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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 ..."
Abstract

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.
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 ..."
Abstract

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