{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE Safe #-}
{-# LANGUAGE StandaloneDeriving #-}

--------------------------------------------------------------------------------
-- |
-- \"Applicative Effects in Free Monads\"
--
-- Often times, the '(\<*\>)' operator can be more efficient than 'ap'.
-- Conventional free monads don't provide any means of modeling this.
-- The free monad can be modified to make use of an underlying applicative.
-- But it does require some laws, or else the '(\<*\>)' = 'ap' law is broken.
-- When interpreting this free monad with 'foldFree',
-- the natural transformation must be an applicative homomorphism.
-- An applicative homomorphism @hm :: (Applicative f, Applicative g) => f x -> g x@
-- will satisfy these laws.
--
-- * @hm (pure a) = pure a@
-- * @hm (f \<*\> a) = hm f \<*\> hm a@
--
-- This is based on the \"Applicative Effects in Free Monads\" series of articles by Will Fancher
--
-- * <http://elvishjerricco.github.io/2016/04/08/applicative-effects-in-free-monads.html Applicative Effects in Free Monads>
--
-- * <http://elvishjerricco.github.io/2016/04/13/more-on-applicative-effects-in-free-monads.html More on Applicative Effects in Free Monads>
--------------------------------------------------------------------------------
module Control.Monad.Free.Ap
  ( MonadFree(..)
  , Free(..)
  , retract
  , liftF
  , iter
  , iterA
  , iterM
  , hoistFree
  , foldFree
  , toFreeT
  , cutoff
  , unfold
  , unfoldM
  , _Pure, _Free
  ) where

import Control.Applicative
import Control.Arrow ((>>>))
import Control.Monad (liftM, MonadPlus(..), (>=>))
import Control.Monad.Fix
import Control.Monad.Trans.Class
import qualified Control.Monad.Trans.Free.Ap as FreeT
import Control.Monad.Free.Class
import Control.Monad.Reader.Class
import Control.Monad.Writer.Class
import Control.Monad.State.Class
import Control.Monad.Error.Class
import Control.Monad.Cont.Class
import Data.Functor.Bind
import Data.Functor.Classes
import Data.Foldable
import Data.Profunctor
import Data.Traversable
import Data.Semigroup.Foldable
import Data.Semigroup.Traversable
import Data.Data
import GHC.Generics
import Prelude hiding (foldr)

-- $setup
-- >>> import Control.Applicative (Const (..))
-- >>> import Data.Functor.Identity (Identity (..))
-- >>> import Data.Monoid (First (..))
-- >>> import Data.Tagged (Tagged (..))
-- >>> let preview l x = getFirst (getConst (l (Const . First . Just) x))
-- >>> let review l x = runIdentity (unTagged (l (Tagged (Identity x))))

-- | A free monad given an applicative
data Free f a = Pure a | Free (f (Free f a))
  deriving ((forall x. Free f a -> Rep (Free f a) x)
-> (forall x. Rep (Free f a) x -> Free f a) -> Generic (Free f a)
forall x. Rep (Free f a) x -> Free f a
forall x. Free f a -> Rep (Free f a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall (f :: * -> *) a x. Rep (Free f a) x -> Free f a
forall (f :: * -> *) a x. Free f a -> Rep (Free f a) x
$cfrom :: forall (f :: * -> *) a x. Free f a -> Rep (Free f a) x
from :: forall x. Free f a -> Rep (Free f a) x
$cto :: forall (f :: * -> *) a x. Rep (Free f a) x -> Free f a
to :: forall x. Rep (Free f a) x -> Free f a
Generic, (forall a. Free f a -> Rep1 (Free f) a)
-> (forall a. Rep1 (Free f) a -> Free f a) -> Generic1 (Free f)
forall a. Rep1 (Free f) a -> Free f a
forall a. Free f a -> Rep1 (Free f) a
forall k (f :: k -> *).
(forall (a :: k). f a -> Rep1 f a)
-> (forall (a :: k). Rep1 f a -> f a) -> Generic1 f
forall (f :: * -> *) a. Functor f => Rep1 (Free f) a -> Free f a
forall (f :: * -> *) a. Functor f => Free f a -> Rep1 (Free f) a
$cfrom1 :: forall (f :: * -> *) a. Functor f => Free f a -> Rep1 (Free f) a
from1 :: forall a. Free f a -> Rep1 (Free f) a
$cto1 :: forall (f :: * -> *) a. Functor f => Rep1 (Free f) a -> Free f a
to1 :: forall a. Rep1 (Free f) a -> Free f a
Generic1)

deriving instance
  ( Typeable f
  , Data a, Data (f (Free f a))
  ) => Data (Free f a)

instance Eq1 f => Eq1 (Free f) where
  liftEq :: forall a b. (a -> b -> Bool) -> Free f a -> Free f b -> Bool
liftEq a -> b -> Bool
eq = Free f a -> Free f b -> Bool
forall {f :: * -> *}. Eq1 f => Free f a -> Free f b -> Bool
go
    where
      go :: Free f a -> Free f b -> Bool
go (Pure a
a)  (Pure b
b)  = a -> b -> Bool
eq a
a b
b
      go (Free f (Free f a)
fa) (Free f (Free f b)
fb) = (Free f a -> Free f b -> Bool)
-> f (Free f a) -> f (Free f b) -> Bool
forall a b. (a -> b -> Bool) -> f a -> f b -> Bool
forall (f :: * -> *) a b.
Eq1 f =>
(a -> b -> Bool) -> f a -> f b -> Bool
liftEq Free f a -> Free f b -> Bool
go f (Free f a)
fa f (Free f b)
fb
      go Free f a
_ Free f b
_                 = Bool
False

instance (Eq1 f, Eq a) => Eq (Free f a) where
  == :: Free f a -> Free f a -> Bool
(==) = Free f a -> Free f a -> Bool
forall (f :: * -> *) a. (Eq1 f, Eq a) => f a -> f a -> Bool
eq1

