Abstract. LEO-II is a standalone, resolution-based higher-order theorem prover designed for effective cooperation with specialist provers for natural fragments of higher-order logic. At present LEO-II can cooperate with the first-order automated theorem provers E, SPASS, and Vampire. The improved performance of LEO-II, especially in comparison to its predecessor LEO, is due to several novel features including the exploitation of term sharing and term indexing techniques, support for primitive equality reasoning, and improved heuristics at the calculus level. LEO-II is implemented in Objective Caml and its problem representation language is the new TPTP THF language. 1

Abstract. Leo-II, a resolution based theorem prover for classical higherorder logic, is currently being developed in a one year research project at the University of Cambridge, UK, with support from Saarland University, Germany. We report on the current stage of development of Leo-II. In particular, we sketch some main aspects of Leo-II’s automated proof search procedure, discuss its cooperation with first-order specialist provers, show that Leo-II is also an interactive proof assistant, and explain its shared term data structure and its term indexing mechanism. 1

We report on work in progress regarding a foundation for the notion of meta-variable in logical frameworks and type theories. Our proposal is to treat meta-variables as modal variables in a modal type theory, which is logically clean and justifies several low-level implementation techniques for meta-variables. We also speculate on other logical extensions of our modal type theory, at present without clear applications.

Abstract. We instrument a higher-order logic programming search procedure to generate and check small proof witnesses for the Twelf system, an implementation of the logical framework LF. In particular, we extend and generalize ideas from Necula and Rahul [16] in two main ways: 1) We consider the full fragment of LF including dependent types and higher-order terms and 2) We study the use of caching of sub-proofs to further compact proof representations. Our experimental results demonstrate that many of the restrictions in previous work can be overcome and generating and checking small witnesses within Twelf provides valuable addition to its general safety infrastructure. 1

LEO-II, a resolution based theorem prover for classical higher-order logic, is currently being developed in a one year

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We present a new term indexing approach which shall support efficient automated theorem proving in classical higher order logic. Key features of our indexing method are a shared representation of terms, the use of partial syntax trees to speedup logical computations and indexing of subterm occurrences. For the implementation of explicit substitutions, additional support is offered by indexing of bound variable occurrences. A preliminary evaluation of our approach shows some encouraging first results. 1

A logical framework is a general meta-language for specifying and implementing de-ductive systems, given by axioms and inference rules. Examples of deductive systems are plentiful in computer science. In computer security, we find authentication and security logics to describe access and security criteria. In programming languages, we use deductive systems to specify the operational semantics, type-systems or other as-pects of the run-time behavior of programs. Recently, one major application of logical frameworks has been in the area of “certified code”. To provide guarantees about the behavior of mobile code, safety properties are expressed as deductive systems. The code producer then verifies the program according to some predetermined safety pol-icy, and supplies a binary executable together with its safety proof (certificate). Before executing the program, the host machine then quickly checks the code’s safety proof against the binary. The safety policy and the safety proofs can be expressed in the logical framework thereby providing a general safety infrastructure. There are two main variants of logical frameworks which are specifically designed to support the implementation of deductive systems. λProlog and Isabelle are based