Safe Haskell  Trustworthy 

Language  Haskell2010 
 data Stream f m r
 yields :: (Monad m, Functor f) => f r > Stream f m r
 effect :: (Monad m, Functor f) => m (Stream f m r) > Stream f m r
 wrap :: (Monad m, Functor f) => f (Stream f m r) > Stream f m r
 replicates :: (Monad m, Functor f) => Int > f () > Stream f m ()
 repeats :: (Monad m, Functor f) => f () > Stream f m r
 repeatsM :: (Monad m, Functor f) => m (f ()) > Stream f m r
 unfold :: (Monad m, Functor f) => (s > m (Either r (f s))) > s > Stream f m r
 never :: (Monad m, Applicative f) => Stream f m r
 untilJust :: (Monad m, Applicative f) => m (Maybe r) > Stream f m r
 streamBuild :: (forall b. (r > b) > (m b > b) > (f b > b) > b) > Stream f m r
 delays :: (MonadIO m, Applicative f) => Double > Stream f m r
 maps :: (Monad m, Functor f) => (forall x. f x > g x) > Stream f m r > Stream g m r
 mapsM :: (Monad m, Functor f) => (forall x. f x > m (g x)) > Stream f m r > Stream g m r
 mapped :: (Monad m, Functor f) => (forall x. f x > m (g x)) > Stream f m r > Stream g m r
 distribute :: (Monad m, Functor f, MonadTrans t, MFunctor t, Monad (t (Stream f m))) => Stream f (t m) r > t (Stream f m) r
 groups :: (Monad m, Functor f, Functor g) => Stream (Sum f g) m r > Stream (Sum (Stream f m) (Stream g m)) m r
 inspect :: (Functor f, Monad m) => Stream f m r > m (Either r (f (Stream f m r)))
 splitsAt :: (Monad m, Functor f) => Int > Stream f m r > Stream f m (Stream f m r)
 takes :: (Monad m, Functor f) => Int > Stream f m r > Stream f m ()
 chunksOf :: (Monad m, Functor f) => Int > Stream f m r > Stream (Stream f m) m r
 concats :: (Monad m, Functor f) => Stream (Stream f m) m r > Stream f m r
 intercalates :: (Monad m, Monad (t m), MonadTrans t) => t m x > Stream (t m) m r > t m r
 cutoff :: (Monad m, Functor f) => Int > Stream f m r > Stream f m (Maybe r)
 zipsWith :: (Monad m, Functor f, Functor g, Functor h) => (forall x y. f x > g y > h (x, y)) > Stream f m r > Stream g m r > Stream h m r
 zips :: (Monad m, Functor f, Functor g) => Stream f m r > Stream g m r > Stream (Compose f g) m r
 unzips :: (Monad m, Functor f, Functor g) => Stream (Compose f g) m r > Stream f (Stream g m) r
 interleaves :: (Monad m, Applicative h) => Stream h m r > Stream h m r > Stream h m r
 separate :: (Monad m, Functor f, Functor g) => Stream (Sum f g) m r > Stream f (Stream g m) r
 unseparate :: (Monad m, Functor f, Functor g) => Stream f (Stream g m) r > Stream (Sum f g) m r
 decompose :: (Monad m, Functor f) => Stream (Compose m f) m r > Stream f m r
 mapsM_ :: (Functor f, Monad m) => (forall x. f x > m x) > Stream f m r > m r
 run :: Monad m => Stream m m r > m r
 streamFold :: (Functor f, Monad m) => (r > b) > (m b > b) > (f b > b) > Stream f m r > b
 iterTM :: (Functor f, Monad m, MonadTrans t, Monad (t m)) => (f (t m a) > t m a) > Stream f m a > t m a
 iterT :: (Functor f, Monad m) => (f (m a) > m a) > Stream f m a > m a
 destroy :: (Functor f, Monad m) => Stream f m r > (f b > b) > (m b > b) > (r > b) > b
 data Of a b = !a :> b
 lazily :: Of a b > (a, b)
 strictly :: (a, b) > Of a b
 bracketStream :: (Functor f, MonadResource m) => IO a > (a > IO ()) > (a > Stream f m b) > Stream f m b
 class MFunctor t where
 class (MFunctor t, MonadTrans t) => MMonad t where
 class MonadTrans t where
 class Monad m => MonadIO m where
 newtype Compose f g a :: (* > *) > (* > *) > * > * = Compose {
 getCompose :: f (g a)
 data Sum f g a :: (* > *) > (* > *) > * > *
 newtype Identity a :: * > * = Identity {
 runIdentity :: a
 class Applicative f => Alternative f where
 (<>) :: f a > f a > f a
 class Monad m => MonadThrow m where
 class (MonadThrow m, MonadIO m, Applicative m, MonadBase IO m) => MonadResource m where
 liftResourceT :: ResourceT IO a > m a
 class (Applicative b, Applicative m, Monad b, Monad m) => MonadBase b m  m > b where
 liftBase :: b α > m α
 data ResourceT m a :: (* > *) > * > *
 runResourceT :: MonadBaseControl IO m => ResourceT m a > m a
 class Bifunctor p where
 join :: Monad m => m (m a) > m a
 liftM :: Monad m => (a1 > r) > m a1 > m r
 liftM2 :: Monad m => (a1 > a2 > r) > m a1 > m a2 > m r
 liftA2 :: Applicative f => (a > b > c) > f a > f b > f c
 liftA3 :: Applicative f => (a > b > c > d) > f a > f b > f c > f d
 void :: Functor f => f a > f ()
 (<>) :: Monoid m => m > m > m
An iterable streaming monad transformer
The Stream
data type can be used to represent any effectful
succession of steps arising in some monad.
