## A conservative look at term deduction systems with variable binding (1995)

Citations: | 10 - 4 self |

### BibTeX

@MISC{Fokkink95aconservative,

author = {Wan Fokkink and Chris Verhoef},

title = {A conservative look at term deduction systems with variable binding },

year = {1995}

}

### OpenURL

### Abstract

We set up a formal framework to describe term deduction systems, such as transition system speci cations in the style of Plotkin, and conditional term rewriting systems. This framework has the power to express many-sortedness, general binding mechanisms and substitutions, among other notions such as negative premises and unary predicates on terms. The framework is used to present a conservativity format in operational semantics, which states sufficient criteria to ensure that the extension of a transition system specification with new rules does not affect the behaviour of the original terms. Furthermore, we showhowgeneral theorems in structured operational semantics can be transformed into results in conditional term rewriting. We apply this approach to the conservativity theorem, which yields a result that is useful in the field of abstract data types.

### Citations

3501 | Communicating Sequential Processes - Hoare - 1985 |

3278 |
Communication and Concurrency
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(Show Context)
Citation Context ... premises [21, 13, 20], or to find which extensions of TSSs are operationally conservative [22, 21, 13, 39]. Our paper is devoted to this last topic. Over and over again, process theories such as CCS =-=[28]-=-, CSP [23] and ACP [8] have been extended with new features, and the original TSSs, which provide the semantics for these process algebras, were extended with rules to describe these features. A quest... |

1520 | The Stable Model Semantics for Logic Programming
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Citation Context ...ere are negative hypotheses around it is no longer straightforward to define a sensible transition relation. We will use the notion of a stable model for a TSS, which stems from Gelfond and Lifschitz =-=[18]-=-, in the setting of logic programming, and which was adapted to structured operational semantics by Bol and Groote [13]. See Van Glabbeek [20] for an overview of other possibilities to give meaning to... |

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Citation Context ... data types. 1 Introduction A current method to provide process algebras and specification languages with an operational semantics is based on the use of structured operational semantics from Plotkin =-=[33]-=-. Given a set of states, the transitions between these states are obtained inductively from a transition system specification (TSS), which consists of transition rules. Deducing desirable properties f... |

1131 |
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Citation Context ...t way. We use a notational approach based on [2]; it is the notation for terms in the Nuprl proof development system, see [14]. Our choice for the Nuprl notation, instead of for example the -calculus =-=[6]-=-, is simply a matter of taste. 2.1 The actual world In this section we describe the actual world, which contains actual terms, actual substitutions, and so forth. In the sequel, ~ O will denote a sequ... |

1017 | A calculus of mobile processes
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- 1992
(Show Context)
Citation Context ... because of the fact that nowadays many transition rules use parametrized labels. We will see an example of such a parametrized label, in the setting of the ��-calculus from Milner, Parrow and Wal=-=ker [30]-=-, in example 2.14. Definition 2.11 An actual (transition) rule is an expression of the form H=c, where H is a collection of positive and negative transitions over an actual signature, and c is a posit... |

365 | Process Algebra for Synchronous Communication
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(Show Context)
Citation Context ... or to find which extensions of TSSs are operationally conservative [22, 21, 13, 39]. Our paper is devoted to this last topic. Over and over again, process theories such as CCS [28], CSP [23] and ACP =-=[8]-=- have been extended with new features, and the original TSSs, which provide the semantics for these process algebras, were extended with rules to describe these features. A question that arises natura... |

207 |
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(Show Context)
Citation Context ...for closed stable models applies. 2 4 Applications In this section we will give the reader an idea of the range of applications of our results. For a start, we wish to mention that Baeten and Verhoef =-=[5]-=- and Aceto, Bloom and Vaandrager [1] give several applications of our conservativity result in the case of operational semantics without types and binding mechanisms. Some systems with variable bindin... |

196 |
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Citation Context ...S is often a technical and mechanic labour. Therefore, in recent years several general theories for TSSs have been developed, for instance to discover which TSSs satisfy a certain congruence property =-=[37, 11, 22, 21, 13, 4, 40, 16, 24, 10]-=-, or to study the meaning of negative premises [21, 13, 20], or to find which extensions of TSSs are operationally conservative [22, 21, 13, 39]. Our paper is devoted to this last topic. Over and over... |

192 | A Calculus of Mobile Processes, part I
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Citation Context ...s, because of the fact that nowadays many transition rules use parametrized labels. We will see an example of such a parametrized label, in the setting of the -calculus from Milner, Parrow and Walker =-=[30]-=-, in example 2.14. De nition 2.11 An actual (transition) rule is an expression of the form H=c, where H is a collection of positive and negative transitions over an actual signature, and c is a positi... |

