Safe Haskell | Trustworthy |
---|---|
Language | Haskell2010 |
This module is the recommended entry point to the pipes
library.
Read Pipes.Tutorial if you want a tutorial explaining how to use this library.
Synopsis
- data Proxy a' a b' b m r
- type X = Void
- type Effect = Proxy X () () X
- type Effect' m r = forall x' x y' y. Proxy x' x y' y m r
- runEffect :: Monad m => Effect m r -> m r
- type Producer b = Proxy X () () b
- type Producer' b m r = forall x' x. Proxy x' x () b m r
- yield :: Functor m => a -> Proxy x' x () a m ()
- for :: Functor m => Proxy x' x b' b m a' -> (b -> Proxy x' x c' c m b') -> Proxy x' x c' c m a'
- (~>) :: Functor m => (a -> Proxy x' x b' b m a') -> (b -> Proxy x' x c' c m b') -> a -> Proxy x' x c' c m a'
- (<~) :: Functor m => (b -> Proxy x' x c' c m b') -> (a -> Proxy x' x b' b m a') -> a -> Proxy x' x c' c m a'
- type Consumer a = Proxy () a () X
- type Consumer' a m r = forall y' y. Proxy () a y' y m r
- await :: Functor m => Consumer' a m a
- (>~) :: Functor m => Proxy a' a y' y m b -> Proxy () b y' y m c -> Proxy a' a y' y m c
- (~<) :: Functor m => Proxy () b y' y m c -> Proxy a' a y' y m b -> Proxy a' a y' y m c
- type Pipe a b = Proxy () a () b
- cat :: Functor m => Pipe a a m r
- (>->) :: Functor m => Proxy a' a () b m r -> Proxy () b c' c m r -> Proxy a' a c' c m r
- (<-<) :: Functor m => Proxy () b c' c m r -> Proxy a' a () b m r -> Proxy a' a c' c m r
- newtype ListT m a = Select {}
- runListT :: Monad m => ListT m a -> m ()
- class Enumerable t where
- next :: Monad m => Producer a m r -> m (Either r (a, Producer a m r))
- each :: (Functor m, Foldable f) => f a -> Proxy x' x () a m ()
- every :: (Monad m, Enumerable t) => t m a -> Proxy x' x () a m ()
- discard :: Monad m => a -> m ()
- class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where
- void :: Functor f => f a -> f ()
- class Monad m => MonadIO (m :: Type -> Type) where
- class MonadTrans (t :: (Type -> Type) -> Type -> Type) where
- class (MFunctor t, MonadTrans t) => MMonad (t :: (Type -> Type) -> Type -> Type) where
- class MFunctor (t :: (Type -> Type) -> k -> Type) where
- class Foldable (t :: Type -> Type)
The Proxy Monad Transformer
data Proxy a' a b' b m r Source #
A Proxy
is a monad transformer that receives and sends information on both
an upstream and downstream interface.
The type variables signify:
a'
anda
- The upstream interface, where(a')
s go out and(a)
s come inb'
andb
- The downstream interface, where(b)
s go out and(b')
s come inm
- The base monadr
- The return value
Instances
MFunctor (Proxy a' a b' b :: (Type -> Type) -> Type -> Type) Source # | |
MonadError e m => MonadError e (Proxy a' a b' b m) Source # | |
Defined in Pipes.Internal throwError :: e -> Proxy a' a b' b m a0 Source # catchError :: Proxy a' a b' b m a0 -> (e -> Proxy a' a b' b m a0) -> Proxy a' a b' b m a0 Source # | |
MonadReader r m => MonadReader r (Proxy a' a b' b m) Source # | |
MonadState s m => MonadState s (Proxy a' a b' b m) Source # | |
MonadWriter w m => MonadWriter w (Proxy a' a b' b m) Source # | |
MMonad (Proxy a' a b' b) Source # | |
MonadTrans (Proxy a' a b' b) Source # | |
MonadFail m => MonadFail (Proxy a' a b' b m) Source # | |
MonadIO m => MonadIO (Proxy a' a b' b m) Source # | |
Functor m => Applicative (Proxy a' a b' b m) Source # | |
Defined in Pipes.Internal pure :: a0 -> Proxy a' a b' b m a0 Source # (<*>) :: Proxy a' a b' b m (a0 -> b0) -> Proxy a' a b' b m a0 -> Proxy a' a b' b m b0 Source # liftA2 :: (a0 -> b0 -> c) -> Proxy a' a b' b m a0 -> Proxy a' a b' b m b0 -> Proxy a' a b' b m c Source # (*>) :: Proxy a' a b' b m a0 -> Proxy a' a b' b m b0 -> Proxy a' a b' b m b0 Source # (<*) :: Proxy a' a b' b m a0 -> Proxy a' a b' b m b0 -> Proxy a' a b' b m a0 Source # | |
Functor m => Functor (Proxy a' a b' b m) Source # | |
Functor m => Monad (Proxy a' a b' b m) Source # | |
MonadCatch m => MonadCatch (Proxy a' a b' b m) Source # | |
MonadThrow m => MonadThrow (Proxy a' a b' b m) Source # | |
(Functor m, Monoid r, Semigroup r) => Monoid (Proxy a' a b' b m r) Source # | |
(Functor m, Semigroup r) => Semigroup (Proxy a' a b' b m r) Source # | |
type Effect' m r = forall x' x y' y. Proxy x' x y' y m r Source #
Like Effect
, but with a polymorphic type
runEffect :: Monad m => Effect m r -> m r Source #
Run a self-contained Effect
, converting it back to the base monad
Producers
Use yield
to produce output and (~>
) / for
to substitute yield
s.
yield
and (~>
) obey the Category
laws:
-- Substituting 'yield' with 'f' gives 'f'yield
~>
f = f -- Substituting every 'yield' with another 'yield' does nothing f~>
yield
= f -- 'yield' substitution is associative (f~>
g)~>
h = f~>
(g~>
h)
These are equivalent to the following "for loop laws":
-- Looping over a single yield simplifies to function applicationfor
(yield
x) f = f x -- Re-yielding every element of a stream returns the original streamfor
syield
= s -- Nested for loops can become a sequentialfor
loops if the inner loop -- body ignores the outer loop variablefor
s (\a ->for
(f a) g) =for
(for
s f) g =for
s (f~>
g)
type Producer' b m r = forall x' x. Proxy x' x () b m r Source #
Like Producer
, but with a polymorphic type
for :: Functor m => Proxy x' x b' b m a' -> (b -> Proxy x' x c' c m b') -> Proxy x' x c' c m a' Source #
(for p body)
loops over p
replacing each yield
with body
.
for
::Functor
m =>Producer
b m r -> (b ->Effect
m ()) ->Effect
m rfor
::Functor
m =>Producer
b m r -> (b ->Producer
c m ()) ->Producer
c m rfor
::Functor
m =>Pipe
x b m r -> (b ->Consumer
x m ()) ->Consumer
x m rfor
::Functor
m =>Pipe
x b m r -> (b ->Pipe
x c m ()) ->Pipe
x c m r
The following diagrams show the flow of information:
.---> b
/ |
+-----------+ / +-----|-----+ +---------------+
| | / | v | | |
| | / | | | |
x ==> p ==> b ---' x ==> body ==> c = x ==> for
p body ==> c
| | | | | |
| | | | | | | | |
+-----|-----+ +-----|-----+ +-------|-------+
v v v
r () r
For a more complete diagram including bidirectional flow, see Pipes.Core.
