Introduction to higher order categorical logic
Introduction to higher order categorical logic
Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Information and Computation - Semantics of Data Types
Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Category theory for computing science
Category theory for computing science
Telescopic mappings in typed lambda calculus
Information and Computation
The logic of first order intuitionistic type theory with weak sigma-elimination
Journal of Symbolic Logic
Algebraic set theory
Handbook of logic in computer science
Extensional Constructs in Intensional Type Theory
Extensional Constructs in Intensional Type Theory
The Internal Type Theory of a Heyting Pretopos
TYPES '96 Selected papers from the International Workshop on Types for Proofs and Programs
On the Interpretation of Type Theory in Locally Cartesian Closed Categories
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Journal of Logic and Computation
Reflection Into Models of Finite Decidable FP-sketches in an Arithmetic Universe
Electronic Notes in Theoretical Computer Science (ENTCS)
Quotients over Minimal Type Theory
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
The identity type weak factorisation system
Theoretical Computer Science
Mathematical Structures in Computer Science
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We present a modular correspondence between various categorical structures and their internal languages in terms of extensional dependent type theories à la Martin-Löf. Starting from lex categories, through regular ones, we provide internal languages of pretopoi and topoi and some variations of them, such as, for example, Heyting pretopoi.With respect to the internal languages already known for some of these categories, such as topoi, the novelty of these calculi is that formulas corresponding to subobjects can be regained as particular types that are equipped with proof-terms according to the isomorphism ‘propositions as mono types’, which was invisible in previously described internal languages.