191 |
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Citation Context ...S is often a technical and mechanic labour. Therefore, in recent years several general theories for TSSs have been developed, for instance to discover which TSSs satisfy a certain congruence property =-=[37, 11, 22, 21, 13, 4, 40, 16, 24, 10]-=-, or to study the meaning of negative premises [21, 13, 20], or to find which extensions of TSSs are operationally conservative [22, 21, 13, 39]. Our paper is devoted to this last topic. Over and over... |

175 |
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Citation Context ...original term as its source. Examples of extensions that are within the scope of Verhoef's criteria, but that do not fit the previous formats, are the extension of CCS with time from Moller and Tofts =-=[31]-=-, and BPA with discrete time from Baeten and Bergstra [3]. (In the current version of BPA with discrete time, the operational semantics has been adapted in such a way that the extension with discrete ... |

159 | Implementing mathematics with the Nuprl proof development system
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Citation Context ... describe these mechanisms as general as possible, in a notationally convenient way. We use a notational approach based on [2]� it is the notation for terms in the Nuprl proof development system, see =-=[14]-=-. Our choice for the Nuprl notation, instead of for example the -calculus [6], is simply a matter of taste. 2.1 The actual world In this section we describe the actual world, which contains actual ter... |

156 | Real time process algebra
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(Show Context)
Citation Context ...re within the scope of Verhoef's criteria, but that do not fit the previous formats, are the extension of CCS with time from Moller and Tofts [31], and BPA with discrete time from Baeten and Bergstra =-=[3]-=-. (In the current version of BPA with discrete time, the operational semantics has been adapted in such a way that the extension with discrete time is no longer operationally conservative over BPA.) I... |

115 | Transition system specifications with negative premises - Groote - 1993 |

108 | A congruence theorem for structured operational semantics with predicates and negative premises. Nordic Journal of Computing 2 (2), 274–302. A. Proof of Theorem 9 We show that the problem of deciding whether a universal two-counter machine diverges on inp
- Verhoef
- 1995
(Show Context)
Citation Context ...S is often a technical and mechanic labour. Therefore, in recent years several general theories for TSSs have been developed, for instance to discover which TSSs satisfy a certain congruence property =-=[37, 11, 22, 21, 13, 4, 40, 16, 24, 10]-=-, or to study the meaning of negative premises [21, 13, 20], or to find which extensions of TSSs are operationally conservative [22, 21, 13, 39]. Our paper is devoted to this last topic. Over and over... |

106 | Proving congruence of bisimulation in functional programming languages
- Howe
- 1996
(Show Context)
Citation Context |

106 | Modal Logics for Mobile Processes
- Milner, Parrow, et al.
- 1993
(Show Context)
Citation Context ... [36], which is a subset of the full ��-calculus. Basically, one could say that the ��I-calculus is made out of CCS combined with ff-conversion. The transition rules for the ��-calculus as=-= defined in [29] satisfy-=- our criteria too, so our conservativity results can be applied to this formalism just as well. However, we prefer ��I over �� here, because it has a simpler operational semantics, and we want... |

106 | The algebra of timed processes ATP: Theory and application
- Nicollin, Sifakis
- 1994
(Show Context)
Citation Context ...onservative over an original TSS, it is necessary that the rules in the original TSS are source-dependent. In practical cases, this criterion is sometimes neglected. For example, Nicollin and Sifakis =-=[32]-=- consider an extended TSS in which each rule in the extension contains a new operator in its source, and from this fact they conclude that the extension is operationally conservative. In general howev... |

90 | The Semantics of Reflected Proof
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- 1990
(Show Context)
Citation Context ...ing. Binding mechanisms exist in many and diverse forms, so we have chosen to describe these mechanisms as general as possible, in a notationally convenient way. We use a notational approach based on =-=[2]-=-; it is the notation for terms in the Nuprl proof development system, see [14]. Our choice for the Nuprl notation, instead of for example the -calculus [6], is simply a matter of taste. 2.1 The actual... |

88 | Turning SOS rules into equations
- Aceto, Bloom, et al.
(Show Context)
Citation Context ...4 Applications In this section we will give the reader an idea of the range of applications of our results. For a start, we wish to mention that Baeten and Verhoef [5] and Aceto, Bloom and Vaandrager =-=[1]-=- give several applications of our conservativity result in the case of operational semantics without types and binding mechanisms. Some systems with variable binding mechanisms to which our results ca... |

88 |
Conditional Rewrite Rules: Confluence and Termination
- Bergstra, Klop
- 1986
(Show Context)
Citation Context ...our results. We will provide some examples from the term rewriting literature to exemplify the results. For detailed information on conditional rewriting we refer to Kaplan [25] and Bergstra and Klop =-=[9]-=-. Bergstra and Klop [9] classify the various kinds of CTRSs that occur in the literature into four types: I (or `semi-equational'), II (or `join'), III and III n (or `normal'). These types differ in t... |

