SICP第四章部分习题解答(一)
by wqpw
使用Racket并安装sicp包.
4.1
#lang sicp
(define (no-operands? ops) (null? ops))
(define (first-operand ops) (car ops))
(define (rest-operands ops) (cdr ops))
(define (eval exp env)
(display exp) (newline)
exp)
(define (list-of-values exps env)
(if (no-operands? exps)
'()
(cons (eval (first-operand exps) env)
(list-of-values (rest-operands exps) env))))
(define (list-of-values-lr exps env)
(let ((res (cons 'left 'right)))
(if (no-operands? exps)
'()
(begin
(set-car! res (eval (first-operand exps) env))
(set-cdr! res (list-of-values-lr (rest-operands exps) env))
res))))
(define (list-of-values-rl exps env)
(let ((res (cons 'left 'right)))
(if (no-operands? exps)
'()
(begin
(set-cdr! res (list-of-values-rl (rest-operands exps) env))
(set-car! res (eval (first-operand exps) env))
res))))
(list-of-values '(1 2 3) '())
(list-of-values-rl '(1 2 3) '())
(list-of-values-lr '(1 2 3) '())
4.2
(a)define会被当成过程. (b)修改application?认定’call开头为过程应用.
4.3
大概是这个感觉.
(define (install-eval-package)
(define (self-evaluating? exp)
(cond ((number? exp) true)
((string? exp) true)
(else false)))
(put 'self-evaluating? self-evaluating?)
(define (variable? exp) (symbol? exp))
(put 'variable? variable?)
(define (tagged-list? exp tag)
(if (pair? exp)
(eq? (car exp) tag)
false))
(define (quoted? exp)
(tagged-list? exp 'quote))
(put 'quoted? quoted?)
(define (text-of-quotation exp) (cadr exp))
(put 'text-of-quotation text-of-quotation)
(define (application? exp) (pair? exp))
(put 'application? application?)
(define (operator exp) (car exp))
(put 'operator operator)
(define (operands exp) (cdr exp))
(put 'operands operands)
(define (eval-assignment exp env)
(set-variable-value! (assignment-variable exp)
(eval (assignment-value exp) env)
env)
'ok)
(put 'set! eval-assignment)
(define (eval-definition exp env)
(define-variable! (definition-variable exp)
(eval (definition-value exp) env)
env)
'ok)
(put 'define eval-definition)
(define (eval-if exp env)
(if (true? (eval (if-predicate exp) env))
(eval (if-consequent exp) env)
(eval (if-alternative exp) env)))
(put 'if eval-if)
; 后略...
'ok)
(define (self-evaluating? exp)
((get 'self-evaluating?) exp))
(define (variable? exp)
((get 'variable?) exp))
(define (lookup-variable-value exp env)
((get 'lookup-variable-value) exp env))
(define (quoted? exp)
((get 'quoted?) exp))
(define (text-of-quotation exp)
((get 'text-of-quotation) exp))
(define (application? exp)
((get 'application?) exp))
(define (operator exp)
((get 'operator) exp))
(define (list-of-values exps env)
((get 'list-of-values) exps env))
(define (operands exp)
((get 'operands) exp))
(define (eval exp env)
(cond ((self-evaluating? exp) exp)
((variable? exp) (lookup-variable-value exp env))
((quoted? exp) (text-of-quotation exp))
((get (car exp)) ((get (car exp)) exp env))
((application? exp)
(apply (eval (operator exp) env)
(list-of-values (operands exp) env))))
(else
(error "Unknown expression type -- EVAL" exp)))
4.4
在eval的cond的分支里添加识别和处理and, or形式的代码.
(define (eval exp env)
(cond ((self-evaluating? exp) exp)
((variable? exp) (lookup-variable-value exp env))
((quoted? exp) (text-of-quotation exp))
((assignment? exp) (eval-assignment exp env))
((definition? exp) (eval-definition exp env))
((if? exp) (eval-if exp env))
((lambda? exp)
(make-procedure (lambda-parameters exp)
(lambda-body exp)
env))
((begin? exp)
(eval-sequence (begin-actions exp) env))
((cond? exp) (eval (cond->if exp) env))
((and? exp) (eval-and (cdr exp) env))
((or? exp) (eval-or (cdr exp) env))
((application? exp)
(apply (eval (operator exp) env)
(list-of-values (operands exp) env)))
(else
(error "Unknown expression type -- EVAL" exp))))
语法过程和求值过程:
(define (and? exp) (tagged-list? exp 'and))
(define (eval-and exps env)
(define (iter exps last-res)
(if (null? exps)
last-res
(let ((res (eval (car exps) env)))
(if (true? res)
(iter (cdr exps) res)
false))))
(if (null? exps)
true
(iter exps true)))
(define (or? exp) (tagged-list? exp 'or))
(define (eval-or exps env)
(define (iter exps)
(if (null? exps)
false
(let ((res (eval (car exps) env)))
(if (true? res)
true
(iter (cdr exps))))))
(iter exps))
另一种方式, 实现为派生表达式:
参考: https://beautifulracket.com/explainer/macros.html
(define (eval exp env)
(cond ((self-evaluating? exp) exp)
......
((and? exp) (eval (and->if exp) env))
((or? exp) (eval (or->if exp) env))
......))
