Add CofreeT (#26)

Author: Vladimir Ciobanu

CHANGELOG.md

@@ -6,6 +6,8 @@ Notable changes to this project are documented in this file. The format is based
 
 Breaking changes (😱!!!):
 
+- added the `CofreeT`, the cofree monad transformer in a new module (`Control.Monad.Cofree.Trans`) ([#26](https://github.com/purescript-contrib/purescript-freet/pull/26))
+
 New features:
 
 Bugfixes:

spago.dhall

@@ -6,9 +6,11 @@
   , "effect"
   , "either"
   , "exists"
+  , "free"
   , "prelude"
   , "psci-support"
   , "tailrec"
+  , "tuples"
   , "transformers"
   ]
 , packages = ./packages.dhall

src/Control/Comonad/Cofree/Trans.purs

@@ -0,0 +1,149 @@
+-- | This module defines a lazy implementation of the _cofree monad transformer_.
+
+-- | Given a `CofreeT` f m a:
+-- | - 'f' is a `Functor`, generally representing an AST,
+-- | - 'm' is a 'Monad', generally representing an effect,
+-- | - and 'a' is the type of the annotation.
+-- |
+-- | Usually, you would use `CofreeT` to annotate an existing AST with
+-- | metadata such as source locations, file names, etc.
+
+module Control.Comonad.Cofree.Trans where
+
+import Prelude
+
+import Control.Alternative (class Alt, class Plus, empty, (<|>))
+import Control.Apply (lift2)
+import Control.Comonad (class Comonad, class Extend, extend, extract)
+import Control.Comonad.Cofree.Class (class ComonadCofree)
+import Control.Comonad.Env.Class (class ComonadAsk, ask)
+import Control.Comonad.Trans.Class (class ComonadTrans)
+import Control.Monad.Trans.Class (class MonadTrans)
+import Data.Bifunctor (bimap)
+import Data.Foldable (class Foldable, foldMap, foldlDefault, foldrDefault)
+import Data.Traversable (class Traversable, sequenceDefault, traverse)
+import Data.Tuple (Tuple(..))
+import Data.Tuple as T
+import Effect.Aff.Class (class MonadAff, liftAff)
+import Effect.Class (class MonadEffect, liftEffect)
+
+-- | The cofree comonad transformer for the functor 'f'.
+newtype CofreeT f w a = CofreeT (Unit -> w (Tuple a (f (CofreeT f w a))))
+
+-- | Construct a `CofreeT` from a lazy computation with an annotation 'a'.
+cofreeT
+    :: forall f w a
+     . (Unit -> w (Tuple a (f (CofreeT f w a))))
+    -> CofreeT f w a
+cofreeT = CofreeT
+
+-- | Construct a `CofreeT` from a computation with an annotation 'a'.
+cofreeT'
+    :: forall f w a
+     . w (Tuple a (f (CofreeT f w a)))
+    -> CofreeT f w a
+cofreeT' t = CofreeT $ (\_ -> t)
+
+-- | Unpack `CofreeT` into the inner computation.
+runCofreeT :: forall f w a. CofreeT f w a -> w (Tuple a (f (CofreeT f w a)))
+runCofreeT (CofreeT f) = f unit
+
+-- | Obtain the annotation stored within a `CofreeT`.
+head :: forall f w a. Functor w => CofreeT f w a -> w a
+head = map T.fst <<< runCofreeT
+
+-- | Obtain the inner computation stored within a `CofreeT`.
+tail :: forall f w a. Functor w => CofreeT f w a -> w (f (CofreeT f w a))
+tail = map T.snd <<< runCofreeT
+
+-- Note: This cannot be automatically derived because 'a' also appears in the
+-- 'fst' position of the inner Tuple.
+instance functorCofreeT :: (Functor w, Functor f) => Functor (CofreeT f w) where
+  map f (CofreeT inner) = CofreeT $ map (map (bimap f (map (map f)))) inner
+
+instance applyCofreeT :: (Apply w, Apply f) => Apply (CofreeT f w) where
+  apply (CofreeT innerF) (CofreeT inner) =
+    CofreeT
+      $ \_ ->
+        go <$> innerF unit <*> inner unit
+    where
+      go (Tuple f nextF) (Tuple x nextX) =
+        Tuple (f x) (lift2 (<*>) nextF nextX)
+
+instance applicativeCofreeT :: (Applicative w, Apply f, Plus f) => Applicative (CofreeT f w) where
+  pure a = CofreeT $ \_ -> pure (Tuple a empty)
+
+instance bindCofreeT :: (Monad w, Alt f, Apply f) => Bind (CofreeT f w) where
+  bind (CofreeT inner) f =