instance Ord1 f => Ord1 (Free f) where
  liftCompare :: forall a b.
(a -> b -> Ordering) -> Free f a -> Free f b -> Ordering
liftCompare a -> b -> Ordering
cmp = Free f a -> Free f b -> Ordering
forall {f :: * -> *}. Ord1 f => Free f a -> Free f b -> Ordering
go
    where
      go :: Free f a -> Free f b -> Ordering
go (Pure a
a)  (Pure b
b)  = a -> b -> Ordering
cmp a
a b
b
      go (Pure a
_)  (Free f (Free f b)
_)  = Ordering
LT
      go (Free f (Free f a)
_)  (Pure b
_)  = Ordering
GT
      go (Free f (Free f a)
fa) (Free f (Free f b)
fb) = (Free f a -> Free f b -> Ordering)
-> f (Free f a) -> f (Free f b) -> Ordering
forall a b. (a -> b -> Ordering) -> f a -> f b -> Ordering
forall (f :: * -> *) a b.
Ord1 f =>
(a -> b -> Ordering) -> f a -> f b -> Ordering
liftCompare Free f a -> Free f b -> Ordering
go f (Free f a)
fa f (Free f b)
fb

instance (Ord1 f, Ord a) => Ord (Free f a) where
  compare :: Free f a -> Free f a -> Ordering
compare = Free f a -> Free f a -> Ordering
forall (f :: * -> *) a. (Ord1 f, Ord a) => f a -> f a -> Ordering
compare1

instance Show1 f => Show1 (Free f) where
  liftShowsPrec :: forall a.
(Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Free f a -> ShowS
liftShowsPrec Int -> a -> ShowS
sp [a] -> ShowS
sl = Int -> Free f a -> ShowS
forall {f :: * -> *}. Show1 f => Int -> Free f a -> ShowS
go
    where
      go :: Int -> Free f a -> ShowS
go Int
d (Pure a
a) = (Int -> a -> ShowS) -> String -> Int -> a -> ShowS
forall a. (Int -> a -> ShowS) -> String -> Int -> a -> ShowS
showsUnaryWith Int -> a -> ShowS
sp String
"Pure" Int
d a
a
      go Int
d (Free f (Free f a)
fa) = (Int -> f (Free f a) -> ShowS)
-> String -> Int -> f (Free f a) -> ShowS
forall a. (Int -> a -> ShowS) -> String -> Int -> a -> ShowS
showsUnaryWith ((Int -> Free f a -> ShowS)
-> ([Free f a] -> ShowS) -> Int -> f (Free f a) -> ShowS
forall a.
(Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS
forall (f :: * -> *) a.
Show1 f =>
(Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS
liftShowsPrec Int -> Free f a -> ShowS
go ((Int -> a -> ShowS) -> ([a] -> ShowS) -> [Free f a] -> ShowS
forall a.
(Int -> a -> ShowS) -> ([a] -> ShowS) -> [Free f a] -> ShowS
forall (f :: * -> *) a.
Show1 f =>
(Int -> a -> ShowS) -> ([a] -> ShowS) -> [f a] -> ShowS
liftShowList Int -> a -> ShowS
sp [a] -> ShowS
sl)) String
"Free" Int
d f (Free f a)
fa

instance (Show1 f, Show a) => Show (Free f a) where
  showsPrec :: Int -> Free f a -> ShowS
showsPrec = Int -> Free f a -> ShowS
forall (f :: * -> *) a. (Show1 f, Show a) => Int -> f a -> ShowS
showsPrec1

instance Read1 f => Read1 (Free f) where
  liftReadsPrec :: forall a. (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Free f a)
liftReadsPrec Int -> ReadS a
rp ReadS [a]
rl = Int -> ReadS (Free f a)
go
    where
      go :: Int -> ReadS (Free f a)
go = (String -> ReadS (Free f a)) -> Int -> ReadS (Free f a)
forall a. (String -> ReadS a) -> Int -> ReadS a
readsData ((String -> ReadS (Free f a)) -> Int -> ReadS (Free f a))
-> (String -> ReadS (Free f a)) -> Int -> ReadS (Free f a)
forall a b. (a -> b) -> a -> b
$
        (Int -> ReadS a)
-> String -> (a -> Free f a) -> String -> ReadS (Free f a)
forall a t.
(Int -> ReadS a) -> String -> (a -> t) -> String -> ReadS t
readsUnaryWith Int -> ReadS a
rp String
"Pure" a -> Free f a
forall (f :: * -> *) a. a -> Free f a
Pure (String -> ReadS (Free f a))
-> (String -> ReadS (Free f a)) -> String -> ReadS (Free f a)
forall a. Monoid a => a -> a -> a
`mappend`
        (Int -> ReadS (f (Free f a)))
-> String
-> (f (Free f a) -> Free f a)
-> String
-> ReadS (Free f a)
forall a t.
(Int -> ReadS a) -> String -> (a -> t) -> String -> ReadS t
readsUnaryWith ((Int -> ReadS (Free f a))
-> ReadS [Free f a] -> Int -> ReadS (f (Free f a))
forall a. (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (f a)
forall (f :: * -> *) a.
Read1 f =>
(Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (f a)
liftReadsPrec Int -> ReadS (Free f a)
go ((Int -> ReadS a) -> ReadS [a] -> ReadS [Free f a]
forall a. (Int -> ReadS a) -> ReadS [a] -> ReadS [Free f a]
forall (f :: * -> *) a.
Read1 f =>
(Int -> ReadS a) -> ReadS [a] -> ReadS [f a]
liftReadList Int -> ReadS a
rp ReadS [a]
rl)) String
"Free" f (Free f a) -> Free f a
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free

instance (Read1 f, Read a) => Read (Free f a) where
  readsPrec :: Int -> ReadS (Free f a)
readsPrec = Int -> ReadS (Free f a)
forall (f :: * -> *) a. (Read1 f, Read a) => Int -> ReadS (f a)
readsPrec1

