Functional Programming

Question 1

What is a function type?

How would you write this?

Answer 1

It describes what the input and output values are.
E.g. inputting integers, outputting real numbers
Written like this: f: integer –> real (f: A –> B)
A is the argument type and B is the result type

Question 2

What could changing the function type do?

Answer 2

The functionality could change without changing the instructions as different input values would be accepted.

Question 3

Explain each part of this f: A –> B

Answer 3

F is the function name, A is the domain, B is the co-domain

Question 4

What is the definition of a function in functional programming?

Answer 4

A rule that for each element in a set of inputs, assigns an output chosen from another set

Question 5

What is the definition of a domain in functional programming?

Answer 5

A domain is a set from which a function’s input values are chosen.

Question 6

What is the definition of a co-domain in functional programming?

Answer 6

A co-domain is a set from which the function’s output values are chosen.

Question 7

What are the benefits of the functional programming paradigm?

Answer 7

• Supports the decomposition and abstraction of computing problems into functions that are made up of other functions
• Is suitable for running parallel and concurrent program execution, which allows programs to run on multiprocessor systems

Question 8

What is a first-class object?

Answer 8

An object which can appear in an expression, be assigned to a variable, be assigned as an argument and be returned in function calls.

Question 9

Not all combinations of functions are possible. Explain why this is.

Answer 9

A combination won’t work if:

• It doesn’t have the same number of inputs as outputs
• The type of the input isn’t the same as the type of the output

Question 10

What is a higher order function?

Answer 10

• A function that can take functions as arguments or/and can return a function as a result

Question 11

What does the map function do?

Answer 11

It applies a function to all the items in a list

Question 12

What does the filter function do?

Answer 12

Returns the elements in the domain that satisfy a given condition.

Question 13

What does the fold function do?
What is the difference between foldl and foldr?

Fold is also known as reduce

Answer 13

Reduces the list to a single value by applying a given operator to the values in the list. (usually adding)

Foldl means fold left, foldr means fold right
for example: foldr (-) 100 {2,4,6,8,10) would equal -94
whereas foldl (-) 100 {2,4,6,8,10) would equal 70

Question 14

Name the three first class objects in functional programming.

Answer 14

Functions
Integers
Variables

Question 15

How many arguments can a haskell function take?

Answer 15

1, though it can look like 2 arguments are being taken, they are taken as a pair, which is treated as1 argument

Question 16

What is the purpose of partial function application?

Answer 16

It allows the processing of multiple arguments by a function.

Question 17

What is meant by the head of a list in functional programming?

Answer 17

The first item in the list.

Question 18

What is meant by the tail of a list in functional programming?

Answer 18

All the items in the list apart from the first.

Question 19

How many data types can a list in a purely functional language contain?

Answer 19

1

Question 20

In functional programming languages, data structures like lists are immutable. What does this mean?

Answer 20

The list cannot be changed once created.

Question 21

Two functions are defined as follows f x y = x + y and g x = x * x. Why is it not possible to combine these functions as f.g?

Answer 21

Because f takes two arguments and g only takes one.

Question 22

What is a higher order function?

Answer 22

A function which takes a function as an argument, returns a function as a result, or does both.

Question 23

What is an argument?

Answer 23

The pieces of data that are passed into a function

Question 24

Give an example of type declaration of a function for multiplying two integers

Answer 24

MultiplyUs : : : int –> int –> int

the first two int’s tell us the argument type, the last int tells us the result type

Question 25

Give an example of declaring a function for multiplying two integers

Answer 25

MultiplyUs x y = x * y

for example MultiplyUs 3 5 would return 15

Question 26

How are partial function applications implemented?

Answer 26

One of the arguments is fixed, leading to a more restricted, specialised function.

Question 27

What is functional composition?

Answer 27

• The process of combining two functions to create a new function

Question 28

What is the benefit of functional composition?

Answer 28

User’s cane use the functions both separately, and in conjunction.

Question 29

What is required of functions that are combined?

Answer 29

One function’s domain (data type and number of arguments) must be the same as the other functions Co-Domain

Question 30

What do higher order functions use?

Answer 30

They use recursion

Question 31

What is function application?

Answer 31

The process of giving a function a particular input

Question 32

In functional programming, programs are stateless, what does this mean?

Answer 32

That when a program is running, the variables cannot change (e.g. they cannot change state)