#lang sicp (#%require (only racket/base print-as-expression print-mpair-curly-braces)) (print-as-expression #f) (print-mpair-curly-braces #f) ;; Chapter 4 ;; Metalinguistic Abstraction ;; 4.1 ;; The Metacircular Evaluator ;; The Core of the Evaluator (#%provide eval) (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 (and-conjuncts exp) 'true env)) ((or? exp) (eval-or (or-disjuncts 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) (apply- (eval (operator exp) env) (list-of-values (operands exp) env))) (else (error "Unknown expression type -- EVAL" exp)))) (define (apply- procedure arguments) (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) #| 4.1 |# (define (list-of-values-left exps env) (if (no-operands? exps) '() (let ((first-value (eval (first-operand exps) env))) (let ((rest-values (list-of-values-left (rest-operands exps) env))) (cons first-value rest-values))))) (define (list-of-values-right exps env) (if (no-operands? exps) '() (let ((rest-values (list-of-values-right (rest-operands exps) env))) (let ((first-value (eval (first-operand exps) env))) (cons first-value rest-values))))) ;; Representing Expressions (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))) (#%provide definition-value) (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)) (#%provide lambda-body) (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 (sequence->exp seq) (cond ((null? seq) seq) ((last-exp? seq) (first-exp seq)) (else (make-begin seq)))) (define (make-begin seq) (cons '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)) (#%provide cond-predicate) (define (cond-predicate clause) (car clause)) (define (cond-else-clause? clause) (eq? (cond-predicate clause) 'else)) (define (cond-actions clause) (cdr clause)) (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) (if (cond-extended? first) (list (cond-recipient first) (cond-predicate first)) (sequence->exp (cond-actions first))) (expand-clauses rest)))))) #| 4.2 |# (#%provide application?-) (define (application?- exp) (tagged-list? exp 'call)) (#%provide operator-) (define (operator- exp) (cadr exp)) (#%provide operands-) (define (operands- exp) (cddr exp)) #| 4.4 |# (define (and? exp) (tagged-list? exp 'and)) (define (and-conjuncts exp) (cdr exp)) (define (eval-and conjuncts last-value env) (if (null? conjuncts) last-value (let ((value (eval (car conjuncts) env))) (if (true? value) (eval-and (cdr conjuncts) value env) 'false)))) (define (or? exp) (tagged-list? exp 'or)) (define (or-disjuncts exp) (cdr exp)) (define (eval-or disjuncts env) (if (null? disjuncts) 'false (let ((value (eval (car disjuncts) env))) (if (true? value) value (eval-or (cdr disjuncts) env))))) #| 4.5 |# (#%provide cond-recipient) (define (cond-recipient clause) (caddr clause)) (#%provide cond-extended?) (define (cond-extended? clause) (tagged-list? (cdr clause) '=>)) (#%provide expand-clauses-) (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) (if (cond-extended? first) (list (cond-recipient first) (cond-predicate first)) (sequence->exp (cond-actions first))) (expand-clauses- rest)))))) #| 4.6 |# (#%provide let?) (define (let? exp) (tagged-list? exp 'let)) (#%provide binding-var) (define (binding-var binding) (car binding)) (#%provide binding-exp) (define (binding-exp binding) (cadr binding)) (#%provide let-bindings) (define (let-bindings exp) (if (named-let? exp) (caddr exp) (cadr exp))) (#%provide let-body) (define (let-body exp) (if (named-let? exp) (cdddr exp) (cddr exp))) #| (#%provide let->combination) |# #| (define (let->combination exp) |# #| (if (null? (let-bindings exp)) |# #| (if (null? (cdr (let-body exp))) |# #| (car (let-body exp)) |# #| (cons 'begin (let-body exp))) |# #| (list |# #| (cons 'lambda |# #| (cons |# #| (map binding-var (let-bindings exp)) |# #| (let-body exp))) |# #| (map binding-exp (let-bindings exp))))) |# (#%provide let->combination) (define (let->combination exp) (if (null? (let-bindings exp)) (if (null? (cdr (let-body-extended exp))) (car (let-body-extended exp)) (cons 'begin (let-body-extended exp))) (cons (cons 'lambda (cons (map binding-var (let-bindings exp)) (let-body-extended exp))) (map binding-exp (let-bindings exp))))) (define (let-body-extended exp) (if (named-let? exp) (let ((name-vars (cons (let-name exp) (map binding-var (let-bindings exp))))) (list (cons 'define (cons name-vars (let-body exp))) name-vars)) (let-body exp))) #| 4.7 |# (#%provide let*?) (define (let*? exp) (tagged-list? exp 'let*)) (#%provide make-let) (define (make-let bindings body) (cons 'let (cons bindings body))) (#%provide