This exam is worth 70 points, or about 23% of your total course grade. The exam contains 15 questions.

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2 Question 1 (4 points): What will the Scheme interpreter print in response to each of the following expressions? Also, draw a box and pointer diagram for the result of each printed expression. If any expression results in an error, just write ERROR ; you don t have to give the precise message. Hint: It ll be a lot easier if you draw the box and pointer diagram first! (let ((foo (list a b c)) (bar (list x y z))) (set-car! (cdr foo) (cadr bar)) (set-car! (cddr foo) (cdr bar)) foo) (let ((foo (list a b c)) (bar (list x y z))) (set-cdr! (cddr bar) (cdr foo)) (set-cdr! (cdr bar) (car foo)) bar) 2

3 Your name login cs61a Question 2 (3 points): (define (foo x y) (+ x (* y x))) (foo (* 2 2) (+ 8 4)) How many times are + and * called from the invocation of foo above... in applicative order? + invocations * invocations in normal order without memoization? + invocations * invocations in normal order with memoization? + invocations * invocations Question 3 (4 points): Mark whether each of the following generate an iterative or recursive process by circling the appropriate word, and fill in the order of growth: (define (foo x) ; Assume factorial is Θ(n) (define (helper n) (if (= n x) 0 (* (factorial n) (helper (+ n 1))))) (helper 0)) ; ITERATIVE / RECURSIVE Θ( ) (define (mystery sent) (define (help sent result) (if (empty? sent) result (if (member? (first sent) (help (bf sent) result)) (help (bf sent) (se (first sent) result)) (help (bl sent) (se result (last sent)))))) (help sent ())) ; ITERATIVE / RECURSIVE Θ( ) 3

4 Question 4 (3 points): (define (transform1 f) (lambda (x) (word (f x) (f x)))) (define (transform2 f) (lambda (x) (f (word x x)))) (define (transform3 f) (lambda (x) (f (f x)))) (define f1 (transform1 count)) (define f2 (transform2 count)) (define f3 (transform3 count)) Fill in the blanks with what Scheme returns. (Remember that numbers are words too.) (f1 hello) => (f2 bye) => (f3 abcdefghijklmnopqrstuvwxyz) => Question 5 (4 points): (define (startpoint segment) (car segment)) (define (endpoint segment) (cdr segment)) (define (x-coord point) (car point)) (define (y-coord point) (cdr point)) (define (datum tree) (car tree)) (define (children tree) (cdr tree)) (define (slope segment) (/ (- (cddr segment) (cdar segment)) (- (cadr segment) (caar segment)))) Rewrite slope to fix the data abstraction violations. 4

6 (define-class (thing name) (parent (basic-object)) (instance-vars (possessor no-one)) (method (thing?) #t) (method (type) thing) (method (change-possessor new-possessor) (set! possessor new-possessor)) (method (may-take? who) (cond ((eq? possessor no-one) self) ((> (ask who strength) (ask possessor strength)) self) (else #f))) ) (define-class (place name) (parent (basic-object)) (instance-vars (directions-and-neighbors ()) (things ()) (people ()) (entry-procs ()) (exit-procs ())) (method (place?) #t) (method (type) place) (method (neighbors) (map cdr directions-and-neighbors)) (method (exits) (map car directions-and-neighbors)) (method (look-in direction) (let ((pair (assoc direction directions-and-neighbors))) (if (not pair) () ;; nothing in that direction (cdr pair)))) ;; return the place object (method (appear new-thing) (if (memq new-thing things) (error "Thing already in this place" (list name new-thing))) (set! things (cons new-thing things)) appeared) (method (enter new-person) (if (memq new-person people) (error "Person already in this place" (list name new-person))) (set! people (cons new-person people)) (for-each (lambda (proc) (proc)) entry-procs) (for-each (lambda (pers) (ask pers notice new-person)) (delete new-person people)) appeared) 6

9 Your name login cs61a Question 7 (3 points): (define wd foo) (define s (make-serializer)) (define (f) (set! wd (word wd d))) (define (g) (set! wd (word wd wd))) (a) List all the possible values of wd after (parallel-execute (s f) (s g)). (b) List all the possible values of wd (starting from its initial value, without part (a) s effect) after (parallel-execute f g). Question 8 (4 points): Consider the following stream procedure: (define (process-stream S) (cons-stream (stream-car S) (stream-filter (lambda (x) (not (equal? x (stream-car S)))) (process-stream (stream-cdr S))))) (a) In one sentence, what function does process-stream compute? (b) We also have these streams: (define ones (cons-stream 1 ones)) (define twos (cons-stream 2 twos)) (define integers (cons-stream 1 (stream-map + ones integers))) Remember that (ss stream 10) displays the first 10 elements of a stream. What does scheme print for each of the following? > (ss (process-stream (interleave ones integers)) 10) > (ss (process-stream (interleave ones twos)) 10) 9

