Unity in nominal equational reasoning: The algebra of equality on nominal sets
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چکیده
منابع مشابه
Unity in nominal equational reasoning: The algebra of equality on nominal sets
There are currently no fewer than four dedicated logics for equality reasoning over nominal sets: nominal algebra, nominal equational logic, nominal equational logic with equality only, and permissive-nominal algebra. In this survey and research paper we present these logics side-by-side in a common notation, survey their similarities and differences, discuss their proofand model-theories, and ...
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We analyse the relationship between nominal algebra and nominal rewriting, giving a new and concise presentation of equational deduction in nominal theories. With some new results, we characterise a subclass of equational theories for which nominal rewriting provides a complete procedure to check nominal algebra equality. This subclass includes specifications of lambda-calculus and first-order ...
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Nominal sets were introduced by Gabbay and Pitts (Gabbay and Pitts, 1999). This paper describes a step towards universal algebra over nominal sets. There has been some work in this direction, most notably by M.J. Gabbay (Gabbay, 2008). The originality of our approach is that we do not start from the analogy between sets and nominal sets. As shown in (Gabbay, 2008), this is possible, but it requ...
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This paper studies the notion of “freshness” that often occurs in the meta-theory of computer science languages involving various kinds of names. Nominal Equational Logic is an extension of ordinary equational logic with assertions about the freshness of names. It is shown to be both sound and complete for the support interpretation of freshness and equality provided by the Gabbay-Pitts nominal...
متن کاملNominal Algebra
Universal algebra [5, 9, 4] is the theory of equalities t = u. It is a simple framework within which we can study mathematical structures, for example groups, rings, and fields. It has also been applied to study the mathematical properties of mathematical truth and computability. For example boolean algebras correspond to classical truth, heyting algebras correspond to intuitionistic truth, cyl...
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ژورنال
عنوان ژورنال: Journal of Applied Logic
سال: 2012
ISSN: 1570-8683
DOI: 10.1016/j.jal.2012.03.001