The form of the steps is specified by the first ("functor")
parameter in Stream f m r
. The monad of the underlying effects
is expressed by the second parameter.
This module exports combinators that pertain to that general case. Some of these are quite abstract and pervade any use of the library, e.g.
maps :: (forall x . f x > g x) > Stream f m r > Stream g m r mapped :: (forall x . f x > m (g x)) > Stream f m r > Stream g m r hoist :: (forall x . m x > n x) > Stream f m r > Stream f n r  from the MFunctor instance concats :: Stream (Stream f m) m r > Stream f m r
(assuming here and thoughout that m
or n
satisfies a Monad
constraint, and
f
or g
a Functor
constraint.)
Others are surprisingly determinate in content:
chunksOf :: Int > Stream f m r > Stream (Stream f m) m r splitsAt :: Int > Stream f m r > Stream f m (Stream f m r) zipsWith :: (forall x y. f x > g y > h (x, y)) > Stream f m r > Stream g m r > Stream h m r intercalates :: Stream f m () > Stream (Stream f m) m r > Stream f m r unzips :: Stream (Compose f g) m r > Stream f (Stream g m) r separate :: Stream (Sum f g) m r > Stream f (Stream g) m r  cp. partitionEithers unseparate :: Stream f (Stream g) m r > Stream (Sum f g) m r groups :: Stream (Sum f g) m r > Stream (Sum (Stream f m) (Stream g m)) m r
One way to see that any streaming library needs some such general type is
that it is required to represent the segmentation of a stream, and to
express the equivalents of Prelude/Data.List
combinators that involve
'lists of lists' and the like. See for example this
post
on the correct expression of a streaming 'lines' function.
The module Streaming.Prelude
exports combinators relating to
Stream (Of a) m r
where Of a r = !a :> r
is a leftstrict pair.
This expresses the concept of a Producer
or Source
or Generator
and
easily interoperates with types with such names in e.g. conduit
,
iostreams
and pipes
.
Constructing a Stream
on a given functor
yields :: (Monad m, Functor f) => f r > Stream f m r Source
yields
is like lift
for items in the streamed functor.
It makes a singleton or onelayer succession.
lift :: (Monad m, Functor f) => m r > Stream f m r yields :: (Monad m, Functor f) => f r > Stream f m r
Viewed in another light, it is like a functorgeneral version of yield
:
S.yield a = yields (a :> ())
effect :: (Monad m, Functor f) => m (Stream f m r) > Stream f m r Source
Wrap an effect that returns a stream
effect = join . lift
replicates :: (Monad m, Functor f) => Int > f () > Stream f m () Source
Repeat a functorial layer, command or instruction a fixed number of times.
replicates n = takes n . repeats
repeats :: (Monad m, Functor f) => f () > Stream f m r Source
Repeat a functorial layer (a "command" or "instruction") forever.
repeatsM :: (Monad m, Functor f) => m (f ()) > Stream f m r Source
Repeat an effect containing a functorial layer, command or instruction forever.
unfold :: (Monad m, Functor f) => (s > m (Either r (f s))) > s > Stream f m r Source
Build a Stream
by unfolding steps starting from a seed. See also
the specialized unfoldr
in the prelude.
unfold inspect = id  modulo the quotient we work with unfold Pipes.next :: Monad m => Producer a m r > Stream ((,) a) m r unfold (curry (:>) . Pipes.next) :: Monad m => Producer a m r > Stream (Of a) m r
never :: (Monad m, Applicative f) => Stream f m r Source
never
interleaves the pure applicative action with the return of the monad forever.
