :: (a -> a -> a) -> MaybeT f a -> a # elem :: Eq a => a -> MaybeT f a -> Bool # maximum :: Ord a => MaybeT f a -> a # minimum :: Ord a => MaybeT f a -> a # | |
Foldable f => Foldable (Cofree f) | |
Defined in Control.Comonad.Cofree Methods fold :: Monoid m => Cofree f m -> m # foldMap :: Monoid m => (a -> m) -> Cofree f a -> m # foldr :: (a -> b -> b) -> b -> Cofree f a -> b # foldr' :: (a -> b -> b) -> b -> Cofree f a -> b # foldl :: (b -> a -> b) -> b -> Cofree f a -> b # foldl' :: (b -> a -> b) -> b -> Cofree f a -> b # foldr1 :: (a -> a -> a) -> Cofree f a -> a # foldl1 :: (a -> a -> a) -> Cofree f a -> a # elem :: Eq a => a -> Cofree f a -> Bool # maximum :: Ord a => Cofree f a -> a # minimum :: Ord a => Cofree f a -> a # | |
Foldable f => Foldable (Free f) | |
Defined in Control.Monad.Free Methods fold :: Monoid m => Free f m -> m # foldMap :: Monoid m => (a -> m) -> Free f a -> m # foldr :: (a -> b -> b) -> b -> Free f a -> b # foldr' :: (a -> b -> b) -> b -> Free f a -> b # foldl :: (b -> a -> b) -> b -> Free f a -> b # foldl' :: (b -> a -> b) -> b -> Free f a -> b # foldr1 :: (a -> a -> a) -> Free f a -> a # foldl1 :: (a -> a -> a) -> Free f a -> a # elem :: Eq a => a -> Free f a -> Bool # maximum :: Ord a => Free f a -> a # minimum :: Ord a => Free f a -> a # | |
Foldable (ImpossibleM1 :: Type -> Type) | |
Defined in Data.Impossible Methods fold :: Monoid m => ImpossibleM1 m -> m # foldMap :: Monoid m => (a -> m) -> ImpossibleM1 a -> m # foldr :: (a -> b -> b) -> b -> ImpossibleM1 a -> b # foldr' :: (a -> b -> b) -> b -> ImpossibleM1 a -> b # foldl :: (b -> a -> b) -> b -> ImpossibleM1 a -> b # foldl' :: (b -> a -> b) -> b -> ImpossibleM1 a -> b # foldr1 :: (a -> a -> a) -> ImpossibleM1 a -> a # foldl1 :: (a -> a -> a) -> ImpossibleM1 a -> a # toList :: ImpossibleM1 a -> [a] # null :: ImpossibleM1 a -> Bool # length :: ImpossibleM1 a -> Int # elem :: Eq a => a -> ImpossibleM1 a -> Bool # maximum :: Ord a => ImpossibleM1 a -> a # minimum :: Ord a => ImpossibleM1 a -> a # sum :: Num a => ImpossibleM1 a -> a # product :: Num a => ImpossibleM1 a -> a # | |
Foldable f => Foldable (Yoneda f) | |
Defined in Data.Functor.Yoneda Methods fold :: Monoid m => Yoneda f m -> m # foldMap :: Monoid m => (a -> m) -> Yoneda f a -> m # foldr :: (a -> b -> b) -> b -> Yoneda f a -> b # foldr' :: (a -> b -> b) -> b -> Yoneda f a -> b # foldl :: (b -> a -> b) -> b -> Yoneda f a -> b # foldl' :: (b -> a -> b) -> b -> Yoneda f a -> b # foldr1 :: (a -> a -> a) -> Yoneda f a -> a # foldl1 :: (a -> a -> a) -> Yoneda f a -> a # elem :: Eq a => a -> Yoneda f a -> Bool # maximum :: Ord a => Yoneda f a -> a # minimum :: Ord a => Yoneda f a -> a # | |
Foldable (Level i) | |
Defined in Control.Lens.Internal.Level Methods fold :: Monoid m => Level i m -> m # foldMap :: Monoid m => (a -> m) -> Level i a -> m # foldr :: (a -> b -> b) -> b -> Level i a -> b # foldr' :: (a -> b -> b) -> b -> Level i a -> b # foldl :: (b -> a -> b) -> b -> Level i a -> b # foldl' :: (b -> a -> b) -> b -> Level i a -> b # foldr1 :: (a -> a -> a) -> Level i a -> a # foldl1 :: (a -> a -> a) -> Level i a -> a # elem :: Eq a => a -> Level i a -> Bool # maximum :: Ord a => Level i a -> a # minimum :: Ord a => Level i a -> a # | |
Foldable (ListF a) | |
Defined in Data.Functor.Foldable Methods fold :: Monoid m => ListF a m -> m # foldMap :: Monoid m => (a0 -> m) -> ListF a a0 -> m # foldr :: (a0 -> b -> b) -> b -> ListF a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> ListF a a0 -> b # foldl :: (b -> a0 -> b) -> b -> ListF a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> ListF a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> ListF a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> ListF a a0 -> a0 # toList :: ListF a a0 -> [a0] # elem :: Eq a0 => a0 -> ListF a a0 -> Bool # maximum :: Ord a0 => ListF a a0 -> a0 # minimum :: Ord a0 => ListF a a0 -> a0 # | |
Foldable (NonEmptyF a) | |
Defined in Data.Functor.Base Methods fold :: Monoid m => NonEmptyF a m -> m # foldMap :: Monoid m => (a0 -> m) -> NonEmptyF a a0 -> m # foldr :: (a0 -> b -> b) -> b -> NonEmptyF a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> NonEmptyF a a0 -> b # foldl :: (b -> a0 -> b) -> b -> NonEmptyF a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> NonEmptyF a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> NonEmptyF a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> NonEmptyF a a0 -> a0 # toList :: NonEmptyF a a0 -> [a0] # null :: NonEmptyF a a0 -> Bool # length :: NonEmptyF a a0 -> Int # elem :: Eq a0 => a0 -> NonEmptyF a a0 -> Bool # maximum :: Ord a0 => NonEmptyF a a0 -> a0 # minimum :: Ord a0 => NonEmptyF a a0 -> a0 # | |
Foldable f => Foldable (Rec1 f) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Rec1 f m -> m # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b # foldr1 :: (a -> a -> a) -> Rec1 f a -> a # foldl1 :: (a -> a -> a) -> Rec1 f a -> a # elem :: Eq a => a -> Rec1 f a -> Bool # maximum :: Ord a => Rec1 f a -> a # minimum :: Ord a => Rec1 f a -> a # | |
