Lecture 7: Using the Recipes

1. A minor point:

   value = 
       0 | +1 | -1 | ...
     | #t | #f 
     | 'hello | 'world 
     | empty
     | list
   
   list = 
       empty
     | (cons value list)
   

   All constants are values. And lists are values.

   Some strange examples

   (cons (cons 1 (cons 2 empty)) empty)
   

   How many items are in this list?

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2. Given: the position of an object (a Cartesian point), its velocity (a vector), and a time. Question: develop a program that produces the new position.

   Is this about core knowledge or computational knowledge?

     * t = 0 
      \
       \
        \
         v
          * t = 1 
          ...       
   

   Core knowledge: Multiply velocity by time, add to position. Even if that means mulitplying vectors etc.

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3. Given: a sequence of names [Celsius]. Eliminate all those over 100.

   What form of data? Lists of numbers. Contract. Examples. Template.

   #|
      elim : (listof number) -> (listof number)
   
      Purpose: produce a list of numbers from the input by removing all those greater than 100
   
      Data Def.: list-of-number = empty | (cons number list-of-number)
   
      Examples: 
       (elim (list 20 30 100 40 20 30 100)) = (list 20 30 40 20 30)
       (elim empty) = empty
   
      Template: 
        (define (elim alon)
          (cond
   	 ((empty? alon) ...)
   	 (else ... (first alon) ... (elim (rest alon)) ...)))
        
   |#
   (define (elim alon)
     (cond
       ((empty? alon) empty)
       (else (cond
   	    ((> (first alon) 100) (elim (rest alon)))
   	    (else (cons (first alon) (elim (rest alon))))))))
   

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4. The above looks silly. Who would want to remove numbers from a list using a computer program? Okay, let's look at the following example:

   Given a table of names, salaries, and ranks.

   Name	Age	Salary
   Man	23	120000
   BigMan	46	800000
   Little	19	30000
   Woman	32	300000
   Kiddo	18	20000

   Develop a program that consumes a table and produces one with all those rows removed where age is below some threshold A.

   #|
      project : db number[A] -> db
   
      Purpose: produce a db from the input by including only those whose age
        is greater than A
   
      Data def: 
   
      db is a list of db-records: db = empty | (cons db-record db)
   
      db-record: 
      (define-struct record (name age salary))
   
      A db record is (make-record symbol a s)
        where a is an integer between MIN-AGE and MAX-AGE (incl)
        and s is an integer between MIN-SALARY and MAX-SALARY (incl)
   
      Examples: 
       (project DB1 
       
       (project empty 100) = empty
   
      Template: 
        (define (project alon)
          (cond
   	 ((empty? alon) ...)
   	 (else ... (first alon) ... (project (rest alon)) ...)))
        
   |#
   (define (project db)
     (cond
       ((empty? db) empty)
       (else (cond
   	    ((<= (record-age (first db)) A) (project (rest db)))
   	    (else (cons (first db) (project (rest db))))))))
   
   (define-struct record (name age salary))
   
   (define DB1
     (cons
     (make-record 'Man    23    120000 )
     (cons
     (make-record 'BigMan  46   800000 )
     (cons
     (make-record 'Little  19    30000 )
     (cons 
     (make-record 'Woman   32   300000 )
     (cons 
     (make-record 'Kiddo   18    20000 )
     empty))))))