(define (and-body and-exp) (cdr and-exp))
(define (or-body or-exp) (cdr or-exp))
(define (and->if exp)
(define (expand exps)
(if (not (null? exps))
(make-if (car exps)
(if (null? (cddr exps))
(cadr exps)
(expand (cdr exps)))
false)))
(let ((body (and-body exp)))
(cond ((null? body) true)
((null? (cdr body)) (car body))
(else (expand (and-body exp))))))
(define (or->if exp)
(define (expand exps)
(if (not (null? exps))
(make-if (car exps)
true
(if (null? (cddr exps))
(cadr exps)
(expand (cdr exps))))))
(let ((body (or-body exp)))
(cond ((null? body) false)
((null? (cdr body)) (car body))
(else (expand (or-body exp))))))
(and->if '(and (expr a) (expr b)))
(and->if '(and (expr a) (expr b) (expr c)))
(or->if '(or (expr a) (expr b)))
(or->if '(or (expr a) (expr b) (expr c)))
(and->if '(and))
(and->if '(and (x 1)))
(or->if '(or))
(or->if '(or false))
4.5
(define (expand-clauses clauses)
(if (null? clauses)
'false ; clause else no
(let ((first (car clauses))
(rest (cdr clauses)))
(if (cond-else-clause? first)
(if (null? rest)
(sequence->exp (cond-actions first))
(error "ELSE clause isn't last -- COND->IF"
clauses))
(if (eq? (car (cond-actions first)) '=>)
(let ((recipient (cadr (cond-actions first))))
(list (make-lambda
'(__@ImplyRes)
(list
(make-if '__@ImplyRes
(list recipient '__@ImplyRes)
(expand-clauses rest))))
(cond-predicate first)))
(make-if (cond-predicate first)
(sequence->exp (cond-actions first))
(expand-clauses rest)))))))
(cond->if '(cond ((expr 1) => x) ((expr 2) => y) ((expr 3) 3) (else 4)))
(cond->if '(cond ((assoc 'b '((a 1) (b 2))) => cadr) (else false)))
; =>
((lambda (__@ImplyRes) (if __@ImplyRes (cadr __@ImplyRes) (begin false))) (assoc (quote b) (quote ((a 1) (b 2)))))
看wiki发现RaphyJake思路和我一样, 用lambda防止执行两次(cond-predicate first),
然后下面说可能出现内部lambda参数与外部绑定同名的问题, 或许可以考虑把用户代码绑定的名字都预处理下.
wiki里的代码有看不懂的, 提前执行的, 执行两次的, 只执行一次(make-lambda; make-let)但可能存在同名冲突的…只有x3v的代码只执行一次且没有冲突, 但超出了题目要求改的范围.
4.6
; eval条件分支添加
((let? exp) (eval (let->combination exp) env))
;;;;
; let表达式
(define (let? exp) (tagged-list? exp 'let))
(define (let-bindings exp) (cadr exp))
(define (let-body exp) (cddr exp))
(define (let->combination exp)
(let ((bindings (let-bindings exp)))
(cons (make-lambda (map car bindings)
(let-body exp))
(map cadr bindings))))
测试
#lang sicp
; (let ((v1 e1) (v2 e2) .. (vn en)) body) -> ((lambda (v1 v2 ... vn) body) e1 e2 .. en)
(define t '(let ((v1 e1) (v2 e2) (vn en)) body))
(let->combination t)
(define (lambda-parameters exp) (cadr exp))
(define (lambda-body exp) (cddr exp))
(lambda-parameters '(lambda (v1 v2 vn) body))
(lambda-body '(lambda (v1 v2 vn) (+ v1 v2 vn) (newline)))
4.7
;;; eval条件分支添加
((let*? exp) (eval (let*->nested-lets exp) env))
;;;
(define (let*? exp) (tagged-list? exp 'let*))
(define (let*-bindings exp) (cadr exp))
(define (let*-body exp) (cddr exp))
(define (make-let bindings body)
(cons 'let (cons bindings body)))
(define (let*->nested-lets exp)
(define (iter bindings body)
(if (not (null? (cdr bindings)))
(make-let (list (car bindings))
(list (iter (cdr bindings) body)))
(make-let (list (car bindings)) body)))
(iter (let*-bindings exp) (let*-body exp)))
4.8
(define (named-let? exp) (not (pair? (cadr exp))))
(define (named-let-bindings exp)
(caddr exp))
(define (named-let-body exp)
(cdddr exp))
(define (named-let-name exp) (cadr exp))
(define (named-let->define exp)
(let ((name (named-let-name exp))
(bindings (named-let-bindings exp))
(body (named-let-body exp)))
(list
(list 'define
name
(make-lambda (map car bindings)
body))
(cons name (map cadr bindings)))))
(define (let->combination exp)
(if (named-let? exp)
(make-lambda '() (named-let->define exp))
(let ((bindings (let-bindings exp)))
(cons (make-lambda (map car bindings)
(let-body exp))
(map cadr bindings)))))
4.9
(while? t)
(while-cond t)
(while-body t)
(define (while->lambda exp)
(list (make-lambda
'()
(list (list 'define
'(while)
(list 'cond
(list
(while-cond exp)
(sequence->exp (while-body exp))
'(while))))
'(while)))))
(define x 0)
(while->lambda '(while (< x 5) (set! x (+ x 1)) (display x)))
((lambda () (define (while) (cond ((< x 5) (begin (set! x (+ x 1)) (display x)) (while)))) (while)))
4.10
修改各个选择器就可以拓展或修改语法.
