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The Open Calculus of Constructions: An Equational Type Theory with Dependent Types for Programming, Specification, and Interactive Theorem Proving
"... The open calculus of constructions integrates key features of MartinLöf's type theory, the calculus of constructions, Membership Equational Logic, and Rewriting Logic into a single uniform language. The two key ingredients are dependent function types and conditional rewriting modulo equational t ..."
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The open calculus of constructions integrates key features of MartinLöf's type theory, the calculus of constructions, Membership Equational Logic, and Rewriting Logic into a single uniform language. The two key ingredients are dependent function types and conditional rewriting modulo equational theories. We explore the open calculus of constructions as a uniform framework for programming, specification and interactive verification in an equational higherorder style. By having equational logic and rewriting logic as executable sublogics we preserve the advantages of a firstorder semantic and logical framework and especially target applications involving symbolic computation and symbolic execution of nondeterministic and concurrent systems.
An executable formalization of the HOL/Nuprl connection in the metalogical framework Twelf
 In Geoff Sutcliffe and Andrei Voronkov, editors, Proceedings of Logic for Programming, Artificial Intelligence, and Reasoning (LPAR), Montego
, 2005
"... Abstract. Howe’s HOL/Nuprl connection is an interesting example of a translation between two fundamentally different logics, namely a typed higherorder logic and a polymorphic extensional type theory. In earlier work we have established a prooftheoretic correctness result of the translation in a w ..."
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Abstract. Howe’s HOL/Nuprl connection is an interesting example of a translation between two fundamentally different logics, namely a typed higherorder logic and a polymorphic extensional type theory. In earlier work we have established a prooftheoretic correctness result of the translation in a way that complements Howe’s semanticsbased justification and furthermore goes beyond the original HOL/Nuprl connection by providing the foundation for a proof translator. Using the Twelf logical framework, the present paper goes one step further. It presents the first rigorous formalization of this treatment in a logical framework, and hence provides a safe alternative to the translation of proofs. 1
An interpretation of isabelle/hol in hol light
 In Furbach and Shankar [20
"... Abstract. We define an interpretation of the Isabelle/HOL logic in HOL Light and its metalanguage, OCaml. Some aspects of the Isabelle logic are not representable directly in the HOL Light object logic. The interpretation thus takes the form of a set of elaboration rules, where features of the Isabe ..."
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Cited by 2 (1 self)
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Abstract. We define an interpretation of the Isabelle/HOL logic in HOL Light and its metalanguage, OCaml. Some aspects of the Isabelle logic are not representable directly in the HOL Light object logic. The interpretation thus takes the form of a set of elaboration rules, where features of the Isabelle logic that cannot be represented directly are elaborated to functors in OCaml. We demonstrate the effectiveness of the interpretation via an implementation, translating a significant part of the Isabelle standard library into HOL Light. 1