Results 1  10
of
171
A New Approach to Abstract Syntax Involving Binders
 In 14th Annual Symposium on Logic in Computer Science
, 1999
"... Syntax Involving Binders Murdoch Gabbay Cambridge University DPMMS Cambridge CB2 1SB, UK M.J.Gabbay@cantab.com Andrew Pitts Cambridge University Computer Laboratory Cambridge CB2 3QG, UK ap@cl.cam.ac.uk Abstract The FraenkelMostowski permutation model of set theory with atoms (FMsets) ..."
Abstract

Cited by 176 (20 self)
 Add to MetaCart
(Show Context)
Syntax Involving Binders Murdoch Gabbay Cambridge University DPMMS Cambridge CB2 1SB, UK M.J.Gabbay@cantab.com Andrew Pitts Cambridge University Computer Laboratory Cambridge CB2 3QG, UK ap@cl.cam.ac.uk Abstract The FraenkelMostowski permutation model of set theory with atoms (FMsets) can serve as the semantic basis of metalogics for specifying and reasoning about formal systems involving name binding, ffconversion, capture avoiding substitution, and so on. We show that in FMset theory one can express statements quantifying over `fresh' names and we use this to give a novel settheoretic interpretation of name abstraction. Inductively defined FMsets involving this nameabstraction set former (together with cartesian product and disjoint union) can correctly encode objectlevel syntax modulo ffconversion. In this way, the standard theory of algebraic data types can be extended to encompass signatures involving binding operators. In particular, there is an associated n...
Structural Operational Semantics
 Handbook of Process Algebra
, 1999
"... Structural Operational Semantics (SOS) provides a framework to give an operational semantics to programming and specification languages, which, because of its intuitive appeal and flexibility, has found considerable application in the theory of concurrent processes. Even though SOS is widely use ..."
Abstract

Cited by 148 (19 self)
 Add to MetaCart
Structural Operational Semantics (SOS) provides a framework to give an operational semantics to programming and specification languages, which, because of its intuitive appeal and flexibility, has found considerable application in the theory of concurrent processes. Even though SOS is widely used in programming language semantics at large, some of its most interesting theoretical developments have taken place within concurrency theory. In particular, SOS has been successfully applied as a formal tool to establish results that hold for whole classes of process description languages. The concept of rule format has played a major role in the development of this general theory of process description languages, and several such formats have been proposed in the research literature. This chapter presents an exposition of existing rule formats, and of the rich body of results that are guaranteed to hold for any process description language whose SOS is within one of these formats. As far as possible, the theory is developed for SOS with features like predicates and negative premises.
Deriving Bisimulation Congruences for Reactive Systems
 In Proc. of CONCUR 2000, 2000. LNCS 1877
, 2000
"... . The dynamics of reactive systems, e.g. CCS, has often been de ned using a labelled transition system (LTS). More recently it has become natural in de ning dynamics to use reaction rules  i.e. unlabelled transition rules  together with a structural congruence. But LTSs lead more naturally to beha ..."
Abstract

Cited by 136 (13 self)
 Add to MetaCart
(Show Context)
. The dynamics of reactive systems, e.g. CCS, has often been de ned using a labelled transition system (LTS). More recently it has become natural in de ning dynamics to use reaction rules  i.e. unlabelled transition rules  together with a structural congruence. But LTSs lead more naturally to behavioural equivalences. So one would like to derive from reaction rules a suitable LTS. This paper shows how to derive an LTS for a wide range of reactive systems. A label for an agent a is de ned to be any context F which intuitively is just large enough so that the agent Fa (\a in context F ") is able to perform a reaction. The key contribution of this paper is a precise de nition of \just large enough", in terms of the categorical notion of relative pushout (RPO), which ensures that bisimilarity is a congruence when sucient RPOs exist. Two examples  a simpli ed form of action calculi and termrewriting  are given, for which it is shown that su cient RPOs indeed exist. The thrust of thi...
The origins of structural operational semantics
 Journal of Logic and Algebraic Programming
, 2004
"... We review the origins of structural operational semantics. The main publication ‘A Structural Approach to Operational Semantics, ’ also known as the ‘Aarhus Notes, ’ appeared in 1981 [G.D. Plotkin, A structural approach to operational semantics, DAIMI FN19, Computer Science Department, Aarhus Unive ..."
Abstract