4.11
#lang sicp
(define (enclosing-environment env) (cdr env))
(define (first-frame env) (car env))
(define the-empty-environment '())
(define (make-frame variables values)
(cons (cons 'frame 'head) (map cons variables values)))
(define (extend-environment vars vals base-env)
(if (= (length vars) (length vals))
(cons (make-frame vars vals) base-env)
(if (< (length vars) (length vals))
(error "Too many arguments supplied" vars vals)
(error "Too few arguments supplied" vars vals))))
(define (lookup-variable-value var env)
(define (env-loop env)
(if (eq? env the-empty-environment)
(error "Unbound variable" var)
(let ((frame (first-frame env)))
(let ((res (assoc var frame)))
(if res
(cdr res)
(env-loop (enclosing-environment env)))))))
(env-loop env))
(define (set-variable-value! var val env)
(define (env-loop env)
(define (scan frame)
(cond ((null? frame)
(env-loop (enclosing-environment env)))
((eq? var (caar frame))
(set-cdr! (car frame) val))
(else (scan (cdr frame)))))
(if (eq? env the-empty-environment)
(error "Unbound variable -- SET!" var)
(scan (first-frame env))))
(env-loop env))
(define (add-binding-to-frame! var val frame)
(set-cdr! frame (cons (cons var val) (cdr frame))))
(define (define-variable! var val env)
(let ((frame (first-frame env)))
(define (scan f)
(cond ((null? f)
(add-binding-to-frame! var val frame))
((eq? var (caar f))
(set-cdr! (car f) val))
(else (scan (cdr f)))))
(scan frame)))
(define test-env
(extend-environment
'(a b c d)
'(1 2 3 4)
the-empty-environment))
(lookup-variable-value 'c test-env)
(set-variable-value! 'b 6 test-env)
(lookup-variable-value 'b test-env)
(define-variable! 'e 5 test-env)
(display test-env)
4.12
(define (make-frame variables values)
; 从frame中查找var, 返回 (var . val), 不存在返回 false
(define (getv var)
1)
; 修改frame中的var对应的val
; 没有找到var时返回'failure
(define (setv var val)
1)
; 在frame中添加或修改一对var, val
(define (defv var val)
1)
; 打印 frame
(define (print)
1)
(define (dispatch msg)
(cond ((eq? msg 'getv) getv)
((eq? msg 'setv) setv)
((eq? msg 'defv) defv)
((eq? msg 'print) print)
(else (error "?"))))
dispatch)
(define (get-var var frame)
((frame 'getv) var))
(define (frame-set var val frame)
((frame 'setv) var val))
(define (frame-define var val frame)
((frame 'defv) var val))
(define (print-frame frame)
((frame 'print)))
(define (enclosing-environment env) (cdr env))
(define (first-frame env) (car env))
(define the-empty-environment '())
(define (extend-environment vars vals base-env)
(if (= (length vars) (length vals))
(cons (make-frame vars vals) base-env)
(if (< (length vars) (length vals))
(error "Too many arguments supplied" vars vals)
(error "Too few arguments supplied" vars vals))))
(define (env-loop var val env action)
(if (eq? env the-empty-environment)
(error "Unbound variable" var)
(let ((frame (first-frame env)))
(cond ((eq? action 'lookup)
(let ((res (get-var var frame)))
(if res
(cdr res)
(env-loop var val (enclosing-environment env) 'lookup))))
((eq? action 'set)
(let ((res (frame-set var val frame)))
(if (eq? res 'failure)
(env-loop var val (enclosing-environment env) 'set))))))))
(define (lookup-variable-value var env)
(env-loop var nil env 'lookup))
(define (set-variable-value! var val env)
(env-loop var val env 'set))
(define (define-variable! var val env)
(let ((frame (first-frame env)))
(frame-define var val frame)))
(define test-env
(extend-environment
'(a b c d)
'(1 2 3 4)
the-empty-environment))
(lookup-variable-value 'c test-env)
(set-variable-value! 'b 6 test-env)
(lookup-variable-value 'b test-env)
(define-variable! 'e 5 test-env)
(display test-env)
一种实现:
(define (make-frame variables values)
(define the-frame '())
; 从frame中查找var, 返回 (var . val), 不存在返回 false
(define (getv var)
(define (scan vars vals)
(cond ((null? vars) false)
((eq? var (car vars))
(cons var (car vals)))
(else (scan (cdr vars) (cdr vals)))))
(scan (car the-frame) (cdr the-frame)))
; 修改frame中的var对应的val
; 没有找到var时返回'failure
(define (setv var val)
(define (scan vars vals)
(cond ((null? vars) 'failure)
((eq? var (car vars))
(set-car! vals val))
(else (scan (cdr vars) (cdr vals)))))
(scan (car the-frame) (cdr the-frame)))
; 在frame中添加或修改一对var, val
(define (defv var val)
(define (add-binding-to-frame! var val)
(set-car! the-frame (cons var (car the-frame)))
(set-cdr! the-frame (cons val (cdr the-frame))))
(define (scan vars vals)
(cond ((null? vars)
(add-binding-to-frame! var val))
((eq? var (car vars))
(set-car! vals val))
(else (scan (cdr vars) (cdr vals)))))
(scan (car the-frame) (cdr the-frame)))
(define (print)
(display the-frame)
(newline))
(define (dispatch msg)
(cond ((eq? msg 'getv) getv)
((eq? msg 'setv) setv)
((eq? msg 'defv) defv)
((eq? msg 'print) print)
(else (error "?"))))
(set! the-frame (cons variables values))
dispatch)
4.13
只删除第一个框架里的约束.
(define (make-unbound! var env)
(let ((frame (first-frame env)))
(define (scan last-var last-val vars vals)
(cond ((eq? var (car vars))
(cond ((eq? '() (cdr vars))
(set-cdr! last-var '())
(set-cdr! last-val '()))
(else
(set-car! vars (cadr vars))
(set-cdr! vars (cddr vars))
(set-car! vals (cadr vals))
(set-cdr! vals (cddr vals)))))
(else (if (not (null? vars))
(scan vars vals (cdr vars) (cdr vals))))))
(scan '() '()
(frame-variables frame)
(frame-values frame))))
4.14
经过eval的处理后map的第一个参数会变成第一个元素为primitive或procedure的表, 所以系统的map会出错.
