Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Computational category theory
Category theory for computing science
Category theory for computing science
Topology and category theory in computer science
Topology and category theory in computer science
Building reliable, high-performance communication systems from components
Proceedings of the seventeenth ACM symposium on Operating systems principles
A Proof Environment for the Development of Group Communication Systems
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
The Nuprl Open Logical Environment
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Building reliable, high-performance networks with the Nuprl proof development system
Journal of Functional Programming
Automating proofs in category theory
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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We describe the construction of a semi-automated proof system for elementary category theory using the Nuprl proof development system as logical framework. We have used Nuprl's display mechanism to implement the basic vocabulary and Nuprl's rule compiler to implemented a first-order proof calculus for reasoning about categories, functors and natural transformations. To automate proofs we have formalized both standard techniques from automated theorem proving and reasoning patterns that are specific to category theory and used Nuprl's tactic mechanism for the actual implementation. We illustrate our approach by automating proofs of natural isomorphisms between categories.