SAT-Inspired Higher-Order Eliminations

We generalize several propositional preprocessing techniques to higher-orderlogic, building on existing first-order generalizations. These techniqueseliminate literals, clauses, or predicate symbols from the problem, with theaim of making it more amenable to automatic proof search. We also introduce anew technique, which we call quasipure literal elimination, that strictlysubsumes pure literal elimination. The new techniques are implemented in theZipperposition theorem prover. Our evaluation shows that they sometimes helpprove problems originating from the TPTP library and Isabelle formalizations.<br

A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014

Extending a Brainiac Prover to Lambda-Free Higher-Order Logic

International audienceDecades of work have gone into developing efficient proof calculi, data structures, algorithms, and heuristics for first-order automatic theorem proving. Higher-order provers lag behind in terms of efficiency. Instead of developing a new higher-order prover from the ground up, we propose to start with the state-of-the-art superposition prover E and gradually enrich it with higher-order features. We explain how to extend the prover’s data structures, algorithms, and heuristics to $$\lambda$$ λ -free higher-order logic, a formalism that supports partial application and applied variables. Our extension outperforms the traditional encoding and appears promising as a stepping stone toward full higher-order logic

A NLTE model atmosphere analysis of the pulsating sdO star SDSS J1600+0748

We started a program to construct several grids of suitable model atmospheres and synthetic spectra for hot subdwarf O stars computed, for comparative purposes, in LTE, NLTE, with and without metals. For the moment, we use our grids to perform fits on our spectrum of SDSS J160043.6+074802.9 (J1600+0748 for short), this unique pulsating sdO star. Our best fit is currently obtained with NLTE model atmospheres including carbon, nitrogen and oxygen in solar abundances, which leads to the following parameters for SDSS J1600+0748 : Teff = 69 060 +/- 2080 K, log g = 6.00 +/- 0.09 and log N(He)/N(H) = -0.61 +/- 0.06. Improvements are needed, however, particularly for fitting the available He II lines. It is hoped that the inclusion of Fe will help remedy the situation.Comment: 4 pages, 4 figures, accepted in Astrophysics and Space Science (24/02/2010), Special issue Hot sudbwarf star

Superposition for Full Higher-order Logic

International audienceWe recently designed two calculi as stepping stones towards superposition for full higher-order logic: Boolean-free $\lambda$-superposition and superposition for first-order logic with interpreted Booleans. Stepping on these stones, we finally reach a sound and refutationally complete calculus for higher-order logic with polymorphism, extensionality, Hilbert choice, and Henkin semantics. In addition to the complexity of combining the calculus’s two predecessors, new challenges arise from the interplay between $\lambda$-terms and Booleans. Our implementation in Zipperposition outperforms all other higher-order theorem provers and is on a par with an earlier, pragmatic prototype of Booleans in Zipperposition

A Proof Strategy Language and Proof Script Generation for Isabelle/HOL

We introduce a language, PSL, designed to capture high level proof strategies in Isabelle/HOL. Given a strategy and a proof obligation, PSL's runtime system generates and combines various tactics to explore a large search space with low memory usage. Upon success, PSL generates an efficient proof script, which bypasses a large part of the proof search. We also present PSL's monadic interpreter to show that the underlying idea of PSL is transferable to other ITPs.Comment: This paper has been submitted to CADE2

Superposition with Lambdas

We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on βη-equivalence classes of λ-terms and rely on higher-order unification to achieve refutational completeness. We implemented the calculus in the Zipperposition prover and evaluated it on TPTP and Isabelle benchmarks. The results suggest that superposition is a suitable basis for higher-order reasoning