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Fast Tacticbased Theorem Proving
 TPHOLs 2000, LNCS 1869
, 2000
"... Theorem provers for higherorder logics often use tactics to implement automated proof search. Tactics use a generalpurpose metalanguage to implement both generalpurpose reasoning and computationally intensive domainspecific proof procedures. The generality of tactic provers has a performance pe ..."
Abstract

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Theorem provers for higherorder logics often use tactics to implement automated proof search. Tactics use a generalpurpose metalanguage to implement both generalpurpose reasoning and computationally intensive domainspecific proof procedures. The generality of tactic provers has a performance penalty; the speed of proof search lags far behind specialpurpose provers. We present a new modular proving architecture that significantly increases the speed of the core logic engine.
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.
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...