A Practical Approach to Partiality – A Proof Based Approach

Mehta, Farhad

doi:10.1007/978-3-540-88194-0_16

Cited by 12 publications

(25 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our main sources of information are [1,12,13]; these sources give an intuition about the intended semantics, but also leave questions open. We have resolved these questions through discussions with other Rodin developers.…”

Section: Semanticsmentioning

confidence: 99%

“…It is therefore not surprising that different logics are based on different semantics: Event-B [12] and PVS [17] choose SW-semantics; LPF [4], the logic underlying VDM, is based on SS-semantics; Owe [16] favors WS-semantics. To our best knowledge, only Owe explains his choice by a comparison between the four semantics.…”

Section: Term Rewritingmentioning

confidence: 99%

“…Note that the premise of (11) is true under the instantiations in (12). It can also be checked that the conclusion of (11) under the instantiations in (12) is equivalent to Γ ; that last step relies on the assumption that $f is applied only to ordinary variables in Γ , because ordinary variables are well-defined.…”

Section: Proving User Supplied Rules Soundmentioning

confidence: 99%

“…Other work introducing Event-B's logic disregards the details about partial functions [1] or is confined to an untyped fragment of Event-B's logic [12], in particular excluding sets. We therefore start our exposition with a novel presentation of syntax and semantics of Event-B's logic.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Term Rewriting in Logics of Partial Functions

Schmalz¹

2011

Formal Methods and Software Engineering

View full text Add to dashboard Cite

Abstract. We devise a theoretical foundation of directed rewriting, a term rewriting strategy for logics of partial functions, inspired by term rewriting in the Rodin platform. We prove that directed rewriting is sound and show how to supply new rewrite rules in a soundness preserving fashion. In the context of Rodin, we show that directed rewriting makes a significant number of conditional rewrite rules unconditional. Our work not only allows us to point out a number of concrete ways of improving directed rewriting in Rodin, but also has applications in other logics of partial functions. Additionally, we give a semantics for the logic of Event-B.

show abstract

Section: Semanticsmentioning

confidence: 99%

Section: Term Rewritingmentioning

confidence: 99%

Section: Proving User Supplied Rules Soundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Term Rewriting in Logics of Partial Functions

Schmalz¹

2011

Formal Methods and Software Engineering

View full text Add to dashboard Cite

show abstract

“…Schmalz provides a comprehensive specification of the logic of Event-B. He gives semantics, devises soundness preserving extension methods, develops a proof calculus similar to [9], and proves its soundness. He presents a formal language for expressing rules (including non-freeness conditions) and shows how to reason about the soundness of Event-B rules.…”

mentioning

confidence: 99%

Practical Theory Extension in Event-B

Butler

Maamria²

2013

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. The Rodin tool for Event-B supports formal modelling and proof using a mathematical language that is based on predicate logic and set theory. Although Rodin has in-built support for a rich set of operators and proof rules, for some application areas there may be a need to extend the set of operators and proof rules supported by the tool. This paper outlines a new feature of the Rodin tool, the theory component, that allows users to extend the mathematical language supported by the tool. Using theories, Rodin users may define new data types and polymorphic operators in a systematic and practical way. Theories also allow users to extend the proof capabilities of Rodin by defining new proof rules that get incorporated into the proof mechanisms. Soundness of new definitions and rules is provided through validity proof obligations.

show abstract

Fast and Effective Well-Definedness Checking

Leuschel

2020

Lecture Notes in Computer Science

View full text Add to dashboard Cite

A Practical Approach to Partiality – A Proof Based Approach

Cited by 12 publications

References 10 publications

Term Rewriting in Logics of Partial Functions

Term Rewriting in Logics of Partial Functions

Practical Theory Extension in Event-B

Fast and Effective Well-Definedness Checking

Contact Info

Product

Resources

About