(~>) :: Functor m => (a -> Proxy x' x b' b m a') -> (b -> Proxy x' x c' c m b') -> a -> Proxy x' x c' c m a' infixr 4 Source #
Compose loop bodies
(~>
) ::Functor
m => (a ->Producer
b m r) -> (b ->Effect
m ()) -> (a ->Effect
m r) (~>
) ::Functor
m => (a ->Producer
b m r) -> (b ->Producer
c m ()) -> (a ->Producer
c m r) (~>
) ::Functor
m => (a ->Pipe
x b m r) -> (b ->Consumer
x m ()) -> (a ->Consumer
x m r) (~>
) ::Functor
m => (a ->Pipe
x b m r) -> (b ->Pipe
x c m ()) -> (a ->Pipe
x c m r)
The following diagrams show the flow of information:
a .---> b a
| / | |
+-----|-----+ / +-----|-----+ +------|------+
| v | / | v | | v |
| | / | | | |
x ==> f ==> b ---' x ==> g ==> c = x ==> f ~>
g ==> c
| | | | | |
| | | | | | | | |
+-----|-----+ +-----|-----+ +------|------+
v v v
r () r
For a more complete diagram including bidirectional flow, see Pipes.Core.
(<~) :: Functor m => (b -> Proxy x' x c' c m b') -> (a -> Proxy x' x b' b m a') -> a -> Proxy x' x c' c m a' infixl 4 Source #
(~>
) with the arguments flipped
Consumers
Use await
to request input and (>~
) to substitute await
s.
await
and (>~
) obey the Category
laws:
-- Substituting every 'await' with another 'await' does nothingawait
>~
f = f -- Substituting 'await' with 'f' gives 'f' f>~
await
= f -- 'await' substitution is associative (f>~
g)>~
h = f>~
(g>~
h)
type Consumer' a m r = forall y' y. Proxy () a y' y m r Source #
Like Consumer
, but with a polymorphic type
(>~) :: Functor m => Proxy a' a y' y m b -> Proxy () b y' y m c -> Proxy a' a y' y m c infixr 5 Source #
(draw >~ p)
loops over p
replacing each await
with draw
(>~
) ::Functor
m =>Effect
m b ->Consumer
b m c ->Effect
m c (>~
) ::Functor
m =>Consumer
a m b ->Consumer
b m c ->Consumer
a m c (>~
) ::Functor
m =>Producer
y m b ->Pipe
b y m c ->Producer
y m c (>~
) ::Functor
m =>Pipe
a y m b ->Pipe
b y m c ->Pipe
a y m c
The following diagrams show the flow of information:
+-----------+ +-----------+ +-------------+
| | | | | |
| | | | | |
a ==> f ==> y .---> b ==> g ==> y = a ==> f >~
g ==> y
| | / | | | |
| | | / | | | | | |
+-----|-----+ / +-----|-----+ +------|------+
v / v v
b ----' c c
For a more complete diagram including bidirectional flow, see Pipes.Core.
(~<) :: Functor m => Proxy () b y' y m c -> Proxy a' a y' y m b -> Proxy a' a y' y m c infixl 5 Source #
(>~
) with the arguments flipped
Pipes
Use await
and yield
to build Pipe
s and (>->
) to connect Pipe
s.
cat
and (>->
) obey the Category
laws:
-- Useless use of catcat
>->
f = f -- Redirecting output to cat does nothing f>->
cat
= f -- The pipe operator is associative (f>->
g)>->
h = f>->
(g>->
h)
(>->) :: Functor m => Proxy a' a () b m r -> Proxy () b c' c m r -> Proxy a' a c' c m r infixl 7 Source #
Pipe
composition, analogous to the Unix pipe operator
(>->
) ::Functor
m =>Producer
b m r ->Consumer
b m r ->Effect
m r (>->
) ::Functor
m =>Producer
b m r ->Pipe
b c m r ->Producer
c m r (>->
) ::Functor
m =>Pipe
a b m r ->Consumer
b m r ->Consumer
a m r (>->
) ::Functor
m =>Pipe
a b m r ->Pipe
b c m r ->Pipe
a c m r
The following diagrams show the flow of information:
+-----------+ +-----------+ +-------------+
| | | | | |
| | | | | |
a ==> f ==> b ==> g ==> c = a ==> f >->
g ==> c
| | | | | |
| | | | | | | | |
+-----|-----+ +-----|-----+ +------|------+
v v v
r r r
For a more complete diagram including bidirectional flow, see Pipes.Core.
(<-<) :: Functor m => Proxy () b c' c m r -> Proxy a' a () b m r -> Proxy a' a c' c m r infixr 7 Source #
(>->
) with the arguments flipped
ListT
The list monad transformer, which extends a monad with non-determinism
The type variables signify:
m
- The base monada
- The values that the computationyield
s throughout its execution
For basic construction and composition of ListT
computations, much can be
accomplished using common typeclass methods.
return
corresponds toyield
, yielding a single value.- (
>>=
) corresponds tofor
, calling the second computation once for each time the first computationyield
s. mempty
neitheryield
s any values nor produces any effects in the base monad.- (
<>
) sequences two computations,yield
ing all the values of the first followed by all the values of the second. lift
converts an action in the base monad into a ListT computation which performs the action andyield
s a single value.
ListT
is a newtype wrapper for Producer
. You will likely need to use
Select
and enumerate
to convert back and forth between these two types
to take advantage of all the Producer
-related utilities that
Pipes.Prelude has to offer.
- To lift a plain list into a
ListT
computation, first applyeach
to turn the list into aProducer
. Then apply theSelect
constructor to convert fromProducer
toListT
. - For other ways to construct
ListT
computations, see the “Producers” section in Pipes.Prelude to buildProducer
s. These can then be converted toListT
usingSelect
. - To aggregate the values from a
ListT
computation (for example, to compute the sum of aListT
of numbers), first applyenumerate
to obtain aProducer
. Then see the “Folds” section in Pipes.Prelude to proceed.
Instances
class Enumerable t where Source #
Enumerable
generalizes Foldable
, converting effectful
containers to ListT
s.
Instances of Enumerable
must satisfy these two laws:
toListT (return r) = return r toListT $ do x <- m = do x <- toListT m f x toListT (f x)
In other words, toListT
is monad morphism.
