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Generalising and dualising the third list-homomorphism theorem

Shin-Cheng Mu, Akimasa Morihata
<span title="2011-09-18">2011</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xu5bk2lj5rbdxlx6222nw7tsxi" style="color: black;">SIGPLAN notices</a> </i> &nbsp;
The third list-homomorphism theorem says that a function is a list homomorphism if it can be described as an instance of both a foldr and a foldl .  ...  We prove a dual theorem for unfolds and generalise both theorems to trees: if a function generating a list can be described both as an unfoldr and an unfoldl , the list can be generated from the middle  ...  This pearl was inspired by a question proposed by Zhenjiang Hu, who also cooperated with the authors throughout the development of this paper and made plenty of important technical contributions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2034574.2034824">doi:10.1145/2034574.2034824</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lz72a67dufcnzll72niebuemty">fatcat:lz72a67dufcnzll72niebuemty</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120124181509/http://www.iis.sinica.edu.tw/~scm/pub/icfp055fp-mu.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/36/02/36024925d7d40c535791b9bc604455e672568dfd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2034574.2034824"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Generalising and dualising the third list-homomorphism theorem

Shin-Cheng Mu, Akimasa Morihata
<span title="">2011</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ug3n3jfg4jdcpdvbrhe3m4txqa" style="color: black;">Proceeding of the 16th ACM SIGPLAN international conference on Functional programming - ICFP &#39;11</a> </i> &nbsp;
The third list-homomorphism theorem says that a function is a list homomorphism if it can be described as an instance of both a foldr and a foldl .  ...  We prove a dual theorem for unfolds and generalise both theorems to trees: if a function generating a list can be described both as an unfoldr and an unfoldl , the list can be generated from the middle  ...  This pearl was inspired by a question proposed by Zhenjiang Hu, who also cooperated with the authors throughout the development of this paper and made plenty of important technical contributions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2034773.2034824">doi:10.1145/2034773.2034824</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icfp/MuM11.html">dblp:conf/icfp/MuM11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r2g5vblayzg7vmlnamuduedhya">fatcat:r2g5vblayzg7vmlnamuduedhya</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120124181509/http://www.iis.sinica.edu.tw/~scm/pub/icfp055fp-mu.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/36/02/36024925d7d40c535791b9bc604455e672568dfd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2034773.2034824"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>