1 (define (ambeval exp env succeed fail)
2 ((analyze exp) env succeed fail))
4 (cond ((self-evaluating? exp)
5 (analyze-self-evaluating exp))
6 ((quoted? exp) (analyze-quoted exp))
7 ((variable? exp) (analyze-variable exp))
8 ((assignment? exp) (analyze-assignment exp))
9 ((permanent-assignment? exp)
10 (analyze-permanent-assignment exp))
11 ((definition? exp) (analyze-definition exp))
12 ((if? exp) (analyze-if exp))
13 ((and? exp) (analyze (and->if exp)))
14 ((or? exp) (analyze (or->if exp)))
15 ((not? exp) (analyze (not->if exp)))
16 ((xor? exp) (analyze (xor->or-and-not exp)))
17 ((lambda? exp) (analyze-lambda exp))
18 ((let? exp) (analyze (let->combination exp)))
19 ((let*? exp) (analyze (let*->nested-lets exp)))
20 ((named-let? exp) (analyze (named-let->combination exp)))
21 ((letrec? exp) (analyze (letrec->let exp)))
22 ((do? exp) (analyze (do->combination exp)))
23 ((begin? exp) (analyze-sequence (begin-actions exp)))
24 ((cond? exp) (analyze (cond->if exp)))
25 ((amb? exp) (analyze-amb exp))
26 ((ramb? exp) (analyze (ramb->amb exp)))
27 ((if-fail? exp) (analyze-if-fail exp))
28 ;; ((if-fail? exp) (analyze (if-fail->amb exp)))
29 ((application? exp) (analyze-application exp))
31 (error "Unknown expression type -- ANALYZE" exp))))
34 ;; analyzing procedures
35 (define (analyze-self-evaluating exp)
36 (lambda (env succeed fail)
38 (define (analyze-quoted exp)
39 (let ((qval (text-of-quotation exp)))
40 (lambda (env succeed fail)
41 (succeed qval fail))))
42 (define (analyze-variable exp)
43 (lambda (env succeed fail)
44 (succeed (lookup-variable-value exp env)
46 (define (analyze-lambda exp)
47 (let ((vars (lambda-parameters exp))
48 (bproc (analyze-sequence (scan-out-defines (lambda-body exp)))))
49 ;; (bproc (analyze-sequence (lambda-body exp))))
50 (lambda (env succeed fail)
51 (succeed (make-procedure vars bproc env)
53 (define (analyze-if exp)
54 (let ((pproc (analyze (if-predicate exp)))
55 (cproc (analyze (if-consequent exp)))
56 (aproc (analyze (if-alternative exp))))
57 (lambda (env succeed fail)
59 ;; success continuation for evaluating the predicate
60 ;; to obtain pred-value
61 (lambda (pred-value fail2)
62 (if (true? pred-value)
63 (cproc env succeed fail2)
64 (aproc env succeed fail2)))
65 ;; failure continuation for evaluating the predicate
67 (define (analyze-if-fail exp)
68 (let ((dproc (analyze (if-fail-default exp)))
69 (aproc (analyze (if-fail-alternative exp))))
70 (lambda (env succeed fail)
74 (aproc env succeed fail))))))
75 (define (analyze-sequence exps)
76 (define (sequentially a b)
77 (lambda (env succeed fail)
79 ;; success continuation for calling a
80 (lambda (a-value fail2)
81 (b env succeed fail2))
82 ;; failure continuation for calling a
84 (define (loop first-proc rest-procs)
85 (if (null? rest-procs)
87 (loop (sequentially first-proc (car rest-procs))
89 (let ((procs (map analyze exps)))
91 (error "Empty sequence -- ANALYZE"))
92 (loop (car procs) (cdr procs))))
93 (define (analyze-definition exp)
94 (let ((var (definition-variable exp))
95 (vproc (analyze (definition-value exp))))
96 (lambda (env succeed fail)
99 (define-variable! var val env)
