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A uniform approach to domain theory in realizability models
| Content Provider | Scilit |
|---|---|
| Author | Longley, John R. Simpson, Alex K. |
| Copyright Year | 1997 |
| Description | We propose a uniform way of isolating a subcategory of predomains within the category of modest sets determined by a partial combinatory algebra (PCA). Given a divergence on a PCA (which determines a notion of partiality), we identify a candidate category of predomains, the well-complete objects. We show that, whenever a single strong completeness axiom holds, the category satisfies appropriate closure properties. We consider a range of examples of PCAs with associated divergences and show that in each case the axiom does hold. These examples encompass models allowing a ‘parallel’ style of computation (for example, by interleaving), as well as models that seemingly allow only ‘sequential’ computation, such as those based on term-models for the lambda-calculus. Thus, our approach provides a uniform approach to domain theory across a wide class of realizability models. We compare our treatment with previous approaches to domain theory in realizability models. It appears that no other approach applies across such a wide range of models. |
| Related Links | https://www.pure.ed.ac.uk/ws/files/12311506/S0960129502003699a.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C87400C13BBE625A1FE5E820DB97783C/S0960129597002387a.pdf/div-class-title-a-uniform-approach-to-domain-theory-in-realizability-models-div.pdf |
| Ending Page | 505 |
| Page Count | 37 |
| Starting Page | 469 |
| ISSN | 09601295 |
| e-ISSN | 14698072 |
| DOI | 10.1017/s0960129597002387 |
| Journal | Mathematical Structures in Computer Science |
| Issue Number | 5 |
| Volume Number | 7 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1997-02-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Structures in Computer Science |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics Computer Science Applications |
