Institutions: abstract model theory for specification and programming
Journal of the ACM (JACM)
Specification of abstract data types
Specification of abstract data types
Proof, language, and interaction
Theoretical Computer Science
Universal Algebra in Type Theory
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Locally Effective Objects and Artificial Intelligence
AISC '00 Revised Papers from the International Conference on Artificial Intelligence and Symbolic Computation
A Mechanized Proof of the Basic Perturbation Lemma
Journal of Automated Reasoning
Executing in Common Lisp, Proving in ACL2
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Towards Constructive Homological Algebra in Type Theory
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
ACL2 Verification of Simplicial Degeneracy Programs in the Kenzo System
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Developing the algebraic hierarchy with type classes in coq
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
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This work is an attempt to formalize, using the Coq proof assistant, the algebraic specification of the data structures appearing in two symbolic computation systems for algebraic topology called EAT and Kenzo. The specification of these structures have been obtained through an operation, called impoperation, between different specification frameworks as standard algebraic specifications and hidden specifications. Reusing previous Coq implementations of universal algebra and category theory we have proposed a Coq formalization of the impoperation, extending the representation to the particular hidden algebras which take part in this operation.