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2017 | OriginalPaper | Chapter

Partial Evaluation of Order-Sorted Equational Programs Modulo Axioms

Authors : María Alpuente, Angel Cuenca-Ortega, Santiago Escobar, José Meseguer

Published in: Logic-Based Program Synthesis and Transformation

Publisher: Springer International Publishing

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Abstract

Partial evaluation (PE) is a powerful and general program optimization technique with many successful applications. However, it has never been investigated in the context of expressive rule-based languages like Maude, CafeOBJ, OBJ, ASF+SDF, and ELAN, which support: rich type structures with sorts, subsorts and overloading; and equational rewriting modulo axioms such as commutativity, associativity–commutativity, and associativity–commutativity–identity. In this paper, we illustrate the key concepts by showing how they apply to partial evaluation of expressive rule-based programs written in Maude. Our partial evaluation scheme is based on an automatic unfolding algorithm that computes term variants and relies on equational least general generalization for ensuring global termination. We demonstrate the use of the resulting partial evaluator for program optimization on several examples where it shows significant speed-ups.

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next chapter A Formal, Resource Consumption-Preserving Translation of Actors to Haskell
Footnotes
1
In Maude 2.7, only equations with the variant attribute are used by the folding variant narrowing strategy, which is the only narrowing strategy considered in this paper. We sometimes remove the variant attribute for saving space.
 
2
We assume there are no two grammar productions of the form N -> E.M \(_1\) and N -> E.M \(_2\).
 
3
We show narrowing steps in solid arrows and rewriting steps in dotted arrows.
 
4
From now on, we attach a label to each equation.
 
5
To ease reading, the arcs of the narrowing tree are decorated with the label of the corresponding equation applied at the narrowing step.
 
6
Note that this is only true because pattern matching modulo ACU is used for testing closedness.
 
7
The expression X : S represents an explicit definition of a variable X of sort S. It is worth noting that Maude automatically provides B-coherence completion of rules.
 
Literature
1.
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2.
Alpuente, M., Escobar, S., Espert, J., Meseguer, J.: A modular order-sorted equational generalization algorithm. Inf. Comput. 235, 98–136 (2014)MathSciNetCrossRefMATH
3.
Alpuente, M., Falaschi, M., Vidal, G.: Partial evaluation of functional logic programs. ACM Trans. Program. Lang. Syst. 20(4), 768–844 (1998)CrossRef
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Alpuente, M., Falaschi, M., Vidal, G.: A unifying view of functional and logic program specialization. ACM Comput. Surv. 30(3es), 9es (1998)
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Clavel, M., Durán, F., Eker, S., Escobar, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: Maude Manual (version 2.7), March 2015
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Escobar, S., Sasse, R., Meseguer, J.: Folding variant narrowing and optimal variant termination. J. Log. Algebr. Program. 81(7–8), 898–928 (2012)MathSciNetCrossRefMATH
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Jones, N.D., Gomard, C.K., Sestoft, P.: Partial Evaluation and Automatic Program Generation. Prentice-Hall, Englewood Cliffs (1993)MATH
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Jørgensen, J., Leuschel, M., Martens, B.: Conjunctive partial deduction in practice. In: Gallagher, J. (ed.) LOPSTR 1996. LNCS, vol. 1207, pp. 59–82. Springer, Heidelberg (1997). doi:10.​1007/​3-540-62718-9_​5 CrossRef
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Metadata
Title
Partial Evaluation of Order-Sorted Equational Programs Modulo Axioms
Authors
María Alpuente
Angel Cuenca-Ortega
Santiago Escobar
José Meseguer
Copyright Year
2017
Book
Logic-Based Program Synthesis and Transformation

Print ISBN: 978-3-319-63138-7

Electronic ISBN: 978-3-319-63139-4

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-63139-4_1

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