## A Congruence Theorem for Structured Operational Semantics of Higher-Order Languages (1997)

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### BibTeX

@INPROCEEDINGS{Bernstein97acongruence,

author = {Karen L. Bernstein},

title = {A Congruence Theorem for Structured Operational Semantics of Higher-Order Languages},

booktitle = {},

year = {1997},

pages = {153--164},

publisher = {IEEE Computer Society Press}

}

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### Abstract

In this paper we describe the promoted tyft/tyxt rule format for defining higher-order languages. The rule format is a generalization of Groote and Vaandrager 's tyft/tyxt format in which terms are allowed as labels on transitions in rules. We prove that bisimulation is a congruence for any language defined in promoted tyft/tyxt format and demonstrate the usefulness of the rule format by presenting promoted tyft/tyxt definitions for the lazy -calculus, CHOCS and the ß-calculus. 1 Introduction For a programming language definition that uses bisimulation as the notion of equivalence, it is desirable for the bisimulation relation to be compatible with the language constructs; i.e. that bisimulation be a congruence. Several rule formats have been defined, so that as long as a definition satisfies certain syntactic constraints, then the defined bisimulation relation is guaranteed to be a congruence. However these rule formats have not been widely used for defining languages with higher-...

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1017 | A calculus of mobile processes
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Citation Context ...itable for defining higher-order languages, and we demonstrate the expressiveness of the rule format by giving promoted tyft/tyxt definitions for the lazy -calculus, CHOCS [Tho95] and the ��-calcu=-=lus [MPW92]-=-. Although not presented here, the definition of a small strict functional language from [BS95] is also in promoted tyft/tyxt format. The main result of this paper is that for any language defined in ... |

672 |
Concurrency and automata on infinite sequences
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- 1981
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Citation Context ...d if it contains only closed transitions. A transition system (TS) is a structure (S; T ) where: S is a set of states and T is a set of transition relations over S. We use (strong) bisimulation as in =-=[Par81]-=-. Let A = (S; T ) be a transition system, and R ` S \Theta S a symmetric relation. R is a (strong) bisimulation if for all s; s 0 ; t; a 2 S it satisfies, for all labeled transitions ! 2 R : (s R t an... |

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239 | The lazy lambda calculus
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Citation Context ...redicates have made the rule formats of greater practical use [Gro93, BV93, Ver95, BG96]. Abramsky was the first to use bisimulation as the notion of equivalence for a functional programming language =-=[Abr90]-=- and this style of definition is now often used for languages with higher-order features [San92, CG95, FHJ96, Jef95, Gor95, GR96]. These definitions typically prove that bisimulation is a congruence b... |

196 |
Bisimulation can’t be traced
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Citation Context ...regard to the congruence property for bisimulation. Rule formats such as de Simone's format [dS85], the tyft/tyxt by Groote and Vaandrager [GV92], and the GSOS rule format by Bloom, Istrael and Meyer =-=[BIM95]-=- guarantee that bisimulation is a congruence. Extensions of these rule formats for including negative premises and predicates have made the rule formats of greater practical use [Gro93, BV93, Ver95, B... |

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Calculi for Higher Order Communicating Systems
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Citation Context ...a new rule format that is suitable for defining higher-order languages, and we demonstrate the expressiveness of the rule format by giving promoted tyft/tyxt definitions for the lazy -calculus, CHOCS =-=[Tho95] and-=- the ��-calculus [MPW92]. Although not presented here, the definition of a small strict functional language from [BS95] is also in promoted tyft/tyxt format. The main result of this paper is that ... |

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 |

106 | Proving congruence of bisimulation in functional programming languages
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Citation Context ...mats for process algebras have not been useful in general for defining these higher-order languages. These definition typically prove that bisimulation is a congruence by using Howe's proof technique =-=[How96]-=-. The previous proposals for rule formats for languages with high-order features all define substitution as part of the meta-theory and often rely on a particular bisimulation relation (not bisimilari... |

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64 | Higher-level synchronising devices in Meije-SCCS
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Citation Context ...ages, extensive work has been done in metatheories for SOS definitions of process algebras, especially with regard to the congruence property for bisimulation. Rule formats such as de Simone's format =-=[dS85]-=-, the tyft/tyxt by Groote and Vaandrager [GV92], and the GSOS rule format by Bloom, Istrael and Meyer [BIM95] guarantee that bisimulation will be a congruence. Extensions of these rule formats for inc... |

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43 |
A Theory of Bisimulation for the -calculus
- Sangiorgi
- 1993
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Citation Context ...ulus 5 The ��-Calculus In this section, we will present a promoted tyft/tyxt definition for the ��-calculus and show that it is transition equivalent to Sangiorgi's definition with open bisimu=-=lation. [San96]. Th-=-e syntax of our language is: P ::= 0 j ��:P j y(x):P j yx:P j [x = y]P j P 1 + P 2 j P 1 jP 2 j !P j (x)P We will use \Gamma to represent an input, an output, or a silent move. \Gamma ::= a(b) j a... |

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Citation Context ...rmat by giving promoted tyft/tyxt definitions for the lazy -calculus, CHOCS [Tho95] and the ��-calculus [MPW92]. Although not presented here, the definition of a small strict functional language f=-=rom [BS95]-=- is also in promoted tyft/tyxt format. The main result of this paper is that for any language defined in promoted tyft/tyxt format, bisimulation is a congruence. To make the existing definitions for t... |

7 |
Friiso Groote and Frits Vaandrager, Structured operational semantics and bisimulation as a congruence
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Citation Context ...ies for SOS definitions of process algebras, especially with regard to the congruence property for bisimulation. Rule formats such as de Simone's format [dS85], the tyft/tyxt by Groote and Vaandrager =-=[GV92]-=-, and the GSOS rule format by Bloom, Istrael and Meyer [BIM95] guarantee that bisimulation will be a congruence. Extensions of these rule formats for including negative premises and predicates have ma... |

6 | A fully abstract semantics for a nondeterministic functional language with monadic types - Jeffrey - 1995 |

2 | Metatheory of the -calculus - Weber, Bloom - 1996 |

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