functionbut

Functionbut is a theoretical construct in programming language theory and functional programming that formalizes conditional application of a function. It defines an operator, often denoted as but, that combines a function, a predicate, and a fallback, to produce a new function. The resulting function applies the primary function only when the predicate is satisfied; otherwise, it yields a fallback value or applies an alternate function.

Formal definition commonly uses a triple (f, p, k) where f: X -> Y, p: X -> bool, and k: X -> Y. The function h = functionbut(f, p, k) is defined by h(x) = f(x) if p(x) is true, otherwise h(x) = k(x). Some variants allow the fallback to be a constant value d instead of a function, in which case h(x) = d when p(x) is false.

Intuition: functionbut separates the decision about whether to apply f from the actual computation, enabling concise conditional pipelines. In practice, it is similar to a guarded function application or a potential composition with a fallback. It is mainly discussed in academic contexts and small-scale experimental libraries.

Example: let f(x) = x + 2, p(x) = x > 0, and k(x) = 0. Then functionbut(f, p, k)(x) returns x + 2 when x > 0, and 0 otherwise. Alternatively, with k as a function, h(x) = x + 2 if x > 0 else x.

History and usage: The term and operator are not part of standard languages; prototypes have appeared in academic papers and experimental libraries in functional programming languages such as Haskell and JavaScript. It serves as a conceptual tool for illustrating conditional function composition and fallback behavior.