Functional Programming | AQA A Level Computer Science 7517 | 20 Worksheets + Answers

The whole of section 4.12 for AQA A Level Computer Science (7517): twenty
different sheets on function types, partial application, composition, map,
filter and reduce, and list processing - each worked all the way through, and
each with a complete answer key.

Six questions, one for each part of the specification. It is the only pack in
this series with six; 4.12 has three sub-sections and seven bullets, and none
of them is left out.

WHAT YOU GET

• 20 worksheets, 3 pages each, numbered 01 to 20
• 20 matching answer keys
• A contents table giving each sheet’s question 1 function, its
  partially-applied function and its reduce, so you can pick one without
  opening all twenty

WHAT IS ON EVERY SHEET

Question 1 defines a function over a small set: write its type as f: A -> B,
apply it twice, list what it actually produces, and give the smallest member
of the co-domain that is never an output. That last part is there because the
specification is explicit that not all of the co-domain need be produced, and
because “give a member” would have had a hundred right answers.

Question 2 is partial function application - the bullet that says candidates
must be able to USE the notation. The type with brackets, the type without,
the type of what is left after one argument, its value after two, and a
three-argument type whose argument types are not all the same.

Question 3 is composition. Which function is applied first, then g o f and
f o g evaluated at the same point, so the answer to “are they the same
function?” is worked rather than recited.

Question 4 is map, filter and reduce, each on its own and then all three
nested in one expression - where the filter applies to the mapped list, not
to the original one.

Question 5 is lists: the head and the tail, the head:tail form, prepend and
append, the length of a tail, and what the tail of a one-item list is.

Question 6 is written: first-class objects, the co-domain against the outputs,
what makes a function higher-order, partial application, or the empty list.

Every sheet is 30 marks.