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Computational ludics

Kazushige Terui
<span title="">2011</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;
We reformulate the theory of ludics introduced by J.-Y. Girard from a computational point of view. We introduce a handy term syntax for designs, the main objects of ludics. Our syntax also incorporates explicit cuts for attaining computational expressivity. In addition, we consider design generators that allow for finite representation of some infinite designs. A normalization procedure in the style of Krivine's abstract machine directly works on generators, giving rise to an effective means of
more &raquo; ... computation over infinite designs. The acceptance relation between machines and words, a basic concept in computability theory, is well expressed in ludics by the orthogonality relation between designs. Fundamental properties of ludics are then discussed in this concrete context. We prove three characterization results that clarify the computational powers of three classes of designs. (i) Arbitrary designs may capture arbitrary sets of finite data. (ii) When restricted to finitely generated ones, designs exactly capture the recursively enumerable languages. (iii) When further restricted to cut-free ones as in Girard's original definition, designs exactly capture the regular languages. We finally describe a way of defining data sets by means of logical connectives, where the internal completeness theorem plays an essential role.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2010.12.026">doi:10.1016/j.tcs.2010.12.026</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gtwfqbwzezeqpmcqlfpbmadmia">fatcat:gtwfqbwzezeqpmcqlfpbmadmia</a> </span>
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A feasible algorithm for typing in Elementary Affine Logic [article]

Patrick Baillot, Kazushige Terui
<span title="2004-12-08">2004</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We give a new type inference algorithm for typing lambda-terms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction. Following previous references on this topic, the variant of EAL type system we consider (denoted EAL*) is a variant without sharing and without polymorphism. Our algorithm improves over the ones already known in that it offers a better complexity bound: if a simple type derivation for the term t is given our algorithm performs EAL* type inference in polynomial time.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0412028v1">arXiv:cs/0412028v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s4qaxtdd6zebbhcgp7lowpzbgq">fatcat:s4qaxtdd6zebbhcgp7lowpzbgq</a> </span>
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MacNeille completions of FL-algebras

Agata Ciabattoni, Nikolaos Galatos, Kazushige Terui
<span title="2011-10-30">2011</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3g7sk2fqarhcrmieipwvp62bfe" style="color: black;">Algebra Universalis</a> </i> &nbsp;
We show that a large number of equations are preserved by Dedekind-MacNeille completions when applied to subdirectly irreducible FL-algebras/residuated lattices. These equations are identified in a systematic way, based on proof-theoretic ideas and techniques in substructural logics. It follows that a large class of varieties of Heyting algebras and FL-algebras admits completions.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00012-011-0160-1">doi:10.1007/s00012-011-0160-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gsxilfihh5d4hinfne6zuql3lq">fatcat:gsxilfihh5d4hinfne6zuql3lq</a> </span>
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Densification of FL chains via residuated frames

Paolo Baldi, Kazushige Terui
<span title="2016-02-12">2016</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3g7sk2fqarhcrmieipwvp62bfe" style="color: black;">Algebra Universalis</a> </i> &nbsp;
We introduce a systematic method for densification, i.e., embedding a given chain into a dense one preserving certain identities, in the framework of FL algebras (pointed residuated lattices). Our method, based on residuated frames, offers a uniform proof to many of the known densification and standard completeness results in the literature. We propose a syntactic criterion for densification, called semi-anchoredness. We then prove that the semilinear varieties of integral FL algebras defined
more &raquo; ... semianchored equations admit densification, so that the corresponding fuzzy logics are standard complete. Our method also applies to (possibly non-integral) commutative FL chains. We prove that the semilinear varieties of commutative FL algebras defined by knotted axioms x m ≤ x n (with m, n > 1) admit densification. It provides a purely algebraic proof to the standard completeness of uninorm logic as well as its extensions by knotted axioms.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00012-016-0372-5">doi:10.1007/s00012-016-0372-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iapgwlvjyjbvdbiuk5o4cszhfi">fatcat:iapgwlvjyjbvdbiuk5o4cszhfi</a> </span>
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Proof Theory and Algebra in Substructural Logics [chapter]

