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-{-# LANGUAGE CPP #-}
-{-# LANGUAGE DeriveFunctor #-}
-{-# LANGUAGE UndecidableInstances #-}
-{-# LANGUAGE Rank2Types #-}
-{-# LANGUAGE FlexibleInstances #-}
-{-# LANGUAGE MultiParamTypeClasses #-}
-
--------------------------------------------------------------------------
--- |
--- Module : Control.Monad.Logic
--- Copyright : (c) Dan Doel
--- License : BSD3
---
--- Maintainer : dan.doel@gmail.com
--- Stability : experimental
--- Portability : non-portable (multi-parameter type classes)
---
--- A backtracking, logic programming monad.
---
--- Adapted from the paper
--- /Backtracking, Interleaving, and Terminating
--- Monad Transformers/, by
--- Oleg Kiselyov, Chung-chieh Shan, Daniel P. Friedman, Amr Sabry
--- (<http://www.cs.rutgers.edu/~ccshan/logicprog/ListT-icfp2005.pdf>).
--------------------------------------------------------------------------
-
-module ListT (
- ListT(..),
- runListT,
- select,
- fold
- ) where
-
-import GhcPrelude
-
-import Control.Applicative
-
-import Control.Monad
-import Control.Monad.Fail as MonadFail
-
--------------------------------------------------------------------------
--- | A monad transformer for performing backtracking computations
--- layered over another monad 'm'
-newtype ListT m a =
- ListT { unListT :: forall r. (a -> m r -> m r) -> m r -> m r }
- deriving (Functor)
-
-select :: Monad m => [a] -> ListT m a
-select xs = foldr (<|>) mzero (map pure xs)
-
-fold :: ListT m a -> (a -> m r -> m r) -> m r -> m r
-fold = runListT
-
--------------------------------------------------------------------------
--- | Runs a ListT computation with the specified initial success and
--- failure continuations.
-runListT :: ListT m a -> (a -> m r -> m r) -> m r -> m r
-runListT = unListT
-
-instance Applicative (ListT f) where
- pure a = ListT $ \sk fk -> sk a fk
- f <*> a = ListT $ \sk fk -> unListT f (\g fk' -> unListT a (sk . g) fk') fk
-
-instance Alternative (ListT f) where
- empty = ListT $ \_ fk -> fk
- f1 <|> f2 = ListT $ \sk fk -> unListT f1 sk (unListT f2 sk fk)
-
-instance Monad (ListT m) where
- m >>= f = ListT $ \sk fk -> unListT m (\a fk' -> unListT (f a) sk fk') fk
-#if !MIN_VERSION_base(4,13,0)
- fail = MonadFail.fail
-#endif
-
-instance MonadFail.MonadFail (ListT m) where
- fail _ = ListT $ \_ fk -> fk
-
-instance MonadPlus (ListT m) where
- mzero = ListT $ \_ fk -> fk
- m1 `mplus` m2 = ListT $ \sk fk -> unListT m1 sk (unListT m2 sk fk)