1 ;; (define apply-in-underlying-scheme apply)
4 (cond ((self-evaluating? exp) exp)
5 ((variable? exp) (lookup-variable-value exp env))
6 ((quoted? exp) (text-of-quotation exp))
7 ((assignment? exp) (eval-assignment exp env))
8 ((definition? exp) (eval-definition exp env))
9 ((unbound? exp) (eval-unbound exp env))
10 ((if? exp) (eval-if exp env))
11 ((and? exp) (eval-and exp env))
12 ((or? exp) (eval-or exp env))
14 (make-procedure (lambda-parameters exp)
18 (eval-sequence (begin-actions exp) env))
19 ((cond? exp) (eval (cond->if exp) env))
20 ((let? exp) (eval (let->combination exp) env))
21 ((let*? exp) (eval (let*->nested-lets exp) env))
22 ((named-let? exp) (eval (named-let->combination exp) env))
23 ((do? exp) (eval (do->combination exp) env))
25 (apply (eval (operator exp) env)
26 (list-of-values (operands exp) env)))
28 (error "Unknown expression type -- EVAL" exp))))
29 (define (apply procedure arguments)
30 (cond ((primitive-procedure? procedure)
31 (apply-primitive-procedure procedure arguments))
32 ((compound-procedure? procedure)
34 (procedure-body procedure)
36 (procedure-parameters procedure)
38 (procedure-environment procedure))))
41 "Unknown procedure type -- APPLY" procedure))))
43 (define (list-of-values exps env)
44 (if (no-operands? exps)
46 (cons (eval (first-operand exps) env)
47 (list-of-values (rest-operands exps) env))))
49 (define (tagged-list? exp tag)
54 ;; self-evaluating/variable/quoted
55 (define (self-evaluating? exp)
56 (cond ((number? exp) true)
59 (define (variable? exp) (symbol? exp))
61 (tagged-list? exp 'quote))
62 (define (text-of-quotation exp) (cadr exp))
64 ;; assignment/definition
65 (define (assignment? exp)
66 (tagged-list? exp 'set!))
67 (define (assignment-variable exp) (cadr exp))
68 (define (assignment-value exp) (caddr exp))
69 (define (definition? exp)
70 (tagged-list? exp 'define))
71 (define (definition-variable exp)
72 (if (symbol? (cadr exp))
75 (define (definition-value exp)
76 (if (symbol? (cadr exp))
78 (make-lambda (cdadr exp) ; formal parameters
80 (define (eval-assignment exp env)
81 (set-variable-value! (assignment-variable exp)
82 (eval (assignment-value exp) env)
85 (define (eval-definition exp env)
86 (define-variable! (definition-variable exp)
87 (eval (definition-value exp) env)
90 (define (make-definition var val)
95 (define (unbound? exp)
96 (tagged-list? exp 'make-unbound!))
97 (define (unbound-var exp)
99 (define (eval-unbound exp env)
100 (remove-binding-from-frame! (unbound-var exp) (first-frame env)))
105 (define (if? exp) (tagged-list? exp 'if))
106 (define (if-predicate exp) (cadr exp))
107 (define (if-consequent exp) (caddr exp))
108 (define (if-alternative exp)
109 (if (not (null? (cdddr exp)))
112 (define (make-if predicate consequent alternative)
113 (list 'if predicate consequent alternative))
114 (define (eval-if exp env)
115 (if (true? (eval (if-predicate exp) env))
116 (eval (if-consequent exp) env)
117 (eval (if-alternative exp) env)))
120 (tagged-list? exp 'and))
121 (define (and-clauses exp)
124 (tagged-list? exp 'or))
125 (define (or-clauses exp)
127 (define (eval-and exp env)
128 (define (eval-clauses clauses)
129 (cond ((null? clauses) true)
130 ((null? (cdr clauses)) (eval (car clauses) env))
131 (else (and (eval (car clauses) env)
132 (eval-clauses (cdr clauses))))))
133 (eval-clauses (and-clauses exp)))
134 (define (eval-or exp env)
135 (define (eval-clauses clauses)
138 (or (eval (car clauses) env)
139 (eval-clauses (cdr clauses)))))
140 (eval-clauses (or-clauses exp)))
