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    188宝金博页面版: 【精品】Pure type systems in rewriting logic Specifying typed higher-order languages in a first-ord

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    内容提示： Pure Type Systems in Rewriting Logic:Specifying Typed Higher-Order Languagesin a First-Order Logical FrameworkMark-Oliver StehrJos? e MeseguerUniversit¨ at HamburgFachbereich Informatik - TGI22527 Hamburg, Germanystehr@informatik. uni-hamburg. deUniversity of Illinoisat Urbana-ChampaignComputer Science DepartmentUrbana, IL 61801, USAmeseguer@cs. uiuc. eduDedicated to the memory of Ole-Johan DahlAbstract. The logical and operational aspects of rewriting logic as a logi-cal framework are tested and illus...

    文档格式：PDF | 页数：36 | 浏览次数：17 | 上传日期：2015-12-31 23:12:26 | 文档星级：
    Pure Type Systems in Rewriting Logic:Specifying Typed Higher-Order Languagesin a First-Order Logical FrameworkMark-Oliver StehrJos´ e MeseguerUniversit¨ at HamburgFachbereich Informatik - TGI22527 Hamburg, Germanystehr@informatik. uni-hamburg. deUniversity of Illinoisat Urbana-ChampaignComputer Science DepartmentUrbana, IL 61801, USAmeseguer@cs. uiuc. eduDedicated to the memory of Ole-Johan DahlAbstract. The logical and operational aspects of rewriting logic as a logi-cal framework are tested and illustrated in detail by representing pure typesystems as object logics. More precisely, we apply membership equationallogic, the equational sublogic of rewriting logic, to specify pure type sys-tems as they can be found in the literature and also a new variant of puretype systems with explicit names that solves the problems with closure un-der α-conversion in a very satisfactory way. Furthermore, we use rewritinglogic itself to give a formal operational description of type checking, thatdirectly serves as an efficient type checking algorithm. The work reportedhere is part of a more ambitious project concerned with the developmentof the open calculus of constructions, an equational extension of the cal-culus of constructions that incorporates rewriting logic as a computationalsublanguage.This paper is a detailed study on the ease and naturalness with which a family ofhigher-order formal systems, namely pure type systems (PTSs) [6, 50], can be rep-resented in the first-order logical framework of rewriting logic [36]. PTSs generalizethe λ-cube [1], which already contains important calculi like λ→ [12], the systems F[23, 43] and Fω [23], a system λP close to the logical framework LF [24], and theircombination, the calculus of constructions CC [16]. PTSs are considered to be ofkey importance, since their generality and simplicity makes them an ideal basis forrepresenting higher-order logics, either via the propositions-as-types interpretation[21], or via their use as a higher-order logical framework in the spirit of LF [24, 20]or Isabelle [39].Exploiting the fact that rewriting logic (RWL) and its membership equational sublogic(MEL) [10] have initial and free models, we can define the representation of PTSsas a parameterized theory in the framework logic; that is, we define in a single para-metric way all the representations for the infinite family of PTSs. Furthermore, therepresentational versatility of RWL, and of MEL, are also exercised by consideringfour different representations of PTSs at different levels of abstraction, from a moreabstract textbook version in which terms are identified up to α-conversion, to amore concrete version with a calculus of names and explicit substitutions, and witha type checking inference system that can in fact be used as a reasonably efficientCurrently visiting University of Illinois at Urbana-Champaign, Computer Science De-partment Urbana, IL 61801, USA, e-mail: stehr@cs. uiuc. edu

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