{-| General purpose utilities

    The names in this module clash heavily with the Haskell Prelude, so I
    recommend the following import scheme:

> import Pipes
> import qualified Pipes.Prelude as P  -- or use any other qualifier you prefer

    Note that 'String'-based 'IO' is inefficient.  The 'String'-based utilities
    in this module exist only for simple demonstrations without incurring a
    dependency on the @text@ package.

    Also, 'stdinLn' and 'stdoutLn' remove and add newlines, respectively.  This
    behavior is intended to simplify examples.  The corresponding @stdin@ and
    @stdout@ utilities from @pipes-bytestring@ and @pipes-text@ preserve
    newlines.
-}

{-# LANGUAGE RankNTypes, Trustworthy #-}
{-# OPTIONS_GHC -fno-warn-unused-do-bind #-}

module Pipes.Prelude (
    -- * Producers
    -- $producers
      stdinLn
    , readLn
    , fromHandle
    , repeatM
    , replicateM

    -- * Consumers
    -- $consumers
    , stdoutLn
    , stdoutLn'
    , mapM_
    , print
    , toHandle
    , drain

    -- * Pipes
    -- $pipes
    , map
    , mapM
    , sequence
    , mapFoldable
    , filter
    , filterM
    , take
    , takeWhile
    , takeWhile'
    , drop
    , dropWhile
    , concat
    , elemIndices
    , findIndices
    , scan
    , scanM
    , chain
    , read
    , show
    , seq

    -- * Folds
    -- $folds
    , fold
    , fold'
    , foldM
    , foldM'
    , all
    , any
    , and
    , or
    , elem
    , notElem
    , find
    , findIndex
    , head
    , index
    , last
    , length
    , maximum
    , minimum
    , null
    , sum
    , product
    , toList
    , toListM
    , toListM'

    -- * Zips
    , zip
    , zipWith

    -- * Utilities
    , tee
    , generalize
    ) where

import Control.Exception (throwIO, try)
import Control.Monad (liftM, replicateM_, when, unless)
import Control.Monad.Trans.State.Strict (get, put)
import Data.Functor.Identity (Identity, runIdentity)
import Foreign.C.Error (Errno(Errno), ePIPE)
import Pipes
import Pipes.Core
import Pipes.Internal
import Pipes.Lift (evalStateP)
import qualified GHC.IO.Exception as G
import qualified System.IO as IO
import qualified Prelude
import Prelude hiding (
      all
    , and
    , any
    , concat
    , drop
    , dropWhile
    , elem
    , filter
    , head
    , last
    , length
    , map
    , mapM
    , mapM_
    , maximum
    , minimum
    , notElem
    , null
    , or
    , print
    , product
    , read
    , readLn
    , sequence
    , show
    , seq
    , sum
    , take
    , takeWhile
    , zip
    , zipWith
    )

{- $producers
    Use 'for' loops to iterate over 'Producer's whenever you want to perform the
    same action for every element:

> -- Echo all lines from standard input to standard output
> runEffect $ for P.stdinLn $ \str -> do
>     lift $ putStrLn str

    ... or more concisely:

>>> runEffect $ for P.stdinLn (lift . putStrLn)
Test<Enter>
Test
ABC<Enter>
ABC
...

-}

{-| Read 'String's from 'IO.stdin' using 'getLine'

    Terminates on end of input
-}
stdinLn :: MonadIO m => Producer' String m ()
stdinLn = fromHandle IO.stdin
{-# INLINABLE stdinLn #-}

-- | 'read' values from 'IO.stdin', ignoring failed parses
readLn :: (MonadIO m, Read a) => Producer' a m ()
readLn = stdinLn >-> read
{-# INLINABLE readLn #-}

{-| Read 'String's from a 'IO.Handle' using 'IO.hGetLine'

    Terminates on end of input
-}
fromHandle :: MonadIO m => IO.Handle -> Producer' String m ()
fromHandle h = go
  where
    go = do
        eof <- liftIO $ IO.hIsEOF h
        unless eof $ do
            str <- liftIO $ IO.hGetLine h
            yield str
            go
{-# INLINABLE fromHandle #-}

-- | Repeat a monadic action indefinitely, 'yield'ing each result
repeatM :: Monad m => m a -> Producer' a m r
repeatM m = lift m >~ cat
{-# INLINABLE repeatM #-}

{-# RULES
  "repeatM m >-> p" forall m p . repeatM m >-> p = lift m >~ p
  #-}

{-| Repeat a monadic action a fixed number of times, 'yield'ing each result

> replicateM  0      x = return ()
>
> replicateM (m + n) x = replicateM m x >> replicateM n x  -- 0 <= {m,n}
-}
replicateM :: Monad m => Int -> m a -> Producer' a m ()
replicateM n m = lift m >~ take n
{-# INLINABLE replicateM #-}

{- $consumers
    Feed a 'Consumer' the same value repeatedly using ('>~'):

>>> runEffect $ lift getLine >~ P.stdoutLn
Test<Enter>
Test
ABC<Enter>
ABC
...

