Introduction to higher order categorical logic
Introduction to higher order categorical logic
Cartesian closure—higher types in categories
Proceedings of a tutorial and workshop on Category theory and computer programming
Algebra of constructions. I. The word problem for partial algebras
Information and Computation
Confluence results for the pure strong categorical logic CCL. &lgr;-calculi as subsystems of CCL
Theoretical Computer Science
Abstract and concrete categories
Abstract and concrete categories
Categorical combinators, sequential algorithms, and functional programming (2nd ed.)
Categorical combinators, sequential algorithms, and functional programming (2nd ed.)
Eta-Expansions in Dependent Type Theory - The Calculus of Constructions
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
On the Power of Simple Diagrams
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Subtyping with Singleton Types
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
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We introduce a method of extending arbitrary categories by a terminal object and apply this method in various type theoretic settings. In particular, we show that categories that are cartesian closed except for the lack of a terminal object have a universal full extension to a cartesian closed category, and we characterize categories for which the latter category is a topos. Both the basic construction and its correctness proof are extremely simple. This is quite surprising in view of the fact that the corresponding results for the simply typed λ-calculus with surjective pairing, in particular concerning the decision problem for equality of terms in the presence of a terminal type, are comparatively involved.