<aside> 💡 While writing functions processing two one-of types (e.g. 2 lists), drawing a cross product table can assist by visualising the possible paths the function could take (depending on the form each one-of type assumes).

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Cross Product Table

“What's going to happen in this video is, we're going to see that we can use the type comments to reason about the actual behavior of a function. We're going to take one more step towards designing a function based on a model of the function. What I mean by model is a more abstract representation of the function, or a less detailed representation of the function that tells us enough about what the function has to do that we can make some real design decisions based only on the model. In some sense, we're going to be programming using a picture before we're programming using code.”

• When we encounter functions that process two one-of types, drawing a table that visualises all possible routes the function would expedite function design.
  • Example: prefix=?, a function that processes 2 lists and returns true if the 1st list lsta is a prefix of the 2nd list lstb.

Cross Product Code

• Example part (a): Implementing the cross product table in the function body of prefix=?
• Example part (b): Transforming the cross product function template into a working function

;; For this example:

;; Cases:
;; 1. both lists are empty
;; 2. lsta is not empty, but lstb is empty
;; 3. lstb is not empty, but lsta is empty
;; 4. both lists are non-empty

(define (prefix=? lsta lstb)
  (cond [(and (empty? lsta)(empty? lstb)) true]       ; case 1
        [(and (cons? lsta)(empty? lstb)) false]       ; case 2
        [(and (empty? lsta)(cons? lstb)) true]        ; case 3
        [(and (cons? lsta)(cons? lstb))
				 (if (string=? (first lsta)(first lstb))      ; reference rule: (cons String ListOfString))
						 (prefix=? (rest lsta)(rest lstb))        ; self-reference rule: ListOfString is one of: empty, (cons String ListOfString) 
						 false)]))                                ; case 4