Theory Presentation Combinators

We motivate and give semantics to theory presentation combinators as the foundational building blocks for a scalable library of theories. The key observation is that the category of contexts and fibered categories are the ideal theoretical tools for this purpose.

💡 Research Summary

This paper introduces and defines the semantics of theory presentation combinators as foundational building blocks for a scalable library of theories. The authors emphasize that these combinators are designed to combine existing theories effectively, generating new ones in the process. They argue that this approach is crucial for managing complex theoretical structures efficiently. Central to their argument are categories of contexts and fibered categories, which they propose serve as ideal theoretical tools for this purpose. Fibered categories, in particular, offer a valuable means of integrating theories from various fields, leading to more efficient and scalable theoretical systems. The paper underscores the importance of these combinators in precisely expressing relationships between existing theories and handling complex theoretical structures effectively. This approach not only enhances the integration of diverse theories but also supports the development of comprehensive and adaptable theoretical frameworks that can be scaled across different domains.