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A linear-non-linear model for a computational call-by-value lambda calculus (extended abstract) [article]

Peter Selinger Dalhousie University,
<span title="2008-01-05">2008</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We give a categorical semantics for a call-by-value linear lambda calculus.  ...  Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation.  ...  Conclusion We have developed a call-by-value, computational lambda-calculus for manipulating duplicable and non-duplicable data, together with an axiomatic equivalence relation on typed terms.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0801.0813v1">arXiv:0801.0813v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ryf5svfuyvh6dfjyq5pogwdf74">fatcat:ryf5svfuyvh6dfjyq5pogwdf74</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-0801.0813/0801.0813.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> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0801.0813v1" 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>

A Linear-non-Linear Model for a Computational Call-by-Value Lambda Calculus (Extended Abstract) [chapter]

Peter Selinger, Benoît Valiron
<i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lliksjpywfcx3dtw7aj2vkybvi" style="color: black;">Foundations of Software Science and Computational Structures</a> </i> &nbsp;
We give a categorical semantics for a call-by-value linear lambda calculus.  ...  Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation.  ...  Towards a Denotational Model of Quantum Lambda Calculus As noted in the introduction, this paper is mostly concerned with the categorical requirements for modeling a generic call-by-value linear lambda  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-78499-9_7">doi:10.1007/978-3-540-78499-9_7</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/fossacs/SelingerV08.html">dblp:conf/fossacs/SelingerV08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sc5e6vnzhrbzbkyjuuxa4lespa">fatcat:sc5e6vnzhrbzbkyjuuxa4lespa</a> </span>
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On Quantum and Probabilistic Linear Lambda-calculi (Extended Abstract)

Benoît Valiron
<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;
In this paper we give a fully complete model for a linear probabilistic lambda-calculus. The model is a Kripke semantics based on the category of stochastic relations.  ...  We sketch how this relates to quantum computation.  ...  Acknowledgement I would like to thanks Peter Selinger for suggesting the problem of characterizing the definable higher-order probabilistic functions, and for providing the counterexample in Section 7.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2011.01.011">doi:10.1016/j.entcs.2011.01.011</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iah3slvv7vbyzoawbw5tbfn3yi">fatcat:iah3slvv7vbyzoawbw5tbfn3yi</a> </span>
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Abstracting abstract control

James Ian Johnson, David Van Horn
<span title="">2014</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p43mwg6eyzg4jelnsclwsbnuuy" style="color: black;">Proceedings of the 10th ACM Symposium on Dynamic languages - DLS &#39;14</a> </i> &nbsp;
The approach, so called because it derives a function for the sound and computable approximation of program behavior starting from the abstract machine semantics of a language, provides a viable approach  ...  We revise the abstracting abstract machines technique to target the stronger computational model of pushdown systems. In place of automata theory, we use only abstract machines and memoization.  ...  The method is strongly tied to the simply-typed call-by-name lambda calculus and depends on finite sized base-types.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2661088.2661098">doi:10.1145/2661088.2661098</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/dls/JohnsonH14.html">dblp:conf/dls/JohnsonH14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jftogwomxjhs3ob62mihglncom">fatcat:jftogwomxjhs3ob62mihglncom</a> </span>
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A Categorical Model for a Quantum Circuit Description Language (Extended Abstract)

Francisco Rios, Peter Selinger
<span title="2018-02-27">2018</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;
Quipper is a practical programming language for describing families of quantum circuits. In this paper, we formalize a small, but useful fragment of Quipper called Proto-Quipper-M.  ...  We design Proto-Quipper-M from the ground up, by first giving a general categorical model of parameters and state.  ...  Most of the evaluation rules are those of a standard call-by-value lambda calculus. The rules that do all of the interesting "work" of Proto-Quipper-M are those for "box" and "apply".  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.266.11">doi:10.4204/eptcs.266.11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mecmm3uhunh5nncitcnx6i4baa">fatcat:mecmm3uhunh5nncitcnx6i4baa</a> </span>
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Some Programming Languages Suggested by Game Models (Extended Abstract)

