מבוא מורחב למדעי המחשב בשפת Scheme

מבוא מורחב למדעי המחשב Scheme בשפת

13תרגול

Metacircular Evaluator

4.1, pages 362-398

definitions file on web

2

Overview

1. Eval, apply

2. Change definition

3. Add let, let*

4. Add special forms and, or

5. Abstraction of frame scanning

3

4

Evaluator: a program that

determines meaning of expressions

in a programming language.

Metacircular: written in the same language that it evaluates

Read-Eval-Print Loop

(define (driver-loop)1. PRINT PROMPT (prompt-for-input input-prompt)2. READ INPUT EXPRESSION (let ((input (read))) 3. EVALUATE EXPRESSION (let ((output (mc-eval input the-global-environment)))

…4. PRINT RESULT (user-print output)5. LOOP (driver-loop))))))

5

Eval-Apply

Mutual recursion between eval and apply

To evaluate a compound expression means to evaluate the sub-expressions recursively, then apply the operator to the arguments.

To apply a function to arguments means to evaluate the body of the function in a new environment.

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Eval

Evaluate expression in given environment

(define (mc-eval exp env) (cond ((self-evaluating? exp) exp)… ((application? exp) (mc-apply (mc-eval (operator exp) env) (list-of-values (operands exp) env)))

The name mc-eval is used to differ from the primitive eval

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Apply

Apply procedure to list of arguments

(define (mc-apply procedure arguments)…(eval-sequence (procedure-body procedure) (extend-environment (procedure-parameters procedure) arguments (procedure-environment procedure))))

The name mc-apply is used to differ from the primitive apply

8

Change definition

from (define x 7)

to (x := 7)

and

from (define (square x) (* x x))

to ((square x) := (* x x))

9

Change eval case

from:(define (definition? exp) (tagged-list? exp 'define))

(define (tagged-list? exp tag) (if (pair? exp) (eq? (car exp) tag) false))to:(define (definition? exp) (and (pair? exp) (pair? (cdr exp)) (eq? (cadr exp) ':=)))

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Change selectors

(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))))

(car(car

(car

(caar

(cdar

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Adding let, let*

Rearranging as another expression

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let

(let ((<var1> <exp1>) … (<varn> <expn>)) <body>)

is equivalent to

((lambda (<var1> … <varn>) <body>) <exp1> … <expn>)

add a syntactic transformationlet->combination

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let - case in eval

((let? exp)

(mc-eval (let->combination exp) env))

(define (let? exp)

(tagged-list? exp ‘let))

let - predicate

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let - constructors

(define (make-combination

function expressions)

(cons function expressions))

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let - selectors

(define (let-bindings exp) (cadr exp))

(define (let-body exp) (cddr exp))

(define (let-variables exp) (map car (let-bindings exp)))

(define (let-expressions exp) (map cadr (let-bindings exp)))

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let - evaluation

(define (let->combination exp)

(make-combination

(make-lambda

(let-variables exp)

(let-body exp))

(let-expressions exp)))

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let*

The bindings of are performed sequentially.

Each binding is made in an environment inwhich all of the preceding bindings arevisible.

(let* ((x 3) (y (+ x 2)) (z (+ x y 5))) (* x z))> 39

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let*

(let* ((<var1> <exp1>)…(<varn> <expn>))

<body>)

is equivalent to

(let ((<var1> <exp1>)) (let* ((<var2> <exp2>)… (<varn> <expn>)) <body>))

add a syntactic transformationlet*->nested-let

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let* - example(let* ((<var1> <exp1>) (<var2> <exp2>)) <body>)=(let ((<var1> <exp1>)) (let* (<var2> <exp2>)) <body>))=(let ((<var1> <exp1>)) (let ((<var2> <exp2>)) (let* () <body>)))=(let ((<var1> <exp1>)) (let ((<var2> <exp2>)) (let () <body>)))

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let* - case in eval

((let*? exp)

(mc-eval (let*->nested-let exp) env))

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let* - constructors

(define (make-let bindings body)

(cons ‘let (cons bindings body)))

(define (make-let* bindings body)

(cons ‘let* (cons bindings body)))

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let* - predicates

(define (let*? exp)

(tagged-list exp ‘let*))

(define (no-bindings? bindings)

(null? bindings))

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let* - selectors

(define (let*-bindings exp) (cadr exp))