102 (define (analyze-assignment exp)
103 (let ((var (assignment-variable exp))
104 (vproc (analyze (assignment-value exp))))
105 (lambda (env succeed fail)
107 (lambda (val fail2) ; *1*
109 (lookup-variable-value var env)))
110 (set-variable-value! var val env)
113 (set-variable-value! var
118 (define (analyze-permanent-assignment exp)
119 (let ((var (permanent-assignment-variable exp))
120 (vproc (analyze (permanent-assignment-value exp))))
121 (lambda (env succeed fail)
124 (lambda (val val-fail)
125 (set-variable-value! var val env)
126 (succeed 'ok val-fail))
129 (define (analyze-application exp)
130 (let ((fproc (analyze (operator exp)))
131 (aprocs (map analyze (operands exp))))
132 (lambda (env succeed fail)
139 proc args succeed fail3))
142 (define (get-args aprocs env succeed fail)
146 ;; success continuation for this aproc
148 (get-args (cdr aprocs)
150 ;; success continuation for recursive
153 (succeed (cons arg args)
158 (define (analyze-amb exp)
159 (let ((cprocs (map analyze (amb-choices exp))))
160 (lambda (env succeed fail)
161 (define (try-next choices)
167 (try-next (cdr choices))))))
175 (define (tagged-list? exp tag)
181 (define (amb? exp) (tagged-list? exp 'amb))
182 (define (amb-choices exp) (cdr exp))
183 (define (make-amb choices)
187 (tagged-list? exp 'ramb))
188 (define (ramb->amb exp)
189 (make-amb (shuffle (amb-choices exp))))
191 (define (shuffle items)
194 (let ((first (list-ref items (random (length items)))))
196 (shuffle (remove (lambda (i) (eq? first i))
201 ;; self-evaluating/variable/quoted
202 (define (self-evaluating? exp)
203 (cond ((number? exp) true)
206 (define (variable? exp) (symbol? exp))
207 (define (quoted? exp)
208 (tagged-list? exp 'quote))
209 (define (text-of-quotation exp) (cadr exp))
211 ;; assignment/permanent-assignment/definition
212 (define (assignment? exp)
213 (tagged-list? exp 'set!))
214 (define (assignment-variable exp) (cadr exp))
215 (define (assignment-value exp) (caddr exp))
216 (define (make-assignment var val)
217 (list 'set! var val))
218 (define (permanent-assignment? exp)
219 (tagged-list? exp 'permanent-set!))
220 (define permanent-assignment-variable assignment-variable)
221 (define permanent-assignment-value assignment-value)
222 (define (definition? exp)
223 (tagged-list? exp 'define))
224 (define (definition-variable exp)
225 (if (symbol? (cadr exp))
228 (define (definition-value exp)
229 (if (symbol? (cadr exp))
231 (make-lambda (cdadr exp) ; formal parameters
233 (define (make-definition var val)
236 ;; if/and/or/not/xor/if-fail
237 (define (if? exp) (tagged-list? exp 'if))
238 (define (if-predicate exp) (cadr exp))
239 (define (if-consequent exp) (caddr exp))
240 (define (if-alternative exp)
241 (if (not (null? (cdddr exp)))
244 (define (make-if predicate consequent alternative)
245 (list 'if predicate consequent alternative))
248 (tagged-list? exp 'and))
249 (define (and-clauses exp)
252 (tagged-list? exp 'or))
253 (define (or-clauses exp)
255 (define (and->if exp)
256 (define (expand-clauses clauses)
257 (cond ((null? clauses) 'true)
258 ((null? (cdr clauses)) (car clauses))