74 |
The meaning of negative premises in transition system specifications
- Bol, Groote
- 1996
(Show Context)
Citation Context |

64 | Higher-level synchronising devices in Meije-SCCS
- Simone
- 1985
(Show Context)
Citation Context |

55 | Confluence of Conditional Rewrite Systems
- Dershowitz, Okada, et al.
- 1987
(Show Context)
Citation Context ...ion oe, and a context C[ ] such that s j C[oe(l)] and t j C[oe(r)] and oe(s i ) i oe(t i ) is provable from the CTRS for i = 1; : : : ; n. Before we continue, we give an example of a CTRS, taken from =-=[15]-=-, which will serve as a running example to demonstrate our conservativity result. Example 4.6 The following CTRS of type III is built from two modules N 0 and N 1 . The CTRS N 0 implements addition on... |

55 | The Lazy Lambda Calculus in a Concurrency Scenario. En LICS’92
- Sangiorgi
- 1992
(Show Context)
Citation Context ...x =x] a \Gamma!z ysb \Gamma!z where x and x are unrelated. The distinction of formal variables in structured operational semantics with variable binding was also propagated independently by Sangiorgi =-=[35]-=- and by Howe [24]. There, they are called `meta-variables'. Now that we have an idea of the framework, we will first introduce the notion of actual terms (as opposed to formal terms), in which it is p... |

54 | Ntyft/ntyxt rules reduce to ntree rules
- Fokkink, Glabbeek
- 1996
(Show Context)
Citation Context |

50 |
Conditional rewrite rules
- Kaplan
- 1984
(Show Context)
Citation Context ...iscuss the connection with our results. We will provide some examples from the term rewriting literature to exemplify the results. For detailed information on conditional rewriting we refer to Kaplan =-=[25]-=- and Bergstra and Klop [9]. Bergstra and Klop [9] classify the various kinds of CTRSs that occur in the literature into four types: I (or `semi-equational'), II (or `join'), III and III n (or `normal'... |

43 |
Structural operational semantics for weak bisimulations
- Bloom
- 1995
(Show Context)
Citation Context |

38 | R.: The meaning of negative premises in transition system specifications II
- Glabbeek
- 2004
(Show Context)
Citation Context ... theories for TSSs have been developed, for instance to discover which TSSs satisfy a certain congruence property [37, 11, 22, 21, 13, 4, 40, 16, 24, 10], or to study the meaning of negative premises =-=[21, 13, 20]-=-, or to find which extensions of TSSs are operationally conservative [22, 21, 13, 39]. Our paper is devoted to this last topic. Over and over again, process theories such as CCS [28], CSP [23] and ACP... |

36 | A general conservative extension theorem in process algebra
- Verhoef
- 1994
(Show Context)
Citation Context ...fy a certain congruence property [37, 11, 22, 21, 13, 4, 40, 16, 24, 10], or to study the meaning of negative premises [21, 13, 20], or to find which extensions of TSSs are operationally conservative =-=[22, 21, 13, 39]-=-. Our paper is devoted to this last topic. Over and over again, process theories such as CCS [28], CSP [23] and ACP [8] have been extended with new features, and the original TSSs, which provide the s... |

28 |
Substitution revisited
- Stoughton
- 1988
(Show Context)
Citation Context ...plying ff-conversion, that is, by renaming bound variables. In the sequel, actual terms are considered modulo ff-conversion, and when a substitution is applied, bound variables are renamed. Stoughton =-=[38]-=- presented a nice treatment of this technique. Remark 2.5 Bloom and Vaandrager [12] develop a framework for transition rules with types and a binding mechanism, in which they make a clear distinction ... |

23 |
Modular properties of conditional term rewriting systems
- Middeldorp
- 1993
(Show Context)
Citation Context .... No extra variables occur in the conditions. Restrictions A and B are quite natural in the unconditional case, because then they are essential in order to obtain termination. According to Middeldorp =-=[27]-=-, restriction C is often imposed to prevent severe complications of a technical nature. We leave out these restrictions, because our results do not require to impose them. However, we will see that fo... |

20 |
Positive/negative conditional rewriting
- Kaplan
- 1987
(Show Context)
Citation Context ...tution at the right-hand side is not a real substitution, but a substitution harness. Even so, negative conditions are relevant for conditional rewriting, and have been studied for instance by Kaplan =-=[26]-=-. In order to find out how the conservativity results apply to CTRSs with variable bindings and negative conditions, the reader is referred to the previous sections. Remark 4.2 In structured operation... |

