Lecture 5: Why Programming is Like American Football

1. We emersed you in Scheme programming. You have seen a whole lotta kinds of data: numbers, symbols, truth values, fixed-length lists, lists. And you have seen define, cond, placeholders for arguments (inputs), etc. [Draw picture!]

   Whew! WHAT'S GOING ON?

   We need order in this chaos. We need a systematic way to design programs.

   Question: When we are given a problem and a white sheet of paper, what strategy should we follow to design programs?

   We are faced with the problem of a football team:

   • we must learn the basic plays
   • we must learn to choose the "right" play when there are several options
   • we must learn to introduce some variation
   And yes, painting and composing and novel-writing are just like that. We need basic techniques -- and then we can use our creativity to construct neat things using those techniques. (Every other notion of creativity is crap.)
   
   
2. Where do we begin? Because programs are "little machines" that consume and produce data:

   		*--------------------------*
   		|                          |
      In  --->	|          MyProgram       |   ---> Out
   		|                          |
   		*--------------------------*	
   

   The picture suggests that we start by studying the data especially the kind of data that goes in. We write down a rigorous description of all possible inputs. (We may have to be generous and include a few extra elements in this collection, but so be it.)
   
   
3. Now we can write down:

   ;; data definition for In
   
   ;; data definition for Out
   
   ;; MyProgram : In -> Out
   ;; MyProgram computes the foo from the boo in an In-element
   (define (MyProgram an-In) ...)
   

   
   
   
4. And now? Once we have nailed down the data collections, we make up program examples i.e. examples of what kind of output should be produced for some given input. At a minimum we make up a variety of input examples.

   (Input) Data	Simple	Intervals	Compound	Mixed	Self-referential
   	numbers	small set of symbols, ---(------]---[------)---	a spider: 8 legs, N flies a day, K m3	an animal is: a spider, a giraffe, a monkey	a list of symbols: - empty - (cons S L) where S: symbol L: list of symbols
   Contracts	f : number -> XYZ	f : number -> XYZ	f : spider -> XYZ	f : animal -> XYZ	f : list-of-symbol -> XYZ
   Input Examples	random sample	all symbols, all boundary points, interior points for all piecs	a spider: 8 legs, 10 flies a day, 5 m3	pick one animal from each kind!	at least one example from each clause
   The Output
   Templates		cond-expression	selector expressions	cond plus selectors/clause	cond plus selectors/clause plus recursion
   Definitions	domain knowledge	remind yourself of what the program computes (purpose) annotate each expression with what kind of data it computes for recursive data, do simple cases first for inductive cases, write down what the natural recursion computes what primitive operations can produce the desired output by combining what we have? use examples, how did you do it there
   Tests	use domain knowledge	goal: to find errors use examples to make sure that they are covered

   
   
   
5. Let's do an example: animals (does it fit) and list of symbols (is ant in there?)

   An animal is either 
     - a spider
     - a giraffe
     - a monkey
   
   A spider is (make-spider 8 5).
   
   A giraffe is (make-giraffe 8 500).
   
   A monkey is (make-monkey 8 50).
   

   ;; fits? : animal number -> boolean
   (define (fits? an-animal a-number)
     (cond
       ((spider? an-animal) ...)
       ((giraffe? an-animal) ...)
       ((monkey? an-animal) ...)))
   

   ;; how-many-ants? : list-of-symbols -> number
   (define ...)