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Mendler-style Iso-(Co)inductive predicates: a strongly normalizing approach

Favio Ezequiel Miranda-Perea, Lourdes del Carmen González-Huesca
<span title="2012-03-24">2012</span> <i title="Open Publishing Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qzezkwolyvf33pglm2jldjklca" style="color: black;">Electronic Proceedings in Theoretical Computer Science</a> </i> &nbsp;
We present an extension of the second-order logic AF2 with iso-style inductive and coinductive definitions specifically designed to extract programs from proofs a la Krivine-Parigot by means of primitive  ...  monotonicity, instead we use the Mendler-style, motivated here by the concept of monotonization of an arbitrary operator on a complete lattice.  ...  To our knowledge, this is the first such extension that includes Mendler-style (co)inductive predicates while keeping the strong normalization property.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.81.3">doi:10.4204/eptcs.81.3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xvohdbnz6jcztinbg5mwdzhdgy">fatcat:xvohdbnz6jcztinbg5mwdzhdgy</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1203.6158/1203.6158.pdf" title="fulltext PDF download [not primary version]" 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> File Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.81.3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

The Recursion Scheme from the Cofree Recursive Comonad

Tarmo Uustalu, Varmo Vene
<span title="">2011</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 develop a Mendler formulation of the scheme via a generalized Yoneda lemma for initial algebras involving strong dinaturality and hint a relation to circular proofsà la Cockett, Santocanale.  ...  We instantiate the general comonad-based construction of recursion schemes for the initial algebra of a functor F to the cofree recursive comonad on F .  ...  Acknowledgements Tarmo Uustalu is grateful to the PC of HOR 2007 for the invitation to give a talk and to Robin Cockett for many useful discussions on circular proofs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2011.02.020">doi:10.1016/j.entcs.2011.02.020</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yql7ngvdkvdjrmqxos57omvjiu">fatcat:yql7ngvdkvdjrmqxos57omvjiu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922224811/http://www.cs.ioc.ee/%7Etarmo/papers/msfp08.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/1f/30/1f3080a1b0268daf927bead1916501a45dc6f0df.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2011.02.020"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>

Monotone recursive types and recursive data representations in Cedille

Christopher Jenkins, Aaron Stump
<span title="2021-12-10">2021</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jdpukxfslnfmradqb65llq43na" style="color: black;">Mathematical Structures in Computer Science</a> </i> &nbsp;
a generic induction principle.  ...  For both encodings, we prove induction and examine the computational and extensional properties of their destructor, iterator, and primitive recursor in Cedille.  ...  Working with a logical framework, Parigot (1988) showed how to derive with "metareasoning" a strongly normalizing recursor for Scott naturals.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s0960129521000402">doi:10.1017/s0960129521000402</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sq5rxjpb2jfzferkpqbbz4pl6y">fatcat:sq5rxjpb2jfzferkpqbbz4pl6y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211221232055/https://www.cambridge.org/core/services/aop-cambridge-core/content/view/49B54AE2D6EAEC542726B65DA7CFC140/S0960129521000402a.pdf/div-class-title-monotone-recursive-types-and-recursive-data-representations-in-cedille-div.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/69/32/693259d97a3bff0bf9ec6ba08db75d2273468b4c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s0960129521000402"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> cambridge.org </button> </a>

Monotone recursive types and recursive data representations in Cedille [article]

Christopher Jenkins, Aaron Stump
<span title="2021-05-14">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
generic induction principle.  ...  For our Scott encoding in particular, we translate into Cedille a construction due to Lepigre and Raffalli that equips Scott naturals with primitive recursion, then extend this construction to derive a  ...  In this section, we use the induction principle derived for our generic Parigot encoding to take this second approach, proving an induction principle for rose trees in the style expected of a mutual inductive  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2001.02828v2">arXiv:2001.02828v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cohsc3e5vvcnhm6agsj7wu23qi">fatcat:cohsc3e5vvcnhm6agsj7wu23qi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210518100312/https://arxiv.org/pdf/2001.02828v2.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/69/b7/69b7e9b4261048441847b6a2b56f8fea956e1764.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2001.02828v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

