2014
DOI: 10.1016/j.ic.2014.01.006
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Abstract: Generalization, also called anti-unification, is the dual of unification. Given terms t and t , a generalization is a term t of which t and t are substitution instances. The dual of a most general unifier (mgu) is that of least general generalization (lgg). In this work, we extend the known untyped generalization algorithm to, first, an order-sorted typed setting with sorts, subsorts, and subtype polymorphism; second, we extend it to work modulo equational theories, where function symbols can obey any combinat… Show more

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Cited by 33 publications
(74 citation statements)
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“…In [9], the notion of least general generalization is extended to work modulo (order-sorted) equational theories, where function symbols can obey any combination of associativity, commutativity, and identity axioms (including the empty set of such axioms). Unlike the untyped case, for a pair of terms t 1 , t 2 there is generally no single lgg, due to order-sortedness or to the equational axioms.…”
Section: Rewriting and Generalization Modulo Equational Theoriesmentioning
confidence: 99%
“…In [9], the notion of least general generalization is extended to work modulo (order-sorted) equational theories, where function symbols can obey any combination of associativity, commutativity, and identity axioms (including the empty set of such axioms). Unlike the untyped case, for a pair of terms t 1 , t 2 there is generally no single lgg, due to order-sortedness or to the equational axioms.…”
Section: Rewriting and Generalization Modulo Equational Theoriesmentioning
confidence: 99%
“…Note that the empty set, denoted by ∅, belongs to People. Then, the above expressions (i) and This work presents ACUOS, a mature and highly developed implementation of the order-sorted ACU least general generalization algorithm that we formalized in [1]. ACUOS has been written in the high-performance language Maude [11] that supports reasoning modulo algebraic properties and reflection.…”
Section: Introductionmentioning
confidence: 99%
“…Roughly speaking, the generalization problem for two terms t 1 and t 2 means finding their least general generalization (lgg), i.e., the least general term t such that both t 1 and t 2 are instances of t under appropriate substitutions. While studying order-sorted modular ACU 1 generalization in [1], we found that our algorithm spends a large amount of time performing computations that, although different from previous ones, are somehow symmetrical to them and lead to equivalent (and thus redundant) results. Since this problem cannot be mitigated with mere memoization, we set out to find a way of preprocessing the terms to detect symmetries and instrument our algorithm to exploit them.…”
Section: Introductionmentioning
confidence: 93%
“…In this paper, we define an encoding of order-sorted modular ACU terms [4] in flat normal form (see [1]) into colored directed graphs that satisfy the following properties:…”
Section: The Encodingmentioning
confidence: 99%
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