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Relevant bibliographies by topics / Combinatory logic

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Academic literature on the topic 'Combinatory logic'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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Journal articles on the topic "Combinatory logic"

1

Bimbó, Katalin. "The Church-Rosser property in symmetric combinatory logic." Journal of Symbolic Logic 70, no. 2 (2005): 536–56. http://dx.doi.org/10.2178/jsl/1120224727.

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AbstractSymmetic combinatory logic with the symmetric analogue of a combinatorially complete base (in the form of symmetric λ-calculus) is known to lack the Church-Rosser property. We prove a much stronger theorem that no symmetric combinatory logic that contains at least two proper symmetric combinatory has the Church-Rosser property. Although the statement of the result looks similar to an earlier one concerning dual combinatory logic, the proof is different because symmetric combinators may form redexes in both left and right associated terms. Perhaps surprisingly, we are also able to show

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Legrand, Remi. "A basis result in combinatory logic." Journal of Symbolic Logic 53, no. 4 (1988): 1224–26. http://dx.doi.org/10.1017/s0022481200028048.

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The aim of this article is to show that a basis for combinatory logic [2] must contain at least one combinator with rank strictly greater than two. We use notation of [1].Let Q be a primitive combinator given by its reduction rule Qx1 … xn → C, where C is a pure combination of the variables x1,…, xn. n is called the rank of the combinator.A set {Q1,…,Qn} of combinators is a basis for combinatory logic if for every finite set {x1,…,xm} of variables and every pure combination C of these variables, there exists a pure combinator Q of Q1,…,Qn such that Qx1…xm↠C.Property. The Church-Rosser theorem

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Bimbó, Katalin. "The Church-Rosser property in dual combinatory logic." Journal of Symbolic Logic 68, no. 1 (2003): 132–52. http://dx.doi.org/10.2178/jsl/1045861508.

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AbstractDual combinators emerge from the aim of assigning formulas containing ← as types to combinators. This paper investigates formally some of the properties of combinatory systems that include both combinators and dual combinators. Although the addition of dual combinators to a combinatory system does not affect the unique decomposition of terms, it turns out that some terms might be redexes in two ways (with a combinator as its head, and with a dual combinator as its head). We prove a general theorem stating that no dual combinatory system possesses the Church-Rosser property. Although th

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4

Broda, Sabine, and Luís Damas. "Compact bracket abstraction in combinatory logic." Journal of Symbolic Logic 62, no. 3 (1997): 729–40. http://dx.doi.org/10.2307/2275570.

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AbstractTranslations from Lambda calculi into combinatory logics can be used to avoid some implementational problems of the former systems. However, this scheme can only be efficient if the translation produces short output with a small number of combinators, in order to reduce the time and transient storage space spent during reduction of combinatory terms. In this paper we present a combinatory system and an abstraction algorithm, based on the original bracket abstraction operator of Schönfinkel [9]. The algorithm introduces at most one combinator for each abstraction in the initial Lambda t

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Bellot, P. "A new proof for Craig's theorem." Journal of Symbolic Logic 50, no. 2 (1985): 395–96. http://dx.doi.org/10.2307/2274227.

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Craig's theorem is a result about the cardinality of a proper basis for the theory of combinators. Its proof given in [3] was shown to be incomplete by André Chauvin [2]. By using a different approach, we give a very short proof of this theorem. We use the notation of [1].Definition 1. A combinator Q is proper if there exists a natural number n such that for arbitrary variables x1,…,xn we have the following contraction rule:where C is a pure combination of the variables x1,…,xn. Q is to be understood as an abstract symbol, not as a combination of S and K's. Therefore Q comes with a contraction

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Fehlmann, Thomas, and Eberhard Kranich. "The Fixpoint Combinator in Combinatory Logic – A Step towards Autonomous Real-time Testing of Software?" ATHENS JOURNAL OF SCIENCES 9, no. 1 (2022): 47–64. http://dx.doi.org/10.30958/ajs.9-1-3.

