Results 1  10
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157
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 Schema", whichgenera ..."
Abstract

Cited by 755 (22 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.
Term Rewriting Systems
, 1992
"... Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstract Re ..."
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Cited by 567 (16 self)
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Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstract Reduction Systems
A Scheme for Integrating Concrete Domains into Concept Languages
, 1991
"... A drawback which concept languages based on klone have is that all the terminological knowledge has to be defined on an abstract logical level. In many applications, one would like to be able to refer to concrete domains and predicates on these domains when defining concepts. Examples for such conc ..."
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Cited by 262 (20 self)
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A drawback which concept languages based on klone have is that all the terminological knowledge has to be defined on an abstract logical level. In many applications, one would like to be able to refer to concrete domains and predicates on these domains when defining concepts. Examples for such concrete domains are the integers, the real numbers, or also nonarithmetic domains, and predicates could be equality, inequality, or more complex predicates. In the present paper we shall propose a scheme for integrating such concrete domains into concept languages rather than describing a particular extension by some specific concrete domain. We shall define a terminological and an assertional language, and consider the important inference problems such as subsumption, instantiation, and consistency. The formal semantics as well as the reasoning algorithms are given on the scheme level. In contrast to existing klone based systems, these algorithms will be not only sound but also complete. The...
HiLog: A foundation for higherorder logic programming
 JOURNAL OF LOGIC PROGRAMMING
, 1993
"... We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higherorder syntax and allows arbitrary terms to appear in places where predicates, functions and atomic formulas occur in predicate calc ..."
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Cited by 213 (40 self)
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We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higherorder syntax and allows arbitrary terms to appear in places where predicates, functions and atomic formulas occur in predicate calculus. But its semantics is firstorder and admits a sound and complete proof procedure. Applications of HiLog are discussed, including DCG grammars, higherorder and modular logic programming, and deductive databases.
Rippling: A Heuristic for Guiding Inductive Proofs
, 1993
"... We describe rippling: a tactic for the heuristic control of the key part of proofs by mathematical induction. This tactic significantly reduces the search for a proof of a wide variety of inductive theorems. We first present a basic version of rippling, followed by various extensions which are neces ..."
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Cited by 162 (39 self)
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We describe rippling: a tactic for the heuristic control of the key part of proofs by mathematical induction. This tactic significantly reduces the search for a proof of a wide variety of inductive theorems. We first present a basic version of rippling, followed by various extensions which are necessary to capture larger classes of inductive proofs. Finally, we present a generalised form of rippling which embodies these extensions as special cases. We prove that generalised rippling always terminates, and we discuss the implementation of the tactic and its relation with other inductive proof search heuristics.
The Syntax Definition Formalism SDF  Reference Manual
, 2001
"... SDF is a formalism for the definition of syntax which is comparable to BNF in some respect, but has a wider scope in that it also covers the definition... ..."
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Cited by 141 (24 self)
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SDF is a formalism for the definition of syntax which is comparable to BNF in some respect, but has a wider scope in that it also covers the definition...
Completion Without Failure
, 1989
"... We present an "unfailing" extension of the standard KnuthBendix completion procedure that is guaranteed to produce a desired canonical system, provided certain conditions are met. Weprove that this unfailing completion method is refutationally complete for theorem proving in equational theories. The ..."
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Cited by 122 (19 self)
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We present an "unfailing" extension of the standard KnuthBendix completion procedure that is guaranteed to produce a desired canonical system, provided certain conditions are met. Weprove that this unfailing completion method is refutationally complete for theorem proving in equational theories. The method can also be applied to Horn clauses with equality, in which case it corresponds to positive unit resolution plus oriented paramodulation, with unrestricted simplification.
Equations and rewrite rules: a survey
 In Formal Language Theory: Perspectives and Open Problems
, 1980
"... bY ..."
Termination of Term Rewriting: Interpretation and Type Elimination
 Journal of Symbolic Computation
, 1994
"... this paper we introduce the notion of a monotone algebra as the natural concept for semantical methods. Though we focus on `pure' TRS, the ideas are easily extended to conditional TRS, typed TRS and TRS modulo equations. We propose a classification of types of termination based upon the types of ord ..."
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Cited by 85 (13 self)
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this paper we introduce the notion of a monotone algebra as the natural concept for semantical methods. Though we focus on `pure' TRS, the ideas are easily extended to conditional TRS, typed TRS and TRS modulo equations. We propose a classification of types of termination based upon the types of orderings of the underlying monotone algebras. Some remarks and examples are not claimed to be new but are included for completeness and for illustrating the setting of monotone algebras.