Instances
Enumerable ListT Source # | |
Enumerable MaybeT Source # | |
Enumerable (ExceptT e) Source # | |
Enumerable (IdentityT :: (Type -> Type) -> Type -> Type) Source # | |
Utilities
every :: (Monad m, Enumerable t) => t m a -> Proxy x' x () a m () Source #
Convert an Enumerable
to a Producer
every
:: (Monad
m,Enumerable
t) => t m a ->Producer
a m ()
Re-exports
Control.Monad re-exports void
Control.Monad.IO.Class re-exports MonadIO
.
Control.Monad.Trans.Class re-exports MonadTrans
.
Control.Monad.Morph re-exports MFunctor
.
Data.Foldable re-exports Foldable
(the class name only).
class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where Source #
Monads that also support choice and failure.
Nothing
The identity of mplus
. It should also satisfy the equations
mzero >>= f = mzero v >> mzero = mzero
The default definition is
mzero = empty
mplus :: m a -> m a -> m a Source #
An associative operation. The default definition is
mplus = (<|>
)
Instances
void :: Functor f => f a -> f () Source #
discards or ignores the result of evaluation, such
as the return value of an void
valueIO
action.
Examples
Replace the contents of a
with unit:Maybe
Int
>>>
void Nothing
Nothing>>>
void (Just 3)
Just ()
Replace the contents of an
with unit, resulting in an Either
Int
Int
:Either
Int
()
>>>
void (Left 8675309)
Left 8675309>>>
void (Right 8675309)
Right ()
Replace every element of a list with unit:
>>>
void [1,2,3]
[(),(),()]
Replace the second element of a pair with unit:
>>>
void (1,2)
(1,())
Discard the result of an IO
action:
>>>
mapM print [1,2]
1 2 [(),()]>>>
void $ mapM print [1,2]
1 2
class Monad m => MonadIO (m :: Type -> Type) where Source #
Monads in which IO
computations may be embedded.
Any monad built by applying a sequence of monad transformers to the
IO
monad will be an instance of this class.
Instances should satisfy the following laws, which state that liftIO
is a transformer of monads:
liftIO :: IO a -> m a Source #
Lift a computation from the IO
monad.
This allows us to run IO computations in any monadic stack, so long as it supports these kinds of operations
(i.e. IO
is the base monad for the stack).
Example
import Control.Monad.Trans.State -- from the "transformers" library printState :: Show s => StateT s IO () printState = do state <- get liftIO $ print state
Had we omitted
, we would have ended up with this error:liftIO
• Couldn't match type ‘IO’ with ‘StateT s IO’ Expected type: StateT s IO () Actual type: IO ()
The important part here is the mismatch between StateT s IO ()
and
.IO
()
Luckily, we know of a function that takes an
and returns an IO
a(m a)
:
,
enabling us to run the program and see the expected results:liftIO
> evalStateT printState "hello" "hello" > evalStateT printState 3 3
Instances
MonadIO IO | Since: base-4.9.0.0 |
MonadIO Q | |
MonadIO m => MonadIO (ListT m) Source # | |
MonadIO m => MonadIO (ListT m) | |
MonadIO m => MonadIO (MaybeT m) | |
(Error e, MonadIO m) => MonadIO (ErrorT e m) | |
MonadIO m => MonadIO (ExceptT e m) | |
MonadIO m => MonadIO (IdentityT m) | |
MonadIO m => MonadIO (ReaderT r m) | |
MonadIO m => MonadIO (StateT s m) | |
MonadIO m => MonadIO (StateT s m) | |
(Monoid w, MonadIO m) => MonadIO (WriterT w m) | |
(Monoid w, MonadIO m) => MonadIO (WriterT w m) | |
MonadIO m => MonadIO (ContT r m) | |
(Monoid w, MonadIO m) => MonadIO (RWST r w s m) | |
(Monoid w, MonadIO m) => MonadIO (RWST r w s m) | |
MonadIO m => MonadIO (Proxy a' a b' b m) Source # | |
class MonadTrans (t :: (Type -> Type) -> Type -> Type) where Source #
The class of monad transformers. Instances should satisfy the
following laws, which state that lift
is a monad transformation:
lift :: Monad m => m a -> t m a Source #
Lift a computation from the argument monad to the constructed monad.
Instances
MonadTrans ListT Source # | |
MonadTrans ListT | |
MonadTrans MaybeT | |
MonadTrans (ErrorT e) | |
MonadTrans (ExceptT e) | |
MonadTrans (IdentityT :: (Type -> Type) -> Type -> Type) | |
MonadTrans (ReaderT r) | |
MonadTrans (StateT s) | |
MonadTrans (StateT s) | |
Monoid w => MonadTrans (WriterT w) | |
Monoid w => MonadTrans (WriterT w) | |
MonadTrans (ContT r) | |
Monoid w => MonadTrans (RWST r w s) | |
Monoid w => MonadTrans (RWST r w s) | |
MonadTrans (Proxy a' a b' b) Source # | |
class (MFunctor t, MonadTrans t) => MMonad (t :: (Type -> Type) -> Type -> Type) where Source #
A monad in the category of monads, using lift
from MonadTrans
as the
analog of return
and embed
as the analog of (=<<
):
embed lift = id embed f (lift m) = f m embed g (embed f t) = embed (\m -> embed g (f m)) t
embed :: forall (n :: Type -> Type) m b. Monad n => (forall a. m a -> t n a) -> t m b -> t n b Source #
class MFunctor (t :: (Type -> Type) -> k -> Type) where Source #
A functor in the category of monads, using hoist
as the analog of fmap
:
hoist (f . g) = hoist f . hoist g hoist id = id
hoist :: forall m n (b :: k). Monad m => (forall a. m a -> n a) -> t m b -> t n b Source #
Lift a monad morphism from m
to n
into a monad morphism from
(t m)
to (t n)
The first argument to hoist
must be a monad morphism, even though the
type system does not enforce this
Instances
MFunctor ListT Source # | |
MFunctor Lift | |
MFunctor MaybeT | |
MFunctor (Backwards :: (Type -> Type) -> Type -> Type) | |
MFunctor (ExceptT e :: (Type -> Type) -> Type -> Type) | |
MFunctor (IdentityT :: (Type -> Type) -> Type -> Type) | |
MFunctor (ReaderT r :: (Type -> Type) -> Type -> Type) | |
MFunctor (StateT s :: (Type -> Type) -> Type -> Type) | |
MFunctor (StateT s :: (Type -> Type) -> Type -> Type) | |
MFunctor (WriterT w :: (Type -> Type) -> Type -> Type) | |
MFunctor (WriterT w :: (Type -> Type) -> Type -> Type) | |
MFunctor (Product f :: (Type -> Type) -> Type -> Type) | |
Functor f => MFunctor (Compose f :: (Type -> Type) -> Type -> Type) | |
MFunctor (RWST r w s :: (Type -> Type) -> Type -> Type) | |
MFunctor (RWST r w s :: (Type -> Type) -> Type -> Type) | |
MFunctor (Proxy a' a b' b :: (Type -> Type) -> Type -> Type) Source # | |
class Foldable (t :: Type -> Type) Source #
The Foldable class represents data structures that can be reduced to a summary value one element at a time. Strict left-associative folds are a good fit for space-efficient reduction, while lazy right-associative folds are a good fit for corecursive iteration, or for folds that short-circuit after processing an initial subsequence of the structure's elements.
