Functioninos

Functioninos are a conceptual term used in discussions of modular function design to denote small, single-purpose function units that can be combined to form larger transformations. A functionino typically takes a single input and produces a single output, and is defined with a specific domain and codomain. The core idea is modularity: by designing each functionino to perform one well-defined operation, complex behavior emerges through composition rather than through a single, monolithic function.

In formal terms, a functionino is a total function from a type A to a type B. The collection of functioninos is closed under composition: if f: A→B and g: B→C are functioninos, then g∘f: A→C is also a functionino. The identity function id_A: A→A serves as a neutral element under composition. This gives rise to familiar algebraic structures such as monoids under composition and, more broadly, a categorical view where objects are types and arrows are functioninos.

Examples include f(x) = x+3, g(y) = 2y, and h(z) = exp(z) with suitable domains. In practice, functioninos appear in functional programming, data-flow graphs, and mathematical pedagogy as relatable building blocks for teaching function composition and modular design.

See also: function, composition, type theory, category theory, functional programming, modular design.