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Combinatory Logic is an elegant and powerful logical theory that is used in computer science as a theoretical model for computation. Its algebraic structure supports self-application and is Turing-complete. However, contrary to Lambda Calculus, it untangles the problem of substitution, because bound variables are eliminated by inserting specific terms called Combinators. It was introduced by Schönfinkel (1924) and Curry (1930). Combinatory Logic uses just one algebraic operation, namely combining two terms, yielding another valid term of Combinatory Logic. Terms in models of Combinatory Logic

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Jay, Barry, and Thomas Given-Wilson. "A combinatory account of internal structure." Journal of Symbolic Logic 76, no. 3 (2011): 807–26. http://dx.doi.org/10.2178/jsl/1309952521.

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AbstractTraditional combinatory logic uses combinators S and K to represent all Turing-computable functions on natural numbers, but there are Turing-computable functions on the combinators themselves that cannot be so represented, because they access internal structure in ways that S and K cannot. Much of this expressive power is captured by adding a factorisation combinator F. The resulting SF-calculus is structure complete, in that it supports all pattern-matching functions whose patterns are in normal form, including a function that decides structural equality of arbitrary normal forms. A g

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Bunder, M. W. "Expedited Broda-Damas bracket abstraction." Journal of Symbolic Logic 65, no. 4 (2000): 1850–57. http://dx.doi.org/10.2307/2695081.

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AbstractA bracket abstraction algorithm is a means of translating λ-terms into combinators. Broda and Damas, in [1], introduce a new, rather natural set of combinators and a new form of bracket abstraction which introduces at most one combinator for each λ-abstraction. This leads to particularly compact combinatory terms. A disadvantage of their abstraction process is that it includes the whole Schönfinkel [4] algorithm plus two mappings which convert the Schönfinkel abstract into the new abstract. This paper shows how the new abstraction can be done more directly, in fact, using only 2n − 1 a

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Barendregt, Henk, Martin Bunder, and Wil Dekkers. "Systems of illative combinatory logic complete for first-order propositional and predicate calculus." Journal of Symbolic Logic 58, no. 3 (1993): 769–88. http://dx.doi.org/10.2307/2275096.

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AbstractIllative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers systems of illative combinatory logic that are sound for first-order propositional and predicate calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators or, in a more direct way, in which derivations are not translated. Both translations are closely related in a

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Dekkers, Wil, Martin Bunder, and Henk Barendregt. "Completeness of the propositions-as-types interpretation of intuitionistic logic into illative combinatory logic." Journal of Symbolic Logic 63, no. 3 (1998): 869–90. http://dx.doi.org/10.2307/2586717.

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AbstractIllative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. In a preceding paper, [2], we considered 4 systems of illative combinatory logic that are sound for first order intuitionistic propositional and predicate logic. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators, or in a more direct way, in which derivations are not translated. Both tr

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Dissertations / Theses on the topic "Combinatory logic"

1

Datta, Neil Anirvan Sagomisa. "A quantitative combinatory logic." Thesis, Imperial College London, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.502442.

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Amrhein, Beatrice. "Universal algebra in combinatory logic /." [S.l.] : [s.n.], 1992. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=10005.

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Weibel, Trudy. "Some representation problems in combinatory logic /." [S.l.] : [s.n.], 1989. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=8903.

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Hoxha, Armend. "Generating Members of a Software Product Line Using Combinatory Logic." Digital WPI, 2015. https://digitalcommons.wpi.edu/etd-theses/727.

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A Product Line Family contains similar applications that differ only in the sets of sup-ported features from the family. To properly engineer these product lines, programmers design a common code base used by all members of the product line. The structure of this common code base is often an Object-Oriented (OO) framework, designed to contain the detailed domain-specific knowledge needed to implement these applications. However, these frameworks are often quite complex and implement detailed dynamic behavior with complex coordination among their classes. Extending an OO framework to realize a

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Deshpande, Sushant, and University of Lethbridge Faculty of Arts and Science. "A new program for combinatory reduction and abstraction." Thesis, Lethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science, c2009, 2009. http://hdl.handle.net/10133/1296.