Instances can be derived automatically by enabling the DeriveFoldable
extension. For example, a derived instance for a binary tree might be:
{-# LANGUAGE DeriveFoldable #-} data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a) deriving Foldable
A more detailed description can be found in the Overview section of Data.Foldable.
For the class laws see the Laws section of Data.Foldable.
Instances
Foldable ZipList | Since: base-4.9.0.0 |
Defined in Control.Applicative fold :: Monoid m => ZipList m -> m Source # foldMap :: Monoid m => (a -> m) -> ZipList a -> m Source # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m Source # foldr :: (a -> b -> b) -> b -> ZipList a -> b Source # foldr' :: (a -> b -> b) -> b -> ZipList a -> b Source # foldl :: (b -> a -> b) -> b -> ZipList a -> b Source # foldl' :: (b -> a -> b) -> b -> ZipList a -> b Source # foldr1 :: (a -> a -> a) -> ZipList a -> a Source # foldl1 :: (a -> a -> a) -> ZipList a -> a Source # toList :: ZipList a -> [a] Source # null :: ZipList a -> Bool Source # length :: ZipList a -> Int Source # elem :: Eq a => a -> ZipList a -> Bool Source # maximum :: Ord a => ZipList a -> a Source # minimum :: Ord a => ZipList a -> a Source # | |
Foldable Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity fold :: Monoid m => Identity m -> m Source # foldMap :: Monoid m => (a -> m) -> Identity a -> m Source # foldMap' :: Monoid m => (a -> m) -> Identity a -> m Source # foldr :: (a -> b -> b) -> b -> Identity a -> b Source # foldr' :: (a -> b -> b) -> b -> Identity a -> b Source # foldl :: (b -> a -> b) -> b -> Identity a -> b Source # foldl' :: (b -> a -> b) -> b -> Identity a -> b Source # foldr1 :: (a -> a -> a) -> Identity a -> a Source # foldl1 :: (a -> a -> a) -> Identity a -> a Source # toList :: Identity a -> [a] Source # null :: Identity a -> Bool Source # length :: Identity a -> Int Source # elem :: Eq a => a -> Identity a -> Bool Source # maximum :: Ord a => Identity a -> a Source # minimum :: Ord a => Identity a -> a Source # | |
Foldable First | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # | |
Foldable Last | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # | |
Foldable Down | Since: base-4.12.0.0 |
Defined in Data.Foldable fold :: Monoid m => Down m -> m Source # foldMap :: Monoid m => (a -> m) -> Down a -> m Source # foldMap' :: Monoid m => (a -> m) -> Down a -> m Source # foldr :: (a -> b -> b) -> b -> Down a -> b Source # foldr' :: (a -> b -> b) -> b -> Down a -> b Source # foldl :: (b -> a -> b) -> b -> Down a -> b Source # foldl' :: (b -> a -> b) -> b -> Down a -> b Source # foldr1 :: (a -> a -> a) -> Down a -> a Source # foldl1 :: (a -> a -> a) -> Down a -> a Source # toList :: Down a -> [a] Source # null :: Down a -> Bool Source # length :: Down a -> Int Source # elem :: Eq a => a -> Down a -> Bool Source # maximum :: Ord a => Down a -> a Source # minimum :: Ord a => Down a -> a Source # | |
Foldable First | Since: base-4.9.0.0 |
Defined in Data.Semigroup fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # | |
Foldable Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # | |
Foldable Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup fold :: Monoid m => Max m -> m Source # foldMap :: Monoid m => (a -> m) -> Max a -> m Source # foldMap' :: Monoid m => (a -> m) -> Max a -> m Source # foldr :: (a -> b -> b) -> b -> Max a -> b Source # foldr' :: (a -> b -> b) -> b -> Max a -> b Source # foldl :: (b -> a -> b) -> b -> Max a -> b Source # foldl' :: (b -> a -> b) -> b -> Max a -> b Source # foldr1 :: (a -> a -> a) -> Max a -> a Source # foldl1 :: (a -> a -> a) -> Max a -> a Source # toList :: Max a -> [a] Source # null :: Max a -> Bool Source # length :: Max a -> Int Source # elem :: Eq a => a -> Max a -> Bool Source # maximum :: Ord a => Max a -> a Source # minimum :: Ord a => Max a -> a Source # | |
Foldable Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup fold :: Monoid m => Min m -> m Source # foldMap :: Monoid m => (a -> m) -> Min a -> m Source # foldMap' :: Monoid m => (a -> m) -> Min a -> m Source # foldr :: (a -> b -> b) -> b -> Min a -> b Source # foldr' :: (a -> b -> b) -> b -> Min a -> b Source # foldl :: (b -> a -> b) -> b -> Min a -> b Source # foldl' :: (b -> a -> b) -> b -> Min a -> b Source # foldr1 :: (a -> a -> a) -> Min a -> a Source # foldl1 :: (a -> a -> a) -> Min a -> a Source # toList :: Min a -> [a] Source # null :: Min a -> Bool Source # length :: Min a -> Int Source # elem :: Eq a => a -> Min a -> Bool Source # maximum :: Ord a => Min a -> a Source # minimum :: Ord a => Min a -> a Source # | |
Foldable Dual | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => Dual m -> m Source # foldMap :: Monoid m => (a -> m) -> Dual a -> m Source # foldMap' :: Monoid m => (a -> m) -> Dual a -> m Source # foldr :: (a -> b -> b) -> b -> Dual a -> b Source # foldr' :: (a -> b -> b) -> b -> Dual a -> b Source # foldl :: (b -> a -> b) -> b -> Dual a -> b Source # foldl' :: (b -> a -> b) -> b -> Dual a -> b Source # foldr1 :: (a -> a -> a) -> Dual a -> a Source # foldl1 :: (a -> a -> a) -> Dual a -> a Source # toList :: Dual a -> [a] Source # null :: Dual a -> Bool Source # length :: Dual a -> Int Source # elem :: Eq a => a -> Dual a -> Bool Source # maximum :: Ord a => Dual a -> a Source # minimum :: Ord a => Dual a -> a Source # | |
Foldable Product | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => Product m -> m Source # foldMap :: Monoid m => (a -> m) -> Product a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product a -> m Source # foldr :: (a -> b -> b) -> b -> Product a -> b Source # foldr' :: (a -> b -> b) -> b -> Product a -> b Source # foldl :: (b -> a -> b) -> b -> Product a -> b Source # foldl' :: (b -> a -> b) -> b -> Product a -> b Source # foldr1 :: (a -> a -> a) -> Product a -> a Source # foldl1 :: (a -> a -> a) -> Product a -> a Source # toList :: Product a -> [a] Source # null :: Product a -> Bool Source # length :: Product a -> Int Source # elem :: Eq a => a -> Product a -> Bool Source # maximum :: Ord a => Product a -> a Source # minimum :: Ord a => Product a -> a Source # | |