144 (define (lambda? exp) (tagged-list? exp 'lambda))
145 (define (lambda-parameters exp) (cadr exp))
146 (define (lambda-body exp) (cddr exp))
147 (define (make-lambda parameters body)
148 (cons 'lambda (cons parameters body)))
150 (define (make-let vars vals body)
152 (cons (map list vars vals)
155 (and (tagged-list? exp 'let)
156 (not (symbol? (cadr exp)))))
157 (define (let-vars exp)
158 (map car (cadr exp)))
159 (define (let-vals exp)
160 (map cadr (cadr exp)))
161 (define (let-body exp)
163 (define (let->combination exp)
164 (make-application (make-lambda (let-vars exp) (let-body exp))
166 (define (named-let? exp)
167 (and (tagged-list? exp 'let)
168 (symbol? (cadr exp))))
169 (define (named-let-name exp)
171 (define (named-let-vars exp)
172 (map car (caddr exp)))
173 (define (named-let-vals exp)
174 (map cadr (caddr exp)))
175 (define (named-let-body exp)
177 (define (named-let->combination exp)
179 (list (make-definition (named-let-name exp)
180 (make-lambda (named-let-vars exp)
181 (named-let-body exp)))
182 (make-application (named-let-name exp)
183 (named-let-vals exp)))))
184 (define (make-named-let name vars vals body)
187 (cons (map list vars vals)
190 (define (make-application op args)
194 (tagged-list? exp 'let*))
195 (define let*-vars let-vars)
196 (define let*-vals let-vals)
197 (define let*-body let-body)
198 (define (let*->nested-lets exp)
199 (define (expand-lets vars vals)
200 (if (null? (cdr vars))
201 (make-let (list (car vars))
204 (make-let (list (car vars))
206 (list (expand-lets (cdr vars) (cdr vals))))))
207 (let ((vars (let*-vars exp))
208 (vals (let*-vals exp)))
210 (sequence->exp (let*-body exp))
211 (expand-lets vars vals))))
215 (tagged-list? exp 'do))
216 (define (do-vars exp)
217 (map car (cadr exp)))
218 (define (do-inits exp)
219 (map cadr (cadr exp)))
220 (define (do-steps exp)
221 (map (lambda (var-init-step)
222 (if (null? (cddr var-init-step))
224 (caddr var-init-step)))
226 (define (do-test exp)
228 (define (do-expressions exp)
229 (if (null? (cdaddr exp))
232 (define (do-commands exp)
234 (define (do->combination exp)
242 (sequence->exp (do-expressions exp))
244 (append (do-commands exp)
245 (list (make-application
247 (do-steps exp)))))))))
251 (define (begin? exp) (tagged-list? exp 'begin))
252 (define (begin-actions exp) (cdr exp))
253 (define (last-exp? seq) (null? (cdr seq)))
254 (define (first-exp seq) (car seq))
255 (define (rest-exps seq) (cdr seq))
256 (define (sequence->exp seq)
257 (cond ((null? seq) seq)
258 ((last-exp? seq) (first-exp seq))
259 (else (make-begin seq))))
260 (define (make-begin seq) (cons 'begin seq))
261 (define (eval-sequence exps env)
262 (display "Evaluating: ")
265 (cond ((last-exp? exps) (eval (first-exp exps) env))
266 (else (eval (first-exp exps) env)
267 (eval-sequence (rest-exps exps) env))))
270 (define (application? exp) (pair? exp))
271 (define (operator exp) (car exp))
272 (define (operands exp) (cdr exp))
273 (define (no-operands? ops) (null? ops))
274 (define (first-operand ops) (car ops))
275 (define (rest-operands ops) (cdr ops))
278 (define (cond? exp) (tagged-list? exp 'cond))
279 (define (cond-clauses exp) (cdr exp))
280 (define (cond-else-clause? clause)
281 (eq? (cond-predicate clause) 'else))
282 (define (cond-predicate clause) (car clause))
283 (define (cond-actions clause) (cdr clause))
284 (define (cond-extended-clause? clause)
285 (and (not (null? (cdr clause))) (eq? (cadr clause) '=>)))
286 (define (cond-extended-proc clause)
288 (define (cond->if exp)
