המחשב למדעי מורחב מבוא13תרגול

Lazy Evaluation

Lazy Evaluation Implementation

• Two types of values– Delayed Values – Actual Values

• Introduce two functions– (actual-value exp env) returns real value

– (delay-it exp env) returns a “thunk”

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

delayed objects • (l-eval exp env) may return delayed value• We use actual-value only if we have to,

otherwise we use l-eval• Primitives must receive the actual value• Print-on-screen is actual value

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Lazy Evaluation – l-eval(define (l-eval exp env) (cond ((self-evaluating? exp) exp) ... ((application? exp (l-apply (actual-value (operator exp) env)

(operands exp) env))

(else (error "Unknown expression" exp))))

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

Lazy Evaluation – l-apply(define (l-apply procedure arguments env) ; changed (cond ((primitive-procedure? procedure) (apply-primitive-procedure

procedure (list-of-arg-values arguments env)))

((compound-procedure? procedure) (l-eval-sequence (procedure-body procedure)

(extend-environment (procedure-parameters procedure) (list-of-delayed-args arguments env)

(procedure-environment procedure)))) (else (error "Unknown proc" procedure))))

Actual vs. Delayed Values(define (actual-value exp env) (force-it (l-eval exp env)))

(define (list-of-delayed-args exps env) (if (no-operands? exps) '() (cons (delay-it (first-operand exps) env) (list-of-delayed-args (rest-operands exps) env))))

(define (list-of-arg-values exps env) (if (no-operands? exps) '() (cons (actual-value (first-operand exps) env) (list-of-arg-values (rest-operands exps) env))))

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Representing Thunks

• In our implementation we represent “Thunks” using a tagged list:

thunk envexp

Thunks – abstractionConstructor:(define (delay-it exp env) (list 'thunk exp env))

Selectors:(define (thunk? obj) (tagged-list? obj 'thunk))(define (thunk-exp thunk) (cadr thunk))(define (thunk-env thunk) (caddr thunk))

(define (force-it obj) (cond ((thunk? obj) (actual-value (thunk-exp obj) (thunk-env obj))) (else obj)))

Lazy Evaluation – other changes needed

• Example – need actual predicate value in conditional if...(define (l-eval-if exp env) (if (true? (actual-value (if-predicate exp) env)) (l-eval (if-consequent exp) env) (l-eval (if-alternative exp) env)))

• Example – don't need actual value in assignment...

(define (l-eval-assignment exp env) (set-variable-value! (assignment-variable exp) (l-eval (assignment-value exp) env) env) 'ok)

Might return delayed values

No change relative to mc-eval version!

Lazy Evaluation – more changes(define input-prompt ";;; L-Eval input:")(define output-prompt ";;; L-Eval value:")

(define (driver-loop) (prompt-for-input input-prompt) (let ((input (read))) (let ((output (actual-value input the-global-environment))) (cond ((eq? output exit-object) 'done) (else (announce-output output-prompt) (user-print output) (driver-loop))))))

Lazy Evaluation - Example

• What happens when this code is executed using mc-eval?

• Can we add “unless” to the metacircular evaluator?

(define (unless condition usual exceptional) (if condition exceptional usual))

(define (factorial n) (unless (= n 1) (* n (factorial (- n 1))) 1))

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Memoizing Thunks• Only evaluate

Thunks once

• Mutate our data structure when the thunk is first evaluated

thunk envexp

evaluated-thunk

result

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Thunks – Memoizing Implementation (define (evaluated-thunk? obj) (tagged-list? obj 'evaluated-thunk))(define (thunk-value evaluated-thunk) (cadr evaluated-thunk))

(define (force-it obj) (cond ((thunk? obj) (let ((result (actual-value (thunk-exp obj) (thunk-env obj)))) (set-car! obj 'evaluated-thunk) (set-car! (cdr obj) result) (set-cdr! (cdr obj) '()) result)) ((evaluated-thunk? obj) (thunk-value obj)) (else obj)))

Timing Comparison

• How would the different implementations (mc-eval, lazy, lazy + memoization) compute the following:

(define (square x) (* x x))(square (fib 100))

Example

• What is the result of (func 1)?• Is it similar to evaluation with mc-eval?

(define (func x) (define (p e) e x) (p (set! x (cons x '(2)))))

lazy and lazy-memo

• We want to extend the original mc-eval:

(lambda (a (b lazy) c (d lazy-memo)) ...)