John Longley
<span title="">2009</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;
In each case, we present an extension of Plotkin's language FPC (or a suitable linearization thereof) which defines all computable strategies of appropriate types.  ...  The quest for such languages results in a novel selection of language primitives for state encapsulation, coroutining and backtracking.  ...  For example, one might prove that an interpretation [[ − ]] of a language L in a model M is fully abstract, or that all computable elements of M are definable by programs of L.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2009.07.087">doi:10.1016/j.entcs.2009.07.087</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ayy7zyab6ndqrbmnkj6wkl4nlu">fatcat:ayy7zyab6ndqrbmnkj6wkl4nlu</a> </span>
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On the Ubiquity of Certain Total Type Structures(Extended Abstract)

J LONGLEY
<span title="2004-10-25">2004</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;
In each case, we present an extension of Plotkin's language FPC (or a suitable linearization thereof) which defines all computable strategies of appropriate types.  ...  The quest for such languages results in a novel selection of language primitives for state encapsulation, coroutining and backtracking.  ...  Thus, a call-by-value interpretation of FPC in Fam(G ! i ) works for i = 1, 3 but not for i = 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1571-0661(04)05085-6">doi:10.1016/s1571-0661(04)05085-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gsykszwdmnaehmezpisla3btbq">fatcat:gsykszwdmnaehmezpisla3btbq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180719150339/https://www.pure.ed.ac.uk/ws/files/17650933/1_s2.0_S1571066109003090_main.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/28/47/2847670518625d9443c70ea626015ece44f5c235.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1571-0661(04)05085-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Symbolic mathematics system evaluators (extended abstract)

Richard J. Fateman
<span title="">1996</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p5cu7ybzmnd3jpp7pphgogfzpi" style="color: black;">Proceedings of the 1996 international symposium on Symbolic and algebraic computation - ISSAC &#39;96</a> </i> &nbsp;
Evaluation" of expressions and programs in a computer algebra system is central to every system, but inevitably fails to provide complete satisfaction.  ...  We give examples primarily from Axiom, Macsyma, Maple, Mathematica, with passing mention of a few other systems.  ...  In simple cases, this model is intuitive for the user and efficiently implemented by a computer. But a system design must also handle cases that are not so simple or intuitive.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/236869.236907">doi:10.1145/236869.236907</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/issac/Fateman96.html">dblp:conf/issac/Fateman96</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bzwdnup5ifh6jjgzcfpsyffy5y">fatcat:bzwdnup5ifh6jjgzcfpsyffy5y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170814024443/https://people.eecs.berkeley.edu/~fateman/papers/evalnew.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/5e/c1/5ec19bc5a55744a4ff9643ca5631a73cdfccd5cf.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/236869.236907"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Optimal representations of polymorphic types with subtyping (Extended abstract) [chapter]

Alexander Aiken, Edward L. Wimmers, Jens Palsberg
<span title="">1997</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 present an algorithm for simplifying quanti ed types in the presence of subtyping and prove it is sound and complete for non-recursive and recursive types. 4 The source code for the Illyria system and  ...  When used together, these two features induce equivalences that allow types to be simpli ed by eliminating quanti ed variables.  ...  Acknowledgements The authors would like to thank Martin Abadi for useful discussions about connections to the ideal model as well as the anonymous referees for their criticisms.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bfb0014547">doi:10.1007/bfb0014547</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/m3unkvrjhvd2rctuektuvrmjqq">fatcat:m3unkvrjhvd2rctuektuvrmjqq</a> </span>
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A Lambda Calculus for Quantum Computation

