Algorithmic algebra
IMPS: an interactive mathematical proof system
Journal of Automated Reasoning
A Skeptic’s Approach to Combining HOL and Maple
Journal of Automated Reasoning
Type Classes and Overloading in Higher-Order Logic
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
Locales - A Sectioning Concept for Isabelle
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Organizing Numerical Theories Using Axiomatic Type Classes
Journal of Automated Reasoning
Dealing with algebraic expressions over a field in Coq using Maple
Journal of Symbolic Computation
Constructive type classes in Isabelle
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Interpretation of locales in isabelle: theories and proof contexts
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
Verifying and reflecting quantifier elimination for presburger arithmetic
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Verifying mixed real-integer quantifier elimination
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Proving equalities in a commutative ring done right in coq
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Parametric Linear Arithmetic over Ordered Fields in Isabelle/HOL
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Local Theory Specifications in Isabelle/Isar
Types for Proofs and Programs
Reasoning about memory layouts
Formal Methods in System Design
Proof certificates for algebra and their application to automatic geometry theorem proving
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
Journal of Automated Reasoning
Formalization of wu's simple method in coq
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
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We address some aspects of a system architecture for mathematical assistants that integrates calculations and deductions by common infrastructure within the Isabelle theorem proving environment. Here calculations may refer to arbitrary extra-logical mechanisms, operating on the syntactic structure of logical statements. Deductions are devoid of any computational content, but driven by procedures external to the logic, following to the traditional "LCF system approach". The latter is extended towards explicit dependency on abstract theory contexts, with separate mechanisms to interpret both logical and extra-logical content uniformly. Thus we are able to implement proof methods that operate on abstract theories and a range of particular theory interpretations. Our approach is demonstrated in Isabelle/HOL by a proof-procedure for generic ring equalities via Gröbner Bases.