Add initial implementation of MonadLogic and SFKT-based LogicT

spago.dhall

@@ -10,8 +10,9 @@ When creating a new Spago project, you can use
 `spago init --no-comments` or `spago init -C`
 to generate this file without the comments in this block.
 -}
-{ name = "my-project"
-, dependencies = [ "console", "effect", "prelude" ]
+{ name = "logic"
+, dependencies =
+  [ "control", "lists", "maybe", "prelude", "transformers", "tuples" ]
 , packages = ./packages.dhall
 , sources = [ "src/**/*.purs", "test/**/*.purs" ]
 }

src/Main.purs

@@ -2,9 +2,92 @@ module Main where
 
 import Prelude
 
-import Effect (Effect)
-import Effect.Console (log)
+import Control.MonadPlus (class MonadPlus, class Alternative, class Alt, class Plus, (<|>), empty)
+import Control.Monad.Trans.Class (class MonadTrans, lift)
+import Control.Monad.Reader.Class (class MonadReader, local, class MonadAsk, ask)
+import Control.Monad.State.Class (class MonadState, state)
+import Control.Monad.State (runStateT)
+import Control.Monad.State.Trans (StateT(..))
+import Data.Tuple.Nested (type (/\), (/\))
+import Data.Maybe (Maybe(..))
 
-main :: Effect Unit
-main = do
-  log "🍝"
+class (MonadPlus m) <= MonadLogic m where
+    msplit :: forall a. m a -> m (Maybe (a /\ (m a)))
+    interleave :: forall a. m a -> m a -> m a
+
+fbind :: forall a b m. MonadLogic m => m a -> (a -> m b) -> m b
+fbind m f = do
+    r <- msplit m
+    case r of
+        Nothing -> empty
+        Just (a /\ m') -> interleave (f a) (m' `fbind` f)
+
+reflect :: forall a m. MonadLogic m => Maybe (a /\ m a) -> m a
+reflect Nothing = empty
+reflect (Just (a /\ ma)) = pure a <|> ma
+
+infixl 1 fbind as >>-
+
+type FK :: Type -> Type
+type FK ans = ans
+
+type SK :: Type -> Type -> Type
+type SK ans a = a -> FK ans -> ans
+
+newtype SFKT :: (Type -> Type) -> Type -> Type
+newtype SFKT m a = SFKT (forall ans. SK (m ans) a -> FK (m ans) -> m ans)
+
+unSFKT :: forall a m. SFKT m a -> forall ans. SK (m ans) a -> FK (m ans) -> m ans
+unSFKT (SFKT f) = f
+
+instance Functor (SFKT m) where
+    map f m = SFKT (\sk -> unSFKT m (\a -> sk (f a)))
+
+instance Apply m => Apply (SFKT m) where
+    apply mf ma = SFKT (\sk -> unSFKT mf (\f -> unSFKT ma (\a -> sk (f a))))
+
+instance Applicative m => Applicative (SFKT m) where
+    pure a = SFKT (\sk fk -> sk a fk)
+
+instance Bind m => Bind (SFKT m) where
+    bind m f = SFKT (\sk -> unSFKT m (\a -> unSFKT (f a) sk))
+
+instance Monad m => Monad (SFKT m)
+
+instance Alt (SFKT m) where
+    alt m1 m2 = SFKT (\sk fk -> unSFKT m1 sk (unSFKT m2 sk fk))
+
+instance Plus (SFKT m) where
+    empty = SFKT (\_ fk -> fk)
+
+instance Applicative m => Alternative (SFKT m)
+
+instance Monad m => MonadPlus (SFKT m)
+
+instance MonadTrans SFKT where
+    lift m = SFKT (\sk fk -> m >>= (\a -> sk a fk))
+
+instance Monad m => MonadLogic (SFKT m) where
+    msplit ma = lift (unSFKT ma (\a fk -> pure (Just (a /\ (lift fk >>= reflect)))) (pure Nothing))
+    interleave m1 m2 = do
+        r <- msplit m1
+        case r of
+            Nothing -> m2
+            Just (a /\ m1') -> pure a <|> interleave m2 m1'
+
+instance MonadAsk r m => MonadAsk r (SFKT m) where
+    ask = lift ask
+
+instance MonadReader r m => MonadReader r (SFKT m) where
+    local f m = SFKT (\sk -> unSFKT m (\a -> local f <<< sk a))
+
+instance MonadState s m => MonadState s (SFKT m) where
+    state f = lift $ state f
+
+instance MonadLogic m => MonadLogic (StateT s m) where
+    msplit sm = StateT $ \s -> do
+        r <- msplit (runStateT sm s)
+        case r of
+            Nothing -> pure (Nothing /\ s)
+            Just ((a /\ s') /\ m) -> pure (Just (a /\ (StateT $ const m)) /\ s')
+    interleave m1 m2 = StateT $ \s -> runStateT m1 s <|> runStateT m2 s