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Polymorphic extensions of simple type structures. With an application to a bar recursive minimization

Erik Barendsen, Marc Bezem
<span title="">1996</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bnojym2hjzcgnpa4wixi2axhnq" style="color: black;">Annals of Pure and Applied Logic</a> </i> &nbsp;
Second, by combining the previous result with the model construction based on partial equivalence relations, we show how to extend a i-closed simple type structure to a model of the polymorphic I-calculus  ...  First we show how to encode ftmctionals in a 'flat' applicative structure by adding oracles to untyped I-calculus and mimicking the applicative behaviour of the functionals with an impredicatively defined  ...  Acknowledgements The research in this paper has been supported by the Netherlands Computer Science Research Foundation (SION) with ~n~cial support of the Netherl~ds Organization for Scientific Research  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0168-0072(95)00025-9">doi:10.1016/0168-0072(95)00025-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/aala6zlqqnephjumuowjxl3alm">fatcat:aala6zlqqnephjumuowjxl3alm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190309205058/https://core.ac.uk/download/pdf/82465632.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/c8/36c82bd3cd51da0c3b72d2bf0b8cb210746b239e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0168-0072(95)00025-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Page 5450 of Mathematical Reviews Vol. , Issue 98I [page]

<span title="">1998</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;
With an application to a bar recursive minimization. (English summary) Ann. Pure Appl. Logic 79 (1996), no. 3, 221-280. Summary: “The technical contribution of this paper is threefold.  ...  Second, by combining the previous result with the model construction based on partial equivalence relations, we show how to extend a /-closed simple type structure to a model of the polymorphic /-calculus  ... 
<span class="external-identifiers"> </span>
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Extensible programming with first-class cases

Matthias Blume, Umut A. Acar, Wonseok Chae
<span title="">2006</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ug3n3jfg4jdcpdvbrhe3m4txqa" style="color: black;">Proceedings of the eleventh ACM SIGPLAN international conference on Functional programming - ICFP &#39;06</a> </i> &nbsp;
We give a type system for the language and provide rules for a 2-phase transformation: first into an explicitly typed λ-calculus with record polymorphism, and finally to efficient index-passing code.  ...  We present language mechanisms for polymorphic, extensible records and their exact dual, polymorphic sums with extensible first-class cases.  ...  Acknowledgments We would like to thank Atsushi Ohori for helpful discussions. Jacques Garrigue as well as the anonymous reviewers provided valuable feedback.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1159803.1159836">doi:10.1145/1159803.1159836</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icfp/BlumeAC06.html">dblp:conf/icfp/BlumeAC06</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mm43vfniz5eovgew2ghil5q4ka">fatcat:mm43vfniz5eovgew2ghil5q4ka</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922235144/https://www.brinckerhoff.org/clements/csc530-sp08/Readings/blume-2006.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/73/11/73113c3629fc996fa7cc3e59533a4f3e92a81d69.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1159803.1159836"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Extensible programming with first-class cases

Matthias Blume, Umut A. Acar, Wonseok Chae
<span title="2006-09-16">2006</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;
We give a type system for the language and provide rules for a 2-phase transformation: first into an explicitly typed λ-calculus with record polymorphism, and finally to efficient index-passing code.  ...  We present language mechanisms for polymorphic, extensible records and their exact dual, polymorphic sums with extensible first-class cases.  ...  Acknowledgments We would like to thank Atsushi Ohori for helpful discussions. Jacques Garrigue as well as the anonymous reviewers provided valuable feedback.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1160074.1159836">doi:10.1145/1160074.1159836</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nxza4vp2p5c4ja5q3rfjqogakm">fatcat:nxza4vp2p5c4ja5q3rfjqogakm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922235144/https://www.brinckerhoff.org/clements/csc530-sp08/Readings/blume-2006.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/73/11/73113c3629fc996fa7cc3e59533a4f3e92a81d69.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1160074.1159836"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

The expression problem, trivially!

Yanlin Wang, Bruno C. d. S. Oliveira
<span title="">2016</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/scibxvvu3nguvnnafnqcwt7lcy" style="color: black;">Proceedings of the 15th International Conference on Modularity - MODULARITY 2016</a> </i> &nbsp;
The key to the solution is the use of covariant type refinement of return types (or fields): a simple feature available in many object-oriented languages, but not as widely known or used as it should be  ...  Furthermore our results have immediate applicability as practical design patterns for improving the extensibility of programs.  ...  involving recursive data structures.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2889443.2889448">doi:10.1145/2889443.2889448</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/aosd/WangO16.html">dblp:conf/aosd/WangO16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fhqugmzisvhrrm34o54mhion54">fatcat:fhqugmzisvhrrm34o54mhion54</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171215081110/http://i.cs.hku.hk:80/~bruno/papers/Modularity2016.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/c8/a8/c8a8b96051f27f9615c2c05454781abbbb26e67d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2889443.2889448"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Typed iterators for XML