instance Functor f => Functor (Free f) where
  fmap :: forall a b. (a -> b) -> Free f a -> Free f b
fmap a -> b
f = Free f a -> Free f b
forall {f :: * -> *}. Functor f => Free f a -> Free f b
go where
    go :: Free f a -> Free f b
go (Pure a
a)  = b -> Free f b
forall (f :: * -> *) a. a -> Free f a
Pure (a -> b
f a
a)
    go (Free f (Free f a)
fa) = f (Free f b) -> Free f b
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (Free f a -> Free f b
go (Free f a -> Free f b) -> f (Free f a) -> f (Free f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f (Free f a)
fa)
  {-# INLINE fmap #-}

instance Apply f => Apply (Free f) where
  Pure a -> b
a  <.> :: forall a b. Free f (a -> b) -> Free f a -> Free f b
<.> Pure a
b = b -> Free f b
forall (f :: * -> *) a. a -> Free f a
Pure (a -> b
a a
b)
  Pure a -> b
a  <.> Free f (Free f a)
fb = f (Free f b) -> Free f b
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (f (Free f b) -> Free f b) -> f (Free f b) -> Free f b
forall a b. (a -> b) -> a -> b
$ (a -> b) -> Free f a -> Free f b
forall a b. (a -> b) -> Free f a -> Free f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
a (Free f a -> Free f b) -> f (Free f a) -> f (Free f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f (Free f a)
fb
  Free f (Free f (a -> b))
fa <.> Pure a
b = f (Free f b) -> Free f b
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (f (Free f b) -> Free f b) -> f (Free f b) -> Free f b
forall a b. (a -> b) -> a -> b
$ ((a -> b) -> b) -> Free f (a -> b) -> Free f b
forall a b. (a -> b) -> Free f a -> Free f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((a -> b) -> a -> b
forall a b. (a -> b) -> a -> b
$ a
b) (Free f (a -> b) -> Free f b)
-> f (Free f (a -> b)) -> f (Free f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f (Free f (a -> b))
fa
  Free f (Free f (a -> b))
fa <.> Free f (Free f a)
fb = f (Free f b) -> Free f b
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (f (Free f b) -> Free f b) -> f (Free f b) -> Free f b
forall a b. (a -> b) -> a -> b
$ (Free f (a -> b) -> Free f a -> Free f b)
-> f (Free f (a -> b)) -> f (Free f a -> Free f b)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Free f (a -> b) -> Free f a -> Free f b
forall a b. Free f (a -> b) -> Free f a -> Free f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
(<.>) f (Free f (a -> b))
fa f (Free f a -> Free f b) -> f (Free f a) -> f (Free f b)
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> f (Free f a)
fb

instance Applicative f => Applicative (Free f) where
  pure :: forall a. a -> Free f a
pure = a -> Free f a
forall (f :: * -> *) a. a -> Free f a
Pure
  {-# INLINE pure #-}
  Pure a -> b
a <*> :: forall a b. Free f (a -> b) -> Free f a -> Free f b
<*> Pure a
b = b -> Free f b
forall (f :: * -> *) a. a -> Free f a
Pure (b -> Free f b) -> b -> Free f b
forall a b. (a -> b) -> a -> b
$ a -> b
a a
b
  Pure a -> b
a <*> Free f (Free f a)
mb = f (Free f b) -> Free f b
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (f (Free f b) -> Free f b) -> f (Free f b) -> Free f b
forall a b. (a -> b) -> a -> b
$ (a -> b) -> Free f a -> Free f b
forall a b. (a -> b) -> Free f a -> Free f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
a (Free f a -> Free f b) -> f (Free f a) -> f (Free f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f (Free f a)
mb
  Free f (Free f (a -> b))
ma <*> Pure a
b = f (Free f b) -> Free f b
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (f (Free f b) -> Free f b) -> f (Free f b) -> Free f b
forall a b. (a -> b) -> a -> b
$ ((a -> b) -> b) -> Free f (a -> b) -> Free f b
forall a b. (a -> b) -> Free f a -> Free f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((a -> b) -> a -> b
forall a b. (a -> b) -> a -> b
$ a
b) (Free f (a -> b) -> Free f b)
-> f (Free f (a -> b)) -> f (Free f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f (Free f (a -> b))
ma
  Free f (Free f (a -> b))
ma <*> Free f (Free f a)
mb = f (Free f b) -> Free f b
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (f (Free f b) -> Free f b) -> f (Free f b) -> Free f b
forall a b. (a -> b) -> a -> b
$ (Free f (a -> b) -> Free f a -> Free f b)
-> f (Free f (a -> b)) -> f (Free f a -> Free f b)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Free f (a -> b) -> Free f a -> Free f b
forall a b. Free f (a -> b) -> Free f a -> Free f b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
(<*>) f (Free f (a -> b))
ma f (Free f a -> Free f b) -> f (Free f a) -> f (Free f b)
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f (Free f a)
mb

instance Apply f => Bind (Free f) where
  Pure a
a >>- :: forall a b. Free f a -> (a -> Free f b) -> Free f b
>>- a -> Free f b
f = a -> Free f b
f a
a
  Free f (Free f a)
m >>- a -> Free f b
f = f (Free f b) -> Free f b
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free ((Free f a -> (a -> Free f b) -> Free f b
forall a b. Free f a -> (a -> Free f b) -> Free f b
forall (m :: * -> *) a b. Bind m => m a -> (a -> m b) -> m b
>>- a -> Free f b
f) (Free f a -> Free f b) -> f (Free f a) -> f (Free f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f (Free f a)
m)

instance Applicative f => Monad (Free f) where
  return :: forall a. a -> Free f a
return = a -> Free f a
forall a. a -> Free f a
forall (f :: * -> *) a. Applicative f => a -> f a
pure
  {-# INLINE return #-}
  Pure a
a >>= :: forall a b. Free f a -> (a -> Free f b) -> Free f b
>>= a -> Free f b
f = a -> Free f b
f a
a
  Free f (Free f a)
m >>= a -> Free f b
f = f (Free f b) -> Free f b
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free ((Free f a -> (a -> Free f b) -> Free f b
forall a b. Free f a -> (a -> Free f b) -> Free f b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= a -> Free f b
f) (Free f a -> Free f b) -> f (Free f a) -> f (Free f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f (Free f a)
m)

instance Applicative f => MonadFix (Free f) where
  mfix :: forall a. (a -> Free f a) -> Free f a
mfix a -> Free f a
f = Free f a
a where a :: Free f a
a = a -> Free f a
f (Free f a -> a
forall {f :: * -> *} {a}. Free f a -> a
impure Free f a
a); impure :: Free f a -> a
impure (Pure a
x) = a
x; impure (Free f (Free f a)
_) = String -> a
forall a. HasCallStack => String -> a
error String
"mfix (Free f): Free"