4.15
停机问题, 相关资料有很多.
4.16
(define (lookup-variable-value var env)
(define (env-loop env)
(define (scan vars vals)
(cond ((null? vars)
(env-loop (enclosing-environment env)))
((eq? var (car vars))
(if (eq? (car vals) '*unassigned*)
(error "ERROR *UNASSIGNED VARIABLE*" var)
(car vals)))
(else (scan (cdr vars) (cdr vals)))))
(if (eq? env the-empty-environment)
(error "Unbound variable" var)
(let ((frame (first-frame env)))
(scan (frame-variables frame)
(frame-values frame)))))
(env-loop env))
(define (scan-out-defines body)
(define (scan b bindings let-b)
(let ((expr (car b)))
(if (tagged-list? expr 'define)
(let ((vr (definition-variable expr))
(vl (definition-value expr)))
(scan (cdr b)
(cons (list vr ''*unassigned*) bindings)
(cons (list 'set! vr vl) let-b)))
(if (null? bindings)
body
(list (make-let (reverse bindings) (append (reverse let-b) b)))))))
(scan body '() '()))
(define (make-procedure parameters body env)
(list 'procedure parameters (scan-out-defines body) env))
4.19
我觉得`Alyssa`的观点更合理.
4.20
;; eval条件分支添加
((letrec? exp) (eval (letrec->let exp) env))
;;
(define (letrec? exp) (tagged-list? exp 'letrec))
(define (letrec->let exp)
(let ((bindings (let-bindings exp)))
(make-let (map (lambda (x) (list (car x) ''unassigned)) bindings)
(append (map (lambda (vr vl) (list 'set! vr vl))
(map car bindings)
(map cadr bindings))
(let-body exp)))))
4.21
a)
((lambda (n)
((lambda (fib)
(fib fib n))
(lambda (fibo k)
(if (< k 3)
1
(+ (fibo fibo (- k 1)) (fibo fibo (- k 2)))))))
12)
b)
(define (f x)
((lambda (even? odd?)
(even? even? odd? x))
(lambda (ev? od? n)
(if (= n 0) true (od? ev? od? (- n 1))))
(lambda (ev? od? n)
(if (= n 0) false (ev? ev? od? (- n 1))))))
到这里为止的求值器的代码. 每次执行程序对同一个过程都需要重复做语法分析, 非常低效.
#lang sicp
(define apply-in-underlying-scheme apply)
(define (enclosing-environment env) (cdr env))
(define (first-frame env) (car env))
(define the-empty-environment '())
(define (make-frame variables values)
(cons variables values))
(define (frame-variables frame) (car frame))
(define (frame-values frame) (cdr frame))
(define (add-binding-to-frame! var val frame)
(set-car! frame (cons var (car frame)))
(set-cdr! frame (cons val (cdr frame))))
(define (extend-environment vars vals base-env)
(if (= (length vars) (length vals))
(cons (make-frame vars vals) base-env)
(if (< (length vars) (length vals))
(error "Too many arguments supplied" vars vals)
(error "Too few arguments supplied" vars vals))))
(define (lookup-variable-value var env)
(define (env-loop env)
(define (scan vars vals)
(cond ((null? vars)
(env-loop (enclosing-environment env)))
((eq? var (car vars))
(if (eq? (car vals) '*unassigned*)
(error "ERROR *UNASSIGNED VARIABLE*" var)
(car vals)))
(else (scan (cdr vars) (cdr vals)))))
(if (eq? env the-empty-environment)
(error "Unbound variable" var)
(let ((frame (first-frame env)))
(scan (frame-variables frame)
(frame-values frame)))))
(env-loop env))
(define (set-variable-value! var val env)
(define (env-loop env)
(define (scan vars vals)
(cond ((null? vars)
(env-loop (enclosing-environment env)))
((eq? var (car vars))
(set-car! vals val))
(else (scan (cdr vars) (cdr vals)))))
(if (eq? env the-empty-environment)
(error "Unbound variable -- SET!" var)
(let ((frame (first-frame env)))
(scan (frame-variables frame)
(frame-values frame)))))
(env-loop env))
(define (define-variable! var val env)
(let ((frame (first-frame env)))
(define (scan vars vals)
(cond ((null? vars)
(add-binding-to-frame! var val frame))
((eq? var (car vars))
(set-car! vals val))
(else (scan (cdr vars) (cdr vals)))))
(scan (frame-variables frame)
(frame-values frame))))
(define (make-unbound! var env)
(let ((frame (first-frame env)))
(define (scan last-var last-val vars vals)
(cond ((eq? var (car vars))
(cond ((eq? '() (cdr vars))
(set-cdr! last-var '())
(set-cdr! last-val '()))
(else
(set-car! vars (cadr vars))
(set-cdr! vars (cddr vars))
(set-car! vals (cadr vals))
(set-cdr! vals (cddr vals)))))
(else (if (not (null? vars))
(scan vars vals (cdr vars) (cdr vals))))))
(scan '() '()
(frame-variables frame)
(frame-values frame))))
;;
(define (setup-environment)
(let ((initial-env
(extend-environment (primitive-procedure-names)
(primitive-procedure-objects)
the-empty-environment)))
(define-variable! 'true true initial-env)
(define-variable! 'false false initial-env)
initial-env))
(define (primitive-procedure? proc)
(tagged-list? proc 'primitive))
(define (primitive-implementation proc) (cadr proc))
(define primitive-procedures
(list (list 'car car)
(list 'cdr cdr)
(list 'cons cons)
(list 'null? null?)
; other primitive procedures ...