259 (else (make-if (car clauses)
260 (expand-clauses (cdr clauses))
262 (expand-clauses (and-clauses exp)))
264 (define (expand-clauses clauses)
267 (make-if (car clauses)
269 (expand-clauses (cdr clauses)))))
270 (expand-clauses (or-clauses exp)))
272 (tagged-list? exp 'not))
273 (define (not->if exp)
274 `(if ,(cadr exp) false true))
276 (tagged-list? exp 'xor))
277 (define (xor->or-and-not exp)
278 (let ((pred-1 (cadr exp))
279 (pred-2 (caddr exp)))
280 `(or (and ,pred-1 (not ,pred-2))
281 (and (not ,pred-1) ,pred-2))))
282 ;; (define (if-fail->amb exp)
283 ;; (make-amb (list (if-fail-default exp)
284 ;; (if-fail-alternative exp))))
285 (define (if-fail? exp)
286 (tagged-list? exp 'if-fail))
287 (define (if-fail-default exp)
289 (define (if-fail-alternative exp)
292 ;; lambda/let/let*/letrec
293 (define (lambda? exp) (tagged-list? exp 'lambda))
294 (define (lambda-parameters exp) (cadr exp))
295 (define (lambda-body exp) (cddr exp))
296 (define (make-lambda parameters body)
297 (cons 'lambda (cons parameters body)))
299 (define (make-let vars vals body)
301 (cons (map list vars vals)
304 (and (tagged-list? exp 'let)
305 (not (symbol? (cadr exp)))))
306 (define (let-vars exp)
307 (map car (cadr exp)))
308 (define (let-vals exp)
309 (map cadr (cadr exp)))
310 (define (let-body exp)
312 (define (let->combination exp)
313 (make-application (make-lambda (let-vars exp) (let-body exp))
315 (define (named-let? exp)
316 (and (tagged-list? exp 'let)
317 v (symbol? (cadr exp))))
318 (define (named-let-name exp)
320 (define (named-let-vars exp)
321 (map car (caddr exp)))
322 (define (named-let-vals exp)
323 (map cadr (caddr exp)))
324 (define (named-let-body exp)
326 (define (named-let->combination exp)
328 (list (make-definition (named-let-name exp)
329 (make-lambda (named-let-vars exp)
330 (named-let-body exp)))
331 (make-application (named-let-name exp)
332 (named-let-vals exp)))))
333 (define (make-named-let name vars vals body)
336 (cons (map list vars vals)
339 (define (letrec? exp)
340 (tagged-list? exp 'letrec))
342 (define (letrec-vars exp)
343 (map car (cadr exp)))
344 (define (letrec-vals exp)
345 (map cadr (cadr exp)))
346 (define (letrec-body exp)
348 (define (letrec->let exp)
349 (let* ((vars (letrec-vars exp))
350 (unassigneds (map (lambda (var) ''*unassigned*)
352 (vals (letrec-vals exp))
353 (assignments (map (lambda (var val)
354 (make-assignment var val))
357 (body (letrec-body exp)))
360 (append assignments body))))
362 (define (make-application op args)
366 (tagged-list? exp 'let*))
367 (define let*-vars let-vars)
368 (define let*-vals let-vals)
369 (define let*-body let-body)
370 (define (let*->nested-lets exp)
371 (define (expand-lets vars vals)
372 (if (null? (cdr vars))
373 (make-let (list (car vars))
376 (make-let (list (car vars))
378 (list (expand-lets (cdr vars) (cdr vals))))))
379 (let ((vars (let*-vars exp))
380 (vals (let*-vals exp)))
382 (sequence->exp (let*-body exp))
383 (expand-lets vars vals))))
387 (tagged-list? exp 'do))
388 (define (do-vars exp)
389 (map car (cadr exp)))
390 (define (do-inits exp)
391 (map cadr (cadr exp)))
392 (define (do-steps exp)
