Interactive Simplifier Tracing and Debugging in Isabelle

The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not in the form the user expected, or the simplifier fails to apply a rule. We describe a new, interactive tracing facility which offers insight into the hierarchical structure of the simplification with user-defined filtering, memoization and search. The new simplifier trace is integrated into the Isabelle/jEdit Prover IDE.Comment: Conferences on Intelligent Computer Mathematics, 201

Concrete Semantics with Coq and CoqHammer

The "Concrete Semantics" book gives an introduction to imperative programming languages accompanied by an Isabelle/HOL formalization. In this paper we discuss a re-formalization of the book using the Coq proof assistant. In order to achieve a similar brevity of the formal text we extensively use CoqHammer, as well as Coq Ltac-level automation. We compare the formalization efficiency, compactness, and the readability of the proof scripts originating from a Coq re-formalization of two chapters from the book

ENIGMA: Efficient Learning-based Inference Guiding Machine

ENIGMA is a learning-based method for guiding given clause selection in saturation-based theorem provers. Clauses from many proof searches are classified as positive and negative based on their participation in the proofs. An efficient classification model is trained on this data, using fast feature-based characterization of the clauses . The learned model is then tightly linked with the core prover and used as a basis of a new parameterized evaluation heuristic that provides fast ranking of all generated clauses. The approach is evaluated on the E prover and the CASC 2016 AIM benchmark, showing a large increase of E's performance.Comment: Submitted to LPAR 201

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

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

A formalized general theory of syntax with bindings

We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying numbers of inputs, quotiented to alpha-equivalence and sorted according to a binding signature. The theory includes a rich collection of properties of the standard operators on terms, such as substitution and freshness. It also includes induction and recursion principles and support for semantic interpretation, all tailored for smooth interaction with the bindings and the standard operators

The Human Adenovirus Type 5 E4orf6/E1B55K E3 Ubiquitin Ligase Complex Enhances E1A Functional Activity

Human adenovirus (Ad) E1A proteins have long been known as the central regulators of virus infection as well as the major source of adenovirus oncogenic potential. Not only do they activate expression of other early viral genes, they make viral replication possible in terminally differentiated cells, at least in part, by binding to the retinoblastoma (Rb) tumor suppressor family of proteins to activate E2F transcription factors and thus viral and cellular DNA synthesis. We demonstrate in an accompanying article (F. Dallaire et al., mSphere 1:00014-15, 2016) that the human adenovirus E3 ubiquitin ligase complex formed by the E4orf6 and E1B55K proteins is able to mimic E1A activation of E2F transactivation factors. Acting alone in the absence of E1A, the Ad5 E4orf6 protein in complex with E1B55K was shown to bind E2F, disrupt E2F/Rb complexes, and induce hyperphosphorylation of Rb, leading to induction of viral and cellular DNA synthesis, as well as stimulation of early and late viral gene expression and production of viral progeny. While these activities were significantly lower than those exhibited by E1A, we report here that this ligase complex appeared to enhance E1A activity in two ways. First, the E4orf6/E1B55K complex was shown to stabilize E1A proteins, leading to higher levels in infected cells. Second, the complex was demonstrated to enhance the activation of E2F by E1A products. These findings indicated a new role of the E4orf6/E1B55K ligase complex in promoting adenovirus replication

Witnessing (co)datatypes

Datatypes and codatatypes are useful for specifying and reasoning about (possibly infinite) computational processes. The Isabelle/HOL proof assistant has recently been extended with a definitional package that supports both. We describe a complete procedure for deriving nonemptiness witnesses in the general mutually recursive, nested case—nonemptiness being a proviso for introducing types in higher-order logic

Efficient Certified RAT Verification

Clausal proofs have become a popular approach to validate the results of SAT solvers. However, validating clausal proofs in the most widely supported format (DRAT) is expensive even in highly optimized implementations. We present a new format, called LRAT, which extends the DRAT format with hints that facilitate a simple and fast validation algorithm. Checking validity of LRAT proofs can be implemented using trusted systems such as the languages supported by theorem provers. We demonstrate this by implementing two certified LRAT checkers, one in Coq and one in ACL2

Sharing HOL4 and HOL Light proof knowledge

New proof assistant developments often involve concepts similar to already formalized ones. When proving their properties, a human can often take inspiration from the existing formalized proofs available in other provers or libraries. In this paper we propose and evaluate a number of methods, which strengthen proof automation by learning from proof libraries of different provers. Certain conjectures can be proved directly from the dependencies induced by similar proofs in the other library. Even if exact correspondences are not found, learning-reasoning systems can make use of the association between proved theorems and their characteristics to predict the relevant premises. Such external help can be further combined with internal advice. We evaluate the proposed knowledge-sharing methods by reproving the HOL Light and HOL4 standard libraries. The learning-reasoning system HOL(y)Hammer, whose single best strategy could automatically find proofs for 30% of the HOL Light problems, can prove 40% with the knowledge from HOL4