It is the empty
of the Alternative
instance, thus
never <> a = a a <> never = a
and so on. If w is a monoid then never :: Stream (Of w) m r
is
the infinite sequence of mempty
, and
str1 <> str2
appends the elements monoidally until one of streams ends.
Thus we have, e.g.
>>>
S.stdoutLn $ S.take 2 $ S.stdinLn <> S.repeat " " <> S.stdinLn <> S.repeat " " <> S.stdinLn
1<Enter> 2<Enter> 3<Enter> 1 2 3 4<Enter> 5<Enter> 6<Enter> 4 5 6
This is equivalent to
>>>
S.stdoutLn $ S.take 2 $ foldr (<>) never [S.stdinLn, S.repeat " ", S.stdinLn, S.repeat " ", S.stdinLn ]
Where f
is a monad, (<>)
sequences the conjoined streams stepwise. See the
definition of paste
here,
where the separate steps are bytestreams corresponding to the lines of a file.
Given, say,
data Branch r = Branch r r deriving Functor  add obvious applicative instance
then never :: Stream Branch Identity r
is the pure infinite binary tree with
(inaccessible) r
s in its leaves. Given two binary trees, tree1 <> tree2
intersects them, preserving the leaves that came first,
so tree1 <> never = tree1
Stream Identity m r
is an action in m
that is indefinitely delayed. Such an
action can be constructed with e.g. untilJust
.
untilJust :: (Monad m, Applicative f) => m (Maybe r) > Stream f m r
Given two such items, <>
instance races them.
It is thus the iterative monad transformer specially defined in
Control.Monad.Trans.Iter
So, for example, we might write
>>>
let justFour str = if length str == 4 then Just str else Nothing
>>>
let four = untilJust (liftM justFour getLine)
>>>
run four
one<Enter> two<Enter> three<Enter> four<Enter> "four"
The Alternative
instance in
Control.Monad.Trans.Free
is avowedly wrong, though no explanation is given for this.
streamBuild :: (forall b. (r > b) > (m b > b) > (f b > b) > b) > Stream f m r Source
Reflect a churchencoded stream; cp. GHC.Exts.build
streamFold return_ effect_ step_ (streamBuild psi) = psi return_ effect_ step_
Transforming streams
maps :: (Monad m, Functor f) => (forall x. f x > g x) > Stream f m r > Stream g m r Source
Map layers of one functor to another with a transformation. Compare
hoist, which has a similar effect on the monadic
parameter.
maps id = id maps f . maps g = maps (f . g)
mapsM :: (Monad m, Functor f) => (forall x. f x > m (g x)) > Stream f m r > Stream g m r Source
Map layers of one functor to another with a transformation involving the base monad
maps
is more fundamental than mapsM
, which is best understood as a convenience
for effecting this frequent composition:
mapsM phi = decompose . maps (Compose . phi)
The streaming prelude exports the same function under the better name mapped
,
which overlaps with the lens libraries.
mapped :: (Monad m, Functor f) => (forall x. f x > m (g x)) > Stream f m r > Stream g m r Source
Map layers of one functor to another with a transformation involving the base monad. This could be trivial, e.g.
let noteBeginning text x = putStrLn text >> return text
this puts the is completely functorgeneral
maps
and mapped
obey these rules:
maps id = id mapped return = id maps f . maps g = maps (f . g) mapped f . mapped g = mapped (f <=< g) maps f . mapped g = mapped (liftM f . g) mapped f . maps g = mapped (f <=< liftM g)
maps
is more fundamental than mapped
, which is best understood as a convenience
for effecting this frequent composition:
mapped phi = decompose . maps (Compose . phi)
distribute :: (Monad m, Functor f, MonadTrans t, MFunctor t, Monad (t (Stream f m))) => Stream f (t m) r > t (Stream f m) r Source
Make it possible to 'run' the underlying transformed monad.
groups :: (Monad m, Functor f, Functor g) => Stream (Sum f g) m r > Stream (Sum (Stream f m) (Stream g m)) m r Source
Group layers in an alternating stream into adjoining substreams of one type or another.
Inspecting a stream
inspect :: (Functor f, Monad m) => Stream f m r > m (Either r (f (Stream f m r))) Source
Inspect the first stage of a freely layered sequence.
Compare Pipes.next
and the replica Streaming.Prelude.next
.
This is the uncons
for the general unfold
.
unfold inspect = id Streaming.Prelude.unfoldr StreamingPrelude.next = id
Splitting and joining Stream
s
splitsAt :: (Monad m, Functor f) => Int > Stream f m r > Stream f m (Stream f m r) Source
Split a succession of layers after some number, returning a streaming or effectful pair.
