Associative-commutative discrimination nets

Bachmair, Leo; Ta, Chen; Ramakrishnan, I. V.

doi:10.1007/3-540-56610-4_56

Cited by 36 publications

(17 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So, in our case, conditional rewriting requires AC matching problems to be solved in a particular way: the first solution has to be found as fast as possible, and the others have to be provided "on request". AC matching has already been extensively studied, for instance in (Hullot, 1980;Benanav et al, 1987;Kounalis & Lugiez, 1991;Bachmair et al, 1993;Lugiez & Moysset, 1994;Eker, 1995). In this paper, we borrow from these works some techniques for the compilation of AC-matching, but we go further and address the more global problem of its integration in a normalisation procedure.…”

Section: Preliminary Conceptsmentioning

confidence: 99%

“…is a syntactic term if we consider F as a constant. A formal definition of the top layer and a few properties can be found in (Bachmair et al, 1993;Moreau, 1999).…”

Section: Preliminary Conceptsmentioning

confidence: 99%

“…In the case of AC theories, the matching problems are decomposed according to the syntactic top layers and the different AC symbols occurring in the patterns. This decomposition gives rise to a hierarchically structured collection of standard discrimination nets, called an AC discrimination net (Bachmair et al, 1993;Graf, 1996). Given a set of patterns P i = P = {p 1 , .…”

Section: Preliminary Conceptsmentioning

confidence: 99%

See 2 more Smart Citations

Promoting rewriting to a programming language: a compiler for non-deterministic rewrite programs in associative-commutative theories

Kirchner

Moreau

2001

J. Funct. Prog.

View full text Add to dashboard Cite

First-order languages based on rewrite rules share many features with functional languages, but one difference is that matching and rewriting can be made much more expressive and powerful by incorporating some built-in equational theories. To provide reasonable programming environments, compilation techniques for such languages based on rewriting have to be designed. This is the topic addressed in this paper. The proposed techniques are independent from the rewriting language, and may be useful to build a compiler for any system using rewriting modulo Associative and Commutative (AC) theories. An algorithm for many-to-one AC matching is presented, that works efficiently for a restricted class of patterns. Other patterns are transformed to fit into this class. A refined data structure, namely compact bipartite graph, allows encoding of all matching problems relative to a set of rewrite rules. A few optimisations concerning the construction of the substitution and of the reduced term are described. We also address the problem of non-determinism related to AC rewriting, and show how to handle it through the concept of strategies. We explain how an analysis of the determinism can be performed at compile time, and we illustrate the benefits of this analysis for the performance of the compiled evaluation process. Then we briefly introduce the ELAN system and its compiler, in order to give some experimental results and comparisons with other languages or rewrite engines.

show abstract

Section: Preliminary Conceptsmentioning

confidence: 99%

“…is a syntactic term if we consider F as a constant. A formal definition of the top layer and a few properties can be found in (Bachmair et al, 1993;Moreau, 1999).…”

Section: Preliminary Conceptsmentioning

confidence: 99%

Section: Preliminary Conceptsmentioning

confidence: 99%

See 1 more Smart Citation

Promoting rewriting to a programming language: a compiler for non-deterministic rewrite programs in associative-commutative theories

Kirchner

Moreau

2001

J. Funct. Prog.

View full text Add to dashboard Cite

show abstract

“…First calls to tabled subgoals correspond to generator nodes (depicted by white oval boxes), and for generators, a new entry, representing the subgoal call, is added to the table space with the variables in the call replaced by distinct VARi identifiers . The subgoal call path(a, Z) is thus added to the table space as path(a, VAR1) (step 0).…”

Section: Introductionmentioning

confidence: 99%

Multi‐dimensional lock‐free arrays for multithreaded mode‐directed tabling in Prolog

Areias

Rocha

2018

Concurrency and Computation

View full text Add to dashboard Cite

Summary This work proposes a new design for the supporting data structures used to implement multithreaded tabling in Prolog systems. Tabling is an implementation technique that improves the expressiveness of traditional Prolog systems in dealing with recursion and redundant computations. Mode‐directed tabling is an extension to the tabling technique that supports the definition of alternative criteria for specifying how answers are aggregated, thus being very suitable for problems where the goal is to dynamically calculate optimal or selective answers. In this work, we leverage the intrinsic potential that mode‐directed tabling has to express dynamic programming problems by creating a new design that improves the representation of multi‐dimensional arrays in the context of multithreaded tabling. To do so, we introduce a new mode for indexing arguments in mode‐directed tabled evaluations, named dim, where each dim argument features a uni‐dimensional lock‐free array. Experimental results using well‐known dynamic programming problems on a 32‐core machine show that the new design introduces less overheads and clearly improves the execution time for sequential and multithreaded tabled evaluations.

show abstract

“…Although the associative-commutative matching problem is known to be NP-complete [8], there are several available implementations of pattern-matching algorithms. We chose Storm, a many-to-one associative-commutative matcher [9] which uses a discrimination net mechanism [5].…”

Section: Expression Preprocessingmentioning

confidence: 99%

Using algebraic transformations to optimize expression evaluation in scientific code

Zory¹,

Coelho²

Proceedings. 1998 International Conference on Parallel Architectures and Compilation Techniques (Cat. No.98EX192)

View full text Add to dashboard Cite

Algebraic properties such as associativity or distributivity allow the manipulation of a set of mathematically equivalent expressions. However, as shown in this paper, the cost of evaluating such expressions on a computer is not constant within this domain. We suggest the use of algebraic transformations to improve the performance of computationally intensive applications on modern computer architectures. We claim that taking into account instruction-level parallelism and the new capabilities of processors when applying these transformations leads to large run-time improvements. Due to a combinatorial explosion, associativecommutative pattern-matching techniques cannot systematically be used in this context. Thus, we introduce two performance enhancing algorithms providing factorization and multiply-add extraction heuristics and choice criteria based on a simple cost model. This paper describes our approach and a first implementation. Experiments on real code, including an excerpt from SPEC FP95, are very promising since we automatically obtain the same results as manual transformations, with a performance improvement by a factor of up to 3.

show abstract

Associative-commutative discrimination nets

Cited by 36 publications

References 12 publications

Promoting rewriting to a programming language: a compiler for non-deterministic rewrite programs in associative-commutative theories

Promoting rewriting to a programming language: a compiler for non-deterministic rewrite programs in associative-commutative theories

Multi‐dimensional lock‐free arrays for multithreaded mode‐directed tabling in Prolog

Using algebraic transformations to optimize expression evaluation in scientific code

Contact Info

Product

Resources

About