Types and Programming Languages chapter 3

Arith.hs

module Arith where

import Prelude hiding (True, False)

data Arith = Zero
           | True
           | False
           | If Arith Arith Arith
           | Succ Arith
           | Pred Arith
           | IsZero Arith
             deriving (Eq, Show)

eval :: Arith -> Arith
eval True          = True
eval False         = False
eval Zero          = Zero
eval (IsZero a)    = if eval a == Zero then True else False
eval (If p q1 q2)  = eval $ if (eval p) == True then q1 else q2
eval (Succ a)      = case a of
                       Pred a1 -> eval a1
                       Zero    -> Succ Zero
                       a1      -> eval (Succ (eval a1))
eval (Pred a)      = case a of
                       Succ a1 -> eval a1
                       Zero    -> Pred Zero
                       a1      -> eval (Pred (eval a1))

{--
test1 :: Arith
test1 = IsZero (Pred $ Pred $ Succ $ Pred $ Succ $ Succ Zero)

test2 :: Arith
test2 = eval $ IsZero $ Pred $ (If (IsZero test1) (Pred Zero) (Succ Zero))
--}