Foldable (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => URec Char m -> m # foldMap :: Monoid m => (a -> m) -> URec Char a -> m # foldr :: (a -> b -> b) -> b -> URec Char a -> b # foldr' :: (a -> b -> b) -> b -> URec Char a -> b # foldl :: (b -> a -> b) -> b -> URec Char a -> b # foldl' :: (b -> a -> b) -> b -> URec Char a -> b # foldr1 :: (a -> a -> a) -> URec Char a -> a # foldl1 :: (a -> a -> a) -> URec Char a -> a # toList :: URec Char a -> [a] # length :: URec Char a -> Int # elem :: Eq a => a -> URec Char a -> Bool # maximum :: Ord a => URec Char a -> a # minimum :: Ord a => URec Char a -> a # | |
Foldable (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => URec Double m -> m # foldMap :: Monoid m => (a -> m) -> URec Double a -> m # foldr :: (a -> b -> b) -> b -> URec Double a -> b # foldr' :: (a -> b -> b) -> b -> URec Double a -> b # foldl :: (b -> a -> b) -> b -> URec Double a -> b # foldl' :: (b -> a -> b) -> b -> URec Double a -> b # foldr1 :: (a -> a -> a) -> URec Double a -> a # foldl1 :: (a -> a -> a) -> URec Double a -> a # toList :: URec Double a -> [a] # null :: URec Double a -> Bool # length :: URec Double a -> Int # elem :: Eq a => a -> URec Double a -> Bool # maximum :: Ord a => URec Double a -> a # minimum :: Ord a => URec Double a -> a # | |
Foldable (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => URec Float m -> m # foldMap :: Monoid m => (a -> m) -> URec Float a -> m # foldr :: (a -> b -> b) -> b -> URec Float a -> b # foldr' :: (a -> b -> b) -> b -> URec Float a -> b # foldl :: (b -> a -> b) -> b -> URec Float a -> b # foldl' :: (b -> a -> b) -> b -> URec Float a -> b # foldr1 :: (a -> a -> a) -> URec Float a -> a # foldl1 :: (a -> a -> a) -> URec Float a -> a # toList :: URec Float a -> [a] # null :: URec Float a -> Bool # length :: URec Float a -> Int # elem :: Eq a => a -> URec Float a -> Bool # maximum :: Ord a => URec Float a -> a # minimum :: Ord a => URec Float a -> a # | |
Foldable (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => URec Int m -> m # foldMap :: Monoid m => (a -> m) -> URec Int a -> m # foldr :: (a -> b -> b) -> b -> URec Int a -> b # foldr' :: (a -> b -> b) -> b -> URec Int a -> b # foldl :: (b -> a -> b) -> b -> URec Int a -> b # foldl' :: (b -> a -> b) -> b -> URec Int a -> b # foldr1 :: (a -> a -> a) -> URec Int a -> a # foldl1 :: (a -> a -> a) -> URec Int a -> a # elem :: Eq a => a -> URec Int a -> Bool # maximum :: Ord a => URec Int a -> a # minimum :: Ord a => URec Int a -> a # | |
Foldable (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => URec Word m -> m # foldMap :: Monoid m => (a -> m) -> URec Word a -> m # foldr :: (a -> b -> b) -> b -> URec Word a -> b # foldr' :: (a -> b -> b) -> b -> URec Word a -> b # foldl :: (b -> a -> b) -> b -> URec Word a -> b # foldl' :: (b -> a -> b) -> b -> URec Word a -> b # foldr1 :: (a -> a -> a) -> URec Word a -> a # foldl1 :: (a -> a -> a) -> URec Word a -> a # toList :: URec Word a -> [a] # length :: URec Word a -> Int # elem :: Eq a => a -> URec Word a -> Bool # maximum :: Ord a => URec Word a -> a # minimum :: Ord a => URec Word a -> a # | |
Foldable (URec (Ptr ()) :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => URec (Ptr ()) m -> m # foldMap :: Monoid m => (a -> m) -> URec (Ptr ()) a -> m # foldr :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b # foldr' :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b # foldl :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b # foldl' :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b # foldr1 :: (a -> a -> a) -> URec (Ptr ()) a -> a # foldl1 :: (a -> a -> a) -> URec (Ptr ()) a -> a # toList :: URec (Ptr ()) a -> [a] # null :: URec (Ptr ()) a -> Bool # length :: URec (Ptr ()) a -> Int # elem :: Eq a => a -> URec (Ptr ()) a -> Bool # maximum :: Ord a => URec (Ptr ()) a -> a # minimum :: Ord a => URec (Ptr ()) a -> a # | |
Foldable (Const m :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # 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 Methods fold :: Monoid m => Ap f m -> 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 Methods fold :: Monoid m => Alt f m -> 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 # | |
Bifoldable p => Foldable (Join p) | |
Defined in Data.Bifunctor.Join Methods fold :: Monoid m => Join p m -> m # foldMap :: Monoid m => (a -> m) -> Join p a -> m # foldr :: (a -> b -> b) -> b -> Join p a -> b # foldr' :: (a -> b -> b) -> b -> Join p a -> b # foldl :: (b -> a -> b) -> b -> Join p a -> b # foldl' :: (b -> a -> b) -> b -> Join p a -> b # foldr1 :: (a -> a -> a) -> Join p a -> a # foldl1 :: (a -> a -> a) -> Join p a -> a # elem :: Eq a => a -> Join p a -> Bool # maximum :: Ord a => Join p a -> a # minimum :: Ord a => Join p a -> a # | |
Bifoldable p => Foldable (Fix p) | |
