Introduction to higher order categorical logic
Introduction to higher order categorical logic
Type systems for programming languages
Handbook of theoretical computer science (vol. B)
Kripke logical relations and PCF
Information and Computation
A characterization of lambda definability in categorical models of implicit polymorphism
Theoretical Computer Science
A New Characterization of Lambda Definability
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Equality Between Functionals in the Presence of Coproducts
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
A Relational Account of Call-by-Value Sequentially
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Logical Relations for Monadic Types
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
A Characterisation of Lambda Definability with Sums Via T T-Closure Operators
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
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We introduce a notion of Grothendieck logical relation and use it to characterise the definability of morphisms in stable bicartesian closed categories by terms of the simply-typed lambda calculus with finite products and finite sums. Our techniques are based on concepts from topos theory, however our exposition is elementary.