A proof of weak termination providing the right way to terminate
Identifieur interne : 000527 ( PascalFrancis/Checkpoint ); précédent : 000526; suivant : 000528A proof of weak termination providing the right way to terminate
Auteurs : Olivier Fissore [France] ; Isabelle Gnaedig [France] ; Hélène Kirchner [France]Source :
- Lecture notes in computer science [ 0302-9743 ] ; 2005.
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Abstract
We give an inductive method for proving weak innermost termination of rule-based programs, from which we automatically infer, for each successful proof, a finite strategy for data evaluation. We first present the proof principle, using an explicit induction on the termination property, to prove that any input data has at least one finite evaluation. For that, we observe proof trees built from the rewrite system, schematizing the innermost rewriting tree of any ground term, and generated with two mechanisms: abstraction, schematizing normalization of sub-terms, and narrowing, schematizing rewriting steps. Then, we show how, for any ground term, a normalizing rewriting strategy can be extracted from the proof trees, even if the ground term admits infinite rewriting derivations.
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(région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName></affiliation></author><author><name sortKey="Gnaedig, Isabelle" sort="Gnaedig, Isabelle" uniqKey="Gnaedig I" first="Isabelle" last="Gnaedig">Isabelle Gnaedig</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>LORIA-INRIA & LORIA-CNRS, BP 239</s1><s2>54506 Vandœuvre-lès-Nancy</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName></affiliation></author><author><name sortKey="Kirchner, Helene" sort="Kirchner, Helene" uniqKey="Kirchner H" first="Hélène" last="Kirchner">Hélène Kirchner</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>LORIA-INRIA & LORIA-CNRS, BP 239</s1><s2>54506 Vandœuvre-lès-Nancy</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName></affiliation></author></analytic><series><title level="j" type="main">Lecture notes in computer science</title><idno type="ISSN">0302-9743</idno><imprint><date when="2005">2005</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Lecture notes in computer science</title><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Abstraction</term><term>Expert system</term><term>Induction</term><term>Knowledge base</term><term>Narrowing(logics)</term><term>Rewriting systems</term><term>Termination problem</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Système expert</term><term>Induction</term><term>Système réécriture</term><term>Abstraction</term><term>Problème terminaison</term><term>Base connaissance</term><term>Surréduction</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We give an inductive method for proving weak innermost termination of rule-based programs, from which we automatically infer, for each successful proof, a finite strategy for data evaluation. We first present the proof principle, using an explicit induction on the termination property, to prove that any input data has at least one finite evaluation. For that, we observe proof trees built from the rewrite system, schematizing the innermost rewriting tree of any ground term, and generated with two mechanisms: abstraction, schematizing normalization of sub-terms, and narrowing, schematizing rewriting steps. Then, we show how, for any ground term, a normalizing rewriting strategy can be extracted from the proof trees, even if the ground term admits infinite rewriting derivations.</div></front></TEI><inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0302-9743</s0></fA01><fA05><s2>3407</s2></fA05><fA08 i1="01" i2="1" l="ENG"><s1>A proof of weak termination providing the right way to terminate</s1></fA08><fA09 i1="01" i2="1" l="ENG"><s1>Theoretical aspects of computing - ICTAC 2004 : Guiyang, 20-24 September 2004, revised selected papers</s1></fA09><fA11 i1="01" i2="1"><s1>FISSORE (Olivier)</s1></fA11><fA11 i1="02" i2="1"><s1>GNAEDIG (Isabelle)</s1></fA11><fA11 i1="03" i2="1"><s1>KIRCHNER (Hélène)</s1></fA11><fA12 i1="01" i2="1"><s1>LIU (Zhiming)</s1><s9>ed.</s9></fA12><fA12 i1="02" i2="1"><s1>ARAKI (Keijiro)</s1><s9>ed.</s9></fA12><fA14 i1="01"><s1>LORIA-INRIA & LORIA-CNRS, BP 239</s1><s2>54506 Vandœuvre-lès-Nancy</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ></fA14><fA20><s1>356-371</s1></fA20><fA21><s1>2005</s1></fA21><fA23 i1="01"><s0>ENG</s0></fA23><fA26 i1="01"><s0>3-540-25304-1</s0></fA26><fA43 i1="01"><s1>INIST</s1><s2>16343</s2><s5>354000124475210240</s5></fA43><fA44><s0>0000</s0><s1>© 2005 INIST-CNRS. 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International colloquium</s1><s2>1</s2><s3>Guiyang CHN</s3><s4>2004-09-20</s4></fA30></pR></standard></inist><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Vandœuvre-lès-Nancy</li></settlement></list><tree><country name="France"><region name="Grand Est"><name sortKey="Fissore, Olivier" sort="Fissore, Olivier" uniqKey="Fissore O" first="Olivier" last="Fissore">Olivier Fissore</name></region><name sortKey="Gnaedig, Isabelle" sort="Gnaedig, Isabelle" uniqKey="Gnaedig I" first="Isabelle" last="Gnaedig">Isabelle Gnaedig</name><name sortKey="Kirchner, Helene" sort="Kirchner, Helene" uniqKey="Kirchner H" first="Hélène" last="Kirchner">Hélène Kirchner</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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