(list '+ +)
(list '* *)
(list '= =)
(list '- -)
))
(define (primitive-procedure-names)
(map car primitive-procedures))
(define (primitive-procedure-objects)
(map (lambda (proc) (list 'primitive (cadr proc)))
primitive-procedures))
(define (apply-primitive-procedure proc args)
(apply-in-underlying-scheme
(primitive-implementation proc) args))
;;
(define (scan-out-defines body)
(define (scan b bindings let-b)
(let ((expr (car b)))
(if (tagged-list? expr 'define)
(let ((vr (definition-variable expr))
(vl (definition-value expr)))
(scan (cdr b)
(cons (list vr ''*unassigned*) bindings)
(cons (list 'set! vr vl) let-b)))
(if (null? bindings)
body
(list (make-let (reverse bindings) (append (reverse let-b) b)))))))
(scan body '() '()))
(define (make-procedure parameters body env)
(list 'procedure parameters (scan-out-defines body) env))
(define (compound-procedure? p)
(tagged-list? p 'procedure))
(define (procedure-body p) (caddr p))
(define (procedure-parameters p) (cadr p))
(define (procedure-environment p) (cadddr p))
(define (true? x)
(not (eq? x false)))
(define (false? x)
(eq? x false))
;;
(define (eval exp env)
(cond ((self-evaluating? exp) exp)
((variable? exp) (lookup-variable-value exp env))
((quoted? exp) (text-of-quotation exp))
((assignment? exp) (eval-assignment exp env))
((definition? exp) (eval-definition exp env))
((if? exp) (eval-if exp env))
((lambda? exp)
(make-procedure (lambda-parameters exp)
(lambda-body exp)
env))
((begin? exp)
(eval-sequence (begin-actions exp) env))
((cond? exp) (eval (cond->if exp) env))
((and? exp) (eval (and->if exp) env))
((or? exp) (eval (or->if exp) env))
((let? exp) (eval (let->combination exp) env))
((let*? exp) (eval (let*->nested-lets exp) env))
((letrec? exp) (eval (letrec->let exp) env))
((application? exp)
(applyx (eval (operator exp) env)
(list-of-values (operands exp) env)))
(else
(error "Unknown expression type -- EVAL" exp))))
(define (applyx procedure arguments) ;apply的话racket会报错, 和apply-primitive-procedure有关
(cond ((primitive-procedure? procedure)
(apply-primitive-procedure procedure arguments))
((compound-procedure? procedure)
(eval-sequence
(procedure-body procedure)
(extend-environment
(procedure-parameters procedure)
arguments
(procedure-environment procedure))))
(else
(error "Unknown procedure type -- APPLY" procedure))))
;;
(define (list-of-values exps env)
(if (no-operands? exps)
'()
(cons (eval (first-operand exps) env)
(list-of-values (rest-operands exps) env))))
(define (eval-if exp env)
(if (true? (eval (if-predicate exp) env))
(eval (if-consequent exp) env)
(eval (if-alternative exp) env)))
(define (eval-sequence exps env)
(cond ((last-exp? exps) (eval (first-exp exps) env))
(else (eval (first-exp exps) env)
(eval-sequence (rest-exps exps) env))))
(define (eval-assignment exp env)
(set-variable-value! (assignment-variable exp)
(eval (assignment-value exp) env)
env)
'ok)
(define (eval-definition exp env)
(define-variable! (definition-variable exp)
(eval (definition-value exp) env)
env)
'ok)
(define (self-evaluating? exp)
(cond ((number? exp) true)
((string? exp) true)
(else false)))
(define (variable? exp) (symbol? exp))
(define (quoted? exp)
(tagged-list? exp 'quote))
(define (text-of-quotation exp) (cadr exp))
(define (tagged-list? exp tag)
(if (pair? exp)
(eq? (car exp) tag)
false))
(define (assignment? exp) (tagged-list? exp 'set!))
(define (assignment-variable exp) (cadr exp))
(define (assignment-value exp) (caddr exp))
(define (definition? exp)
(tagged-list? exp 'define))
(define (definition-variable exp)
(if (symbol? (cadr exp))
(cadr exp)
(caadr exp)))
(define (definition-value exp)
(if (symbol? (cadr exp))
(caddr exp)
(make-lambda (cdadr exp)
(cddr exp))))
(define (lambda? exp) (tagged-list? exp 'lambda))
(define (lambda-parameters exp) (cadr exp))
(define (lambda-body exp) (cddr exp))
(define (make-lambda parameters body)
(cons 'lambda (cons parameters body)))
(define (if? exp) (tagged-list? exp 'if))
(define (if-predicate exp) (cadr exp))
(define (if-consequent exp) (caddr exp))
(define (if-alternative exp)
(if (not (null? (cdddr exp)))
(cadddr exp)
'false))
(define (make-if predicate consequent alternative)
(list 'if predicate consequent alternative))
(define (begin? exp) (tagged-list? exp 'begin))
(define (begin-actions exp) (cdr exp))
(define (last-exp? seq) (null? (cdr seq)))
(define (first-exp seq) (car seq))
(define (rest-exps seq) (cdr seq))
(define (make-begin seq) (cons 'begin seq))
(define (sequence->exp seq)
(cond ((null? seq) seq)
((last-exp? seq) (first-exp seq))
(else (make-begin seq))))
(define (application? exp) (pair? exp))
(define (operator exp) (car exp))
(define (operands exp) (cdr exp))
(define (no-operands? ops) (null? ops))
(define (first-operand ops) (car ops))
