ReduceFunktionen

ReduceFunktionen is a term used in computer science to describe a class of operations that convert a collection of values into a single result by repeatedly applying a binary function. The process is typically called reducing, folding, or accumulation.

In practice, a reduce operation uses a function f and an initial accumulator a0. A left-fold applies f to the accumulator and each element from left to right; a right-fold applies f from right to left. Some languages provide a single reduce operator while others distinguish foldl and foldr.

Formally, given a sequence x1, x2, ..., xn and a binary function f, a reduce computes r = f(... f(f(a0, x1), x2) ..., xn). When the operation is associative and has an identity element e, it forms a monoid, enabling parallel and incremental implementations.

Historically rooted in functional programming, reduce and fold appear in Lisp, eventually in Haskell, Scheme, and more recently in imperative languages such as Python (functools.reduce) and JavaScript (Array.prototype.reduce). They are widely used for summation, product, minimum, maximum, string concatenation, and data aggregation.

Common considerations include whether an initial value is required, how to handle empty sequences, and how to enable parallelism. ReduceFunktionen also underlie streaming and map-reduce workflows, where partial reductions are combined later.