Write You a Haskell Stephen Diehl

data Expr
= Var Int
| Lam Expr
| App Expr Expr
| Lit Int
| Prim PrimOp Expr Expr
deriving Show
data PrimOp = Add | Mul
deriving Show
data Value
= VInt Int
| VClosure Expr Env
deriving Show
type Env = [Value]
emptyEnv :: Env
emptyEnv = []
e evaluator function simply maps the local scope and a term to the final value. Whenever a variable is
referred to it is looked up in the environment. Whenever a lambda is entered it extends the environment
with the local scope of the closure.
eval :: Env -> Expr -> Value
eval env term = case term of
Var n -> env !! n
Lam a -> VClosure a env
App a b ->
let VClosure c env’ = eval env a in
let v = eval env b in
eval (v : env’) c
Lit n -> VInt n
Prim p a b -> (evalPrim p) (eval env a) (eval env b)
evalPrim :: PrimOp -> Value -> Value -> Value
evalPrim Add (VInt a) (VInt b) = VInt (a + b)
evalPrim Mul (VInt a) (VInt b) = VInt (a * b)
Call-by-name
In call-by-name evaluation, the arguments to lambda expressions are substituted as is, evaluation simply
proceeds from left to right substituting the outermost lambda or reducing a value. If a substituted
expression is not used it is never evaluated.
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