utils/ListT.hs

    {-# 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 Control.Applicative

    import Control.Monad

    -------------------------------------------------------------------------
    -- | 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 }

    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 Functor (ListT f) where
        fmap f lt = ListT $ \sk fk -> unListT lt (sk . f) fk

    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
        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)