Second Order Isomorphic Types: A Proof Theoretic Study on Second Order λ-Calculus with Surjective Pairing and Terminal Object
Identifieur interne : 00C707 ( Main/Exploration ); précédent : 00C706; suivant : 00C708Second Order Isomorphic Types: A Proof Theoretic Study on Second Order λ-Calculus with Surjective Pairing and Terminal Object
Auteurs : R. Dicosmo [États-Unis]Source :
- Information and Computation [ 0890-5401 ] ; 1995.
Abstract
Abstract: We investigate invertible terms and isomorphic types in the second order lambda calculus extended with surjective pairs and terminal (or Unit) type. These two topics are closely related: on one side, the study of invertibility is a necessary tool for the characterization of isomorphic types; on the other hand, we need the notion of isomorphic types to study the typed invertible terms. The result of our investigation is twofold: we give a constructive characterization of the invertible terms, extending previous work by Dezani and Bruce-Longo, and a decidable equational theory of the isomorphisms of types which hold in all models of the calculus, which is a conservative extension to the second order case of the results previously achieved for the case of first order typed calculi. Via the Curry-Howard correspondence, this work also provides a decision procedure for strong equivalence of formulae in second order intuitionistic positive propositional logic, that is suitable to search equivalent proofs in automated deduction systems.
Url:
DOI: 10.1006/inco.1995.1085
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 002363
- to stream Istex, to step Curation: 002332
- to stream Istex, to step Checkpoint: 002B22
- to stream Main, to step Merge: 00CF64
- to stream Main, to step Curation: 00C707
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Second Order Isomorphic Types: A Proof Theoretic Study on Second Order λ-Calculus with Surjective Pairing and Terminal Object</title><author><name sortKey="Dicosmo, R" sort="Dicosmo, R" uniqKey="Dicosmo R" first="R." last="Dicosmo">R. Dicosmo</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:988356788C8947A113E5083C19A074DD6F667BEC</idno><date when="1995" year="1995">1995</date><idno type="doi">10.1006/inco.1995.1085</idno><idno type="url">https://api.istex.fr/ark:/67375/6H6-GRJ6JHJT-F/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">002363</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002363</idno><idno type="wicri:Area/Istex/Curation">002332</idno><idno type="wicri:Area/Istex/Checkpoint">002B22</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">002B22</idno><idno type="wicri:doubleKey">0890-5401:1995:Dicosmo R:second:order:isomorphic</idno><idno type="wicri:Area/Main/Merge">00CF64</idno><idno type="wicri:Area/Main/Curation">00C707</idno><idno type="wicri:Area/Main/Exploration">00C707</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Second Order Isomorphic Types: A Proof Theoretic Study on Second Order λ-Calculus with Surjective Pairing and Terminal Object</title><author><name sortKey="Dicosmo, R" sort="Dicosmo, R" uniqKey="Dicosmo R" first="R." last="Dicosmo">R. Dicosmo</name><affiliation wicri:level="2"><country xml:lang="fr">États-Unis</country><wicri:regionArea>Ecole Normale Super, Liens, CNRS, 45 Rue Ulm, F 75005 Paris, France; Corso Italia, Dipartimento Informat, I 56100 Pisa, Italy and Cornell Univ, Dept Comp Sci, Ithaca, NY 14853</wicri:regionArea><placeName><region type="state">État de New York</region></placeName></affiliation></author></analytic><monogr></monogr><series><title level="j">Information and Computation</title><title level="j" type="abbrev">YINCO</title><idno type="ISSN">0890-5401</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1995">1995</date><biblScope unit="volume">119</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="176">176</biblScope><biblScope unit="page" to="201">201</biblScope></imprint><idno type="ISSN">0890-5401</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0890-5401</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We investigate invertible terms and isomorphic types in the second order lambda calculus extended with surjective pairs and terminal (or Unit) type. These two topics are closely related: on one side, the study of invertibility is a necessary tool for the characterization of isomorphic types; on the other hand, we need the notion of isomorphic types to study the typed invertible terms. The result of our investigation is twofold: we give a constructive characterization of the invertible terms, extending previous work by Dezani and Bruce-Longo, and a decidable equational theory of the isomorphisms of types which hold in all models of the calculus, which is a conservative extension to the second order case of the results previously achieved for the case of first order typed calculi. Via the Curry-Howard correspondence, this work also provides a decision procedure for strong equivalence of formulae in second order intuitionistic positive propositional logic, that is suitable to search equivalent proofs in automated deduction systems.</div></front></TEI><affiliations><list><country><li>États-Unis</li></country><region><li>État de New York</li></region></list><tree><country name="États-Unis"><region name="État de New York"><name sortKey="Dicosmo, R" sort="Dicosmo, R" uniqKey="Dicosmo R" first="R." last="Dicosmo">R. Dicosmo</name></region></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 00C707 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 00C707 | 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= ISTEX:988356788C8947A113E5083C19A074DD6F667BEC
|texte= Second Order Isomorphic Types: A Proof Theoretic Study on Second Order λ-Calculus with Surjective Pairing and Terminal Object
}}
| This area was generated with Dilib version V0.6.33. |  |