26 research outputs found
A Generalisation of Pre-Logical Predicates and Its Applications
This thesis proposes a generalisation of pre-logical predicates to
simply typed formal systems and their categorical models. We analyse
the three elements involved in pre-logical predicates --- syntax,
semantics and predicates --- within a categorical framework for typed
binding syntax and semantics. We then formulate generalised
pre-logical predicates and show two distinguishing properties: a)
equivalence with the basic lemma and b) closure of binary pre-logical
relations under relational composition.
To test the adequacy of this generalisation, we derive pre-logical
predicates for various calculi and their categorical models including
variations of lambda calculi and non-lambda calculi such as
many-sorted algebras as well as first-order logic. We then apply
generalised pre-logical predicates to characterising behavioural
equivalence. Examples of constructive data refinement of typed formal
systems are shown, where behavioural equivalence plays a crucial role
in achieving data abstraction
Fully abstract models for effectful λ-calculi via category-theoretic logical relations
We present a construction which, under suitable assumptions, takes a model of Moggiâs computational λ-calculus with sum types, effect operations and primitives, and yields a model that is adequate and fully abstract. The construction, which uses the theory of fibrations, categorical glueing, â€â€-lifting, and â€â€-closure, takes inspiration from OâHearn & Rieckeâs fully abstract model for PCF. Our construction can be applied in the category of sets and functions, as well as the category of diffeological spaces and smooth maps and the category of quasi-Borel spaces, which have been studied as semantics for differentiable and probabilistic programming
Programming Languages and Systems
This open access book constitutes the proceedings of the 28th European Symposium on Programming, ESOP 2019, which took place in Prague, Czech Republic, in April 2019, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems
Union, intersection, and refinement types and reasoning about type disjointness for security protocol analysis
In this thesis we present two new type systems for verifying the security of cryptographic protocol models expressed in a spi-calculus and, respectively, of protocol implementations expressed in a concurrent lambda calculus. In this thesis we present two new type systems for verifying the security of cryptographic protocol models expressed in a spi-calculus and, respectively, of protocol implementations expressed in a concurrent lambda calculus. The two type systems combine prior work on refinement types with union and intersection types and with the novel ability to reason statically about the disjointness of types. The increased expressivity enables the analysis of important protocol classes that were previously out of scope for the type-based analyses of cryptographic protocols. In particular, our type systems can statically analyze protocols that are based on zero-knowledge proofs, even in scenarios when certain protocol participants are compromised. The analysis is scalable and provides security proofs for an unbounded number of protocol executions. The two type systems come with mechanized proofs of correctness and efficient implementations.In dieser Arbeit werden zwei neue Typsysteme vorgestellt, mit denen die Sicherheit kryptographischer Protokolle, modelliert in einem spi-KalkĂŒl, und Protokollimplementierungen, beschrieben in einem nebenlĂ€ufigen LambdakalkĂŒl, verifiziert werden kann. Die beiden Typsysteme verbinden vorausgehende Arbeiten zu Verfeinerungstypen mit disjunktiven und konjunktiven Typen, und ermöglichen auĂerdem, statisch zu folgern, dass zwei Typen disjunkt sind. Die AusdrucksstĂ€rke der Systeme erlaubt die Analyse wichtiger Klassen von Protokollen, die bisher nicht durch typbasierte Protokollanalysen behandelt werden konnten. Insbesondere ist mit den vorgestellten Typsystemen auch die statische Analyse von Protokollen möglich, die auf Zero-Knowledge-Beweisen basieren, selbst unter der Annahme, dass einige Protokollteilnehmer korrumpiert sind. Die Analysetechnik skaliert und erlaubt Sicherheitsbeweise fĂŒr eine unbeschrĂ€nkte Anzahl von ProtokollausfĂŒhrungen. Die beiden Typsysteme sind formal korrekt bewiesen und effizient implementiert
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science
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
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems
Automated Deduction â CADE 28
This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions