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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 ..."
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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.
Hierarchical Reflection
"... Abstract. The technique of reflection is a way to automate proof construction in type theoretical proof assistants. Reflection is based on the definition of a type of syntactic expressions that gets interpreted in the domain of discourse. By allowing the interpretation function to be partial or even ..."
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Cited by 3 (3 self)
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Abstract. The technique of reflection is a way to automate proof construction in type theoretical proof assistants. Reflection is based on the definition of a type of syntactic expressions that gets interpreted in the domain of discourse. By allowing the interpretation function to be partial or even a relation one gets a more general method known as ``partial reflection''. In this paper we show how one can take advantage of the partiality of the interpretation to uniformly define a family of tactics for equational reasoning that will work in different algebraic structures. The tactics then follow the hierarchy of those algebraic structures in a natural way.
Formal Design Environments
 International Conference on Theorem Proving in Higher Order Logics (TPHOLs), 2002. Appears in NASA technical report NASA
, 2002
"... We present the design of a formal integrated design environment. The longterm goal of this effort is to allow seamless interaction between software production tools and formal design and analysis tools, especially between compilers and higherorder theorem provers. The work in this report is the in ..."
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We present the design of a formal integrated design environment. The longterm goal of this effort is to allow seamless interaction between software production tools and formal design and analysis tools, especially between compilers and higherorder theorem provers. The work in this report is the initial design and architecture for integration of 1) the MetaPRL logical framework, 2) a multilanguage compiler we call Mojave, and 3) a generic extensible parser we call Phobos. The integration is currently performed at the level of the Mojave functional intermediate representation, allowing the use of the theorem prover for program analysis, transformation, and optimization.
Tacticbased modeling of cognitive inference on logically structured notation
, 2000
"... Computational (algorithmic) models of highlevel cognitive inference tasks such as logical inference, mathematical inference, and decision making can have both theoretical and practical impact. They can improve our theoretical understanding of how people think and also provide practical direction f ..."
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Cited by 1 (1 self)
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Computational (algorithmic) models of highlevel cognitive inference tasks such as logical inference, mathematical inference, and decision making can have both theoretical and practical impact. They can improve our theoretical understanding of how people think and also provide practical direction for applications such as automated reasoning systems, systems attuned to userinteraction in decisioncritical environments, and computeraided education. To support those benets, cognitive models need to be detailed, compositional, based in wellunderstood mathematics, and, to whatever extent possible, descriptively accurate. We introduce a new, interdisciplinary approach that could be used to develop cognitive models of highlevel inference with these properties. Two signicant aspects of this approach are tactics and eyetracking methods. Tactics are used to express highlevel inferences in fully formalized mathematics for automated theorem proving systems; eyetracking methods provide insight into realtime and microcognitive information processing by permitting
Reflection and PropositionsasTypes
"... Reection is the ability of a deductive system to internalize aspects of its own structure and thereby reason to some extent about itself. In this paper we present a theoretical framework for exploring reection in type theories that use the \PropositionsasTypes" principle, such as MartinL ..."
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Reection is the ability of a deductive system to internalize aspects of its own structure and thereby reason to some extent about itself. In this paper we present a theoretical framework for exploring reection in type theories that use the \PropositionsasTypes" principle, such as MartinLof style theories. One of the main results is that it is unnecessary to build a complete Godel style \reection" layer on top of the logical theory. This makes it possible to use our framework for an ecient implementation of reection in theorem provers for such type theories. We are doing this for the NuPRL and MetaPRL systems.