-}

{-| Write 'String's to 'IO.stdout' using 'putStrLn'

    Unlike 'toHandle', 'stdoutLn' gracefully terminates on a broken output pipe
-}
stdoutLn :: MonadIO m => Consumer' String m ()
stdoutLn = go
  where
    go = do
        str <- await
        x   <- liftIO $ try (putStrLn str)
        case x of
           Left (G.IOError { G.ioe_type  = G.ResourceVanished
                           , G.ioe_errno = Just ioe })
                | Errno ioe == ePIPE
                    -> return ()
           Left  e  -> liftIO (throwIO e)
           Right () -> go
{-# INLINABLE stdoutLn #-}

{-| Write 'String's to 'IO.stdout' using 'putStrLn'

    This does not handle a broken output pipe, but has a polymorphic return
    value
-}
stdoutLn' :: MonadIO m => Consumer' String m r
stdoutLn' = for cat (\str -> liftIO (putStrLn str))
{-# INLINABLE stdoutLn' #-}

{-# RULES
    "p >-> stdoutLn'" forall p .
        p >-> stdoutLn' = for p (\str -> liftIO (putStrLn str))
  #-}

-- | Consume all values using a monadic function
mapM_ :: Monad m => (a -> m ()) -> Consumer' a m r
mapM_ f = for cat (\a -> lift (f a))
{-# INLINABLE mapM_ #-}

{-# RULES
    "p >-> mapM_ f" forall p f .
        p >-> mapM_ f = for p (\a -> lift (f a))
  #-}

-- | 'print' values to 'IO.stdout'
print :: (MonadIO m, Show a) => Consumer' a m r
print = for cat (\a -> liftIO (Prelude.print a))
{-# INLINABLE print #-}

{-# RULES
    "p >-> print" forall p .
        p >-> print = for p (\a -> liftIO (Prelude.print a))
  #-}

-- | Write 'String's to a 'IO.Handle' using 'IO.hPutStrLn'
toHandle :: MonadIO m => IO.Handle -> Consumer' String m r
toHandle handle = for cat (\str -> liftIO (IO.hPutStrLn handle str))
{-# INLINABLE toHandle #-}

{-# RULES
    "p >-> toHandle handle" forall p handle .
        p >-> toHandle handle = for p (\str -> liftIO (IO.hPutStrLn handle str))
  #-}

-- | 'discard' all incoming values
drain :: Monad m => Consumer' a m r
drain = for cat discard
{-# INLINABLE drain #-}

{-# RULES
    "p >-> drain" forall p .
        p >-> drain = for p discard
  #-}

{- $pipes
    Use ('>->') to connect 'Producer's, 'Pipe's, and 'Consumer's:

>>> runEffect $ P.stdinLn >-> P.takeWhile (/= "quit") >-> P.stdoutLn
Test<Enter>
Test
ABC<Enter>
ABC
quit<Enter>
>>>

-}

{-| Apply a function to all values flowing downstream

> map id = cat
>
> map (g . f) = map f >-> map g
-}
map :: Monad m => (a -> b) -> Pipe a b m r
map f = for cat (\a -> yield (f a))
{-# INLINABLE map #-}

{-# RULES
    "p >-> map f" forall p f . p >-> map f = for p (\a -> yield (f a))

  ; "map f >-> p" forall p f . map f >-> p = (do
        a <- await
        return (f a) ) >~ p
  #-}

{-| Apply a monadic function to all values flowing downstream

> mapM return = cat
>
> mapM (f >=> g) = mapM f >-> mapM g
-}
mapM :: Monad m => (a -> m b) -> Pipe a b m r
mapM f = for cat $ \a -> do
    b <- lift (f a)
    yield b
{-# INLINABLE mapM #-}