>>>
rest < S.print $ S.splitAt 1 $ each [1..3]
1>>>
S.print rest
2 3
splitAt 0 = return splitAt n >=> splitAt m = splitAt (m+n)
Thus, e.g.
>>>
rest < S.print $ splitsAt 2 >=> splitsAt 2 $ each [1..5]
1 2 3 4>>>
S.print rest
5
chunksOf :: (Monad m, Functor f) => Int > Stream f m r > Stream (Stream f m) m r Source
Break a stream into substreams each with n functorial layers.
>>>
S.print $ mapped S.sum $ chunksOf 2 $ each [1,1,1,1,1]
2 2 1
concats :: (Monad m, Functor f) => Stream (Stream f m) m r > Stream f m r Source
Dissolves the segmentation into layers of Stream f m
layers.
intercalates :: (Monad m, Monad (t m), MonadTrans t) => t m x > Stream (t m) m r > t m r Source
Interpolate a layer at each segment. This specializes to e.g.
intercalates :: (Monad m, Functor f) => Stream f m () > Stream (Stream f m) m r > Stream f m r
Zipping, unzipping, separating and unseparating streams
zipsWith :: (Monad m, Functor f, Functor g, Functor h) => (forall x y. f x > g y > h (x, y)) > Stream f m r > Stream g m r > Stream h m r Source
zips :: (Monad m, Functor f, Functor g) => Stream f m r > Stream g m r > Stream (Compose f g) m r Source
unzips :: (Monad m, Functor f, Functor g) => Stream (Compose f g) m r > Stream f (Stream g m) r Source
interleaves :: (Monad m, Applicative h) => Stream h m r > Stream h m r > Stream h m r Source
Interleave functor layers, with the effects of the first preceding the effects of the second.
interleaves = zipsWith (liftA2 (,))
>>>
let paste = \a b > interleaves (Q.lines a) (maps (Q.cons' '\t') (Q.lines b))
>>>
Q.stdout $ Q.unlines $ paste "hello\nworld\n" "goodbye\nworld\n"
hello goodbye world world
separate :: (Monad m, Functor f, Functor g) => Stream (Sum f g) m r > Stream f (Stream g m) r Source
Given a stream on a sum of functors, make it a stream on the left functor,
with the streaming on the other functor as the governing monad. This is
useful for acting on one or the other functor with a fold. It generalizes
partitionEithers
massively, but actually streams properly.
>>>
let odd_even = S.maps (S.distinguish even) $ S.each [1..10::Int]
>>>
:t separate odd_even
separate odd_even :: Monad m => Stream (Of Int) (Stream (Of Int) m) ()
Now, for example, it is convenient to fold on the left and right values separately:
>>>
S.toList $ S.toList $ separate odd_even
[2,4,6,8,10] :> ([1,3,5,7,9] :> ())
Or we can write them to separate files or whatever:
>>>
runResourceT $ S.writeFile "even.txt" . S.show $ S.writeFile "odd.txt" . S.show $ S.separate odd_even
>>>
:! cat even.txt
2 4 6 8 10>>>
:! cat odd.txt
1 3 5 7 9
Of course, in the special case of Stream (Of a) m r
, we can achieve the above
effects more simply by using copy
>>>
S.toList . S.filter even $ S.toList . S.filter odd $ S.copy $ each [1..10::Int]
[2,4,6,8,10] :> ([1,3,5,7,9] :> ())
But separate
and unseparate
are functorgeneral.
unseparate :: (Monad m, Functor f, Functor g) => Stream f (Stream g m) r > Stream (Sum f g) m r Source
decompose :: (Monad m, Functor f) => Stream (Compose m f) m r > Stream f m r Source
Rearrange a succession of layers of the form Compose m (f x)
.
we could as well define decompose
by mapsM
:
decompose = mapped getCompose
but mapped
is best understood as:
mapped phi = decompose . maps (Compose . phi)
since maps
and hoist
are the really fundamental operations that preserve the
shape of the stream:
maps :: (Monad m, Functor f) => (forall x. f x > g x) > Stream f m r > Stream g m r hoist :: (Monad m, Functor f) => (forall a. m a > n a) > Stream f m r > Stream f n r
Eliminating a Stream
mapsM_ :: (Functor f, Monad m) => (forall x. f x > m x) > Stream f m r > m r Source
Map each layer to an effect, and run them all.
streamFold :: (Functor f, Monad m) => (r > b) > (m b > b) > (f b > b) > Stream f m r > b Source
streamFold
reorders the arguments of destroy
to be more akin
to foldr
It is more convenient to query in ghci to figure out
what kind of 'algebra' you need to write.
