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Here's an example interpreter where the type system lets you cover all the cases:
{-# LANGUAGE GADTs #-}
module Exp
where
data Exp a where
Num :: (Num a) => a -> Exp a
Bool :: Bool -> Exp Bool
Plus :: (Num a) => Exp a -> Exp a -> Exp a
If :: Exp Bool -> Exp a -> Exp a -> Exp a
Lt :: (Num a, Ord a) => Exp a -> Exp a -> Exp Bool
Lam :: (a -> Exp b) -> Exp (a -> b) -- higher order abstract syntax
App :: Exp (a -> b) -> Exp a -> Exp b
-- deriving (Show) -- failse
eval :: Exp a -> a
eval (Num n) = n
eval (Bool b) = b
eval (Plus e1 e2) = eval e1 + eval e2
eval (If p t f) = eval $ if eval p then t else f
eval (Lt e1 e2) = eval e1 < eval e2
eval (Lam body) = \x -> eval $ body x
eval (App f a) = eval f $ eval a
instance Eq a => Eq (Exp a) where
e1 == e2 = eval e1 == eval e2
instance Show (Exp a) where
show e = "<exp>" -- very weak show instance
instance (Num a) => Num (Exp a) where
fromInteger = Num
(+) = Plus
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Recommendations
Generalized algebraic data types
Recommended 11 years ago
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