Lecture 14: More Power, More Control

1. Here are two programs (assign as warm-up work):

   #| Sigma : list-of-numbers -> number Purpose: add the nunbers in alon (define (Sigma alon) ... ) Examples: (Sigma (list 1 2 3)) = 6 (Sigma (list 10 2 13)) = 25 |#	#| Pi : list-of-numbers -> number Purpose: multiply the nunbers in alon (define (Pi alon) ... ) Examples: (Pi (list 1 2 3)) = 6 (Sigma (list 10 2 13)) = 260 |#
   (define (Sigma alon) (cond ((empty? alon) 0) (else (+ (first alon) (Sigma (rest alon))))))	(define (Pi alon) (cond ((empty? alon) 1) (else (* (first alon) (Pi (rest alon))))))
   Now abstract over the two:
   (define (F base combine alon) (cond ((empty? alon) base) (else (combine (first alon) (F base combine (rest alon))))))
   How do we get back Sigma and Pi:
   (define (Sigma alon) (F 0 + alon))	(define (Pi alon) (F 1 * alon))

2. Okay, so let's define smallest

   ;; smallest : alon [not empty] -> number
   ;; Purpose: finds smallest number in non-empty list
   (define (smallest alon)
     (F (first alon) min alon))
   

3. Okay, let's define demands-going-up

   ;; demands-going-up : number alon -> alon
   ;; Purpose: filters out all those n's in alon that are larger than number 
   (define (demands-going-up cf alon)
     (local ((define (greater-than f rst)
   	    (cond
   	      ((> f cf) (cons f rst))
   	      (else rst))))
       (F empty greater-than alon)))
   

4. And how about project from database?

   ;; project : db -> list-of-symbols
   ;; Purpose: it produces the names of those employees in a-db 
   ;;    who earn more than $1000000 (as a list)
   (define (project a-db)
     (local ((define (more-than-100000 f rst)
   	    (cond
   	      ((> (pr-salary f) 1000000) (cons f rst))
   	      (else rst))))
       (F empty more-than-100000 a-db)))
   

   Wow: F now consumes a list of personnel records, not just a list of numbers. How can that be?

5. A list-of-numbers is either - empty or - (cons N L) where N is a number and L is a list-of-numbers.	A list-of-PRs is either - empty or - (cons N L) where N is a PR and L is a list-of-PRs.
   Now abstract over the two:
   A list-of-XYZs is either - empty or - (cons N L) where N is a XYZ and L is a list-of-XYZs.

   We will use (listof XYZ) to write down lists in the future.