T. Coquand

Publications240
h-index38
Citations6,811
Highly Influential Citations471
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The Calculus of Constructions
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Cubical Type Theory: A Constructive Interpretation of the Univalence Axiom
TLDR
A type theory in which it is possible to directly manipulate n-dimensional cubes based on an interpretation of dependenttype theory in a cubical set model that enables new ways to reason about identity types, for instance, function extensionality is directly provable in the system.
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Inductively defined types
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A Model of Type Theory in Cubical Sets
TLDR
A model of type theory with dependent product, sum, and identity, in cubical sets is presented, and is a step towards a computational interpretation of Voevodsky's Univalence Axiom.
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Pattern Matching with Dependent Types
For a more complete presentation of Martin-Lof's logical framework, which is implemented in ALF, we refer to the book \Programming in Martin-Lof's Type Theory" [16], chapter 19 and 20. We recall…
On the Computational Content of the Axiom of Choice
TLDR
This work presents a possible computational content of the negative translation of classical analysis with the Axiom of (countable) Choice and shows how to compute witnesses from proofs in classical analysis of ∃-statements and how to extract algorithms from proofs of ∀∃-Statements.
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Constructions: A Higher Order Proof System for Mechanizing Mathematics
  • T. Coquand, G. Huet
  • Mathematics, Computer Science
    European Conference on Computer Algebra
  • 1 April 1985
We present an extensive set of mathematical propositions and proofs in order to demonstrate the power of expression of the theory of constructions.
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An Analysis of Girard's Paradox
Infinite Objects in Type Theory
TLDR
According to this analysis, the proof expressions should have the same structure as the program expressions of a pure functional lazy language: variable, constructor, application, abstraction, case expressions, and local let expressions.
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Inheritance as Implicit Coercion
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