{-# RULES
    "p >-> mapM f" forall p f . p >-> mapM f = for p (\a -> do
        b <- lift (f a)
        yield b )

  ; "mapM f >-> p" forall p f . mapM f >-> p = (do
        a <- await
        b <- lift (f a)
        return b ) >~ p
  #-}

-- | Convert a stream of actions to a stream of values
sequence :: Monad m => Pipe (m a) a m r
sequence = mapM id
{-# INLINABLE sequence #-}

{- | Apply a function to all values flowing downstream, and
     forward each element of the result.
-}
mapFoldable :: (Monad m, Foldable t) => (a -> t b) -> Pipe a b m r
mapFoldable f = for cat (\a -> each (f a))
{-# INLINABLE mapFoldable #-}

{-# RULES
    "p >-> mapFoldable f" forall p f .
        p >-> mapFoldable f = for p (\a -> each (f a))
  #-}

{-| @(filter predicate)@ only forwards values that satisfy the predicate.

> filter (pure True) = cat
>
> filter (liftA2 (&&) p1 p2) = filter p1 >-> filter p2
-}
filter :: Monad m => (a -> Bool) -> Pipe a a m r
filter predicate = for cat $ \a -> when (predicate a) (yield a)
{-# INLINABLE filter #-}

{-# RULES
    "p >-> filter predicate" forall p predicate.
        p >-> filter predicate = for p (\a -> when (predicate a) (yield a))
  #-}

{-| @(filterM predicate)@ only forwards values that satisfy the monadic
    predicate

> filterM (pure (pure True)) = cat
>
> filterM (liftA2 (liftA2 (&&)) p1 p2) = filterM p1 >-> filterM p2
-}
filterM :: Monad m => (a -> m Bool) -> Pipe a a m r
filterM predicate = for cat $ \a -> do
    b <- lift (predicate a)
    when b (yield a)
{-# INLINABLE filterM #-}

{-# RULES
    "p >-> filterM predicate" forall p predicate .
        p >-> filterM predicate = for p (\a -> do
            b <- lift (predicate a)
            when b (yield a) )
  #-}

{-| @(take n)@ only allows @n@ values to pass through

> take 0 = return ()
>
> take (m + n) = take m >> take n

> take <infinity> = cat
>
> take (min m n) = take m >-> take n
-}
take :: Monad m => Int -> Pipe a a m ()
take n = replicateM_ n $ do
    a <- await
    yield a
{-# INLINABLE take #-}

{-| @(takeWhile p)@ allows values to pass downstream so long as they satisfy
    the predicate @p@.

> takeWhile (pure True) = cat
>
> takeWhile (liftA2 (&&) p1 p2) = takeWhile p1 >-> takeWhile p2
-}
takeWhile :: Monad m => (a -> Bool) -> Pipe a a m ()
takeWhile predicate = go
  where
    go = do
        a <- await
        if (predicate a)
            then do
                yield a
                go
            else return ()
{-# INLINABLE takeWhile #-}

{-| @(takeWhile' p)@ is a version of takeWhile that returns the value failing
    the predicate.

> takeWhile' (pure True) = cat
>
> takeWhile' (liftA2 (&&) p1 p2) = takeWhile' p1 >-> takeWhile' p2
-}
takeWhile' :: Monad m => (a -> Bool) -> Pipe a a m a
takeWhile' predicate = go
  where
    go = do
        a <- await
        if (predicate a)
            then do
                yield a
                go
            else return a
{-# INLINABLE takeWhile' #-}

{-| @(drop n)@ discards @n@ values going downstream

> drop 0 = cat
>
> drop (m + n) = drop m >-> drop n
-}
drop :: Monad m => Int -> Pipe a a m r
drop n = do
    replicateM_ n await
    cat
{-# INLINABLE drop #-}

{-| @(dropWhile p)@ discards values going downstream until one violates the
    predicate @p@.

