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A Decidable Case of the SemiUnification Problem (Draft Version)
, 1991
"... Semiunification is a common generalization of unification and matching. The semiunification problem is to decide solvability of finite sets of equations s = t and inequations ˜s ≤i ˜t between firstorder terms, with different inequality relations ≤i, i ∈ I. A solution consists of a substitution T0 ..."
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Semiunification is a common generalization of unification and matching. The semiunification problem is to decide solvability of finite sets of equations s = t and inequations ˜s ≤i ˜t between firstorder terms, with different inequality relations ≤i, i ∈ I. A solution consists of a substitution T0
SemiUnification
"... Semiunifiability is a generalization of both unification and matching. It is used to check nontermination of rewrite rules. In this paper an inference system is presented that decides semiunifiability of two terms s and t and computes a semiunifier. In contrast to an algorithm by Kapur, Musser et ..."
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Semiunifiability is a generalization of both unification and matching. It is used to check nontermination of rewrite rules. In this paper an inference system is presented that decides semiunifiability of two terms s and t and computes a semiunifier. In contrast to an algorithm by Kapur, Musser
On QuasiMonadic SemiUnification
, 1991
"... Semiunification is a generalization of both unification and matching with applications in proof theory, term rewriting systems, polymorphic type inference, and natural language processing. It is the problem of solving a set of term inequalities M1 ≤ N1,..., Mk ≤ Nk, where ≤ is interpreted as the su ..."
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as the subsumption preordering on (firstorder) terms. The general problem has been shown to be undecidable. As one of several special classes leftlinear semiunification, a generalization of monadic semiunification has been shown to be efficiently decidable, though. In this paper we extend the decidability result
A General Theory of SemiUnification
, 1993
"... Various restrictions on the terms allowed for substitution give rise to different cases of semiunification. Semiunification on finite and regular terms has already been considered in the literature. We introduce a general case of semiunification where substitutions are allowed on nonregular term ..."
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regular terms, and we prove the equivalence of this general case to a wellknown undecidable data base dependency problem , thus establishing the undecidability of general semiunification. We present a unified way of looking at the various problems of semiunification. We give some properties that are common
Fast leftlinear semiunification
 In Proc. Int’l. Conf. on Computing and Information
, 1990
"... Semiunification is a generalization of both unification and matching with applications in proof theory, term rewriting systems, polymorphic type inference, and natural language processing. It is the problem of solving a set of term inequalities M1 ≤ N1,..., Mk ≤ Nk, where ≤ is interpreted as the su ..."
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Cited by 6 (2 self)
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as the subsumption preordering on (firstorder) terms. Whereas the general problem has recently been shown to be undecidable, several special cases are decidable. Kfoury, Tiuryn, and Urzyczyn proved that leftlinear semiunification (LLSU) is decidable by giving an exponential time decision procedure. We improve
Fast Algorithms for Uniform SemiUnification
, 1999
"... We present a fast algorithm for uniform semiunification based on adapting the Huet unification closure method for standard unification. It solves the following decision problem in O(n 2 ff(n) 2 ), where n is the size of the two terms, and ff is the functional inverse of Ackermann 's funct ..."
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Cited by 3 (1 self)
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We present a fast algorithm for uniform semiunification based on adapting the Huet unification closure method for standard unification. It solves the following decision problem in O(n 2 ff(n) 2 ), where n is the size of the two terms, and ff is the functional inverse of Ackermann &apos
Type inference and semiunification
 In Proceedings of the ACM Conference on LISP and Functional Programming (LFP ) (Snowbird
, 1988
"... In the last ten years declarationfree programming languages with a polymorphic typing discipline (ML, B) have been developed to approximate the flexibility and conciseness of dynamically typed languages (LISP, SETL) while retaining the safety and execution efficiency of conventional statically type ..."
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Cited by 32 (7 self)
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polymorphism found in, e.g., ML with a polymorphic typing rule for recursive definitions. We show that semiunification, the problem of solving inequalities over firstorder terms, characterizes type checking in the MilnerMycroft Calculus to polynomial time, even in the restricted case where nested definitions
Logic Program Schemas, SemiUnification and Constraints
 In: N.E. Fuchs (ed), Proc. of LOPSTR'97 (this volume
"... The use of schemas is a classical way of synthesizing, transforming and analyzing logic programs. Operations on schemas are needed, in particular, the semiunification of schemas with programs. Since schemas are secondorder objects, the related semiunification is the secondorder semiunification, ..."
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Cited by 2 (0 self)
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, which is decidable but NPcomplete. The nondeterminism implied by the NPcompleteness slows down the search for a substitution. The present paper expresses the semiunification process over schemas as rewriting and reduction rules. Global and local constraints are associated to the schema to extend
Semiunification of Two Terms in Abelian Groups
, 1994
"... A substitution oe AGsemiunifies the inequation s ? AG t iff there is another substitution ae such that ae(oe(s)) =AG oe(t), where =AG is equality in Abelian groups. I give an algorithm that decides if an inequation has an AGsemiunifier and, if so, returns a most general one. This is a firs ..."
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Cited by 3 (2 self)
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A substitution oe AGsemiunifies the inequation s ? AG t iff there is another substitution ae such that ae(oe(s)) =AG oe(t), where =AG is equality in Abelian groups. I give an algorithm that decides if an inequation has an AGsemiunifier and, if so, returns a most general one. This is a
Results 1  10
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