מבוא מורחב למדעי המחשב Scheme בשפת

21תרגול

Overview

1. Dynamic Binding

2. Lazy Evaluation

3. More MC-Eval

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3

Dynamic vs. Static Binding

(define (factorial n)(if (= n 1) 1

(* n (factorial (- n 1)))))

• Draw environments in static and dynamic binding for (factorial 5)

• What is the maximal number of environments that the ‘*’ operator is looked for (in one search)?

(Appeared on a final exam)

4

Variations on a Scheme: dynamic MCE

Lexical (static) binding

Free variables are searched in the surrounding lexical environment

Dynamic binding

Free variables are searched in calling procedures.

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Static binding

GE

factorial:

p: n

b: (if (= n 1) 1…)

n:5 n:4 n:3 n:2 n:1

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GE

factorial:

p: n

b: (if (= n 1) 1…)

n:5

n:4

n:3 n:2 n:1

Dynamic binding

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Example: if>=<

Format: (if>=< exp1 exp2 if> if= if<)

exp1 and exp2 evaluate to numerical values

if exp1>exp2 evaluate and return if>

if exp1=exp2 evaluate and return if=

otherwise, evaluate and return if<

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Predicate and Selectors

(define (if>=<? exp)

(tagged-list? exp ‘if>=<))

(define (if>=<exp1 exp) (cadr exp))

(define (if>=<exp2 exp) (caddr exp))

(define (if> exp) (cadddr exp))

(define (if= exp) (list-ref exp 4))

(define (if< exp) (list-ref exp 5))

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mc-eval implementation

(define (eval-if>=< exp env)

(let ((exp1 (mc-eval (if>=<exp1 exp) env))

(exp2 (mc-eval (if>=<exp2 exp) env))

(cond ((> exp1 exp2)

(mc-eval (if> exp) env))

((= exp1 exp2)

(mc-eval (if= exp) env))

(else (mc-eval (if< exp) env)))))

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Lazy Evaluation

• Normal order - delay operands (only)• Special forms and compound procedures may

return delayed objects • Primitives must receive the actual value• Print-on-screen is actual value• (l-eval exp env) may return delayed value• (actual-value exp env) returns real value• We use actual-value only if we have to,

otherwise we use l-eval

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delayed if>=<

(define (eval-if>=< exp env)

(let ((exp1 (actual-value (if>=<exp1 exp) env))

(exp2 (actual-value (if>=<exp2 exp) env))

(cond ((> exp1 exp2)

(l-eval (if> exp) env))

((= exp1 exp2)

(l-eval (if= exp) env))

(else (l-eval (if< exp) env)))))

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Example

In mc-eval(define count 0)

(define (id x) (set! count (+ count 1)) x)

(define w (id (id 10)))

count w count

2

10

2

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In l-eval(define count 0)

(define (id x) (set! count (+ count 1)) x)

(define w (id (id 10)))

count w count

1

10

2

Example (cont.)

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delay and memoization

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

(define count 0)

(define (id x) (set! count (+ count 1)) x)

(square (id 10)) ?

count ?

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Practice Question

• When a procedure with no parameters is applied, an empty frame is opened

• Change the MCE code such that parameter-less procedures will be applied in the parent environment

• Is the modified evaluator equivalent to the original one? Explain or give a contradicting example

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Modification to apply

(define (mc-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 ….))))

(if (null? (procedure-parameters procedure)) (eval-sequence (procedure-body procedure) (procedure-environment procedure)) )

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Practice Question

Suppose we can manipulate environments as if they were data types, using the following imaginary special forms:

(this-env)

(get-env proc)

(set-env! proc env)

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Example

(define x 2)

(define (f y) (+ x y))

(define (make-env x) (this-env))

GE

x:2

f: make-env

p: y

b: (+ x y)

p: x

b: (this-env)

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(define env1 (make-env 3))

GE

x:2

f: env1 make-env

p: y

b: (+ x y)

p: x

b: (this-env)

E1

x:3

Example (cont.)

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(set-env! f env1)

GE

x:2

f: env1 make-env

p: y

b: (+ x y)

p: x

b: (this-env)

E1

x:3

Example (cont.)

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Section A

What will evaluating the following code return?

Apply changes to the env. diagram.

(f 5)

(define (mystery g)

(define (aux x y)

(set-env! g (this-env)))

(aux 1 4))

(mystery f)

(f 5)

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(f 5)

GE

x:2

f: env1 make-env

p: y

b: (+ x y)

p: x

b: (this-env)

E1

x:3

E2

y:5

Solution

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(mystery f)

GE

x:2

f: env1 make-env mystery:

E1

x:3

E2

y:5

E3

g:

aux:E4

x:1

y:4

Solution (cont.)

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(f 5)

GE

x:2

f: env1 make-env mystery:

E1

x:3

E2

y:5

E3

g:

aux:E4

x:1

y:4E5

y:5

Solution (cont.)

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Section B

Complete(call-from-env proc vars env)

which applies proc on vars from environment env, instead of proc’s original environment

When returning, proc’s environment is restored to its original environment

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Code

(define (call-from-env proc vars env (let ((original-env ))

? (let ((result )) ?

?)))

(get-env proc) (set-env! proc env)

(apply proc vars)

(set-env! proc original-env)

result

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Section C,D,E

• Add support for this-env, get-env and set-env! in the mc-eval

• The representation of an environment is the interior data structure inside the evaluator

• Relaxation: In set-env! you may assume that the proc operand is evaluated to a compound (not primitive) procedure

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mc-eval additions

Add in mc-eval:((this-env? exp) (eval-this-env exp env))

((get-env? exp) (eval-get-env exp env))

((set-env? exp) (eval-set-env exp env))

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Predicates

(define (this-env? exp) )(define (get-env? exp) ) (define (set-env? exp) )

(tagged-list? exp ‘this-env) (tagged-list? exp ‘get-env) (tagged-list? exp ‘set-env!)

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Selectors

(this-env)no selectors

(get-env proc)(define (get-env-proc exp) (cadr exp))

(set-env! proc env)(define (set-env-proc exp) (cadr exp))(define (set-env-env exp) (caddr exp))

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eval-this-env

eval-this-env is simply:(define (eval-this-env exp env) env)

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eval-get-env

(define (eval-get-env exp env)

(let ((proc _______________________________))

(if (primitive-procedure? proc)

_______________________________

_______________________________ )))

(mc-eval (get-env-proc exp) env)

the-global-environment

(procedure-environment proc)

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eval-set-env

(define (eval-set-env exp env)

(let ((proc

________________________________ )

(new-env

________________________________ ))

__________________________________ ))

Reminder: a compound procedure is represented by:(list ‘procedure parameters body env)

(mc-eval (set-env-proc exp) env)

(mc-eval (set-env-env exp) env)

(set-car! (cdddr proc) new-env)