Rowe, Reuben (2015) Encoding the Factorisation Calculus. In: Electronic Proceedings in Theoretical Computer Science. Proceedings of the Combined 22th International Workshop on Expressiveness in Concurrency and 12th Workshop on Structural Operational Semantics. 190. pp. 76-90. (doi:10.4204/EPTCS.190.6) (KAR id:64718)
PDF
Author's Accepted Manuscript
Language: English
This work is licensed under a Creative Commons Attribution 4.0 International License.
|
|
Download this file (PDF/204kB) |
Preview |
Request a format suitable for use with assistive technology e.g. a screenreader | |
Official URL: https://doi.org/10.4204/EPTCS.190.6 |
Abstract
Jay and Given-Wilson have recently introduced the Factorisation (or SF-) calculus as a minimal fundamental model of intensional computation. It is a combinatory calculus containing a special combinator, F, which is able to examine the internal structure of its first argument. The calculus is significant in that as well as being combinatorially complete it also exhibits the property of structural completeness, i.e. it is able to represent any function on terms definable using pattern matching on arbitrary normal forms. In particular, it admits a term that can decide the structural equality of any two arbitrary normal forms.
Since SF-calculus is combinatorially complete, it is clearly at least as powerful as the more familiar and paradigmatic Turing-powerful computational models of Lambda Calculus and Combinatory Logic. Its relationship to these models in the converse direction is less obvious, however. Jay and Given-Wilson have suggested that SF-calculus is strictly more powerful than the aforementioned models, but a detailed study of the connections between these models is yet to be undertaken.
This paper begins to bridge that gap by presenting a faithful encoding of the Factorisation Calculus into the Lambda Calculus preserving both reduction and strong normalisation. The existence of such an encoding is a new result. It also suggests that there is, in some sense, an equivalence between the former model and the latter. We discuss to what extent our result constitutes an equivalence by considering it in the context of some previously defined frameworks for comparing computational power and expressiveness.
Item Type: | Conference or workshop item (Paper) |
---|---|
DOI/Identification number: | 10.4204/EPTCS.190.6 |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing |
Depositing User: | Reuben Rowe |
Date Deposited: | 24 Nov 2017 13:41 UTC |
Last Modified: | 16 Feb 2021 13:50 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/64718 (The current URI for this page, for reference purposes) |
- Link to SensusAccess
- Export to:
- RefWorks
- EPrints3 XML
- BibTeX
- CSV
- Depositors only (login required):