CSC 160 Computer Programming for Non-Majors Lecture #6: Function Composition

1. CSC 160Computer Programmingfor Non-MajorsLecture #6: Function Composition Prof. Adam M. Wittenstein Wittenstein@adelphi.edu http://www.adelphi.edu/~wittensa/csc160/

2. A preview… • A Scheme program includes one or more functions, defined using the rule: (define (function-name parameter-names) (expression)) • A Scheme program may also includes one or more variables, defined using the rule: (define VARIABLE-NAME its-value)

3. REVIEW: Meaning of the Function Definition • In the function: (define (square r) (* r r)) we tell Scheme that: (square r) is the same thing as typing: (* r r)

4. Example 1: area-of-disk • Suppose we want to write a function to find the area of a circle. • The formula is A = PI * r2 • We could write: (define (area-of-disk r) (* PI (* r r))) • However, notice that (* r r) is actually just the function body of the square function.

5. Example 1: area-of-disk • So we can instead write: (define (area-of-disk r) (* PI (square r))) replacing (* r r) with (square r). • Even if we named our parameter something different in the square function, it is still allowed.

6. Example 1: area-of-disk • Then, we have: (define (square num) (* num num)) (define (area-of-disk r) (* PI (square r)) • Since our goal here is to write area-of-disk, we call that the main function. Then, square which helps us write area-of-disk, is called an auxiliary function.

7. Example 2: checkerboard • The checkerboard function can be written as: (define (checkerboard color1 color2) (image-above (image-beside (rectangle 50 50 ‘solid color1) (rectangle 50 50 ‘solid color2) ) (image-beside (rectangle 50 50 ‘solid color2) (rectangle 50 50 ‘solid color1) ) ) )

8. Example 2: checkerboard • The program can more succinctly (and clearly) be written using function composition: • Since we are using the following setup, (image-above (image-beside ____ _____) (image-beside ____ _____) ) we can write a separate function for that part.

9. Example 2: checkerboard ;Auxiliary function: (define (counterchange img1 img2) (image-above (image-beside img1 img2) (image-beside img2 img1) ) )

10. Example 2: checkerboard ; This allows the checkerboard function to be ; written in this shorter way. ;Main function: (define (checkerboard color1 color2) (counterchange (rectangle 50 50 ‘solid color1) (rectangle 50 50 ‘solid color2) ) )

11. Writing Multi-Function Programs • While developing a Scheme function, you may realize the need or benefit of an auxiliary function. • One example is when you have a setup of several functions like image-above and image-beside. You can create a separate function that incorporates those three. We called that separate function counterchange. • Another example is when you have the same or similar code twice in a single function. Then you can write an auxiliary function that addresses just the part of the function with that same or similar code.

12. Writing Multi-Function Programs • Sometimes the auxiliary function is predefined, like + or first. • If the auxiliary function is not predefined, you will have to define it yourself. • You should pause the designing of your main function, while you complete a separate Design Recipe for the auxiliary function(s). • Then complete the Design Recipe for the main function.

13. CW3: For Section 02 only(the 4:30 class) • Develop a Scheme function called add-question-mark that takes in a sentence and returns the same sentence with a question mark at the end of the last word. • Submit the Definitions Window ONLY using the Digital Dropbox on Blackboard with the file name: “CW3-02[LastName]Def.scm”

14. Exercise 5.21: query • Develop a Scheme function, query, that turns a statement into a question by swapping the first two words and adding a question mark to the last word. • Example: ; (query ‘(you are experienced)) “should be” ; (ARE YOU EXPERIENCED?)

15. Preparing for Next Time…

16. In summary… • When there are multiple things that need to happen in a program, write them as separate functions. • When the auxiliary function you want to use is not predefined, define your own. • Whenever developing a function that requires auxiliary functions, complete the steps of the Design Recipe separately for every function you write.

17. Next time… • More on variables • If you haven’t already, please read the following before next class: • Simply Scheme, pages 89-93. • How to Design Programs, section 3.