-- | This violates the Alternative laws, handle with care.
instance Alternative v => Alternative (Free v) where
  empty :: forall a. Free v a
empty = v (Free v a) -> Free v a
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free v (Free v a)
forall a. v a
forall (f :: * -> *) a. Alternative f => f a
empty
  {-# INLINE empty #-}
  Free v a
a <|> :: forall a. Free v a -> Free v a -> Free v a
<|> Free v a
b = v (Free v a) -> Free v a
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (Free v a -> v (Free v a)
forall a. a -> v a
forall (f :: * -> *) a. Applicative f => a -> f a
pure Free v a
a v (Free v a) -> v (Free v a) -> v (Free v a)
forall a. v a -> v a -> v a
forall (f :: * -> *) a. Alternative f => f a -> f a -> f a
<|> Free v a -> v (Free v a)
forall a. a -> v a
forall (f :: * -> *) a. Applicative f => a -> f a
pure Free v a
b)
  {-# INLINE (<|>) #-}

-- | This violates the MonadPlus laws, handle with care.
instance MonadPlus v => MonadPlus (Free v) where
  mzero :: forall a. Free v a
mzero = v (Free v a) -> Free v a
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free v (Free v a)
forall a. v a
forall (m :: * -> *) a. MonadPlus m => m a
mzero
  {-# INLINE mzero #-}
  Free v a
a mplus :: forall a. Free v a -> Free v a -> Free v a
`mplus` Free v a
b = v (Free v a) -> Free v a
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (Free v a -> v (Free v a)
forall a. a -> v a
forall (m :: * -> *) a. Monad m => a -> m a
return Free v a
a v (Free v a) -> v (Free v a) -> v (Free v a)
forall a. v a -> v a -> v a
forall (m :: * -> *) a. MonadPlus m => m a -> m a -> m a
`mplus` Free v a -> v (Free v a)
forall a. a -> v a
forall (m :: * -> *) a. Monad m => a -> m a
return Free v a
b)
  {-# INLINE mplus #-}

-- | This is not a true monad transformer. It is only a monad transformer \"up to 'retract'\".
instance MonadTrans Free where
  lift :: forall (m :: * -> *) a. Monad m => m a -> Free m a
lift = m (Free m a) -> Free m a
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (m (Free m a) -> Free m a)
-> (m a -> m (Free m a)) -> m a -> Free m a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Free m a) -> m a -> m (Free m a)
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM a -> Free m a
forall (f :: * -> *) a. a -> Free f a
Pure
  {-# INLINE lift #-}

instance Foldable f => Foldable (Free f) where
  foldMap :: forall m a. Monoid m => (a -> m) -> Free f a -> m
foldMap a -> m
f = Free f a -> m
forall {t :: * -> *}. Foldable t => Free t a -> m
go where
    go :: Free t a -> m
go (Pure a
a) = a -> m
f a
a
    go (Free t (Free t a)
fa) = (Free t a -> m) -> t (Free t a) -> m
forall m a. Monoid m => (a -> m) -> t a -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap Free t a -> m
go t (Free t a)
fa
  {-# INLINE foldMap #-}

  foldr :: forall a b. (a -> b -> b) -> b -> Free f a -> b
foldr a -> b -> b
f = b -> Free f a -> b
forall {t :: * -> *}. Foldable t => b -> Free t a -> b
go where
    go :: b -> Free t a -> b
go b
r Free t a
free =
      case Free t a
free of
        Pure a
a -> a -> b -> b
f a
a b
r
        Free t (Free t a)
fa -> (Free t a -> b -> b) -> b -> t (Free t a) -> b
forall a b. (a -> b -> b) -> b -> t a -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr ((b -> Free t a -> b) -> Free t a -> b -> b
forall a b c. (a -> b -> c) -> b -> a -> c
flip b -> Free t a -> b
go) b
r t (Free t a)
fa
  {-# INLINE foldr #-}

  foldl' :: forall b a. (b -> a -> b) -> b -> Free f a -> b
foldl' b -> a -> b
f = b -> Free f a -> b
forall {t :: * -> *}. Foldable t => b -> Free t a -> b
go where
    go :: b -> Free t a -> b
go b
r Free t a
free =
      case Free t a
free of
        Pure a
a -> b -> a -> b
f b
r a
a
        Free t (Free t a)
fa -> (b -> Free t a -> b) -> b -> t (Free t a) -> b
forall b a. (b -> a -> b) -> b -> t a -> b
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl' b -> Free t a -> b
go b
r t (Free t a)
fa
  {-# INLINE foldl' #-}

instance Foldable1 f => Foldable1 (Free f) where
  foldMap1 :: forall m a. Semigroup m => (a -> m) -> Free f a -> m
foldMap1 a -> m
f = Free f a -> m
forall {t :: * -> *}. Foldable1 t => Free t a -> m
go where
    go :: Free t a -> m
go (Pure a
a) = a -> m
f a
a
    go (Free t (Free t a)
fa) = (Free t a -> m) -> t (Free t a) -> m
forall m a. Semigroup m => (a -> m) -> t a -> m
forall (t :: * -> *) m a.
(Foldable1 t, Semigroup m) =>
(a -> m) -> t a -> m
foldMap1 Free t a -> m
go t (Free t a)
fa
  {-# INLINE foldMap1 #-}

