منابع مشابه
On universal algebra over nominal sets
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...
متن کاملNominal Sets over Algebraic Atoms
Nominal sets, introduced to Computer Science by Gabbay and Pitts, are useful for modeling computation on data structures built of atoms that can only be compared for equality. In certain contexts it is useful to consider atoms equipped with some nontrivial structure that can be tested in computation. Here, we study nominal sets over atoms equipped with both relational and algebraic structure. O...
متن کاملAlgebraic Theories over Nominal Sets
We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to introduce new notions of finitary based monads and uniform monads. In a second part we spell out these notions in the language of universal algebra, show how to r...
متن کاملUnity 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 ...
متن کاملNominal (Universal) Algebra: Equational Logic with Names and Binding
In informal mathematical discourse (such as the text of a paper on theoretical computer science) we often reason about equalities involving binding of object-variables. We find ourselves writing assertions involving meta-variables and capture-avoidance constraints on where object-variables can and cannot occur free. Formalising such assertions is problematic because the standard logical framewo...
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ژورنال
عنوان ژورنال: Mathematical Structures in Computer Science
سال: 2010
ISSN: 0960-1295,1469-8072
DOI: 10.1017/s0960129509990399