Minimal lambda-theories by ultraproducts
A longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the least lambda-theory lambda-beta or the least sensible lambda-theory H (generated by equating all the unsolvable terms). A related question is whether, gi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2013-03-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1303.7329v1 |
| _version_ | 1818642685808869376 |
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| author | Antonio Bucciarelli Alberto Carraro Antonino Salibra |
| author_facet | Antonio Bucciarelli Alberto Carraro Antonino Salibra |
| author_sort | Antonio Bucciarelli |
| collection | DOAJ |
| description | A longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the least lambda-theory lambda-beta or the least sensible lambda-theory H (generated by equating all the unsolvable terms). A related question is whether, given a class of lambda models, there is a minimal lambda-theory represented by it. In this paper, we give a general tool to answer positively to this question and we apply it to a wide class of webbed models: the i-models. The method then applies also to graph models, Krivine models, coherent models and filter models. In particular, we build an i-model whose theory is the set of equations satisfied in all i-models. |
| first_indexed | 2024-12-16T23:47:00Z |
| format | Article |
| id | doaj.art-7558b670461b49e6a1670b203fc77777 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-12-16T23:47:00Z |
| publishDate | 2013-03-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-7558b670461b49e6a1670b203fc777772022-12-21T22:11:27ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802013-03-01113Proc. LSFA 2012617610.4204/EPTCS.113.8Minimal lambda-theories by ultraproductsAntonio BucciarelliAlberto CarraroAntonino SalibraA longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the least lambda-theory lambda-beta or the least sensible lambda-theory H (generated by equating all the unsolvable terms). A related question is whether, given a class of lambda models, there is a minimal lambda-theory represented by it. In this paper, we give a general tool to answer positively to this question and we apply it to a wide class of webbed models: the i-models. The method then applies also to graph models, Krivine models, coherent models and filter models. In particular, we build an i-model whose theory is the set of equations satisfied in all i-models.http://arxiv.org/pdf/1303.7329v1 |
| spellingShingle | Antonio Bucciarelli Alberto Carraro Antonino Salibra Minimal lambda-theories by ultraproducts Electronic Proceedings in Theoretical Computer Science |
| title | Minimal lambda-theories by ultraproducts |
| title_full | Minimal lambda-theories by ultraproducts |
| title_fullStr | Minimal lambda-theories by ultraproducts |
| title_full_unstemmed | Minimal lambda-theories by ultraproducts |
| title_short | Minimal lambda-theories by ultraproducts |
| title_sort | minimal lambda theories by ultraproducts |
| url | http://arxiv.org/pdf/1303.7329v1 |
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