Incremental Proofs of Termination, Confluence and Sufficient Completeness of OBJ Specifications

Nakamura, Masaki; Ogata, Kôichi; Futatsugi, Kokichi

doi:10.1007/978-3-642-54624-2_5

Cited by 6 publications

(3 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Each specification is better to satisfy these properties as much as possible depending on each context. There are many studies on these properties, e.g., [7], [25], [53], that help to make a specification satisfy them.…”

Section: Initiality Termination Confluence Sufficient Completenessmentioning

confidence: 99%

Advances of Proof Scores in CafeOBJ

Futatsugi¹

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Critical flaws continue to exist at the level of domain, requirement, and/or design specification, and specification verification (i.e., to check whether a specification has desirable properties) is still one of the most important challenges in software/system engineering. CafeOBJ is an executable algebraic specification language system and domain/requirement/design engineers can write proof scores for improving quality of specifications by the specification verification. This paper describes advances of the proof scores for the specification verification in CafeOBJ.

show abstract

Section: Initiality Termination Confluence Sufficient Completenessmentioning

confidence: 99%

Advances of Proof Scores in CafeOBJ

Futatsugi¹

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…eq [14]: {M} in {{}} = false . eq [15]: {M} in {{M'}} = M in {M'} and M' in {M} . eq [16] The Church-Rosser check of the HF-SETS module using the CRC tool says that the specification is sort-decreasing, but it cannot show that it is locally confluent, returning eight critical pairs as proof obligations.…”

Section: An Equational Specification For Hereditarily Finite Setsmentioning

confidence: 99%

“…The main difference between the two approaches is that the one presented in this paper can handle both conditional specifications and reasoning modulo axioms, while [2] does not support reasoning modulo axioms. More recently, Nakamura et al [15] propose incremental techniques for proving termination, confluence, and sufficient completeness of OBJ specifications. Their inference system is also based on the notion of constructor subsignatures, handles conditional equations, and provides sufficient conditions for ensuring such an incremental extension in a modular way.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Proving Ground Confluence of Equational Specifications Modulo Axioms

Durán¹,

Meseguer

Rocha

2018

Rewriting Logic and Its Applications

View full text Add to dashboard Cite

Abstract. Terminating functional programs should be deterministic, i.e., should evaluate to a unique result, regardless of the evaluation order. For equational functional programs such determinism is exactly captured by the ground confluence property. For terminating equations this is equivalent to ground local confluence, which follows from local confluence. Checking local confluence by computing critical pairs is the standard way to check ground confluence. The problem is that some perfectly reasonable equational programs are not locally confluent and it can be very hard or even impossible to make them so by adding more equations. We propose a three-step strategy to prove that an equational program as is is ground confluent: First: apply the strategy proposed in [8] to use non-joinable critical pairs as completion hints to either achieve local confluence or reduce the number of critical pairs. Second: use the inductive inference system proposed in this paper to prove the remaining critical pairs ground joinable. Third: to show ground confluence of the original specification, prove also ground joinable the equations added. These methods apply to order-sorted and possibly conditional equational programs modulo axioms such as, e.g., Maude functional modules.

show abstract

On Ground Convergence and Completeness of Conditional Equational Program Hierarchies

Meseguer

Skeirik

2022

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Incremental Proofs of Termination, Confluence and Sufficient Completeness of OBJ Specifications

Cited by 6 publications

References 14 publications

Advances of Proof Scores in CafeOBJ

Advances of Proof Scores in CafeOBJ

Proving Ground Confluence of Equational Specifications Modulo Axioms

On Ground Convergence and Completeness of Conditional Equational Program Hierarchies

Contact Info

Product

Resources

About