289 (expand-clauses (cond-clauses exp)))
290 (define (expand-clauses clauses)
292 'false ; no else clause
293 (let ((first (car clauses))
294 (rest (cdr clauses)))
295 (if (cond-else-clause? first)
297 (sequence->exp (cond-actions first))
298 (error "ELSE clause isn't last -- COND->IF"
300 (if (cond-extended-clause? first)
301 (make-if (cond-predicate first)
303 (cond-extended-proc first)
304 (list (cond-predicate first)))
305 (expand-clauses rest))
306 (make-if (cond-predicate first)
307 (sequence->exp (cond-actions first))
308 (expand-clauses rest)))))))
315 (define (make-procedure parameters body env)
316 (list 'procedure parameters (scan-out-defines body) env))
317 (define (compound-procedure? p)
318 (tagged-list? p 'procedure))
319 (define (procedure-parameters p) (cadr p))
320 (define (procedure-body p) (caddr p))
321 (define (procedure-environment p) (cadddr p))
324 (define (enclosing-environment env) (cdr env))
325 (define (first-frame env) (car env))
326 (define the-empty-environment '())
327 (define (make-frame variables values)
328 (cons variables values))
329 (define (frame-variables frame) (car frame))
330 (define (frame-values frame) (cdr frame))
331 (define (add-binding-to-frame! var val frame)
332 (set-car! frame (cons var (car frame)))
333 (set-cdr! frame (cons val (cdr frame))))
334 (define (extend-environment vars vals base-env)
335 (if (= (length vars) (length vals))
336 (cons (make-frame vars vals) base-env)
337 (if (< (length vars) (length vals))
338 (error "Too many arguments supplied" vars vals)
339 (error "Too few arguments supplied" vars vals))))
340 (define (lookup-variable-value var env)
341 (define (env-loop env)
342 (define (scan vars vals)
344 (env-loop (enclosing-environment env)))
345 ((eq? var (car vars))
346 (let ((val (car vals)))
347 (if (eq? val '*unassigned*)
348 (error "Var not yet defined -- LOOKUP-VARIABLE-VALUE" var)
350 (else (scan (cdr vars) (cdr vals)))))
351 (if (eq? env the-empty-environment)
352 (error "Unbound variable" var)
353 (let ((frame (first-frame env)))
354 (scan (frame-variables frame)
355 (frame-values frame)))))
357 (define (set-variable-value! var val env)
358 (define (env-loop env)
359 (define (scan vars vals)
361 (env-loop (enclosing-environment env)))
362 ((eq? var (car vars))
364 (else (scan (cdr vars) (cdr vals)))))
365 (if (eq? env the-empty-environment)
366 (error "Unbound variable -- SET!" var)
367 (let ((frame (first-frame env)))
368 (scan (frame-variables frame)
369 (frame-values frame)))))
371 (define (define-variable! var val env)
372 (let ((frame (first-frame env)))
373 (define (scan vars vals)
375 (add-binding-to-frame! var val frame))
376 ((eq? var (car vars))
378 (else (scan (cdr vars) (cdr vals)))))
379 (scan (frame-variables frame)
380 (frame-values frame))))
382 (define (remove-binding-from-frame! var frame)
383 (define (scan vars vals)
384 (cond ((null? (cdr vars))
385 (error "Binding not found -- REMOVE-BINDING-FROM-FRAME!" var))
386 ((eq? var (cadr vars))
387 (set-cdr! vars (cddr vars))
388 (set-cdr! vals (cddr vals)))
389 (else (scan (cdr vars) (cdr vals)))))
390 (let ((vars (frame-variables frame))
391 (vals (frame-values frame)))
392 (if (eq? var (car vars))
393 (begin (set-car! frame (cdr vars))
394 (set-cdr! frame (cdr vals)))
398 (define (primitive-procedure? proc)
399 (tagged-list? proc 'primitive))
400 (define (primitive-implementation proc) (cadr proc))
401 (define primitive-procedures
402 (list (list 'car car)
418 (list 'remainder remainder)
420 (list 'equal? equal?)
