Families of inductive types defined by recursion arise in the formalization of mathematical theories. An example is the family of term algebras on the type ...

Oct 22, 2024 · Families of inductive types defined by recursion arise in the formalization of mathematical theories. An example is the family of term ...

Oct 5, 2023 · In type theory, induction-recursion is a principle for mutually defining types of the form A type a : A ⊢ B ( a ) type A \; \mathrm{type} \qquad

Inductive types include natural numbers, lists and well-founded trees. Inhabitants of inductive types can recursively nest only a finite number of constructors.

Abstract. Families of inductive types defined by recursion arise in the formalization of mathematical theories. An example is the family of term.

Mar 1, 2022 · W-types are said to be a well-founded inductive type that is parameterized over arities and constructors, similar to a tree of possible constructions.

Sep 8, 2019 · Recursively, a type T T is a constructor-type for an inductive type ... Such inductive type families are a simple generalization of inductive ...

Induction-recursion is a feature for simultaneously declaring a type and function on that type. It allows the creation of larger types than inductive types.

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Inductive-recursive types are types in which are mutually defined at the same time. One of the key motivating examples of inductive-recursive types are ...