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Nominal Lawvere theories. (English) Zbl 1326.68087

Beklemishev, Lev D. (ed.) et al., Logic, language, information and computation. 18th international workshop, WoLLIC 2011, Philadelphia, PA, USA, May 18–20, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-20919-2/pbk). Lecture Notes in Computer Science 6642. Lecture Notes in Artificial Intelligence, 67-83 (2011).
Summary: Lawvere theories provide a category theoretic view of equational logic, identifying equational theories with small categories equipped with finite products. This formulation allows equational theories to be investigated as first class mathematical entities. However, many formal systems, particularly in computer science, are described by equations modulated by side conditions asserting the “freshness of names”; these may be expressed as theories of Nominal Equational Logic (NEL). This paper develops a correspondence between NEL-theories and certain categories that we call nominal Lawvere theories.
For the entire collection see [Zbl 1214.03002].

MSC:

68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
03B70 Logic in computer science
18C10 Theories (e.g., algebraic theories), structure, and semantics
18C50 Categorical semantics of formal languages
68N18 Functional programming and lambda calculus
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