Kazushige Terui
<span title="">2011</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;
It is quite well understood that propositional logics are tightly connected to ordered algebras via algebraic completeness, and because of this connection proof theory is often useful in the algebraic context too. A prominent example is that one deductively proves the interpolation theorem for a given logic in order to derive the algebraic amalgamation property for the corresponding variety as a corollary. Other examples include uniform interpolation, disjunction property, local deduction
more &raquo; ... m, and termination of complete proof search with their corresponding algebraic properties. Proof theory is, however, not merely an external device for deriving algebraic consequences as corollaries. The connection is even tighter, and it also works inside algebra as a source of various algebraic constructions. For instance, Maehara's sequent-based method for proving the interpolation theorem gives rise to a direct construction of an algebra required for the amalgamation property. Finding a new variant of sequent calculus (such as hypersequent calculus) amounts to finding a new variant of MacNeille completions (generalizations of Dedekind's completion Q → R). Proving cut elimination for such a generalized sequent calculus is closely related to proving that a variety is closed under the corresponding generalized completions. Finally, transforming Hilbert axioms into Gentzen rules is not only important for proving cut elimination and related conservativity results, but also crucial for ensuring that the above proof theoretic constructions do work in algebra properly. In this talk, we will discuss such internal contributions of proof theory in algebra. Our basic framework is substructural logics, which comprise linear, relevance, fuzzy and superintuitionistic logics. Algebraically, they correspond to varieties of residuated lattices, that include Heyting algebras and many others. We will exemplify several proof theoretic methods that directly work for residuated lattices, then develop a general theory for such internal constructions in terms of residuated frames, and see their possibilities and limitations in terms of the substructural hierarchy -a hierarchy that classifies nonclassical axioms according to how difficult they are to deal with in proof theory. K. Brünnler and G. Metcalfe (Eds.): TABLEAUX
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-22119-4_3">doi:10.1007/978-3-642-22119-4_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vcf3dmefgzc4zhm2gnwvqiitfe">fatcat:vcf3dmefgzc4zhm2gnwvqiitfe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190304150116/http://pdfs.semanticscholar.org/c84a/195a56deff1eb29140c9522cdee7a8e89cc4.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/c8/4a/c84a195a56deff1eb29140c9522cdee7a8e89cc4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-22119-4_3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On the Meaning of Focalization [chapter]

Michele Basaldella, Alexis Saurin, Kazushige Terui
<span title="">2011</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;
In this paper, we use Girard's Ludics to analyze focalization, a fundamental property of linear logic. In particular, we show how this can be realized interactively thanks to section-retraction pairs (u αβ , f αβ ) between behaviours α ˆ(β Y ), X and αβ Y, X . Introduction Focalization is a deep outcome of linear logic proof theory, putting to the foreground the role of polarity in logic. It resulted in important advances in various fields ranging from proof-search (the original motivation for
more &raquo; ... ndreoli's study [1] of focalization) and the ability to define synthetic connectives and hypersequentialized calculi [10, 11] to game semantical analysis of logic. In particular, Focalization deeply influenced Girard's Ludics [12] which is a pre-logical framework which aims to analyze various logical and computational phenomena at a foundational level. For instance, the concluding results of Locus Solum are a full completeness theorem with respect to focalized multiplicative-additive linear logic (MALL). Another characteristics of ludics is that types are built from untyped proofs (called designs). More specifically, types (called behaviours) are sets of designs closed under a certain closure operation. This view of types as sets of proofs opens a new possibility to discuss focalization and other properties of proofs at the level of types. The purpose of this abstract is to show that Ludics is suitable for analyzing Focalization and that this interactive analysis of Focalization is fruitful. In particular, our study of Focalization in Ludics was primarily motivated by the concluding remarks of the third author's paper on Computational Ludics [17] where focalization on data designs was conjectured to correspond to the tape compression theorem of Turing Machines. Still, for the very reason that Ludics abstracts over Focalization (being built on hypersequentialized calculi) it is not clear whether an analysis of Focalization can (or shall) be pursued in Ludics: an obstacle is, however, that ludics is already fully focalized, so that there seems not to be room to discuss and prove focalization internally. This can be settled by using a dummy shift operator. For instance, a compound formula L ⊕ (M ⊗ N ) of linear logic can be expressed in ludics in two ways; either as a flat behaviour ⊕ ⊗ (L, M, N ) built by a single synthetic connective ⊕⊗ from three subbehaviours L, M, N , or as a compound behaviour L⊕ ↑ (M ⊗ N ), which consists of three layers: M ⊗ N (positive), ↑ (M ⊗ N ) (negative), and L⊕ ↑ (M ⊗ N ) (positive). Focalization can then be expressed as a mapping from the latter to the former behaviour. Hence we can deal with it as if it were an algebraic law, which may be compared with other logical isomorphisms such as associativity, distributivity, etc. To be precise, however, focalization is not an isomorphism but is an assymmetric relation. In this paper, we think
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-19211-1_5">doi:10.1007/978-3-642-19211-1_5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2jqf6is5t5dzlnbb57hhjbii2q">fatcat:2jqf6is5t5dzlnbb57hhjbii2q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170830055421/http://www.lix.polytechnique.fr/Labo/Alexis.Saurin/Recherche/Publi/BST-focalization-ludics.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/55/2a/552a58750a0ec5f207fb9686229bce5112d7bede.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-19211-1_5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On the Meaning of Logical Completeness [chapter]

