Conference Paper
A Dependent Type Theory with Names and Binding.
DOI: 10.1007/9783540301240_20 Conference: Computer Science Logic, 18th International Workshop, CSL 2004, 13th Annual Conference of the EACSL, Karpacz, Poland, September 2024, 2004, Proceedings
Source: DBLP

Article: Linear Types and Locality
[Show abstract] [Hide abstract]
ABSTRACT: We introduce a system of linear dependent types, extended with quantifiers that ensure separation between distinct bound variables. Such variables may be interpreted as resources that can be accessed only locally. The main motivation for this system, is to make more manageable the logic encoding of specification formalisms based on graphs and statetransition models. The proof system is based on a sequent calculus presentation of quantified intuitionistic linear logic, relying on doubleentry sequents. We prove the admissibility of cut, and show that this result can be used to prove subject reduction.Journal of Logic and Computation 01/2014; Volume 24(Issue 3):Pages 655685. · 0.50 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present a logical framework based on the nominal approach to representing syntax with binders. First we extend nominal terms, which have a builtin nameabstraction operator and a firstorder notion of substitution for variables, with a captureavoiding substitution operator for names. We then build a dependent type system for this extended syntax and show how it can be used to formalise systems with binding operators.  [Show abstract] [Hide abstract]
ABSTRACT: Nominal logic is a variant of firstorder logic that provides support for reasoning about bound names in abstract syntax. A key feature of nominal logic is the newquantifier, which quantifies over fresh names (names not appearing in any values considered so far). Previous attempts have been made to develop convenient rules for reasoning with the newquantifier, but we argue that none of these attempts is completely satisfactory. In this article we develop a new sequent calculus for nominal logic in which the rules for the new quantifier are much simpler than in previous attempts. We also prove several structural and metatheoretic properties, including cutelimination, consistency, and equivalence to Pitts' axiomatization of nominal logic.Journal of Logic and Computation 12/2013; · 0.50 Impact Factor
Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.