> dropWhile (pure False) = cat
>
> dropWhile (liftA2 (||) p1 p2) = dropWhile p1 >-> dropWhile p2
-}
dropWhile :: Monad m => (a -> Bool) -> Pipe a a m r
dropWhile predicate = go
  where
    go = do
        a <- await
        if (predicate a)
            then go
            else do
                yield a
                cat
{-# INLINABLE dropWhile #-}

-- | Flatten all 'Foldable' elements flowing downstream
concat :: (Monad m, Foldable f) => Pipe (f a) a m r
concat = for cat each
{-# INLINABLE concat #-}

{-# RULES
    "p >-> concat" forall p . p >-> concat = for p each
  #-}

-- | Outputs the indices of all elements that match the given element
elemIndices :: (Monad m, Eq a) => a -> Pipe a Int m r
elemIndices a = findIndices (a ==)
{-# INLINABLE elemIndices #-}

-- | Outputs the indices of all elements that satisfied the predicate
findIndices :: Monad m => (a -> Bool) -> Pipe a Int m r
findIndices predicate = loop 0
  where
    loop n = do
        a <- await
        when (predicate a) (yield n)
        loop $! n + 1
{-# INLINABLE findIndices #-}

{-| Strict left scan

> Control.Foldl.purely scan :: Monad m => Fold a b -> Pipe a b m r
-}
scan :: Monad m => (x -> a -> x) -> x -> (x -> b) -> Pipe a b m r
scan step begin done = loop begin
  where
    loop x = do
        yield (done x)
        a <- await
        let x' = step x a
        loop $! x'
{-# INLINABLE scan #-}

{-| Strict, monadic left scan

> Control.Foldl.impurely scan :: Monad m => FoldM a m b -> Pipe a b m r
-}
scanM :: Monad m => (x -> a -> m x) -> m x -> (x -> m b) -> Pipe a b m r
scanM step begin done = do
    x <- lift begin
    loop x
  where
    loop x = do
        b <- lift (done x)
        yield b
        a  <- await
        x' <- lift (step x a)
        loop $! x'
{-# INLINABLE scanM #-}

{-| Apply an action to all values flowing downstream

> chain (pure (return ())) = cat
>
> chain (liftA2 (>>) m1 m2) = chain m1 >-> chain m2
-}
chain :: Monad m => (a -> m ()) -> Pipe a a m r
chain f = for cat $ \a -> do
    lift (f a)
    yield a
{-# INLINABLE chain #-}

{-# RULES
    "p >-> chain f" forall p f .
        p >-> chain f = for p (\a -> do
            lift (f a)
            yield a )
  ; "chain f >-> p" forall p f .
        chain f >-> p = (do
            a <- await
            lift (f a)
            return a ) >~ p
  #-}

-- | Parse 'Read'able values, only forwarding the value if the parse succeeds
read :: (Monad m, Read a) => Pipe String a m r
read = for cat $ \str -> case (reads str) of
    [(a, "")] -> yield a
    _         -> return ()
{-# INLINABLE read #-}

{-# RULES
    "p >-> read" forall p .
        p >-> read = for p (\str -> case (reads str) of
            [(a, "")] -> yield a
            _         -> return () )
  #-}

-- | Convert 'Show'able values to 'String's
show :: (Monad m, Show a) => Pipe a String m r
show = map Prelude.show
{-# INLINABLE show #-}

-- | Evaluate all values flowing downstream to WHNF
seq :: Monad m => Pipe a a m r
seq = for cat $ \a -> yield $! a
{-# INLINABLE seq #-}

{- $folds
    Use these to fold the output of a 'Producer'.  Many of these folds will stop
    drawing elements if they can compute their result early, like 'any':

>>> P.any null P.stdinLn
Test<Enter>
ABC<Enter>
<Enter>
True
>>>

-}

{-| Strict fold of the elements of a 'Producer'

> Control.Foldl.purely fold :: Monad m => Fold a b -> Producer a m () -> m b
-}
fold :: Monad m => (x -> a -> x) -> x -> (x -> b) -> Producer a m () -> m b
fold step begin done p0 = loop p0 begin
  where
    loop p x = case p of
        Request v  _  -> closed v
        Respond a  fu -> loop (fu ()) $! step x a
        M          m  -> m >>= \p' -> loop p' x
        Pure    _     -> return (done x)
{-# INLINABLE fold #-}

{-| Strict fold of the elements of a 'Producer' that preserves the return value

> Control.Foldl.purely fold' :: Monad m => Fold a b -> Producer a m r -> m (b, r)
-}
fold' :: Monad m => (x -> a -> x) -> x -> (x -> b) -> Producer a m r -> m (b, r)
fold' step begin done p0 = loop p0 begin
  where
    loop p x = case p of
        Request v  _  -> closed v
        Respond a  fu -> loop (fu ()) $! step x a
        M          m  -> m >>= \p' -> loop p' x
        Pure    r     -> return (done x, r)
{-# INLINABLE fold' #-}

