Functional programming (A Level) flashcards

Topic 12: Functional programming

What do f: A → B, the domain and the co-domain mean?

f takes arguments of type A and returns results of type B. The domain (A) is the set inputs come from; the co-domain (B) is the set outputs come from, though not every member has to be output.

What is a first-class object?

A value that may appear in expressions, be assigned to a variable, be passed as an argument and be returned from a function call. In functional languages, functions are first-class objects.

What is function composition g ∘ f?

It combines f: A → B and g: B → C into one function of type A → C, with f applied first. The co-domain of f must match the domain of g.

What is a higher-order function?

A function that takes a function as an argument, returns a function, or both, e.g. map, filter and fold.

What do map, filter and fold do?

map applies a function to every element of a list. filter keeps the elements for which a condition is true. fold (foldl or foldr) combines the elements into one value, starting from a given value.

What do head, tail and null return for the list [5, 2]?

head gives 5 (the first element). tail gives [2] (the rest, always a list). null gives False (the list is not empty).

How does Haskell choose which equation of a function to use?

By pattern matching: it tries the equations from top to bottom and uses the first pattern that fits, such as 0, [], a name, (x:xs) for any non-empty list or [x] for a one-item list.

How is a function applied in Haskell, and how is whole-number division written?

Arguments follow the name with spaces and no brackets or commas, e.g. name 7 2. div and mod are written between back-quotes: 17 div 5 = 3 and 17 mod 5 = 2.

Name the number sets ℕ, ℤ, ℚ and ℝ

ℕ: natural numbers 0, 1, 2, ... (zero included). ℤ: integers. ℚ: rational numbers p/q with integers p and q. ℝ: real numbers, including π and √2.