Defined in Data.Bifunctor.Fix Methods fold :: Monoid m => Fix p m -> m # foldMap :: Monoid m => (a -> m) -> Fix p a -> m # foldr :: (a -> b -> b) -> b -> Fix p a -> b # foldr' :: (a -> b -> b) -> b -> Fix p a -> b # foldl :: (b -> a -> b) -> b -> Fix p a -> b # foldl' :: (b -> a -> b) -> b -> Fix p a -> b # foldr1 :: (a -> a -> a) -> Fix p a -> a # foldl1 :: (a -> a -> a) -> Fix p a -> a # elem :: Eq a => a -> Fix p a -> Bool # maximum :: Ord a => Fix p a -> a # minimum :: Ord a => Fix p a -> a # | |
Foldable f => Foldable (IdentityT f) | |
Defined in Control.Monad.Trans.Identity Methods fold :: Monoid m => IdentityT f m -> m # foldMap :: Monoid m => (a -> m) -> IdentityT f a -> m # foldr :: (a -> b -> b) -> b -> IdentityT f a -> b # foldr' :: (a -> b -> b) -> b -> IdentityT f a -> b # foldl :: (b -> a -> b) -> b -> IdentityT f a -> b # foldl' :: (b -> a -> b) -> b -> IdentityT f a -> b # foldr1 :: (a -> a -> a) -> IdentityT f a -> a # foldl1 :: (a -> a -> a) -> IdentityT f a -> a # toList :: IdentityT f a -> [a] # null :: IdentityT f a -> Bool # length :: IdentityT f a -> Int # elem :: Eq a => a -> IdentityT f a -> Bool # maximum :: Ord a => IdentityT f a -> a # minimum :: Ord a => IdentityT f a -> a # | |
Foldable f => Foldable (ExceptT e f) | |
Defined in Control.Monad.Trans.Except Methods fold :: Monoid m => ExceptT e f m -> m # foldMap :: Monoid m => (a -> m) -> ExceptT e f a -> m # foldr :: (a -> b -> b) -> b -> ExceptT e f a -> b # foldr' :: (a -> b -> b) -> b -> ExceptT e f a -> b # foldl :: (b -> a -> b) -> b -> ExceptT e f a -> b # foldl' :: (b -> a -> b) -> b -> ExceptT e f a -> b # foldr1 :: (a -> a -> a) -> ExceptT e f a -> a # foldl1 :: (a -> a -> a) -> ExceptT e f a -> a # toList :: ExceptT e f a -> [a] # null :: ExceptT e f a -> Bool # length :: ExceptT e f a -> Int # elem :: Eq a => a -> ExceptT e f a -> Bool # maximum :: Ord a => ExceptT e f a -> a # minimum :: Ord a => ExceptT e f a -> a # | |
Foldable f => Foldable (FreeF f a) | |
Defined in Control.Monad.Trans.Free Methods fold :: Monoid m => FreeF f a m -> m # foldMap :: Monoid m => (a0 -> m) -> FreeF f a a0 -> m # foldr :: (a0 -> b -> b) -> b -> FreeF f a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> FreeF f a a0 -> b # foldl :: (b -> a0 -> b) -> b -> FreeF f a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> FreeF f a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> FreeF f a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> FreeF f a a0 -> a0 # toList :: FreeF f a a0 -> [a0] # null :: FreeF f a a0 -> Bool # length :: FreeF f a a0 -> Int # elem :: Eq a0 => a0 -> FreeF f a a0 -> Bool # maximum :: Ord a0 => FreeF f a a0 -> a0 # minimum :: Ord a0 => FreeF f a a0 -> a0 # | |
(Foldable m, Foldable f) => Foldable (FreeT f m) | |
Defined in Control.Monad.Trans.Free Methods fold :: Monoid m0 => FreeT f m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> FreeT f m a -> m0 # foldr :: (a -> b -> b) -> b -> FreeT f m a -> b # foldr' :: (a -> b -> b) -> b -> FreeT f m a -> b # foldl :: (b -> a -> b) -> b -> FreeT f m a -> b # foldl' :: (b -> a -> b) -> b -> FreeT f m a -> b # foldr1 :: (a -> a -> a) -> FreeT f m a -> a # foldl1 :: (a -> a -> a) -> FreeT f m a -> a # toList :: FreeT f m a -> [a] # length :: FreeT f m a -> Int # elem :: Eq a => a -> FreeT f m a -> Bool # maximum :: Ord a => FreeT f m a -> a # minimum :: Ord a => FreeT f m a -> a # | |
Foldable f => Foldable (CofreeF f a) | |
Defined in Control.Comonad.Trans.Cofree Methods fold :: Monoid m => CofreeF f a m -> m # foldMap :: Monoid m => (a0 -> m) -> CofreeF f a a0 -> m # foldr :: (a0 -> b -> b) -> b -> CofreeF f a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> CofreeF f a a0 -> b # foldl :: (b -> a0 -> b) -> b -> CofreeF f a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> CofreeF f a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> CofreeF f a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> CofreeF f a a0 -> a0 # toList :: CofreeF f a a0 -> [a0] # null :: CofreeF f a a0 -> Bool # length :: CofreeF f a a0 -> Int # elem :: Eq a0 => a0 -> CofreeF f a a0 -> Bool # maximum :: Ord a0 => CofreeF f a a0 -> a0 # minimum :: Ord a0 => CofreeF f a a0 -> a0 # | |
(Foldable f, Foldable w) => Foldable (CofreeT f w) | |
Defined in Control.Comonad.Trans.Cofree Methods fold :: Monoid m => CofreeT f w m -> m # foldMap :: Monoid m => (a -> m) -> CofreeT f w a -> m # foldr :: (a -> b -> b) -> b -> CofreeT f w a -> b # foldr' :: (a -> b -> b) -> b -> CofreeT f w a -> b # foldl :: (b -> a -> b) -> b -> CofreeT f w a -> b # foldl' :: (b -> a -> b) -> b -> CofreeT f w a -> b # foldr1 :: (a -> a -> a) -> CofreeT f w a -> a # foldl1 :: (a -> a -> a) -> CofreeT f w a -> a # toList :: CofreeT f w a -> [a] # null :: CofreeT f w a -> Bool # length :: CofreeT f w a -> Int # elem :: Eq a => a -> CofreeT f w a -> Bool # maximum :: Ord a => CofreeT f w a -> a # minimum :: Ord a => CofreeT f w a -> a # | |
Foldable f => Foldable (ErrorT e f) | |