{-| Strict, monadic fold of the elements of a 'Producer'

> Control.Foldl.impurely foldM :: Monad m => FoldM a b -> Producer a m () -> m b
-}
foldM
    :: Monad m
    => (x -> a -> m x) -> m x -> (x -> m b) -> Producer a m () -> m b
foldM step begin done p0 = do
    x0 <- begin
    loop p0 x0
  where
    loop p x = case p of
        Request v  _  -> closed v
        Respond a  fu -> do
            x' <- step x a
            loop (fu ()) $! x'
        M          m  -> m >>= \p' -> loop p' x
        Pure    _     -> done x
{-# INLINABLE foldM #-}

{-| Strict, monadic fold of the elements of a 'Producer'

> Control.Foldl.impurely foldM' :: Monad m => FoldM a b -> Producer a m r -> m (b, r)
-}
foldM'
    :: Monad m
    => (x -> a -> m x) -> m x -> (x -> m b) -> Producer a m r -> m (b, r)
foldM' step begin done p0 = do
    x0 <- begin
    loop p0 x0
  where
    loop p x = case p of
        Request v  _  -> closed v
        Respond a  fu -> do
            x' <- step x a
            loop (fu ()) $! x'
        M          m  -> m >>= \p' -> loop p' x
        Pure    r     -> do
            b <- done x
            return (b, r)
{-# INLINABLE foldM' #-}

{-| @(all predicate p)@ determines whether all the elements of @p@ satisfy the
    predicate.
-}
all :: Monad m => (a -> Bool) -> Producer a m () -> m Bool
all predicate p = null $ p >-> filter (\a -> not (predicate a))
{-# INLINABLE all #-}

{-| @(any predicate p)@ determines whether any element of @p@ satisfies the
    predicate.
-}
any :: Monad m => (a -> Bool) -> Producer a m () -> m Bool
any predicate p = liftM not $ null (p >-> filter predicate)
{-# INLINABLE any #-}

-- | Determines whether all elements are 'True'
and :: Monad m => Producer Bool m () -> m Bool
and = all id
{-# INLINABLE and #-}

-- | Determines whether any element is 'True'
or :: Monad m => Producer Bool m () -> m Bool
or = any id
{-# INLINABLE or #-}

{-| @(elem a p)@ returns 'True' if @p@ has an element equal to @a@, 'False'
    otherwise
-}
elem :: (Monad m, Eq a) => a -> Producer a m () -> m Bool
elem a = any (a ==)
{-# INLINABLE elem #-}

{-| @(notElem a)@ returns 'False' if @p@ has an element equal to @a@, 'True'
    otherwise
-}
notElem :: (Monad m, Eq a) => a -> Producer a m () -> m Bool
notElem a = all (a /=)
{-# INLINABLE notElem #-}

-- | Find the first element of a 'Producer' that satisfies the predicate
find :: Monad m => (a -> Bool) -> Producer a m () -> m (Maybe a)
find predicate p = head (p >-> filter predicate)
{-# INLINABLE find #-}

{-| Find the index of the first element of a 'Producer' that satisfies the
    predicate
-}
findIndex :: Monad m => (a -> Bool) -> Producer a m () -> m (Maybe Int)
findIndex predicate p = head (p >-> findIndices predicate)
{-# INLINABLE findIndex #-}

-- | Retrieve the first element from a 'Producer'
head :: Monad m => Producer a m () -> m (Maybe a)
head p = do
    x <- next p
    return $ case x of
        Left   _     -> Nothing
        Right (a, _) -> Just a
{-# INLINABLE head #-}

-- | Index into a 'Producer'
index :: Monad m => Int -> Producer a m () -> m (Maybe a)
index n p = head (p >-> drop n)
{-# INLINABLE index #-}

-- | Retrieve the last element from a 'Producer'
last :: Monad m => Producer a m () -> m (Maybe a)
last p0 = do
    x <- next p0
    case x of
        Left   _      -> return Nothing
        Right (a, p') -> loop a p'
  where
    loop a p = do
        x <- next p
        case x of
            Left   _       -> return (Just a)
            Right (a', p') -> loop a' p'
{-# INLINABLE last #-}

-- | Count the number of elements in a 'Producer'
length :: Monad m => Producer a m () -> m Int
length = fold (\n _ -> n + 1) 0 id
{-# INLINABLE length #-}

