SICP元循环求值器

关于环境的表示和操作
将环境表示为一个框架的表，一个环境的外围环境就是这个表的cdr，空环境则直接用空表表示

(define (enclosing-environment env) (cdr env))
(define (first-frame env) (car env))
(define the-empty-environment '())
;每个框架都是一对表形成的序对：一个是这一框架中的所有变量的表，还是就是它们的约束值的表
(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))))

创建初始环境，在其中建立起基本过程的名字与一个唯一对象的关联。

(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 the-global-environment (setup-environment))
;定义基本过程的名字和相应的实现过程
(define primitive-procedures
    (list (list 'car car)
          (list 'cdr cdr)
          (list 'cons cons)
          (list 'null? null?)
          ;;其他基本过程
          ))
(define (primitive-procedure-names)
    (map car primitive-procedures))
(define (primitive-procedure-objects)
    (map (lambda (proc) (list 'primitive (cadr proc)))
         primitive-procedures))

eval对表达式进行分类，依此引导自己的求值工作。eval的构造就像是一个针对被求值表达式的语法类型的分情况分析。针对每类表达式有一个谓词完成相应的检测，有一套抽象方法去选择表达式里的各个部分。

(define (eval exp env)  ;参数是一个表达式和一个环境
    (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))
          ((application? exp)
           (apply (eval (operator exp) env) (list-of-values (operands exp) env)))
          (else
              (error "Unknown expression type -- EVAL" exp))))

谓词检测，把除了false对象之外的所有东西就接受为真

(define (true? x)
    (not (eq? x false)))
(define (false? x)
    (eq? x false))

过程tagged-list?确定一个表的开始是不是某个给定符号

(define (tagged-list? exp tag)
    (if (pair? exp)
        (eq? (car exp) tag)
        false))

对于自求值表达式，例如各种数，eval直接返回这个表达式本身。

(define (self-evaluating? exp)
    (cond ((number? exp) true)
          ((string? exp) true)
          (else false)))

对于变量，eval必须在环境中查找变量，找出它们的值。

(define (variable? exp)
    (symbol? exp))
;返回exp在环境env里的约束值
(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)) (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))

对于加引号的表达式，eval返回被引的表达式。

;;求值器看到的引号表达式是以quote开头的表，即使这种表达式在输入时用的是一个引号
(define (quoted? exp)
    (tagged-list? exp 'quote))
(define (text-of-quotation exp) (cadr exp))

对于变量的赋值（或者定义），就需要递归地调用eval去计算出需要关联于这个对象的新值。而后修改环境，以改变（或者建立）相应变量的约束。

;赋值
(define (assignment-variable exp) (cadr exp))
(define (assignment-value exp) (caddr exp))

(define (assignment? exp)
    (tagged-list? exp 'set!))
(define (eval-assignment exp env)
    (set-variable-value! (assignment-variable exp)
                         (assignment-value exp)
                         env)
    'ok)
;修改变量var在环境env里的约束，使得该变量现在约束到值value
(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" var)
            (let ((frame (first-frame env) (scan (frame-variables frame) (frame-values frame)))))
    (env-loop env))

;定义
(define (definition-variable exp)
    (if (symbol? (cadr exp) (cadr exp) ;若为变量定义，则获取变量名 (caadr exp) ;若为过程定义，则获取过程名 (define (definition-value exp) (if (symbol? (cadr exp) (caddr exp) (make-lambda (cdadr exp) (cddr exp)))) (define (make-lambda parameters body) (cons 'lambda (cons parameters body))) (define (definition? exp) (tagged-list? exp 'define)) (define (eval-definiton exp env) (define-variable! (definition-variable exp) (eval (definition-value exp) env) env)) ;在环境env的第一个框架里加入一个新约束，关联起变量var和值value (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)))) 

一个if表达式要求对其中各部分的特殊处理方式，在谓词为真时求值其推论部分，否则求值其替代部分。

(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 (if? exp)
    (tagged-list? exp 'if))
(define (eval-if exp env)
    (if (true? (eval (if-predicate exp) env))
        (eval (if-consequent exp) env)
        (eval (if-alternative exp) env)))

