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2015

2015

Homotopy type theory may be seen as an internal language for the ∞-category of weak ∞-groupoids. Moreover, weak ∞-groupoids model… Expand

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2013

2013

There are several different approaches to the theory of data types. At the simplest level, polynomials and containers give a… Expand

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2012

2012

Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of… Expand

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2010

2010

ML5 is a programming language for spatially distributed computing, based on a Curry-Howard correspondence with the modal logic S5… Expand

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2007

2007

We address the problem of representing mathematical structures in a proof assistant which: 1) is based on a type theory with… Expand

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2006

2006

Abstract An indexed inductive definition (IID) is a simultaneous inductive definition of an indexed family of sets. An inductive… Expand

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Highly Cited

2006

Highly Cited

2006

We present a practical tool for defining and proving properties of recursive functions in the Coq proof assistant. The tool… Expand

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Highly Cited

2003

Highly Cited

2003

Induction-recursion is a powerful definition method in intuitionistic type theory. It extends (generalized) inductive definitions… Expand

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2001

2001

We give two finite axiomatizations of indexed inductive-recursive definitions in intuitionistic type theory. They extend our… Expand

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Highly Cited

2000

Highly Cited

2000

The first example of a simultaneous inductive-recursive definition in intuitionistic type theory is Martin-LUf's universe a la… Expand

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