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Generic Fibrational Induction

Neil Ghani ; Patricia Johann ; Clement Fumex.

This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs' elegant algebraic formulation of induction for&nbsp;[&hellip;]

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Refining Inductive Types

Robert Atkey ; Patricia Johann ; Neil Ghani.

Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful information. For example, the N-indexed type of vectors refines lists&nbsp;[&hellip;]

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Positive Inductive-Recursive Definitions

Neil Ghani ; Fredrik Nordvall Forsberg ; Lorenzo Malatesta.

A new theory of data types which allows for the definition of types as initial algebras of certain functors Fam(C) -> Fam(C) is presented. This theory, which we call positive inductive-recursive definitions, is a generalisation of Dybjer and Setzer's theory of inductive-recursive definitions within&nbsp;[&hellip;]

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