combOp

combOp is a term used in computing and data processing to denote a binary operation that combines two inputs into a single output according to a user-specified combining function. It functions as an abstraction for merging, pairing, or composing data from two sources and is commonly realized as a higher-order operator in programming languages.

In formal terms, if f is a binary function, combOp f a b yields f(a, b). This simple form underpins various practical patterns, such as arithmetic combination, string concatenation, or the merging of collections. When applied to data streams or sequences, combOp pairs elements from two sources and applies f to each pair, producing a new data stream or list of results.

Examples include:

- combOp(add, 3, 4) producing 7

- combOp(concat, "Hello, ", "world!") producing "Hello, world!"

- In stream processing, combOp(sum, S1, S2) could produce a stream of sums of corresponding elements: c_i = a_i + b_i

Applications of combOp appear across functional programming, data fusion, streaming pipelines, and parallel computation. It supports currying and partial application, allowing the creation of new functions by fixing the combining function f while leaving operands open. It is also flexible regarding operand types, so a single combOp can be used with numbers, strings, lists, or more complex data structures, provided a suitable binary function is supplied.

Variants of the concept exist under different names in libraries and languages, such as zip-with, merge with a function, or reduce-like combinators, reflecting the broad utility of combining two inputs via a user-defined operation. See also: combinator, operator, zip, fold, map, reduce.