393 (map (lambda (var-init-step)
394 (if (null? (cddr var-init-step))
396 (caddr var-init-step)))
398 (define (do-test exp)
400 (define (do-expressions exp)
401 (if (null? (cdaddr exp))
404 (define (do-commands exp)
406 (define (do->combination exp)
414 (sequence->exp (do-expressions exp))
416 (append (do-commands exp)
417 (list (make-application
419 (do-steps exp)))))))))
423 (define (begin? exp) (tagged-list? exp 'begin))
424 (define (begin-actions exp) (cdr exp))
425 (define (last-exp? seq) (null? (cdr seq)))
426 (define (first-exp seq) (car seq))
427 (define (rest-exps seq) (cdr seq))
428 (define (sequence->exp seq)
429 (cond ((null? seq) seq)
430 ((last-exp? seq) (first-exp seq))
431 (else (make-begin seq))))
432 (define (make-begin seq) (cons 'begin seq))
435 (define (application? exp) (pair? exp))
436 (define (operator exp) (car exp))
437 (define (operands exp) (cdr exp))
438 (define (no-operands? ops) (null? ops))
439 (define (first-operand ops) (car ops))
440 (define (rest-operands ops) (cdr ops))
443 (define (cond? exp) (tagged-list? exp 'cond))
444 (define (cond-clauses exp) (cdr exp))
445 (define (cond-else-clause? clause)
446 (eq? (cond-predicate clause) 'else))
447 (define (cond-predicate clause) (car clause))
448 (define (cond-actions clause) (cdr clause))
449 (define (cond-extended-clause? clause)
450 (and (not (null? (cdr clause))) (eq? (cadr clause) '=>)))
451 (define (cond-extended-proc clause)
453 (define (cond->if exp)
454 (expand-clauses (cond-clauses exp)))
455 (define (expand-clauses clauses)
457 'false ; no else clause
458 (let ((first (car clauses))
459 (rest (cdr clauses)))
460 (if (cond-else-clause? first)
462 (sequence->exp (cond-actions first))
463 (error "ELSE clause isn't last -- COND->IF"
465 (if (cond-extended-clause? first)
466 (make-if (cond-predicate first)
468 (cond-extended-proc first)
469 (list (cond-predicate first)))
470 (expand-clauses rest))
471 (make-if (cond-predicate first)
472 (sequence->exp (cond-actions first))
473 (expand-clauses rest)))))))
480 (define (make-procedure parameters body env)
481 (list 'procedure parameters body env))
482 (define (scan-out-defines body)
483 (let* ((definitions (filter definition? body))
484 (vars (map definition-variable definitions))
485 (unassigneds (map (lambda (var) ''*unassigned*)
487 (vals (map definition-value definitions))
489 (map (lambda (var val)
490 (make-assignment var val))
492 (exps (remove definition? body)))
493 (if (null? definitions)
498 (append assignments exps))))))
499 (define (compound-procedure? p)
500 (tagged-list? p 'procedure))
501 (define (procedure-parameters p) (cadr p))
502 (define (procedure-body p) (caddr p))
503 (define (procedure-environment p) (cadddr p))
506 (define (enclosing-environment env) (cdr env))
507 (define (first-frame env) (car env))
508 (define the-empty-environment '())
509 (define (make-frame variables values)
510 (cons variables values))
511 (define (frame-variables frame) (car frame))
512 (define (frame-values frame) (cdr frame))
513 (define (add-binding-to-frame! var val frame)
514 (set-car! frame (cons var (car frame)))
515 (set-cdr! frame (cons val (cdr frame))))
