Applyvary

Applyvary is a conceptual programming pattern that enables applying a function to each element of a collection while varying one of its parameters across elements. It combines a base function f(x, p) with a parameter variation function v(i) that supplies a value p for the i-th item. The resulting outputs are y_i = f(x_i, v(i)).

Etymology and scope: The term applyvary blends “apply” with “vary” and is used in discussions of higher‑order functions and data processing patterns. It is not tied to a single language and is described in theoretical texts and practical guides as a way to separate the core computation from its configuration.

Mechanics and typical use: An applyvary operation takes a function f, a variation function v, and a sequence X. For each index i and element x_i in X, it computes p = v(i) and yields f(x_i, p). This approach is common in parameter sweeps, simulations with per-sample settings, and data pipelines that require per-item configuration.

Example:

f(x, p) = x * p

vary(i) = 1 + 0.1*i

inputs = [2, 4, 6, 8]

applyvary(f, vary, inputs) -> [2.0, 4.4, 7.2, 10.4]

Relation and limitations: Applyvary is related to map, currying, and parameterized testing. It can improve flexibility but may reduce readability and add cognitive load if overused. Efficient implementations may precompute parameter values or fuse computations in a compiler.