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Rule formats for determinism and idempotence
 In Proceedings of the 3rd International Conference on Fundamentals of Software Engineering (FSEN’09), Lecture Notes in Computer Science, Kish Island
, 2009
"... Abstract. Determinism is a semantic property of (a fragment of) a language that specifies that a program cannot evolve operationally in several different ways. Idempotency is a property of binary composition operators requiring that the composition of two identical specifications or programs will re ..."
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Abstract. Determinism is a semantic property of (a fragment of) a language that specifies that a program cannot evolve operationally in several different ways. Idempotency is a property of binary composition operators requiring that the composition of two identical specifications or programs will result in a piece of specification or program that is equivalent to the original components. In this paper, we propose two (related) metatheorems for guaranteeing determinism and idempotency of binary operators. These metatheorems are formulated in terms of syntactic templates for operational semantics, called rule formats. We show the applicability of our formats by applying them to various operational semantics from the literature. 1
A Rule Format for Associativity
"... Abstract. We propose a rule format that guarantees associativity of binary operators with respect to all notions of behavioral equivalence that are defined in terms of (im)possibility of transitions, e.g., the notions below strong bisimilarity in van Glabbeek’s spectrum. The initial format is a subs ..."
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Cited by 7 (5 self)
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Abstract. We propose a rule format that guarantees associativity of binary operators with respect to all notions of behavioral equivalence that are defined in terms of (im)possibility of transitions, e.g., the notions below strong bisimilarity in van Glabbeek’s spectrum. The initial format is a subset of the De Simone format. We show that all trivial generalizations of our format are bound for failure. We further extend the format in a few directions and illustrate its application to several formalisms in the literature. A subset of the format is studied to obtain associativity with respect to graph isomorphism. 1
A rule format for unit elements
, 2009
"... This paper offers a metatheorem for languages with a Structural Operational Semantics (SOS) in the style of Plotkin. Namely, it proposes a generic rule format for SOS guaranteeing that certain constants act as left or rightunit elements for a set of binary operators. We show the generality of o ..."
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Cited by 7 (6 self)
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This paper offers a metatheorem for languages with a Structural Operational Semantics (SOS) in the style of Plotkin. Namely, it proposes a generic rule format for SOS guaranteeing that certain constants act as left or rightunit elements for a set of binary operators. We show the generality of our format by applying it to a wide range of operators from the literature on process calculi.
A Hierarchy of SOS Rule Formats
, 2005
"... In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [62]. Subsequently, the format of SOS rules became the object of study. Using socalled Transition System Specifications (TS ..."
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Cited by 6 (1 self)
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In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [62]. Subsequently, the format of SOS rules became the object of study. Using socalled Transition System Specifications (TSS’s) several authors syntactically restricted the format of rules and showed several useful properties about the semantics induced by any TSS adhering to the format. This has resulted in a line of research proposing several syntactical rule formats and associated metatheorems. Properties that are guaranteed by such rule formats range from welldefinedness of the operational semantics and compositionality of behavioral equivalences to security and probabilityrelated issues. In this paper, we provide an initial hierarchy of SOS rules formats and metatheorems formulated around them.
SOS Rule Formats for Idempotent Terms and Idempotent Unary Operators
"... A unary operator f is idempotent if the equation f(x) = f(f(x)) holds. On the other end, an element a of an algebra is said to be an idempotent for a binary operator ⊙ if a = a ⊙ a. This paper presents a rule format for Structural Operational Semantics that guarantees that a unary operator be idemp ..."
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A unary operator f is idempotent if the equation f(x) = f(f(x)) holds. On the other end, an element a of an algebra is said to be an idempotent for a binary operator ⊙ if a = a ⊙ a. This paper presents a rule format for Structural Operational Semantics that guarantees that a unary operator be idempotent modulo bisimilarity. The proposed rule format relies on a companion one ensuring that certain terms are idempotent with respect to some binary operator. This study also offers a variety of examples showing the applicability of both formats.