Principal Types for Nominal Theories

Fairweather, Elliot; Fernández, Maribel; Gabbay, Murdoch J.

doi:10.1007/978-3-642-22953-4_14

Cited by 5 publications

(5 citation statements)

References 12 publications

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“…Since nominal terms have good algorithmic properties, we could translate CRSs to NRSs in order to take advantage of existing nominal procedures (i.e., orderings, completion) and then transfer back the results. The extension to typed systems (adapting the type systems developed for NRSs [12,13] to CRSs) is also left for future work.…”

Section: Discussionmentioning

confidence: 99%

From nominal to higher-order rewriting and back again

Domínguez¹,

Fernández²

2015

Logical Methods in Computer Science

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Abstract. We present a translation function from nominal rewriting systems (NRSs) to combinatory reduction systems (CRSs), transforming closed nominal rules and ground nominal terms to CRSs rules and terms, respectively, while preserving the rewriting relation. We also provide a reduction-preserving translation in the other direction, from CRSs to NRSs, improving over a previously defined translation. These tools, together with existing translations between CRSs and other higher-order rewriting formalisms, open up the path for a transfer of results between higher-order and nominal rewriting. In particular, techniques and properties of the rewriting relation, such as termination, can be exported from one formalism to the other.

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Section: Discussionmentioning

confidence: 99%

From nominal to higher-order rewriting and back again

Domínguez¹,

Fernández²

2015

Logical Methods in Computer Science

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“…In the latter case, an extended syntax is used, where noncapturing atom-substitution is a primitive notion. 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.…”

Section: Related Workmentioning

confidence: 99%

Nominal essential intersection types

Ayala-Rincón

Fernández

Rocha-Oliveira

et al. 2018

Theoretical Computer Science

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“…The work of Section 3 was first presented in [29]. An earlier version of the material presented in Section 4 and Section 5 was published in [30] in collaboration with Murdoch J. Gabbay. It was subsequently improved upon in [29].…”

Section: Introductionmentioning

confidence: 99%

“…For nominal terms, a Curry-style type system is given in [32], later simplified in [30]. Nominal terms are given sorts in [69] where atoms inhabit base atom sorts and term-formers yield terms of base 'data' sorts.…”

Section: Introductionmentioning

confidence: 99%