516 (define (extend-environment vars vals base-env)
517 (if (= (length vars) (length vals))
518 (cons (make-frame vars vals) base-env)
519 (if (< (length vars) (length vals))
520 (error "Too many arguments supplied" vars vals)
521 (error "Too few arguments supplied" vars vals))))
522 (define (lookup-variable-value var env)
523 (define (env-loop env)
524 (define (scan vars vals)
526 (env-loop (enclosing-environment env)))
527 ((eq? var (car vars))
528 ;; (let ((val (car vals)))
529 ;; (if (eq? val '*unassigned*)
530 ;; (error "Var not yet defined -- LOOKUP-VARIABLE-VALUE" var)
533 (else (scan (cdr vars) (cdr vals)))))
534 (if (eq? env the-empty-environment)
535 (error "Unbound variable" var)
536 (let ((frame (first-frame env)))
537 (scan (frame-variables frame)
538 (frame-values frame)))))
540 (define (set-variable-value! var val env)
541 (define (env-loop env)
542 (define (scan vars vals)
544 (env-loop (enclosing-environment env)))
545 ((eq? var (car vars))
547 (else (scan (cdr vars) (cdr vals)))))
548 (if (eq? env the-empty-environment)
549 (error "Unbound variable -- SET!" var)
550 (let ((frame (first-frame env)))
551 (scan (frame-variables frame)
552 (frame-values frame)))))
554 (define (define-variable! var val env)
555 (let ((frame (first-frame env)))
556 (define (scan vars vals)
558 (add-binding-to-frame! var val frame))
559 ((eq? var (car vars))
561 (else (scan (cdr vars) (cdr vals)))))
562 (scan (frame-variables frame)
563 (frame-values frame))))
565 ;; (define (remove-binding-from-frame! var frame)
566 ;; (define (scan vars vals)
567 ;; (cond ((null? (cdr vars))
568 ;; (error "Binding not found -- REMOVE-BINDING-FROM-FRAME!" var))
569 ;; ((eq? var (cadr vars))
570 ;; (set-cdr! vars (cddr vars))
571 ;; (set-cdr! vals (cddr vals)))
572 ;; (else (scan (cdr vars) (cdr vals)))))
573 ;; (let ((vars (frame-variables frame))
574 ;; (vals (frame-values frame)))
575 ;; (if (eq? var (car vars))
576 ;; (begin (set-car! frame (cdr vars))
577 ;; (set-cdr! frame (cdr vals)))
578 ;; (scan vars vals))))
581 (define (primitive-procedure? proc)
582 (tagged-list? proc 'primitive))
583 (define (primitive-implementation proc) (cadr proc))
584 (define primitive-procedures
585 (list (list 'car car)
606 (list 'remainder remainder)
609 (list 'equal? equal?)
610 (list 'member member)
612 (list 'display display)
613 (list 'error error)))
614 (define (primitive-procedure-names)
616 primitive-procedures))
617 (define (primitive-procedure-objects)
618 (map (lambda (proc) (list 'primitive (cadr proc)))
619 primitive-procedures))
620 (define (apply-primitive-procedure proc args)
622 (primitive-implementation proc) args))
624 ;; execute application
626 (define (execute-application proc args succeed fail)
627 (cond ((primitive-procedure? proc)
628 (succeed (apply-primitive-procedure proc args)
630 ((compound-procedure? proc)
631 ((procedure-body proc)
632 (extend-environment (procedure-parameters proc)
634 (procedure-environment proc))
639 "Unknown procedure type -- EXECUTE-APPLICATION"
644 (define (prompt-for-input string)
645 (newline) (newline) (display string) (newline))
