Wright State University
Department of Computer Science and Engineering
CS 480/680 Comparative Languages

     Summer 2012                               Assignment  1                                   Prasad


Recursive Definitions (15 pts)  (Due: July 18)

1.   Write a function init, which takes a list of symbols L, and produces a list of all (top-level) symbols of L except the last one. The input must be a non-empty list (precondition). E.g.,
(init  '(a b c d)) =  (a b c)

2.   Write a function duplicate, which takes a nested list of symbols L, and produces a nested list of symbols by "immediately duplicating" each symbol at all levels. E.g.,
(duplicate '(a b c)) =  (a a b b c c)
(duplicate '( (a) b ((c)) ) = ( (a a) b b ((c c)) )

3.   Write a function lastLess, which takes a nested list of symbols L and a symbol S, and produces another nested list which resembles L except for the elimination of the last occurrence of the symbol S.  
E.g., (lastLess   '(a b  a  (c e) d)    'e)  =  (a b a (c) d)
(Hint: Define a membership test function for nested lists by generalizing built-in member that can be used to set up lastLess recursive calls.)

4. Write a function matmul, which takes two nested lists of numbers representing rectangular matrices, and produces their product (or reports their incompatibility).
E.g., (matmul   '((1 2)(3 4))   '((5 6)(7 8))  =  ((19 22)(43 50))
(matmul   '((1 2 3)(4 5 6))   '((7 8)(9 10)(11 12))  =  ((58 64)(139 154))
(Hint: Define helper functions such as transpose and dotproduct using map.)

5. Foldr function is defined in the "Intermediate Student"-language. Experiment with the following examples and their variants to understand its behavior.

    (foldr + 0 (list -1 5 -3 4 2))
    (foldr - 0 (list -1 5 -3 4 2))
    (foldr cons empty (list -1 5 -3 4 2))
    (foldr append empty (list (list 1 2) (list 4) empty (list 8 1 2)))

Now define the higher-order function foldr in Scheme that satisfies the following template and test it at least on the R5RS-Scheme-compatible variants of the above examples (obtained by replacing empty with '() ):
 
(foldr f base '(x1 x2 … xn)) = (f 'x1 (f 'x2 … (f 'xn base)))
 

Sample "Well-documented" Definition

The following example is for Intermediate-Student language of DrRacket. The equivalent renditions for R5RS (Standard Scheme) are shown in asg1.ppt.

; HtDP book Exercise 5.1.2
; Develop the function chkgss. It consumes two numbers, guess and target.
; Depending on how guess relates to target, the function produces one of the following three answers:
;'TooSmall, 'Perfect, or 'TooLarge.


; CONTRACT: chkgss : number   number -> { TooSmall, Perfect, TooLarge }
; PURPOSE:  chkgss takes two numbers - a guess and a target, and
;           returns a symbol TooSmall, Perfect or TooLarge
;           depending on whether target is more, equal or less than guess
; CODE:
(define (chkgss guess target)
             (cond [(> guess target) 'TooLarge ]
                   [(< guess target) 'TooSmall ]
                   [(= guess target) 'Perfect ]
             )
)
; TEST CASES and EXPECTED OUTCOMES
;(in general, focus on boundary conditions and coverage)
(check-expect (chkgss 3 5) 'TooSmall)
(check-expect (chkgss 5 5) 'Perfect)
(check-expect (chkgss 7 5) 'TooLarge)

What to hand in?    
     
        Turn-in your well-documented solution as a Scheme (Racket) file egs.scm  (egs.scm) by running the following command on unixapps1.wright.edu. 

/common/public/tkprasad/cs480/turnin-pa1  egs.scm