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Abella: A System for Reasoning about Relational Specifications

Abstract : The Abella interactive theorem prover is based on an intuitionistic logic that allows for inductive and co-inductive reasoning over relations. Abella supports the λ-tree approach to treating syntax containing binders: it allows simply typed λ-terms to be used to represent such syntax and it provides higher-order (pattern) unification, the ∇ quantifier, and nominal constants for reasoning about these representations. As such, it is a suitable vehicle for formalizing the meta-theory of formal systems such as logics and programming languages. This tutorial exposes Abella incrementally, starting with its capabilities at a first-order logic level and gradually presenting more sophisticated features, ending with the support it offers to the two-level logic approach to meta-theoretic reasoning. Along the way, we show how Abella can be used prove theorems involving natural numbers, lists, and automata, as well as involving typed and untyped λ-calculi and the π-calculus.
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Contributor : Kaustuv Chaudhuri Connect in order to contact the contributor
Submitted on : Tuesday, January 13, 2015 - 1:27:13 PM
Last modification on : Friday, November 18, 2022 - 9:27:19 AM
Long-term archiving on: : Tuesday, April 14, 2015 - 10:51:08 AM


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David Baelde, Kaustuv Chaudhuri, Andrew Gacek, Dale Miller, Gopalan Nadathur, et al.. Abella: A System for Reasoning about Relational Specifications. Journal of Formalized Reasoning, 2014, Special Issue: User Tutorials 2, 7 (2), pp.1-89. ⟨10.6092/issn.1972-5787/4650⟩. ⟨hal-01102709⟩



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