Simple Functions

PAL Week 3: Simple Functions

Activity 1: Putting the fun in functions

Haskell is a functional programmming. This means we should have a good idea of what a function is. In groups, discuss the following topics on the whiteboard:

-What is a function in simple terms? -Give examples of functions in mathematics (e.g., f(x) = 5x), and real life (e.g., f (smiling) = happy, f (frowning) = angry). -How do functions relate to programming in Haskell.

Activity 2: Writing Functions

See adjoining sheet.

Activity 3: Functional Composition

Consider a mathematical function that doubles a number f(x) = 2 x. We can write a new function that uses f(x) twice in order to quadruple a number. This is called functional composition. For example, g(x) = f( f (x) ).

a) Write a function in haskell that doubles a number. b) Quadruples a number by writing a new function composed of the function you wrote in (a). c) You’re able to use functions that you don’t understand every aspect of to compose a new function. If you understand the inputs and outputs of a function you can use this to determine what the function does, and use it in a new function composition. In this exercise, imagine you have an object called a ‘list’. It holds an unknown quantity of numbers, like a list. If you have one function called ‘count’ that, given a list, returns how many numbers are in that list, and another function called ‘sum’, that returns the sum of all the numbers in that list, can you create a new function called ‘average’ that returns the average of the list of numbers? Hint : the average of our list is the sum of numbers in the list, divided by the length of the list. Hint 2 : What are the inputs and outputs of ‘count’ and ‘sum’?