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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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Original languageEnglish
Pages (from-to)57-105
Number of pages49
JournalJournal of Automated Reasoning
Issue number1
Publication statusPublished - Jun 2011


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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