Foldable Sum | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => Sum m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum a -> m Source # foldr :: (a -> b -> b) -> b -> Sum a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum a -> b Source # foldl :: (b -> a -> b) -> b -> Sum a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum a -> b Source # foldr1 :: (a -> a -> a) -> Sum a -> a Source # foldl1 :: (a -> a -> a) -> Sum a -> a Source # toList :: Sum a -> [a] Source # null :: Sum a -> Bool Source # length :: Sum a -> Int Source # elem :: Eq a => a -> Sum a -> Bool Source # maximum :: Ord a => Sum a -> a Source # minimum :: Ord a => Sum a -> a Source # | |
Foldable Par1 | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => Par1 m -> m Source # foldMap :: Monoid m => (a -> m) -> Par1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> Par1 a -> m Source # foldr :: (a -> b -> b) -> b -> Par1 a -> b Source # foldr' :: (a -> b -> b) -> b -> Par1 a -> b Source # foldl :: (b -> a -> b) -> b -> Par1 a -> b Source # foldl' :: (b -> a -> b) -> b -> Par1 a -> b Source # foldr1 :: (a -> a -> a) -> Par1 a -> a Source # foldl1 :: (a -> a -> a) -> Par1 a -> a Source # toList :: Par1 a -> [a] Source # null :: Par1 a -> Bool Source # length :: Par1 a -> Int Source # elem :: Eq a => a -> Par1 a -> Bool Source # maximum :: Ord a => Par1 a -> a Source # minimum :: Ord a => Par1 a -> a Source # | |
Foldable NonEmpty | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => NonEmpty m -> m Source # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldr1 :: (a -> a -> a) -> NonEmpty a -> a Source # foldl1 :: (a -> a -> a) -> NonEmpty a -> a Source # toList :: NonEmpty a -> [a] Source # null :: NonEmpty a -> Bool Source # length :: NonEmpty a -> Int Source # elem :: Eq a => a -> NonEmpty a -> Bool Source # maximum :: Ord a => NonEmpty a -> a Source # minimum :: Ord a => NonEmpty a -> a Source # | |
Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable fold :: Monoid m => Maybe m -> m Source # foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source # foldr :: (a -> b -> b) -> b -> Maybe a -> b Source # foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source # foldl :: (b -> a -> b) -> b -> Maybe a -> b Source # foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source # foldr1 :: (a -> a -> a) -> Maybe a -> a Source # foldl1 :: (a -> a -> a) -> Maybe a -> a Source # toList :: Maybe a -> [a] Source # null :: Maybe a -> Bool Source # length :: Maybe a -> Int Source # elem :: Eq a => a -> Maybe a -> Bool Source # maximum :: Ord a => Maybe a -> a Source # minimum :: Ord a => Maybe a -> a Source # | |
Foldable Solo | Since: base-4.15 |
Defined in Data.Foldable fold :: Monoid m => Solo m -> m Source # foldMap :: Monoid m => (a -> m) -> Solo a -> m Source # foldMap' :: Monoid m => (a -> m) -> Solo a -> m Source # foldr :: (a -> b -> b) -> b -> Solo a -> b Source # foldr' :: (a -> b -> b) -> b -> Solo a -> b Source # foldl :: (b -> a -> b) -> b -> Solo a -> b Source # foldl' :: (b -> a -> b) -> b -> Solo a -> b Source # foldr1 :: (a -> a -> a) -> Solo a -> a Source # foldl1 :: (a -> a -> a) -> Solo a -> a Source # toList :: Solo a -> [a] Source # null :: Solo a -> Bool Source # length :: Solo a -> Int Source # elem :: Eq a => a -> Solo a -> Bool Source # maximum :: Ord a => Solo a -> a Source # minimum :: Ord a => Solo a -> a Source # | |
Foldable [] | Since: base-2.1 |
Defined in Data.Foldable fold :: Monoid m => [m] -> m Source # foldMap :: Monoid m => (a -> m) -> [a] -> m Source # foldMap' :: Monoid m => (a -> m) -> [a] -> m Source # foldr :: (a -> b -> b) -> b -> [a] -> b Source # foldr' :: (a -> b -> b) -> b -> [a] -> b Source # foldl :: (b -> a -> b) -> b -> [a] -> b Source # foldl' :: (b -> a -> b) -> b -> [a] -> b Source # foldr1 :: (a -> a -> a) -> [a] -> a Source # foldl1 :: (a -> a -> a) -> [a] -> a Source # elem :: Eq a => a -> [a] -> Bool Source # maximum :: Ord a => [a] -> a Source # minimum :: Ord a => [a] -> a Source # | |
Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable fold :: Monoid m => Either a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # toList :: Either a a0 -> [a0] Source # null :: Either a a0 -> Bool Source # length :: Either a a0 -> Int Source # elem :: Eq a0 => a0 -> Either a a0 -> Bool Source # maximum :: Ord a0 => Either a a0 -> a0 Source # minimum :: Ord a0 => Either a a0 -> a0 Source # | |
Foldable (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Data.Foldable fold :: Monoid m => Proxy m -> m Source # foldMap :: Monoid m => (a -> m) -> Proxy a -> m Source # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m Source # foldr :: (a -> b -> b) -> b -> Proxy a -> b Source # foldr' :: (a -> b -> b) -> b -> Proxy a -> b Source # foldl :: (b -> a -> b) -> b -> Proxy a -> b Source # foldl' :: (b -> a -> b) -> b -> Proxy a -> b Source # foldr1 :: (a -> a -> a) -> Proxy a -> a Source # foldl1 :: (a -> a -> a) -> Proxy a -> a Source # toList :: Proxy a -> [a] Source # null :: Proxy a -> Bool Source # length :: Proxy a -> Int Source # elem :: Eq a => a -> Proxy a -> Bool Source # maximum :: Ord a => Proxy a -> a Source # minimum :: Ord a => Proxy a -> a Source # | |
Foldable (Arg a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup fold :: Monoid m => Arg a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # toList :: Arg a a0 -> [a0] Source # null :: Arg a a0 -> Bool Source # length :: Arg a a0 -> Int Source # elem :: Eq a0 => a0 -> Arg a a0 -> Bool Source # maximum :: Ord a0 => Arg a a0 -> a0 Source # minimum :: Ord a0 => Arg a a0 -> a0 Source # | |
Foldable (Array i) | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => Array i m -> m Source # foldMap :: Monoid m => (a -> m) -> Array i a -> m Source # foldMap' :: Monoid m => (a -> m) -> Array i a -> m Source # foldr :: (a -> b -> b) -> b -> Array i a -> b Source # foldr' :: (a -> b -> b) -> b -> Array i a -> b Source # foldl :: (b -> a -> b) -> b -> Array i a -> b Source # foldl' :: (b -> a -> b) -> b -> Array i a -> b Source # foldr1 :: (a -> a -> a) -> Array i a -> a Source # foldl1 :: (a -> a -> a) -> Array i a -> a Source # toList :: Array i a -> [a] Source # null :: Array i a -> Bool Source # length :: Array i a -> Int Source # elem :: Eq a => a -> Array i a -> Bool Source # maximum :: Ord a => Array i a -> a Source # minimum :: Ord a => Array i a -> a Source # | |
