Intrinsic reasoning about functional programs II: unipolar induction and primitive-recursion
Identifieur interne : 006D05 ( Main/Exploration ); précédent : 006D04; suivant : 006D06Intrinsic reasoning about functional programs II: unipolar induction and primitive-recursion
Auteurs : Daniel Leivant [États-Unis]Source :
- Theoretical computer science [ 0304-3975 ] ; 2004.
Descripteurs français
- Pascal (Inist)
English descriptors
- KwdEn :
Abstract
We continue from (Ann. Pure Appl. logic 114 (2002) 117) our study of reasoning about recursion equations in rudimentary theories for inductive data, dubbed intrinsic theories. We show that the functions that are provable using unipolar induction are precisely the primitive-recursive functions, where we call an instance of induction unipolar if data predicates do not occur in the induction formula both positively and negatively. Two special cases of this result are well known, namely induction over Σ01 and Π01. Here, however, induction formulas may have unrestricted quantifier alternations as long as those quantifiers that are relativized to data do not violate the prescribed restriction. The main technical challenge is in showing that the functions provable by unipolar induction, even in classical logic, are primitive-recursive. The result is generic with respect to the underlying inductive data, suggesting a potentially useful formalization of primitive-recursive mathematics.
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream PascalFrancis, to step Corpus: 000660
- to stream PascalFrancis, to step Curation: 000381
- to stream PascalFrancis, to step Checkpoint: 000597
- to stream Main, to step Merge: 007032
- to stream Main, to step Curation: 006D05
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" level="a">Intrinsic reasoning about functional programs II: unipolar induction and primitive-recursion</title><author><name sortKey="Leivant, Daniel" sort="Leivant, Daniel" uniqKey="Leivant D" first="Daniel" last="Leivant">Daniel Leivant</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Department of Computer Science, Indiana University</s1><s2>Bloomington, IN 47405</s2><s3>USA</s3><sZ>1 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>Bloomington, IN 47405</wicri:noRegion></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">04-0318327</idno><date when="2004">2004</date><idno type="stanalyst">PASCAL 04-0318327 INIST</idno><idno type="RBID">Pascal:04-0318327</idno><idno type="wicri:Area/PascalFrancis/Corpus">000660</idno><idno type="wicri:Area/PascalFrancis/Curation">000381</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">000597</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000597</idno><idno type="wicri:doubleKey">0304-3975:2004:Leivant D:intrinsic:reasoning:about</idno><idno type="wicri:Area/Main/Merge">007032</idno><idno type="wicri:Area/Main/Curation">006D05</idno><idno type="wicri:Area/Main/Exploration">006D05</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Intrinsic reasoning about functional programs II: unipolar induction and primitive-recursion</title><author><name sortKey="Leivant, Daniel" sort="Leivant, Daniel" uniqKey="Leivant D" first="Daniel" last="Leivant">Daniel Leivant</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Department of Computer Science, Indiana University</s1><s2>Bloomington, IN 47405</s2><s3>USA</s3><sZ>1 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>Bloomington, IN 47405</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>Computer theory</term><term>Formalization</term><term>Functional programming</term><term>Quantifier</term><term>Reasoning</term><term>Recursive function</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Raisonnement</term><term>Programmation fonctionnelle</term><term>Fonction récursive</term><term>Quantificateur</term><term>Formalisation</term><term>Informatique théorique</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We continue from (Ann. Pure Appl. logic 114 (2002) 117) our study of reasoning about recursion equations in rudimentary theories for inductive data, dubbed intrinsic theories. We show that the functions that are provable using unipolar induction are precisely the primitive-recursive functions, where we call an instance of induction unipolar if data predicates do not occur in the induction formula both positively and negatively. Two special cases of this result are well known, namely induction over Σ<sup>0</sup>1 and Π<sup>0</sup>1. Here, however, induction formulas may have unrestricted quantifier alternations as long as those quantifiers that are relativized to data do not violate the prescribed restriction. The main technical challenge is in showing that the functions provable by unipolar induction, even in classical logic, are primitive-recursive. The result is generic with respect to the underlying inductive data, suggesting a potentially useful formalization of primitive-recursive mathematics.</div></front></TEI><affiliations><list><country><li>États-Unis</li></country></list><tree><country name="États-Unis"><noRegion><name sortKey="Leivant, Daniel" sort="Leivant, Daniel" uniqKey="Leivant D" first="Daniel" last="Leivant">Daniel Leivant</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 006D05 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 006D05 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Main
|étape= Exploration
|type= RBID
|clé= Pascal:04-0318327
|texte= Intrinsic reasoning about functional programs II: unipolar induction and primitive-recursion
}}
| This area was generated with Dilib version V0.6.33. |  |