Introduction to higher order categorical logic
Introduction to higher order categorical logic
Information and Computation
A note on inconsistencies caused by fixpoints in a Cartesian closed category
Theoretical Computer Science
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
A Categorical Approach to Realizability and Polymorphic Types
Proceedings of the 3rd Workshop on Mathematical Foundations of Programming Language Semantics
On the Interpretation of Type Theory in Locally Cartesian Closed Categories
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Type Theory via Exact Categories
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Developing theories of types and computability via realizability
Developing theories of types and computability via realizability
Theoretical Computer Science - Mathematical foundations of programming semantics
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
An Abstract Look at Realizability
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Theoretical Computer Science - Mathematical foundations of programming semantics
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We present a general notion of realizability encompassing both standard Kleene style realizability over partial combinatory algebras and Kleene style realizability over more general structures, including all partial Cartesian closed categories. We show how the general notion of realizability can be used to get models of dependent predicate logic, thus obtaining as a corollary (the known result) that the category Equ of equilogical spaces models dependent predicate logic. Moreover, we characterize when the general notion of realizability gives rise to a topos.