+    CofreeT
+      $ \_ -> do
+        (Tuple a m) <- inner unit
+        let (CofreeT next) = f a
+        (Tuple b n) <- next unit
+        pure $ Tuple b (n <|> map (_ >>= f) m)
+
+instance monadCofreeT :: (Monad w, Plus f, Apply f) => Monad (CofreeT f w)
+
+instance monadTransCofreeT :: Plus f => MonadTrans (CofreeT f) where
+  lift = cofreeT' <<< map go
+    where
+      go x = Tuple x empty
+
+instance monadEffectCofreeT :: (MonadEffect w, Plus f, Apply f) => MonadEffect (CofreeT f w) where
+  liftEffect eff = cofreeT' $ go <$> liftEffect eff
+    where
+      go a = Tuple a empty
+
+instance monadAffCofreeT :: (MonadAff w, Plus f, Apply f) => MonadAff (CofreeT f w) where
+  liftAff aff = cofreeT' $ go <$> liftAff aff
+    where
+      go a = Tuple a empty
+
+instance comonadCofreeCofreeT :: (Comonad w, Functor f) => ComonadCofree f (CofreeT f w) where
+  unwrapCofree = extract <<< tail
+
+instance comonadTransCofreeT :: ComonadTrans (CofreeT f) where
+  lower = head
+
+instance comonadAskCofreeT :: (Functor f, ComonadAsk e w) => ComonadAsk e (CofreeT f w) where
+  ask = ask <<< tail
+
+instance foldableCofreeT :: (Foldable w, Foldable f) => Foldable (CofreeT f w) where
+  foldMap f (CofreeT inner) = foldMap go $ inner unit
+    where
+      go (Tuple a next) = f a <> foldMap (foldMap f) next
+
+  foldr abb b = foldrDefault abb b
+
+  foldl bab b = foldlDefault bab b
+
+instance traversableCofreeT :: (Traversable w, Traversable f) => Traversable (CofreeT f w) where
+  traverse f (CofreeT inner) =
+    cofreeT' <$> traverse go (inner unit)
+    where
+      go (Tuple a next) = Tuple <$> f a <*> traverse (traverse f) next
+
+  sequence = sequenceDefault
+
+instance extendCofreeT :: (Comonad w, Functor f) => Extend (CofreeT f w) where
+  extend f (CofreeT inner) = CofreeT $ \_ -> extend go (inner unit)
+    where
+      go w = Tuple (f $ cofreeT' w) $ extend f <$> T.snd (extract w)
+
+instance comonadCofreeT :: (Comonad w, Functor f) => Comonad (CofreeT f w) where
+  extract = extract <<< head
+
+-- | 'hoist' the effect type using a natural transform.
+hoistCofreeT :: forall f w u a. Functor f => Functor u => (w ~> u) -> CofreeT f w a -> CofreeT f u a
+hoistCofreeT nm = bimapCofreeT identity nm
+
+-- | 'interpret' the inner functor using a natural transform.
+interpretCofreeT :: forall f g w a. Functor g => Functor w => (f ~> g) -> CofreeT f w a -> CofreeT g w a
+interpretCofreeT nf = bimapCofreeT nf identity
+
+-- | Both 'interpret' and 'hoist' the inner functor as well as the effect using natural transforms.
+bimapCofreeT :: forall f g w u a. Functor u => Functor g => (f ~> g) -> (w ~> u) -> CofreeT f w a -> CofreeT g u a
+bimapCofreeT nf nm (CofreeT inner) = CofreeT $ (map (map (map go))) $ map nm inner
+  where
+    go :: f (CofreeT f w a) -> g (CofreeT g u a)
+    go = map (bimapCofreeT nf nm) <<< nf

test/CofreeTExample.purs

@@ -0,0 +1,26 @@
+module Test.CofreeTExample where
+
+import Prelude
+
+import Control.Comonad.Cofree.Trans (CofreeT, cofreeT, head, tail)
+import Data.List (List(..), fromFoldable, (:))
+import Data.Maybe (Maybe(..), fromMaybe)
+import Data.Tuple (Tuple(..))
+import Effect (Effect)
+import Effect.Console (logShow)
+
+type IndexedList = CofreeT List Maybe Int
+
+list :: IndexedList
+list = cofreeT (go 5)
+  where
+    go :: Int -> Unit -> Maybe (Tuple Int (List IndexedList))
+    go 0 _ = Just $ Tuple 0 Nil
+    go 5 _ = Just $ Tuple 5 (fromFoldable $ cofreeT <$> (go <$> [4, 3]))
+    go i _ = Just $ Tuple i (pure $ cofreeT (go (i - 1)))
+
+annotations :: IndexedList -> List (Maybe Int)
+annotations il = head il : join (annotations <$> fromMaybe mempty (tail il))
+
+main :: Effect Unit
+main = logShow $ annotations list