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The Use of Embeddings to Provide a Clean Separation of Term and Annotation for Higher Order Rippling

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Abstract

Rippling is a proof search guidance technique with particular application to proof by mathematical induction. It is based on a concept of annotating the differences between two terms. In its original formulation this annotation was only appropriate to first-order formulae. We use a notion of embedding to adapt these annotations appropriately for higher-order syntax. This representation simplifies the theory of annotated terms, no longer requiring special substitution and unification theorems. A key feature of the representation is that it provides a clean separation of the term and the annotation. We illustrate this with selected examples using our implementation of these ideas in λClam.

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Authors and Affiliations

  1. School of Computer Science, University of Liverpool, Liverpool, L69 3BX, UK

    Louise Abigail Dennis

  2. Edinburgh Development Laboratory, IBM, 21 St. Andrew Square, Edinburgh, EH2 1AY, UK

    Ian Green

  3. Centre for Intelligent Systems and their Applications, Division of Informatics, University of Edinburgh, Appleton Tower, Edinburgh, UK

    Alan Smaill

Authors
  1. Louise Abigail Dennis
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  2. Ian Green
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  3. Alan Smaill
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Corresponding author

Correspondence to Louise Abigail Dennis.

Additional information

Research funded by EPSRC grants Gr/M45030 and Gr/SO1771/01. We thank members of the Mathematical Reasoning Group in Edinburgh and especially Alan Bundy and Lucas Dixon for input to this work. Some earlier ideas related to this work are due to Jason Gallagher. The anonymous referees of an earlier draft of this paper also contributed many helpful comments and suggestions.

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Dennis, L.A., Green, I. & Smaill, A. The Use of Embeddings to Provide a Clean Separation of Term and Annotation for Higher Order Rippling. J Autom Reasoning 47, 57–105 (2011). https://doi.org/10.1007/s10817-010-9177-y

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  • DOI: https://doi.org/10.1007/s10817-010-9177-y

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