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Narrowing, Abstraction and Constraints for Proving Properties of Reduction Relations

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Rewriting, Computation and Proof

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4600))

Abstract

We describe in this paper an inductive proof method for properties of reduction relations. The reduction trees are simulated with proof trees generated by narrowing and an abstraction mechanism. While narrowing simulates reduction, abstraction relies on the induction principle to replace subterms by variables representing specific reduced forms that trivially satisfy the property to be proved. The induction ordering is not given a priori, but defined with ordering constraints, incrementally set during the proof. Abstraction constraints are used to control the narrowing mechanism, well-known to easily diverge. The proof method is briefly illustrated on various examples of properties.

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  1. INRIA & LORIA,  

    Isabelle Gnaedig

  2. CNRS & LORIA,  

    Hélène Kirchner

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  1. Isabelle Gnaedig
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  2. Hélène Kirchner
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Hubert Comon-Lundh Claude Kirchner Hélène Kirchner

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Gnaedig, I., Kirchner, H. (2007). Narrowing, Abstraction and Constraints for Proving Properties of Reduction Relations. In: Comon-Lundh, H., Kirchner, C., Kirchner, H. (eds) Rewriting, Computation and Proof. Lecture Notes in Computer Science, vol 4600. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73147-4_3

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  • DOI: https://doi.org/10.1007/978-3-540-73147-4_3

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