我在网上找到了本课的代码(http://groups.csail.mit.edu/mac/ftpdir/6.001-fall91/ps4/matcher-from-lecture.scm),我有点时间了试图调试它。该代码看起来与Sussman编写的内容相当:
;;; Scheme code from the Pattern Matcher lecture
;; Pattern Matching and Simplification
(define (match pattern expression dictionary)
(cond ((eq? dictionary 'failed) 'failed)
((atom? pattern)
(if (atom? expression)
(if (eq? pattern expression)
dictionary
'failed)
'failed))
((arbitrary-constant? pattern)
(if (constant? expression)
(extend-dictionary pattern expression dictionary)
'failed))
((arbitrary-variable? pattern)
(if (variable? expression)
(extend-dictionary pattern expression dictionary)
'failed))
((arbitrary-expression? pattern)
(extend-dictionary pattern expression dictionary))
((atom? expression) 'failed)
(else
(match (cdr pattern)
(cdr expression)
(match (car pattern)
(car expression)
dictionary)))))
(define (instantiate skeleton dictionary)
(cond ((atom? skeleton) skeleton)
((skeleton-evaluation? skeleton)
(evaluate (evaluation-expression skeleton)
dictionary))
(else (cons (instantiate (car skeleton) dictionary)
(instantiate (cdr skeleton) dictionary)))))
(define (simplifier the-rules)
(define (simplify-exp exp)
(try-rules (if (compound? exp)
(simplify-parts exp)
exp)))
(define (simplify-parts exp)
(if (null? exp)
'()
(cons (simplify-exp (car exp))
(simplify-parts (cdr exp)))))
(define (try-rules exp)
(define (scan rules)
(if (null? rules)
exp
(let ((dictionary (match (pattern (car rules))
exp
(make-empty-dictionary))))
(if (eq? dictionary 'failed)
(scan (cdr rules))
(simplify-exp (instantiate (skeleton (car rules))
dictionary))))))
(scan the-rules))
simplify-exp)
;; Dictionaries
(define (make-empty-dictionary) '())
(define (extend-dictionary pat dat dictionary)
(let ((vname (variable-name pat)))
(let ((v (assq vname dictionary)))
(cond ((null? v)
(cons (list vname dat) dictionary))
((eq? (cadr v) dat) dictionary)
(else 'failed)))))
(define (lookup var dictionary)
(let ((v (assq var dictionary)))
(if (null? v)
var
(cadr v))))
;; Expressions
(define (compound? exp) (pair? exp))
(define (constant? exp) (number? exp))
(define (variable? exp) (atom? exp))
;; Rules
(define (pattern rule) (car rule))
(define (skeleton rule) (cadr rule))
;; Patterns
(define (arbitrary-constant? pattern)
(if (pair? pattern) (eq? (car pattern) '?c) false))
(define (arbitrary-expression? pattern)
(if (pair? pattern) (eq? (car pattern) '? ) false))
(define (arbitrary-variable? pattern)
(if (pair? pattern) (eq? (car pattern) '?v) false))
(define (variable-name pattern) (cadr pattern))
;; Skeletons & Evaluations
(define (skeleton-evaluation? skeleton)
(if (pair? skeleton) (eq? (car skeleton) ':) false))
(define (evaluation-expression evaluation) (cadr evaluation))
;; Evaluate (dangerous magic)
(define (evaluate form dictionary)
(if (atom? form)
(lookup form dictionary)
(apply (eval (lookup (car form) dictionary)
user-initial-environment)
(mapcar (lambda (v) (lookup v dictionary))
(cdr form)))))
;;
;; A couple sample rule databases...
;;
;; Algebraic simplification
(define algebra-rules
'(
( ((? op) (?c c1) (?c c2)) (: (op c1 c2)) )
( ((? op) (? e ) (?c c )) ((: op) (: c) (: e)) )
( (+ 0 (? e)) (: e) )
( (* 1 (? e)) (: e) )
( (* 0 (? e)) 0 )
( (* (?c c1) (* (?c c2) (? e ))) (* (: (* c1 c2)) (: e)) )
( (* (? e1) (* (?c c ) (? e2))) (* (: c ) (* (: e1) (: e2))) )
( (* (* (? e1) (? e2)) (? e3)) (* (: e1) (* (: e2) (: e3))) )
( (+ (?c c1) (+ (?c c2) (? e ))) (+ (: (+ c1 c2)) (: e)) )
( (+ (? e1) (+ (?c c ) (? e2))) (+ (: c ) (+ (: e1) (: e2))) )
( (+ (+ (? e1) (? e2)) (? e3)) (+ (: e1) (+ (: e2) (: e3))) )
( (+ (* (?c c1) (? e)) (* (?c c2) (? e))) (* (: (+ c1 c2)) (: e)) )
( (* (? e1) (+ (? e2) (? e3))) (+ (* (: e1) (: e2))
(* (: e1) (: e3))) )
))
(define algsimp (simplifier algebra-rules))
;; Symbolic Differentiation
(define deriv-rules
'(
( (dd (?c c) (? v)) 0 )
( (dd (?v v) (? v)) 1 )
( (dd (?v u) (? v)) 0 )
( (dd (+ (? x1) (? x2)) (? v)) (+ (dd (: x1) (: v))
(dd (: x2) (: v))) )
( (dd (* (? x1) (? x2)) (? v)) (+ (* (: x1) (dd (: x2) (: v)))
(* (dd (: x1) (: v)) (: x2))) )
( (dd (** (? x) (?c n)) (? v)) (* (* (: n) (+ (: x) (: (- n 1))))
(dd (: x) (: v))) )
))
(define dsimp (simplifier deriv-rules))
(define scheme-rules
'(( (square (?c n)) (: (* n n)) )
( (fact 0) 1 )
( (fact (?c n)) (* (: n) (fact (: (- n 1)))) )
( (fib 0) 0 )
( (fib 1) 1 )
( (fib (?c n)) (+ (fib (: (- n 1)))
(fib (: (- n 2)))) )
( ((? op) (?c e1) (?c e2)) (: (op e1 e2)) ) ))
(define scheme-evaluator (simplifier scheme-rules))
我用Dr Racket用R5RS运行它,我遇到的第一个问题是那个原子?是一个未定义的标识符。所以,我发现我可以添加以下内容:
(define (atom? x) ; atom? is not in a pair or null (empty)
(and (not (pair? x))
(not (null? x))))
然后我试图弄清楚如何实际运行这个野兽,所以我再次观看视频并看到他使用以下内容:
(dsimp '(dd (+ x y) x))
正如Sussman所说,我应该回来(+ 1 0)。相反,使用R5RS我似乎在行的扩展字典过程中打破:
((eq? (cadr v) dat) dictionary)
它返回的具体错误是:mcdr:expect类型为mutable-pair的参数;给定#f
当使用neil / sicp时,我在该行的评估过程中打破了:
(apply (eval (lookup (car form) dictionary)
user-initial-environment)
它返回的具体错误是:模块中的未绑定标识符:user-initial-environment
所以,尽管如此,我还是会感谢一些帮助,或者是正确方向的推动。谢谢!