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Polymorphic call-by-value calculus based on classical proofs [chapter]

Ken-etsu Fujita
<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 introduce a polymorphic call-by-value calculus, λ v exc , based on 2nd order classical logic.  ...  The call-by-value computation rules are defined based on proof reductions, in which classical proof reductions are regarded as a logical permutative reduction in the sense of Prawitz and a dual permutative  ...  Ong&Stewart [20] extensively studied a call-by-value programming language based on a call-by-value variant of Parigot's λµ-calculus.  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190303112740/http://pdfs.semanticscholar.org/acbf/3ec94b4115ff4bb4c89048a358c927c92777.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/ac/bf/acbf3ec94b4115ff4bb4c89048a358c927c92777.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bfb0055911"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Programming and Proving with Classical Types [chapter]

Cristina Matache, Victor B. F. Gomes, Dominic P. Mulligan
<span title="">2017</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;
In particular, we define an extended call-by-value λµ-calculus with a type system in correspondence with full classical logic.  ...  In this work, we use the λµ-calculus as the foundation for a system of proof terms for classical first-order logic.  ...  Accordingly, we designed µML-either a prototype classical programming language or a system of proof terms for classical logic-based on the call-by-value λµ-calculus extended with data types and a distinguished  ... 
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Computable values can be classical

V. Breazu-Tannen, A. R. Meyer
<span title="">1987</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2qaxtqe2rfgjnfefqcokcnzelq" style="color: black;">Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages - POPL &#39;87</a> </i> &nbsp;
In another recently proposed logic of partial computable functions based on partial lambda calculus [Plotkin 19851, [Moggi] , divergent values are eliminated but well-formed expressions with undefined  ...  Part 2 is obtained by establishing the same oneto-one correspondence between the observables and the polymorphic integers as in the proof hint for Theorem 2.  ... 
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Page 3624 of Mathematical Reviews Vol. , Issue 89G [page]

<span title="">1989</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;
Polymorphic lambda calculus has four sorts of objects, called orders, operators, types and terms. The types make up an order called Omega.  ...  relevant logics based on a simple type of semantics.  ... 
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Page 1466 of Mathematical Reviews Vol. , Issue 2001C [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;
Herbrand called such a proof “prototype”, and here the author formalizes the notion of “prototype proof” for second-order logic after translating into the polymorphic /-calculus.  ...  The notion of solvability in the call-by-value A-calculus is defined and completely characterized, from both an operational and a logical point of view.  ... 
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Propositions as types

Philip Wadler
<span title="2015-11-23">2015</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/i6iajiiyxvgz3ob6jwcn2pufni" style="color: black;">Communications of the ACM</a> </i> &nbsp;
The principle of Propositions as Types describes a fundamental connection between logic and computation which views propositions as types, proofs as programs, and normalisation of proofs as evaluation  ...  (Based on Wadler [2007] .) • Application of the correspondence to classical logic and sequent calculus.  ...  Call-by-value is dual to call-by-name. In International Conference on Functional Programming (ICFP), pages 189-201. ACM, 2003. Philip Wadler. The Girard-Reynolds isomorphism (second edition).  ... 
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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;
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.  ...  This novel theory entails a notion of observational equivalence which distinguishes more points than other existing theories for the call-by-value lambda calculus.  ...  From a formal systems standpoint, the thesis discloses a novel consistent theory for the call-by-value variant of the lambda calculus which accounts for full reduction.  ... 
<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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Page 6651 of Mathematical Reviews Vol. , Issue 90K [page]

<span title="">1990</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;
Summary: “We present a general method for constructing ex- tensional models for the Girard-Reynolds polymorphic lambda calculus—the polymorphic extensional collapse.  ...  We might call it a ‘polymorphic set theory’. Our theory combines the A-caiculus with traditional set theories.  ... 
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Extensional Higher-Order Paramodulation in Leo-III [article]

Alexander Steen, Christoph Benzmüller
<span title="2021-02-28">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Reasoning with primitive equality is enabled by adapting paramodulation-based proof search to higher-order logic.  ...  Its development had initiated the ongoing extension of the TPTP infrastructure to reasoning within non-classical logics.  ...  These decisions are based on current features of the proof search progress and user-provided parameter values; such information is bundled in a dedicated State object.  ... 
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A Proof Theoretical Account of Continuation Passing Style [chapter]

