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Issue title: Program Transformation: Theoretical Foundations and Basic Techniques. Part 1
Article type: Research Article
Authors: Cunha, Alcino | Pinto, Jorge Sousa
Affiliations: Departamento de Informática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal. alcino@di.uminho.pt; jsp@di.uminho.pt
Note: [] Address for correspondence: Departamento de Informática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal
Abstract: Functional programs are particularly well suited to formal manipulation by equational reasoning. In particular, it is straightforward to use calculational methods for program transformation. Well-known transformation techniques, like tupling or the introduction of accumulating parameters, can be implemented using calculation through the use of the fusion (or promotion) strategy. In this paper we revisit this transformation method, but, unlike most of the previous work on this subject, we adhere to a pure point-free calculus that emphasizes the advantages of equational reasoning. We focus on the accumulation strategy initially proposed by Bird, where the transformed programs are seen as higher-order folds calculated systematically from a specification. The machinery of the calculus is expanded with higher-order point-free operators that simplify the calculations. A substantial number of examples (both classic and new) are fully developed, and we introduce several shortcut optimization rules that capture typical transformation patterns.
Keywords: Functional Programming, Program Transformation, Program Calculation, Point-free Programming, Accumulation Strategy
Journal: Fundamenta Informaticae, vol. 66, no. 4, pp. 315-352, 2005
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