Functional Programming

Question 1

What do side-effects do?

Answer 1

The potential for side-effects means you cannot guarantee that a given function will provide exactly the same output for a given input.

Question 2

What is referential transparency?

Answer 2

A property of functions in which the output value is determined solely by its input values, without any side effects or dependence on external state.

• This means that you can more easily determine whether a program will run correctly, leading to fewer bugs and run-time errors

Question 3

What is a function?

Answer 3

A rule (or set of rules) that maps each element from the input set A (the function’s domain) to a particular value from its output set B (the function’s co-domain).

• This is expessed as f : A -> B where f is the function identifier

Question 4

What is the image of a function?

Answer 4

The subset of values from the co-domain that are mapped to as outputs.

Question 5

What are types?

Answer 5

Sets of values (determines what kind of data a value is able to store)

Question 6

What is a function classified as in functional program?

Answer 6

Functions are first-class objects, meaning that they can be used just as literal values of of other types / classes.

For example:
- Functions can appear in expressions
- Functions can be assigned to variables
- Functions can be passed as an argument to another function
- Functions can be returned as the result of a function.

Question 7

What is a higher-order function? (MS)

Answer 7

A function that takes a function as an argument; and/or returns a function as a result;

Question 8

How to define a function in functional programming?

Answer 8

1) Declare the function’s type using a function signature
2) State the function’s expression that will map its input arguments to output values

E.g.

AddNums :: Int -> Int -> Int
AddNums x y = x + y

Question 9

What is the definition of function appliction?

Answer 9

Function application means to apply a function to its argument and can be described as the process of giving particular inputs to a function.

Question 10

What is the requirements for two functions to be combined?

Answer 10

• f : A -> B
• g : B -> C
• g o f : A -> C

Question 11

What is pattern matching and how is it used in defining functions in functional programming?

Answer 11

Pattern matching is used to define multiple function bodies depending on the function’s argument value.

E.g.
Factioral :: Int -> Int
Factorial 0 = 1
Factorial n = n * Factorial (n-1)

• In this case, the function will iterate through each definition until finding one that its argument’s value is suitable for

Question 12

What is a bound variable in functional programming?

Answer 12

Usually n, usedd to catch any arguments that are not explicitly stated
E.g. if input is Int and there are cases for 1 and 2, n can be used to define a case for every other possible argument value which avoids the non-exhaustive error

Question 13

Where should the bound variable be in the cases?

Answer 13

Last because pattern matching is applied top-down

Question 14

How are lists constructed in functional languages?

Answer 14

• First item in a list is its head
• Remaining items in the list are its tails
• Lists are thought of as a concatenation of a head and a tail
• Represented as (a:as) where a is head and as is tail

Question 15

What are the higher-order functions in functional programming?

Answer 15

• map
• filter
• fold

Question 16

How does the map function work?

Answer 16

• Applies a function to a list of items and returns a new list of results
• Applies function to head of list
• Recursive call of function on tail of list

E.g.

Map (+1) [1 .. 10] returns [2 .. 11]

MS for how map function works:

Question 17

How does the filter function work?

Answer 17

Applies a predicate function to a list of items and returns a list of items that match the given criteria

E.g.

Filter (>3) [1 .. 10] returns [4 .. 10]

Question 18

How does the fold function work?

Answer 18

Reduces a list to single value by recursively applying a combining function to each element in the list. Combining function takes two arguments and returns a single value.

foldl is fold for exams

E.g.

foldl (+) 0 [1 .. 10] returns 0 + 1 + 2 + .. + 10 = 55

Question 19

Why are functional programs parallelisable?

Answer 19

• Makes it easier to write correct code that can be efficiently distributed across more than one processing unit

Offers several ideal characteristics :
- Immutable data structures
- Statelessness
- Higher-order functions

Question 20

What are the key characteristics of functional programming and what do they do?

Answer 20

1) Immutable data structures - states or values stored in data structures cannot be changed once created
- Different processing units can apply functions to different items in a list without altering them since they don’t use variables

2) Statelessness - functions do not have side-effects so they do not affect wider state of the programs and outputs only dependent on input
- No need to wait for result of other processes to complete or use results of external processing

3) Higher-order functions - take a function as an a argument and apply to each item
- No need to follow a particular sequence so different processing units can perform at the same time and results can be combined

4) Order of execution determined at runtime - allows instructions to be distribute across different processing units and performed independently

Question 21

How to combine multiple functions simply in functional programming?

Answer 21

K(g(f(x))) = (k.g.f) x

Question 22

What is the function signature for FunctionA 5 where FunctionA :: Int -> Int -> Int?

Answer 22

Int -> Int

Question 23

How to write infix notation in functional programming?

Answer 23

• div 9 4 is the integer division of the 9 by 4
• to write infix notation, 9 div 4 is the same thing
• use backticks

Question 24

The add function takes two arguments.
Describe how the add function could be partially applied to the arguments 4 and 6. MS

Answer 24

Question 25

Figure 14 shows some code written in a functional programming language. total [] = 0 total (x:xs) = x + total (xs) Describe how the total function works to add up all of the numbers in a list. (MS)

Answer 25