Ichiro Ogata
<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 study "classical proofs as programs" paradigm in Call-By-Value (CBV) setting.  ...  We also show the translation we use can be thought of a familiar CBV CPS-translation without translation on types. keywords: Classical Logic, Classical Natural Deduction, LKQ, Call-By-Value, CPS-translation  ...  We use () * to indicate this restriction. 3 Calculi for Call-By-Value Classical Natural Deduction 3.1 A Call-By-Value Calculus: λµ v In this subsection, we shall introduce a Call-By-Value λµ-calculus,  ... 
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Page 5759 of Mathematical Reviews Vol. , Issue 2000h [page]

<span title="">2000</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;
Summary: “This paper concentrates on a polymorphic type sys- tem with constraints based on constrained types.  ...  That compiler is a generalised call-by-value CPS- transform. We get our direct models by identifying the algebraic structure on the Kleisli category that arises from a monadic model.  ... 
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Propositions as sessions

Philip Wadler
<span title="">2012</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ug3n3jfg4jdcpdvbrhe3m4txqa" style="color: black;">Proceedings of the 17th ACM SIGPLAN international conference on Functional programming - ICFP &#39;12</a> </i> &nbsp;
Continuing a line of work by Abramsky (1994) , by Bellin and Scott (1994) , and by Caires and Pfenning (2010), among others, this paper presents CP, a calculus in which propositions of classical linear  ...  Continuing a line of work by Honda (1993), by Honda, Kubo, and Vasconcelos (1998) , and by Gay and Vasconcelos (2010) , among others, this paper presents GV, a linear functional language with session types  ...  CLL Caires et al. (2012b) consider a variant of πDILL based on one-sided sequents of classical linear logic, which they call πCLL.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2364527.2364568">doi:10.1145/2364527.2364568</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icfp/Wadler12.html">dblp:conf/icfp/Wadler12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/56asdlyqrva75iudjx7l3hgmju">fatcat:56asdlyqrva75iudjx7l3hgmju</a> </span>
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A Curry-Howard foundation for functional computation with control

C.-H. L. Ong, C. A. Stewart
<span title="">1997</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2qaxtqe2rfgjnfefqcokcnzelq" style="color: black;">Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL &#39;97</a> </i> &nbsp;
We introduce the type theory v , a call-by-value variant of Parigot's -calculus, as a Curry-Howard representation theory of classical propositional proofs.  ...  The attendant call-by-value programming language pcf v is obtained from v by augmenting it by basic arithmetic, conditionals and xpoints.  ...  Acknowledgements We are grateful to Tony Hoare for detailed comments on an earlier draft of the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/263699.263722">doi:10.1145/263699.263722</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/popl/OngS97.html">dblp:conf/popl/OngS97</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k4e4l3thefhhdf2kgvpmsbex7y">fatcat:k4e4l3thefhhdf2kgvpmsbex7y</a> </span>
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The typed polymorphic label-selective λ-calculus

Jacques Garrigue, Hassan Aït-Kaci
<span title="">1994</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2qaxtqe2rfgjnfefqcokcnzelq" style="color: black;">Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL &#39;94</a> </i> &nbsp;
In this paper, we propose a simply typed version of the calculus, then extend it to one with ML-like polymorphic types.  ...  Thanks to the fact that label-selective -calculus is a conservative extension of -calculus by adding numeric labels to stand for argument positions, its polymorphic typing provides us with a keyword argument-passing  ...  October 1993 Digital PRL The Typed Polymorphic Label-Selective -Calculus 25  ... 
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Page 5756 of Mathematical Reviews Vol. , Issue 95j [page]

<span title="">1995</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;
This paper provides a general framework for extracting programs from proofs based on the now famous formal analogy between term formation rules in typed lambda-calculus and proofs in natu- ral deduction  ...  In the framework presented, the process which leads from a logical proof to a unique term in a typed lambda-calculus is called the Curry-Howard process, and the terms constructed in the process are called  ... 
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