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PCF extended with real numbers

Martin Hötzel Escardó
<span title="">1996</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
We extend the programming language PCF with a type for (total and partial) real numbers.  ...  We use this fact to give an operational semantics to the above referred extension of PCF. We prove that the operational semantics is sound and complete with respect to the denotational semantics.  ...  I have benefited from endless discussions with him and Abbas Edalat. Several useful comments by Abbas Edalat on the draft versions of this paper have allowed me to improve the presentation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(95)00250-2">doi:10.1016/0304-3975(95)00250-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pg2nn3ij6nbhvcbsfmzrrlnm6q">fatcat:pg2nn3ij6nbhvcbsfmzrrlnm6q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20070127033524/http://www.cs.bham.ac.uk:80/~mhe/papers/realpcf.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1c/e9/1ce96f562fa9b793bb363e6268aa41e0078c1b57.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(95)00250-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Comparing Functional Paradigms for Exact Real-Number Computation [chapter]

Andrej Bauer, Martín Hötzel Escardó, Alex Simpson
<span title="">2002</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
of real numbers; and the intensional approach, in which one encodes real numbers using ordinary datatypes.  ...  We compare the definability of total functionals over the reals in two functional-programming approaches to exact real-number computation: the extensional approach, in which one has an abstract datatype  ...  For the intensional approach, we encode real numbers within Plotkin's PCF++, which is PCF extended by parallel-conditional and existential operators [Plo77] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45465-9_42">doi:10.1007/3-540-45465-9_42</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2hnypgcb7fal7dvjfqj5yegdoq">fatcat:2hnypgcb7fal7dvjfqj5yegdoq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190305123828/http://pdfs.semanticscholar.org/c9a2/436ce1a865b8f3ac136e6c5241f48ccd56bd.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c9/a2/c9a2436ce1a865b8f3ac136e6c5241f48ccd56bd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45465-9_42"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Integration in Real PCF

Abbas Edalat, Martı́n Hötzel Escardó
<span title="">2000</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
The second author has been supervised by Mike Smyth and has bene ted from endless discussions with him.  ...  a Real PCF consists of PCF extended with a ground type for generalized real numbers and constants for the primitive operations introduced in this subsection.  ...  Theorem 4.7 (Adequacy) Every term in Real PCF extended with integration is computable.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/inco.1999.2844">doi:10.1006/inco.1999.2844</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yde5bytsjbei5bjhlrqqq6no24">fatcat:yde5bytsjbei5bjhlrqqq6no24</a> </span>
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First-order universality for real programs

T. Anberree
<span title="2011-11-30">2011</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/crzmi3qeiramtlvcrfycib3qg4" style="color: black;">Journal of Logic and Computation</a> </i> &nbsp;
Escardó described a functional programming language with an abstract data type Real for the real numbers and a non-deterministic operator rtest : Real → Bool.  ...  We show that this language is universal at first order, as conjectured by these authors: all computable, first-order total functions on the real numbers are definable.  ...  Introduction We prove that all computable total functions f : R → R are definable in a certain extension of PCF with a type for real numbers.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/exr044">doi:10.1093/logcom/exr044</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4kgltq5h2re75pzqqhzoncrspm">fatcat:4kgltq5h2re75pzqqhzoncrspm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120712150752/http://www.cs.nott.ac.uk/~tfa/papers/draft1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1b/22/1b22618c48d2d0165366dae384f5a409d7fc7ec7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/exr044"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> oup.com </button> </a>

Polyhedral conic kernel-like functions for SVMs

GÜRKAN ÖZTÜRK, EMRE ÇİMEN
<span title="2019-03-01">2019</span> <i title="The Scientific and Technological Research Council of Turkey"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ewkcv4t6w5f2pc7j2w426gox7a" style="color: black;">Turkish Journal of Electrical Engineering and Computer Sciences</a> </i> &nbsp;
We combined polyhedral conic functions (PCFs) with the SVM method. To get nonlinear classification surfaces, kernel functions are used with SVMs.  ...  The results are competitive with those of the other methods.  ...  Polyhedral conic functions (PCFs) have been introduced to solve classification problems [1] . These functions can be obtained by extending linear functions with l 1 -normed term.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3906/elk-1806-45">doi:10.3906/elk-1806-45</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vaswolcukvdijd3azaxqiiatlm">fatcat:vaswolcukvdijd3azaxqiiatlm</a> </span>
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Refinement of rational end-points real numbers by means of floating-point numbers

