{-# LANGUAGE TypeOperators #-} {-# LANGUAGE PatternGuards #-} {-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE FlexibleContexts #-} -- | An example of non-trivial interaction of effects, handling of two -- effects together -- Non-determinism with control (cut) -- For the explanation of cut, see Section 5 of Hinze ICFP 2000 paper. -- Hinze suggests expressing cut in terms of cutfalse: -- -- > = return () `mplus` cutfalse -- > where -- > cutfalse :: m a -- -- satisfies the following laws: -- -- > cutfalse >>= k = cutfalse (F1) -- > cutfalse | m = cutfalse (F2) -- -- (note: @m \``mplus`\` cutfalse@ is different from @cutfalse \``mplus`\` m@) -- In other words, cutfalse is the left zero of both bind and mplus. -- -- Hinze also introduces the operation @`call` :: m a -> m a@ that -- delimits the effect of cut: @`call` m@ executes m. If the cut is -- invoked in m, it discards only the choices made since m was called. -- Hinze postulates the axioms of `call`: -- -- > call false = false (C1) -- > call (return a | m) = return a | call m (C2) -- > call (m | cutfalse) = call m (C3) -- > call (lift m >>= k) = lift m >>= (call . k) (C4) -- -- @`call` m@ behaves like @m@ except any cut inside @m@ has only a local effect, -- he says. -- -- Hinze noted a problem with the \"mechanical\" derivation of backtracing -- monad transformer with cut: no axiom specifying the interaction of -- call with bind; no way to simplify nested invocations of call. -- -- We use exceptions for cutfalse -- Therefore, the law @cutfalse >>= k = cutfalse@ -- is satisfied automatically since all exceptions have the above property. module Control.Eff.Cut( CutFalse , call , cutfalse ) where import Control.Applicative ((<$>)) import Data.Typeable import Control.Eff import Control.Eff.Choose import Control.Eff.Exception data CutFalse = CutFalse deriving Typeable cutfalse :: Member (Exc CutFalse) r => Eff r a cutfalse = throwExc CutFalse -- | The interpreter -- it is like reify . reflect with a twist -- Compare this implementation with the huge implementation of call -- in Hinze 2000 (Figure 9) -- Each clause corresponds to the axiom of call or cutfalse. -- All axioms are covered. -- The code clearly expresses the intuition that call watches the choice points -- of its argument computation. When it encounteres a cutfalse request, -- it discards the remaining choicepoints. -- It completely handles CutFalse effects but not non-determinism. call :: Member Choose r => Eff (Exc CutFalse :> r) a -> Eff r a call m = loop [] (admin m) where loop jq (Val x) = return x `mplus'` next jq -- (C2) loop jq (E u) = case decomp u of Right (Exc CutFalse) -> mzero' -- drop jq (F2) Left u' -> check jq u' check jq u | Just (Choose [] _) <- prj u = next jq -- (C1) check jq u | Just (Choose [x] k) <- prj u = loop jq (k x) -- (C3), optim check jq u | Just (Choose lst k) <- prj u = next $ map k lst ++ jq -- (C3) check jq u = send (<$> u) >>= loop jq -- (C4) next [] = mzero' next (h:t) = loop t h