Theorem provers for higher-order logics often use tactics to implement automated proof search. Tactics use a general-purpose meta-language to implement both general-purpose reasoning and computationally intensive domain-specific proof procedures. The generality of tactic provers has a performance penalty; the speed of proof search lags far behind special-purpose provers. We present a new modular proving architecture that significantly increases the speed of the core logic engine.

We present the design of a formal integrated design environment. The long-term goal of this effort is to allow seamless interaction between software production tools and formal design and analysis tools, especially between compilers and higher-order 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.

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.

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 \Propositions-as-Types" principle, such as Martin-Lof 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.