information:classification, linguistic:voice_change, quality:corruption, stylistic:style_transfer
Axiom of choice in type theory

In type theory, a different kind of statement is known as the axiom of choice. This form begins with two types, σ and τ, and a relation R between objects of type σ and objects of type τ. The axiom of choice states that if for each x of type σ there exists a y of type τ such that R (x, y), then there is a function f from objects of type σ to objects of type τ such that R (x, f (x)) holds for all x of type σ:

Unlike in set theory, the axiom of choice in type theory is typically stated as an axiom scheme, in which R varies over all formulas or over all formulas of a particular logical form.