Defined in Control.Monad.Trans.Error Methods fold :: Monoid m => ErrorT e f m -> m # foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m # foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldr1 :: (a -> a -> a) -> ErrorT e f a -> a # foldl1 :: (a -> a -> a) -> ErrorT e f a -> a # toList :: ErrorT e f a -> [a] # null :: ErrorT e f a -> Bool # length :: ErrorT e f a -> Int # elem :: Eq a => a -> ErrorT e f a -> Bool # maximum :: Ord a => ErrorT e f a -> a # minimum :: Ord a => ErrorT e f a -> a # | |
Foldable (Tagged s) | |
Defined in Data.Tagged Methods fold :: Monoid m => Tagged s m -> m # foldMap :: Monoid m => (a -> m) -> Tagged s a -> m # foldr :: (a -> b -> b) -> b -> Tagged s a -> b # foldr' :: (a -> b -> b) -> b -> Tagged s a -> b # foldl :: (b -> a -> b) -> b -> Tagged s a -> b # foldl' :: (b -> a -> b) -> b -> Tagged s a -> b # foldr1 :: (a -> a -> a) -> Tagged s a -> a # foldl1 :: (a -> a -> a) -> Tagged s a -> a # elem :: Eq a => a -> Tagged s a -> Bool # maximum :: Ord a => Tagged s a -> a # minimum :: Ord a => Tagged s a -> a # | |
Foldable (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => K1 i c m -> m # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m # foldr :: (a -> b -> b) -> b -> K1 i c a -> b # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b # foldl :: (b -> a -> b) -> b -> K1 i c a -> b # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b # foldr1 :: (a -> a -> a) -> K1 i c a -> a # foldl1 :: (a -> a -> a) -> K1 i c a -> a # 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 Methods fold :: Monoid m => (f :+: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a # toList :: (f :+: g) a -> [a] # 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 Methods fold :: Monoid m => (f :*: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b # foldr1 :: (a -> a -> a) -> (f :*: g) a -> a # foldl1 :: (a -> a -> a) -> (f :*: g) a -> a # toList :: (f :*: g) a -> [a] # 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 (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m # foldMap :: Monoid m => (a -> m) -> Product f g a -> m # foldr :: (a -> b -> b) -> b -> Product f g a -> b # foldr' :: (a -> b -> b) -> b -> Product f g a -> b # foldl :: (b -> a -> b) -> b -> Product f g a -> b # foldl' :: (b -> a -> b) -> b -> Product f g a -> b # foldr1 :: (a -> a -> a) -> Product f g a -> a # foldl1 :: (a -> a -> a) -> Product f g a -> a # toList :: Product f g a -> [a] # null :: Product f g a -> Bool # length :: Product f g a -> Int # elem :: Eq a => a -> Product f g a -> Bool # maximum :: Ord a => Product f g a -> a # minimum :: Ord a => Product f g a -> a # | |
(Foldable f, Foldable g) => Foldable (Sum f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m # foldr :: (a -> b -> b) -> b -> Sum f g a -> b # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b # foldl :: (b -> a -> b) -> b -> Sum f g a -> b # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b # foldr1 :: (a -> a -> a) -> Sum f g a -> a # foldl1 :: (a -> a -> a) -> Sum f g a -> a # elem :: Eq a => a -> Sum f g a -> Bool # maximum :: Ord a => Sum f g a -> a # minimum :: Ord a => Sum f g a -> a # | |
Foldable (ImpossibleM2 t1 :: Type -> Type) | |
Defined in Data.Impossible Methods fold :: Monoid m => ImpossibleM2 t1 m -> m # foldMap :: Monoid m => (a -> m) -> ImpossibleM2 t1 a -> m # foldr :: (a -> b -> b) -> b -> ImpossibleM2 t1 a -> b # foldr' :: (a -> b -> b) -> b -> ImpossibleM2 t1 a -> b # foldl :: (b -> a -> b) -> b -> ImpossibleM2 t1 a -> b # foldl' :: (b -> a -> b) -> b -> ImpossibleM2 t1 a -> b # foldr1 :: (a -> a -> a) -> ImpossibleM2 t1 a -> a # foldl1 :: (a -> a -> a) -> ImpossibleM2 t1 a -> a # toList :: ImpossibleM2 t1 a -> [a] # null :: ImpossibleM2 t1 a -> Bool # length :: ImpossibleM2 t1 a -> Int # elem :: Eq a => a -> ImpossibleM2 t1 a -> Bool # maximum :: Ord a => ImpossibleM2 t1 a -> a # minimum :: Ord a => ImpossibleM2 t1 a -> a # sum :: Num a => ImpossibleM2 t1 a -> a # product :: Num a => ImpossibleM2 t1 a -> a # | |
Foldable (Magma i t b) | |
Defined in Control.Lens.Internal.Magma Methods fold :: Monoid m => Magma i t b m -> m # foldMap :: Monoid m => (a -> m) -> Magma i t b a -> m # foldr :: (a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # foldr' :: (a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # foldl :: (b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # foldl' :: (b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # foldr1 :: (a -> a -> a) -> Magma i t b a -> a # foldl1 :: (a -> a -> a) -> Magma i t b a -> a # toList :: Magma i t b a -> [a] # null :: Magma i t b a -> Bool # length :: Magma i t b a -> Int # elem :: Eq a => a -> Magma i t b a -> Bool # maximum :: Ord a => Magma i t b a -> a # minimum :: Ord a => Magma i t b a -> a # | |
