מבוא מורחב למדעי המחשב תרגול 13 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”

3 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

4 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))))

7 Representing Thunks In our implementation we represent “Thunks” using a tagged list: thunk envexp

Thunks – abstraction Constructor : (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))

12 Memoizing Thunks Only evaluate Thunks once Mutate our data structure when the thunk is first evaluated thunk envexp evaluated- thunk result

13 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 when forced Thunk Memo 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 ) Evaluation – If exists in the global environment, do nothing – Otherwise evaluate in the current environment and bind 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) 7 4 5

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

GE id: p:x b:… foobar: p:counter b:… E1 counter:10 E2 x:10 counter:5/6 E3 x:10 /7 mc-eval, static binding counter 7 (foobar 10) 10

GE id: p:x b:… foobar: p:counter b:… E1 counter:10 E2 x: /1 E3 x:10 l-eval, static binding thunk (begin…) counter:0 In (driver-loop) : (let ((output (actual-value input the-global-environment))) /2 counter 2 (foobar 10) 10

GE id: p:x b:… foobar: p:counter b:… E1 counter:10 E2 x:10 counter:5 XX 11 E3 x:10 XX 12 mc-eval, dynamic binding counter 5 (foobar 10) 10

GE id: p:x b:… foobar: p:counter b:… E1 counter:10 E2 x: counter:0 XX 11 E3 x:11 XX 12 l-eval, dynamic binding counter 0 (foobar 10) 11 thunk (begin…) In (driver-loop) : (let ((output (actual-value input the-global-environment)))