4.12.2.1 Writing functional programs Quiz: AQA Computer Science, Unit 12

The 20 questions

1. What is a higher-order function?

   • A function that can only be called from another module at a higher level.
   • A function that takes a function as an argument, returns a function as a result, or does both.
   • A function that runs at a higher priority than the other functions in the program.
   • A function that is written in a higher-level language than the rest of the program, so that it can call the others without any extra setup.

2. What does map do?

   • Returns the first element of a list together with the remaining elements of the list.
   • Combines the elements of a list into a single value using a combining function.
   • Applies a given function to each element of a list, returning a list of the results.
   • Returns only the elements of a list that satisfy a given condition in the list.

3. What does filter do?

   • Combines all the elements of a list into one value by repeatedly applying a function.
   • Applies a function to every element of a list and returns the results in order.
   • Returns a new list containing exactly those elements that satisfy a given condition.
   • Returns the number of elements in a list without changing any of the elements.

4. What does reduce or fold do?

   • Creates a new list containing only the first few elements of the original list.
   • Sorts a list into ascending order using a supplied comparison function for values, which returns the list in a new and sorted order.
   • Applies a condition to each element and keeps only those that fail the condition.
   • Combines the values of a list into a single value by repeatedly applying a combining function.

5. What is the result of applying a function that doubles its input to every element of [1,2,3] using map?

   • [3,4,5]
   • [6]
   • [1,2,3]
   • [2,4,6]

6. What is the result of filter (> 1) applied to [1,2,3]?

   • [3]
   • [2,3]
   • [1]
   • [1,2,3]

7. What is the result of fold (+) 0 applied to [1,2,3,4]?

   • 24
   • 10
   • 4
   • 0

8. Which of these is a higher-order function?

   • length, because it returns the number of items that are in a list.
   • head, because it returns only the first element of the list it is given.
   • map, because it takes a function and a list as its arguments.
   • +, because it simply adds two numbers together and returns the total.

9. Which function call returns only the even numbers from [1,2,3,4]?

   • map even [1,2,3,4]
   • fold even [1,2,3,4]
   • filter even [1,2,3,4]
   • head [1,2,3,4]

10. Using fold, how would you find the largest number in a non-empty list?

    • Fold with a function that returns the larger of its two arguments.
    • Head applied to the list after it has been sorted into reverse order.
    • Map with a function that returns the smaller of two numbers from the list.
    • Filter with a function that removes every number from the list in turn.

11. A program needs the square of every number in a list. Which higher-order function is most suitable?

    • fold, with a function that adds each square to a running total for the list.
    • map, with a function that squares each element.
    • reverse, with a function that squares each element before the list is reversed.
    • filter, with a function that squares each element and removes the original value.

12. Which statement correctly describes a function that returns a function?

    • Returning a function is only possible when the function has no arguments in its definition.
    • A function that returns a function must always return the same function on every call.
    • A higher-order function may return a new function, such as one created by partially applying add to 4.
    • A function cannot return another function in any functional programming language at all.

13. To count how many elements of a list are negative, which combination is most natural?

    • fold with a multiplication function, then tail of the list that is supplied.
    • reduce with a sorting function, then length of the original list before filtering.
    • filter with a test for negative numbers, then length of the result.
    • map with a test for negative numbers, then head of the result that is produced.

14. Which statement about the length of map's output is correct?

    • map returns a list of the same length as its input list.
    • map returns a list with one element for each pair of elements in the input list.
    • map returns a list that is always shorter than the list it was given as input.
    • map returns a single value, so the length of its result is always one element.

15. Which statement about filter's output is correct?

    • The result contains only the elements that satisfy the condition, kept in their original order.
    • The result contains only the elements that fail the condition, sorted into ascending order by value, so the largest values appear last.
    • The result contains every element of the list, each one changed by the condition in turn.
    • The result is always a single value, which is the number of elements that pass the test.

16. Evaluate: why are map, filter and fold preferred in many functional programs over loops that change a variable?

    • They let the programmer change a global variable from many places in the program at once.
    • They run faster on every machine because they bypass the processor and use memory directly.
    • They are the only way to write any kind of loop in a functional language at all.
    • They avoid changing shared state, which makes the code easier to reason about and to run in parallel.

17. In a language with first-class functions, why can map be written as a general-purpose tool?

    • Because map always applies the same built-in addition to every element of the list.
    • Because map changes the original list directly in memory without making a copy of it.
    • Because map can only be used with lists of integers as its input and nothing else.
    • Because the function to apply is passed as an argument, so map does not need to know what that function does.

18. A list of records must be grouped and totalled. Which higher-order function is most suitable for building the total?

    • map, applied to the list to remove each record before the total is built.
    • length, applied to the list to total the records and then group them together, which returns the record count for each group in the list.
    • fold, applying a combining function to each record in turn to build the total.
    • filter, applied to the list to keep only the record names for the total.

19. Which statement correctly contrasts map and fold?

    • map returns the first element of a list, whereas fold returns the last element of the list.
    • map keeps one output for each input element, whereas fold combines all of the elements into one value.
    • map and fold always produce identical results when they are applied to the same list.
    • fold keeps one output for each input element, whereas map combines all of the elements of the list into one single value at the end.

20. Which is true of higher-order functions in a language such as Haskell?

    • They let a program be built from small general functions, each of which is passed the specific behaviour it needs.
    • They are only available in programs that also rely on loops and changeable variables.
    • They are not allowed to call other functions, so they must be written as one large block.
    • They can only work with numbers and cannot be used to process strings or lists at all.

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