Nominaalsets
Nominaalsets, or nominal sets, are a mathematical framework used to model data that involve names and binding, such as variables in programming languages and formal logics. The standard setting begins with a countably infinite set A of atoms (names). The group G of interest is the group of all finite permutations of A, acting on A and on any set X equipped with a G-action: g ⋅ x.
An element x in a nominal set X is said to have finite support S ⊆ A if,
Examples include the set A itself, with the natural permutation action, and finite products or function spaces
Nominal sets provide a natural treatment of alpha-equivalence and freshness: two elements related by a name
Applications include the formalization of syntax with binders, such as lambda-calculus, in a way that makes