Yamine Ait-Ameur
<span title="">1999</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hq6x4whtd5hhlhsxzculyeamey" style="color: black;">Science of Computer Programming</a> </i> &nbsp;
It considers real numbers as intervals whose end-points are rational numbers.  ...  This paper addresses the topic of the refinement of exact real numbers. It presents a three-steps formal development towards the implementation of exact real numbers.  ...  The denotational semantics of the PCF language extended with real numbers is given below.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0167-6423(98)00008-2">doi:10.1016/s0167-6423(98)00008-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pzu2axqunzgchfrdhzg44mf6oq">fatcat:pzu2axqunzgchfrdhzg44mf6oq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190417052819/https://core.ac.uk/download/pdf/82671387.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d4/5d/d45df0d38d7764f74bb06882b18643dc410b834b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0167-6423(98)00008-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Induction and recursion on the partial real line with applications to Real PCF

Martín Hötzel Escardó, Thomas Streicher
<span title="">1999</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
The partial real line is an extension of the Euclidean real line with partial real numbers, which has been used to model exact real number computation in the programming language Real PCF.  ...  The principles are applied to show that Real PCF is universal in the sense that all computable elements of its universe of discourse are definable.  ...  Acknowledgements The first named author was supported by the Brazilian agency CNPq, an EPSRC project "Programming Languages for Real Number Computation: Theory and Implementation", and an ARC project "  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0304-3975(98)00099-1">doi:10.1016/s0304-3975(98)00099-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qyvuo43ikvhm7jybqt56qzkrtm">fatcat:qyvuo43ikvhm7jybqt56qzkrtm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190416004059/https://core.ac.uk/download/pdf/82595986.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d6/97/d6974a9a160436849a6e8bdb790f8e8327664556.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0304-3975(98)00099-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

A Stream Calculus of Bottomed Sequences for Real Number Computation

Kei Terayama, Hideki Tsuiki
<span title="">2013</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
It has applications in real number computation in that the unit interval I is topologically embedded in the set Σ ω ⊥,1 of 1⊥-sequences and a real function on I can be written as a program which inputs  ...  Then, its value for a sequence starting with a bottom is calculated by taking the meet of the values for the sequences obtained by filling the bottom with 0 and 1.  ...  This work was partly supported by JSPS KAKENHI Grant Number 22500014.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2013.09.023">doi:10.1016/j.entcs.2013.09.023</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qjyxg2pdpvh53otu2kzwmifili">fatcat:qjyxg2pdpvh53otu2kzwmifili</a> </span>
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Infrastructure-based MAC in wireless mobile ad-hoc networks

Hossam Hassanein, Tiantong You, Hussein T. Mouftah
<span title="">2005</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/l3w5c2fk6bh2fiux4zxdhtupaa" style="color: black;">Ad hoc networks</a> </i> &nbsp;
Priority access for real-time traffic Compatibility with the IEEE 802.11 standard.  ...  MPCs that can communicate with a large number of other MPCs are given preference. 4.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.adhoc.2004.01.003">doi:10.1016/j.adhoc.2004.01.003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iwresld7cncyxhfigfsvnoatc4">fatcat:iwresld7cncyxhfigfsvnoatc4</a> </span>
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Analysis and synthesis of point distributions based on pair correlation

A. Cengiz Öztireli, Markus Gross
<span title="2012-11-01">2012</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cqrugwalkvcezgalqorn4fwnuu" style="color: black;">ACM Transactions on Graphics</a> </i> &nbsp;
Base simulation With synthesized particles Original 1 PCF r max Original (Photo) Synthesized 1 PCF r max Synthesized (Rendering) PCF Irregularity 1 5 r max r max 1 1 r max r max PCF Irregularity Figure  ...  We illustrate applications of our method to real world distributions.  ...  Tobias Pfaff for his help with the fluid simulations and renderings. A. CengizÖztireli is supported by the Swiss National Science Foundation (grant No. 200021-132438 / 1).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2366145.2366189">doi:10.1145/2366145.2366189</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mrw36s5y7fbs5dty6ap4uspibi">fatcat:mrw36s5y7fbs5dty6ap4uspibi</a> </span>
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Pair Correlation Functions with Free-Form Boundaries for Distribution Inpainting and Decomposition

