首页    期刊浏览 2024年12月13日 星期五
登录注册

文章基本信息

  • 标题:Linear Abadi and Plotkin Logic
  • 本地全文:下载
  • 作者:Lars Birkedal ; Rasmus E. Møgelberg ; Rasmus Lerchedahl Petersen
  • 期刊名称:Logical Methods in Computer Science
  • 印刷版ISSN:1860-5974
  • 电子版ISSN:1860-5974
  • 出版年度:2006
  • 卷号:2
  • 期号:05
  • DOI:10.2168/LMCS-2(5:2)2006
  • 出版社:Technical University of Braunschweig
  • 摘要:

    We present a formalization of a version of Abadi and Plotkin's logic for parametricity for a polymorphic dual intuitionistic/linear type theory with fixed points, and show, following Plotkin's suggestions, that it can be used to define a wide collection of types, including existential types, inductive types, coinductive types and general recursive types. We show that the recursive types satisfy a universal property called dinaturality, and we develop reasoning principles for the constructed types. In the case of recursive types, the reasoning principle is a mixed induction/coinduction principle, with the curious property that coinduction holds for general relations, but induction only for a limited collection of ``admissible'' relations. A similar property was observed in Pitts' 1995 analysis of recursive types in domain theory. In a future paper we will develop a category theoretic notion of models of the logic presented here, and show how the results developed in the logic can be transferred to the models.

  • 关键词:Domain Theories;Formalization;Polymorphics
国家哲学社会科学文献中心版权所有