André van Tonder
<span title="">2004</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7dys7zoberdktmxyjciuy5bnse" style="color: black;">SIAM journal on computing (Print)</a> </i> &nbsp;
The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation.  ...  We set up a computational model and an equational proof system for this calculus, and we argue that it is equivalent to the quantum Turing machine.  ...  in figure 2. v ::= values: x variable (λx. t) abstraction value Values in the call-by-value calculus λ v , Figure 3 : 3 Reduction rules for the call-by-value calculus λ v Figure 4 : 4 Syntax of the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/s0097539703432165">doi:10.1137/s0097539703432165</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/w5qgqihfdbeajp4b6zkfwnpafa">fatcat:w5qgqihfdbeajp4b6zkfwnpafa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180726011539/http://cds.cern.ch/record/629742/files/0307150.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/e0/23/e02329fcf1c4172be5a1cf42073bdccaee477424.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/s0097539703432165"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Linearly Used Effects: Monadic and CPS Transformations into the Linear Lambda Calculus [chapter]

Masahito Hasegawa
<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;
We propose a semantic and syntactic framework for modelling linearly used effects, by giving the monadic transforms of the computational lambda calculus (considered as the core calculus of typed call-by-value  ...  As a technical result we show the full completeness of the CPS transform into the linear lambda calculus.  ...  Thanks also to anonymous reviewers for helpful comments. Part of this work was carried out while the author was visiting Laboratory for Foundations of Computer Science, University of Edinburgh.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45788-7_10">doi:10.1007/3-540-45788-7_10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yci7e6djxfa43amh2mdd5373ty">fatcat:yci7e6djxfa43amh2mdd5373ty</a> </span>
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PhD Abstracts

GRAHAM HUTTON
<span title="">2015</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uxwkeespobabbhdznzmxrfucny" style="color: black;">Journal of functional programming</a> </i> &nbsp;
If a student or advisor would like to submit a dissertation abstract for publication in this series, please contact the editor for further details.  ...  The abstracts are made freely available on the JFP website, i.e. not behind any paywall, and do not require any transfer for copyright, merely a license from the author.  ...  Part III: The Krivine abstract machine is a mechanism for call-by-name evaluation of lambda terms (which has been extended by De Groote for lambda mu-calculus).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s0956796815000040">doi:10.1017/s0956796815000040</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g7yt23qxivevte45fkiqv6xwna">fatcat:g7yt23qxivevte45fkiqv6xwna</a> </span>
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Presheaf Models of Quantum Computation: An Outline [chapter]

Octavio Malherbe, Philip Scott, Peter Selinger
<span title="">2013</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 first give an abstract description of the properties required of the base categories for the model construction to work.  ...  We construct a concrete denotational semantics of Selinger and Valiron's quantum lambda calculus, which was previously an open problem.  ...  This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the Program for the Development of Basic Sciences, Uruguay (PEDECIBA).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-38164-5_13">doi:10.1007/978-3-642-38164-5_13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vphga3zfbfa35kyhrhziem7bzi">fatcat:vphga3zfbfa35kyhrhziem7bzi</a> </span>
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Call-by-name, call-by-value, call-by-need and the linear lambda calculus

J. Maraist, M. Odersky, D.N. Turner, P. Wadler
<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;
Our results extend neatly to translations of extensions for recursion in the call-by-name and call-by-value calculi, and in general to extensions for products and for the corresponding untyped systems.  ...  We detail the action of these translations on terms and show that the ÿrst corresponds to a call-by-name calculus, while the second corresponds to call-by-value.  ...  and call-by-value into a similarly extended recursive linear calculus.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0304-3975(98)00358-2">doi:10.1016/s0304-3975(98)00358-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wpm6kbycovabhlkibythzok3mu">fatcat:wpm6kbycovabhlkibythzok3mu</a> </span>
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From Linear Logic to Cyclic Sharing

Masahito Hasegawa
<span title="2019-04-12">2019</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 a translation from Multiplicative Exponential Linear Logic to a simply-typed lambda calculus with cyclic sharing.  ...  It turns out that the translation is a mixture of the call-by-name CPS translation and the Geometry of Interaction-based interpretation.  ...  Acknowledgements I thank Ken Sakayori and Takeshi Tsukada for stimulating discussions related to this work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.292.3">doi:10.4204/eptcs.292.3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cznwpsweuvfnrlguxy4dzdaepy">fatcat:cznwpsweuvfnrlguxy4dzdaepy</a> </span>
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