vastefunction

Vastefunction is a term used in speculative mathematics and computer science to describe a class of functions whose output depends on an external context in addition to the input value. In this sense, a vastefunction models context-sensitive computation, where the same input can yield different results under different conditions.

Formally, a vastefunction is defined as a mapping F from a product X × C to Y, where X is the input space, C is the context space, and Y is the output space. The same x ∈ X may map to different F(x, c) as c varies. When the context is fixed, F reduces to a standard one-argument function on X. Because the context participates in evaluation, such functions are inherently multi-parameter.

Notation and examples: One writes F: X × C → Y, or F(x; c). Example: F(x, c) = x if c = 'default', and F(x, c) = 2x if c = 'alternate'. A more subtle example uses a context-dependent rule that changes behavior at different thresholds of c. In practice, vastefunctions appear in discussions of contextual semantics, configuration-driven algorithms, and exploratory thought experiments.

Relationship and status: The term vastefunction is not a standard concept in mainstream mathematics. It is primarily used informally or within fiction and discussions about context-sensitive computation. It contrasts with context-free functions or ordinary dependent types, although it shares ideas with dependent function concepts. The notion is often used to illustrate how external state can influence evaluation, or to discuss design patterns in programmable systems.