>>>
:t streamFold return join
(Monad m, Functor f) => (f (m a) > m a) > Stream f m a > m a  iterT
>>>
:t streamFold return (join . lift)
(Monad m, Monad (t m), Functor f, MonadTrans t) => (f (t m a) > t m a) > Stream f m a > t m a  iterTM
>>>
:t streamFold return effect
(Monad m, Functor f, Functor g) => (f (Stream g m r) > Stream g m r) > Stream f m r > Stream g m r
>>>
:t \f > streamFold return effect (wrap . f)
(Monad m, Functor f, Functor g) => (f (Stream g m a) > g (Stream g m a)) > Stream f m a > Stream g m a  maps
>>>
:t \f > streamFold return effect (effect . liftM wrap . f)
(Monad m, Functor f, Functor g) => (f (Stream g m a) > m (g (Stream g m a))) > Stream f m a > Stream g m a  mapped
iterTM :: (Functor f, Monad m, MonadTrans t, Monad (t m)) => (f (t m a) > t m a) > Stream f m a > t m a Source
Specialized fold following the usage of Control.Monad.Trans.Free
iterTM alg = streamFold return (join . lift)
iterT :: (Functor f, Monad m) => (f (m a) > m a) > Stream f m a > m a Source
Specialized fold following the usage of Control.Monad.Trans.Free
iterT alg = streamFold return join alg
destroy :: (Functor f, Monad m) => Stream f m r > (f b > b) > (m b > b) > (r > b) > b Source
Map a stream directly to its church encoding; compare Data.List.foldr
Base functor for streams of individual items
A leftstrict pair; the base functor for streams of individual elements.
!a :> b infixr 5 
Bifunctor Of Source  
Monoid a => Monad (Of a) Source  
Functor (Of a) Source  
Monoid a => Applicative (Of a) Source  
Foldable (Of a) Source  
Traversable (Of a) Source  
(Eq a, Eq b) => Eq (Of a b) Source  
(Data a, Data b) => Data (Of a b) Source  
(Ord a, Ord b) => Ord (Of a b) Source  
(Read a, Read b) => Read (Of a b) Source  
(Show a, Show b) => Show (Of a b) Source  
(Monoid a, Monoid b) => Monoid (Of a b) Source 
lazily :: Of a b > (a, b) Source
Note that lazily
, strictly
, fst'
, and mapOf
are all socalled natural transformations on the primitive Of a
functor
If we write
type f ~~> g = forall x . f x > g x
then we can restate some types as follows:
mapOf :: (a > b) > Of a ~~> Of b  Bifunctor first lazily :: Of a ~~> (,) a Identity . fst' :: Of a ~~> Identity a
Manipulation of a Stream f m r
by mapping often turns on recognizing natural transformations of f
.
Thus maps
is far more general the the map
of the Streaming.Prelude
, which can be
defined thus:
S.map :: (a > b) > Stream (Of a) m r > Stream (Of b) m r S.map f = maps (mapOf f)
i.e.
S.map f = maps (\(a :> x) > (f a :> x))
This rests on recognizing that mapOf
is a natural transformation; note though
that it results in such a transformation as well:
S.map :: (a > b) > Stream (Of a) m ~> Stream (Of b) m
Thus we can maps
it in turn.
