沒有了with表達，with，exp，body的id換成exp的lambda函數，從而可以沒有with來進行實現。即，{with {id exp} body}換成了{{fun {id} body} exp}。 FAE : Concrete syntax FAE : Abstrac syntax pa ...
沒有了with表達，with，exp，body的id換成exp的lambda函數，從而可以沒有with來進行實現。即，{with {id exp} body}換成了{{fun {id} body} exp}。
FAE : Concrete syntax
<FWAE> ::= <num>
| {+ <FWAE> <FWAE>}
| {- <FWAE> <FWAE>}
| <id>
| {fun {<id>} <FWAE>}
| {<FWAE> <FWAE>}
FAE : Abstrac syntax
(define-type FAE
[num (n number?)]
[add (lhs FAE?) (rhs FAE?)]
[sub (lhs FAE?) (rhs FAE?)]
[id (name symbol?)]
[fun (param symbol?) (body FAE?)]
[app (ftn FAE?) (arg FAE?)])
parse : sexp -> FAE
(define (parse sexp)
(match sexp
[(? number?) (num sexp)]
[(list '+ l r) (add (parse l) (parse r))]
[(list '- l r) (sub (parse l) (parse r))]
[(? symbol?) (id sexp)]
[(list 'fun (list x) b) (fun x (parse b))]
[(list f a) (app (parse f) (parse a))]
[else (error 'parse "bad syntax: ~a" sexp)]))
interp : FAE -> 'FAE'
(define (num+ x y)
(num (+ (num-n x) (num-n y))))
(define (num- x y)
(num (- (num-n x) (num-n y))))
(define (interp fae)
(type-case FAE fae
[num (n) fae]
[add (l r) (num+ (interp l) (interp r))]
[sub (l r) (num- (interp l) (interp r))]
[id (s) (error 'interp "free variable")]
[fun (x b) fae]
[app (f a) (local [(define ftn (interp f))]
(interp (subst (fun-body ftn)
(fun-param ftn)
(interp a))))]))
subst : 'FAE' 'symbol' 'FAE' -> 'FAE'
(define (subst exp sub-id val)
(type-case FAE exp
[num (n) exp]
[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))]
[id (name) (cond [(equal? name sub-id) val]
[else exp])]
[app (f arg) (app (subst f sub-id val)
(subst arg sub-id val))]
[fun (id body) (if (equal? sub-id id)
exp
(fun id (subst body sub-id val)))]))
