A logical foundation for session-based concurrent computation

Linear logic has long been heralded for its potential of providing a logical basis for concurrency. While over the years many research attempts were made in this regard, a Curry-Howard correspondence between linear logic and concurrent computation was only found recently, bridging the proof theory of linear logic and session-typed process calculus. Building upon this work, we have developed a theory of intuitionistic linear logic as a logical foundation for session-based concurrent computation, exploring several concurrency related phenomena such as value-dependent session types and polymorphic sessions within our logical framework in an arguably clean and elegant way, establishing with relative ease strong typing guarantees due to the logical basis, which ensure the fundamental properties of type preservation and global progress, entailing the absence of deadlocks in communication. We develop a general purpose concurrent programming language based on the logical interpretation, combining functional programming with a concurrent, session-based process layer through the form of a contextual monad, preserving our strong typing guarantees of type preservation and deadlock-freedom in the presence of general recursion and higher-order process communication. We introduce a notion of linear logical relations for session typed concurrent processes, developing an arguably uniform technique for reasoning about sophisticated properties of session-based concurrent computation such as termination or equivalence based on our logical approach, further supporting our goal of establishing intuitionistic linear logic as a logical foundation for sessionbased concurrency

Refinement kinds: type-safe programming with practical type-level computation

UID/CEC/04516/2019 PTDC/EEICTP/4293/2014This work introduces the novel concept of kind refinement, which we develop in the context of an explicitly polymorphic ML-like language with type-level computation. Just as type refinements embed rich specifications by means of comprehension principles expressed by predicates over values in the type domain, kind refinements provide rich kind specifications by means of predicates over types in the kind domain. By leveraging our powerful refinement kind discipline, types in our language are not just used to statically classify program expressions and values, but also conveniently manipulated as tree-like data structures, with their kinds refined by logical constraints on such structures. Remarkably, the resulting typing and kinding disciplines allow for powerful forms of type reflection, ad-hoc polymorphism and type-directed meta-programming, which are often found in modern software development, but not typically expressible in a type-safe manner in general purpose languages. We validate our approach both formally and pragmatically by establishing the standard meta-theoretical results of type safety and via a prototype implementation of a kind checker, type checker and interpreter for our language.publishersversionpublishe

A Logic and Tool for Local Reasoning about Security Protocols

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia InformáticaThis thesis tackles the problem of developing a formal logic and associated model-checking techniques to verify security properties, and its integration in the Spatial Logic Model Checker(SLMC) tool. In the areas of distributed system design and analysis, there exists a substantial amount of work related to the verification of correctness properties of systems, in which the work aimed at the verification of security properties mostly relies on precise yet informal methods of reasoning. This work follows a line of research that applies formal methodologies to the verification of security properties in distributed systems, using formal tools originally developed for the study of concurrent and distributed systems in general. Over the years, several authors have proposed spatial logics for local and compositional reasoning about algebraic models of distributed systems known as process calculi. In this work, we present a simplification of a process calculus known as the Applied - calculus, introduced by Abadi and Fournet, designed for the study of security protocols. We then develop a spatial logic for this calculus, extended with knowledge modalities, aimed at reasoning about security protocols using the concept of local knowledge of processes. Furthermore, we conclude that the extensions are sound and complete regarding their intended semantics and that they preserve decidability, under reasonable assumptions. We also present a model-checking algorithm and the proof of its completeness for a large class of processes. Finally, we present an OCaml implementation of the algorithm, integrated in the Spatial Logic Model Checker tool, developed by Hugo Vieira and Luis Caires, thus producing the first tool for security protocol analysis that employs spatial logics