(define (rest-operands ops) (cdr ops))
(define (cond? exp) (tagged-list? exp 'cond))
(define (cond-clauses exp) (cdr exp))
(define (cond-else-clause? clause)
(eq? (cond-predicate clause) 'else))
(define (cond-predicate clause) (car clause))
(define (cond-actions clause) (cdr clause))
(define (cond->if exp)
(expand-clauses (cond-clauses exp)))
(define (expand-clauses clauses)
(if (null? clauses)
'false ; clause else no
(let ((first (car clauses))
(rest (cdr clauses)))
(if (cond-else-clause? first)
(if (null? rest)
(sequence->exp (cond-actions first))
(error "ELSE clause isn't last -- COND->IF"
clauses))
(if (eq? (car (cond-actions first)) '=>)
(let ((recipient (cadr (cond-actions first))))
(list (make-lambda
'(__@ImplyRes)
(list
(make-if '__@ImplyRes
(list recipient '__@ImplyRes)
(expand-clauses rest))))
(cond-predicate first)))
(make-if (cond-predicate first)
(sequence->exp (cond-actions first))
(expand-clauses rest)))))))
(define (and? exp) (tagged-list? exp 'and))
(define (eval-and exps env)
(define (iter exps last-res)
(if (null? exps)
last-res
(let ((res (eval (car exps) env)))
(if (true? res)
(iter (cdr exps) res)
false))))
(iter exps true))
(define (or? exp) (tagged-list? exp 'or))
(define (eval-or exps env)
(define (iter exps)
(if (null? exps)
false
(let ((res (eval (car exps) env)))
(if (true? res)
true
(iter (cdr exps))))))
(iter exps))
(define (and-body and-exp) (cdr and-exp))
(define (or-body or-exp) (cdr or-exp))
(define (and->if exp)
(define (expand exps)
(if (not (null? exps))
(make-if (car exps)
(if (null? (cddr exps))
(cadr exps)
(expand (cdr exps)))
false)))
(let ((body (and-body exp)))
(cond ((null? body) true)
((null? (cdr body)) (car body))
(else (expand (and-body exp))))))
(define (or->if exp)
(define (expand exps)
(if (not (null? exps))
(make-if (car exps)
true
(if (null? (cddr exps))
(cadr exps)
(expand (cdr exps))))))
(let ((body (or-body exp)))
(cond ((null? body) false)
((null? (cdr body)) (car body))
(else (expand (or-body exp))))))
(define (let? exp) (tagged-list? exp 'let))
(define (let-bindings exp) (cadr exp))
(define (let-body exp) (cddr exp))
(define (named-let? exp) (not (pair? (cadr exp))))
(define (named-let-bindings exp)
(caddr exp))
(define (named-let-body exp)
(cdddr exp))
(define (named-let-name exp) (cadr exp))
(define (named-let->define exp)
(let ((name (named-let-name exp))
(bindings (named-let-bindings exp))
(body (named-let-body exp)))
(list
(list 'define
name
(make-lambda (map car bindings)
body))
(cons name (map cadr bindings)))))
(define (let->combination exp)
(if (named-let? exp)
(make-lambda '() (named-let->define exp))
(let ((bindings (let-bindings exp)))
(cons (make-lambda (map car bindings)
(let-body exp))
(map cadr bindings)))))
(define (let*? exp) (tagged-list? exp 'let*))
(define (let*-bindings exp) (cadr exp))
(define (let*-body exp) (cddr exp))
(define (make-let bindings body)
(cons 'let (cons bindings body)))
(define (let*->nested-lets exp)
(define (iter bindings body)
(if (not (null? (cdr bindings)))
(make-let (list (car bindings))
(list (iter (cdr bindings) body)))
(make-let (list (car bindings)) body)))
(iter (let*-bindings exp) (let*-body exp)))
(define (letrec? exp) (tagged-list? exp 'letrec))
(define (letrec->let exp)
(let ((bindings (let-bindings exp)))
(make-let (map (lambda (x) (list (car x) ''unassigned)) bindings)
(append (map (lambda (vr vl) (list 'set! vr vl))
(map car bindings)
(map cadr bindings))
(let-body exp)))))
;;
(define input-prompt ";;; M-Eval input:")
(define output-prompt ";;; M-Eval value:")
(define (driver-loop)
(prompt-for-input input-prompt)
(let ((input (read)))
(let ((output (eval input the-global-environment)))
(announce-output output-prompt)
(user-print output)))
(driver-loop))
(define (prompt-for-input string)
(newline) (newline) (display string) (newline))
(define (announce-output string)
(newline) (display string) (newline))
(define (user-print object)
(if (compound-procedure? object)
(display (list 'compound-procedure
(procedure-parameters object)
(procedure-body object)
(procedure-environment object)))
(display object)))
(define the-global-environment (setup-environment))
;(driver-loop)
(eval '(define (append x y) (if (null? x) y (cons (car x) (append (cdr x) y))))
the-global-environment)
(eval '(append '(a b c) '(d e f)) the-global-environment)
(eval '(define (map proc lst) (if (null? lst) '() (cons (proc (car lst)) (map proc (cdr lst)))))
the-global-environment)
(eval '(map (lambda (x) (+ x 1)) '(1 2 3 4)) the-global-environment)
(eval '(define (f) (define u (+ 2 1)) (+ u 2) (define v (+ 3 2)) (+ u v) (* u v))
the-global-environment)
(eval '(f) the-global-environment)
(eval '(letrec ((fact (lambda (n) (if (= n 1) 1 (* n (fact (- n 1))))))) (fact 5)) the-global-environment)
将语法分析与执行分离.
4.22
#lang sicp
;;
(define apply-in-underlying-scheme apply)
(define (enclosing-environment env) (cdr env))
(define (first-frame env) (car env))
(define the-empty-environment '())
(define (make-frame variables values)
(cons variables values))
(define (frame-variables frame) (car frame))
(define (frame-values frame) (cdr frame))
(define (add-binding-to-frame! var val frame)
(set-car! frame (cons var (car frame)))
(set-cdr! frame (cons val (cdr frame))))
(define (extend-environment vars vals base-env)
(if (= (length vars) (length vals))
(cons (make-frame vars vals) base-env)
(if (< (length vars) (length vals))
(error "Too many arguments supplied" vars vals)
(error "Too few arguments supplied" vars vals))))
(define (lookup-variable-value var env)
(define (env-loop env)
(define (scan vars vals)
(cond ((null? vars)
(env-loop (enclosing-environment env)))
((eq? var (car vars))
(if (eq? (car vals) '*unassigned*)
(error "ERROR *UNASSIGNED VARIABLE*" var)
(car vals)))
(else (scan (cdr vars) (cdr vals)))))
(if (eq? env the-empty-environment)
(error "Unbound variable" var)
(let ((frame (first-frame env)))
(scan (frame-variables frame)
(frame-values frame)))))
(env-loop env))
(define (set-variable-value! var val env)
(define (env-loop env)
(define (scan vars vals)
(cond ((null? vars)
(env-loop (enclosing-environment env)))
((eq? var (car vars))
(set-car! vals val))
(else (scan (cdr vars) (cdr vals)))))
(if (eq? env the-empty-environment)
(error "Unbound variable -- SET!" var)
(let ((frame (first-frame env)))
(scan (frame-variables frame)
(frame-values frame)))))
(env-loop env))
(define (define-variable! var val env)
(let ((frame (first-frame env)))
(define (scan vars vals)
(cond ((null? vars)
(add-binding-to-frame! var val frame))
((eq? var (car vars))
(set-car! vals val))
(else (scan (cdr vars) (cdr vals)))))
(scan (frame-variables frame)
(frame-values frame))))
(define (make-unbound! var env)
(let ((frame (first-frame env)))
(define (scan last-var last-val vars vals)
(cond ((eq? var (car vars))
(cond ((eq? '() (cdr vars))
(set-cdr! last-var '())
(set-cdr! last-val '()))
(else
(set-car! vars (cadr vars))
(set-cdr! vars (cddr vars))
(set-car! vals (cadr vals))
(set-cdr! vals (cddr vals)))))
(else (if (not (null? vars))
(scan vars vals (cdr vars) (cdr vals))))))
(scan '() '()
(frame-variables frame)
(frame-values frame))))
;;
;;
(define (setup-environment)
(let ((initial-env
(extend-environment (primitive-procedure-names)
(primitive-procedure-objects)
the-empty-environment)))
(define-variable! 'true true initial-env)
(define-variable! 'false false initial-env)
initial-env))
(define (primitive-procedure? proc)
(tagged-list? proc 'primitive))
(define (primitive-implementation proc) (cadr proc))
(define primitive-procedures
(list (list 'car car)
(list 'cdr cdr)
(list 'cons cons)
(list 'null? null?)
; other primitive procedures ...
(list '+ +)
(list '* *)
(list '= =)
(list '- -)
))
(define (primitive-procedure-names)
(map car primitive-procedures))
(define (primitive-procedure-objects)
(map (lambda (proc) (list 'primitive (cadr proc)))
primitive-procedures))
(define (apply-primitive-procedure proc args)
(apply-in-underlying-scheme
(primitive-implementation proc) args))
;;
(define (make-procedure parameters body env)
(list 'procedure parameters body env))
(define (compound-procedure? p)
(tagged-list? p 'procedure))
(define (procedure-body p) (caddr p))
(define (procedure-parameters p) (cadr p))
(define (procedure-environment p) (cadddr p))
(define (true? x)
(not (eq? x false)))
(define (false? x)
(eq? x false))
(define (self-evaluating? exp)
(cond ((number? exp) true)
((string? exp) true)
(else false)))
(define (variable? exp) (symbol? exp))
(define (quoted? exp)
(tagged-list? exp 'quote))
(define (text-of-quotation exp) (cadr exp))
(define (tagged-list? exp tag)
(if (pair? exp)
(eq? (car exp) tag)
false))
(define (assignment? exp) (tagged-list? exp 'set!))
