Thierry Coquand
Showing 96 publications
An Introduction to Lorenzen's 'Algebraic and Logistic Investigations on Free Lattices' (1951)
Controlling unfolding in type theory
A Foundation for Synthetic Stone Duality
A foundation for synthetic algebraic geometry
A Variation of Reynolds-Hurkens Paradox
REDUCTION FREE NORMALIZATION FOR A PROOF-IRRELEVANT TYPE OF PROPOSITIONS
Type Theory with Explicit Universe Polymorphism
Constructive theory of ordinals
Loop-checking and the uniform word problem for join-semilattices with an inflationary endomorphism
Canonicity and homotopy canonicity for cubical type theory
Constructive sheaf models of type theory
Formal Topology and Univalent Foundations
Lorenzen and constructive mathematics
Syntax and models of Cartesian cubical type theory
On generalized algebraic theories and categories with families
Homotopy canonicity for cubical type theory
A Normalizing Computation Rule for Propositional Extensionality in Higher-Order Minimal Logic
RING DIVIDERS AND KRULL RINGS (A CONSTRUCTIVE APPROACH)
A Kripke model for simplicial sets
Théorie des types dépendants et axiome d'univalence
A generalization of the Takeuti-Gandy interpretation
A Presheaf Model of Parametric Type Theory
A Sheaf Model of the Algebraic Closure
Revisiting Zariski Main Theorem from a constructive point of view
Recursive Functions and Constructive Mathematics
Dynamic Newton-Puiseux theorem
Computing persistent homology within Coq/SSReflect
A constructive version of Laplace's proof on the existence of complex roots
Coherent and Strongly Discrete Rings in Type Theory
A Formal Proof of the Sasaki-Murao Algorithm
A computational interpretation of forcing in type theory
A Decision Procedure for Regular Expression Equivalence in Type Theory
Constructive Finite Free Resolutions
Metric complements of overt closed sets
A Modular Type-checking algorithm for Type Theory with Singleton Types and Proof Irrelevance
A modular type-checking algorithm for type theory with singleton types
A Note on Forcing and Type Theory
Curves and coherent Prüfer rings
Constructive Gelfand duality for C*-algebras
Constructive Krull Dimension. I: Integral Extensions
Spectral schemes as ringed lattices
A Modular Type-Checking Algorithm for Type Theory with Singleton Types and Proof Irrelevance
A simple type-theoretic language: Mini-TT
On the Algebraic Foundation of Proof Assistants for Intuitionistic Type Theory
A note on the axiomatisation of real numbers
Verifying a semantic βη-conversion test for martin-löf type theory
The completeness of typing for context-semantics
Normalization by Evaluation for Martin-Löf Type Theory with Equality Judgements
Untyped algorithmic equality for Martin-Löf's logical framework with surjective pairs
Towards constructive homological algebra in type theory
A logical approach to abstract algebra
Remarks on the equational theory of non-normalizing pure type systems
Preface of special issue on formal topology
A Proof of Strong Normalisation Using Domain Theory
A constructive proof of the Peter-Weyl theorem
Untyped Algorithmic Equality for Martin-Löf's Logical Framework with Surjective Pairs.
About Stone Notion of Spectrum
An elementary characterization of Krull dimension
A Completeness Proof for Geometrical Logic
A logical approach to abstract algebra
A Logical Framework with Dependently Typed Records.
Connecting a Logical Framework to a First-Order Logic Prover.
Formalising Bitonic Sort in Type Theory
Formal topology and constructive mathematics: the Gelfand and Stone-Yosida representation theorems.
A nilregular element property.
A note on measures with values in a partially ordered vector space.
Sur un théorème de Kronecker concernant les variétés algébriques
Generating non-Noetherian modules constructively
Proof-theoretical analysis of order relations
Generating non noetherian modules constructively
La contribution de Kolmogoroven logique intuitioniste
On a theorem of Kronecker about algebraic sets
Compact spaces and distributive lattices
Inductively generated formal topologies
A Logical Framework with Dependently Typed Records
A syntactical proof of the marriage lemma
Newman's lemma - a case study in proof automation and geometric logic
Intuitionistic model constructions and normalization proofs
Inductive definitions and type theory an introduction (preliminary version)
Intuitionistic model constructions and normalization proofs
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