2002
DOI: 10.1145/504077.504080
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Reasoning with higher-order abstract syntax in a logical framework

Abstract: Logical frameworks based on intuitionistic or linear logics with higher-type quantification have been successfully used to give high-level, modular, and formal specifications of many important judgments in the area of programming languages and inference systems. Given such specifications, it is natural to consider proving properties about the specified systems in the framework: for example, given the specification of evaluation for a functional programming language, prove that the language is deterministic or … Show more

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Cited by 76 publications
(88 citation statements)
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“…Otherwise, different logics (say linear) can be employed, without changing infrastructure. This would allow, for example, the utilization of the most elegant encodings of the meta-theory of functional programming with references proposed, for instance, in [14].…”
Section: Discussionmentioning
confidence: 99%
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“…Otherwise, different logics (say linear) can be employed, without changing infrastructure. This would allow, for example, the utilization of the most elegant encodings of the meta-theory of functional programming with references proposed, for instance, in [14].…”
Section: Discussionmentioning
confidence: 99%
“…Inducting HOAS-style over open terms is a major challenge [21]; in this setting generic judgments are particularly problematic, but can be dealt with by switching to a more expressive SL, based on a eigenvariable encoding [14]. While it is already simple enough to implement such a logic, the new theory of n-ary abstractions which underlines the next version of the Hybrid infrastructure will directly support this syntax, as well as a form of Isabelle HOL-like datatypes over HOAS signatures.…”
Section: Discussionmentioning
confidence: 99%
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“…Hypothetical and parametric judgments are encoded in the SL layer. In this paper, we use a simple SL, a sequent formulation of a fragment of second-order minimal logic with backchaining, adapted from [MM02] (and also used in [MMF08]). Its syntax and inference rules can be encoded directly as follows:…”
Section: Mechanization In Two-level Hybridmentioning
confidence: 99%
“…-(II.a) The HOAS-tailored framework approach [61], [59], [38], [40], [65], [25], [1], [16], [53]. This is characterized by the extension of the pure logical frameworks as in (I) with meta-reasoning capabilities.…”
Section: Introduction Hoas (Higher-ordermentioning
confidence: 99%