Shostak's congruence closure as completion

Kapur, Deepak

doi:10.1007/3-540-62950-5_59

Cited by 55 publications

(67 citation statements)

References 14 publications

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“…Nevertheless, the relation between our work and previous work on congruence closure is especially clear for Shostak's algorithm (see, e.g. [4,7]). The so-called signatures that are used, in all variants of this algorithm, to detect that different terms are equivalent, are very similar to our structures f (i 1 , i 2 ) : i.…”

Section: Related Worksupporting

confidence: 51%

“…Preliminary results on this issue have been reported in [5]. It however happens that, although designed independently, our work can be strongly related to existing work on computing the congruence closure of a relation over ground terms (see, e.g., [1] (Chapter 9), [2,4,6,7] ). In Section 5, we have shown that collections of structures are convenient to tackle the decision problem that motivates this related work.…”

Section: Related Workmentioning

confidence: 86%

“…In Section 5, we have shown that collections of structures are convenient to tackle the decision problem that motivates this related work. Our method allows us to "solve" a set of ground equations with time complexity O(N log N ) where N is the number of distinct sub-terms in the equations, while the algorithms presented in [1,4,6] are O(N 2 ). The algorithms in [2,7] are O(N log N ) as our method.…”

Section: Related Workmentioning

confidence: 99%

“…In fact, there is a strong correspondence between the two notions but our algorithms directly work on the structures (the signatures), not on the original terms (which only remain implicitely present in the collection of structures). It is argued in [4] that Shostak's algorithm can be viewed as computing a Knuth-Bendix completion of the set of ground equations to which it is applied. Our collections of structures can also be viewed as a confluent set of rewrite rules (when the collection is normalized).…”

Section: Related Workmentioning

confidence: 99%

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A Data Structure to Handle Large Sets of Equal Terms

Charlier¹,

Atindehou²

EPiC Series in Computing

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We present a data structure to represent and manipulate large sets of (equal) terms (or expressions). Our initial and main motivation for this data structure is the simplification of expressions with respect to a formal theory, typically, an equational one. However, it happens that the data structure is also efficient to compute the congruence closure of a relation over a set of terms. We provide an abstract definition of the data structure, including a precise semantics, and we explain how to implement it efficiently. We prove the correctness of the proposed algorithms, with a complexity analysis and experimental results. We compare these algorithms with previous algorithms to compute the congruence closure and we also sketch how we use the data structure to tackle the expression simplification problem.

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Section: Related Worksupporting

confidence: 51%

Section: Related Workmentioning

confidence: 86%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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A Data Structure to Handle Large Sets of Equal Terms

Charlier¹,

Atindehou²

EPiC Series in Computing

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“…Our solver is based on ideas from completion and congruence closure in termrewriting systems (Kapur, 1997;Bachmair & Tiwari, 2000;Beckert, 1994;Nieuwenhuis & Oliveras, 2005), and is an improvement and simplification of previous work by Schrijvers et al (Schrijvers et al, 2008a). That work presented a completionbased solver, where the top-level set of axioms was transformed to a strongly normalizing and confluent rewrite system, along with the current given equations.…”

Section: Solving Equalities Involving Type Familiesmentioning

confidence: 99%

OutsideIn(X)Modular type inference with local assumptions

Vytiniotis¹,

et al. 2011

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Advanced type system features, such as GADTs, type classes, and type families have proven to be invaluable language extensions for ensuring data invariants and program correctness among others. Unfortunately, they pose a tough problem for type inference, because they introduce local type assumptions.In this article we present a novel constraint-based type inference approach for local type assumptions. Our system, called OutsideIn(X), is parameterised over the particular underlying constraint domain X, in the same way as HM(X). This stratification allows us to use a common metatheory and inference algorithm.Going beyond the general framework, we also give a particular constraint solver for X = type classes + GADTs + type families, a non-trivial challenge in its own right.

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