#| |
<expr> ::= <num> |
| {+ <expr> <expr>} |
| {- <expr> <expr>} |
| {if0 <expr> <expr> <expr>} |
| {with {<sym> <expr>} <expr>} |
| <id> |
|# |
(deftype Expr |
(num n) |
(add l r) |
(sub l r) |
(if0 c t f) |
(with id named-expr body) |
(id s)) |
|
|
;; 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>) |
|# |
(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) |
(with x (parse e) (parse b))])) |
|
;; subst :: Expr symbol Expr |
(define (subst expr sub-id val) |
(match expr |
[(num n) expr] |
[(add l r) (add (subst l sub-id val) |
(subst r sub-id val))] |
[(sub l r) (sub (subst l sub-id val) |
(subst r sub-id val))] |
[(if0 c t f) (if0 (subst c sub-id val) |
(subst t sub-id val) |
(subst f sub-id val))] |
[(with bound-id named-expr body) |
(with bound-id |
(subst named-expr sub-id val) |
(if (symbol=? bound-id sub-id) |
body |
(subst body sub-id val)))] |
[(id x) (if (symbol=? x sub-id) val expr)])) |
|
|
;; calc :: Expr -> number |
(define (calc expr) |
(match expr |
[(num n) n] |
[(add l r) (+ (calc l) (calc r))] |
[(sub l r) (- (calc l) (calc r))] |
[(if0 c t f) |
(if (zero? (calc c)) |
(calc t) |
(calc f))] |
[(with bound-id named-expr bound-body) |
(calc (subst bound-body |
bound-id |
(num (calc named-expr))))] |
[(id x) (error 'calc "free identifier: ~a" x)])) |
|
;; run :: s-expr -> number |
(define (run prog) |
(calc (parse prog))) |