Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
A higher-order calculus and theory abstraction
Information and Computation
Larch: languages and tools for formal specification
Larch: languages and tools for formal specification
IMPS: an interactive mathematical proof system
Journal of Automated Reasoning
Using dependent types to express modular structure
POPL '86 Proceedings of the 13th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A Formal Proof of Sylow‘s Theorem
Journal of Automated Reasoning
Object-Oriented Verification Based on Record Subtyping in Higher-Order Logic
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
CAAP '83 Proceedings of the 8th Colloquium on Trees in Algebra and Programming
Locales - A Sectioning Concept for Isabelle
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Dependently Typed Records for Representing Mathematical Structure
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
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This paper describes a method of representing algebraic structures in the theorem prover Isabelle. We use Isabelle's higher order logic extended with set theoretic constructions. Dependent types, constructed as HOL sets, are used to represent modular structures by semantical embedding. The modules remain first class citizen of the logic. Hence, they enable adequate formalization of abstract algebraic structures and a natural proof style. Application examples drawn from abstract algebra and lattice theory -- the full version of Tarski's fixpoint theorem -- validate the concept.