instance Traversable f => Traversable (Free f) where
  traverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Free f a -> f (Free f b)
traverse a -> f b
f = Free f a -> f (Free f b)
forall {f :: * -> *}. Traversable f => Free f a -> f (Free f b)
go where
    go :: Free f a -> f (Free f b)
go (Pure a
a) = b -> Free f b
forall (f :: * -> *) a. a -> Free f a
Pure (b -> Free f b) -> f b -> f (Free f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a
    go (Free f (Free f a)
fa) = f (Free f b) -> Free f b
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (f (Free f b) -> Free f b) -> f (f (Free f b)) -> f (Free f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (Free f a -> f (Free f b)) -> f (Free f a) -> f (f (Free f b))
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> f a -> f (f b)
traverse Free f a -> f (Free f b)
go f (Free f a)
fa
  {-# INLINE traverse #-}

instance Traversable1 f => Traversable1 (Free f) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Free f a -> f (Free f b)
traverse1 a -> f b
f = Free f a -> f (Free f b)
forall {f :: * -> *}. Traversable1 f => Free f a -> f (Free f b)
go where
    go :: Free f a -> f (Free f b)
go (Pure a
a) = b -> Free f b
forall (f :: * -> *) a. a -> Free f a
Pure (b -> Free f b) -> f b -> f (Free f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a
    go (Free f (Free f a)
fa) = f (Free f b) -> Free f b
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (f (Free f b) -> Free f b) -> f (f (Free f b)) -> f (Free f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (Free f a -> f (Free f b)) -> f (Free f a) -> f (f (Free f b))
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 Free f a -> f (Free f b)
go f (Free f a)
fa
  {-# INLINE traverse1 #-}

instance MonadWriter e m => MonadWriter e (Free m) where
  tell :: e -> Free m ()
tell = m () -> Free m ()
forall (m :: * -> *) a. Monad m => m a -> Free m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (m () -> Free m ()) -> (e -> m ()) -> e -> Free m ()
forall b c a. (b -> c) -> (a -> b) -> a -> c
. e -> m ()
forall w (m :: * -> *). MonadWriter w m => w -> m ()
tell
  {-# INLINE tell #-}
  listen :: forall a. Free m a -> Free m (a, e)
listen = m (a, e) -> Free m (a, e)
forall (m :: * -> *) a. Monad m => m a -> Free m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (m (a, e) -> Free m (a, e))
-> (Free m a -> m (a, e)) -> Free m a -> Free m (a, e)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. m a -> m (a, e)
forall a. m a -> m (a, e)
forall w (m :: * -> *) a. MonadWriter w m => m a -> m (a, w)
listen (m a -> m (a, e)) -> (Free m a -> m a) -> Free m a -> m (a, e)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Free m a -> m a
forall (f :: * -> *) a. Monad f => Free f a -> f a
retract
  {-# INLINE listen #-}
  pass :: forall a. Free m (a, e -> e) -> Free m a
pass = m a -> Free m a
forall (m :: * -> *) a. Monad m => m a -> Free m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (m a -> Free m a)
-> (Free m (a, e -> e) -> m a) -> Free m (a, e -> e) -> Free m a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. m (a, e -> e) -> m a
forall a. m (a, e -> e) -> m a
forall w (m :: * -> *) a. MonadWriter w m => m (a, w -> w) -> m a
pass (m (a, e -> e) -> m a)
-> (Free m (a, e -> e) -> m (a, e -> e))
-> Free m (a, e -> e)
-> m a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Free m (a, e -> e) -> m (a, e -> e)
forall (f :: * -> *) a. Monad f => Free f a -> f a
retract
  {-# INLINE pass #-}

instance MonadReader e m => MonadReader e (Free m) where
  ask :: Free m e
ask = m e -> Free m e
forall (m :: * -> *) a. Monad m => m a -> Free m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift m e
forall r (m :: * -> *). MonadReader r m => m r
ask
  {-# INLINE ask #-}
  local :: forall a. (e -> e) -> Free m a -> Free m a
local e -> e
f = m a -> Free m a
forall (m :: * -> *) a. Monad m => m a -> Free m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (m a -> Free m a) -> (Free m a -> m a) -> Free m a -> Free m a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (e -> e) -> m a -> m a
forall a. (e -> e) -> m a -> m a
forall r (m :: * -> *) a. MonadReader r m => (r -> r) -> m a -> m a
local e -> e
f (m a -> m a) -> (Free m a -> m a) -> Free m a -> m a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Free m a -> m a
forall (f :: * -> *) a. Monad f => Free f a -> f a
retract
  {-# INLINE local #-}

instance MonadState s m => MonadState s (Free m) where
  get :: Free m s
get = m s -> Free m s
forall (m :: * -> *) a. Monad m => m a -> Free m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift m s
forall s (m :: * -> *). MonadState s m => m s
get
  {-# INLINE get #-}
  put :: s -> Free m ()
put s
s = m () -> Free m ()
forall (m :: * -> *) a. Monad m => m a -> Free m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (s -> m ()
forall s (m :: * -> *). MonadState s m => s -> m ()
put s
s)
  {-# INLINE put #-}

instance MonadError e m => MonadError e (Free m) where
  throwError :: forall a. e -> Free m a
throwError = m a -> Free m a
forall (m :: * -> *) a. Monad m => m a -> Free m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (m a -> Free m a) -> (e -> m a) -> e -> Free m a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. e -> m a
forall a. e -> m a
forall e (m :: * -> *) a. MonadError e m => e -> m a
throwError
  {-# INLINE throwError #-}
  catchError :: forall a. Free m a -> (e -> Free m a) -> Free m a
catchError Free m a
as e -> Free m a
f = m a -> Free m a
forall (m :: * -> *) a. Monad m => m a -> Free m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (m a -> (e -> m a) -> m a
forall a. m a -> (e -> m a) -> m a
forall e (m :: * -> *) a.
MonadError e m =>
m a -> (e -> m a) -> m a
catchError (Free m a -> m a
forall (f :: * -> *) a. Monad f => Free f a -> f a
retract Free m a
as) (Free m a -> m a
forall (f :: * -> *) a. Monad f => Free f a -> f a
retract (Free m a -> m a) -> (e -> Free m a) -> e -> m a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. e -> Free m a
f))
  {-# INLINE catchError #-}

