37 research outputs found
Meta SOS - A Maude Based SOS Meta-Theory Framework
Meta SOS is a software framework designed to integrate the results from the
meta-theory of structural operational semantics (SOS). These results include
deriving semantic properties of language constructs just by syntactically
analyzing their rule-based definition, as well as automatically deriving sound
and ground-complete axiomatizations for languages, when considering a notion of
behavioural equivalence. This paper describes the Meta SOS framework by
blending aspects from the meta-theory of SOS, details on their implementation
in Maude, and running examples.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690
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
Presenting Distributive Laws
Distributive laws of a monad T over a functor F are categorical tools for
specifying algebra-coalgebra interaction. They proved to be important for
solving systems of corecursive equations, for the specification of well-behaved
structural operational semantics and, more recently, also for enhancements of
the bisimulation proof method. If T is a free monad, then such distributive
laws correspond to simple natural transformations. However, when T is not free
it can be rather difficult to prove the defining axioms of a distributive law.
In this paper we describe how to obtain a distributive law for a monad with an
equational presentation from a distributive law for the underlying free monad.
We apply this result to show the equivalence between two different
representations of context-free languages
Enhanced Coalgebraic Bisimulation
International audienceWe present a systematic study of bisimulation-up-to techniques for coalgebras. This enhances the bisimulation proof method for a large class of state based systems, including labelled transition systems but also stream systems and weighted automata. Our approach allows for compositional reasoning about the soundness of enhancements. Applications include the soundness of bisimulation up to bisimilarity, up to equivalence and up to congruence. All in all, this gives a powerful and modular framework for simplified coinductive proofs of equivalence
CPO Models for GSOS Languages - Part I: Compact GSOS Languages
In this paper, we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the GSOS format of Bloom, Istrail and Meyer. The canonical model used for this purpose will be Abramsky's domain of synchronization trees, and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract with respect to the finitely observable part of the bisimulation preorder. In the process of establishing the full abstraction result, we also obtain several general results on the bisimulation preorder (including a complete axiomatization for it), and give a novel operational interpretation of GSOS languages
A general account of coinduction up-to
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 modeled as coalgebras. The fact that bisimulations up to context can be safely used in any language specified by GSOS rules can also be seen as an instance of our framework, using the well-known observation by Turi and Plotkin that such languages form bialgebras. In the second part of the paper, we provide a new categorical treatment of weak bisimilarity on labeled transition systems and we prove the soundness of up-to context for weak bisimulations of systems specified by cool rule formats, as defined by Bloom to ensure congruence of weak bisimilarity. The weak transition systems obtained from such cool rules give rise to lax bialgebras, rather than to bialgebras. Hence, to reach our goal, we extend the categorical framework developed in the first part to an ordered setting