646 (define (announce-output string)
647 (newline) (display string) (newline))
648 (define (user-print object)
649 (if (compound-procedure? object)
650 (display (list 'compound-procedure
651 (procedure-parameters object)
652 (procedure-body object)
655 (define (setup-environment)
657 (extend-environment (primitive-procedure-names)
658 (primitive-procedure-objects)
659 the-empty-environment)))
660 (define-variable! 'true true initial-env)
661 (define-variable! 'false false initial-env)
663 (define the-global-environment (setup-environment))
665 (define input-prompt ";;; Amb-Eval input:")
666 (define output-prompt ";;; Amb-Eval value:")
667 (define (driver-loop)
668 (define (internal-loop try-again)
669 (prompt-for-input input-prompt)
670 (let ((input (read)))
671 (if (eq? input 'try-again)
675 (display ";;; Starting a new problem ")
677 the-global-environment
679 (lambda (val next-alternative)
680 (announce-output output-prompt)
682 (internal-loop next-alternative))
686 ";;; There are no more values of")
692 (display ";;; There is no current problem")
697 (define (test-case actual expected)
702 (display "Expected: ")
707 "No current problem"))
708 (define (geval exp) ;; eval globally
709 (if (eq? exp 'try-again)
712 the-global-environment
713 (lambda (val next-alternative)
714 (set! try-again next-alternative)
719 "No current problem"))
720 "No alternatives"))))
721 (define (test-eval exp expected)
722 (test-case (geval exp) expected))
723 (define (print-eval exp)
724 (user-print (geval exp)))
728 ;; procedure definitions
731 '(define (append x y)
734 (cons (car x) (append (cdr x) y)))))
736 '(define (list-ref items n)
739 (list-ref (cdr items) (- n 1)))))
741 '(define (fold-left f init seq)
748 '(define (enumerate-interval low high)
751 (cons low (enumerate-interval (+ low 1) high)))))
753 '(define (assoc key records)
754 (cond ((null? records) false)
755 ((equal? key (caar records)) (car records))
756 (else (assoc key (cdr records))))))
759 '(define (map proc list)
762 (cons (proc (car list))
763 (map proc (cdr list))))))
765 '(define (map-2 proc l1 l2)
768 (cons (proc (car l1) (car l2))
769 (map-2 proc (cdr l1) (cdr l2))))))
772 '(define (accumulate op initial sequence)
776 (accumulate op initial (cdr sequence))))))
778 ;; ;; ;; all special forms
779 ;; (test-eval '(begin 5 6) 6)
780 ;; (test-eval '10 10)
781 ;; (geval '(define x 3))
783 ;; (test-eval '(set! x -25) 'ok)
784 ;; (test-eval 'x -25)
785 ;; (geval '(define z (lambda (x y) (+ x (* x y)))))
786 ;; (test-eval '(z 3 4) 15)
787 ;; (test-eval '(cond ((= x -2) 'x=-2)
788 ;; ((= x -25) 'x=-25)
791 ;; (test-eval '(if true false true) false)
794 ;; '(let ((x 4) (y 7))
800 ;; (geval '(define x (+ 3 8)))
801 ;; (test-eval '(and 0 true x) 11)
802 ;; (test-eval '(and 0 true x false) false)
803 ;; (test-eval '(and 0 true x (set! x -2) false) false)
805 ;; (test-eval '(and 0 true x false (set! x -5)) false)
807 ;; (test-eval '(or false (set! x 25)) 'ok)
809 ;; (test-eval '(or (set! x 2) (set! x 4)) 'ok)
811 ;; (test-eval '(or false (set! x 25) true false) 'ok)
813 ;; (test-eval '(or ((lambda (x) x) 5)) 5)
