An inductive–recursive definition (IRD) is a simultaneous inductive definition of a set and a recursive definition of a function on that set. An indexed inductive–recursive definition (IIRD) is a combination of both.
Jul 1, 2005
An inductive–recursive definition (IRD) is a simultaneous inductive definition of a set and a recursive definition of a function on that set. An indexed ...
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Feb 4, 2024 · In most cases, the indexed inductive type would be a greater option. The recursive fashion may require less effort and appear to be intuitive, but it is ...
Abstract. We give two finite axiomatizations of indexed inductive-re- cursive definitions in intuitionistic type theory. They extend our previous.
Abstract. We give two finite axiomatizations of indexed inductive-re- cursive definitions in intuitionistic type theory. They extend our previous.
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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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
I write about inductive-recursive types here. "Generally" means "higher inductive-inductive-recursive" or "quotient inductive-inductive-recursive".
Oct 2, 2001 · The class of indexed inductive-recursive definitions properly contains the class of indexed inductive definitions (so called “inductive families ...
Jul 31, 2022 · The recursive case of a recursive algorithm is the induction step. Proving the correctness of the recursive case and proving the inductive step ...
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