Assignment 6: Functional Abstraction (due Oct 20)

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Note: For the following problems, you may not use Scheme's built-in abstract functions, such as filter, map, and fold. If you wish, you may define and use your own versions of these functions; you are not, however, required to do this.

1. (5 pts) Consider the following two programs (the first is from the first exam, the second is a variation on a problem from the first exam).

   (define (only-two-syms? sym1 sym2 alos)
     (cond [(empty? alos) true]
   	[else (and (or (symbol=? sym1 (first alos))
   		       (symbol=? sym2 (first alos)))
   		   (only-two-syms? sym1 sym2 (rest alos)))]))
   
   (define (all-alive? aloc)
     (cond [(empty? aloc) true]
   	[else (and (> (character-lives (first aloc)) 0)
   		   (all-alive? (rest aloc)))]))
   

   1. (3 pts) Write an abstract program that captures both of these definitions.

   2. (2 pts) Provide new definitions of only-two-syms? and all-alive? in terms of your abstract program.

2. (5 pts) Consider the following two programs

   (define (double-last alon)
     (cond [(empty? (rest alon)) (* 2 (first alon))]
   	[else (double-last (rest alon))]))
   
   ;; The function max is built-in in DrScheme
   (define (max-of-list alon)
     (cond [(empty? (rest alon)) (first alon)]
   	[else (max (first alon) (max-of-list (rest alon)))]))
   

   1. (3 pts) Write an abstract program that captures both of these definitions.

   2. (2 pts) Provide new definitions of double-last and max-of-list in terms of your abstract program.