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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.
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.
Semantic Unification for Convergent Systems
, 1994
"... Equation solving is the process of finding a substitution of terms for variables that makes two terms equal in a given theory, while semantic unification is the process that generates a basis set of such unifying substitutions. A simpler variant of the problem is semantic matching, where the substit ..."
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Cited by 4 (2 self)
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Equation solving is the process of finding a substitution of terms for variables that makes two terms equal in a given theory, while semantic unification is the process that generates a basis set of such unifying substitutions. A simpler variant of the problem is semantic matching, where the substitution is made in only one of the terms. Semantic unification and matching constitute an important component of theorem proving and programming language interpreters. In this thesis we formulate a unification procedure based on a system of transformation rules that looks at goals in a lazy, topdown fashion, and prove its soundness and completeness for equational theories described by convergent rewrite systems (finite sets of equations that compute unique output values when applied from lefttoright to input values). We consider different variants of the system of transformation rules. We describe syntactic restrictions on the equations under which simpler sets of transformation rules are sufficient for generating a complete set of semantic matchings. We show that our firstorder unification procedure, with slight modifications, can be used to solve the satis ability problem in combinatory logic together with a convergent set of algebraic axioms, resulting in a complete higherorder unifi cation procedure for the given algebra. We also provide transformation rules to handle sit
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....
Semantic Matching in Rewrite Theories
, 1997
"... #Semantic matching" is the process of generating a basis set of substitutions #of terms for variables# that makes one term equal to another in a speci#ed theory.We restrict ourselves here to matching problems in equational theories that can be presented as programs in the form of convergent r ..."
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#Semantic matching" is the process of generating a basis set of substitutions #of terms for variables# that makes one term equal to another in a speci#ed theory.We restrict ourselves here to matching problems in equational theories that can be presented as programs in the form of convergent rewrite systems, that is, #nite sets of equations that compute unique output values when applied #from lefttoright # to input values #a generalization of functional programs#. Decidable matching can help in program veri#cation and synthesis. We describe a new class of programs for which matching is decidable, whichwith some negative resultsprovide a #ner characterization of decidability than was available before. 0 1 Introduction Equation solving is the process of #nding a substitution #of terms for variables# that makes two terms equal inagiven theory,whilesemantic uni#cation is the process which generates a basis set of such unifying substitutions. For any solution to a given goal...