814 ;; (test-eval '(or (begin (set! x (+ x 1)) x)) 26) ;; this fails because or->if repeats the same clause twice
816 ;; (display "Failure expected")
822 ;; '(cond ((assoc 'b '((a 1) (b 2))) => cadr)
827 ;; '(cond ((= 3 4) 'not-true)
828 ;; ((= (* 2 4) 3) 'also-false)
834 ;; (accumulate + 0 x)))
835 ;; (else 'never-reach))
840 ;; ;; procedure definition and application
842 ;; '(define (factorial n)
845 ;; (* n (factorial (- n 1))))))
846 ;; (test-eval '(factorial 5) 120)
854 ;; '(6 2 20 6 72 12))
858 ;; '(accumulate + 0 '(1 2 3 4 5))
863 ;; (make-let '(x y) '(3 5) '((+ x y)))
881 ;; (+ (let ((x (+ y 2))
890 ;; (z (let ((a (* 3 2)))
918 ;; (+ (let* ((x (+ y 2))
926 ;; (a (let* ((x (* 3 x)))
942 ;; '(let loop ((count 0))
945 ;; (loop (+ count 1))))
948 ;; '(define (prime? x)
949 ;; (let prime-iter ((i 2))
950 ;; (cond ((> (* i i) x) true)
951 ;; ((= (remainder x i) 0) false)
952 ;; (else (prime-iter (+ i 1)))))))
954 ;; '(let primes ((x 2)
956 ;; (cond ((= n 0) '())
959 ;; (primes (+ x 1) (- n 1))))
960 ;; (else (primes (+ x 1) n))))
961 ;; '(2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71))
965 ;; (let fib-iter ((a 1)
970 ;; (fib-iter (+ a b) a (- count 1))))))
971 ;; (test-eval '(fib 19) 4181)
976 ;; (do ((x 0 (+ x 1)))
978 ;; (set! y (+ y 1))))
992 ;; (set! y (+ y 1))))
996 ;; '(do ((y '(1 2 3 4)))
1002 ;; (do ((x 0 (+ x 1)))
1004 ;; (set! y (+ y 1))))
1007 ;; '(let ((x '(1 3 5 7 9)))
1008 ;; (do ((x x (cdr x))
1009 ;; (sum 0 (+ sum (car x))))
1010 ;; ((null? x) sum)))
1014 ;; (do ((x '(1 2 3 4) (cdr x))
1015 ;; (y '(1 2 3 4 5 6 7 8) (cddr y)))
1016 ;; ((null? x) y x z)
1017 ;; (set! z (cons (car x) z))))
1023 ;; ;; broken now due to scan-out-defines
1028 ;; ;; (make-unbound! x)
1036 ;; ;; (make-unbound! x)
1041 ;; ;; '(let ((y -1) (x 3))
1042 ;; ;; (let ((y 0.5) (x 5))
1045 ;; ;; (make-unbound! x)
1046 ;; ;; (make-unbound! y)
1048 ;; ;; (* 5 3 -1 0.5))
1051 ;; ;; '(let ((x 3) (y 4))
1053 ;; ;; (make-unbound! x)
1058 ;; ;; '(let ((a 1) (b 2) (c 3) (d 4))
1059 ;; ;; (make-unbound! b)
1064 ;; ;; '(let ((x 4) (y 5))
1065 ;; ;; (let ((a 1) (b 2) (c 3))
1066 ;; ;; (let ((x (+ a b)) (y (+ c a)))
1067 ;; ;; (make-unbound! x)
1068 ;; ;; (let ((a x) (b (+ x y)))
1070 ;; ;; (make-unbound! b)
1072 ;; ;; (+ a b y))))))
1081 ;; ;; scan-out-defines
1085 ;; (define (even? n)
1092 ;; (even? (- n 1))))
1094 ;; (test-eval '(f 5) false)
1095 ;; (test-eval '(f 10) true)
1102 ;; ;; signal an error because x is undefined if variables are scanned out
1112 ;; (odd? (- n 1)))))
1117 ;; (even? (- n 1))))))
1119 ;; (test-eval '(f 11) false)
1120 ;; (test-eval '(f 16) true)
1127 ;; (* n (fact (- n 1)))))))
1132 (geval '(define (require p) (if (not p) (amb))))
1134 ;; (test-eval '(amb 1 2 3) 1)
1135 ;; (test-eval 'try-again 2)
1136 ;; (test-eval 'try-again 3)
1137 ;; (test-eval 'try-again "No alternatives")
1138 ;; (test-eval 'try-again "No current problem")
1139 ;; (test-eval 'try-again "No current problem")
1140 ;; (test-eval '(amb (amb 1 2) (amb 'a 'b))
1142 ;; (test-eval 'try-again 2)
1143 ;; (test-eval 'try-again 'a)
1144 ;; (test-eval 'try-again 'b)
1145 ;; (test-eval 'try-again "No alternatives")