instance MonadCont m => MonadCont (Free m) where
  callCC :: forall a b. ((a -> Free m b) -> Free m a) -> Free m a
callCC (a -> Free m b) -> Free m a
f = m a -> Free m a
forall (m :: * -> *) a. Monad m => m a -> Free m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (((a -> m b) -> m a) -> m a
forall a b. ((a -> m b) -> m a) -> m a
forall (m :: * -> *) a b. MonadCont m => ((a -> m b) -> m a) -> m a
callCC (Free m a -> m a
forall (f :: * -> *) a. Monad f => Free f a -> f a
retract (Free m a -> m a) -> ((a -> m b) -> Free m a) -> (a -> m b) -> m a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Free m b) -> Free m a
f ((a -> Free m b) -> Free m a)
-> ((a -> m b) -> a -> Free m b) -> (a -> m b) -> Free m a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (m b -> Free m b) -> (a -> m b) -> a -> Free m b
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM m b -> Free m b
forall (m :: * -> *) a. Monad m => m a -> Free m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift))
  {-# INLINE callCC #-}

instance Applicative f => MonadFree f (Free f) where
  wrap :: forall a. f (Free f a) -> Free f a
wrap = f (Free f a) -> Free f a
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free
  {-# INLINE wrap #-}

-- |
-- 'retract' is the left inverse of 'lift' and 'liftF'
--
-- @
-- 'retract' . 'lift' = 'id'
-- 'retract' . 'liftF' = 'id'
-- @
retract :: Monad f => Free f a -> f a
retract :: forall (f :: * -> *) a. Monad f => Free f a -> f a
retract = (forall x. f x -> f x) -> Free f a -> f a
forall (f :: * -> *) (m :: * -> *) a.
(Applicative f, Monad m) =>
(forall x. f x -> m x) -> Free f a -> m a
foldFree f x -> f x
forall a. a -> a
forall x. f x -> f x
id

-- | Given an applicative homomorphism from @f@ to 'Identity', tear down a 'Free' 'Monad' using iteration.
iter :: Applicative f => (f a -> a) -> Free f a -> a
iter :: forall (f :: * -> *) a.
Applicative f =>
(f a -> a) -> Free f a -> a
iter f a -> a
_ (Pure a
a) = a
a
iter f a -> a
phi (Free f (Free f a)
m) = f a -> a
phi ((f a -> a) -> Free f a -> a
forall (f :: * -> *) a.
Applicative f =>
(f a -> a) -> Free f a -> a
iter f a -> a
phi (Free f a -> a) -> f (Free f a) -> f a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f (Free f a)
m)

-- | Like 'iter' for applicative values.
iterA :: (Applicative p, Applicative f) => (f (p a) -> p a) -> Free f a -> p a
iterA :: forall (p :: * -> *) (f :: * -> *) a.
(Applicative p, Applicative f) =>
(f (p a) -> p a) -> Free f a -> p a
iterA f (p a) -> p a
_   (Pure a
x) = a -> p a
forall a. a -> p a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
x
iterA f (p a) -> p a
phi (Free f (Free f a)
f) = f (p a) -> p a
phi ((f (p a) -> p a) -> Free f a -> p a
forall (p :: * -> *) (f :: * -> *) a.
(Applicative p, Applicative f) =>
(f (p a) -> p a) -> Free f a -> p a
iterA f (p a) -> p a
phi (Free f a -> p a) -> f (Free f a) -> f (p a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f (Free f a)
f)

-- | Like 'iter' for monadic values.
iterM :: (Monad m, Applicative f) => (f (m a) -> m a) -> Free f a -> m a
iterM :: forall (m :: * -> *) (f :: * -> *) a.
(Monad m, Applicative f) =>
(f (m a) -> m a) -> Free f a -> m a
iterM f (m a) -> m a
_   (Pure a
x) = a -> m a
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return a
x
iterM f (m a) -> m a
phi (Free f (Free f a)
f) = f (m a) -> m a
phi ((f (m a) -> m a) -> Free f a -> m a
forall (m :: * -> *) (f :: * -> *) a.
(Monad m, Applicative f) =>
(f (m a) -> m a) -> Free f a -> m a
iterM f (m a) -> m a
phi (Free f a -> m a) -> f (Free f a) -> f (m a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f (Free f a)
f)

-- | Lift an applicative homomorphism from @f@ to @g@ into a monad homomorphism from @'Free' f@ to @'Free' g@.
hoistFree :: (Applicative f, Applicative g) => (forall a. f a -> g a) -> Free f b -> Free g b
hoistFree :: forall (f :: * -> *) (g :: * -> *) b.
(Applicative f, Applicative g) =>
(forall a. f a -> g a) -> Free f b -> Free g b
hoistFree forall a. f a -> g a
f = (forall x. f x -> Free g x) -> Free f b -> Free g b
forall (f :: * -> *) (m :: * -> *) a.
(Applicative f, Monad m) =>
(forall x. f x -> m x) -> Free f a -> m a
foldFree (g x -> Free g x
forall (f :: * -> *) (m :: * -> *) a.
(Functor f, MonadFree f m) =>
f a -> m a
liftF (g x -> Free g x) -> (f x -> g x) -> f x -> Free g x
forall b c a. (b -> c) -> (a -> b) -> a -> c
. f x -> g x
forall a. f a -> g a
f)

-- | Given an applicative homomorphism, you get a monad homomorphism.
foldFree :: (Applicative f, Monad m) => (forall x . f x -> m x) -> Free f a -> m a
foldFree :: forall (f :: * -> *) (m :: * -> *) a.
(Applicative f, Monad m) =>
(forall x. f x -> m x) -> Free f a -> m a
foldFree forall x. f x -> m x
_ (Pure a
a)  = a -> m a
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return a
a
foldFree forall x. f x -> m x
f (Free f (Free f a)
as) = f (Free f a) -> m (Free f a)
forall x. f x -> m x
f f (Free f a)
as m (Free f a) -> (Free f a -> m a) -> m a
forall a b. m a -> (a -> m b) -> m b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= (forall x. f x -> m x) -> Free f a -> m a
forall (f :: * -> *) (m :: * -> *) a.
(Applicative f, Monad m) =>
(forall x. f x -> m x) -> Free f a -> m a
foldFree f x -> m x
forall x. f x -> m x
f