Cited by 92 (0 self)
 Add to MetaCart
(Show Context)
We review the origins of structural operational semantics. The main publication ‘A Structural Approach to Operational Semantics, ’ also known as the ‘Aarhus Notes, ’ appeared in 1981 [G.D. Plotkin, A structural approach to operational semantics, DAIMI FN19, Computer Science Department, Aarhus University, 1981]. The development of the ideas dates back to the early 1970s, involving many people and building on previous work on programming languages and logic. The former included abstract syntax, the SECD machine, and the abstract interpreting machines of the Vienna school; the latter included the λcalculus and formal systems. The initial development of structural operational semantics was for simple functional languages, more or less variations of the λcalculus; after that the ideas were gradually extended to include languages with parallel features, such as Milner’s CCS. This experience set the ground for a more systematic exposition, the subject of an invited course of lectures at Aarhus University; some of these appeared in print as the 1981 Notes. We discuss the content of these lectures and some related considerations such as ‘small state’ versus ‘grand state, ’ structural versus compositional semantics, the influence of the Scott–Strachey approach to denotational semantics, the treatment of recursion and jumps, and static semantics. We next discuss relations with other work and some immediate further development. We conclude with an account of an old, previously unpublished, idea: an alternative, perhaps more readable, graphical presentation of systems of rules for operational semantics.
Modular structural operational semantics
, 2004
"... Modular SOS (MSOS) is a variant of conventional Structural Operational Semantics (SOS). Using MSOS, the transition rules for each construct of a programming language can be given incrementally, once and for all, and do not need reformulation when further constructs are added to the language. MSOS th ..."
Abstract

Cited by 77 (8 self)
 Add to MetaCart
Modular SOS (MSOS) is a variant of conventional Structural Operational Semantics (SOS). Using MSOS, the transition rules for each construct of a programming language can be given incrementally, once and for all, and do not need reformulation when further constructs are added to the language. MSOS thus provides an exceptionally high degree of modularity in language descriptions, removing a shortcoming of the original SOS framework. After sketching the background and reviewing the main features of SOS, the paper explains the crucial differences between SOS and MSOS, and illustrates how MSOS descriptions are written. It also discusses standard notions of semantic equivalence based on MSOS. Appendix A shows how the illustrative MSOS rules given in the paper would be formulated in conventional SOS.
From Rewrite Rules to Bisimulation Congruences
 THEORETICAL COMPUTER SCIENCE
, 1998
"... The dynamics of many calculi can be most clearly defined by a reduction semantics. To work with a calculus, however, an understanding of operational congruences is fundamental; these can often be given tractable definitions or characterisations using a labelled transition semantics. This paper consi ..."
Abstract

Cited by 77 (2 self)
 Add to MetaCart
The dynamics of many calculi can be most clearly defined by a reduction semantics. To work with a calculus, however, an understanding of operational congruences is fundamental; these can often be given tractable definitions or characterisations using a labelled transition semantics. This paper considers calculi with arbitrary reduction semantics of three simple classes, firstly ground term rewriting, then leftlinear term rewriting, and then a class which is essentially the action calculi lacking substantive name binding. General definitions of labelled transitions are given in each case, uniformly in the set of rewrite rules, and without requiring the prescription of additional notions of observation. They give rise to bisimulation congruences. As a test of the theory it is shown that bisimulation for a fragment of CCS is recovered. The transitions generated for a fragment of the Ambient Calculus of Cardelli and Gordon, and for SKI combinators, are also discussed briefly.
On Generalised Coinduction and Probabilistic Specification Formats: Distributive Laws in Coalgebraic Modelling
, 2004
"... ..."
Presheaf Models for Concurrency
, 1999
"... In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their wo ..."
Abstract

Cited by 49 (19 self)
 Add to MetaCart
(Show Context)
In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their work inspired this thesis by suggesting that presheaf categories could provide abstract models for concurrency with a builtin notion of bisimulation. We show how
Adequacy for algebraic effects
 In 4th FoSSaCS
, 2001
"... We present a logic for algebraic effects, based on the algebraic representation of computational effects by operations and equations. We begin with the acalculus, a minimal calculus which separates values, effects, and computations and thereby canonises the order of evaluation. This is extended to ..."
Abstract

Cited by 42 (14 self)
 Add to MetaCart
We present a logic for algebraic effects, based on the algebraic representation of computational effects by operations and equations. We begin with the acalculus, a minimal calculus which separates values, effects, and computations and thereby canonises the order of evaluation. This is extended to obtain the logic, which is a classical firstorder multisorted logic with higherorder value and computation types, as in Levy’s callbypushvalue, a principle of induction over computations, a free algebra principle, and predicate fixed points. This logic embraces Moggi’s computational λcalculus, and also, via definable modalities, HennessyMilner logic, and evaluation logic, though Hoare logic presents difficulties. 1
PSPACE bounds for rank 1 modal logics
 IN LICS’06
, 2006
"... For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal logics. Our main result is that all rank1 logics enjoy a sh ..."
Abstract

Cited by 37 (19 self)
 Add to MetaCart
(Show Context)
For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal logics. Our main result is that all rank1 logics enjoy a shallow model property and thus are, under mild assumptions on the format of their axiomatisation, in PSPACE. This leads to a unified derivation of tight PSPACEbounds for a number of logics including K, KD, coalition logic, graded modal logic, majority logic, and probabilistic modal logic. Our generic algorithm moreover finds tableau proofs that witness pleasant prooftheoretic properties including a weak subformula property. This generality is made possible by a coalgebraic semantics, which conveniently abstracts from the details of a given model class and thus allows covering a broad range of logics in a uniform way.