Foldable f => Foldable (M1 i c f) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => M1 i c f m -> m # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b # foldr1 :: (a -> a -> a) -> M1 i c f a -> a # foldl1 :: (a -> a -> a) -> M1 i c f a -> a # 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 Methods fold :: Monoid m => (f :.: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a # toList :: (f :.: g) a -> [a] # 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 (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods fold :: Monoid m => Compose f g m -> m # foldMap :: Monoid m => (a -> m) -> Compose f g a -> m # foldr :: (a -> b -> b) -> b -> Compose f g a -> b # foldr' :: (a -> b -> b) -> b -> Compose f g a -> b # foldl :: (b -> a -> b) -> b -> Compose f g a -> b # foldl' :: (b -> a -> b) -> b -> Compose f g a -> b # foldr1 :: (a -> a -> a) -> Compose f g a -> a # foldl1 :: (a -> a -> a) -> Compose f g a -> a # toList :: Compose f g a -> [a] # null :: Compose f g a -> Bool # length :: Compose f g a -> Int # elem :: Eq a => a -> Compose f g a -> Bool # maximum :: Ord a => Compose f g a -> a # minimum :: Ord a => Compose f g a -> a # | |
Bifoldable p => Foldable (WrappedBifunctor p a) | |
Defined in Data.Bifunctor.Wrapped Methods fold :: Monoid m => WrappedBifunctor p a m -> m # foldMap :: Monoid m => (a0 -> m) -> WrappedBifunctor p a a0 -> m # foldr :: (a0 -> b -> b) -> b -> WrappedBifunctor p a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> WrappedBifunctor p a a0 -> b # foldl :: (b -> a0 -> b) -> b -> WrappedBifunctor p a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> WrappedBifunctor p a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> WrappedBifunctor p a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> WrappedBifunctor p a a0 -> a0 # toList :: WrappedBifunctor p a a0 -> [a0] # null :: WrappedBifunctor p a a0 -> Bool # length :: WrappedBifunctor p a a0 -> Int # elem :: Eq a0 => a0 -> WrappedBifunctor p a a0 -> Bool # maximum :: Ord a0 => WrappedBifunctor p a a0 -> a0 # minimum :: Ord a0 => WrappedBifunctor p a a0 -> a0 # sum :: Num a0 => WrappedBifunctor p a a0 -> a0 # product :: Num a0 => WrappedBifunctor p a a0 -> a0 # | |
Foldable g => Foldable (Joker g a) | |
Defined in Data.Bifunctor.Joker Methods fold :: Monoid m => Joker g a m -> m # foldMap :: Monoid m => (a0 -> m) -> Joker g a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Joker g a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Joker g a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Joker g a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Joker g a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Joker g a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Joker g a a0 -> a0 # toList :: Joker g a a0 -> [a0] # null :: Joker g a a0 -> Bool # length :: Joker g a a0 -> Int # elem :: Eq a0 => a0 -> Joker g a a0 -> Bool # maximum :: Ord a0 => Joker g a a0 -> a0 # minimum :: Ord a0 => Joker g a a0 -> a0 # | |
Bifoldable p => Foldable (Flip p a) | |
Defined in Data.Bifunctor.Flip Methods fold :: Monoid m => Flip p a m -> m # foldMap :: Monoid m => (a0 -> m) -> Flip p a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Flip p a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Flip p a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Flip p a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Flip p a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Flip p a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Flip p a a0 -> a0 # toList :: Flip p a a0 -> [a0] # length :: Flip p a a0 -> Int # elem :: Eq a0 => a0 -> Flip p a a0 -> Bool # maximum :: Ord a0 => Flip p a a0 -> a0 # minimum :: Ord a0 => Flip p a a0 -> a0 # | |
Foldable (Clown f a :: Type -> Type) | |
Defined in Data.Bifunctor.Clown Methods fold :: Monoid m => Clown f a m -> m # foldMap :: Monoid m => (a0 -> m) -> Clown f a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Clown f a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Clown f a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Clown f a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Clown f a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Clown f a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Clown f a a0 -> a0 # toList :: Clown f a a0 -> [a0] # null :: Clown f a a0 -> Bool # length :: Clown f a a0 -> Int # elem :: Eq a0 => a0 -> Clown f a a0 -> Bool # maximum :: Ord a0 => Clown f a a0 -> a0 # minimum :: Ord a0 => Clown f a a0 -> a0 # | |
Foldable (ImpossibleM3 t1 t2 :: Type -> Type) | |
Defined in Data.Impossible Methods fold :: Monoid m => ImpossibleM3 t1 t2 m -> m # foldMap :: Monoid m => (a -> m) -> ImpossibleM3 t1 t2 a -> m # foldr :: (a -> b -> b) -> b -> ImpossibleM3 t1 t2 a -> b # foldr' :: (a -> b -> b) -> b -> ImpossibleM3 t1 t2 a -> b # foldl :: (b -> a -> b) -> b -> ImpossibleM3 t1 t2 a -> b # foldl' :: (b -> a -> b) -> b -> ImpossibleM3 t1 t2 a -> b # foldr1 :: (a -> a -> a) -> ImpossibleM3 t1 t2 a -> a # foldl1 :: (a -> a -> a) -> ImpossibleM3 t1 t2 a -> a # toList :: ImpossibleM3 t1 t2 a -> [a] # null :: ImpossibleM3 t1 t2 a -> Bool # length :: ImpossibleM3 t1 t2 a -> Int # elem :: Eq a => a -> ImpossibleM3 t1 t2 a -> Bool # maximum :: Ord a => ImpossibleM3 t1 t2 a -> a # minimum :: Ord a => ImpossibleM3 t1 t2 a -> a # sum :: Num a => ImpossibleM3 t1 t2 a -> a # product :: Num a => ImpossibleM3 t1 t2 a -> a # | |
