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CSSE 304 Exam #1  Winter 2021-2022  Section  02 (11:00)    03 (2:00)

1. (6 points) Consider the execution of the code below.  Draw the box-and-pointer diagrams that represent the results of the defines.  Then show what Scheme would output from the execution of each of the last three expressions.
Be careful!  “Almost correct” answers will usually receive no partial credit.

1a (2 points).

  (define var1 '((1 2)))

var1  □

1b (2 points).

  (define var2 '(3 4))

  (define var3 '(5 6))

  (define var4 (cons var2 var3))

var2  □

var3  □

var4  □

1c (2 points).

  (define var5 '(7 8))

  (define var6 (append var5 (cdr var5)))
var5  □

var6  □

2. (5 points)  Though we often curry bigger functions into 1-parameter functions, there’s nothing magical about 1-parameter functions.  Write a function double-curry4 that takes a 4 parameter function and curries it into a curried function that takes two parameters.  See the usage below:

(define dc-list (double-curry4 list))

(define partial (dc-list 1 2))

(partial 3 4) ;; returns (1 2 3 4)

(define double-curry4

3. (5 points) Imagine I have a list of some combination of symbols and numbers.  I want to compute the sum of that list, ignoring any symbols.  For example:

(sum-mixed ‘(1 a 3 10 q)) yields 14

Write sum-mixed using some combination of map, filter, and apply.  Do not use any recursion or looping constructs in your solution.

(define sum-mixed

4. (4 points) Write a definition for a procedure make-counter that returns a procedure.  When this procedure is first called, it should return 1.  Then the second call returns 2, etc.  See the code example to see how make-counter is used.  It should be possible to create any number of counters, each with their own count.  Mutation is allowed on this question.

(define c1 (make-counter))

(define c2 (make-counter))

(c1) ; returns 1

(c1) ; returns 2

(c2) ; returns 1

(define make-counter

<LcExpr> ::=

 <identifier> |

 (lambda (<identifier>) <LcExpr>) |

 ( <LcExpr> <LcExpr> )

5. (5 points) Our original grammar for lambda-calculus expressions:

     Consider the expression  ((lambda (y) (x x)) (lambda (x) (y y)))

(a) (2 points ) In that expression, which variables occur bound? _____________      occur free? ____________

(b) (3 points) Draw  the derivation tree for that expression.  To make it easier to draw this (as I did on the whiteboard in the Day 11 class), you are allowed to write L in place of <LcExpr>, λ in place of lambda, and id in place of <identifier>.