let*->nested-lets) (define (let*->nested-lets exp) (expand-lets (let-bindings exp) (let-body exp))) (#%provide expand-lets) (define (expand-lets bindings body) (if (null? bindings) (if (null? (cdr body)) (car body) (cons 'begin body)) (make-let (list (car bindings)) (list (expand-lets (cdr bindings) body))))) #| 4.8 |# (#%provide named-let?) (define (named-let? exp) (and (tagged-list? exp 'let) (symbol? (cadr exp)))) (#%provide let-name) (define (let-name exp) (cadr exp)) (#%provide let->combination-) (define (let->combination- exp) (let ((variables (map binding-var (let-bindings exp)))) (list (cons 'lambda (cons variables (if (named-let? exp) (let ((name-vars (cons (let-name exp) variables))) (list (cons 'define (cons name-vars (let-body exp))) name-vars)) (let-body exp)))) (map binding-exp (let-bindings exp))))) #| 4.9 |# (#%provide make-named-let) (define (make-named-let name bindings body) (cons 'let (cons name (cons bindings body)))) (#%provide while?) (define (while? exp) (tagged-list? exp 'do)) (#%provide while-condition) (define (while-condition exp) (cadr exp)) (#%provide while-body) (define (while-body exp) (cddr exp)) (#%provide while->named-let) (define (while->named-let exp) (make-named-let 'loop '() (list (make-if (while-condition exp) (cons 'begin (append (while-body exp) (list (list 'loop)))) ''done)))) ;; Evaluator Data Structures (define (true? x) (not (eq? x false))) (define (false? x) (eq? x false)) (define (make-procedure parameters body env) #| (list 'procedure parameters (scan-out-defines body) env)) |# (list 'procedure parameters body env)) (define (compound-procedure? p) (tagged-list? p 'procedure)) (#%provide procedure-parameters) (define (procedure-parameters p) (cadr p)) (#%provide procedure-body) (define (procedure-body p) (caddr p)) (#%provide procedure-environment) (define (procedure-environment p) (cadddr p)) (#%provide enclosing-environment) (define (enclosing-environment env) (cdr env)) (#%provide first-frame) (define (first-frame env) (car env)) (#%provide the-empty-environment) (define the-empty-environment '()) (#%provide make-frame) (define (make-frame variables values) (cons variables values)) (#%provide frame-variables) (define (frame-variables frame) (car frame)) (#%provide frame-values) (define (frame-values frame) (cdr frame)) (#%provide add-binding-to-frame!) (define (add-binding-to-frame! var val frame) (set-car! frame (cons var (car frame))) (set-cdr! frame (cons val (cdr frame)))) (#%provide extend-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)))) (#%provide lookup-variable-value) (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)) |# (if (eq? (car vals) '*unassigned*) (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)) (#%provide set-variable-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)) (#%provide define-variable!) (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)))) #| 4.11 |# (#%provide make-frame-) (define (make-frame- variables values) (define (loop variables values) (if (null? variables) '() (cons (cons (car variables) (car values)) (loop (cdr variables) (cdr values))))) (cons 'frame (loop variables values))) (#%provide frame-variables-) (define (frame-variables- frame) (map car (cdr frame))) (#%provide frame-values-) (define (frame-values- frame) (map cdr (cdr frame))) (#%provide add-binding-to-frame!-) (define (add-binding-to-frame!- var val frame) (set-cdr! frame (cons (cons var val) (cdr frame)))) (#%provide extend-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)))) (#%provide lookup-variable-value-) (define (lookup-variable-value- var env) (define (env-loop env) (define (scan bindings) (cond ((null? bindings) (env-loop (enclosing-environment env))) ((eq? var (car (car bindings))) (cdr (car bindings))) (else (scan (cdr bindings))))) (if (eq? env the-empty-environment) (error "Unbound variable" var) (scan (cdr (first-frame env))))) (env-loop env)) (#%provide set-variable-value!-) (define (set-variable-value!- var val env) (define (env-loop env) (define (scan bindings) (cond ((null? bindings) (env-loop (enclosing-environment env))) ((eq? var (car (car bindings))) (set-car! bindings (cons (car (car bindings)) val))) (else (scan (cdr bindings))))) (if (eq? env the-empty-environment) (error "Unbound variable" var) (scan (cdr (first-frame env))))) (env-loop env)) (#%provide define-variable!-) (define (define-variable!- var val env) (let ((frame (first-frame env))) (define (scan bindings) (cond ((null? bindings) (add-binding-to-frame!