(Foldable f, Bifoldable p) => Foldable (Tannen f p a) | |
Defined in Data.Bifunctor.Tannen Methods fold :: Monoid m => Tannen f p a m -> m # foldMap :: Monoid m => (a0 -> m) -> Tannen f p a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Tannen f p a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Tannen f p a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Tannen f p a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Tannen f p a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Tannen f p a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Tannen f p a a0 -> a0 # toList :: Tannen f p a a0 -> [a0] # null :: Tannen f p a a0 -> Bool # length :: Tannen f p a a0 -> Int # elem :: Eq a0 => a0 -> Tannen f p a a0 -> Bool # maximum :: Ord a0 => Tannen f p a a0 -> a0 # minimum :: Ord a0 => Tannen f p a a0 -> a0 # | |
Foldable (ImpossibleM4 t1 t2 t3 :: Type -> Type) | |
Defined in Data.Impossible Methods fold :: Monoid m => ImpossibleM4 t1 t2 t3 m -> m # foldMap :: Monoid m => (a -> m) -> ImpossibleM4 t1 t2 t3 a -> m # foldr :: (a -> b -> b) -> b -> ImpossibleM4 t1 t2 t3 a -> b # foldr' :: (a -> b -> b) -> b -> ImpossibleM4 t1 t2 t3 a -> b # foldl :: (b -> a -> b) -> b -> ImpossibleM4 t1 t2 t3 a -> b # foldl' :: (b -> a -> b) -> b -> ImpossibleM4 t1 t2 t3 a -> b # foldr1 :: (a -> a -> a) -> ImpossibleM4 t1 t2 t3 a -> a # foldl1 :: (a -> a -> a) -> ImpossibleM4 t1 t2 t3 a -> a # toList :: ImpossibleM4 t1 t2 t3 a -> [a] # null :: ImpossibleM4 t1 t2 t3 a -> Bool # length :: ImpossibleM4 t1 t2 t3 a -> Int # elem :: Eq a => a -> ImpossibleM4 t1 t2 t3 a -> Bool # maximum :: Ord a => ImpossibleM4 t1 t2 t3 a -> a # minimum :: Ord a => ImpossibleM4 t1 t2 t3 a -> a # sum :: Num a => ImpossibleM4 t1 t2 t3 a -> a # product :: Num a => ImpossibleM4 t1 t2 t3 a -> a # | |
(Bifoldable p, Foldable g) => Foldable (Biff p f g a) | |
Defined in Data.Bifunctor.Biff Methods fold :: Monoid m => Biff p f g a m -> m # foldMap :: Monoid m => (a0 -> m) -> Biff p f g a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Biff p f g a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Biff p f g a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Biff p f g a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Biff p f g a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Biff p f g a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Biff p f g a a0 -> a0 # toList :: Biff p f g a a0 -> [a0] # null :: Biff p f g a a0 -> Bool # length :: Biff p f g a a0 -> Int # elem :: Eq a0 => a0 -> Biff p f g a a0 -> Bool # maximum :: Ord a0 => Biff p f g a a0 -> a0 # minimum :: Ord a0 => Biff p f g a a0 -> a0 # | |
Foldable (ImpossibleM5 t1 t2 t3 t4 :: Type -> Type) | |
Defined in Data.Impossible Methods fold :: Monoid m => ImpossibleM5 t1 t2 t3 t4 m -> m # foldMap :: Monoid m => (a -> m) -> ImpossibleM5 t1 t2 t3 t4 a -> m # foldr :: (a -> b -> b) -> b -> ImpossibleM5 t1 t2 t3 t4 a -> b # foldr' :: (a -> b -> b) -> b -> ImpossibleM5 t1 t2 t3 t4 a -> b # foldl :: (b -> a -> b) -> b -> ImpossibleM5 t1 t2 t3 t4 a -> b # foldl' :: (b -> a -> b) -> b -> ImpossibleM5 t1 t2 t3 t4 a -> b # foldr1 :: (a -> a -> a) -> ImpossibleM5 t1 t2 t3 t4 a -> a # foldl1 :: (a -> a -> a) -> ImpossibleM5 t1 t2 t3 t4 a -> a # toList :: ImpossibleM5 t1 t2 t3 t4 a -> [a] # null :: ImpossibleM5 t1 t2 t3 t4 a -> Bool # length :: ImpossibleM5 t1 t2 t3 t4 a -> Int # elem :: Eq a => a -> ImpossibleM5 t1 t2 t3 t4 a -> Bool # maximum :: Ord a => ImpossibleM5 t1 t2 t3 t4 a -> a # minimum :: Ord a => ImpossibleM5 t1 t2 t3 t4 a -> a # sum :: Num a => ImpossibleM5 t1 t2 t3 t4 a -> a # product :: Num a => ImpossibleM5 t1 t2 t3 t4 a -> a # | |
Foldable (ImpossibleM6 t1 t2 t3 t4 t5 :: Type -> Type) | |
Defined in Data.Impossible Methods fold :: Monoid m => ImpossibleM6 t1 t2 t3 t4 t5 m -> m # foldMap :: Monoid m => (a -> m) -> ImpossibleM6 t1 t2 t3 t4 t5 a -> m # foldr :: (a -> b -> b) -> b -> ImpossibleM6 t1 t2 t3 t4 t5 a -> b # foldr' :: (a -> b -> b) -> b -> ImpossibleM6 t1 t2 t3 t4 t5 a -> b # foldl :: (b -> a -> b) -> b -> ImpossibleM6 t1 t2 t3 t4 t5 a -> b # foldl' :: (b -> a -> b) -> b -> ImpossibleM6 t1 t2 t3 t4 t5 a -> b # foldr1 :: (a -> a -> a) -> ImpossibleM6 t1 t2 t3 t4 t5 a -> a # foldl1 :: (a -> a -> a) -> ImpossibleM6 t1 t2 t3 t4 t5 a -> a # toList :: ImpossibleM6 t1 t2 t3 t4 t5 a -> [a] # null :: ImpossibleM6 t1 t2 t3 t4 t5 a -> Bool # length :: ImpossibleM6 t1 t2 t3 t4 t5 a -> Int # elem :: Eq a => a -> ImpossibleM6 t1 t2 t3 t4 t5 a -> Bool # maximum :: Ord a => ImpossibleM6 t1 t2 t3 t4 t5 a -> a # minimum :: Ord a => ImpossibleM6 t1 t2 t3 t4 t5 a -> a # sum :: Num a => ImpossibleM6 t1 t2 t3 t4 t5 a -> a # product :: Num a => ImpossibleM6 t1 t2 t3 t4 t5 a -> a # | |
