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InductiveDataType Systems
, 2002
"... In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "General Schem ..."
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Cited by 821 (23 self)
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In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "General Schema", whichgeneral39I theusual recursor definitions fornatural numbers and simil9 "basic inductive types". This combined lmbined was shown to bestrongl normalIk39f The purpose of this paper is toreformul33 and extend theGeneral Schema in order to make it easil extensibl3 to capture a more general cler of inductive types, cals, "strictly positive", and to ease the strong normalgAg9Ik proof of theresulGGg system. Thisresul provides a computation model for the combination of anal"DAfGI specification language based on abstract data types and of astrongl typed functional language with strictly positive inductive types.
Basic Paramodulation
 Information and Computation
, 1995
"... We introduce a class of restrictions for the ordered paramodulation and superposition calculi (inspired by the basic strategy for narrowing), in which paramodulation inferences are forbidden at terms introduced by substitutions from previous inference steps. In addition we introduce restrictions bas ..."
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Cited by 70 (12 self)
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We introduce a class of restrictions for the ordered paramodulation and superposition calculi (inspired by the basic strategy for narrowing), in which paramodulation inferences are forbidden at terms introduced by substitutions from previous inference steps. In addition we introduce restrictions based on term selection rules and redex orderings, which are general criteria for delimiting the terms which are available for inferences. These refinements are compatible with standard ordering restrictions and are complete without paramodulation into variables or using functional reflexivity axioms. We prove refutational completeness in the context of deletion rules, such as simplification by rewriting (demodulation) and subsumption, and of techniques for eliminating redundant inferences.
Decidable Matching for Convergent Systems
, 1992
"... We describe decision procedures for certain classes of semantic matching problems, where the equational theory with respect to which the semantic matching is performed has a convergent rewrite system. We give counterexamples to show that semantic matching becomes undecidable (as it generally is) ..."
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Cited by 14 (5 self)
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We describe decision procedures for certain classes of semantic matching problems, where the equational theory with respect to which the semantic matching is performed has a convergent rewrite system. We give counterexamples to show that semantic matching becomes undecidable (as it generally is) when the conditions wegive are weakened.
Applying Rewriting Techniques to the Verification of Erlang Processes
"... Erlang is a functional programming language developed by Ericsson Telecom which is particularly well suited for implementing concurrent processes. In this paper we show how methods from the area of term rewriting are presently used at Ericsson. To verify properties of processes, such a property is ..."
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Cited by 4 (0 self)
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Erlang is a functional programming language developed by Ericsson Telecom which is particularly well suited for implementing concurrent processes. In this paper we show how methods from the area of term rewriting are presently used at Ericsson. To verify properties of processes, such a property is transformed into a termination problem of a conditional term rewriting system (CTRS). Subsequently, this termination proof can be performed automatically using dependency pairs. The paper illustrates how the dependency pair technique can be applied for termination proofs of conditional TRSs. Secondly, we present two refinements of this technique, viz. narrowing and rewriting dependency pairs. These refinements are not only of use in the industrial application sketched in this paper, but they are generally applicable to arbitrary (C)TRSs. Thus,inthisway dependency pairs can be used to prove termination of even more (C)TRSs automatically.
Matching and Unification in Rewrite Theories
, 1996
"... "Semantic unification" is the process of generating a basis set of substitutions (of terms for variables) that makes two given terms equal in a specified theory. Semantic unification is an important component of some theorem provers. "Semantic matching," a simpler variantof u ..."
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"Semantic unification" is the process of generating a basis set of substitutions (of terms for variables) that makes two given terms equal in a specified theory. Semantic unification is an important component of some theorem provers. "Semantic matching," a simpler variantof unification, where the substitution is made in only one of the terms, has potential usage in programming language interpreters. Decidable matching is required for pattern application in patterndirected languages, while decidable unification is useful for theorem proving modulo an equational theory. In this paper we restrict ourselves to matching and unification problems in theories that can be presented as convergent rewrite systems, that is, finite sets of equations that compute unique output values when applied (from lefttoright) to input values. The new results presented here, together with existing results, provide a much#nercharacterization of decidable matching and unification than was available before....