Phantom type evaluator example

Phantoms.hs

module Phantom (
    ei, eb, plus, iff, -- Smart constructors
    eval -- Evaluation
) where

data Expr a = EI Int
            | EB Bool
            | Plus (Expr Int) (Expr Int)
            | If (Expr Bool) (Expr a) (Expr a)
            deriving Show

ei :: Int -> Expr Int
ei i = EI i

eb :: Bool -> Expr Bool
eb b = EB b

plus :: Expr Int -> Expr Int -> Expr Int
plus l r = Plus l r

iff :: Expr Bool -> Expr a -> Expr a -> Expr a
iff p t e = If p t e

data Val = VI Int 
         | VB Bool 
         deriving Show

example = iff (eb True) (ei 1) (ei 2)

eval :: Expr a -> Val
eval (EI i) = VI i
eval (EB b) = VB b
eval (Plus l r) = 
    let (VI i) = eval l 
        (VI j) = eval r
    in VI (i + j)
eval (If p t e) =
    let (VB b) = eval p
    in if b then eval t else eval e