QRB-Domains and the Probabilistic Powerdomain
Is there any Cartesian-closed category of continuous domains that would be closed under Jones and Plotkin's probabilistic powerdomain construction? This is a major open problem in the area of denotational semantics of probabilistic higher-order languages. We relax the question, and look for qua...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2012-02-01
|
| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/956/pdf |
| _version_ | 1827322961811472384 |
|---|---|
| author | Jean Goubault-Larrecq |
| author_facet | Jean Goubault-Larrecq |
| author_sort | Jean Goubault-Larrecq |
| collection | DOAJ |
| description | Is there any Cartesian-closed category of continuous domains that would be
closed under Jones and Plotkin's probabilistic powerdomain construction? This
is a major open problem in the area of denotational semantics of probabilistic
higher-order languages. We relax the question, and look for quasi-continuous
dcpos instead. We introduce a natural class of such quasi-continuous dcpos, the
omega-QRB-domains. We show that they form a category omega-QRB with pleasing
properties: omega-QRB is closed under the probabilistic powerdomain functor,
under finite products, under taking bilimits of expanding sequences, under
retracts, and even under so-called quasi-retracts. But... omega-QRB is not
Cartesian closed. We conclude by showing that the QRB domains are just one half
of an FS-domain, merely lacking control. |
| first_indexed | 2024-04-25T01:37:07Z |
| format | Article |
| id | doaj.art-e4eafdbeadbc4ab991162e77d5af3953 |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:37:07Z |
| publishDate | 2012-02-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-e4eafdbeadbc4ab991162e77d5af39532024-03-08T09:27:54ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742012-02-01Volume 8, Issue 110.2168/LMCS-8(1:14)2012956QRB-Domains and the Probabilistic PowerdomainJean Goubault-LarrecqIs there any Cartesian-closed category of continuous domains that would be closed under Jones and Plotkin's probabilistic powerdomain construction? This is a major open problem in the area of denotational semantics of probabilistic higher-order languages. We relax the question, and look for quasi-continuous dcpos instead. We introduce a natural class of such quasi-continuous dcpos, the omega-QRB-domains. We show that they form a category omega-QRB with pleasing properties: omega-QRB is closed under the probabilistic powerdomain functor, under finite products, under taking bilimits of expanding sequences, under retracts, and even under so-called quasi-retracts. But... omega-QRB is not Cartesian closed. We conclude by showing that the QRB domains are just one half of an FS-domain, merely lacking control.https://lmcs.episciences.org/956/pdfcomputer science - programming languagesd.3.1, f.1.2, f.3.2 |
| spellingShingle | Jean Goubault-Larrecq QRB-Domains and the Probabilistic Powerdomain Logical Methods in Computer Science computer science - programming languages d.3.1, f.1.2, f.3.2 |
| title | QRB-Domains and the Probabilistic Powerdomain |
| title_full | QRB-Domains and the Probabilistic Powerdomain |
| title_fullStr | QRB-Domains and the Probabilistic Powerdomain |
| title_full_unstemmed | QRB-Domains and the Probabilistic Powerdomain |
| title_short | QRB-Domains and the Probabilistic Powerdomain |
| title_sort | qrb domains and the probabilistic powerdomain |
| topic | computer science - programming languages d.3.1, f.1.2, f.3.2 |
| url | https://lmcs.episciences.org/956/pdf |
| work_keys_str_mv | AT jeangoubaultlarrecq qrbdomainsandtheprobabilisticpowerdomain |