Inversion framework: reasoning about inversion by conditional term rewriting systems

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We introduce a language-independent framework for reasoning about program inverters by conditional term rewriting systems. These systems can model the three fundamental forms of inversion, i.e., full, partial and semi-inversion, in declarative languages.

The correctness of the generic inversion algorithm introduced in this contribution is proven for all well-behaved rule inverters, and we demonstrate that this class of inverters encompasses several of the inversion algorithms published throughout the past years.

This new generic approach enables us to establish fundamental properties, e.g., orthogonality, for entire classes of well-behaved full inverters, partial inverters and semi-inverters regardless of their particular local rule inverters. We study known inverters as well as classes of inverters that yield left-to-right deterministic systems; left-to-right determinism is a desirable property, e.g., for functional programs; however, at the same time it is not generally a property of inverted systems. This generic approach enables a more systematic design of program inverters and fills a gap in our knowledge of program inversion.
Original languageEnglish
Title of host publicationPPDP '20: Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming
Number of pages14
PublisherAssociation for Computing Machinery
Publication date2020
ChapterArticle no- 9
ISBN (Electronic)978-1-4503-8821-4
DOIs
Publication statusPublished - 2020
Event22nd International Symposium on Principles and Practice of Declarative Programming - PPDP '20 - Bologna, Italy
Duration: 8 Sep 202010 Sep 2020

Conference

Conference22nd International Symposium on Principles and Practice of Declarative Programming - PPDP '20
LandItaly
ByBologna
Periode08/09/202010/09/2020

ID: 249396044