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arXiv · 0811.4367

Hybrid: A Definitional Two-Level Approach to Reasoning with Higher-Order Abstract Syntax

Amy Felty·Alberto Momigliano
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Abstract

Combining higher-order abstract syntax and (co)induction in a logical framework is well known to be problematic. Previous work described the implementation of a tool called Hybrid, within Isabelle HOL, which aims to address many of these difficulties. It allows object logics to be represented using higher-order abstract syntax, and reasoned about using tactical theorem proving and principles of (co)induction. In this paper we describe how to use it in a multi-level reasoning fashion, similar in spirit to other meta-logics such as Twelf. By explicitly referencing provability in a middle layer called a specification logic, we solve the problem of reasoning by (co)induction in the presence of non-stratifiable hypothetical judgments, which allow very elegant and succinct specifications of object logic inference rules.

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Amy Felty, Alberto Momigliano. 2010-05-26. Hybrid: A Definitional Two-Level Approach to Reasoning with Higher-Order Abstract Syntax. https://arxiv.org/abs/0811.4367

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