19 | Full abstraction in structural operational semantics
- Glabbeek
- 1993
(Show Context)
Citation Context ...y. This definition uses the two distinct notions FV and EV of formal variables in formal terms. In the setting without variable bindings, this notion was also discovered independently by Van Glabbeek =-=[19]-=- and by Howe [24]. Definition 3.16 For a formal rule r , its collection of source-dependent formal variablessSV (r ) is defined inductively as follows. - If t is the source of r , then EV (t ) ` SV (r... |

12 |
Algebraic Speci cation
- Bergstra
- 1989
(Show Context)
Citation Context ...i ed by means of modules of CTRSs. In abstract data typing there is a long tradition in modular specifying systems. In fact, modular specifying means extending conservatively, in our terminology� see =-=[7]-=- for more information. Our conservativity theorem serves only as an example how theorems from structured operational semantics can be transposed to conditional rewriting. In order to keep this exposit... |

11 |
Conditional rewrite rules: con uence and termination
- Bergstra, Klop
- 1986
(Show Context)
Citation Context ...our results. We will provide some examples from the term rewriting literature to exemplify the results. For detailed information on conditional rewriting we refer to Kaplan [25] and Bergstra and Klop =-=[9]-=-. Bergstra and Klop [9] classify the various kinds of CTRSs that occur in the literature into four types: I (or `semi-equational'), II (or `join'), III and IIIn (or `normal'). These types di er in the... |

9 | Transition system speci cations with negative premises - Groote - 1993 |

7 |
An e ective axiomatization for real time ACP
- Fokkink, Klusener
- 1995
(Show Context)
Citation Context ...isms to which our results can be applied are CCS from Milner [28], CSP from Hoare [23], the ��-calculus from Milner, Parrow and Walker [30], and ACP with real-time as proposed by Fokkink and Kluse=-=ner [17], to-=- mention a few. First, we will focus on a process algebra application with both types and variable binding: the ��-calculus. Then we will devote our attention to the formulation of our results in ... |

7 |
The Semantics of Re ected Proof
- Allen, Constable, et al.
- 1990
(Show Context)
Citation Context ...ing. Binding mechanisms exist in many and diverse forms, so we have chosen to describe these mechanisms as general as possible, in a notationally convenient way. We use a notational approach based on =-=[2]-=-� it is the notation for terms in the Nuprl proof development system, see [14]. Our choice for the Nuprl notation, instead of for example the -calculus [6], is simply a matter of taste. 2.1 The actual... |

6 |
I: A symmetric calculus based on internal mobility
- Sangiorgi
- 1995
(Show Context)
Citation Context ...ion in the ��-calculus We show how our conservativity results can be applied to a TSS from the literature that incorporates both types and variable binding. We opt for the ��I-calculus from Sa=-=ngiorgi [36], which is a-=- subset of the full ��-calculus. Basically, one could say that the ��I-calculus is made out of CCS combined with ff-conversion. The transition rules for the ��-calculus as defined in [29] ... |

3 |
rule formats for parameterized and statebearing processes. Unpublished manuscript
- SOS
- 1995
(Show Context)
Citation Context ...erms are considered modulo ff-conversion, and when a substitution is applied, bound variables are renamed. Stoughton [38] presented a nice treatment of this technique. Remark 2.5 Bloom and Vaandrager =-=[12]-=- develop a framework for transition rules with types and a binding mechanism, in which they make a clear distinction between sorts for processes and sorts for data. We have chosen not to adopt this di... |

3 |
Programming Concepts and Paradigms
- Watt
- 1990
(Show Context)
Citation Context ...are bound by the actual parameters. When discussing procedures on a conceptual level, it is often useful to introduce a notational distinction between formal and actual parameters; see, for instance, =-=[41]-=-. We will do the same in this paper: we think of a transition rule as a procedure to establish a transition relation by means of substituting (actual) terms for the (formal) variables. Since we will d... |

1 |
de Pol. Semantics of priority rewrite systems by means of transition system specifications. Unpublished manuscript
- van
- 1995
(Show Context)
Citation Context ...ssions suited for conditional rewriting, they are to be generalized to the form 8x 1 ; : : : ; x n (s\Gamma6!t), where x 1 ; : : : ; x n are the variables that occur in t but not in s; see Van de Pol =-=[34]-=- for more detailed information. CTRSs with such negative conditions can be given a meaning following Van Glabbeek [20]. We define the necessary preliminaries concerning conditional term rewriting and ... |

1 |
Ageneralconservative extension theorem in process algebra
- Verhoef
- 1994
(Show Context)
Citation Context ...isfy a certain congruence property [37, 11, 22, 21, 13, 4, 40, 16, 24, 10], or to study the meaning of negative premises [21, 13, 20], or to nd which extensions of TSSs are operationally conservative =-=[22,21,13,39]-=-.Our paper is devoted to this last topic. 1Over and over again, process theories such as CCS [28], CSP [23] and ACP [8] have been extended with new features, and the original TSSs, which provide the ... |