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ACsuperposition with constraints: No ACunifiers needed
 Proceedings 12th International Conference on Automated Deduction
, 1990
"... We prove the completeness of (basic) deduction strategies with constrained clauses modulo associativity and commutativity (AC). Here each inference generates one single conclusion with an additional equality s = AC t in its constraint (instead of one conclusion for each minimal ACunifier, i.e. expo ..."
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Cited by 29 (5 self)
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We prove the completeness of (basic) deduction strategies with constrained clauses modulo associativity and commutativity (AC). Here each inference generates one single conclusion with an additional equality s = AC t in its constraint (instead of one conclusion for each minimal ACunifier, i.e. exponentially many). Furthermore, computing ACunifiers is not needed at all. A clause C [[ T ]] is redundant if the constraint T is not ACunifiable. If C is the empty clause this has to be decided to know whether C [[ T ]] denotes an inconsistency. In all other cases any sound method to detect unsatisfiable constraints can be used. 1 Introduction Some fundamental ideas on applying symbolic constraints to theorem proving were given in [KKR90], where a constrained clause is a shorthand for its (infinite) set of ground instances satisfying the constraint. In a constrained equation f(x) ' a [[ x = g(y) ]], the equality `=' of the constraint is usually interpreted in T (F) (syntactic equality), ...
Rank 2 Type Systems and Recursive Definitions
, 1995
"... We demonstrate an equivalence between the rank 2 fragments of the polymorphic lambda calculus (System F) and the intersection type discipline: exactly the same terms are typable in each system. An immediate consequence is that typability in the rank 2 intersection system is DEXPTIMEcomplete. We int ..."
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Cited by 26 (1 self)
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We demonstrate an equivalence between the rank 2 fragments of the polymorphic lambda calculus (System F) and the intersection type discipline: exactly the same terms are typable in each system. An immediate consequence is that typability in the rank 2 intersection system is DEXPTIMEcomplete. We introduce a rank 2 system combining intersections and polymorphism, and prove that it types exactly the same terms as the other rank 2 systems. The combined system suggests a new rule for typing recursive definitions. The result is a rank 2 type system with decidable type inference that can type some interesting examples of polymorphic recursion. Finally,we discuss some applications of the type system in data representation optimizations such as unboxing and overloading.
Decidability of Bounded Second Order Unification
 FB INFORMATIK, J.W. GOETHEUNIVERSITAT FRANKFURT AM MAIN
, 1999
"... It is wellknown that first order unification is decidable, whereas second order (and higherorder) unification is undecidable. Bounded second order unification (BSOU) is second order unification under the restriction that only a bounded number of holes in the instantiating terms for second order va ..."
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Cited by 6 (2 self)
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It is wellknown that first order unification is decidable, whereas second order (and higherorder) unification is undecidable. Bounded second order unification (BSOU) is second order unification under the restriction that only a bounded number of holes in the instantiating terms for second order variables is permitted, however, the size of the instantiation is not restricted. In this paper, a decision algorithm for bounded second order unification is described. This is the first nontrivial decidability result for second order unification, where the (finite) signature is not restricted and there are no restrictions on the occurrences of variables. We show that the monadic second order unification (MSOU), a specialization of BSOU is in \Sigma p 2. Since MSOU is related to word unification, this is compares favourably to the best known upper bound NEXPTIME (and also to the announced upper bound PSPACE) for word unification. This supports the claim that bounded second order unification is easier than context unification, whose decidability is currently an open question.
A Survey of Some Recent Trends in RewriteBased and ParamodulationBased Deduction
"... Introduction Deduction with equality is fundamental in mathematics, logics and many applications of formal methods in computer science. During the last two decades this field has importantly progressed through new KnuthBendixlike completion techniques and their extensions to ordered paramodulatio ..."
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Cited by 2 (0 self)
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Introduction Deduction with equality is fundamental in mathematics, logics and many applications of formal methods in computer science. During the last two decades this field has importantly progressed through new KnuthBendixlike completion techniques and their extensions to ordered paramodulation for firstorder clauses. These techniques have lead to important results on deduction in firstorder logic with equality, like [HR91,BDH86,BD94,BG94,BG98,NR01], results that have been applied to stateoftheart theorem provers like Spass [Wei97] and Vampire [RV01]. These techniques have also led to results on logicbased complexity and decidability analysis [BG01,Nie98], on deduction with constrained clauses [KKR90,NR95], on inductive theorem proving [CN00], and on many other applications like symbolic constraint solving, or equationallogic programming. In the handbook chapter [NR01] the fundamental techniques in this area are reviewed and presented in a uniform fr