Chapter 4, Metalinguistic Abstraction
Exercise 4.3
Some additional details
Since it was becoming difficult to verify programs because the whole evaluator is not yet built in the book, i went ahead and read till section 4.1.4.
Now, after reading that, now we can use the evaluator presented in the book whose complete code can be found here.
Note: We should not re-load the same code again while using repl. Else our evaluator code can get in conflict with the implementation language, in particular the apply procedure!
If one wants to reload, then repl should be reset/restarted. In MIT scheme, this can be done using (ge (make-top-level-environment)). I put this line at the top of the evaluator code thus need not to remember resetting, every time when I reload.
I have added a small check for exiting from the evaluator by typing exit on the evaluator prompt.
Solution
Note the use of apply-in-underlying-scheme while invoking exp-handler inside eval. We should not use apply here because we have changed the definition of apply.
But why we used apply in the application? part in eval? Because at that point we are here invoking the procedure defined in our defined language!
Finally consider the use of data-driven style which was the main point of the exercise. The advantage here we can see is when we add a new expression-type we need not to go to the main code i.e. a separate developer using our evaluator can add a new expression type easily without touching our evaluator.
Also, it would have been better if application? part can also become part of this data-driven style using the strategey used in previous exercise.
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(define *op-table* (make-hash-table))
(define (put op type proc)
(hash-table/put! *op-table* (list op type) proc))
(define (get op type)
(hash-table/get *op-table* (list op type) #f))
(define (eval exp env)
(cond ((self-evaluating? exp) exp)
((variable? exp) (lookup-variable-value exp env))
(else (let ((exp-handler (get 'exp (car exp))))
(cond
((not (eq? #f exp-handler)) (apply-in-underlying-scheme exp-handler (list exp env)))
((application? exp)
(apply (eval (operator exp) env)
(list-of-values (operands exp) env)))
(else
(error "Unknown expression type -- EVAL" exp)))))))
;; note that below statements should be added at the bottom of the evaluator else when these statements are
;; executed the repl will look for the procedures not yet defined.
(put 'exp 'quote (lambda(exp env) (text-of-quotation exp)))
(put 'exp 'set! eval-assignment)
(put 'exp 'define eval-definition)
(put 'exp 'if eval-if)
(put 'exp 'lambda
(lambda(exp env)
(make-procedure (lambda-parameters exp) (lambda-body exp) env)))
(put 'exp 'begin (lambda(exp env) (eval-sequence (begin-actions exp) env)))
(put 'exp 'cond (lambda(exp env) (eval (cond->if exp) env)))
I tested this on the example given in section 4.1.4:
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;;; M-Eval input:
(define (append x y)
(if (null? x)
y
(cons (car x)
(append (cdr x) y))))
;;; M-Eval value:
ok
;;; M-Eval input:
(append '(a b c) '(d e f))
;;; M-Eval value:
(a b c d e f)
;;; M-Eval input:
(append '(1 2 3 q w) '(e r t y))
;;; M-Eval value:
(1 2 3 q w e r t y)
;;; M-Eval input:
exit
;Value: exiting..
1 ]=>
Complete working code
The code can be downloaded from mit. Still I am presenting the complete code here with the changes corresponding to this exercise as well as to reset the repl:
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;;;;METACIRCULAR EVALUATOR FROM CHAPTER 4 (SECTIONS 4.1.1-4.1.4) of
;;;; STRUCTURE AND INTERPRETATION OF COMPUTER PROGRAMS
;;;;Matches code in ch4.scm
;;;;This file can be loaded into Scheme as a whole.
;;;;Then you can initialize and start the evaluator by evaluating
;;;; the two commented-out lines at the end of the file (setting up the
;;;; global environment and starting the driver loop).
;;;; resetting the environment so that we can reload the file
(ge (make-top-level-environment))
;;;;This warning here now not applicable in our case because of the statement above.
;;;;**WARNING: Don't load this file twice (or you'll lose the primitives
;;;; interface, due to renamings of apply).
;;;from section 4.1.4 -- must precede def of metacircular apply
(define apply-in-underlying-scheme apply)
;;;SECTION 4.1.1
(define *op-table* (make-hash-table))
(define (put op type proc)
(hash-table/put! *op-table* (list op type) proc))
(define (get op type)
(hash-table/get *op-table* (list op type) #f))
(define (eval exp env)
(cond ((self-evaluating? exp) exp)
((variable? exp) (lookup-variable-value exp env))
(else (let ((exp-handler (get 'exp (car exp))))
(cond
((not (eq? #f exp-handler)) (apply-in-underlying-scheme exp-handler (list exp env)))
((application? exp)
(apply (eval (operator exp) env)
(list-of-values (operands exp) env)))
(else
(error "Unknown expression type -- EVAL" exp)))))))
;; (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))
;; ((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)
;;;SECTION 4.1.2
(define (self-evaluating? exp)
(cond ((number? exp) true)
((string? exp) true)
(else false)))
(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 (variable? exp) (symbol? exp))
(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 (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))
(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 ; no else clause
(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))))))
;;;SECTION 4.1.3
(define (true? x)
(not (eq? x false)))
(define (false? x)
(eq? x false))
(define (make-procedure parameters body env)
(list 'procedure parameters body env))
(define (compound-procedure? p)
(tagged-list? p 'procedure))
(define (procedure-parameters p) (cadr p))
(define (procedure-body p) (caddr p))
(define (procedure-environment p) (cadddr p))
(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))
(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))))
;;;SECTION 4.1.4
(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))
;[do later] (define the-global-environment (setup-environment))
(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?)
;; more primitives
))
(define (primitive-procedure-names)
(map car
primitive-procedures))
(define (primitive-procedure-objects)
(map (lambda (proc) (list 'primitive (cadr proc)))
primitive-procedures))
;[moved to start of file] (define apply-in-underlying-scheme apply)
(define (apply-primitive-procedure proc args)
(apply-in-underlying-scheme
(primitive-implementation proc) args))
(define input-prompt ";;; M-Eval input:")
(define output-prompt ";;; M-Eval value:")
(define exit-symbol 'exit)
(define (driver-loop)
(prompt-for-input input-prompt)
(let ((input (read)))
(if (eq? input exit-symbol)
'exiting..
(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-env>))
(display object)))
(put 'exp 'quote (lambda(exp env) (text-of-quotation exp)))
(put 'exp 'set! eval-assignment)
(put 'exp 'define eval-definition)
(put 'exp 'if eval-if)
(put 'exp 'lambda
(lambda(exp env)
(make-procedure (lambda-parameters exp) (lambda-body exp) env)))
(put 'exp 'begin (lambda(exp env) (eval-sequence (begin-actions exp) env)))
(put 'exp 'cond (lambda(exp env) (eval (cond->if exp) env)))
;;;Following are commented out so as not to be evaluated when
;;; the file is loaded.
(define the-global-environment (setup-environment))
(driver-loop)
'METACIRCULAR-EVALUATOR-LOADED