Write You a Haskell Stephen Diehl

e 1 → e 2
succ e 1 → succ e 2
e 1 → e 2
pred e 1 → pred e 2
pred 0 → 0
pred (succ n) → n
e 1 → e 2
iszero e 1 → iszero e 2
iszero 0 → true
iszero (succ n) → false
if True then e 2 else e 3 → e 2
if False then e 2 else e 3 → e 3
(E-Succ)
(E-Pred)
(E-PredZero)
(E-PredSucc)
(E-IsZero)
(E-IsZeroZero)
(E-IsZeroSucc)
(E-IfTrue)
(E-IfFalse)
e evaluation logic for our interpreter simply reduced an expression by the predefined evaluation rules
until either it reached a normal form ( a value ) or got stuck.
nf :: Expr -> Expr
nf t = fromMaybe t (nf eval1 t)
eval :: Expr -> Maybe Expr
eval t = case isVal (nf t) of
True -> Just (nf t)
False -> Nothing -- term is ”stuck”
Values in our language are defined to be literal numbers or booleans.
isVal :: Expr -> Bool
isVal Tr = True
isVal Fl = True
isVal t | isNum t = True
isVal _ = False
Written in applicative form there is a noticeable correspondence between each of the evaluation rules
and our evaluation logic.
-- Evaluate a single step.
eval1 :: Expr -> Maybe Expr
58