CSC 160 Computer Programming for Non-Majors Lecture #5: Defining Functions Prof. Adam M. Wittenstein

This week…. First, we learn how to write number functions Scheme-style. Then, we will write functions in just the same way for other data types, like words, sentences, and images.

I. Number Functions with One Argument

REVIEW: Ways to cube a number a)(* 5 5 5) “should be” 125 b)(* ) “should be about 30 digits long” b) (define BIG ) (* BIG BIG BIG) c) Even better is to define functions…

Example 1: Defining the cube function Idea: Let cube(num) = num * num * num In Scheme… (define (cube num) (* num num num)) (cube ) (cube (cube )) …

But are we sure cube is right? What does “right” mean? Function must produce correct answers for all legal inputs –Don’t worry about illegal inputs, e.g. (cube “bluebird”) –If even one legal input produces a wrong answer, the function is wrong. –So we need to test every possible legal input. –This is impossible; test a few carefully selected inputs.

But are we sure cube is right? Specifying behavior & test cases “cube” function takes in a number and returns another number Example: (cube 0) “should be” 0 Example: (cube 5) “should be” 125 Example: (cube -6) “should be” -216 Notice that once you have defined cube, you can use it the same way as any other (predefined) function.

Syntax Rule #3: Defining a Function (define (func-name param-name[s] ) (expression)) (define (func-name param-name[s] ) (expression)) Example: Example: (define (cube num) (* num num num))

Before defining the cube function: (define (cube num) (* num num num)) you need to: --include an example of how the function is called: (cube 5) --along with what its answer "should be": 125. Submitting questions on HW3

So, if question 1 were to “define the cube function”, this is what I would expect in the Definitions Window for full credit: ;(cube 5) “should be” 125 (define (cube num) (* num num num))

Example 2: area-of-disk Recall the mathematical formula: A = Πr 2 We could write this as a Scheme function: (define (area-of-disk r) (* 3.14 (* r r))) This defines the function area-of-disk.

Example 2: area-of-disk We can now use (area-of-disk 5) to calculate a disk with a radius of 5: (* 3.14 (* 5 5))

Example 2: area-of-disk We can now use (area-of-disk 5) to calculate a disk with a radius of 5: (* ) = 78.5

When you're Writing a Function… Function names cannot contain spaces. You must spell the function name exactly the same way in contract, examples, and definition. You must spell the parameter name exactly the same way in function header and function body. You cannot assume that the input will be any specific number (like 2, or 7, or …) Refer to the input only by the parameter name (e.g. days), so it works on whatever input is actually provided (stuck into the envelope).

Simply Scheme: Exercise 4.5a Define a Scheme function to convert a temperature from Celsius to Fahrenheit. (Hint: the formula is F = 9/5 * C + 32) Define a Scheme function to convert a temperature from Celsius to Fahrenheit. (Hint: the formula is F = 9/5 * C + 32)

Preparing for Next Time…

In summary… We can define our own functions, and call them the same way as predefined functions. In the function header, we provide a “placeholder” name for the argument(s). Specific arguments are not given until the function is called. (Another name for “calling a function” is “invoking a function”.)

Coming up… Functions with multiple parameters Functions with other data types Homework… No new reading! Make sure you have read and understood ALL of Simply Scheme Chapters 2-5 before next class! Get started on HW3. Consider pairing off with someone.