On an interpretation of safe recursion in light affine logic
Identifieur interne : 006D01 ( Main/Exploration ); précédent : 006D00; suivant : 006D02On an interpretation of safe recursion in light affine logic
Auteurs : A. S. Murawski [Royaume-Uni] ; C.-H. L. Ong [Royaume-Uni]Source :
- Theoretical computer science [ 0304-3975 ] ; 2004.
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Abstract
We introduce a subalgebra BC- of Bellantoni and Cook's safe-recursion function algebra BC. Functions of the subalgebra have safe arguments that are non-contractible (i.e non-duplicable). We propose a definition of safe and normal variables in light affine logic (LAL), and show that BC- is the largest subalgebra that is interpretable in LAL, relative to that definition. Though BC- itself is not PF complete, there are extensions of it (by additional schemes for defining functions with safe arguments) that are, and are still interpretable in LAL and so preserve PF closure. We focus on one such which is BC- augmented by a definition-by-cases construct and a restricted form of definition-by-recursion scheme over safe arguments. As a corollary we obtain a new proof of the PF completeness of LAL.
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S." last="Murawski">A. S. Murawski</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Oxford University Computing Laboratory (OUCL), Wolfson Building, Parks Road</s1><s2>Oxford OX1 3QD</s2><s3>GBR</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ></inist:fA14><country>Royaume-Uni</country><wicri:noRegion>Oxford OX1 3QD</wicri:noRegion></affiliation></author><author><name sortKey="Ong, C H L" sort="Ong, C H L" uniqKey="Ong C" first="C.-H. L." last="Ong">C.-H. L. Ong</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Oxford University Computing Laboratory (OUCL), Wolfson Building, Parks Road</s1><s2>Oxford OX1 3QD</s2><s3>GBR</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ></inist:fA14><country>Royaume-Uni</country><wicri:noRegion>Oxford OX1 3QD</wicri:noRegion></affiliation></author></analytic><series><title level="j" type="main">Theoretical computer science</title><title level="j" type="abbreviated">Theor. comput. sci.</title><idno type="ISSN">0304-3975</idno><imprint><date when="2004">2004</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Theoretical computer science</title><title level="j" type="abbreviated">Theor. comput. sci.</title><idno type="ISSN">0304-3975</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Completeness</term><term>Computer theory</term><term>LAL</term><term>Logic</term><term>PF fermeture</term><term>Recursive method</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Logique</term><term>Méthode récursive</term><term>Complétude</term><term>Informatique théorique</term><term>46J10</term><term>Fermeture PF</term><term>LAL</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We introduce a subalgebra BC- of Bellantoni and Cook's safe-recursion function algebra BC. Functions of the subalgebra have safe arguments that are non-contractible (i.e non-duplicable). We propose a definition of safe and normal variables in light affine logic (LAL), and show that BC- is the largest subalgebra that is interpretable in LAL, relative to that definition. Though BC- itself is not PF complete, there are extensions of it (by additional schemes for defining functions with safe arguments) that are, and are still interpretable in LAL and so preserve PF closure. We focus on one such which is BC- augmented by a definition-by-cases construct and a restricted form of definition-by-recursion scheme over safe arguments. As a corollary we obtain a new proof of the PF completeness of LAL.</div></front></TEI><affiliations><list><country><li>Royaume-Uni</li></country></list><tree><country name="Royaume-Uni"><noRegion><name sortKey="Murawski, A S" sort="Murawski, A S" uniqKey="Murawski A" first="A. S." last="Murawski">A. S. Murawski</name></noRegion><name sortKey="Ong, C H L" sort="Ong, C H L" uniqKey="Ong C" first="C.-H. L." last="Ong">C.-H. L. Ong</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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