Foldable (ImpossibleM7 t1 t2 t3 t4 t5 t6 :: Type -> Type) | |
Defined in Data.Impossible Methods fold :: Monoid m => ImpossibleM7 t1 t2 t3 t4 t5 t6 m -> m # foldMap :: Monoid m => (a -> m) -> ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> m # foldr :: (a -> b -> b) -> b -> ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> b # foldr' :: (a -> b -> b) -> b -> ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> b # foldl :: (b -> a -> b) -> b -> ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> b # foldl' :: (b -> a -> b) -> b -> ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> b # foldr1 :: (a -> a -> a) -> ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> a # foldl1 :: (a -> a -> a) -> ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> a # toList :: ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> [a] # null :: ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> Bool # length :: ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> Int # elem :: Eq a => a -> ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> Bool # maximum :: Ord a => ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> a # minimum :: Ord a => ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> a # sum :: Num a => ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> a # product :: Num a => ImpossibleM7 t1 t2 t3 t4 t5 t6 a -> a # | |
Foldable (ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 :: Type -> Type) | |
Defined in Data.Impossible Methods fold :: Monoid m => ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 m -> m # foldMap :: Monoid m => (a -> m) -> ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> m # foldr :: (a -> b -> b) -> b -> ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> b # foldr' :: (a -> b -> b) -> b -> ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> b # foldl :: (b -> a -> b) -> b -> ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> b # foldl' :: (b -> a -> b) -> b -> ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> b # foldr1 :: (a -> a -> a) -> ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> a # foldl1 :: (a -> a -> a) -> ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> a # toList :: ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> [a] # null :: ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> Bool # length :: ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> Int # elem :: Eq a => a -> ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> Bool # maximum :: Ord a => ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> a # minimum :: Ord a => ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> a # sum :: Num a => ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> a # product :: Num a => ImpossibleM8 t1 t2 t3 t4 t5 t6 t7 a -> a # | |
Foldable (ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 :: Type -> Type) | |
Defined in Data.Impossible Methods fold :: Monoid m => ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 m -> m # foldMap :: Monoid m => (a -> m) -> ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> m # foldr :: (a -> b -> b) -> b -> ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> b # foldr' :: (a -> b -> b) -> b -> ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> b # foldl :: (b -> a -> b) -> b -> ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> b # foldl' :: (b -> a -> b) -> b -> ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> b # foldr1 :: (a -> a -> a) -> ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> a # foldl1 :: (a -> a -> a) -> ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> a # toList :: ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> [a] # null :: ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> Bool # length :: ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> Int # elem :: Eq a => a -> ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> Bool # maximum :: Ord a => ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> a # minimum :: Ord a => ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> a # sum :: Num a => ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> a # product :: Num a => ImpossibleM9 t1 t2 t3 t4 t5 t6 t7 t8 a -> a # |
biall :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool #
Determines whether all elements of the structure satisfy their appropriate predicate argument.
Since: base-4.10.0.0
biany :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool #
Determines whether any element of the structure satisfies its appropriate predicate argument.
Since: base-4.10.0.0
biconcatMap :: Bifoldable t => (a -> [c]) -> (b -> [c]) -> t a b -> [c] #
Given a means of mapping the elements of a structure to lists, computes the concatenation of all such lists in order.
Since: base-4.10.0.0
biproduct :: (Bifoldable t, Num a) => t a a -> a #
The biproduct
function computes the product of the numbers of a
structure.