(define (assignment-variable exp) (cadr exp))
(define (assignment-value exp) (caddr exp))
(define (definition? exp)
(tagged-list? exp 'define))
(define (definition-variable exp)
(if (symbol? (cadr exp))
(cadr exp)
(caadr exp)))
(define (definition-value exp)
(if (symbol? (cadr exp))
(caddr exp)
(make-lambda (cdadr exp)
(cddr exp))))
(define (lambda? exp) (tagged-list? exp 'lambda))
(define (lambda-parameters exp) (cadr exp))
(define (lambda-body exp) (cddr exp))
(define (make-lambda parameters body)
(cons 'lambda (cons parameters body)))
(define (if? exp) (tagged-list? exp 'if))
(define (if-predicate exp) (cadr exp))
(define (if-consequent exp) (caddr exp))
(define (if-alternative exp)
(if (not (null? (cdddr exp)))
(cadddr exp)
'false))
(define (make-if predicate consequent alternative)
(list 'if predicate consequent alternative))
(define (begin? exp) (tagged-list? exp 'begin))
(define (begin-actions exp) (cdr exp))
(define (last-exp? seq) (null? (cdr seq)))
(define (first-exp seq) (car seq))
(define (rest-exps seq) (cdr seq))
(define (make-begin seq) (cons 'begin seq))
(define (sequence->exp seq)
(cond ((null? seq) seq)
((last-exp? seq) (first-exp seq))
(else (make-begin seq))))
(define (application? exp) (pair? exp))
(define (operator exp) (car exp))
(define (operands exp) (cdr exp))
(define (no-operands? ops) (null? ops))
(define (first-operand ops) (car ops))
(define (rest-operands ops) (cdr ops))
(define (cond? exp) (tagged-list? exp 'cond))
(define (cond-clauses exp) (cdr exp))
(define (cond-else-clause? clause)
(eq? (cond-predicate clause) 'else))
(define (cond-predicate clause) (car clause))
(define (cond-actions clause) (cdr clause))
(define (cond->if exp)
(expand-clauses (cond-clauses exp)))
(define (expand-clauses clauses)
(if (null? clauses)
'false ; clause else no
(let ((first (car clauses))
(rest (cdr clauses)))
(if (cond-else-clause? first)
(if (null? rest)
(sequence->exp (cond-actions first))
(error "ELSE clause isn't last -- COND->IF"
clauses))
(if (eq? (car (cond-actions first)) '=>)
(let ((recipient (cadr (cond-actions first))))
(list (make-lambda
'(__@ImplyRes)
(list
(make-if '__@ImplyRes
(list recipient '__@ImplyRes)
(expand-clauses rest))))
(cond-predicate first)))
(make-if (cond-predicate first)
(sequence->exp (cond-actions first))
(expand-clauses rest)))))))
(define (let? exp) (tagged-list? exp 'let))
(define (let-bindings exp) (cadr exp))
(define (let-body exp) (cddr exp))
(define (let->combination exp)
(let ((bindings (let-bindings exp)))
(cons (make-lambda (map car bindings)
(let-body exp))
(map cadr bindings))))
(define (make-let bindings body)
(cons 'let (cons bindings body)))
(define (eval exp env)
((analyze exp) env))
(define (analyze exp)
(cond ((self-evaluating? exp)
(analyze-self-evaluating exp))
((quoted? exp) (analyze-quoted exp))
((variable? exp) (analyze-variable exp))
((assignment? exp) (analyze-assignment exp))
((definition? exp) (analyze-definition exp))
((if? exp) (analyze-if exp))
((lambda? exp) (analyze-lambda exp))
((begin? exp) (analyze-sequence (begin-actions exp)))
((cond? exp) (analyze (cond->if exp)))
((let? exp) (analyze (let->combination exp))) ;ex4.22
((application? exp) (analyze-application exp))
(else
(error "Unknown expression type -- ANALYZE" exp))))
(define (analyze-self-evaluating exp)
(lambda (env) exp))
(define (analyze-quoted exp)
(let ((qval (text-of-quotation exp)))
(lambda (env) qval)))
(define (analyze-variable exp)
(lambda (env) (lookup-variable-value exp env)))
(define (analyze-assignment exp)
(let ((var (assignment-variable exp))
(vproc (analyze (assignment-value exp))))
(lambda (env)
(set-variable-value! var (vproc env) env)
'ok)))
(define (analyze-definition exp)
(let ((var (definition-variable exp))
(vproc (analyze (definition-value exp))))
(lambda (env)
(define-variable! var (vproc env) env)
'ok)))
(define (analyze-if exp)
(let ((pproc (analyze (if-predicate exp)))
(cproc (analyze (if-consequent exp)))
(aproc (analyze (if-alternative exp))))
(lambda (env)
(if (true? (pproc env))
(cproc env)
(aproc env)))))
(define (analyze-lambda exp)
(let ((vars (lambda-parameters exp))
(bproc (analyze-sequence (lambda-body exp))))
(lambda (env) (make-procedure vars bproc env))))
(define (analyze-sequence exps)
(define (sequentially proc1 proc2)
(lambda (env) (proc1 env) (proc2 env)))
(define (loop first-proc rest-procs)
(if (null? rest-procs)
first-proc
(loop (sequentially first-proc (car rest-procs))
(cdr rest-procs))))
(let ((procs (map analyze exps)))
(if (null? procs)
(error "Empty sequence -- ANALYZE"))
(loop (car procs) (cdr procs))))
(define (analyze-application exp)
(let ((fproc (analyze (operator exp)))
(aprocs (map analyze (operands exp))))
(lambda (env)
(execute-application (fproc env)
(map (lambda (aproc) (aproc env))
aprocs)))))
(define (execute-application proc args)
(cond ((primitive-procedure? proc)
(apply-primitive-procedure proc args))
((compound-procedure? proc)
((procedure-body proc)
(extend-environment (procedure-parameters proc)
args
(procedure-environment proc))))
(else
(error "Unknown procedure type -- EXECUTE-APPLICATION" proc))))
;;
(define input-prompt ";;; M-Eval input:")
(define output-prompt ";;; M-Eval value:")
(define (driver-loop)
(prompt-for-input input-prompt)
(let ((input (read)))
(let ((output (eval input the-global-environment)))
(announce-output output-prompt)
(user-print output)))
(driver-loop))
(define (prompt-for-input string)
(newline) (newline) (display string) (newline))
(define (announce-output string)
(newline) (display string) (newline))
(define (user-print object)
(if (compound-procedure? object)
(display (list 'compound-procedure
(procedure-parameters object)
(procedure-body object)
(procedure-environment object)))
(display object)))
(define the-global-environment (setup-environment))
;(driver-loop)
(eval '(define (append x y) (if (null? x) y (cons (car x) (append (cdr x) y))))
the-global-environment)
(eval '(append '(a b c) '(d e f)) the-global-environment)
(eval '(define (map proc lst) (if (null? lst) '() (cons (proc (car lst)) (map proc (cdr lst)))))
the-global-environment)
(eval '(map (lambda (x) (+ x 1)) '(1 2 3 4)) the-global-environment)
(eval '(let ((v 1)) (+ v 4)) the-global-environment)