1146 ;; (test-eval '(require false) "No alternatives")
1147 ;; (test-eval '(require true) false)
1151 '(define (an-integer-between low high)
1152 (require (<= low high))
1153 (amb low (an-integer-between (+ low 1) high))))
1156 '(define (a-pythagorean-triple-between low high)
1157 (let ((i (an-integer-between low high)))
1158 (let ((j (an-integer-between i high)))
1159 (let ((k (an-integer-between j high)))
1160 (require (= (+ (* i i) (* j j)) (* k k)))
1164 ;; '(a-pythagorean-triple-between 1 20)
1166 ;; (test-eval 'try-again '(5 12 13))
1167 ;; (test-eval 'try-again '(6 8 10))
1168 ;; (test-eval 'try-again '(8 15 17))
1169 ;; (test-eval 'try-again '(9 12 15))
1172 '(define (an-integer-starting-from low)
1173 (amb low (an-integer-starting-from (+ low 1)))))
1176 '(define (pythagorean-triples-starting-from low)
1177 (let* ((k (an-integer-starting-from low))
1178 (i (an-integer-between low k))
1179 (j (an-integer-between i k)))
1180 (require (= (+ (* i i) (* j j)) (* k k)))
1183 ;; (test-eval '(pythagorean-triples-starting-from 1)
1185 ;; (test-eval 'try-again '(6 8 10))
1186 ;; (test-eval 'try-again '(5 12 13))
1187 ;; (test-eval 'try-again '(9 12 15))
1188 ;; (test-eval 'try-again '(8 15 17))
1191 '(define (next-triplet trp)
1195 (cond ((= i j k) (list 1 1 (+ k 1)))
1196 ((= j k) (list (+ i 1) (+ i 1) k))
1197 (else (list i (+ j 1) k))))))
1199 '(define (triplet-starting-from trp)
1200 (amb trp (triplet-starting-from (next-triplet trp)))))
1202 '(define (pythagorean-triples-starting-from low)
1203 (let* ((triplet (triplet-starting-from (list low low low)))
1206 (k (caddr triplet)))
1207 (require (= (+ (* i i) (* j j)) (* k k)))
1210 '(define (distinct? items)
1211 (cond ((null? items) true)
1212 ((null? (cdr items)) true)
1213 ((member (car items) (cdr items)) false)
1214 (else (distinct? (cdr items))))))
1217 '(define (an-element-of items)
1218 (require (not (null? items)))
1219 (amb (car items) (an-element-of (cdr items)))))
1224 '(let ((x (an-element-of '(a b c)))
1225 (y (an-element-of '(a b c))))
1226 (permanent-set! count (+ count 1))
1227 (require (not (eq? x y)))
1230 (test-eval 'try-again '(a c 3))
1233 '(if-fail (let ((x (an-element-of '(1 3 5))))
1238 (test-eval 'try-again "No alternatives")
1241 '(if-fail (let ((x (an-element-of '(1 3 5 8))))
1246 (test-eval 'try-again "all-odd")
1247 (test-eval 'try-again "No alternatives")
1249 ;; Exercise 4.53. With permanent-set! as described in exercise 4.51 and if-fail as in exercise 4.52, what will be the result of evaluating
1253 (= n (smallest-divisor n))))
1255 '(define (smallest-divisor n)
1256 (find-divisor n 2)))
1258 '(define (square x) (* x x)))
1260 '(define (find-divisor n test-divisor)
1261 (cond ((> (square test-divisor) n) n)
1262 ((divides? test-divisor n) test-divisor)
1263 (else (find-divisor n (+ test-divisor 1))))))
1265 '(define (divides? a b)
1266 (= (remainder b a) 0)))
1270 '(define (prime-sum-pair list1 list2)
1271 (let ((a (an-element-of list1))
1272 (b (an-element-of list2)))
1273 (require (prime? (+ a b)))
1279 (let ((p (prime-sum-pair '(1 3 5 8)
1281 (permanent-set! pairs (cons p pairs))
1284 '((8 35) (3 110) (3 20)))