A comparative study of two formal semantics of the SIGNAL language

International audienceSIGNAL is a part of the synchronous languages family, which are broadly used in the design of safety-critical real-time systems such as avionics, space systems, and nuclear power plants. There exist several semantics for SIGNAL, such as denotational semantics based on traces (called trace semantics), denotational semantics based on tags (called tagged model semantics), operational semantics presented by structural style through an inductive definition of the set of possible transitions, operational semantics defined by synchronous transition systems (STS), etc. However, there is little research about the equivalence between these semantics.In this work, we would like to prove the equivalence between the trace semantics and the tagged model semantics, to get a determined and precise semantics of the SIGNAL language. These two semantics have several different definitions respectively, we select appropriate ones and mechanize them in the Coq platform, the Coq expressions of the abstract syntax of SIGNAL and the two semantics domains, i.e., the trace model and the tagged model, are also given. The distance between these two semantics discourages a direct proof of equivalence. Instead, we transformthem to an intermediate model, which mixes the features of both the trace semantics and the tagged model semantics. Finally, we get a determined and precise semantics of SIGNAL

Proof Contexts with Late Binding

The focal language (formerly Foc) allows one to incrementally build modules and to prove formally their correctness. focal encourages a development process by refinement, deriving step-by-step implementations from specifications. This refinement process is realized using an inheritance mechanism on structures which can mix primitive operations, axioms, algorithms and proofs. Inheriting from existing structures allows to reuse their components under some conditions, statically checked by the compiler. This paper presents two formal semantics for encoding focal constructions in the Coq proof assistant. The first one is a shallow embedding which gives a practical way to use Coq to check proofs in focal libraries. The second one formalizes the focal structures as Coq types (called mixDrecs) and shows that the informal semantics of focal libraries is coherent with respect to Coq logic. In the last part of the paper, we prove that the first embedding is conform to the mixDrecs model

Modified (PNA, 2'-O-methyl and phosphoramidate) anti-TAR antisense oligonucleotides as strong and specific inhibitors of in vitro HIV-1 reverse transcription.

Natural beta-phosphodiester 16mer and 15mer antisense oligonucleotides targeted against the HIV-1 and HIV-2 TAR RNAs respectively were previously described as sequence-specific inhibitors of in vitro retroviral reverse transcription. In this work, we tested chemically modified oligonucleotide analogues: alpha-phosphodiester, phosphorothioate, methylphosphonate, peptide nucleic acid or PNA, 2'- o -methyl and (N3'-P5') phosphoramidate versions of the 16mer anti-TAR oligonucleotide. PNA, 2'- O -methyl and (N3'-P5') phosphoramidate oligomers showed a strong inhibitory effect compared with the unmodified 16mer, with reverse transcription inhibition (IC50) values in the nanomolar range. The inhibition was sequence-specific, as scrambled and mismatched control oligonucleotides were not able to inhibit cDNA synthesis. No direct binding of the 2'- O -methyl, PNA or (N3'-P5') phosphoramidate anti-TAR oligonucleotides to the HIV-1 reverse transcriptase was observed. The higher T m obtained with 2'- O -methyl, (N3'-P5') phosphoramidate and PNA molecules concerning the annealing with the stem-loop structure of the TAR RNA, in comparison with the beta-phosphodiester oligonucleotides, is correlated with their high inhibitory effect on reverse transcription

A Mechanized Theory of Program Refinement

International audienceWe present a mechanized theory of program refinement that allows for the stepwise development of imperative programs in the Coq proof assistant. We formalize a design language with support for gradual refinement and a calculus which enforces correctness-by-construction. A notion of program design captures the hierarchy of refinement steps resulting from a development. The underlying theory follows the predicative programming paradigm where programs and specifications are both easily expressed as predicates, which fit naturally in the dependent type theory of the proof assistant