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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.
A maximalliteral unit strategy for Horn clauses
 In Proc. CTRS90
, 1991
"... A new positiveunit theoremproving procedure for equational Horn clauses is presented. It uses a term ordering to restrict paxamodulation to potentially maximal sides of equations. Completeness is shown using proof orderings. 1. ..."
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Cited by 13 (0 self)
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A new positiveunit theoremproving procedure for equational Horn clauses is presented. It uses a term ordering to restrict paxamodulation to potentially maximal sides of equations. Completeness is shown using proof orderings. 1.
Abstract saturationbased inference
 IN PROCEEDINGS OF THE 18TH ANNUAL SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE
, 2003
"... Solving goals—like deciding word problems or resolving constraints—is much easier in some theory presentations than in others. What have been called “completion processes”, in particular in the study of equational logic, involve finding appropriate presentations of a given theory to solve easily a g ..."
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Cited by 12 (5 self)
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Solving goals—like deciding word problems or resolving constraints—is much easier in some theory presentations than in others. What have been called “completion processes”, in particular in the study of equational logic, involve finding appropriate presentations of a given theory to solve easily a given class of problems. We provide a general prooftheoretic setting within which completionlike processes can be modelled and studied. This framework centers around wellfounded orderings of proofs. It allows for abstract definitions and very general characterizations of saturation processes and redundancy criteria.
Ordinal arithmetic with list structures
 In Logical Foundations of Computer Science
, 1992
"... We provide a set of \natural " requirements for wellorderings of (binary) list structures. We showthat the resultant ordertype is the successor of the rst critical epsilon number. The checker has to verify that the process comes to an end. Here again he should be assistedbytheprogrammer givin ..."
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We provide a set of \natural " requirements for wellorderings of (binary) list structures. We showthat the resultant ordertype is the successor of the rst critical epsilon number. The checker has to verify that the process comes to an end. Here again he should be assistedbytheprogrammer giving a further de nite assertion to be veri ed. This may take the form of a quantity which is asserted todecrease continually and vanish when the machine stops. To the pure mathematician it is natural to give an ordinal number. In this problem the ordinal might be (n, r)! 2 +(r, s)! + k. A less highbrow form of the same thing would be to give the integer 2 80 (n, r)+2 40 (r, s)+k. Alan M. Turing (1949) 1
OrderingBased Strategies for Horn Clauses*
"... Two new theoremproving procedures for equational Horn clauses are presented. The largest literal is selected for paramodulation in both strategies, except that one method treats positive literals as larger than negative ones and results in a unit strategy. Both use term orderings to restrict paramo ..."
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Two new theoremproving procedures for equational Horn clauses are presented. The largest literal is selected for paramodulation in both strategies, except that one method treats positive literals as larger than negative ones and results in a unit strategy. Both use term orderings to restrict paramodulation to potentially maximal sides of equations and to increase the amount of allowable simplification (demodulation). Completeness is shown using proof orderings. 1
Abstract Abstract Canonical Presentations ⋆
"... Solving goals—like proving properties, deciding word problems or resolving constraints—is much easier with some presentations of the underlying theory than with others. What have been called “completion processes”, in particular in the study of equational logic, involve finding appropriate presentat ..."
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Solving goals—like proving properties, deciding word problems or resolving constraints—is much easier with some presentations of the underlying theory than with others. What have been called “completion processes”, in particular in the study of equational logic, involve finding appropriate presentations of a given theory to more easily solve a given class of problems. We provide a general prooftheoretic setting that relies directly on the fundamental concept of “good ” (that is, normalform) proofs, itself defined using wellfounded orderings on proof objects. This foundational framework allows for abstract definitions of canonical presentations and very general characterizations of saturation and redundancy criteria. Key words: Canonicity, proof orderings, redundancy, saturation, canonical rewriting, completion