Two of the most fundamental higher-order functions included in the standard library are
filter. These functions are generic and can operate on any iterable. In particular, they are well-suited for computations on arrays.
Suppose we have a dataset of schools. Each school teaches a particular subject, has a number of classes, and an average number of students per class. We can model a school with the following immutable type:
immutable School subject::Symbol nclasses::Int nstudents::Int # average no. of students per class end
Our dataset of schools will be a
dataset = [School(:math, 3, 30), School(:math, 5, 20), School(:science, 10, 5)]
Suppose we wish to find the number of students in total enrolled in a math program. To do this, we require several steps:
A naïve (not most performant) solution would simply be to use those three higher-order functions directly.
function nmath(data) maths = filter(x -> x.subject === :math, data) students = map(x -> x.nclasses * x.nstudents, maths) reduce(+, 0, students) end
and we verify there are 190 math students in our dataset:
julia> nmath(dataset) 190
Functions exist to combine these functions and thus improve performance. For instance, we could have used the
mapreduce function to perform the mapping and reduction in one step, which would save time and memory.
reduce is only meaningful for associative operations like
+, but occasionally it is useful to perform a reduction with a non-associative operation. The higher-order functions
foldr are provided to force a particular reduction order.