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{-# LANGUAGE TemplateHaskell, TypeOperators, MultiParamTypeClasses,
FlexibleInstances, FlexibleContexts, UndecidableInstances,
ConstraintKinds #-}
--------------------------------------------------------------------------------
-- |
-- Module : Examples.Eval
-- Copyright : (c) 2011 Patrick Bahr, Tom Hvitved
-- License : BSD3
-- Maintainer : Tom Hvitved <hvitved@diku.dk>
-- Stability : experimental
-- Portability : non-portable (GHC Extensions)
--
-- Expression Evaluation
--
-- The example illustrates how to use compositional data types to implement
-- a small expression language, with a sub language of values, and an evaluation
-- function mapping expressions to values.
--
--------------------------------------------------------------------------------
module Examples.Eval where
import Data.Comp
import Data.Comp.Show ()
import Data.Comp.Derive
import Examples.Common
-- Term evaluation algebra
class Eval f v where
evalAlg :: Alg f (Term v)
$(derive [liftSum] [''Eval])
-- Lift the evaluation algebra to a catamorphism
eval :: (Functor f, Eval f v) => Term f -> Term v
eval = cata evalAlg
instance {-# OVERLAPPABLE #-} (f :<: v) => Eval f v where
evalAlg = inject -- default instance
instance {-# OVERLAPPABLE #-} (Value :<: v) => Eval Op v where
evalAlg (Add x y) = iConst $ projC x + projC y
evalAlg (Mult x y) = iConst $ projC x * projC y
evalAlg (Fst x) = fst $ projP x
evalAlg (Snd x) = snd $ projP x
projC :: (Value :<: v) => Term v -> Int
projC v = case project v of Just (Const n) -> n
projP :: (Value :<: v) => Term v -> (Term v, Term v)
projP v = case project v of Just (Pair x y) -> (x,y)
-- Example: evalEx = iConst 5
evalEx :: Term Value
evalEx = eval (iConst 1 `iAdd` (iConst 2 `iMult` iConst 2) :: Term Sig)
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