- var val frame)) ((eq? var (car (car bindings))) (set-car! bindings (cons (car (car bindings)) val))) (else (scan (cdr bindings))))) (scan (cdr frame)))) #| 4.12 |# (define (get-value binding) (cdr binding)) (define (set-value! val) (lambda (binding) (set-cdr! binding val))) (define (traverse-environment-with proc var env) (define (env-loop env) (define (scan bindings) (cond ((null? bindings) (env-loop (enclosing-environment env))) ((eq? var (car (car bindings))) (proc (car bindings))) (else (scan (cdr bindings))))) (if (eq? env the-empty-environment) (error "Unbound variable" var) (scan (cdr (first-frame env))))) (env-loop env)) (#%provide lookup-variable-value--) (define (lookup-variable-value-- var env) (traverse-environment-with get-value var env)) (#%provide set-variable-value!--) (define (set-variable-value!-- var val env) (traverse-environment-with (set-value! val) var env)) ;; Running the Evaluator as a Program (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?) (list '+ +) (list '- -) (list '* *) (list '/ /) (list '> >) (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 (primitive-implementation proc) args)) (define input-prompt ";;; M-Eval input:") (define output-prompt ";;; M-Eval value:") (#%provide driver-loop) (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) ')) (display object))) (#%provide the-global-environment) (define the-global-environment (setup-environment)) #| 4.14 |# ;; This evaluator's representation of procedures is different ;; from that of the underlying Scheme. Defining map as a ;; primitive won't work because the underlying map expects ;; an underlying procedure object as the second argument ;; Data as Programs #| 4.15 |# (define (run-forever) (run-forever)) #| (define (try p) |# #| (if (halts? p p) |# #| (run-forever) |# #| 'halted)) |# #| (try try) |# ;; Internal Definitions #| (define (f x) |# #| (define (even? n) |# #| (if (= n 0) |# #| true |# #| (odd? (- n 1)))) |# #| (define (odd? n) |# #| (if (= n 0) |# #| false |# #| (even? (- n 1)))) |# #| (even? 6)) |# #| 4.16 |# (#%provide lookup-variable-value---) (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 "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 (filter predicate xs) (if (null? xs) '() (if (predicate (car xs)) (cons (car xs) (filter predicate (cdr xs))) (filter predicate (cdr xs))))) (#%provide scan-out-defines) (define (scan-out-defines body) (let ((not-defs (filter (lambda (exp) (not (definition? exp))) body)) (defs (filter definition? body))) (if (null? defs) body (list (make-let (map (lambda (def) (list (definition-variable def) ''*unassigned*)) defs) (append (map (lambda (def) (list 'set! (definition-variable def) (definition-value def))) defs) not-defs)))))) #| 4.20 |# (#%provide letrec?) (define (letrec? exp) (tagged-list? exp 'letrec)) (#%provide letrec->let) (define (letrec->let exp) (make-let (map (lambda (bind) (list (binding-var bind) ''*unassigned*)) (let-bindings exp)) (append (map (lambda (bind) (list 'set! (binding-var bind) (binding-exp bind))) (let-bindings exp)) (let-body exp)))) #| 4.21 |# (#%provide factorial) (define factorial (lambda (n) ((lambda (fact) (fact fact n)) (lambda (ft k) (if (= k 1) 1 (* k (ft ft (- k 1)))))))) (#%provide qfactorial) (define qfactorial '(lambda (n) ((lambda (fact) (fact fact n)) (lambda (ft k) (if (= k 1) 1 (* k (ft ft (- k 1)))))))) (#%provide fibonacci) (define fibonacci (lambda (n) ((lambda (fib) (fib fib 1 0 n)) (lambda (ft a b k) (if (= k 0) b (ft ft (+ a b) a (- k 1))))))) (#%provide qfibonacci) (define qfibonacci '(lambda (n) ((lambda (fib) (fib fib 1 0 n)) (lambda (ft a b k) (if (= k 0) b (ft ft (+ a b) a (- k 1))))))) (#%provide even-odd) (define (even-odd 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)))))) ;; Separating Syntactic Analysis from Execution (#%provide eval-) (define (eval- exp env) ((analyze exp) env)) (#%provide analyze) (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))) ((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))))) (#%provide analyze-lambda) (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)))) #| 4.22 |# #| ((let? exp) (analyze (let->combination exp))) |# #| 4.23 |# (define (analyze-sequence-bad exps) (define (execute-sequence procs env) (cond ((null? (cdr procs)) ((car procs) env)) (else ((car procs) env) (execute-sequence (cdr procs) env)))) (let ((procs (map analyze exps))) (if (null? procs) (error "Empty sequence -- ANALYZE")) (lambda (env) (execute-sequence procs env)))) #| 4.24 |# (#%provide timed) (define (timed f) (lambda args (let ((start (runtime)) (result (apply f args)) (end (runtime))) (display (- end start)) (newline) result)))