opComposite

opComposite is a formal operator used in programming and data processing to construct composite operations by combining two or more individual operators into a single executable unit. It functions as a higher‑order construct that encapsulates sequential application of its operands, enabling modular pipelines.

Formally, given unary operators f1, f2, ..., fn, opComposite(f1, f2, ..., fn) returns an operator F such that F(x) = fn(...(f2(f1(x)))). Some libraries use the reverse convention, applying the last operator first. Variadic and binary forms exist, with the composite represented as an application function or as a pipeline graph.

Properties: opComposite is typically associative, with opComposite(opComposite(f,g), h) equal to opComposite(f, opComposite(g,h)) under a fixed application order. The identity operator serves as a neutral element. In general, opComposite is not commutative.

Implementation and optimization: In code, opComposite is often a closure or object that stores the sequence of operations. Optimizations may fuse adjacent steps, inline simple operators, or rewrite the pipeline to minimize data materialization, especially for streaming or vectorized contexts.

Use cases: data processing pipelines, image or signal processing, and functional programming. Example: opComposite(f, g)(x) yields f(g(x)). For a three-step pipeline: opComposite(f1, f2, f3)(x) = f3(f2(f1(x))).

Relation and history: Related to mathematical function composition and to pipe or pipeline operators in several languages. It appears in theoretical descriptions of dataflow and in some library APIs that emphasize modular operator composition.

See also: function composition, pipe operator, pipeline, operator fusion, higher-order functions.