| #| |
| <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))) |