The definition of extended ML: a gentle introduction
Theoretical Computer Science - Special issue: algebraic development techniques
Term rewriting and all that
ACM SIGSAM Bulletin - Special issue of OpenMath
A Skeptic’s Approach to Combining HOL and Maple
Journal of Automated Reasoning
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Dealing with algebraic expressions over a field in Coq using Maple
Journal of Symbolic Computation
Integrating multiple sources to answer questions in algebraic topology
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
Combining source, content, presentation, narration, and relational representation
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
Code generation via higher-order rewrite systems
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
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Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages and emphasize computation. Combining the complementary strengths of both approaches while mending their complementary weaknesses has been an important goal of the mechanized mathematics community for some time. We pick up on the idea of biform theories and interpret it in the MMT/OMDoc framework which introduced the foundations-as-theories approach, and can thus represent both logics and programming languages as theories. This yields a formal, modular framework of biform theory graphs which mixes specifications and implementations sharing the module system and typing information. We present automated knowledge management work flows that interface to existing specification/programming tools and enable an OPENMATH Machine, that operationalizes biform theories, evaluating expressions by exhaustively applying the implementations of the respective operators. We evaluate the new biform framework by adding implementations to the OPENMATH standard content dictionaries.