A strong restriction of the inductive completion procedure

Fribourg, Laurent

doi:10.1016/s0747-7171(89)80069-0

Cited by 35 publications

(4 citation statements)

References 14 publications

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“…The constrained rewriting in this paper is a computation model that rewrites a term by applying a constrained rewriting rule if the term satisfies the constraint on interpretable domains attached to the rule [5,1,10,9,2]. Proposed a rewriting induction method on the constrained rewriting [10,7], a decision procedure of reduction-completeness of terms must be extended for constrained terms, terms admitting constraints attached, in order to apply the method to mechanical inductive theorem proving, where a term is said to be reduction-complete [4] if any ground instance of the term is a redex. If a constrained term rewriting system is terminating and all terms are reduction-complete, the rewrite system is said to be sufficient complete, which is useful to relax the application conditions of inference rules in the above method [10].…”

Section: Introductionmentioning

confidence: 99%

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On Constructing Constrained Tree Automata Recognizing Ground Instances of Constrained Terms

Nishida

Sakai

Yasuhiro

2013

Electron. Proc. Theor. Comput. Sci.

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An inductive theorem proving method for constrained term rewriting systems, which is based on rewriting induction, needs a decision procedure for reduction-completeness of constrained terms. In addition, the sufficient complete property of constrained term rewriting systems enables us to relax the side conditions of some inference rules in the proving method. These two properties can be reduced to intersection emptiness problems related to sets of ground instances for constrained terms. This paper proposes a method to construct deterministic, complete, and constraint-complete constrained tree automata recognizing ground instances of constrained terms.

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Section: Introductionmentioning

confidence: 99%

“…Note also that the constructed transition rules are not always optimized via the construction in Definition 12. 4 Theorem 13 The CTA A constructed in Definition 12 is a deterministic, complete, and constraintcomplete CTA such that L(A ) = G(T ).…”

mentioning

confidence: 99%

On Constructing Constrained Tree Automata Recognizing Ground Instances of Constrained Terms

Nishida

Sakai

Yasuhiro

2013

Electron. Proc. Theor. Comput. Sci.

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“…Plaisted has proposed a semantic confluence test [Plaisted 1985], but he has not shown how his test can be automatized. Completion techniques are used in Ganzinger [1987] and Fribourg [1989]. It is generally accepted that such techniques may be very inefficient, since the completion procedure often diverges even for very small specifications.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous checking of completeness and ground confluence for algebraic specifications

Bouhoula

2009

ACM Trans. Comput. Logic

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Algebraic specifications provide a powerful method for the specification of abstract data types in programming languages and software systems. Completeness and ground confluence are fundamental notions for building algebraic specifications in a correct and modular way. Related works for checking ground confluence are based on the completion techniques or on the test that all critical pairs between axioms are valid with respect to a sufficient criterion for ground confluence. It is generally accepted that such techniques may be very inefficient, even for very small specifications. Indeed, the completion procedure often diverges and there often exist many critical pairs of the axioms. In this article, we present a procedure for simultaneously checking completeness and ground confluence for specifications with free/nonfree constructors and parameterized specifications. If the specification is not complete or not ground confluent, then our procedure will output the set of patterns on whose ground instances a function is not defined and it can easily identify the rules that break ground confluence. In contrast to previous work, our method does not rely on completion techniques and does not require the computation of critical pairs of the axioms. The method is entirely implemented and allowed us to prove the completeness and the ground confluence of many specifications in a completely automatic way, where related techniques diverge or generate very complex proofs. Our system offers two main components: (i) a completeness and ground confluence analyzer that computes pattern trees of defined functions and may generate some proof obligations; and (ii) a procedure to prove (joinable) inductive conjectures which is used to discharge these proof obligations.

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“…One main problem is that such a completion often loops, generating infinitely many critical pairs. Fribourg [22] first observed that only overlaps of axioms on conjectures are necessary: it is the so-called "linear strategy". Moreover, whenever E can be turned into a ground convergent and sufficiently complete rewrite system, overlaping can be performed at specific positions.…”

Section: Introductionmentioning

confidence: 99%

Inductive proof search modulo

Nahon

Kirchner

et al. 2009

Ann Math Artif Intell

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We present an original narrowing-based proof search method for inductive theorems in equational rewrite theories given by a rewrite system R and a set E of equalities. It has the specificity to be grounded on deduction modulo and to rely on narrowing to provide both induction variables and instantiation schemas. Whenever the equational rewrite system (R, E) has good properties of termination, sufficient completeness, and when E is constructor and variable preserving, narrowing at defined-innermost positions leads to consider only unifiers which are constructor substitutions. This is especially interesting for associative and associative-commutative theories for which the general proof search system is refined. The method is shown to be sound and refutationally correct and complete. A major feature of our approach is to provide a constructive proof in deduction modulo for each successful instance of the proof search procedure.

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A strong restriction of the inductive completion procedure

Cited by 35 publications

References 14 publications

On Constructing Constrained Tree Automata Recognizing Ground Instances of Constrained Terms

On Constructing Constrained Tree Automata Recognizing Ground Instances of Constrained Terms

Simultaneous checking of completeness and ground confluence for algebraic specifications

Inductive proof search modulo

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