#| |
<expr> ::= <num> |
| {+ <expr> <expr>} |
| {- <expr> <expr>} |
| {if0 <expr> <expr> <expr>} |
| {with {<sym> <expr>} <expr>} --> syntactic sugar |
| <id> |
| {<expr> <expr>} |
| {fun {<sym>} <expr>} |
| {rec {<sym> <expr>} <expr>} --> syntactic sugar |
|# |
(deftype Expr |
(num n) |
(add l r) |
(sub l r) |
(if0 c t f) |
(id s) |
(app fun-expr arg-expr) |
(fun id body)) |
|
;; parse :: s-expr -> Expr |
#| where |
<s-expr> ::= <num> |
| <sym> |
| (list '+ <s-expr> <s-expr>) |
| (list '- <s-expr> <s-expr>) |
| (list 'if0 <s-expr> <s-expr> <s-expr>) |
| (list 'with (list <sym> <s-expr>) <s-expr>) |
| (list 'fun (list <sym>) <s-expr>) |
| (list 'rec (list <sym> <s-expr>) <s-expr>) |
| (list <s-expr> <s-expr>) |
|# |
(define (parse s-expr) |
(match s-expr |
[(? number?) (num s-expr)] |
[(? symbol?) (id s-expr)] |
[(list '+ l r) (add (parse l) (parse r))] |
[(list '- l r) (sub (parse l) (parse r))] |
[(list 'if0 c t f) (if0 (parse c) |
(parse t) |
(parse f))] |
[(list 'with (list x e) b) |
(app (fun x (parse b)) (parse e))] |
[(list 'rec (list x e) b) |
(parse `{with {,x {FIX {fun {,x} ,e}}} ,b})] ;; using FIX |
[(list 'fun (list x) b) (fun x (parse b))] |
[(list f a) (app (parse f) (parse a))])) |
|
;; values |
(deftype Val |
(numV n) |
(closureV id body env)) |
|
;; interp :: Expr Env -> Val |
(define (interp expr env) |
(match expr |
[(num n) (numV n)] |
[(fun id body) (closureV id body env)] |
[(add l r) (num+ (interp l env) (interp r env))] |
[(sub l r) (num- (interp l env) (interp r env))] |
[(if0 c t f) |
(if (num-zero? (interp c env)) |
(interp t env) |
(interp f env))] |
[(id x) (env-lookup x env)] |
[(app fun-expr arg-expr) |
(def (closureV id body fenv) (interp fun-expr env)) |
(interp body |
(extend-env id |
(interp arg-expr env) |
fenv))])) |
|
(define (num+ n1 n2) |
(numV (+ (numV-n n1) (numV-n n2)))) |
|
(define (num- n1 n2) |
(numV (- (numV-n n1) (numV-n n2)))) |
|
(define (num-zero? n) |
(zero? (numV-n n))) |
|
;; the fix-point combinator |
(def fix-comb (closureV 'f |
(parse |
'{with {frec {fun {next} |
{fun {n} |
{{f {next next}} n}}}} |
{frec frec}}) empty-env)) |
|
;; run :: s-expr -> number |
(define (run prog) |
(def init-env (extend-env 'FIX fix-comb empty-env)) |
(match (interp (parse prog) init-env) |
[(numV n) n] |
[(and f (closureV id body env)) f])) |