SOS rule formats for zero and unit elements

Algebra and Coalgebra in Computer Science

Ingólfsdóttir

et al. 2013

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Abstract. In the field of structural operational semantics (SOS), there have been several proposals both for syntactic rule formats guaranteeing the validity of algebraic laws, and for algorithms for automatically generating ground-complete axiomatizations. However, there has been no synergy between these two types of results. This paper takes the first steps in marrying these two areas of research in the meta-theory of SOS and shows that taking algebraic laws into account in the mechanical generation of axiomatizations results in simpler axiomatizations. The proposed theory is applied to some examples from the literature, showing that, in these cases, the generated axiomatizations coincide with hand-crafted ones.

Section: Discussionmentioning

confidence: 99%

Exploiting Algebraic Laws to Improve Mechanized Axiomatizations

Algebra and Coalgebra in Computer Science

Ingólfsdóttir

et al. 2013

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“…In the remainder of this paper, following the work presented in, e.g., [3,5,6,11,21,32], we shall present a rule format ensuring that certain unary operations are idempotent. This rule format will rely on one yielding that terms of a certain form are idempotent for some binary operator.…”

Section: Definition 22 (Gsos Formatmentioning

confidence: 99%

“…In this approach, one gives syntactic templates for the inference rules used in defining the operational semantics for certain operators that guarantee the validity of the desired laws, thus obviating the need for an a posteriori verification. (See [3,5,6,11,21,32] for examples of rule formats for algebraic properties in the literature on SOS.) The definition of SOS rule formats is based on finding a reasonably good trade-off between generality and ease of application.…”

Section: Introductionmentioning

confidence: 99%

SOS Rule Formats for Idempotent Terms and Idempotent Unary Operators

Lecture Notes in Computer Science

Ingólfsdóttir

2013

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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.

“…In order to check for the bisimilarity of the two process terms introduced at the beginning of the current example, one loads the generated specification and uses the Maude command reduce: We successfully used PREG Axiomatizer to further extend the operational semantics of ; with the predictable non-failure predicate = δ (which plays the role of the predicate " = 0" presented in [4]) with the rules:…”

Section: Case Studiesmentioning

confidence: 99%

PREG Axiomatizer – A Ground Bisimilarity Checker for GSOS with Predicates

Caltais

Algebra and Coalgebra in Computer Science

et al. 2011

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PREG Axiomatizer is a tool used for proving strong bisimilarity between ground terms consisting of operations in the GSOS format extended with predicates. It automatically derives sound and groundcomplete axiomatizations using a technique proposed by the authors of this paper. These axiomatizations are provided as input to the Maude system, which, in turn, is used as a reduction engine for provided ground terms. These terms are bisimilar if and only if their normal forms obtained in this fashion are equal. The motivation of this tool is the optimized handling of equivalence checking between complex ground terms within automated provers and checkers.