Foldable (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => U1 m -> m Source # foldMap :: Monoid m => (a -> m) -> U1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> U1 a -> m Source # foldr :: (a -> b -> b) -> b -> U1 a -> b Source # foldr' :: (a -> b -> b) -> b -> U1 a -> b Source # foldl :: (b -> a -> b) -> b -> U1 a -> b Source # foldl' :: (b -> a -> b) -> b -> U1 a -> b Source # foldr1 :: (a -> a -> a) -> U1 a -> a Source # foldl1 :: (a -> a -> a) -> U1 a -> a Source # toList :: U1 a -> [a] Source # length :: U1 a -> Int Source # elem :: Eq a => a -> U1 a -> Bool Source # maximum :: Ord a => U1 a -> a Source # minimum :: Ord a => U1 a -> a Source # | |
Foldable (UAddr :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => UAddr m -> m Source # foldMap :: Monoid m => (a -> m) -> UAddr a -> m Source # foldMap' :: Monoid m => (a -> m) -> UAddr a -> m Source # foldr :: (a -> b -> b) -> b -> UAddr a -> b Source # foldr' :: (a -> b -> b) -> b -> UAddr a -> b Source # foldl :: (b -> a -> b) -> b -> UAddr a -> b Source # foldl' :: (b -> a -> b) -> b -> UAddr a -> b Source # foldr1 :: (a -> a -> a) -> UAddr a -> a Source # foldl1 :: (a -> a -> a) -> UAddr a -> a Source # toList :: UAddr a -> [a] Source # null :: UAddr a -> Bool Source # length :: UAddr a -> Int Source # elem :: Eq a => a -> UAddr a -> Bool Source # maximum :: Ord a => UAddr a -> a Source # minimum :: Ord a => UAddr a -> a Source # | |
Foldable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => UChar m -> m Source # foldMap :: Monoid m => (a -> m) -> UChar a -> m Source # foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source # foldr :: (a -> b -> b) -> b -> UChar a -> b Source # foldr' :: (a -> b -> b) -> b -> UChar a -> b Source # foldl :: (b -> a -> b) -> b -> UChar a -> b Source # foldl' :: (b -> a -> b) -> b -> UChar a -> b Source # foldr1 :: (a -> a -> a) -> UChar a -> a Source # foldl1 :: (a -> a -> a) -> UChar a -> a Source # toList :: UChar a -> [a] Source # null :: UChar a -> Bool Source # length :: UChar a -> Int Source # elem :: Eq a => a -> UChar a -> Bool Source # maximum :: Ord a => UChar a -> a Source # minimum :: Ord a => UChar a -> a Source # | |
Foldable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => UDouble m -> m Source # foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source # foldr :: (a -> b -> b) -> b -> UDouble a -> b Source # foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source # foldl :: (b -> a -> b) -> b -> UDouble a -> b Source # foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source # foldr1 :: (a -> a -> a) -> UDouble a -> a Source # foldl1 :: (a -> a -> a) -> UDouble a -> a Source # toList :: UDouble a -> [a] Source # null :: UDouble a -> Bool Source # length :: UDouble a -> Int Source # elem :: Eq a => a -> UDouble a -> Bool Source # maximum :: Ord a => UDouble a -> a Source # minimum :: Ord a => UDouble a -> a Source # | |
Foldable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => UFloat m -> m Source # foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source # foldr :: (a -> b -> b) -> b -> UFloat a -> b Source # foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source # foldl :: (b -> a -> b) -> b -> UFloat a -> b Source # foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source # foldr1 :: (a -> a -> a) -> UFloat a -> a Source # foldl1 :: (a -> a -> a) -> UFloat a -> a Source # toList :: UFloat a -> [a] Source # null :: UFloat a -> Bool Source # length :: UFloat a -> Int Source # elem :: Eq a => a -> UFloat a -> Bool Source # maximum :: Ord a => UFloat a -> a Source # minimum :: Ord a => UFloat a -> a Source # | |
Foldable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => UInt m -> m Source # foldMap :: Monoid m => (a -> m) -> UInt a -> m Source # foldMap' :: Monoid m => (a -> m) -> UInt a -> m Source # foldr :: (a -> b -> b) -> b -> UInt a -> b Source # foldr' :: (a -> b -> b) -> b -> UInt a -> b Source # foldl :: (b -> a -> b) -> b -> UInt a -> b Source # foldl' :: (b -> a -> b) -> b -> UInt a -> b Source # foldr1 :: (a -> a -> a) -> UInt a -> a Source # foldl1 :: (a -> a -> a) -> UInt a -> a Source # toList :: UInt a -> [a] Source # null :: UInt a -> Bool Source # length :: UInt a -> Int Source # elem :: Eq a => a -> UInt a -> Bool Source # maximum :: Ord a => UInt a -> a Source # minimum :: Ord a => UInt a -> a Source # | |
Foldable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => UWord m -> m Source # foldMap :: Monoid m => (a -> m) -> UWord a -> m Source # foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source # foldr :: (a -> b -> b) -> b -> UWord a -> b Source # foldr' :: (a -> b -> b) -> b -> UWord a -> b Source # foldl :: (b -> a -> b) -> b -> UWord a -> b Source # foldl' :: (b -> a -> b) -> b -> UWord a -> b Source # foldr1 :: (a -> a -> a) -> UWord a -> a Source # foldl1 :: (a -> a -> a) -> UWord a -> a Source # toList :: UWord a -> [a] Source # null :: UWord a -> Bool Source # length :: UWord a -> Int Source # elem :: Eq a => a -> UWord a -> Bool Source # maximum :: Ord a => UWord a -> a Source # minimum :: Ord a => UWord a -> a Source # | |
Foldable (V1 :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => V1 m -> m Source # foldMap :: Monoid m => (a -> m) -> V1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> V1 a -> m Source # foldr :: (a -> b -> b) -> b -> V1 a -> b Source # foldr' :: (a -> b -> b) -> b -> V1 a -> b Source # foldl :: (b -> a -> b) -> b -> V1 a -> b Source # foldl' :: (b -> a -> b) -> b -> V1 a -> b Source # foldr1 :: (a -> a -> a) -> V1 a -> a Source # foldl1 :: (a -> a -> a) -> V1 a -> a Source # toList :: V1 a -> [a] Source # length :: V1 a -> Int Source # elem :: Eq a => a -> V1 a -> Bool Source # maximum :: Ord a => V1 a -> a Source # minimum :: Ord a => V1 a -> a Source # | |
Foldable m => Foldable (ListT m) Source # | |
Defined in Pipes fold :: Monoid m0 => ListT m m0 -> m0 Source # foldMap :: Monoid m0 => (a -> m0) -> ListT m a -> m0 Source # foldMap' :: Monoid m0 => (a -> m0) -> ListT m a -> m0 Source # foldr :: (a -> b -> b) -> b -> ListT m a -> b Source # foldr' :: (a -> b -> b) -> b -> ListT m a -> b Source # foldl :: (b -> a -> b) -> b -> ListT m a -> b Source # foldl' :: (b -> a -> b) -> b -> ListT m a -> b Source # foldr1 :: (a -> a -> a) -> ListT m a -> a Source # foldl1 :: (a -> a -> a) -> ListT m a -> a Source # toList :: ListT m a -> [a] Source # null :: ListT m a -> Bool Source # length :: ListT m a -> Int Source # elem :: Eq a => a -> ListT m a -> Bool Source # maximum :: Ord a => ListT m a -> a Source # minimum :: Ord a => ListT m a -> a Source # | |