-- | Convert a 'Free' monad from "Control.Monad.Free.Ap" to a 'FreeT.FreeT' monad
-- from "Control.Monad.Trans.Free.Ap".
-- WARNING: This assumes that 'liftF' is an applicative homomorphism.
toFreeT :: (Applicative f, Monad m) => Free f a -> FreeT.FreeT f m a
toFreeT :: forall (f :: * -> *) (m :: * -> *) a.
(Applicative f, Monad m) =>
Free f a -> FreeT f m a
toFreeT = (forall x. f x -> FreeT f m x) -> Free f a -> FreeT f m a
forall (f :: * -> *) (m :: * -> *) a.
(Applicative f, Monad m) =>
(forall x. f x -> m x) -> Free f a -> m a
foldFree f x -> FreeT f m x
forall x. f x -> FreeT f m x
forall (f :: * -> *) (m :: * -> *) a.
(Functor f, MonadFree f m) =>
f a -> m a
liftF

-- | Cuts off a tree of computations at a given depth.
-- If the depth is 0 or less, no computation nor
-- monadic effects will take place.
--
-- Some examples (n ≥ 0):
--
-- prop> cutoff 0     _        == return Nothing
-- prop> cutoff (n+1) . return == return . Just
-- prop> cutoff (n+1) . lift   ==   lift . liftM Just
-- prop> cutoff (n+1) . wrap   ==  wrap . fmap (cutoff n)
--
-- Calling 'retract . cutoff n' is always terminating, provided each of the
-- steps in the iteration is terminating.
cutoff :: (Applicative f) => Integer -> Free f a -> Free f (Maybe a)
cutoff :: forall (f :: * -> *) a.
Applicative f =>
Integer -> Free f a -> Free f (Maybe a)
cutoff Integer
n Free f a
_ | Integer
n Integer -> Integer -> Bool
forall a. Ord a => a -> a -> Bool
<= Integer
0 = Maybe a -> Free f (Maybe a)
forall a. a -> Free f a
forall (m :: * -> *) a. Monad m => a -> m a
return Maybe a
forall a. Maybe a
Nothing
cutoff Integer
n (Free f (Free f a)
f) = f (Free f (Maybe a)) -> Free f (Maybe a)
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (f (Free f (Maybe a)) -> Free f (Maybe a))
-> f (Free f (Maybe a)) -> Free f (Maybe a)
forall a b. (a -> b) -> a -> b
$ (Free f a -> Free f (Maybe a))
-> f (Free f a) -> f (Free f (Maybe a))
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (Integer -> Free f a -> Free f (Maybe a)
forall (f :: * -> *) a.
Applicative f =>
Integer -> Free f a -> Free f (Maybe a)
cutoff (Integer
n Integer -> Integer -> Integer
forall a. Num a => a -> a -> a
- Integer
1)) f (Free f a)
f
cutoff Integer
_ Free f a
m = a -> Maybe a
forall a. a -> Maybe a
Just (a -> Maybe a) -> Free f a -> Free f (Maybe a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Free f a
m

-- | Unfold a free monad from a seed.
unfold :: Applicative f => (b -> Either a (f b)) -> b -> Free f a
unfold :: forall (f :: * -> *) b a.
Applicative f =>
(b -> Either a (f b)) -> b -> Free f a
unfold b -> Either a (f b)
f = b -> Either a (f b)
f (b -> Either a (f b))
-> (Either a (f b) -> Free f a) -> b -> Free f a
forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
Category cat =>
cat a b -> cat b c -> cat a c
>>> (a -> Free f a) -> (f b -> Free f a) -> Either a (f b) -> Free f a
forall a c b. (a -> c) -> (b -> c) -> Either a b -> c
either a -> Free f a
forall (f :: * -> *) a. a -> Free f a
Pure (f (Free f a) -> Free f a
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (f (Free f a) -> Free f a)
-> (f b -> f (Free f a)) -> f b -> Free f a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (b -> Free f a) -> f b -> f (Free f a)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((b -> Either a (f b)) -> b -> Free f a
forall (f :: * -> *) b a.
Applicative f =>
(b -> Either a (f b)) -> b -> Free f a
unfold b -> Either a (f b)
f))

-- | Unfold a free monad from a seed, monadically.
unfoldM :: (Applicative f, Traversable f, Monad m) => (b -> m (Either a (f b))) -> b -> m (Free f a)
unfoldM :: forall (f :: * -> *) (m :: * -> *) b a.
(Applicative f, Traversable f, Monad m) =>
(b -> m (Either a (f b))) -> b -> m (Free f a)
unfoldM b -> m (Either a (f b))
f = b -> m (Either a (f b))
f (b -> m (Either a (f b)))
-> (Either a (f b) -> m (Free f a)) -> b -> m (Free f a)
forall (m :: * -> *) a b c.
Monad m =>
(a -> m b) -> (b -> m c) -> a -> m c
>=> (a -> m (Free f a))
-> (f b -> m (Free f a)) -> Either a (f b) -> m (Free f a)
forall a c b. (a -> c) -> (b -> c) -> Either a b -> c
either (Free f a -> m (Free f a)
forall a. a -> m a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (Free f a -> m (Free f a)) -> (a -> Free f a) -> a -> m (Free f a)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Free f a
forall a. a -> Free f a
forall (f :: * -> *) a. Applicative f => a -> f a
pure) ((f (Free f a) -> Free f a) -> m (f (Free f a)) -> m (Free f a)
forall a b. (a -> b) -> m a -> m b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap f (Free f a) -> Free f a
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free (m (f (Free f a)) -> m (Free f a))
-> (f b -> m (f (Free f a))) -> f b -> m (Free f a)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (b -> m (Free f a)) -> f b -> m (f (Free f a))
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> f a -> f (f b)
traverse ((b -> m (Either a (f b))) -> b -> m (Free f a)
forall (f :: * -> *) (m :: * -> *) b a.
(Applicative f, Traversable f, Monad m) =>
(b -> m (Either a (f b))) -> b -> m (Free f a)
unfoldM b -> m (Either a (f b))
f))