6 Algebras and coalgebras [chapter]

Yde Venema
<span title="">2007</span> <i title="Elsevier"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cqvfv3wcgvbi3k536j3o7dl7le" style="color: black;">Studies in Logic and Practical Reasoning</a> </i> &nbsp;
and last part of the chapter we describe how modal logic, and its model theory, provides many natural manifestations of the more general theory of universal coalgebra. 1 This text has been written as a  ...  : A → ΨΩA and τ B : B → ΩΨB are isos.  ...  The formulation of Theorem 6.4 strongly suggests that Kripke completeness is only one of a family of properties pertaining to normal modal logics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1570-2464(07)80009-7">doi:10.1016/s1570-2464(07)80009-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e77uebqxdferlcg2nlfe5hobpq">fatcat:e77uebqxdferlcg2nlfe5hobpq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170811135052/https://staff.fnwi.uva.nl/y.venema/papers/ac.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/19/56/19565f64a63d40b5bec78475315e54e3d20541a1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1570-2464(07)80009-7"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

LIPIcs-Leibniz International Proceedings in Informatics

Tarmo Uustalu, Raimund Seidel, Thomas Schwentick, T Dortmund, Reinhard Wilhelm
<i > 21st International Conference on Types for Proofs and Programs TYPES 2015 </i> &nbsp; <span class="release-stage">unpublished</span>
Acknowledgements Thanks to Paige North for discussion of the subject matter, and to Anders Mörtberg for providing feedback to a draft of this article.  ...  Thanks to the rest of the UniMath team, for providing a sound base for formalization, and, specifically, to Dan Grayson and Anders Mörtberg for helping maintain the code described in this article.  ...  Generalized Iteration in Mendler-style and Fusion Law In this section we discuss "generalized iteration in Mendler-style" and a fusion law that one can prove for this iteration scheme.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kqvhhciwsvgchbns7xyenaijfm">fatcat:kqvhhciwsvgchbns7xyenaijfm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180510045537/http://drops.dagstuhl.de/opus/volltexte/lipics-complete/lipics-vol69-types2015-complete.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/58/c3/58c3247322a39fac25bcce9794bf8517a9915378.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>

LIPIcs, Volume 69, TYPES'15, Complete Volume [article]

Tarmo Uustalu
<span title="2018-03-16">2018</span>
A relationally parametric model of dependent type theory.  ...  Acknowledgements Thanks to Paige North for discussion of the subject matter, and to Anders Mörtberg for providing feedback to a draft of this article.  ...  Generalized Iteration in Mendler-style and Fusion Law In this section we discuss "generalized iteration in Mendler-style" and a fusion law that one can prove for this iteration scheme.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.types.2015">doi:10.4230/lipics.types.2015</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uactb6bsebh3hkxcqlwnr436fu">fatcat:uactb6bsebh3hkxcqlwnr436fu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200531145346/https://drops.dagstuhl.de/opus/volltexte/2018/8622/pdf/lipics-vol69-types2015-complete.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/97/77/97771821125b89cc7f002901a67bc2341a168d96.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.types.2015"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Dagstuhl Reports, Volume 6, Issue 10, September 2016, Complete Issue [article]

<span title="2017-03-14">2017</span>
We show how the Nelson-Oppen method is a particular case of our MCSat-combination method, reconciling the widely-implemented technique with the new MCSat ideas.  ...  Online and Adaptive Methods Markus Wagner University of Adelaide, AU We identify the notion of an MCSat-friendly inference system, and define a generic MCSat calculus that is sound and complete for satisfiability  ...  Co-presence is an important theme that gets lost when we approach languaging from a representationalist perspective.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/dagrep.6.10">doi:10.4230/dagrep.6.10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wq33g6exi5bzll67no5ztodtoy">fatcat:wq33g6exi5bzll67no5ztodtoy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220123034342/https://drops.dagstuhl.de/opus/volltexte/2017/7043/pdf/dagrep-v006-i010-complete.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/c2/ab/c2ab5b1f2731b1045d2c967dbfe79baf3aada08a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/dagrep.6.10"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>