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Even though lambda calculus (λ-calculus) and combinatory logic (CL) appear to be equivalent, they are not. As yet we do not have a reduction in CL which corresponds to β-reduction in λ-calculus. There are three proposals but they all have few problems one of which is the lack of a complete characterization of CL-terms corresponding to λ-terms in β-normal form. Finding such a characterization for any of the three proposals appears to require a lot of examples which are tedious and time consuming to develop by hand. For this reason, a computer program to do reductions and abstractions of CL-term

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Kim, Dongho. "Power estimation for combinational logic and low power design /." Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3008367.

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Bergier, Hugolin. "Vers une logique du mouvement." Thesis, Paris 4, 2016. http://www.theses.fr/2016PA040085.

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Depuis Frege (1893), les développements de la logique moderne ne se sont pas montrés à la hauteur de ses ambitions à l’égard de la détermination des objets, la temporalité, l’action, le langage et, d’une façon suréminente, le mouvement. Pour Rôdl (2012), la logique frégéenne et la logique moderne en général ne peuvent pas formaliser le mouvement parce que, comme il le démontre bien, elles reposent essentiellement sur un ordre logico-déductif. Nous voulons montrer que la source de cette faille n’est pas l’ordre logico-déductif de la logique moderne mais la thématisation de ses éléments selon le

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Chelyah, Hassane. "Analyse phonographématique de l'Arabe en vue d'applications informatiques." Google Book Search Library Project, 1994. http://books.google.com/books?id=gn1jAAAAMAAJ.

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Düdder, Boris [Verfasser], Jakob [Akademischer Betreuer] Rehof, and Fritz [Gutachter] Henglein. "Automatic synthesis of component & connector software architectures with bounded combinatory logic / Boris Düdder. Betreuer: Jakob Rehof. Gutachter: Fritz Henglein." Dortmund : Universitätsbibliothek Dortmund, 2014. http://d-nb.info/1100692428/34.

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Ro, Hee-Jin. "Les référentiels et opérateurs aspecto-temporels : définitions, formalisation logique et informatique." Thesis, Paris 4, 2012. http://www.theses.fr/2012PA040130.

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Le présent travail prend appui sur une synthèse de travaux déjà effectués dans l’équipe LaLIC (Langues,Linguistiques, Informatique, Cognition) ; il insiste sur l’articulation entre différents concepts, centrés sur la notion deréférentiel. Ma thèse fait partie d’une chaîne où sont approfondis certains concepts rendus de plus en plus opératoires.Mon travail prend appui sur les travaux sur le temps et l’aspect d’E. Benveniste, A. Culioli et J.-P. Desclés, enparticulier, il s’inscrit le développement de la théorisation du temps et de l’aspect entreprise par J.-P. Desclés et Z.Guentchéva. Dans cett

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Books on the topic "Combinatory logic"

1

Erwin, Engeler, ed. The combinatory programme. Birkhäuser, 1995.

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2

Pogonowski, Jerzy. Combinatory semantics. Wydawn. Nauk. Uniwersytetu im. Adama Mickiewicza w Poznaniu, 1993.

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Künzel, Werner. Die Ars generalis ultima des Raymundus Lullus: Studien zu einem geheimen Ursprung der Computertheorie. 5th ed. Ed. Künzel, 1991.

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Skordev, Dimitŭr Genchev. Computability in combinatory spaces: An algebraic generalization of abstract first order computability. Kluwer Academic Publishers, 1992.

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Smullyan, Raymond M. To mock a mockingbird: And other logic puzzles including an amazing adventure in combinatory logic. Oxford University Press, 1990.