Giuseppe Castagna, Kim Nguyen
<span title="2008-09-27">2008</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;
Operations on XML documents are performed by iterators that, to be useful, need to be typed by a kind of polymorphism that goes beyond what currently exists.  ...  Therefore, operations, even simple ones, that modify these features may affect the types of documents.  ...  minimal extensions to the core algebra.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1411203.1411210">doi:10.1145/1411203.1411210</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/djro6h5uireufdim5pid2iuzte">fatcat:djro6h5uireufdim5pid2iuzte</a> </span>
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System f-omega with equirecursive types for datatype-generic programming

Yufei Cai, Paolo G. Giarrusso, Klaus Ostermann
<span title="">2016</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2qaxtqe2rfgjnfefqcokcnzelq" style="color: black;">Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL 2016</a> </i> &nbsp;
In this paper, we propose F µ ω , an extension of the higherorder polymorphic lambda calculus Fω with records, variants, and equirecursive types.  ...  To decide type equality we β-normalize types, and then use an extension of equivalence checking for usual equirecursive types.  ...  This problem can be addressed via polymorphic variants [22] or structural typing. With polymorphic variants, we next run against isorecursive types.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2837614.2837660">doi:10.1145/2837614.2837660</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/popl/CaiGO16.html">dblp:conf/popl/CaiGO16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5657xjsdkrbjjl3wlr77wb2xtm">fatcat:5657xjsdkrbjjl3wlr77wb2xtm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190728071514/http://ps.informatik.uni-tuebingen.de:80/research/functors/equirecursion-fomega-popl16.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/de/21/de213d9dbd5eb61bb5f06e2e6c5326be7439dd6d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2837614.2837660"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Enhancing dependency pair method using strong computability in simply-typed term rewriting

Keiichirou Kusakari, Masahiko Sakai
<span title="2007-07-11">2007</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lnpibodwo5cpnp3qbzbnlmdepu" style="color: black;">Applicable Algebra in Engineering, Communication and Computing</a> </i> &nbsp;
The key idea of our method is to analyze recursive structure from the viewpoint of strong computability.  ...  We enhance the dependency pair method in order to prove termination using recursive structure analysis in simply-typed term rewriting systems, which is one of the computational models of functional programs  ...  Acknowledgement We would like to thank the anonymous referees for their helpful comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00200-007-0046-9">doi:10.1007/s00200-007-0046-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v3fbqstypbecfbddurhuwcxbvy">fatcat:v3fbqstypbecfbddurhuwcxbvy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829215344/http://www.ct.info.gifu-u.ac.jp/~kusakari/papers/aaecc07.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/eb/30/eb3061a9968271e398dc44f565adada66aa17fb9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00200-007-0046-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Getting F-bounded polymorphism into shape

Ben Greenman, Fabian Muehlboeck, Ross Tate
<span title="2014-06-05">2014</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;
We present a way to restrict recursive inheritance without sacrificing the benefits of F-bounded polymorphism.  ...  With this Material-Shape Separation, we prove that even naïve type-checking algorithms are sound and complete, some of which address problems that were unsolvable even under the existing proposals for  ...  We are indebted to Avik Chaudhuri, Basil Hosmer, and Michael Vitousek for posing the crazy idea of removing F-bounded polymorphism altogether, and for providing feedback as we made that thought (with compromises  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2666356.2594308">doi:10.1145/2666356.2594308</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/p4ncjvmz6vegxajmmem4nwasjy">fatcat:p4ncjvmz6vegxajmmem4nwasjy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160417043752/http://www.cs.cornell.edu/~blg59/resources/doc/effing-bound-polymorphism.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/cd/d8/cdd8eee174d8e19760d2414c6b1b1eef24e305e0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2666356.2594308"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Getting F-bounded polymorphism into shape

Ben Greenman, Fabian Muehlboeck, Ross Tate
<span title="">2013</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jpubwsjaozha5itdes6pzyz2fm" style="color: black;">Proceedings of the 35th ACM SIGPLAN Conference on Programming Language Design and Implementation - PLDI &#39;14</a> </i> &nbsp;
We present a way to restrict recursive inheritance without sacrificing the benefits of F-bounded polymorphism.  ...  With this Material-Shape Separation, we prove that even naïve type-checking algorithms are sound and complete, some of which address problems that were unsolvable even under the existing proposals for  ...  We are indebted to Avik Chaudhuri, Basil Hosmer, and Michael Vitousek for posing the crazy idea of removing F-bounded polymorphism altogether, and for providing feedback as we made that thought (with compromises  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2594291.2594308">doi:10.1145/2594291.2594308</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/pldi/GreenmanMT14.html">dblp:conf/pldi/GreenmanMT14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/obk4jm44enf4ffrlv2f76agfga">fatcat:obk4jm44enf4ffrlv2f76agfga</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160417043752/http://www.cs.cornell.edu/~blg59/resources/doc/effing-bound-polymorphism.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/cd/d8/cdd8eee174d8e19760d2414c6b1b1eef24e305e0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2594291.2594308"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Java type inference is broken

