288 research outputs found
Distributive Laws for Monotone Specifications
Turi and Plotkin introduced an elegant approach to structural operational
semantics based on universal coalgebra, parametric in the type of syntax and
the type of behaviour. Their framework includes abstract GSOS, a categorical
generalisation of the classical GSOS rule format, as well as its categorical
dual, coGSOS. Both formats are well behaved, in the sense that each
specification has a unique model on which behavioural equivalence is a
congruence. Unfortunately, the combination of the two formats does not feature
these desirable properties. We show that monotone specifications - that
disallow negative premises - do induce a canonical distributive law of a monad
over a comonad, and therefore a unique, compositional interpretation.Comment: In Proceedings EXPRESS/SOS 2017, arXiv:1709.0004
Bisimilarity of Open Terms in Stream GSOS
Stream GSOS is a specification format for operations and calculi on infinite
sequences. The notion of bisimilarity provides a canonical proof technique for
equivalence of closed terms in such specifications. In this paper, we focus on
open terms, which may contain variables, and which are equivalent whenever they
denote the same stream for every possible instantiation of the variables. Our
main contribution is to capture equivalence of open terms as bisimilarity on
certain Mealy machines, providing a concrete proof technique. Moreover, we
introduce an enhancement of this technique, called bisimulation up-to
substitutions, and show how to combine it with other up-to techniques to obtain
a powerful method for proving equivalence of open terms
Coinduction up to in a fibrational setting
Bisimulation up-to enhances the coinductive proof method for bisimilarity,
providing efficient proof techniques for checking properties of different kinds
of systems. We prove the soundness of such techniques in a fibrational setting,
building on the seminal work of Hermida and Jacobs. This allows us to
systematically obtain up-to techniques not only for bisimilarity but for a
large class of coinductive predicates modelled as coalgebras. By tuning the
parameters of our framework, we obtain novel techniques for unary predicates
and nominal automata, a variant of the GSOS rule format for similarity, and a
new categorical treatment of weak bisimilarity
A view of canonical extension
This is a short survey illustrating some of the essential aspects of the
theory of canonical extensions. In addition some topological results about
canonical extensions of lattices with additional operations in finitely
generated varieties are given. In particular, they are doubly algebraic
lattices and their interval topologies agree with their double Scott topologies
and make them Priestley topological algebras.Comment: 24 pages, 2 figures. Presented at the Eighth International Tbilisi
Symposium on Language, Logic and Computation Bakuriani, Georgia, September
21-25 200
Up-to Techniques for Branching Bisimilarity
Ever since the introduction of behavioral equivalences on processes one has
been searching for efficient proof techniques that accompany those
equivalences. Both strong bisimilarity and weak bisimilarity are accompanied by
an arsenal of up-to techniques: enhancements of their proof methods. For
branching bisimilarity, these results have not been established yet. We show
that a powerful proof technique is sound for branching bisimilarity by
combining the three techniques of up to union, up to expansion and up to
context for Bloom's BB cool format. We then make an initial proposal for
casting the correctness proof of the up to context technique in an abstract
coalgebraic setting, covering branching but also {\eta}, delay and weak
bisimilarity
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