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Combining Higher-Order Logic with Set Theory Formalizations
Cezary Kaliszyk1,2, Karol Pąk3
1Department of Computer Science, University of Innsbruck, Innsbruck, Austria.
Journal of Automated Reasoning
|May 30, 2023
Summary
This study connects Isabelle/HOL and Isabelle/Mizar libraries by defining isomorphisms for core concepts like real numbers. This enables simultaneous theorem use and knowledge transfer between these foundational systems.
Area of Science:
- Formal methods
- Mathematical logic
- Computer science
Background:
- Isabelle/HOL and Isabelle/Mizar offer distinct foundational libraries.
- These libraries independently define basic concepts, leading to disconnected results.
- A unified approach is needed to leverage both formal systems.
Purpose of the Study:
- To align significant parts of the Isabelle/HOL and Isabelle/Mizar libraries.
- To establish isomorphisms between their independently defined concepts.
- To enable simultaneous use and transport of theorems between the two foundational systems.
Main Methods:
- Defining isomorphisms between key concepts in Isabelle/HOL and Isabelle/Mizar.
- Focusing on foundational elements such as real numbers and algebraic structures.
- Utilizing formal verification techniques within the Isabelle framework.
Main Results:
- Successful alignment of significant portions of the two libraries.
- Establishment of isomorphisms for concepts including real numbers and algebraic structures.
- Demonstration of theorem transportability between the foundations.
Conclusions:
- The defined isomorphisms bridge the gap between Isabelle/HOL and Isabelle/Mizar.
- This alignment allows for simultaneous utilization of results from both libraries.
- Enables enhanced knowledge sharing and theorem proving capabilities.
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