一个lambda必须转换成一个可以应用的进程，方式就是将这个lambda表达式所描述的参数表和体与相应的求值环境包装起来。

(define (lambda-parameters exp) (cadr exp))
(define (lambda-body exp) (cddr exp))

(define (lambda? exp)
    (tagged-list? exp 'lambda))
(define (make-procedure parameters body env)
    (list 'procedure parameters body env))

一个begin表达式要求求值其中的一系列表达式，按照它们出现的顺序。

(define (begin-actions exp) (cdr exp))
(define (last-exp? exp) (null? (cdr seq)))
(define (first-exp seq) (car seq))
(define (rest-exps seq) (cdr seq))

(define (begin? exp)
    (tagged-list? exp 'begin))
(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))))

分情况分析（cond）将被变换为一组嵌套的if表达式，而后求值。

(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? exp)
    (tagged-list? exp 'cond))
(define (cond->if exp)
    (expand-clauses (cond-clauses exp)))
(define (expand-clauses clauses)
    (if (null? clauses)
        'false
        (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))
                (make-if (cond-predicate first) (sequence->exp (cond-actions first)) (expand-clauses rest))))))
;;将cond表达式变换为if表达式
(define (make-if predicate consequent alternative)
    (list 'if predicate consequent alternative))
;;把一个序列变换为一个表达式，如果需要的话就加上begin作为开头
(define (sequence->exp seq)
    (cond ((null? seq) seq)
          ((last-exp? seq) (first-exp seq))
          (else (make-begin seq))))
(define (make-begin seq)
    (cons 'begin seq))

对于一个过程应用，eval必须递归地求值组合式的运算符部分和运算对象部分。而后将这样得到的过程和参数送给apply，由它去处理实际的过程应用。
apply在求值复合过程的体时需要建立相应的环境，这个环境的构造方式就是扩充该过程所携带的基本环境，并加入一个框架，其中将过程的各个形式参数约束于过程调用的实际参数。

(define (operator exp) (car exp))
(define (operands exp) (cdr exp))
(define (no-operands? ops) (null? ops))
(define (first-operand ops) (car ops))
(define (rest-operand ops) (cdr ops))

(define (application? exp) (pair? exp))
(define (list-of-values exps env)
    (if (no-operands? exps)
        '()
        (cons (eval (first-operand exps) env)
              (list-of-values (rest-operands exps) env))))

;;两个参数，一个是过程，一个是该过程应该去应用的实际参数的表
(define (apply procedure arguments)
    (cond ((primitive-procedure? procedure)
           ;应用基本过程
           (apply-primitive-procedure procedure arguments))
          ((compound-procedure? procedure)
           ;应用复合过程的方式是顺序地求值组成该过程体的那些表达式
           (eval-sequence
               (procedure-body procedure)
               (extend-environment (procedure-parameters procedure) arguments (procedure-environment procedure))))
          (else
              (error
                  "Unknown procedure type -- APPLY" procedure))))


;检查procedure是否为一个基本过程
(define (primitive-procedure? procedure)
    (tagged-list? procedure 'primitive))
;将给定过程应用于arguments里的参数值，并返回这一应用的结果
(define (apply-primitive-procedure procedure arguments)
    (apply-in-underlying-scheme
        (primitive-implementation procedure) arguments))
(define (primitive-implementation procedure)
    (cadr procedure))

(define (compound-procedure? procedure)
    (tagged-list? procedure 'procedure))
(define (procedure-parameters procedure)
    (cadr procedure))
(define (procedure-body procedure)
    (caddr procedure))
(define (procedure-environment procedure)
    (cadddr procedure))
;返回一个新环境，包含一个新的框架，其中的所有位于表vars里的符号约束到约束到表vals里对应的元素，而其外围环境是env
(define (extend-environment vars vals env)
    (if (= (length vars) (length vals))
        (cons (make-frame vars vals)
              env)
        (if (< (length vars) (length vals))
            (error "Too many arguments supplied" vars vals)
            (error "Too few arguments supplied" vars vals))))

关于apply-in-underlying-scheme过程：由于此处实现的是简易Scheme元循环求值器，所以我们应用的是基本过程的apply定义，由于和求值器中的apply重名，所以将apply-in-underlying-scheme作为基本过程apply的一个引用。