51 research outputs found
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Weak Similarity in Higher-Order Mathematical Operational Semantics
Higher-order abstract GSOS is a recent extension of Turi and Plotkin's
framework of Mathematical Operational Semantics to higher-order languages. The
fundamental well-behavedness property of all specifications within the
framework is that coalgebraic strong (bi)similarity on their operational model
is a congruence. In the present work, we establish a corresponding congruence
theorem for weak similarity, which is shown to instantiate to well-known
concepts such as Abramsky's applicative similarity for the lambda-calculus. On
the way, we develop several techniques of independent interest at the level of
abstract categories, including relation liftings of mixed-variance bifunctors
and higher-order GSOS laws, as well as Howe's method
Programs as Diagrams: From Categorical Computability to Computable Categories
This is a draft of the textbook/monograph that presents computability theory
using string diagrams. The introductory chapters have been taught as graduate
and undergraduate courses and evolved through 8 years of lecture notes. The
later chapters contain new ideas and results about categorical computability
and some first steps into computable category theory. The underlying
categorical view of computation is based on monoidal categories with program
evaluators, called *monoidal computers*. This categorical structure can be
viewed as a single-instruction diagrammatic programming language called Run,
whose only instruction is called RUN. This version: improved text, moved the
final chapter to the next volume. (The final version will continue lots of
exercises and workouts, but already this version has severely degraded graphics
to meet the size bounds.)Comment: 150 pages, 81 figure
Coalgebra for the working software engineer
Often referred to as ‘the mathematics of dynamical, state-based systems’, Coalgebra claims to provide a compositional and uniform framework to spec ify, analyse and reason about state and behaviour in computing. This paper addresses this claim by discussing why Coalgebra matters for the design of models and logics for computational phenomena. To a great extent, in this domain one is interested in properties that are preserved along the system’s evolution, the so-called ‘business rules’ or system’s invariants, as well as in liveness requirements, stating that e.g. some desirable outcome will be eventually produced. Both classes are examples of modal assertions, i.e. properties that are to be interpreted across a transition system capturing the system’s dynamics. The relevance of modal reasoning in computing is witnessed by the fact that most university syllabi in the area include some incursion into modal logic, in particular in its temporal variants. The novelty is that, as it happens with the notions of transition, behaviour, or observational equivalence, modalities in Coalgebra acquire a shape . That is, they become parametric on whatever type of behaviour, and corresponding coinduction scheme, seems appropriate for addressing the problem at hand. In this context, the paper revisits Coalgebra from a computational perspective, focussing on three topics central to software design: how systems are modelled, how models are composed, and finally, how properties of their behaviours can be expressed and verified.Fuzziness, as a way to express imprecision, or uncertainty, in computation is an important feature in a number of current application scenarios: from hybrid systems interfacing with sensor networks with error boundaries, to knowledge bases collecting data from often non-coincident human experts. Their abstraction in e.g. fuzzy transition systems led to a number of mathematical structures to model this sort of systems and reason about them. This paper adds two more elements to this family: two modal logics, framed as institutions, to reason about fuzzy transition systems and the corresponding processes. This paves the way to the development, in the second part of the paper, of an associated theory of structured specification for fuzzy computational systems
From enhanced coinduction towards enhanced induction
International audienceThere exist a rich and well-developed theory of enhancements of the coinduction proof method, widely used on behavioural relations such as bisimilarity. We study how to develop an analogous theory for inductive behaviour relations, i.e., relations defined from inductive observables. Similarly to the coinductive setting, our theory makes use of (semi)-progressions of the form R->F(R), where R is a relation on processes and F is a function on relations, meaning that there is an appropriate match on the transitions that the processes in R can perform in which the process derivatives are in F(R). For a given preorder, an enhancement corresponds to a sound function, i.e., one for which R->F(R) implies that R is contained in the preorder; and similarly for equivalences. We introduce weights on the observables of an inductive relation, and a weight-preserving condition on functions that guarantees soundness. We show that the class of functions contains non-trivial functions and enjoys closure properties with respect to desirable function constructors, so to be able to derive sophisticated sound functions (and hence sophisticated proof techniques) from simpler ones. We consider both strong semantics (in which all actions are treated equally) and weak semantics (in which one abstracts from internal transitions). We test our enhancements on a few non-trivial examples
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
Programming Languages and Systems
This open access book constitutes the proceedings of the 29th European Symposium on Programming, ESOP 2020, which was planned to take place in Dublin, Ireland, in April 2020, as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The actual ETAPS 2020 meeting was postponed due to the Corona pandemic. The papers deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems
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