AQA A-Level Computer Science: Functional Programming

The following definitions were written for this exercise.

In a functional language, the higher-order functions map, filter and foldr have the type signatures:

map    :: (a -> b) -> [a] -> [b]
filter :: (a -> Bool) -> [a] -> [a]
foldr  :: (a -> b -> b) -> b -> [a] -> b

Throughout this question use the list:

xs = [3, 8, 11, 4, 15, 6]

(a) Give the value produced by each of the following expressions. [6 marks]

(i)   map (*2) xs
(ii)  filter (> 7) xs
(iii) foldr (+) 0 (filter (> 7) xs)

(b) A function sumEvenSquares should take a list of integers and return the sum of the squares of just the even elements. Using map, filter and foldr (and no explicit recursion or loops), write a definition for sumEvenSquares. [4 marks]

(c) Two functions are defined as f = (*3) and g = (+1). State the value of the composition (f . g) 4. [2 marks]

A company is building a system that reads millions of raw web-server log records, then cleans, transforms and aggregates them into daily summary reports. The work is naturally a pipeline of independent stages (parse → filter out errors → extract fields → group → count), and the team wants to run the stages in parallel across many processor cores. One developer argues the pipeline should be written in a functional style; another prefers a conventional imperative / object-oriented style with mutable objects and loops.

Discuss the advantages and disadvantages of using the functional paradigm, rather than the imperative / object-oriented paradigm, to implement this data-transformation pipeline. Conclude with a justified recommendation. [9 marks]

The following definition was written for this exercise.

The higher-order function foldl reduces a list from the left, carrying an accumulator. The function below uses it to combine a list of single decimal digits into the whole number they represent:

digitsToInt :: [Int] -> Int
digitsToInt ds = foldl (\acc d -> acc * 10 + d) 0 ds

Apply this definition to the call digitsToInt [4, 2, 7, 9]. Show the value of the accumulator at each step of the fold, and state the final result. [6 marks]

In a functional programming language, functions are described as first-class objects, and the language supports higher-order functions.

Explain what each of these two terms means. Support your answer with a short code example for each. [5 marks]

The following definitions were written for this exercise.

Two functions are defined as:

inc = (+1)     -- adds 1
dbl = (*2)     -- multiplies by 2

The composition operator . builds a new function, where $(f \circ g)(x) = f(g(x))$(f∘g)(x)=f(g(x)) - that is, g is applied first.

Determine the value of each of the following, showing the intermediate result, and use them to explain why function composition is not commutative. [4 marks]

(i)  (dbl . inc) 5
(ii) (inc . dbl) 5

A central idea in the functional paradigm is the pure function.

Define what is meant by a pure function, and give one example of a function that is pure and one that is not. [3 marks]