Operational reasoning for functions with local state
Higher order operational techniques in semantics
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
A very modal model of a modern, major, general type system
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The impact of higher-order state and control effects on local relational reasoning
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Step-indexed kripke models over recursive worlds
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Forcing as a Program Transformation
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
First Steps in Synthetic Guarded Domain Theory: Step-Indexing in the Topos of Trees
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
Extensionality in the calculus of constructions
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
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This paper presents an intuitionistic forcing translation for the Calculus of Constructions (CoC), a translation that corresponds to an internalization of the presheaf construction in CoC. Depending on the chosen set of forcing conditions, the resulting type theory can be extended with extra logical principles. The translation is proven correct---in the sense that it preserves type checking---and has been implemented in Coq. As a case study, we show how the forcing translation on integers (which corresponds to the internalization of the topos of trees) allows us to define general inductive types in Coq, without the strict positivity condition. Using such general inductive types, we can construct a shallow embedding of the pure lambda-calculus in Coq, without defining an axiom on the existence of an universal domain. We also build another forcing layer where we prove the negation of the continuum hypothesis.