12: Fundamentals of Functional Programming

Question 1

f: A → B

Answer 1

Function type is A → B, A is the argument type and the domain and B is the result type and the co-domain

Question 2

The domain and co-domain are always ____

Answer 2

Subsets of objects in some data type

Question 3

First-Class Object

Answer 3

A function in functional programming and in imperative programming languages that support such objects

Question 4

First-Class Objects May (4)

Answer 4

• Appear in expressions
• Be assigned to a variable
• Be assigned as arguments
• Be returned in function calls

Question 5

Partial Function Application

Answer 5

Where a function, taking multiple arguments, is parsed less arguments so returns a function, which takes the missing arguments, before returning a value

Question 6

Partial Function Notation (5)

Answer 6

• The function add takes two integers as arguments and gives an integer as a result
• add: integer → (integer → integer)
• add 4 returns a function, which when applied to another integer, adds 4 to that integer
• The brackets may be dropped: add: integer → integer → integer
• The function add is now viewed as taking one argument after another and returning a result of data type integer

Question 7

Composition of Functions (4)

Answer 7

• The operation functional composition combines two functions to get a new function
• Given two functions:
  f: A → B
  g: B → C
• The function g ⚬ f, called the composition of g and f, is a function whose domain is A and co-domain is C
• f is applied first and then g is applied to the result returned by f

Question 8

Head

Answer 8

The first element of a list

Question 9

Tail

Answer 9

The list of all elements apart from the head

Question 10

Prepend

Answer 10

Adds a single item, of the same data type as those in the list, to the start of the list

Question 11

Append

Answer 11

Adds a list of items, with the same data type as those in the other list, to the end of the other list

Question 12

Higher-Order Function

Answer 12

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

Question 13

Map

Answer 13

A higher-order function that applies a given function to each element of a list, returning a list of results

Question 14

Filter

Answer 14

A higher-order function that processes a data structure, typically a list, in some order to produce a new data structure containing exactly those elements of the original data structure that match a given condition.

Question 15

Reduce / Fold

Answer 15

A higher-order function which reduces a list of values to a single value by repeatedly applying a combining function to the list values