## Substitution in Structural Operational Semantics and value-passing process calculi

### BibTeX

@MISC{Staton_substitutionin,

author = {Sam Staton},

title = {Substitution in Structural Operational Semantics and value-passing process calculi},

year = {}

}

### OpenURL

### Abstract

Consider a process calculus that allows agents to communicate values. The structural operational semantics involves substitution of values for variables. Existing rule formats, such as the GSOS format, do not allow this kind of explicit substitution in the semantic rules. We investigate how to derive rule formats for languages with substitution, by using categorical logic to interpret the framework of the GSOS format in different categories. The categories in question are categories of ‘substitution actions’. 1 A simple language for value-passing To set the scene, fix a set of channel names, and consider a set V of value-expressions, that includes the channel names. A simple untyped value-passing process language, V-CCS, is given in Figure 1 (c.f. [8]). The precise value expressions of V are not important, but note that since V includes the (static) channel names, V-CCS is a very primitive applied π-calculus without restriction or name generation; c.f. [1]. For the sake of illustration, consider the set Vex of value expressions determined by the following grammar: v:: = n | v + v | (v, v) | π1(v) | π2(v) | c (n is a number, c is a channel name). We will always work with value expressions up-to the evident equations (2 + 3 = 5; π1(v, w) = v; etc.), rather than explicitly evaluating or normalizing them; this is to simplify the presentation. The following transitions are derivable in Vex-CCS. (¯c〈3〉.0) | (c(v).¯c〈2 + v〉.0) τ

### Citations

3430 |
Communication and Concurrency
- Milner
- 1989
(Show Context)
Citation Context ...t the scene, fix a set of channel names, and consider a set V of value-expressions, that includes the channel names. A simple untyped value-passing process language, V-CCS, is given in Figure 1 (c.f. =-=[8]-=-). The precise value expressions of V are not important, but note that since V includes the (static) channel names, V-CCS is a very primitive applied π-calculus without restriction or name generation;... |

287 | Mobile values, new names, and secure communication
- Abadi, Fournet
- 2001
(Show Context)
Citation Context ... precise value expressions of V are not important, but note that since V includes the (static) channel names, V-CCS is a very primitive applied π-calculus without restriction or name generation; c.f. =-=[1]-=-. For the sake of illustration, consider the set Vex of value expressions determined by the following grammar: v ::= n | v + v | (v, v) | π1(v) | π2(v) | c (n is a number, c is a channel name). We wil... |

226 | A new approach to abstract syntax with variable binding
- Gabbay, Pitts
(Show Context)
Citation Context ...wo sets; the arity of an operator o ∈ O is its inverse image, the set {a ∈ Ar | s(a) = o}. 34 Theories of substitution Nominal sets. Recall the theory of nominal sets, introduced by Pitts and Gabbay =-=[7]-=-. Fix an infinite set A of ‘atoms’. A nominal set is a set X equipped with a permutation action, Perm(A) × X → X, satisfying a finite support requirement. A first example of a nominal set is the set o... |

201 |
Bisimulation can’t be traced
- Bloom, Istrail, et al.
- 1995
(Show Context)
Citation Context ...nel names, and the (input), (output) and (communication) rules carry a side condition that c is a channel name.2 Value-passing systems and the GSOS rule format The GSOS rule format was introduced by =-=[2]-=-. A transition system specification is in the positive GSOS format if it is specified by rules of the following form: (xij l −→ yj | 1 ≤ j ≤ m) o(x1, . . . , xn) L −→ t where the xi’s and yj’s are all... |

53 | A theory of bisimulation for the pi-calculus
- Sangiorgi
- 1996
(Show Context)
Citation Context ...tural to consider V-CCS terms with free valuevariables, in order to define a notion of congruence that respects input contexts. For this reason we recall a more elaborate notion of bisimulation; c.f. =-=[9]-=-: Definition 1. A bisimulation relation R on open V-CCS terms is an open bisimulation if it is closed under substitution: if P R Q then ({ v /a}P ) R ({ v /a}Q). Open bisimilarity is the greatest open... |

23 | Abstract syntax and variable binding (extended abstract
- Fiore, Plotkin, et al.
- 1999
(Show Context)
Citation Context ...e set Vex of open value expressions, with free variables in A, is a first example of a substitution algebra. Various authors have proposed ways to define substitution algebras by structural induction =-=[3,5,6]-=-. Our substitution algebras correspond with those of [3, Def. 3.1], when the carrier presheaves there preserve pullbacks of monos. Heterogeneous substitution. values from V in elements of X. A substit... |

20 | A congruence rule format for name-passing process calculi - Fiore, Staton - 2009 |

12 |
Capture-avoiding substitution as a nominal algebra
- Gabbay, Mathijssen
- 2006
(Show Context)
Citation Context ...e set Vex of open value expressions, with free variables in A, is a first example of a substitution algebra. Various authors have proposed ways to define substitution algebras by structural induction =-=[3,5,6]-=-. Our substitution algebras correspond with those of [3, Def. 3.1], when the carrier presheaves there preserve pullbacks of monos. Heterogeneous substitution. values from V in elements of X. A substit... |

7 | General structural operational semantics through categorical logic
- Staton
- 2008
(Show Context)
Citation Context ...ions of value-passing calculi can be seen as GSOS specifications, by working in a category of substitution actions, rather than the category of sets and functions. We use the techniques introduced in =-=[10]-=- for namepassing calculi. 3 GSOS in type theory To make things slightly more general and abstract, we reformulate the structure and requirements of the positive GSOS format in more fundamental terms. ... |

2 |
Semantics of name and value passing (extended abstract
- Fiore, Turi
- 2001
(Show Context)
Citation Context ...e set Vex of open value expressions, with free variables in A, is a first example of a substitution algebra. Various authors have proposed ways to define substitution algebras by structural induction =-=[3,5,6]-=-. Our substitution algebras correspond with those of [3, Def. 3.1], when the carrier presheaves there preserve pullbacks of monos. Heterogeneous substitution. values from V in elements of X. A substit... |