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Refactor the Logic monad into Class and Trans modules

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This commit is contained in:
Danila Fedorin 2023-02-28 18:54:07 -08:00
parent 124b9a8d56
commit 529879736a
3 changed files with 104 additions and 93 deletions
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37
src/Control/Monad/Logic/Class.purs Normal file
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module Control.Monad.Logic.Class (class MonadLogic, msplit, interleave, fbind, reflect, (>>-)) where
import Prelude
import Control.MonadPlus (class MonadPlus, class Alternative, class Alt, class Plus, (<|>), empty)
import Control.Monad.Reader.Class (class MonadReader, local, class MonadAsk, ask)
import Control.Monad.State (runStateT)
import Control.Monad.State.Class (class MonadState, state)
import Control.Monad.State.Trans (StateT(..))
import Control.Monad.Trans.Class (class MonadTrans, lift)
import Data.Tuple.Nested (type (/\), (/\))
import Data.Maybe (Maybe(..))
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 >>-
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

67
src/Control/Monad/Logic/Trans.purs Normal file
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module Control.Monad.Logic.Trans (SFKT, runSFKT) where
import Prelude (class Applicative, class Apply, class Bind, class Functor, class Monad, bind, pure, ($), (<<<), (>>=))
import Control.Monad.Logic.Class
import Control.MonadPlus (class MonadPlus, class Alternative, class Alt, class Plus, (<|>))
import Control.Monad.Reader.Class (class MonadReader, local, class MonadAsk, ask)
import Control.Monad.State.Class (class MonadState, state)
import Control.Monad.Trans.Class (class MonadTrans, lift)
import Data.Tuple.Nested ((/\))
import Data.Maybe (Maybe(..))
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)
runSFKT :: forall a m. SFKT m a -> forall ans. SK (m ans) a -> FK (m ans) -> m ans
runSFKT (SFKT f) = f
instance Functor (SFKT m) where
map f m = SFKT (\sk -> runSFKT m (\a -> sk (f a)))
instance Apply m => Apply (SFKT m) where
apply mf ma = SFKT (\sk -> runSFKT mf (\f -> runSFKT 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 -> runSFKT m (\a -> runSFKT (f a) sk))
instance Monad m => Monad (SFKT m)
instance Alt (SFKT m) where
alt m1 m2 = SFKT (\sk fk -> runSFKT m1 sk (runSFKT 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 (runSFKT 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 -> runSFKT m (\a -> local f <<< sk a))
instance MonadState s m => MonadState s (SFKT m) where
state f = lift $ state f

93
src/Main.purs
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module Main where
import Prelude
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(..))
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