Michele Basaldella, Kazushige Terui
<span title="">2009</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;
TERUI Lemma 2.8 (1), we get x 0 |a M 1 , . . . , M m |= Γ, x 0 : α N 1 , . . . , N n and by Theorem 2.15 (1) we conclude z|a M 1 , . . . , M m |= Γ.  ...  TERUI Given a negative synthetic connective n, we inductively associate a set n • 0 of negative actions of ludics as follows: Notice that when a( x) ∈ n • 0 , the variables x occur in n.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-02273-9_6">doi:10.1007/978-3-642-02273-9_6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6k4dx42s6rexhj5v5gsstxlslu">fatcat:6k4dx42s6rexhj5v5gsstxlslu</a> </span>
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Infinitary Completeness in Ludics

Michele Basaldella, Kazushige Terui
<span title="">2010</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cnybbxuptncftdgxtodn5edz7m" style="color: black;">2010 25th Annual IEEE Symposium on Logic in Computer Science</a> </i> &nbsp;
Traditional Gödel completeness holds between finite proofs and infinite models over formulas of finite depth, where proofs and models are heterogeneous. Our purpose is to provide an interactive form of completeness between infinite proofs and infinite models over formulas of infinite depth (that include recursive types), where proofs and models are homogenous. We work on a nonlinear extension of ludics, a monistic variant of game semantics which has the same expressive power as the
more &raquo; ... fragment of polarized linear logic. In order to extend the completeness theorem of the original ludics to the infinitary setting, we modify the notion of orthogonality by defining it via safety rather than termination of the interaction. Then the new completeness ensures that the universe of behaviours (interpretations of formulas) is Cauchy-complete, so that every recursive equation has a unique solution. Our work arises from studies on recursive types in denotational and operational semantics, but is conceptually simpler, due to the purely logical setting of ludics, the completeness theorem, and use of coinductive techniques.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/lics.2010.47">doi:10.1109/lics.2010.47</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/lics/BasaldellaT10.html">dblp:conf/lics/BasaldellaT10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vcnjuqapwvbybgv5zo46sf4gki">fatcat:vcnjuqapwvbybgv5zo46sf4gki</a> </span>
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Disjunction property and complexity of substructural logics

Rostislav Horčík, Kazushige Terui
<span title="">2011</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;
We systematically identify a large class of substructural logics that satisfy the disjunction property (DP), and show that every consistent substructural logic with the DP is PSPACE-hard. Our results are obtained by using algebraic techniques. PSPACE-completeness for many of these logics is furthermore established by proof theoretic arguments.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2011.04.004">doi:10.1016/j.tcs.2011.04.004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3x3qwzpgwrachoor56rvpnd5ju">fatcat:3x3qwzpgwrachoor56rvpnd5ju</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20121114194855/http://www.kurims.kyoto-u.ac.jp/~terui/dp.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/e8/6f/e86f7716cd48c43875c03589a0991c06bd1eda49.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2011.04.004"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Modular Cut-Elimination: Finding Proofs or Counterexamples [chapter]

Agata Ciabattoni, Kazushige Terui
<span title="">2006</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;
Modular cut-elimination is a particular notion of "cut-elimination in the presence of non-logical axioms" that is preserved under the addition of suitable rules. We introduce syntactic necessary and sufficient conditions for modular cut-elimination for standard calculi, a wide class of (possibly) multipleconclusion sequent calculi with generalized quantifiers. We provide a "universal" modular cut-elimination procedure that works uniformly for any standard calculus satisfying our conditions. The
more &raquo; ... failure of these conditions generates counterexamples for modular cut-elimination and, in certain cases, for cut-elimination.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11916277_10">doi:10.1007/11916277_10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zgzezwfyy5fehnhtp2eicts6iy">fatcat:zgzezwfyy5fehnhtp2eicts6iy</a> </span>
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Expanding the Realm of Systematic Proof Theory [chapter]

Agata Ciabattoni, Lutz Straßburger, Kazushige Terui
<span title="">2009</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;
This paper is part of a general project of developing a systematic and algebraic proof theory for nonclassical logics. Generalizing our previous work on intuitionistic-substructural axioms and singleconclusion (hyper)sequent calculi, we define a hierarchy on Hilbert axioms in the language of classical linear logic without exponentials. We then give a systematic procedure to transform axioms up to the level P 3 of the hierarchy into inference rules in multiple-conclusion (hyper)sequent calculi,
more &raquo; ... hich enjoy cut-elimination under a certain condition. This allows a systematic treatment of logics which could not be dealt with in the previous approach. Our method also works as a heuristic principle for finding appropriate rules for axioms located at levels higher than P 3 . The case study of Abelian and Lukasiewicz logic is outlined. linear logic: ⊥ 1 0 substructural logics: ⊕ ·/ ∨ ∧ 0 1 ⊥
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-04027-6_14">doi:10.1007/978-3-642-04027-6_14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xofdlspf6jentdd63tha3b7idq">fatcat:xofdlspf6jentdd63tha3b7idq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170330230632/http://www.lix.polytechnique.fr/~lutz/papers/realm-finalforcsl.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/e1/9a/e19a8456a4bac53e0893eaad346ec1d8c8df59ef.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-04027-6_14"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

