Typed Nominal Rewriting

Abstract

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Nominal essential intersection types

“…Fairweather et al (2011) presents a preliminary version of the polymorphic system; the dependent type system is described in Fairweather et al (2015). Typed nominal rewriting and nominal algebra, both in the Church and Curry styles, are presented in Fairweather and Fernández (2018), where conditions for subject reduction with dynamically and statically typed rewrite rules are given. The latter is a refined version of the system presented in Fairweather (2014).…”

“…The latter is a refined version of the system presented in Fairweather (2014). The system in this work is based on Fairweather (2014); Fairweather and Fernández (2018) regarding nominal restrictions to obtain properties such as subject reduction.…”

“…We present an Essential Intersection Type System for nominal terms, such that typings are preserved for α-equivalent terms (see Section 4). Additionally, we present notions of typed nominal matching and typed rewriting, based on Fairweather and Fernández (2018) with appropriate modifications to deal with intersection types and the type operations introduced here. Our notion of typeability also differs from Fairweather and Fernández (2018) in that there is no restriction over permutations suspended on variables, and no condition over type derivations such as the "diamond" or "compatibility property".…”

“…Additionally, we present notions of typed nominal matching and typed rewriting, based on Fairweather and Fernández (2018) with appropriate modifications to deal with intersection types and the type operations introduced here. Our notion of typeability also differs from Fairweather and Fernández (2018) in that there is no restriction over permutations suspended on variables, and no condition over type derivations such as the "diamond" or "compatibility property". To ensure subject reduction the notions of rewriting and matching have to be constrained due to the capturing nature of substitutions.…”

“…Throughout Section 5, examples are given to show the necessity of the conditions added in typed matching, typed rewriting and, finally, in the theorem of subject reduction. The restrictions imposed on the nominal typed rewriting relation are inspired by the polymorphic nominal type system in Fairweather and Fernández (2018).…”