-- | Find the maximum element of a 'Producer'
maximum :: (Monad m, Ord a) => Producer a m () -> m (Maybe a)
maximum = fold step Nothing id
  where
    step x a = Just $ case x of
        Nothing -> a
        Just a' -> max a a'
{-# INLINABLE maximum #-}

-- | Find the minimum element of a 'Producer'
minimum :: (Monad m, Ord a) => Producer a m () -> m (Maybe a)
minimum = fold step Nothing id
  where
    step x a = Just $ case x of
        Nothing -> a
        Just a' -> min a a'
{-# INLINABLE minimum #-}

-- | Determine if a 'Producer' is empty
null :: Monad m => Producer a m () -> m Bool
null p = do
    x <- next p
    return $ case x of
        Left  _ -> True
        Right _ -> False
{-# INLINABLE null #-}

-- | Compute the sum of the elements of a 'Producer'
sum :: (Monad m, Num a) => Producer a m () -> m a
sum = fold (+) 0 id
{-# INLINABLE sum #-}

-- | Compute the product of the elements of a 'Producer'
product :: (Monad m, Num a) => Producer a m () -> m a
product = fold (*) 1 id
{-# INLINABLE product #-}

-- | Convert a pure 'Producer' into a list
toList :: Producer a Identity () -> [a]
toList = loop
  where
    loop p = case p of
        Request v _  -> closed v
        Respond a fu -> a:loop (fu ())
        M         m  -> loop (runIdentity m)
        Pure    _    -> []
{-# INLINABLE toList #-}

{-| Convert an effectful 'Producer' into a list

    Note: 'toListM' is not an idiomatic use of @pipes@, but I provide it for
    simple testing purposes.  Idiomatic @pipes@ style consumes the elements
    immediately as they are generated instead of loading all elements into
    memory.
-}
toListM :: Monad m => Producer a m () -> m [a]
toListM = fold step begin done
  where
    step x a = x . (a:)
    begin = id
    done x = x []
{-# INLINABLE toListM #-}

{-| Convert an effectful 'Producer' into a list alongside the return value

    Note: 'toListM'' is not an idiomatic use of @pipes@, but I provide it for
    simple testing purposes.  Idiomatic @pipes@ style consumes the elements
    immediately as they are generated instead of loading all elements into
    memory.
-}
toListM' :: Monad m => Producer a m r -> m ([a], r)
toListM' = fold' step begin done
  where
    step x a = x . (a:)
    begin = id
    done x = x []
{-# INLINABLE toListM' #-}

-- | Zip two 'Producer's
zip :: Monad m
    => (Producer   a     m r)
    -> (Producer      b  m r)
    -> (Producer' (a, b) m r)
zip = zipWith (,)
{-# INLINABLE zip #-}

-- | Zip two 'Producer's using the provided combining function
zipWith :: Monad m
    => (a -> b -> c)
    -> (Producer  a m r)
    -> (Producer  b m r)
    -> (Producer' c m r)
zipWith f = go
  where
    go p1 p2 = do
        e1 <- lift $ next p1
        case e1 of
            Left r         -> return r
            Right (a, p1') -> do
                e2 <- lift $ next p2
                case e2 of
                    Left r         -> return r
                    Right (b, p2') -> do
                        yield (f a b)
                        go p1' p2'
{-# INLINABLE zipWith #-}

{-| Transform a 'Consumer' to a 'Pipe' that reforwards all values further
    downstream
-}
tee :: Monad m => Consumer a m r -> Pipe a a m r
tee p = evalStateP Nothing $ do
    r <- up >\\ (hoist lift p //> dn)
    ma <- lift get
    case ma of
        Nothing -> return ()
        Just a  -> yield a
    return r
  where
    up () = do
        ma <- lift get
        case ma of
            Nothing -> return ()
            Just a  -> yield a
        a <- await
        lift $ put (Just a)
        return a
    dn v = closed v
{-# INLINABLE tee #-}

{-| Transform a unidirectional 'Pipe' to a bidirectional 'Proxy'

> generalize (f >-> g) = generalize f >+> generalize g
>
> generalize cat = pull
-}
generalize :: Monad m => Pipe a b m r -> x -> Proxy x a x b m r
generalize p x0 = evalStateP x0 $ up >\\ hoist lift p //> dn
  where
    up () = do
        x <- lift get
        request x
    dn a = do
        x <- respond a
        lift $ put x
{-# INLINABLE generalize #-}