Since: base-4.10.0.0
bisum :: (Bifoldable t, Num a) => t a a -> a #
The bisum
function computes the sum of the numbers of a structure.
Since: base-4.10.0.0
biconcat :: Bifoldable t => t [a] [a] -> [a] #
Reduces a structure of lists to the concatenation of those lists.
Since: base-4.10.0.0
bielem :: (Bifoldable t, Eq a) => a -> t a a -> Bool #
Does the element occur in the structure?
Since: base-4.10.0.0
biasum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a #
The sum of a collection of actions, generalizing biconcat
.
Since: base-4.10.0.0
bifor_ :: (Bifoldable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f () #
As bitraverse_
, but with the structure as the primary argument. For a
version that doesn't ignore the results, see bifor
.
>>>
> bifor_ ('a', "bc") print (print . reverse)
'a' "cb"
Since: base-4.10.0.0
bitraverse_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f () #
Map each element of a structure using one of two actions, evaluate these
actions from left to right, and ignore the results. For a version that
doesn't ignore the results, see bitraverse
.
Since: base-4.10.0.0
bifoldlM :: (Bifoldable t, Monad m) => (a -> b -> m a) -> (a -> c -> m a) -> a -> t b c -> m a #
Left associative monadic bifold over a structure.
Since: base-4.10.0.0
bifoldl' :: Bifoldable t => (a -> b -> a) -> (a -> c -> a) -> a -> t b c -> a #
As bifoldl
, but strict in the result of the reduction functions at each
step.
This ensures that each step of the bifold is forced to weak head normal form
before being applied, avoiding the collection of thunks that would otherwise
occur. This is often what you want to strictly reduce a finite structure to
a single, monolithic result (e.g., bilength
).
Since: base-4.10.0.0
bifoldrM :: (Bifoldable t, Monad m) => (a -> c -> m c) -> (b -> c -> m c) -> c -> t a b -> m c #
Right associative monadic bifold over a structure.
Since: base-4.10.0.0
bifoldr' :: Bifoldable t => (a -> c -> c) -> (b -> c -> c) -> c -> t a b -> c #
As bifoldr
, but strict in the result of the reduction functions at each
step.
Since: base-4.10.0.0
class Bifoldable (p :: Type -> Type -> Type) where #
Bifoldable
identifies foldable structures with two different varieties
of elements (as opposed to Foldable
, which has one variety of element).
Common examples are Either
and '(,)':
instance Bifoldable Either where bifoldMap f _ (Left a) = f a bifoldMap _ g (Right b) = g b instance Bifoldable (,) where bifoldr f g z (a, b) = f a (g b z)
A minimal Bifoldable
definition consists of either bifoldMap
or
bifoldr
. When defining more than this minimal set, one should ensure
that the following identities hold:
bifold
≡bifoldMap
id
id
bifoldMap
f g ≡bifoldr
(mappend
. f) (mappend
. g)mempty
bifoldr
f g z t ≡appEndo
(bifoldMap
(Endo . f) (Endo . g) t) z
If the type is also a Bifunctor
instance, it should satisfy:
'bifoldMap' f g ≡ 'bifold' . 'bimap' f g
which implies that
'bifoldMap' f g . 'bimap' h i ≡ 'bifoldMap' (f . h) (g . i)
Since: base-4.10.0.0
Methods
bifold :: Monoid m => p m m -> m #
bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> p a b -> m #
Combines the elements of a structure, given ways of mapping them to a common monoid.
bifoldMap
f g ≡bifoldr
(mappend
. f) (mappend
. g)mempty
Since: base-4.10.0.0
bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> p a b -> c #
Combines the elements of a structure in a right associative manner.
Given a hypothetical function toEitherList :: p a b -> [Either a b]
yielding a list of all elements of a structure in order, the following
would hold:
bifoldr
f g z ≡foldr
(either
f g) z . toEitherList
Since: base-4.10.0.0
bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> p a b -> c #
Combines the elements of a structure in a left associative manner. Given
a hypothetical function toEitherList :: p a b -> [Either a b]
yielding a
list of all elements of a structure in order, the following would hold:
bifoldl
f g z ≡foldl
(acc ->either
(f acc) (g acc)) z . toEitherList
Note that if you want an efficient left-fold, you probably want to use
bifoldl'
instead of bifoldl
. The reason is that the latter does not
force the "inner" results, resulting in a thunk chain which then must be
evaluated from the outside-in.
Since: base-4.10.0.0
Instances
all :: Foldable t => (a -> Bool) -> t a -> Bool #
Determines whether all elements of the structure satisfy the predicate.
any :: Foldable t => (a -> Bool) -> t a -> Bool #
Determines whether any element of the structure satisfies the predicate.
concatMap :: Foldable t => (a -> [b]) -> t a -> [b] #
Map a function over all the elements of a container and concatenate the resulting lists.
concat :: Foldable t => t [a] -> [a] #
The concatenation of all the elements of a container of lists.
asum :: (Foldable t, Alternative f) => t (f a) -> f a #
for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f () #
traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f () #
Map each element of a structure to an action, evaluate these
actions from left to right, and ignore the results. For a version
that doesn't ignore the results see traverse
.
foldlM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b #
Monadic fold over the elements of a structure, associating to the left, i.e. from left to right.
foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b #
Monadic fold over the elements of a structure, associating to the right, i.e. from right to left.
class Foldable t => Foldable1 (t :: Type -> Type) where #
Minimal complete definition
Nothing
Methods
fold1 :: Semigroup m => t m -> m #
foldMap1 :: Semigroup m => (a -> m) -> t a -> m #
toNonEmpty :: t a -> NonEmpty a #