– "a", "c" are strict variables (evaluated before procedure application

– "b" is lazy; it gets (re)-evaluated each time its value is actually needed

– "d" is lazy-memo; it gets evaluated the first time its value is needed, and then that value is returned again any other time it is needed again.

Controllably Memo-izing Thunks• thunk – never gets memoized• thunk-memo – first eval is remembered• evaluated-thunk – memoized-thunk that has

already been evaluated

whenforced

ThunkMemo

envexp

evaluated-thunk

result

A new version of delay-it

• Look at the variable declaration to do the right thing...

(define (delay-it decl exp env) (cond ((not (declaration? decl)) (l-eval exp env)) ((lazy? decl)

(list 'thunk exp env)) ((memo? decl)

(list 'thunk-memo exp env)) (else (error "unknown declaration:" decl))))

Changes to force-it(define (force-it obj) (cond ((thunk? obj) ;eval, but don't remember it (actual-value (thunk-exp obj) (thunk-env obj))) ((memoized-thunk? obj) ;eval and remember (let ((result (actual-value (thunk-exp obj) (thunk-env obj)))) (set-car! obj 'evaluated-thunk) (set-car! (cdr obj) result) (set-cdr! (cdr obj) '()) result)) ((evaluated-thunk? obj) (thunk-value obj)) (else obj)))

Changes to l-apply• Key: in l-apply, only delay "lazy" or "lazy-memo" params

– make thunks for "lazy" parameters– make memoized-thunks for "lazy-memo" parameters

(define (l-apply procedure arguments env) (cond ((primitive-procedure? procedure) ...) ; as before; apply on list-of-arg-values ((compound-procedure? procedure) (l-eval-sequence (procedure-body procedure)

(let ((params (procedure-parameters procedure))) (extend-environment

(map parameter-name params) (list-of-delayed-args params arguments env) (procedure-environment procedure)))))

(else (error "Unknown proc" procedure))))

Deciding when to evaluate an argument...

• Process each variable declaration together with application subexpressions – delay as necessary:

(define (list-of-delayed-args var-decls exps env) (if (no-operands? exps) '() (cons (delay-it (first-variable var-decls) (first-operand exps) env) (list-of-delayed-args (rest-variables var-decls)

(rest-operands exps) env))))

Syntax Extensions – Parameter Declarations

(define (first-variable var-decls) (car var-decls))(define (rest-variables var-decls) (cdr var-decls))(define declaration? pair?)

(define (parameter-name var-decl) (if (pair? var-decl) (car var-decl) var-decl))

(define (lazy? var-decl) (and (pair? var-decl) (eq? 'lazy (cadr var-decl))))

(define (memo? var-decl) (and (pair? var-decl) (eq? 'lazy-memo (cadr var-decl))))

Exam Question

• Assume we have the following special form:– (static <variable> <value>)

• Evaluation– If <variable> exists in the global environment,

do nothing– Otherwise evaluate <value> in the current

environment and bind <variable> to the result of the evaluation in the global environment

> (define (f) (static x 1) x)> (define (g x) (static x (* 2 2)) x)> (g 7)

> (f)

> (set! x (+ x 1))> (f)

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How would the code evaluate?(define (id x) (static counter 0) (set! counter (+ counter 1)) x) (define (foobar counter) (id (begin (static counter 5) (id counter)))) (foobar 10) counter

GEid:

p:xb:…

foobar:

p:counterb:…

E1counter:10

E2x:10

counter:5/6

E3x:10

/7

mc-eval, static binding

counter7

(foobar 10)10

GEid:

p:xb:…

foobar:

p:counterb:…

E1counter:10

E2x:

/1

E3x:10

l-eval, static binding

thunk

(begin…)

counter:0

In (driver-loop):(let ((output (actual-value input the-global-environment)))

/2

counter2

(foobar 10)10

GEid:

p:xb:…

foobar:

p:counterb:…

E1counter:10

E2x:10

counter:5

XX 11

E3x:10

XX 12

mc-eval, dynamic binding

counter5

(foobar 10)10

GEid:

p:xb:…

foobar:

p:counterb:…

E1counter:10

E2x:

counter:0

XX 11

E3x:11

XX 12

l-eval, dynamic binding

counter0

(foobar 10)11

thunk

(begin…)

In (driver-loop):(let ((output (actual-value input the-global-environment)))