ResourceT help
bracketStream :: (Functor f, MonadResource m) => IO a > (a > IO ()) > (a > Stream f m b) > Stream f m b Source
reexports
class MFunctor t where
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 :: Monad m => (forall a. m a > n a) > t m b > t n b
Lift a monad morphism from m
to n
into a monad morphism from
(t m)
to (t n)
MFunctor ListT  
MFunctor ResourceT  Since 0.4.7 
MFunctor Backwards  
MFunctor MaybeT  
MFunctor IdentityT  
MFunctor Lift  
MFunctor (ReaderT r)  
MFunctor (StateT s)  
MFunctor (StateT s)  
MFunctor (ExceptT e)  
MFunctor (ErrorT e)  
MFunctor (WriterT w)  
MFunctor (WriterT w)  
MFunctor (Product f)  
Functor f => MFunctor (Compose f)  
Functor f => MFunctor (Stream f)  
MFunctor (RWST r w s)  
MFunctor (RWST r w s) 
class (MFunctor t, MonadTrans t) => MMonad t where
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
class MonadTrans t where
The class of monad transformers. Instances should satisfy the
following laws, which state that lift
is a monad transformation:
MonadTrans ListT  
MonadTrans ResourceT  
MonadTrans MaybeT  
MonadTrans IdentityT  
MonadTrans (ContT r)  
MonadTrans (ReaderT r)  
MonadTrans (StateT s)  
MonadTrans (StateT s)  
MonadTrans (ExceptT e)  
Error e => MonadTrans (ErrorT e)  
Monoid w => MonadTrans (WriterT w)  
Monoid w => MonadTrans (WriterT w)  
Functor f => MonadTrans (Stream f)  
Monoid w => MonadTrans (RWST r w s)  
Monoid w => MonadTrans (RWST r w s) 
class Monad m => MonadIO m where
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:
MonadIO IO  
MonadIO m => MonadIO (ListT m)  
MonadIO m => MonadIO (ResourceT m)  
MonadIO m => MonadIO (MaybeT m)  
MonadIO m => MonadIO (IdentityT m)  
MonadIO m => MonadIO (ContT r m)  
MonadIO m => MonadIO (ReaderT r m)  
MonadIO m => MonadIO (StateT s m)  
MonadIO m => MonadIO (StateT s m)  
MonadIO m => MonadIO (ExceptT e m)  
(Error e, MonadIO m) => MonadIO (ErrorT e m)  
(Monoid w, MonadIO m) => MonadIO (WriterT w m)  
(Monoid w, MonadIO m) => MonadIO (WriterT w m)  
(MonadIO m, Functor f) => MonadIO (Stream f m)  
(Monoid w, MonadIO m) => MonadIO (RWST r w s m)  
(Monoid w, MonadIO m) => MonadIO (RWST r w s m) 
newtype Compose f g a :: (* > *) > (* > *) > * > * infixr 9
Righttoleft composition of functors. The composition of applicative functors is always applicative, but the composition of monads is not always a monad.
Compose infixr 9  

Functor f => MFunctor (Compose f)  
(Functor f, Functor g) => Functor (Compose f g)  
(Applicative f, Applicative g) => Applicative (Compose f g)  
(Foldable f, Foldable g) => Foldable (Compose f g)  
(Traversable f, Traversable g) => Traversable (Compose f g)  
(Alternative f, Applicative g) => Alternative (Compose f g)  
(Functor f, Eq1 f, Eq1 g) => Eq1 (Compose f g)  
(Functor f, Ord1 f, Ord1 g) => Ord1 (Compose f g)  
(Functor f, Read1 f, Read1 g) => Read1 (Compose f g)  
(Functor f, Show1 f, Show1 g) => Show1 (Compose f g)  
(Functor f, Eq1 f, Eq1 g, Eq a) => Eq (Compose f g a)  
(Functor f, Ord1 f, Ord1 g, Ord a) => Ord (Compose f g a)  
(Functor f, Read1 f, Read1 g, Read a) => Read (Compose f g a)  
(Functor f, Show1 f, Show1 g, Show a) => Show (Compose f g a) 
data Sum f g a :: (* > *) > (* > *) > * > *
Lifted sum of functors.
(Functor f, Functor g) => Functor (Sum f g)  
(Foldable f, Foldable g) => Foldable (Sum f g)  
(Traversable f, Traversable g) => Traversable (Sum f g)  
(Eq1 f, Eq1 g) => Eq1 (Sum f g)  
(Ord1 f, Ord1 g) => Ord1 (Sum f g)  
(Read1 f, Read1 g) => Read1 (Sum f g)  
(Show1 f, Show1 g) => Show1 (Sum f g)  
(Eq1 f, Eq1 g, Eq a) => Eq (Sum f g a)  
(Ord1 f, Ord1 g, Ord a) => Ord (Sum f g a)  
(Read1 f, Read1 g, Read a) => Read (Sum f g a)  
(Show1 f, Show1 g, Show a) => Show (Sum f g a) 
newtype Identity a :: * > *
Identity functor and monad. (a nonstrict monad)
Since: 4.8.0.0
Identity  

Monad Identity  
Functor Identity  
MonadFix Identity  
Applicative Identity  
Foldable Identity  
Traversable Identity  
Generic1 Identity  
MonadZip Identity  
Eq1 Identity  
Ord1 Identity  
Read1 Identity  
Show1 Identity  
MonadBase Identity Identity  
MonadBaseControl Identity Identity  
Eq a => Eq (Identity a)  
Data a => Data (Identity a)  
Ord a => Ord (Identity a)  
Read a => Read (Identity a)  This instance would be equivalent to the derived instances of the

Show a => Show (Identity a)  This instance would be equivalent to the derived instances of the

Generic (Identity a)  
type Rep1 Identity = D1 D1Identity (C1 C1_0Identity (S1 S1_0_0Identity Par1))  
type StM Identity a = a  
type Rep (Identity a) = D1 D1Identity (C1 C1_0Identity (S1 S1_0_0Identity (Rec0 a))) 
class Applicative f => Alternative f where
A monoid on applicative functors.