Baptiste Nicolet, Pierre Ecormier-Nocca, Pooran Memari, Marie-Paule Cani
<span title="">2020</span> <i title="The Eurographics Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2dtbbu6advaujbfzarg22vjkpa" style="color: black;">Annual Conference of the European Association for Computer Graphics</a> </i> &nbsp;
In this work we introduce a triangulationbased local filtering method to extend PCF-based analysis to exemplars with free-form boundaries.  ...  , in which each category of points can be studied together with their intra and inter-class correlations.  ...  In this paper, we extend PCF analysis to exemplars with freeform boundaries.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2312/egs.20201025">doi:10.2312/egs.20201025</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/eurographics/NicoletEMC20.html">dblp:conf/eurographics/NicoletEMC20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hghj3hmherfjhdulmjpsa47kxu">fatcat:hghj3hmherfjhdulmjpsa47kxu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200603032722/https://diglib.eg.org/xmlui/bitstream/handle/10.2312/egs20201025/089-092.pdf;jsessionid=FA8D582F71F314236F36D3CCA5DA7BC0?sequence=1" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1a/0c/1a0c455764ee0b7eb2d5a2a6d8fdfb74a2af9840.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2312/egs.20201025"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 7681 of Mathematical Reviews Vol. , Issue 2001K [page]

<span title="">2001</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Real PCF is a typed A-calculus over the finite types with base types for the reals, the Booleans and the natural numbers.  ...  They further extend the syntax and operational semantics of Real PCF including integration syntactically.  ... 
<span class="external-identifiers"> </span>
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Matching typed and untyped realizability

John Longley
<span title="">1999</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
We consider some examples of logical formulae to illustrate these ideas, in particular their application to exact real-number computability.  ...  We g i v e some examples of this situation for a variety of extensions of PCF.  ...  We begin with an assortment of simple examples, and then give some examples relating to exact real-number computability.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1571-0661(04)00105-7">doi:10.1016/s1571-0661(04)00105-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6zp5v23rfjhkdow3vy7yyhaojy">fatcat:6zp5v23rfjhkdow3vy7yyhaojy</a> </span>
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Exact real number computations relative to hereditarily total functionals

Dag Normann
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
is not deÿnable in Escardà o's Real-PCF from all functionals equivalent to a given total one in a uniform way.  ...  We further prove that relative to any total functional of type (I → I ) → I which gives the maximum-value for any total input, we may, given a computable, total functional of type (R → R) → R ÿnd a Real-PCF-deÿnable  ...  Applications for PCF can be found in Plotkin [10] . It is open if this result can be extended to Real-PCF.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0304-3975(01)00100-1">doi:10.1016/s0304-3975(01)00100-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/77dpybvtqbfrjgbnv4xatsh7n4">fatcat:77dpybvtqbfrjgbnv4xatsh7n4</a> </span>
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Laser Field Distribution Dependence on The Missing Holes of Photonic Crystal Fiber

Abdulghafoor Ibrahim Abdullah
<span title="2009-06-01">2009</span> <i title="University of Mosul"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/i5nnotcxovetpg6y3bdnzuh6ie" style="color: black;">Journal of education and science</a> </i> &nbsp;
µm, while the number of the hole rings (Nr) is one for all the structures.  ...  This study shows, by the field distribution, that the PCFs of large core area are operated in high order mode.  ...  Fig.4 shows the relation between the real part of the refractive index with wavelength for the proposed PCFs. The calculation have been done by using PCF1, PCF2 and PCF3 parameters.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.33899/edusj.2009.57701">doi:10.33899/edusj.2009.57701</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d6tr2unncrabbexsm725dbw3ia">fatcat:d6tr2unncrabbexsm725dbw3ia</a> </span>
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