10 Question 9 (3 points): (define mystery (let ((y 2)) (lambda (z) (let ((x 4)) (lambda () (set! x (+ z y)) (set! y (+ x z)) y))))) (define foo (mystery 3)) ; procedure A (define mystery (lambda (z) (let ((x 4) (y 2)) (lambda () (set! x (+ z y)) (set! y (+ x z)) y)))) (define foo (mystery 3)) ; procedure B (define mystery (lambda (z) (lambda () (let ((x 4) (y 2)) (set! x (+ z y)) (set! y (+ x z)) y)))) (define foo (mystery 3)) ; procedure C On the next page are four environment diagrams. Label three of them A, B, and C, corresponding to the procedures above (write the letter, large, in the global environment box); leave the fourth diagram unlabelled. Question continued on next page. 10

12 Question 10 (3 points): For each of the following code sequences, will the analyzing evaluator be faster than the ordinary metacircular evaluator? Assume the evaluator is restarted for each sequence. (a) (define (member thing ls) (cond ((null? ls) #f) ((equal? thing (car ls)) ls) (else (member thing (cdr ls))))) (member 2000 (enumerate-interval )) Is (a) faster in the analyzing evaluator? Yes. No. (b) (define (member thing ls) (cond ((null? ls) #f) ((equal? thing (car ls)) ls) (else (member thing (cdr ls))))) (member 0 (enumerate-interval )) Is (b) faster in the analyzing evaluator? Yes. No. (c) (define (cube x) (* x x x)) (cube (+ 2 3)) Is (c) faster in the analyzing evaluator? Yes. No. 12

13 Your name login cs61a Question 11 (4 points): Write a mapreduce program to find how often each letter occurs in a document. (You should use the procedure strip-punctuation, which takes a word and removes all punctuation from it. You don t have to write that procedure.) Question 12 (4 points): The following is run in the nondeterministic evaluator. Fill in the blanks. (define z 7) (define (indecisive x y) (if (amb x (not x)) (begin (set! z 2) (cons z (amb y (+ y 3)))) (cons z (+ y 1)))) (indecisive #t 30) try-again try-again try-again 13

14 Question 13 (8 points): This question is about the Tree abstract data type, with selectors datum and children. Write a procedure sib-map that works like tree-map, taking a function f and a Tree as arguments and returning a new Tree. The difference is that f is a function of two arguments: the datum and the sibling number, which is 0 for the leftmost child of a node, 1 for the next child, and so on. If my-tree is the following tree: 3 / \ / \ 7 8 / \ / \ (sib-map (lambda (elt posn) (+ (elt (* 10 posn)))) my-tree) would give 3 / \ / \ 7 18 / \ / \

15 Your name login cs61a Question 14 (8 points): Write a query system rule or rules for next-to, a relation among two names and a list, which can determine whether two names are next to each other in the list. For example: (Jerry is next to Evan in (Albert Brian Evan Jerry Ramesh Yaping)) matches the rule, and the query (?who is next to Evan in (Albert Brian Evan Jerry Ramesh Yaping)) yields (Jerry is next to Evan in (Albert Brian Evan Jerry Ramesh Yaping)) (Brian is next to Evan in (Albert Brian Evan Jerry Ramesh Yaping)) Do not use lisp-value! 15

16 Question 15 (8 points): We want to add optional dynamic scope to the metacircular evaluator. Add a new special form (lambda-dynamic (arg...)...), which creates a dynamic procedure. When a dynamic procedure is invoked, the frame for that procedure should extend the current environment instead of the procedure s creation environment. The relevant metacircular evaluator procedures are listed on the remaining pages of the exam. On this page, write the names of all the procedures that you modify elsewhere. New procedures can go here or on page

17 Your name login cs61a (define (mc-eval exp env) (cond ((self-evaluating? exp) exp) ((variable? exp) (lookup-variable-value exp env)) ((quoted? exp) (text-of-quotation exp)) ((assignment? exp) (eval-assignment exp env)) ((definition? exp) (eval-definition exp env)) ((if? exp) (eval-if exp env)) ((lambda? exp) (make-procedure (lambda-parameters exp) (lambda-body exp) env)) ((begin? exp) (eval-sequence (begin-actions exp) env)) ((cond? exp) (mc-eval (cond->if exp) env)) ((application? exp) (mc-apply (mc-eval (operator exp) env) (list-of-values (operands exp) env))) (else (error "Unknown expression type -- EVAL" exp)))) (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 "Unknown procedure type -- APPLY" procedure)))) (define (eval-assignment exp env) (set-variable-value! (assignment-variable exp) (mc-eval (assignment-value exp) env) env) ok) (define (eval-definition exp env) (define-variable! (definition-variable exp) (mc-eval (definition-value exp) env) env) ok) 17

18 (define (make-procedure parameters body env) (list procedure parameters body env)) (define (compound-procedure? p) (tagged-list? p procedure)) (define (make-frame variables values) (cons variables values)) (define (frame-variables frame) (car frame)) (define (frame-values frame) (cdr frame)) (define (add-binding-to-frame! var val frame) (set-car! frame (cons var (car frame))) (set-cdr! frame (cons val (cdr frame)))) (define (extend-environment vars vals base-env) (if (= (length vars) (length vals)) (cons (make-frame vars vals) base-env) (if (< (length vars) (length vals)) (error "Too many arguments supplied" vars vals) (error "Too few arguments supplied" vars vals)))) 18

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