# FiniteSetAggregateFunctions2(S, A, R, B)¶

FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers, where the function divides each integer by 1000.

map: (S -> R, A) -> B

map(f, a) applies function f to each member of aggregate a, creating a new aggregate with a possibly different underlying domain.

reduce: ((S, R) -> R, A, R) -> R

reduce(f, a, r) applies function f to each successive element of the aggregate a and an accumulant initialised to r. For example, reduce(_+\\$Integer, [1, 2, 3], 0) does a 3+(2+(1+0)). Note: third argument r may be regarded as an identity element for the function.

scan: ((S, R) -> R, A, R) -> B

scan(f, a, r) successively applies reduce(f, x, r) to more and more leading sub-aggregates x of aggregate a. More precisely, if a is [a1, a2, ...], then scan(f, a, r) returns spad {[reduce(f, [a1], r), reduce(f, [a1, a2], r), …]}.