If defined, some
and many
should be the least solutions
of the equations:
(<>) :: f a > f a > f a infixl 3
An associative binary operation
class Monad m => MonadThrow m where
A class for monads in which exceptions may be thrown.
Instances should obey the following law:
throwM e >> x = throwM e
In other words, throwing an exception shortcircuits the rest of the monadic computation.
throwM :: Exception e => e > m a
Throw an exception. Note that this throws when this action is run in
the monad m
, not when it is applied. It is a generalization of
Control.Exception's throwIO
.
Should satisfy the law:
throwM e >> f = throwM e
MonadThrow []  
MonadThrow IO  
MonadThrow Q  
MonadThrow STM  
MonadThrow Maybe  
(~) * e SomeException => MonadThrow (Either e)  
MonadThrow m => MonadThrow (ListT m)  
MonadThrow m => MonadThrow (ResourceT m)  
MonadThrow m => MonadThrow (MaybeT m)  Throws exceptions into the base monad. 
MonadThrow m => MonadThrow (IdentityT m)  
MonadThrow m => MonadThrow (ContT r m)  
MonadThrow m => MonadThrow (ReaderT r m)  
MonadThrow m => MonadThrow (StateT s m)  
MonadThrow m => MonadThrow (StateT s m)  
MonadThrow m => MonadThrow (ExceptT e m)  Throws exceptions into the base monad. 
(Error e, MonadThrow m) => MonadThrow (ErrorT e m)  Throws exceptions into the base monad. 
(MonadThrow m, Monoid w) => MonadThrow (WriterT w m)  
(MonadThrow m, Monoid w) => MonadThrow (WriterT w m)  
(MonadThrow m, Functor f) => MonadThrow (Stream f m)  
(MonadThrow m, Monoid w) => MonadThrow (RWST r w s m)  
(MonadThrow m, Monoid w) => MonadThrow (RWST r w s m) 
class (MonadThrow m, MonadIO m, Applicative m, MonadBase IO m) => MonadResource m where
A Monad
which allows for safe resource allocation. In theory, any monad
transformer stack which includes a ResourceT
can be an instance of
MonadResource
.
Note: runResourceT
has a requirement for a MonadBaseControl IO m
monad,
which allows control operations to be lifted. A MonadResource
does not
have this requirement. This means that transformers such as ContT
can be
an instance of MonadResource
. However, the ContT
wrapper will need to be
unwrapped before calling runResourceT
.
Since 0.3.0
liftResourceT :: ResourceT IO a > m a
Lift a ResourceT IO
action into the current Monad
.
Since 0.4.0
MonadResource m => MonadResource (ListT m)  
(MonadThrow m, MonadBase IO m, MonadIO m, Applicative m) => MonadResource (ResourceT m)  
MonadResource m => MonadResource (MaybeT m)  
MonadResource m => MonadResource (IdentityT m)  
MonadResource m => MonadResource (ContT r m)  
MonadResource m => MonadResource (ReaderT r m)  
MonadResource m => MonadResource (StateT s m)  
MonadResource m => MonadResource (StateT s m)  
MonadResource m => MonadResource (ExceptT e m)  
(Error e, MonadResource m) => MonadResource (ErrorT e m)  
(Monoid w, MonadResource m) => MonadResource (WriterT w m)  
(Monoid w, MonadResource m) => MonadResource (WriterT w m)  
(MonadResource m, Functor f) => MonadResource (Stream f m)  
(Monoid w, MonadResource m) => MonadResource (RWST r w s m)  
(Monoid w, MonadResource m) => MonadResource (RWST r w s m) 
class (Applicative b, Applicative m, Monad b, Monad m) => MonadBase b m  m > b where
liftBase :: b α > m α
Lift a computation from the base monad
MonadBase [] []  
MonadBase IO IO  
MonadBase Identity Identity  
MonadBase STM STM  
MonadBase Maybe Maybe  
MonadBase b m => MonadBase b (ResourceT m)  
MonadBase b m => MonadBase b (MaybeT m)  
MonadBase b m => MonadBase b (ListT m)  
MonadBase b m => MonadBase b (IdentityT m)  
(Monoid w, MonadBase b m) => MonadBase b (WriterT w m)  
(Monoid w, MonadBase b m) => MonadBase b (WriterT w m)  
MonadBase b m => MonadBase b (StateT s m)  
MonadBase b m => MonadBase b (StateT s m)  
MonadBase b m => MonadBase b (ReaderT r m)  
MonadBase b m => MonadBase b (ExceptT e m)  
(Error e, MonadBase b m) => MonadBase b (ErrorT e m)  
MonadBase b m => MonadBase b (ContT r m)  
(MonadBase b m, Functor f) => MonadBase b (Stream f m)  
(Monoid w, MonadBase b m) => MonadBase b (RWST r w s m)  
(Monoid w, MonadBase b m) => MonadBase b (RWST r w s m)  
MonadBase ((>) r) ((>) r)  
MonadBase (Either e) (Either e)  
MonadBase (ST s) (ST s)  
MonadBase (ST s) (ST s) 
data ResourceT m a :: (* > *) > * > *
The Resource transformer. This transformer keeps track of all registered
actions, and calls them upon exit (via runResourceT
). Actions may be
registered via register
, or resources may be allocated atomically via
allocate
. allocate
corresponds closely to bracket
.