421 (list 'display display)))
422 (define (primitive-procedure-names)
424 primitive-procedures))
425 (define (primitive-procedure-objects)
426 (map (lambda (proc) (list 'primitive (cadr proc)))
427 primitive-procedures))
428 (define (apply-primitive-procedure proc args)
429 (apply-in-underlying-scheme
430 (primitive-implementation proc) args))
433 (define input-prompt ";;; M-Eval input:")
434 (define output-prompt ";;; M-Eval value:")
435 (define (driver-loop)
436 (prompt-for-input input-prompt)
437 (let ((input (read)))
438 (let ((output (eval input the-global-environment)))
439 (announce-output output-prompt)
440 (user-print output)))
442 (define (prompt-for-input string)
443 (newline) (newline) (display string) (newline))
445 (define (announce-output string)
446 (newline) (display string) (newline))
447 (define (user-print object)
448 (if (compound-procedure? object)
449 (display (list 'compound-procedure
450 (procedure-parameters object)
451 (procedure-body object)
454 (define (setup-environment)
456 (extend-environment (primitive-procedure-names)
457 (primitive-procedure-objects)
458 the-empty-environment)))
459 (define-variable! 'true true initial-env)
460 (define-variable! 'false false initial-env)
462 (define the-global-environment (setup-environment))
465 (define (test-case actual expected)
470 (display "Expected: ")
473 (define (geval exp) ;; eval globally
474 (eval exp the-global-environment))
475 (define (test-eval exp expected)
476 (test-case (geval exp) expected))
479 ;; Exercise 4.16. In this exercise we implement the method just described for interpreting internal definitions. We assume that the evaluator supports let (see exercise 4.6).
481 ;; a. Change lookup-variable-value (section 4.1.3) to signal an error if the value it finds is the symbol *unassigned*.
485 ;; b. Write a procedure scan-out-defines that takes a procedure body and returns an equivalent one that has no internal definitions, by making the transformation described above.
492 ;; would be transformed into
495 ;; (let ((u '*unassigned*)
496 ;; (v '*unassigned*))
506 (define (make-assignment var val)
507 (list 'set! var val))
509 (define (scan-out-defines body)
510 (let* ((definitions (filter definition? body))
511 (vars (map definition-variable definitions))
512 (unassigneds (map (lambda (var) ''*unassigned*)
514 (vals (map definition-value definitions))
516 (map (lambda (var val)
517 (make-assignment var val))
519 (exps (remove definition? body)))
520 (if (null? definitions)
525 (append assignments exps))))))
527 ;; ((let ((even? (quote *unassigned*))
528 ;; (odd? (quote *unassigned*)))
539 ;; (even? (- n 1)))))
545 ;; c. Install scan-out-defines in the interpreter, either in make-procedure or in procedure-body (see section 4.1.3). Which place is better? Why?
547 ;; better to put it in make-procedure. Otherwise, every time the procedure-body is requested for an application, we'd have to repeat the scanning. This would make applications quite slow and would be very inefficient.
562 (test-eval '(f 5) false)
563 (test-eval '(f 10) true)
565 ;; (define f-proc (eval 'f the-global-environment))
566 ;; (procedure-body f-proc)
567 ;; ((let ((even? (quote *unassigned*)) (odd? (quote *unassigned*))) (set! even? (lambda (n) (if (= n 0) true (odd? (- n 1))))) (set! odd? (lambda (n) (if (= n 0) false (even? (- n 1))))) (even? x)))
568 ;; (user-print (procedure-body f-proc))
569 ;; ((let ((even? (quote *unassigned*)) (odd? (quote *unassigned*))) (set! even? (lambda (n) (if (= n 0) true (odd? (- n 1))))) (set! odd? (lambda (n) (if (= n 0) false (even? (- n 1))))) (even? x)))
570 ;; (first-exp (procedure-body f-proc))
571 ;; (let? (first-exp (procedure-body f-proc)))
575 ;; 1 ]=> (let->combination (first-exp (procedure-body f-proc)))
577 ;Value 14: ((lambda (even? odd?) (set! even? (lambda (n) (if (= n 0) true (odd? (- n 1))))) (set! odd? (lambda (n) (if (= n 0) false (even? (- n 1))))) (even? x)) (quote *unassigned*) (quote *unassigned*))
580 ;Value 13: (let ((even? (quote *unassigned*)) (odd? (quote *unassigned*))) (set! even? (lambda (n) (if (= n 0) true (odd? (- n 1))))) (set! odd? (lambda (n) (if (= n 0) false (even? (- n 1))))) (even? x))
582 ;; (operator (let->combination (first-exp (procedure-body f-proc))))
584 ;Value 15: (lambda (even? odd?) (set! even? (lambda (n) (if (= n 0) true (odd? (- n 1))))) (set! odd? (lambda (n) (if (= n 0) false (even? (- n 1))))) (even? x))
586 ;; 1 ]=> (lambda-parameters (operator (let->combination (first-exp (procedure-body f-proc)))))
588 ;Value 16: (even? odd?)
