4.12 Fundamentals of Functional Programming

Question 1

What is a function

Answer 1

a rule for each element in some set A of inputs (domain), assigns an output chosen from set B (co-domain), but without necessarily using every member

Question 2

How does a function work

Answer 2

An argument is passed to a function, the rule is applied to the argument, creating the return value output

Question 3

What is a higher-order function

Answer 3

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

Question 4

what are first class objects

Answer 4

objects which may
- appear in expressions
- be assigned to a variable
- be assigned as arguments
- be returned in function calls

Question 5

what are some first-class objects

Answer 5

integers, floating-point values, characters, strings and functions

Question 6

what does a function being a first class object mean

Answer 6

it can be passed as arguments or returned as the result of another function

Question 7

what does function application mean

Answer 7

giving particular inputs to a function

Question 8

what is a partial function application

Answer 8

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

Question 9

what is meant by composition of functions and the benefit

Answer 9

combines two functions to create a new function - users are able to use the function both separately and in conjunction

Question 10

criteria for functions that can be combined

Answer 10

the domain of one of the functions is the same as the co domain of the other

Question 11

what order would you do these functions in g ○ f

Answer 11

f is applied first and then g is replied to the result

Question 12

what is the map function

Answer 12

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

Question 13

what is the filter function

Answer 13

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 14

what is the reduce or fold function

Answer 14

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

Question 15

describe the head and tail of
a list and what is the head and tail of the list [3,4,5]

Answer 15

head - first value of the list - 3
tail - list containing all values except for the first element - [4,5]