Sequentially and piecewise-affinity in segments of real-PCF

Amin Farjudian

doi:10.1016/j.entcs.2004.08.002

Sequentially and piecewise-affinity in segments of real-PCF

Amin Farjudian

Research output: Journal Publication › Conference article › peer-review

3 Citations (Scopus)

Abstract

Real PCF(RPCF) was proposed by Martín Escardó [8] as a language for Real number computation. One of the key - and most controversial - constants is parallel-if (pif_I), the existence of which causes a serious inefficiency in the language leading to RPCF being impractical. While search is being undertaken to replace pif_I with a more efficient operator, one needs to be assured of the segment of RPCF without pif_I being sequential. A positive answer to this question is the main result of this paper. On the other hand, we show that non-affine functions - such as f(x) := x² - are not definable in RPCF without pif_I.

Original language	English
Pages (from-to)	3-43
Number of pages	41
Journal	Electronic Notes in Theoretical Computer Science
Volume	73
DOIs	https://doi.org/10.1016/j.entcs.2004.08.002
Publication status	Published - 25 Oct 2004
Externally published	Yes
Event	Proceedings of the Workshop on Domains VI - Birmingham, United Kingdom Duration: 16 Sept 2002 → 19 Sept 2002

Keywords

Interval domain
Logical relations
PCF
Real-PCF
Real-number computation
Sequentially

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1016/j.entcs.2004.08.002

Cite this

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title = "Sequentially and piecewise-affinity in segments of real-PCF",

abstract = "Real PCF(RPCF) was proposed by Mart{\'i}n Escard{\'o} [8] as a language for Real number computation. One of the key - and most controversial - constants is parallel-if (pifI), the existence of which causes a serious inefficiency in the language leading to RPCF being impractical. While search is being undertaken to replace pifI with a more efficient operator, one needs to be assured of the segment of RPCF without pifI being sequential. A positive answer to this question is the main result of this paper. On the other hand, we show that non-affine functions - such as f(x) := x2 - are not definable in RPCF without pifI.",

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PY - 2004/10/25

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N2 - Real PCF(RPCF) was proposed by Martín Escardó [8] as a language for Real number computation. One of the key - and most controversial - constants is parallel-if (pifI), the existence of which causes a serious inefficiency in the language leading to RPCF being impractical. While search is being undertaken to replace pifI with a more efficient operator, one needs to be assured of the segment of RPCF without pifI being sequential. A positive answer to this question is the main result of this paper. On the other hand, we show that non-affine functions - such as f(x) := x2 - are not definable in RPCF without pifI.

AB - Real PCF(RPCF) was proposed by Martín Escardó [8] as a language for Real number computation. One of the key - and most controversial - constants is parallel-if (pifI), the existence of which causes a serious inefficiency in the language leading to RPCF being impractical. While search is being undertaken to replace pifI with a more efficient operator, one needs to be assured of the segment of RPCF without pifI being sequential. A positive answer to this question is the main result of this paper. On the other hand, we show that non-affine functions - such as f(x) := x2 - are not definable in RPCF without pifI.

KW - Interval domain

KW - Logical relations

KW - PCF

KW - Real-PCF

KW - Real-number computation

KW - Sequentially

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DO - 10.1016/j.entcs.2004.08.002

M3 - Conference article

AN - SCOPUS:18944408329

SN - 1571-0661

VL - 73

SP - 3

EP - 43

JO - Electronic Notes in Theoretical Computer Science

JF - Electronic Notes in Theoretical Computer Science

T2 - Proceedings of the Workshop on Domains VI

Y2 - 16 September 2002 through 19 September 2002

ER -

Sequentially and piecewise-affinity in segments of real-PCF

Abstract

Keywords

ASJC Scopus subject areas

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