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Indexed Induction and Coinduction, Fibrationally

Neil Ghani ; Patricia Johann ; Clement Fumex.

This paper extends the fibrational approach to induction and coinduction pioneered by Hermida and Jacobs, and developed by the current authors, in two key directions. First, we present a dual to the sound induction rule for inductive types that we developed previously. That is, we present a sound&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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