Releasing may be performed before exit via the release
function. This is a
highly recommended optimization, as it will ensure that scarce resources are
freed early. Note that calling release
will deregister the action, so that
a release action will only ever be called once.
Since 0.3.0
MFunctor ResourceT  Since 0.4.7 
MMonad ResourceT  Since 0.4.7 
MonadTrans ResourceT  
MonadTransControl ResourceT  
MonadRWS r w s m => MonadRWS r w s (ResourceT m)  
MonadBase b m => MonadBase b (ResourceT m)  
MonadBaseControl b m => MonadBaseControl b (ResourceT m)  
MonadError e m => MonadError e (ResourceT m)  
MonadReader r m => MonadReader r (ResourceT m)  
MonadState s m => MonadState s (ResourceT m)  
MonadWriter w m => MonadWriter w (ResourceT m)  
Monad m => Monad (ResourceT m)  
Functor m => Functor (ResourceT m)  
Applicative m => Applicative (ResourceT m)  
Alternative m => Alternative (ResourceT m)  Since 1.1.5 
MonadPlus m => MonadPlus (ResourceT m)  Since 1.1.5 
MonadThrow m => MonadThrow (ResourceT m)  
MonadCatch m => MonadCatch (ResourceT m)  
MonadMask m => MonadMask (ResourceT m)  
MonadIO m => MonadIO (ResourceT m)  
MonadCont m => MonadCont (ResourceT m)  
(MonadThrow m, MonadBase IO m, MonadIO m, Applicative m) => MonadResource (ResourceT m)  
type StT ResourceT a = a  
type StM (ResourceT m) a = StM m a 
runResourceT :: MonadBaseControl IO m => ResourceT m a > m a
Unwrap a ResourceT
transformer, and call all registered release actions.
Note that there is some reference counting involved due to resourceForkIO
.
If multiple threads are sharing the same collection of resources, only the
last call to runResourceT
will deallocate the resources.
Since 0.3.0
class Bifunctor p where
Formally, the class Bifunctor
represents a bifunctor
from Hask
> Hask
.
Intuitively it is a bifunctor where both the first and second arguments are covariant.
You can define a Bifunctor
by either defining bimap
or by
defining both first
and second
.
If you supply bimap
, you should ensure that:
bimap
id
id
≡id
If you supply first
and second
, ensure:
first
id
≡id
second
id
≡id
If you supply both, you should also ensure:
bimap
f g ≡first
f.
second
g
These ensure by parametricity:
bimap
(f.
g) (h.
i) ≡bimap
f h.
bimap
g ifirst
(f.
g) ≡first
f.
first
gsecond
(f.
g) ≡second
f.
second
g
Since: 4.8.0.0
join :: Monad m => m (m a) > m a
The join
function is the conventional monad join operator. It
is used to remove one level of monadic structure, projecting its
bound argument into the outer level.
liftM2 :: Monad m => (a1 > a2 > r) > m a1 > m a2 > m r
Promote a function to a monad, scanning the monadic arguments from left to right. For example,
liftM2 (+) [0,1] [0,2] = [0,2,1,3] liftM2 (+) (Just 1) Nothing = Nothing
liftA2 :: Applicative f => (a > b > c) > f a > f b > f c
Lift a binary function to actions.
liftA3 :: Applicative f => (a > b > c > d) > f a > f b > f c > f d
Lift a ternary function to actions.
void :: Functor f => f a > f ()
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