Foldable f => Foldable (ListT f) | |
Defined in Control.Monad.Trans.List fold :: Monoid m => ListT f m -> m Source # foldMap :: Monoid m => (a -> m) -> ListT f a -> m Source # foldMap' :: Monoid m => (a -> m) -> ListT f a -> m Source # foldr :: (a -> b -> b) -> b -> ListT f a -> b Source # foldr' :: (a -> b -> b) -> b -> ListT f a -> b Source # foldl :: (b -> a -> b) -> b -> ListT f a -> b Source # foldl' :: (b -> a -> b) -> b -> ListT f a -> b Source # foldr1 :: (a -> a -> a) -> ListT f a -> a Source # foldl1 :: (a -> a -> a) -> ListT f a -> a Source # toList :: ListT f a -> [a] Source # null :: ListT f a -> Bool Source # length :: ListT f a -> Int Source # elem :: Eq a => a -> ListT f a -> Bool Source # maximum :: Ord a => ListT f a -> a Source # minimum :: Ord a => ListT f a -> a Source # | |
Foldable f => Foldable (MaybeT f) | |
Defined in Control.Monad.Trans.Maybe fold :: Monoid m => MaybeT f m -> m Source # foldMap :: Monoid m => (a -> m) -> MaybeT f a -> m Source # foldMap' :: Monoid m => (a -> m) -> MaybeT f a -> m Source # foldr :: (a -> b -> b) -> b -> MaybeT f a -> b Source # foldr' :: (a -> b -> b) -> b -> MaybeT f a -> b Source # foldl :: (b -> a -> b) -> b -> MaybeT f a -> b Source # foldl' :: (b -> a -> b) -> b -> MaybeT f a -> b Source # foldr1 :: (a -> a -> a) -> MaybeT f a -> a Source # foldl1 :: (a -> a -> a) -> MaybeT f a -> a Source # toList :: MaybeT f a -> [a] Source # null :: MaybeT f a -> Bool Source # length :: MaybeT f a -> Int Source # elem :: Eq a => a -> MaybeT f a -> Bool Source # maximum :: Ord a => MaybeT f a -> a Source # minimum :: Ord a => MaybeT f a -> a Source # | |
Foldable ((,) a) | Since: base-4.7.0.0 |
Defined in Data.Foldable fold :: Monoid m => (a, m) -> m Source # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m Source # foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m Source # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b Source # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b Source # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b Source # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b Source # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source # toList :: (a, a0) -> [a0] Source # null :: (a, a0) -> Bool Source # length :: (a, a0) -> Int Source # elem :: Eq a0 => a0 -> (a, a0) -> Bool Source # maximum :: Ord a0 => (a, a0) -> a0 Source # minimum :: Ord a0 => (a, a0) -> a0 Source # | |
Foldable f => Foldable (Ap f) | Since: base-4.12.0.0 |
Defined in Data.Foldable fold :: Monoid m => Ap f m -> m Source # foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m Source # foldr :: (a -> b -> b) -> b -> Ap f a -> b Source # foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source # foldl :: (b -> a -> b) -> b -> Ap f a -> b Source # foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source # foldr1 :: (a -> a -> a) -> Ap f a -> a Source # foldl1 :: (a -> a -> a) -> Ap f a -> a Source # toList :: Ap f a -> [a] Source # null :: Ap f a -> Bool Source # length :: Ap f a -> Int Source # elem :: Eq a => a -> Ap f a -> Bool Source # maximum :: Ord a => Ap f a -> a Source # minimum :: Ord a => Ap f a -> a Source # | |
Foldable f => Foldable (Alt f) | Since: base-4.12.0.0 |
Defined in Data.Foldable fold :: Monoid m => Alt f m -> m Source # foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m Source # foldr :: (a -> b -> b) -> b -> Alt f a -> b Source # foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source # foldl :: (b -> a -> b) -> b -> Alt f a -> b Source # foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source # foldr1 :: (a -> a -> a) -> Alt f a -> a Source # foldl1 :: (a -> a -> a) -> Alt f a -> a Source # toList :: Alt f a -> [a] Source # null :: Alt f a -> Bool Source # length :: Alt f a -> Int Source # elem :: Eq a => a -> Alt f a -> Bool Source # maximum :: Ord a => Alt f a -> a Source # minimum :: Ord a => Alt f a -> a Source # | |
Foldable f => Foldable (Rec1 f) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => Rec1 f m -> m Source # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m Source # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b Source # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b Source # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b Source # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b Source # foldr1 :: (a -> a -> a) -> Rec1 f a -> a Source # foldl1 :: (a -> a -> a) -> Rec1 f a -> a Source # toList :: Rec1 f a -> [a] Source # null :: Rec1 f a -> Bool Source # length :: Rec1 f a -> Int Source # elem :: Eq a => a -> Rec1 f a -> Bool Source # maximum :: Ord a => Rec1 f a -> a Source # minimum :: Ord a => Rec1 f a -> a Source # | |
Foldable f => Foldable (Backwards f) | Derived instance. |
Defined in Control.Applicative.Backwards fold :: Monoid m => Backwards f m -> m Source # foldMap :: Monoid m => (a -> m) -> Backwards f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Backwards f a -> m Source # foldr :: (a -> b -> b) -> b -> Backwards f a -> b Source # foldr' :: (a -> b -> b) -> b -> Backwards f a -> b Source # foldl :: (b -> a -> b) -> b -> Backwards f a -> b Source # foldl' :: (b -> a -> b) -> b -> Backwards f a -> b Source # foldr1 :: (a -> a -> a) -> Backwards f a -> a Source # foldl1 :: (a -> a -> a) -> Backwards f a -> a Source # toList :: Backwards f a -> [a] Source # null :: Backwards f a -> Bool Source # length :: Backwards f a -> Int Source # elem :: Eq a => a -> Backwards f a -> Bool Source # maximum :: Ord a => Backwards f a -> a Source # minimum :: Ord a => Backwards f a -> a Source # | |
Foldable f => Foldable (ErrorT e f) | |
Defined in Control.Monad.Trans.Error fold :: Monoid m => ErrorT e f m -> m Source # foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m Source # foldMap' :: Monoid m => (a -> m) -> ErrorT e f a -> m Source # foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b Source # foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b Source # foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b Source # foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b Source # foldr1 :: (a -> a -> a) -> ErrorT e f a -> a Source # foldl1 :: (a -> a -> a) -> ErrorT e f a -> a Source # toList :: ErrorT e f a -> [a] Source # null :: ErrorT e f a -> Bool Source # length :: ErrorT e f a -> Int Source # elem :: Eq a => a -> ErrorT e f a -> Bool Source # maximum :: Ord a => ErrorT e f a -> a Source # minimum :: Ord a => ErrorT e f a -> a Source # | |
