Combining de Bruijn indices and higher-order abstract syntax in Coq

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Combining de Bruijn indices and higher-order abstract syntax in Coq (2006)

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by Venanzio Capretta , Amy P. Felty

Venue:	Proceedings of TYPES 2006, volume 4502 of Lecture Notes in Computer Science
Citations:	16 - 2 self

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@INPROCEEDINGS{Capretta06combiningde,
    author = {Venanzio Capretta and Amy P. Felty},
    title = {Combining de Bruijn indices and higher-order abstract syntax in Coq},
    booktitle = {Proceedings of TYPES 2006, volume 4502 of Lecture Notes in Computer Science},
    year = {2006},
    pages = {63--77},
    publisher = {Springer-Verlag}
}

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Abstract

Abstract. The use of higher-order abstract syntax is an important approach for the representation of binding constructs in encodings of languages and logics in a logical framework. Formal meta-reasoning about such object languages is a particular challenge. We present a mechanism for such reasoning, formalized in Coq, inspired by the Hybrid tool in Isabelle. At the base level, we define a de Bruijn representation of terms with basic operations and a reasoning framework. At a higher level, we can represent languages and reason about them using higher-order syntax. We take advantage of Coq’s constructive logic by formulating many definitions as Coq programs. We illustrate the method on two examples: the untyped lambda calculus and quantified propositional logic. For each language, we can define recursion and induction principles that work directly on the higher-order syntax. 1

Keyphrases

higher-order abstract syntax bruijn index higher-order syntax bruijn representation basic operation coq program object language hybrid tool logical framework reasoning framework important approach propositional logic formal meta-reasoning constructive logic induction principle many definition base level particular challenge untyped lambda calculus

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