Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Synchronous Kleene algebra

AbstractThe work presented here investigates the combination of Kleene algebra with the synchrony model of concurrency from Milner’s SCCS calculus. The resulting algebraic structure is called synchronous Kleene algebra. Models are given in terms of sets of synchronous strings and finite automata accepting synchronous strings. The extension of synchronous Kleene algebra with Boolean tests is presented together with models on sets of guarded synchronous strings and the associated automata on guarded synchronous strings. Completeness w.r.t. the standard interpretations is given for each of the two new formalisms. Decidability follows from completeness. Kleene algebra with synchrony should be included in the class of true concurrency models. In this direction, a comparison with Mazurkiewicz traces is made which yields their incomparability with synchronous Kleene algebras (one cannot simulate the other). On the other hand, we isolate a class of pomsets which captures exactly synchronous Kleene algebras. We present an application to Hoare-like reasoning about parallel programs in the style of synchrony

ULTRA - A Logic Transaction Programming Language

Rule-based language for the specification of complex database updates and transactions. Formal treatment of the syntax and the declarative semanticsRegelbasierte Sprache zur Spezifikation komplexer Datenbank-Operationen und Transaktionen. Formle Behandlung von Syntax und deklarativer Semantik

Probabilistic Rely-guarantee Calculus

Jones' rely-guarantee calculus for shared variable concurrency is extended to include probabilistic behaviours. We use an algebraic approach which combines and adapts probabilistic Kleene algebras with concurrent Kleene algebra. Soundness of the algebra is shown relative to a general probabilistic event structure semantics. The main contribution of this paper is a collection of rely-guarantee rules built on top of that semantics. In particular, we show how to obtain bounds on probabilities by deriving rely-guarantee rules within the true-concurrent denotational semantics. The use of these rules is illustrated by a detailed verification of a simple probabilistic concurrent program: a faulty Eratosthenes sieve.Comment: Preprint submitted to TCS-QAP

Partial orders and fully abstract models for concurrency

In this thesis sets of labelled partial orders are employed as fundamental mathematical entities for modelling nondeterministic and concurrent processes thereby obtaining so-called noninterleaving semantics. Based on different closures of sets of labelled partial orders, simple algebraic languages are given denotational models fully abstract w.r.t. corresponding behaviourally motivated equivalences. Some of the equivalences are accompanied by adequate logics and sound axiomatisations of which one is complete

Stone-Type Dualities for Separation Logics

Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence, yielding a framework through which both algebraic and topological methods can be brought to bear on a logic. We give a systematic treatment of Stone-type duality for the structures that interpret bunched logics, starting with the weakest systems, recovering the familiar BI and Boolean BI (BBI), and extending to both classical and intuitionistic Separation Logic. We demonstrate the uniformity and modularity of this analysis by additionally capturing the bunched logics obtained by extending BI and BBI with modalities and multiplicative connectives corresponding to disjunction, negation and falsum. This includes the logic of separating modalities (LSM), De Morgan BI (DMBI), Classical BI (CBI), and the sub-classical family of logics extending Bi-intuitionistic (B)BI (Bi(B)BI). We additionally obtain as corollaries soundness and completeness theorems for the specific Kripke-style models of these logics as presented in the literature: for DMBI, the sub-classical logics extending BiBI and a new bunched logic, Concurrent Kleene BI (connecting our work to Concurrent Separation Logic), this is the first time soundness and completeness theorems have been proved. We thus obtain a comprehensive semantic account of the multiplicative variants of all standard propositional connectives in the bunched logic setting. This approach synthesises a variety of techniques from modal, substructural and categorical logic and contextualizes the "resource semantics" interpretation underpinning Separation Logic amongst them

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Pomset logic: a logical and grammatical alternative to the Lambek calculus

Thirty years ago, I introduced a non commutative variant of classical linear logic, called POMSET LOGIC, issued from a particular denotational semantics or categorical interpretation of linear logic known as coherence spaces. In addition to the multiplicative connectives of linear logic, pomset logic includes a non-commutative connective, "$<$" called BEFORE, which is associative and self-dual: $(A<B)^\perp=A^\perp < B^\perp$ (observe that there is no swapping), and pomset logic handles Partially Ordered MultiSETs of formulas. This classical calculus enjoys a proof net calculus, cut-elimination, denotational semantics, but had no sequent calculus, despite my many attempts and the study of closely related deductive systems like the calculus of structures. At the same period, Alain Lecomte introduced me to Lambek calculus and grammars. We defined a grammatical formalism based on pomset logic, with partial proof nets as the deductive systems for parsing-as-deduction, with a lexicon mapping words to partial proof nets. The study of pomset logic and of its grammatical applications has been out of the limelight for several years, in part because computational linguists were not too keen on proof nets. However, recently Sergey Slavnov found a sequent calculus for pomset logic, and reopened the study of pomset logic. In this paper we shall present pomset logic including both published and unpublished material. Just as for Lambek calculus, Pomset logic also is a non commutative variant of linear logic --- although Lambek calculus appeared 30 years before linear logic ! --- and as in Lambek calculus it may be used as a grammar. Apart from this the two calculi are quite different, but perhaps the algebraic presentation we give here, with terms and the semantic correctness criterion, is closer to Lambek's view

Programming Languages and Systems

This open access book constitutes the proceedings of the 31st European Symposium on Programming, ESOP 2022, which was held during April 5-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 21 regular papers presented in this volume were carefully reviewed and selected from 64 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems