# Fall Semester, The Metacircular Evaluator. Today we shift perspective from that of a user of computer langugaes to that of a designer of

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1 1 MASSACHVSETTS INSTITVTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science Structure and Interpretation of Computer Programs Fall Semester, 1996 Lecture Notes { October 31, 1996 The Metacircular Evaluator Today we shift perspective from that of a user of computer langugaes to that of a designer of computer languages. EVAL is an example of a UNIVERSAL machine. That is, it can simulate any other machine. Remember the rules of the environment model: 1. To EVALUATE a combination (a compound expression other than a special form), evaluate the subexpressions and then APPLY the value of the operator subexpression to the values of the operand subexpressions. 2. To APPLY a compound procedure to a set of arguments, EVALUATE the body of the procedure in a new environment. To construct this environment, extend the environment part of the procedure object by a frame in which the formal parameters of the procedure are bound to the arguments to which the procedure is applied. Draw the EVAL/APPLY cycle here: Assume we have some way of representing environments together with the following operations: (lookup-variable-value symbol env) {returns the value bound to the symbol in the environment. (extend-environment vars vals base-env) { returns a new environment, which extends base-env by a frame in which the vars are bound to the corresponding vals.

2 6.001, Fall Semester, 1996 Lecture Notes { October 31, We can sketch the basic idea behind representing environments and frames here: Sketch of overall Scheme system, and how EVAL ts in: When you type the expression: (* x (+ 2 y)), EVAL sees that as (eval '(* x (+ 2 y)) the-global-env). In general, your programs are EVAL's data. Here is the basic form for EVAL { note the primities, the special forms, and the reduction to apply.

3 6.001, Fall Semester, 1996 Lecture Notes { October 31, (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 exp -- EVAL" exp)))) Examples: quoted? lambda? if? Evaluation of if expressions: (define (eval-if exp env) (if (true? (eval (if-predicate exp) env)) (eval (if-consequent exp) env) (eval (if-alternative exp) env))) Begin expressions indicate sequences to be evaluated in order: (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))))

4 6.001, Fall Semester, 1996 Lecture Notes { October 31, Cond is implemented as a derived expression (cond ((> x 0) x) ((= x 0) 0) (else (- x))) can be converted into Key clause in EVAL that handles procedure applications: ((application? exp) (apply (eval (operator exp) env) (list-of-values (operands exp) env))) APPLY: the other half of the cycle. (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 -- APPLY" procedure))))

5 6.001, Fall Semester, 1996 Lecture Notes { October 31, Trace through the evaluation of ((lambda (x y) (* x y)) 5 7) Finally, here is stripped down version of the evaluator:

6 6.001, Fall Semester, 1996 Lecture Notes { October 31, (define mc-eval (lambda (exp env) (cond ((number? exp) exp) ;base-case ((string? exp) exp) ;base-case ((symbol? exp) (lookup exp env)) ;base case ((eq? (car exp) 'quote) (car (cdr exp)));special forms ((eq? (car exp) 'cond) (evcond (cdr exp) env)) ((eq? (car exp) 'sequence) (evseq (cdr exp) env)) ((eq? (car exp) 'lambda) (list 'proc (cdr exp) env)) ((eq? (car exp) 'define) (evdefine (cdr exp) env)) (else (mc-apply (mc-eval (car exp) env) (evlist (cdr exp) env)))))) (define mc-apply (lambda (fun args) (cond ((atom? fun) (apply fun args)) ;ground out ((eq? (car fun) 'proc) (mc-eval (car (cdr (car (cdr fun)))) ;procedure body (bind (car (car (cdr fun))) ;formal params args ;supplied args (car (cdr (cdr fun))))));saved env (else (error '"Unknown function"))))) (define evlist (lambda (lst env) ;map evaluator over list (cond ((null? lst) nil) (else (cons (mc-eval (car lst) env) (evlist (cdr lst) env)))))) (define evcond (lambda (clauses env) (cond ((null? clauses) nil) ((eq? 'else (car (car clauses))) (evseq (cdr (car clauses)) env)) ((mc-eval (car (car clauses)) env) (evseq (cdr (car clauses)) env)) (else (evcond (cdr clauses) env))))) (define evseq (lambda (clauses env) (cond ((null? (cdr clauses)) (mc-eval (car clauses) env)) (else (mc-eval (car clauses) env) (evseq (cdr clauses) env))))) (define evdefine (lambda (body env) ;mutate the first frame (sequence (set-cdr! (car env) (cons (cons (car body) (mc-eval (car (cdr body)) env)) (cdr (car env)))) (car body))))

7 6.001, Fall Semester, 1996 Lecture Notes { October 31, (define bind (lambda (params values env) ;add a new frame (cons (cons 'frame (make-frame-body params values)) env))) (define make-frame-body (lambda (params values) ;frame body is an association list (cond ((null? params) (cond ((null? values) nil) (else (error '"Too many values supplied")))) ((null? values) (error '"Too few values supplied")) (else (cons (cons (car params) (car values)) (make-frame-body (cdr params) (cdr values))))))) (define lookup (lambda (var env) (cond ((null? env) (error '"Unbound variable" var)) ;not in any frames (else ((lambda (binding) (cond ((null? binding) ;check each frame (lookup var (cdr env))) ;in turn (else (cdr binding)))) ;(<varname>. <value>) (find-binding var (cdr (car env)))))))) (define find-binding (lambda (var frame-body) ;this is just assq (cond ((null? frame-body) nil) ((eq? var (car (car frame-body))) (car frame-body)) (else (find-binding var (cdr frame-body)))))) (define global-env (list (list 'frame (cons 'nil '()) (cons '+ +) (cons '- -) (cons '= =) (cons '* *) (cons 'car car) (cons 'cdr cdr) (cons 'cons cons) (cons 'list list) (cons 'set-car! set-car!) (cons 'set-cdr! set-cdr!) (cons 'null? null?) (cons 'eq? eq?) (cons 'atom? atom?) (cons 'number? number?) (cons 'string? string?) (cons 'symbol? symbol?) (cons 'error error) (cons 'apply apply))))

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