Conference Paper
A Dependent Type Theory with Names and Binding.
DOI: 10.1007/b100120 Conference: Computer Science Logic, 18th International Workshop, CSL 2004, 13th Annual Conference of the EACSL, Karpacz, Poland, September 2024, 2004, Proceedings
Source: DBLP

Article: A Simple Nominal Type Theory.
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ABSTRACT: Abstract Nominal logic is an extension of firstorder logic with features useful for reasoning about abstract syntax with bound names. For computational applications such as programming and formal reasoning, it is desirable to develop constructive type theories for nominal logic which extend standard type theories for propositional, firstor higherorder logic. This has proven dicult, largely because of complex interactions between nominal logic’s nameabstraction operation and ordinary functional abstraction. This diculty,already arises in the case of propositional logic and simple type theory. In this paper we show how this diculty can be overcome, and present a simple nominal type theory which enjoys properties such as type soundness and strong normalization, and which can be soundly interpreted using existing nominal set models of nominal,logic. We also sketch how,recursion combinators for languages with binding structure can be provided. This is an important first step towards understanding the constructive content of nominal logic and incorporating it into existing constructive logics and type theories. Keywords: nominal terms, type systemsElectr. Notes Theor. Comput. Sci. 01/2009; 228:3752.  [Show abstract] [Hide abstract]
ABSTRACT: Graph transformation has been used to model concurrent systems in software engineering, as well as in biochemistry and life sciences. The application of a transformation rule can be characterised algebraically as construction of a doublepushout (DPO) diagram in the category of graphs. We show how intuitionistic linear logic can be extended with resourcebound quantification, allowing for an implicit handling of the DPO conditions, and how resource logic can be used to reason about graph transformation systems.Electronic Proceedings in Theoretical Computer Science. 01/2010; 
Conference Paper: Nominal Domain Theory for Concurrency.
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ABSTRACT: This paper investigates a methodology of using FM (Fraenkel Mostowski) sets, and the ideas of nominal set theory, to adjoin name generation to a semantic theory. By developing a domain theory for con currency within FM sets the domain theory inherits types and operations for name generation, essentially without disturbing its original higher order features. The original domain theory had a metalanguage HOPLA (Higher Order Process Language) and accordingly this expands to a met alanguage, Nominal HOPLA, with name generation (closely related to an earlier language newHOPLA). Nominal HOPLA possesses an oper ational and denotational semantics which are related via soundness and adequacy results, again carried out within FM sets.Computer Science Logic, 23rd international Workshop, CSL 2009, 18th Annual Conference of the EACSL, Coimbra, Portugal, September 711, 2009. Proceedings; 01/2009
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