46 research outputs found
Coalgebraic Weak Bisimulation from Recursive Equations over Monads
Strong bisimulation for labelled transition systems is one of the most
fundamental equivalences in process algebra, and has been generalised to
numerous classes of systems that exhibit richer transition behaviour. Nearly
all of the ensuing notions are instances of the more general notion of
coalgebraic bisimulation. Weak bisimulation, however, has so far been much less
amenable to a coalgebraic treatment. Here we attempt to close this gap by
giving a coalgebraic treatment of (parametrized) weak equivalences, including
weak bisimulation. Our analysis requires that the functor defining the
transition type of the system is based on a suitable order-enriched monad,
which allows us to capture weak equivalences by least fixpoints of recursive
equations. Our notion is in agreement with existing notions of weak
bisimulations for labelled transition systems, probabilistic and weighted
systems, and simple Segala systems.Comment: final versio
Resource Transition Systems and Full Abstraction for Linear Higher-Order Effectful Programs
International audienceWe investigate program equivalence for linear higher-order (sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear λ-calculus with explicit copying and algebraic effects à la Plotkin and Power. Such a calculus makes explicit the interaction between copying and linearity, which are intensional aspects of computation, with effects, which are, instead, extensional. We review some of the notions of equivalences for linear calculi proposed in the literature and show their limitations when applied to effectful calculi where copying is a first-class citizen. We then introduce resource transition systems, namely transition systems whose states are built over tuples of programs representing the available resources, as an operational semantics accounting for both intensional and extensional interactive behaviours of programs. Our main result is a sound and complete characterization of contextual equivalence as trace equivalence defined on top of resource transition systems
Resource transition systems and full abstraction for linear higher-order effectful programs
We investigate program equivalence for linear higher-order (sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear \u3b3-calculus with explicit copying and algebraic effects \ue0 la Plotkin and Power. Such a calculus makes explicit the interaction between copying and linearity, which are intensional aspects of computation, with effects, which are, instead, extensional. We review some of the notions of equivalences for linear calculi proposed in the literature and show their limitations when applied to effectful calculi where copying is a first-class citizen. We then introduce resource transition systems, namely transition systems whose states are built over tuples of programs representing the available resources, as an operational semantics accounting for both intensional and extensional interactive behaviours of programs. Our main result is a sound and complete characterization of contextual equivalence as trace equivalence defined on top of resource transition systems
Resource Transition Systems and Full Abstraction for Linear Higher-Order Effectful Programs
International audienceWe investigate program equivalence for linear higher-order (sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear λ-calculus with explicit copying and algebraic effects à la Plotkin and Power. Such a calculus makes explicit the interaction between copying and linearity, which are intensional aspects of computation, with effects, which are, instead, extensional. We review some of the notions of equivalences for linear calculi proposed in the literature and show their limitations when applied to effectful calculi where copying is a first-class citizen. We then introduce resource transition systems, namely transition systems whose states are built over tuples of programs representing the available resources, as an operational semantics accounting for both intensional and extensional interactive behaviours of programs. Our main result is a sound and complete characterization of contextual equivalence as trace equivalence defined on top of resource transition systems
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
Arboreal Categories and Equi-resource Homomorphism Preservation Theorems
The classical homomorphism preservation theorem, due to {\L}o\'s, Lyndon and
Tarski, states that a first-order sentence is preserved under
homomorphisms between structures if, and only if, it is equivalent to an
existential positive sentence . Given a notion of (syntactic) complexity
of sentences, an "equi-resource" homomorphism preservation theorem improves on
the classical result by ensuring that can be chosen so that its
complexity does not exceed that of .
We describe an axiomatic approach to equi-resource homomorphism preservation
theorems based on the notion of arboreal category. This framework is then
employed to establish novel homomorphism preservation results, and improve on
known ones, for various logic fragments, including first-order, guarded and
modal logics.Comment: 44 pages. v3: expanded the Introduction, added a new Section 8,
changed the title to reflect the focus of the pape