4.12.1.4 Partial function application and composition of functions Quiz: AQA Computer Science, Unit 12

The 20 questions

1. What does partial function application mean?

   • Giving a function fewer arguments than it takes, which returns a function that expects the remaining arguments.
   • Running a function only for the part of a list that matches a given condition.
   • Applying a function to all of its arguments and then discarding the result it returns.
   • Splitting a function into two separate programs that run on different machines.

2. With add: integer -> integer -> integer, what does the expression add 4 return?

   • A function which, when applied to an integer, adds 4 to that integer.
   • An error, because add must always be called with two arguments in every case.
   • A list containing the integers 4 and 4 as its two arguments.
   • The integer 4, because add 4 simply returns its single argument unchanged.

3. If inc is add 4, what is the result of inc applied to 5?

   • 20
   • 9
   • 4
   • 5

4. In curried notation, what is the type of add that takes two integers?

   • integer x integer -> integer
   • integer -> integer -> integer
   • integer -> integer x integer
   • integer -> integer

5. What does the composition g o f mean?

   • Store f and g in a list and apply them in a random order each time.
   • Apply f first, then apply g to the result that f returns.
   • Apply f and g to the same input and add the two results together.
   • Apply g first, then apply f to the result that g returns.

6. For the composition g o f with f: A -> B and g: B -> C, what is the domain?

   • The co-domain of g, which is C.
   • The union of the domains of f and g combined together.
   • The domain of f, which is A.
   • The domain of g, which is B.

7. For f(x) = x + 2 and g(y) = y^3, what is g o f?

   • (x + 2)^3
   • (x^3) + 2 in every case
   • x^3 + 2
   • x + 8

8. Using f(x) = x + 2 and g(y) = y^3, what is (g o f)(1)?

   • 27
   • 5
   • 9
   • 7

9. Using f(x) = x + 2 and g(y) = y^3, what is (f o g)(1)?

   • 27
   • 3
   • 4
   • 5

10. Given inc x = x + 1 and double x = 2 * x, what is double (inc 3)?

    • 6
    • 7
    • 8
    • 10

11. Which expression is a partial application of a three-argument function f applied to a, b and c?

    • f alone, which is a syntax error in every functional programming language.
    • f a b, which returns a function that still expects the third argument.
    • a, b and c applied in reverse order to produce a single value directly.
    • f a b c, which returns a function that has no arguments left to take.

12. What does the curried form of a two-argument function allow?

    • Calling it only from inside a loop structure within the same program module.
    • Calling it with one argument at a time, with each call returning a function for the next argument.
    • Calling it only once, with both arguments stored in a global variable first.
    • Calling it with a list of arguments that are sorted into order before being used.

13. Evaluate: why is partial application useful in a functional program?

    • It makes every function run faster by evaluating only half of its arguments at once.
    • It allows a function to be written without any arguments in its definition at all.
    • It prevents any function from ever returning a value to the caller of the function.
    • It lets a general function be specialised, for example producing an add-four function that can be reused inside map.

14. f: A -> B and g: B -> C are functions. What is the composition g o f, and what is its domain?

    • g o f, with domain A and co-domain C.
    • f o g, with domain C and co-domain A, because the function applied first is the one whose output type is the result of the composition.
    • g o f, with domain B and co-domain C.
    • g o f, with domain B and co-domain A.

15. g o f is applied to 2, where f(x) = x + 2 and g(y) = y^3. Which steps happen in order?

    • g(2) = 8 is computed first, then f(8) = 10 is computed.
    • f(2) = 4 is computed, then f(4) = 6 is computed, then g(6) = 216.
    • g(2) = 8 and f(2) = 4 are computed separately and multiplied together for 32.
    • f(2) = 4 is computed first, then g(4) = 64.

16. f: integer -> boolean and g: boolean -> string are functions. What is the type of g o f?

    • integer -> string
    • integer x boolean -> string
    • boolean -> integer
    • string -> integer

17. Which description of composing functions in a functional language is correct?

    • Running two functions in parallel and combining their outputs into a single list, which is always the same as applying one after the other.
    • Passing the output of one function directly as the input to another, to create a new function.
    • Copying the code of one function into the body of another in place of its name.
    • Joining two strings together with a separator placed between them in the output.

18. Does g o f always give the same result as f o g?

    • No, but only when the functions are defined on integers and not on real numbers.
    • No, in general, because changing the order of application changes the result.
    • Yes, because both functions are applied to the input at exactly the same time.
    • Yes, because function composition is always commutative for real numbers.

19. Why does partial application fit the view add: integer -> (integer -> integer)?

    • Because add returns two values at once, which are stored together in a pair.
    • Because add is a list function that processes its arguments in order from the start.
    • Because the function takes one argument and returns a new function that takes the next argument.
    • Because add must always be called with both arguments, otherwise it returns nothing at all, which is why it can never be partially applied.

20. Which function results from partially applying multiply to 3, where multiply x y = x * y?

    • A function that adds 3 to its argument, because the first argument is always added.
    • The number 3, because a partially applied function returns its first argument unchanged.
    • A function that needs two arguments and ignores the number 3 that was supplied.
    • A function that multiplies its argument by 3.

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