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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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Cited by 5 (0 self)
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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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Cited by 2 (2 self)
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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 Executable Formalization of the HOL/Nuprl Connection
 in the Metalogical Framework Twelf. LPAR 2004
"... 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 ..."
Abstract

Cited by 1 (0 self)
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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
Explanation and Justification of Proposed Expenditures
"... Syntax. Proving properties of programming languages, for example type soundness, can involve enormous amounts of detailed formal reasoning. Theorem provers can be advantageous for this kind of task. Properties like these involve formalizing the abstract syntax of the programming language in the logi ..."
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Syntax. Proving properties of programming languages, for example type soundness, can involve enormous amounts of detailed formal reasoning. Theorem provers can be advantageous for this kind of task. Properties like these involve formalizing the abstract syntax of the programming language in the logic of the prover. Conventional formalizations of variablebinding have turned out to be unwieldy in practice, and so there has been a great deal of interest in a higher order representation of syntax [8], where functions in the logic are used to represent binding. It is currently an open problem to find a tractable way to do this that also allows structural induction over abstract syntax. We will investigate using a logic like IOC for this. We will exploit the idea of parametricity and will adapt ideas from, e.g. [4]. Reflection. Reflecting the logic of a theorem prover in itself has appealing applications to automated reasoning. Some of these are outlined in [1], where we describe a useful r...