(define (let*-body exp) (cddr exp))

(define (let*-first-binding bindings)

(car bindings))

(define (let*-rest-bindings bindings)

(cdr bindings))

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let* - evaluation

(define (let*->nested-let exp)

(if (no-bindings? (let*-bindings exp))

(make-let

(let*-bindings exp)

(let*-body exp))

(make-let

(list (let*-first-binding

(let*-bindings exp)) ; ((v1 e1))

(make-let*

(let*-rest-bindings (let*-bindings exp))

(let*-body exp))))

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Special forms: and, or

Direct evaluation

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and, or - cases in eval

(define (mc-eval exp env) (cond ((self-evaluating? exp) exp)…((and? exp) (eval-and (and-exps exp) env))((or? exp) (eval-or (or-exps exp) env))

((application? exp) (mc-apply (mc-eval (operator exp) env) (list-of-values (operands exp) env)))

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and, or - predicates

(define (and? exp) (tagged-list? exp ‘and))

(define (or? exp) (tagged-list? exp ‘or))

(define (no-exps? exps) (null? exps))

(define (last-exp? exps) (null? (cdr exps)))

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and, or - selectors

(define (and-exps exp) (cdr exp))

(define (or-exps exp) (cdr exp))

(define (first-exp exps) (car exps))

(define (rest-exps exps) (cdr exps))

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and - evaluation

from left to right

Evaluation Return value

Any expression evaluates to false

false

All expressions evaluate to true

value of last expression

No expressions true

and - evaluation

(define (eval-and exps env) (if (no-exps? exps) true (let ((first (mc-eval (first-exp exps) env)))

(if (false? first) false (if (last-exp? exps) first (eval-and (rest-exps exps) env)))))

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or - evaluation

from left to right

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Evaluation Return value

Any expression evaluates to true

value of last expression

All expressions evaluate to false

false

No expressions false

or - evaluation

(define (eval-or exps env) (if (no-exps? exps) false (let ((first (mc-eval (first-exp exps) env)))

(if (true? first) first ;(if (last-exp? exps) false (eval-or (rest-exps exps) env)))))

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Abstraction of frame scanning

Exercise 4.12

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Frames

A frame is a set of bindings, represented as a pair of two lists: variables and values

Constructor(make-frame variables values)Selectors(frame-variables frame)(frame-values frame)Mutator(add-binding-to-frame! var val frame)

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EnvironmentsAn environment consists of its first frame and an enclosing

environment

Constructor(extend-environment vars vals base-env)Selectors (first-frame env)(enclosing-environment env)Predefined environmentsthe-global-environmentthe-empty-environment

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Frame Scanning

Performed by:• lookup-variable-value

invoked when evaluating names• set-variable-value!

invoked when evaluating set! expressions• define-value!

invoked when evaluating definitions

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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)) (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))

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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 -- SET!" var) (let ((frame (first-frame env))) (scan (frame-variables frame) (frame-values frame))))) (env-loop env))

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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))))

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All procedures are alike!

• Scan the frame for the variable’s name– If found, success operation

(return value / set value)– If not in frame, failure operation

(continue to next frame / add binding)

• Error on empty environment (if this can happen)

• We can get better abstraction– Capturing common patterns– Hiding frame scanning / mutation

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Generic frame scan

(define (scan-first-frame var env succeed fail)

(define (scan vars vals)

(cond ((null? vars)

(fail))

((eq? var (car vars))

(succeed 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)))))

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lookup-variable-value

(define (lookup-variable-value var env)

(define (succeed vals)

(get-binding-value vals))

(define (fail)

(scan-first-frame

var (enclosing-environment env) succeed fail))

(scan-first-frame var env succeed fail))

(define (get-binding-value vals)

(car vals))

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set-variable-value!

(define (set-variable-value! var val env)


(set-binding-value! vals val))

(define (fail)

(scan-first-frame

var (enclosing-environment env) succeed fail))

(scan-first-frame var env succeed fail))

(define (set-binding-value! vals val)

(set-car! vals val))

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define-variable!

(define (define-variable! var val env)


(set-binding-value! vals val))

(define (fail)

(add-binding-to-frame! var val (first-frame env))) (scan-first-frame var env succeed fail))

מבוא מורחב למדעי המחשב בשפת Scheme

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