Introduction to higher order categorical logic
Introduction to higher order categorical logic
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The geometry of optimal lambda reduction
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Algebra of programming
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Some Lambda Calculi with Categorial Sums and Products
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
Normalization by Evaluation for Typed Lambda Calculus with Coproducts
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
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In this paper we give a graph-based decision procedure for a calculus with sum and product types. Although our motivation comes from the Bird-Meertens approach to reasoning algebraically about functional programs, the language used here can be seen as the internal language of a category with binary products and coproducts. As such, the decision procedure presented has independent interest. A standard approach based on term rewriting would work modulo a set of equations; the present work proposes a simpler approach, based on graph-rewriting. We show in turn how the system covers reflection equational laws, fusion laws, and cancellation laws.