Daniel Smith, Robert Cartwright
<span title="">2008</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6y3m32grtnfktkp2oo6oqjbvta" style="color: black;">Proceedings of the 23rd ACM SIGPLAN conference on Object oriented programming systems languages and applications - OOPSLA &#39;08</a> </i> &nbsp;
Java 5, the most recent major update to the Java Programming Language, introduced a number of sophisticated features, including a major extension to the type system.  ...  While the technical details of these new features are complex, much of this complexity is hidden from the typical Java developer by an ambitious type inference mechanism.  ...  To simplify the definition of structurally-recursive functions, we will refer to the types of which a type is directly composed as its component types.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1449764.1449804">doi:10.1145/1449764.1449804</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/oopsla/SmithC08.html">dblp:conf/oopsla/SmithC08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vttcsya3m5cqhaidrwhpac46hi">fatcat:vttcsya3m5cqhaidrwhpac46hi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110711182312/http://www.cs.rice.edu/~javaplt/papers/oopsla2008.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/95/17/95176ae43fa8435bac03055e61d1a91cc481b9c6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1449764.1449804"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Object-oriented verification based on record subtyping in Higher-Order Logic [chapter]

Wolfgang Naraschewski, Markus Wenzel
<span title="">1998</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;
We show how extensible records with structural subtyping can be represented directly in Higher-Order Logic (HOL).  ...  This paper is structured as follows. Section 2 gives some impression on how to use extensible records in general mathematical modeling. We present a simple example of abstract algebra.  ...  The encoding even turns out to be very simple and natural. Extensible records in HOL give rise to applications in general mathematical modeling.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bfb0055146">doi:10.1007/bfb0055146</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gjxfdall35g5jb2xxfqs2fpc6u">fatcat:gjxfdall35g5jb2xxfqs2fpc6u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20040715025250/http://www4.in.tum.de:80/~wenzelm/papers/HOOL-extended.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/e8/2f/e82f0b18bad74358b1accf1c3dc8381234537fb5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bfb0055146"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Java type inference is broken

Daniel Smith, Robert Cartwright
<span title="2008-10-27">2008</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;
Java 5, the most recent major update to the Java Programming Language, introduced a number of sophisticated features, including a major extension to the type system.  ...  While the technical details of these new features are complex, much of this complexity is hidden from the typical Java developer by an ambitious type inference mechanism.  ...  To simplify the definition of structurally-recursive functions, we will refer to the types of which a type is directly composed as its component types.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1449955.1449804">doi:10.1145/1449955.1449804</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3vwgtb6xnbby5csjmgnpnmpvtq">fatcat:3vwgtb6xnbby5csjmgnpnmpvtq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110711182312/http://www.cs.rice.edu/~javaplt/papers/oopsla2008.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/95/17/95176ae43fa8435bac03055e61d1a91cc481b9c6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1449955.1449804"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Universe Polymorphism in Coq [chapter]

Matthieu Sozeau, Nicolas Tabareau
<span title="">2014</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This provides the same kind of code reuse facilities as ML-style parametric polymorphism. However, the structure and hierarchy of universes is more complex than bare polymorphic type variables.  ...  Benchmarking the implementation as an extension of the Coq proof assistant on real-world examples gives encouraging results.  ...  This is a simple application of the Union-Find algorithm. We canonicalize the constraints to be left with only inequality (<, ≤) constraints between distinct universes.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-08970-6_32">doi:10.1007/978-3-319-08970-6_32</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dpyzwsndangrvfp7g6xvydeasm">fatcat:dpyzwsndangrvfp7g6xvydeasm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922234500/https://www.irif.fr/~sozeau/research/publications/Universe_Polymorphism_in_Coq.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/f5/6b/f56b696e5166787236861f7cc20e2451edb5d2f8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-08970-6_32"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Gödel's Functional ("Dialectica") Interpretation [chapter]

Jeremy Avigad, Solomon Feferman
<span title="">1998</span> <i title="Elsevier"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/oujbud6hwvdhxcn633hkvdwdki" style="color: black;">Studies in Logic and the Foundations of Mathematics</a> </i> &nbsp;
For an interesting extension of bar recursion to transfinite types, see Friedrich [1985] . natural way of interpreting the set variables of PA 2 + (CA) with function variables of type 1.  ...  An interpretation M σ : σ a type of such a typed language is called a functional type structure or simply a type structure.  ...  For example, the types (n) of section 10.1 can be defined by a simple instance of primitive recursion with range U 0 , whereupon the term Π n∈0 (n) is an element of U 0 and hence a type.  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20060925013130/http://www.contrib.andrew.cmu.edu/~avigad/Papers/dialect.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/f6/4f/f64f17d41bd16730494e8af048c3176a00ae7f65.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0049-237x(98)80020-7"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>
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