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A general conservative extension theorem in process algebra
 THEORETICAL COMPUTER SCIENCE
, 1994
"... We prove a general conservative extension theorem for transition system based process theories with easytocheck and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensur ..."
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Cited by 36 (4 self)
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We prove a general conservative extension theorem for transition system based process theories with easytocheck and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions
A Conservative Look at Operational Semantics with Variable Binding
 INFORMATION AND COMPUTATION
, 1998
"... We set up a formal framework to describe transition system specifications in the style of Plotkin. This framework has the power to express manysortedness, general binding mechanisms and substitutions, among other notions such as negative hypotheses and unary predicates on terms. The framework i ..."
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Cited by 32 (5 self)
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We set up a formal framework to describe transition system specifications in the style of Plotkin. This framework has the power to express manysortedness, general binding mechanisms and substitutions, among other notions such as negative hypotheses 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 transition rules does not affect the semantics of the original terms.
Conservative Extension in Positive/Negative Conditional Term Rewriting with Applications to Software Renovation Factories
, 1998
"... We transpose a conservative extension theorem from structural operational semantics to conditional term rewriting. The result is useful for the development of software renovation factories, and for modular specification of abstract data types. ..."
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Cited by 9 (5 self)
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We transpose a conservative extension theorem from structural operational semantics to conditional term rewriting. The result is useful for the development of software renovation factories, and for modular specification of abstract data types.
Operational Semantics of Term Rewriting with Priorities
 Utrecht University
, 1996
"... We study the semantics of term rewriting systems with rule priorities (PRS), as introduced in [1]. Three open problems posed in that paper are solved, by giving counter examples. Moreover, a class of executable PRSs is identified. A translation of PRSs into transition system specifications (TSS) is ..."
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Cited by 2 (0 self)
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We study the semantics of term rewriting systems with rule priorities (PRS), as introduced in [1]. Three open problems posed in that paper are solved, by giving counter examples. Moreover, a class of executable PRSs is identified. A translation of PRSs into transition system specifications (TSS) is given. This translation introduces negative premises. We prove that the translation preserves the operational semantics. Contents 1 Introduction 2 2 Term rewriting with rule priorities 3 2.1 Definition and semantics . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Fixed points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 An executable class of PRSs . . . . . . . . . . . . . . . . . . . . 8 2.4 Counter examples to open questions . . . . . . . . . . . . . . . . 11 3 Transition system specifications 14 3.1 Universal negative premises in TSSs . . . . . . . . . . . . . . . . 15 3.2 Translation of PRSs into TSSs . . . . . . . . . . . . . . . . . . . 18 4 Operational semant...
Operational Semantics of Rewriting with Priorities
, 1997
"... We study the semantics of term rewriting systems with rule priorities (PRS), as introduced in [1]. Three open problems posed in that paper are solved, by giving counter examples. Moreover, a class of executable PRSs is identified. A translation of PRSs into transition system specifications (TSS) is ..."
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Cited by 1 (0 self)
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We study the semantics of term rewriting systems with rule priorities (PRS), as introduced in [1]. Three open problems posed in that paper are solved, by giving counter examples. Moreover, a class of executable PRSs is identified. A translation of PRSs into transition system specifications (TSS) is given. This translation introduces negative premises. We prove that the translation preserves the operational semantics. Key words: term rewriting systems, rule priorities, structural operational semantics, transition system specification, negative premises. 1 Introduction Motivation. In [1], term rewriting with rule priorities has been introduced. A priority rewrite system (PRS) extends an ordinary term rewriting system (TRS) with a partial order on the rules. The main idea is to resolve a conflict between two rules by giving priority to the largest rule. One may hope that by ordering the rules of a nonconfluent TRS, a confluent PRS can be obtained (i.e. a system in which each reduction ev...
An SOS Message: Conservative Extension in HigherOrder Positive/Negative Conditional Term Rewriting
, 1997
"... General theorems in structured operational semantics can be transformed into related results in conditional term rewriting. We apply this approach to obtain a conservative extension theorem for higherorder conditional term rewriting systems with negative conditions. This result is useful, for inst ..."
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Cited by 1 (1 self)
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General theorems in structured operational semantics can be transformed into related results in conditional term rewriting. We apply this approach to obtain a conservative extension theorem for higherorder conditional term rewriting systems with negative conditions. This result is useful, for instance, in modular specification of abstract data types, and in software renovation factories.
Operational semantics of rewriting with priorities
, 1996
"... We study the semantics of term rewriting systems with rule priorities (PRS), as introduced in Baeten et al. (1989). Three open problems posed in that paper are solved, by giving counter examples. Moreover, a class of executable PRSs is identified. A translation of PRSs into transition system specifi ..."
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We study the semantics of term rewriting systems with rule priorities (PRS), as introduced in Baeten et al. (1989). Three open problems posed in that paper are solved, by giving counter examples. Moreover, a class of executable PRSs is identified. A translation of PRSs into transition system specifications (TSS) is given. This translation introduces negative premises. We prove that the translation preserves the operational semantics. @ 1998Elsevier Science B.V. All