University of California, Berkeley
EECS Department - Computer Science Division

CS3 Lecture 2 : Functions

We use functional programming for this course
The core idea is the use of functions
Remember high school algebra when we were given f(x) = 2 x + 1 ?
f is a function which takes x as input, or as an argument, and returns another number
We won't inititally use the normal full scheme interface for now, we'll use functions
It's possible that the functions we show accept more arguments in full scheme than functions shows

Let's explore with some arithmetic functions:
- + - * / sqrt remainder abs truncate
- These all take numbers as input and return numbers as output.
- Many more listed in the inside back book cover, experiment!

A word included english words, numbers and any string of numbers and digits and some punctuation
- Examples: cal 795 soda whassup yrul82-class
Words are another data type
Let's explore some non-numeric functions that deal with words
- word is the main constructor, it takes words and smushes them together into a new bigger word
- Others: word first butfirst bf last butlast bl
- These all take words as input and return words as output
- What happens with butlast a ? Why? Is the return value a valid function?
- There are others, however that don't necessarily return words: count
- There are many others in the inside back book cover, experiment!

What happens when our function is +, our first argument is 1 and our second argument is two?
What is the domain of a function?
- The things a function accepts as an argument.
What is the range of a function?
- All the possible return values of a function
Examples: sin sqrt / + remainder

Sentences are even another data type
Sentences are a bunch of words enclosed in parenthesis, like (cal is number one)
Many of the functions that work with words work with sentences
- sentence is the main constructor, it takes words and sentences
- first butfirst bf last butlast bl
Booleans are true and false values named after George Boole
- Sometimes we need to make decisions, and we need functions to return true and false values
- Example: > < >= <= even? odd? equal? member? vowel?
- Some work purely on boolean values: and or not

Many fish eat plankton and plants; others eat fish themselves.
We can treat functions as data!
- Example: number-of-arguments
- Example: every first (electrical engineering computer science)
- Example: keep vowel? fascetious

Today's big idea: functions are the workhorses of scheme, it's important to understand domain and range
Smaller ideas: we learned about several data types: numbers, words, sentences, booleans & functions

What is the fewest number of folds it takes to fold a dollar bill into a triangle?

You and a friend have a stack of 10 coins.
On each person's turn, they remove either 1 or 2 coins from the stack.
However, on your turn you can now ALSO place 1 or 2 coins back on the stack.
The person who removes the last coin wins.
Should you go first or second, and what's your strategy?

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