590 ;; ((set! even? (lambda (n) (if (= n 0) true (odd? (- n 1))))) (set! odd? (lambda (n) (if (= n 0) false (even? (- n 1))))) (even? x))
592 ;; there is an infinite loop going on
593 ;; the problem is that we scan out definitions and construct a let
594 ;; but, the let itself implies another lambda expression. To
595 ;; evaluate that lambda expression, we must construct another procedure.
596 ;; But then, we have to scan out *that* procedure. It never ends...
600 ;; '((define (even? n)
609 ;; '(let ((even? '*unassigned*)
610 ;; (odd? '*unassigned*))
620 ;; (even? (- n 1)))))
623 ;; ((let ((even? (quote *unassigned*))
624 ;; (odd? (quote *unassigned*)))
626 ;; (lambda (n) (if (= n 0) true (odd? (- n 1)))))
628 ;; (lambda (n) (if (= n 0) false (even? (- n 1)))))
636 ;; signal an error because x is undefined if variables are scanned out
643 ;; procedure definitions
646 '(define (assoc key records)
647 (cond ((null? records) false)
648 ((equal? key (caar records)) (car records))
649 (else (assoc key (cdr records))))))
652 '(define (map proc list)
655 (cons (proc (car list))
656 (map proc (cdr list))))))
659 '(define (accumulate op initial sequence)
663 (accumulate op initial (cdr sequence))))))
666 (test-eval '(begin 5 6) 6)
668 (geval '(define x 3))
670 (test-eval '(set! x -25) 'ok)
672 (geval '(define z (lambda (x y) (+ x (* x y)))))
673 (test-eval '(z 3 4) 15)
674 (test-eval '(cond ((= x -2) 'x=-2)
678 (test-eval '(if true false true) false)
686 (geval '(define x (+ 3 8)))
687 (test-eval '(and 0 true x) 11)
688 (test-eval '(and 0 true x false) false)
689 (test-eval '(and 0 true x (set! x -2) false) false)
691 (test-eval '(and 0 true x false (set! x -5)) false)
693 (test-eval '(or false (set! x 25)) 'ok)
695 (test-eval '(or (set! x 2) (set! x 4)) 'ok)
697 (test-eval '(or false (set! x 25) true false) 'ok)
699 (test-eval '(or ((lambda (x) x) 5)) 5)
700 (test-eval '(or (begin (set! x (+ x 1)) x)) 26)
706 '(cond ((assoc 'b '((a 1) (b 2))) => cadr)
711 '(cond ((= 3 4) 'not-true)
712 ((= (* 2 4) 3) 'also-false)
724 ;; procedure definition and application
726 '(define (factorial n)
729 (* n (factorial (- n 1))))))
730 (test-eval '(factorial 5) 120)
742 '(accumulate + 0 '(1 2 3 4 5))
747 (make-let '(x y) '(3 5) '((+ x y)))
774 (z (let ((a (* 3 2)))
802 (+ (let* ((x (+ y 2))
810 (a (let* ((x (* 3 x)))
826 '(let loop ((count 0))
833 (let prime-iter ((i 2))
834 (cond ((> (* i i) x) true)
835 ((= (remainder x i) 0) false)
836 (else (prime-iter (+ i 1)))))))
843 (primes (+ x 1) (- n 1))))
844 (else (primes (+ x 1) n))))
845 '(2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71))
854 (fib-iter (+ a b) a (- count 1))))))
855 (test-eval '(fib 19) 4181)
880 '(do ((y '(1 2 3 4)))
891 '(let ((x '(1 3 5 7 9)))
893 (sum 0 (+ sum (car x))))
898 (do ((x '(1 2 3 4) (cdr x))
899 (y '(1 2 3 4 5 6 7 8) (cddr y)))
901 (set! z (cons (car x) z))))
941 '(let ((a 1) (b 2) (c 3) (d 4))
948 (let ((a 1) (b 2) (c 3))
949 (let ((x (+ a b)) (y (+ c a)))
951 (let ((a x) (b (+ x y)))