PLAI那些事01 AE

AE : Concrete syntax

<AE> ::= <num>
       | {+ <AE> <AE>}
       | {- <AE> <AE>}

AE : Abstract syntax

(define-type AE
  [num (n number?)]
  [add (lhs AE?)
       (rhs AE?)]
  [sub (lhs AE?)
       (rhs AE?)])

parse : sexp -> AE

(define (parse sexp)
  (cond 
    [(number? sexp) (num sexp)] 
    [(list? sexp) 
     (case (first sexp) 
       [(+) (add (parse (second sexp)) 
                 (parse (third sexp)))] 
       [(-) (sub (parse (second sexp)) 
                 (parse (third sexp)))])]))

(define (parse sexp)
  (cond 
    [(number? sexp) (num sexp)] 
    [(and (= 3 (length sexp)) 
          (eq? (first sexp) ’+)) 
     (add (parse (second sexp))
          (parse (third sexp)))] 
    [(and (= 3 (length sexp)) 
          (eq? (first sexp) ’-)) 
     (sub (parse (second sexp))
          (parse (third sexp)))] 
    [else (error ’parse "bad syntax: ~a" sexp)]))

(define (parse sexp)
  (cond
    [(number? sexp) (num sexp)]
    [(and (= 3 (length sexp)) (eq? (first sexp) '+))
     (add (parse (second sexp)) (parse (third sexp)))]
    [(and (= 3 (length sexp)) (eq? (first sexp) '-))
     (sub (parse (second sexp)) (parse (third sexp)))]
    [else (error 'parse "bad syntax: ~a" sexp)]))

(define (parse sexp)
  (match sexp
    [(? number?) (num sexp)]
    [(list '+ l r) (add (parse l) (parse r))]
    [(list '- l r) (sub (parse l) (parse r))]
    [else (error 'parse "bad syntax: ~a" sexp)]))

interp : AE -> number

(define (interp ae)
  (type-case AE ae
    [num (n) n]
    [add (l r) (+ (interp l) (interp r))]
    [sub (l r) (- (interp l) (interp r))]))