functionwhether

Functionwhether is a conceptual higher-order function used in functional programming and logic to conditionally apply another function. It combines a predicate, a function to apply, and a default result, yielding a new function that only performs its computation when the predicate holds. The construction is useful for guarded computation and for composing pipelines with explicit failure or default behavior.

Formal notation: If p: A -> Bool is a predicate, f: A -> B is a function, and d: B is a default value, then functionwhether(p, f, d): A -> B is defined by g(a) = f(a) when p(a) is true, and g(a) = d otherwise. A variant uses an optional result instead of a concrete default: g(a) = Some(f(a)) if p(a) else None.

Example: Let p(x) be the predicate x > 0, f(x) = x^2, and d = 0. Then functionwhether(p, f, d)(3) = 9, while functionwhether(p, f, d)(-2) = 0. In languages with maybes or options, one might use g(a) = Some(f(a)) if p(a) else None to reflect the absence of a value when the predicate fails.

Relation and use: Functionwhether is related to guard combinators, map-with-predicate, and the concept of a monadic guard in Maybe/Option-based workflows. It aids in constructing safe or defaulted computations without scattering explicit branching logic throughout code.

See also: guard, Maybe/Option, monad, higher-order function, predicate.