מבוא מורחב למדעי המחשב בשפת Scheme תרגול 21

Overview 1. Dynamic Binding 2. Lazy Evaluation 3. More MC-Eval 2

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.

5 Static binding GE factorial: p: n b: (if (= n 1) 1…) n:5n:4n:3n:2n:1

6 GE factorial: p: n b: (if (= n 1) 1…) n:5n:4n:3 n:2n:1 Dynamic binding

7 Example: if>=< Format: (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<

8 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))

9 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)))))

10 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

11 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)))))

12 Example In mc-eval (define count 0) (define (id x) (set! count (+ count 1)) x) (define w (id (id 10))) count  w  count 

13 In l-eval (define count 0) (define (id x) (set! count (+ count 1)) x) (define w (id (id 10))) count  w  count  Example (cont.)

14 delay and memoization (define (square x) (* x x)) (define count 0) (define (id x) (set! count (+ count 1)) x) (square (id 10))  ? count  ?

15 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

16 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)) )

17 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)

18 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)

19 (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.)

20 (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.)

21 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)

22 (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

23 (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.)

24 (f 5) GE x:2 f: env1 make-env mystery: E1 x:3 E2 y:5 E3 g: aux: E4 x:1 y:4 E5 y:5 Solution (cont.)

25 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

26 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

27 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

28 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))

29 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!)

30 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))

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

32 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)

33 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)