Foldable f => Foldable (ExceptT e f) | |
Defined in Control.Monad.Trans.Except fold :: Monoid m => ExceptT e f m -> m Source # foldMap :: Monoid m => (a -> m) -> ExceptT e f a -> m Source # foldMap' :: Monoid m => (a -> m) -> ExceptT e f a -> m Source # foldr :: (a -> b -> b) -> b -> ExceptT e f a -> b Source # foldr' :: (a -> b -> b) -> b -> ExceptT e f a -> b Source # foldl :: (b -> a -> b) -> b -> ExceptT e f a -> b Source # foldl' :: (b -> a -> b) -> b -> ExceptT e f a -> b Source # foldr1 :: (a -> a -> a) -> ExceptT e f a -> a Source # foldl1 :: (a -> a -> a) -> ExceptT e f a -> a Source # toList :: ExceptT e f a -> [a] Source # null :: ExceptT e f a -> Bool Source # length :: ExceptT e f a -> Int Source # elem :: Eq a => a -> ExceptT e f a -> Bool Source # maximum :: Ord a => ExceptT e f a -> a Source # minimum :: Ord a => ExceptT e f a -> a Source # | |
Foldable f => Foldable (IdentityT f) | |
Defined in Control.Monad.Trans.Identity fold :: Monoid m => IdentityT f m -> m Source # foldMap :: Monoid m => (a -> m) -> IdentityT f a -> m Source # foldMap' :: Monoid m => (a -> m) -> IdentityT f a -> m Source # foldr :: (a -> b -> b) -> b -> IdentityT f a -> b Source # foldr' :: (a -> b -> b) -> b -> IdentityT f a -> b Source # foldl :: (b -> a -> b) -> b -> IdentityT f a -> b Source # foldl' :: (b -> a -> b) -> b -> IdentityT f a -> b Source # foldr1 :: (a -> a -> a) -> IdentityT f a -> a Source # foldl1 :: (a -> a -> a) -> IdentityT f a -> a Source # toList :: IdentityT f a -> [a] Source # null :: IdentityT f a -> Bool Source # length :: IdentityT f a -> Int Source # elem :: Eq a => a -> IdentityT f a -> Bool Source # maximum :: Ord a => IdentityT f a -> a Source # minimum :: Ord a => IdentityT f a -> a Source # | |
Foldable f => Foldable (WriterT w f) | |
Defined in Control.Monad.Trans.Writer.Lazy fold :: Monoid m => WriterT w f m -> m Source # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldr1 :: (a -> a -> a) -> WriterT w f a -> a Source # foldl1 :: (a -> a -> a) -> WriterT w f a -> a Source # toList :: WriterT w f a -> [a] Source # null :: WriterT w f a -> Bool Source # length :: WriterT w f a -> Int Source # elem :: Eq a => a -> WriterT w f a -> Bool Source # maximum :: Ord a => WriterT w f a -> a Source # minimum :: Ord a => WriterT w f a -> a Source # | |
Foldable f => Foldable (WriterT w f) | |
Defined in Control.Monad.Trans.Writer.Strict fold :: Monoid m => WriterT w f m -> m Source # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldr1 :: (a -> a -> a) -> WriterT w f a -> a Source # foldl1 :: (a -> a -> a) -> WriterT w f a -> a Source # toList :: WriterT w f a -> [a] Source # null :: WriterT w f a -> Bool Source # length :: WriterT w f a -> Int Source # elem :: Eq a => a -> WriterT w f a -> Bool Source # maximum :: Ord a => WriterT w f a -> a Source # minimum :: Ord a => WriterT w f a -> a Source # | |
(Foldable f, Foldable g) => Foldable (f :*: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => (f :*: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :*: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :*: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :*: g) a -> a Source # toList :: (f :*: g) a -> [a] Source # null :: (f :*: g) a -> Bool Source # length :: (f :*: g) a -> Int Source # elem :: Eq a => a -> (f :*: g) a -> Bool Source # maximum :: Ord a => (f :*: g) a -> a Source # minimum :: Ord a => (f :*: g) a -> a Source # | |
(Foldable f, Foldable g) => Foldable (f :+: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => (f :+: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a Source # toList :: (f :+: g) a -> [a] Source # null :: (f :+: g) a -> Bool Source # length :: (f :+: g) a -> Int Source # elem :: Eq a => a -> (f :+: g) a -> Bool Source # maximum :: Ord a => (f :+: g) a -> a Source # minimum :: Ord a => (f :+: g) a -> a Source # | |
Foldable (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => K1 i c m -> m Source # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m Source # foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m Source # foldr :: (a -> b -> b) -> b -> K1 i c a -> b Source # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b Source # foldl :: (b -> a -> b) -> b -> K1 i c a -> b Source # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b Source # foldr1 :: (a -> a -> a) -> K1 i c a -> a Source # foldl1 :: (a -> a -> a) -> K1 i c a -> a Source # toList :: K1 i c a -> [a] Source # null :: K1 i c a -> Bool Source # length :: K1 i c a -> Int Source # elem :: Eq a => a -> K1 i c a -> Bool Source # maximum :: Ord a => K1 i c a -> a Source # minimum :: Ord a => K1 i c a -> a Source # | |
(Foldable f, Foldable g) => Foldable (f :.: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable fold :: Monoid m => (f :.: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a Source # toList :: (f :.: g) a -> [a] Source # null :: (f :.: g) a -> Bool Source # length :: (f :.: g) a -> Int Source # elem :: Eq a => a -> (f :.: g) a -> Bool Source # maximum :: Ord a => (f :.: g) a -> a Source # minimum :: Ord a => (f :.: g) a -> a Source # | |
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 Source # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m Source # foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m Source # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b Source # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b Source # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b Source # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b Source # foldr1 :: (a -> a -> a) -> M1 i c f a -> a Source # foldl1 :: (a -> a -> a) -> M1 i c f a -> a Source # toList :: M1 i c f a -> [a] Source # null :: M1 i c f a -> Bool Source # length :: M1 i c f a -> Int Source # elem :: Eq a => a -> M1 i c f a -> Bool Source # maximum :: Ord a => M1 i c f a -> a Source # minimum :: Ord a => M1 i c f a -> a Source # |