Computational category theory
The foundation of a generic theorem prover
Journal of Automated Reasoning
Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Categories, types, and structures: an introduction to category theory for the working computer scientist
Handbook of logic in computer science (vol. 2)
Category theory for computing science, 2nd ed.
Category theory for computing science, 2nd ed.
Extracting a Proof of Coherence for Monoidal Categories from a Proof of Normalization for Monoids
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
Proceedings of the 6th ACM SIGPLAN workshop on Generic programming
Towards a categorical foundation for generic programming
Proceedings of the seventh ACM SIGPLAN workshop on Generic programming
Kan extensions for program optimisation or: art and dan explain an old trick
MPC'12 Proceedings of the 11th international conference on Mathematics of Program Construction
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A calculus for a fragment of category theory is presented. The types in the language denote categories and the expressions functors. The judgements of the calculus systematise categorical arguments such as: an expression is functorial in its free variables; two expressions are naturally isomorphic in their free variables. There are special binders for limits and more general ends. The rules for limits and ends support an algebraic manipulation of universal constructions as opposed to a more traditional diagrammatic approach. Duality within the calculus and applications in proving continuity are discussed with examples. The calculus gives a basis for mechanising a theory of categories in a generic theorem prover like Isabelle.