-- | This is @Prism' (Free f a) a@ in disguise
--
-- >>> preview _Pure (Pure 3)
-- Just 3
--
-- >>> review _Pure 3 :: Free Maybe Int
-- Pure 3
_Pure :: forall f m a p. (Choice p, Applicative m)
      => p a (m a) -> p (Free f a) (m (Free f a))
_Pure :: forall (f :: * -> *) (m :: * -> *) a (p :: * -> * -> *).
(Choice p, Applicative m) =>
p a (m a) -> p (Free f a) (m (Free f a))
_Pure = (Free f a -> Either (Free f a) a)
-> (Either (Free f a) (m a) -> m (Free f a))
-> p (Either (Free f a) a) (Either (Free f a) (m a))
-> p (Free f a) (m (Free f a))
forall a b c d. (a -> b) -> (c -> d) -> p b c -> p a d
forall (p :: * -> * -> *) a b c d.
Profunctor p =>
(a -> b) -> (c -> d) -> p b c -> p a d
dimap Free f a -> Either (Free f a) a
forall {f :: * -> *} {b}. Free f b -> Either (Free f b) b
impure ((Free f a -> m (Free f a))
-> (m a -> m (Free f a)) -> Either (Free f a) (m a) -> m (Free f a)
forall a c b. (a -> c) -> (b -> c) -> Either a b -> c
either Free f a -> m (Free f a)
forall a. a -> m a
forall (f :: * -> *) a. Applicative f => a -> f a
pure ((a -> Free f a) -> m a -> m (Free f a)
forall a b. (a -> b) -> m a -> m b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> Free f a
forall (f :: * -> *) a. a -> Free f a
Pure)) (p (Either (Free f a) a) (Either (Free f a) (m a))
 -> p (Free f a) (m (Free f a)))
-> (p a (m a) -> p (Either (Free f a) a) (Either (Free f a) (m a)))
-> p a (m a)
-> p (Free f a) (m (Free f a))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. p a (m a) -> p (Either (Free f a) a) (Either (Free f a) (m a))
forall a b c. p a b -> p (Either c a) (Either c b)
forall (p :: * -> * -> *) a b c.
Choice p =>
p a b -> p (Either c a) (Either c b)
right'
 where
  impure :: Free f b -> Either (Free f b) b
impure (Pure b
x) = b -> Either (Free f b) b
forall a b. b -> Either a b
Right b
x
  impure Free f b
x        = Free f b -> Either (Free f b) b
forall a b. a -> Either a b
Left Free f b
x
  {-# INLINE impure #-}
{-# INLINE _Pure #-}

-- | This is @Prism' (Free f a) (f (Free f a))@ in disguise
--
-- >>> preview _Free (review _Free (Just (Pure 3)))
-- Just (Just (Pure 3))
--
-- >>> review _Free (Just (Pure 3))
-- Free (Just (Pure 3))
_Free :: forall f m a p. (Choice p, Applicative m)
      => p (f (Free f a)) (m (f (Free f a))) -> p (Free f a) (m (Free f a))
_Free :: forall (f :: * -> *) (m :: * -> *) a (p :: * -> * -> *).
(Choice p, Applicative m) =>
p (f (Free f a)) (m (f (Free f a))) -> p (Free f a) (m (Free f a))
_Free = (Free f a -> Either (Free f a) (f (Free f a)))
-> (Either (Free f a) (m (f (Free f a))) -> m (Free f a))
-> p (Either (Free f a) (f (Free f a)))
     (Either (Free f a) (m (f (Free f a))))
-> p (Free f a) (m (Free f a))
forall a b c d. (a -> b) -> (c -> d) -> p b c -> p a d
forall (p :: * -> * -> *) a b c d.
Profunctor p =>
(a -> b) -> (c -> d) -> p b c -> p a d
dimap Free f a -> Either (Free f a) (f (Free f a))
forall {f :: * -> *} {a}.
Free f a -> Either (Free f a) (f (Free f a))
unfree ((Free f a -> m (Free f a))
-> (m (f (Free f a)) -> m (Free f a))
-> Either (Free f a) (m (f (Free f a)))
-> m (Free f a)
forall a c b. (a -> c) -> (b -> c) -> Either a b -> c
either Free f a -> m (Free f a)
forall a. a -> m a
forall (f :: * -> *) a. Applicative f => a -> f a
pure ((f (Free f a) -> Free f a) -> m (f (Free f a)) -> m (Free f a)
forall a b. (a -> b) -> m a -> m b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap f (Free f a) -> Free f a
forall (f :: * -> *) a. f (Free f a) -> Free f a
Free)) (p (Either (Free f a) (f (Free f a)))
   (Either (Free f a) (m (f (Free f a))))
 -> p (Free f a) (m (Free f a)))
-> (p (f (Free f a)) (m (f (Free f a)))
    -> p (Either (Free f a) (f (Free f a)))
         (Either (Free f a) (m (f (Free f a)))))
-> p (f (Free f a)) (m (f (Free f a)))
-> p (Free f a) (m (Free f a))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. p (f (Free f a)) (m (f (Free f a)))
-> p (Either (Free f a) (f (Free f a)))
     (Either (Free f a) (m (f (Free f a))))
forall a b c. p a b -> p (Either c a) (Either c b)
forall (p :: * -> * -> *) a b c.
Choice p =>
p a b -> p (Either c a) (Either c b)
right'
 where
  unfree :: Free f a -> Either (Free f a) (f (Free f a))
unfree (Free f (Free f a)
x) = f (Free f a) -> Either (Free f a) (f (Free f a))
forall a b. b -> Either a b
Right f (Free f a)
x
  unfree Free f a
x        = Free f a -> Either (Free f a) (f (Free f a))
forall a b. a -> Either a b
Left Free f a
x
  {-# INLINE unfree #-}
{-# INLINE _Free #-}