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Induction-recursion

Known as: Induction-recursion (type theory) 
In intuitionistic type theory (ITT), a discipline within mathematical logic, induction-recursion is a feature for simultaneously declaring a type and… Expand
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Papers overview

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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
  • P. Dybjer
  • J. Symb. Log.
  • 2000
  • Corpus ID: 18271311
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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