From Axioms to Analytic Rules in Nonclassical Logics

Agata Ciabattoni, Nikolaos Galatos, Kazushige Terui
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zw5e5duxvbdsthglbdpw3xoqae" style="color: black;">Logic in Computer Science</a> </i> &nbsp;
We introduce a systematic procedure to transform large classes of (Hilbert) axioms into equivalent inference rules in sequent and hypersequent calculi. This allows for the automated generation of analytic calculi for a wide range of propositional nonclassical logics including intermediate, fuzzy and substructural logics. Our work encompasses many existing results, allows for the definition of new calculi and contains a uniform semantic proof of cutelimination for hypersequent calculi.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/lics.2008.39">doi:10.1109/lics.2008.39</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/lics/CiabattoniGT08.html">dblp:conf/lics/CiabattoniGT08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tcoggtfrrfdpfdilqvasooqjam">fatcat:tcoggtfrrfdpfdilqvasooqjam</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809025343/http://web.cs.du.edu/~ngalatos/research/22lics08.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/12/2d/122d92ca80934fa136ac581f6bd41350235bad6a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/lics.2008.39"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

A Feasible Algorithm for Typing in Elementary Affine Logic [chapter]

Patrick Baillot, Kazushige Terui
<span title="">2005</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 give a new type inference algorithm for typing lambda-terms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction. Following previous references on this topic, the variant of EAL type system we consider (denoted EAL ) is a variant where sharing is restricted to variables and without polymorphism. Our algorithm improves over the ones already known in that it offers a better complexity bound: if a simple type derivation for the term t is given
more &raquo; ... our algorithm performs EAL type inference in polynomial time in the size of the derivation. Work partially supported by project CRISS ACI Sécurité informatique and project GEOCAL ACI Nouvelles interfaces des mathématiques.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11417170_6">doi:10.1007/11417170_6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ataltroq2zcxxc6x6ozgpykk34">fatcat:ataltroq2zcxxc6x6ozgpykk34</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20050518072718/http://research.nii.ac.jp:80/~terui/inferEALfinal.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/6a/c4/6ac44e6665168783cf46842ca02283f3b84469e2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11417170_6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Light types for polynomial time computation in lambda-calculus [article]

Patrick Baillot, Kazushige Terui
<span title="2004-05-11">2004</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We propose a new type system for lambda-calculus ensuring that well-typed programs can be executed in polynomial time: Dual light affine logic (DLAL). DLAL has a simple type language with a linear and an intuitionistic type arrow, and one modality. It corresponds to a fragment of Light affine logic (LAL). We show that contrarily to LAL, DLAL ensures good properties on lambda-terms: subject reduction is satisfied and a well-typed term admits a polynomial bound on the reduction by any strategy.
more &raquo; ... establish that as LAL, DLAL allows to represent all polytime functions. Finally we give a type inference procedure for propositional DLAL.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0402059v2">arXiv:cs/0402059v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q2ricscan5giboyeygjk3j5pba">fatcat:q2ricscan5giboyeygjk3j5pba</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-cs0402059/cs0402059.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/35/95/3595a9a5305de57d14de4829498e9bf922155895.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0402059v2" 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>

Light types for polynomial time computation in lambda calculus

Patrick Baillot, Kazushige Terui
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
We present a polymorphic type system for lambda calculus ensuring that well-typed programs can be executed in polynomial time: dual light affine logic (DLAL). DLAL has a simple type language with a linear and an intuitionistic type arrow, and one modality. It corresponds to a fragment of light affine logic (LAL). We show that contrarily to LAL, DLAL ensures good properties on lambda-terms (and not only on proof-nets): subject reduction is satisfied and a well-typed term admits a polynomial
more &raquo; ... on the length of any of its beta reduction sequences. We also give a translation of LAL into DLAL and deduce from it that all polynomial time functions can be represented in DLAL.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ic.2008.08.005">doi:10.1016/j.ic.2008.08.005</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vtr4yo6kz5dsfp6qzoqe3szxte">fatcat:vtr4yo6kz5dsfp6qzoqe3szxte</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170923213047/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/07d/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDg5MDU0MDEwODAwMTExOQ%3D%3D.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/41/16/41160700a95a57941ab83ff421b9c0a45b028a77.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ic.2008.08.005"> <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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