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Smullyan, Raymond M. To mock a mocking bird and other logic puzzles: Including an amazing adventure in combinatory logic. Knopf, 1985.

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7

Révész, György E. Lambda-calculus, combinators, and functional programming. Cambridge University Press, 1988.

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Marco, Matteoli, Pagnoni-Sturlese Maria Rita, and Tirinnanzi Nicoletta, eds. Opere lulliane. Adelphi, 2012.

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9

Colloquim on Algebra, Combinatorics and Logic in Computer Science (1983 Györ, Hungary). Algebra, combinatorics and logic in computer science: [held in Györ, Hungary between September 12-16, 1983]. North Holland, 1986.

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Lipschutz, Seymour. Discrete Mathematics. McGraw-Hill, 2007.

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Book chapters on the topic "Combinatory logic"

1

Bessai, Jan, Andrej Dudenhefner, Boris Düdder, Moritz Martens, and Jakob Rehof. "Combinatory Logic Synthesizer." In Leveraging Applications of Formal Methods, Verification and Validation. Technologies for Mastering Change. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-45234-9_3.

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Engeler, Erwin. "The Existence of Combinatory Algebras: Combinatory Logic." In Foundations of Mathematics. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-78052-3_11.

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Curien, P.-L. "Typed categorical combinatory logic." In Mathematical Foundations of Software Development. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/3-540-15198-2_10.

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Amrhein, Beatrice. "Aspects of Universal Algebra in Combinatory Logic." In The Combinatory Programme. Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4612-4268-0_3.

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Bendkowski, Maciej, Katarzyna Grygiel, and Marek Zaionc. "Asymptotic Properties of Combinatory Logic." In Lecture Notes in Computer Science. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17142-5_7.

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Zashev, J. "Least Fixed Points in Preassociative Combinatory Algebras." In Mathematical Logic. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4613-0609-2_28.

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Bethke, Inge, and Jan Willem Klop. "Collapsing partial combinatory algebras." In Higher-Order Algebra, Logic, and Term Rewriting. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61254-8_19.

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Desclés, Jean-Pierre. "Combinatory Logic, Language, and Cognitive Representations." In Alternative Logics. Do Sciences Need Them? Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05679-0_9.

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Rehof, Jakob, and Paweł Urzyczyn. "Finite Combinatory Logic with Intersection Types." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21691-6_15.

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Saville, Philip. "Clones, closed categories, and combinatory logic." In Lecture Notes in Computer Science. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-57231-9_8.

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AbstractWe explain how to recast the semantics of the simply-typed $$\uplambda $$ λ -calculus, and its linear and ordered variants, using multi-ary structures. We define universal properties for multicategories, and use these to derive familiar rules for products, tensors, and exponentials. Finally we outline how to recover both the category-theoretic syntactic model and its semantic interpretation from the multi-ary framework. We then use these ideas to study the semantic interpretation of combinatory logic and the simply-typed $$\uplambda $$ λ -calculus without products. We introduce extensi

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Conference papers on the topic "Combinatory logic"

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Andrade, Daniel Kiyoshi Hashimoto Vouzella de, and Hugo Musso Gualandi. "Converting Combinatory Logic to and from Concatenative Calculus." In Simpósio Brasileiro de Linguagens de Programação. Sociedade Brasileira de Computação, 2024. http://dx.doi.org/10.5753/sblp.2024.3460.

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Combinatory logic and its combinators BCKWI are a foundation for tacit (point-free) programming. But what does each letter mean? Informally, B stands for composing, C for swapping, K for discarding, W for duplicating and I is the identity function. However, B does more than that: depending on where it appears in the expression, it can also call functions or defer values for later. To help tell these purposes apart, we relate combinatory logic to the concatenative calculus of Kerby, which features separate primitives for the different facets of B. We provide translations from combinatory logic

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Barnden, J., and K. Srinivas. "Dissolving variables in connectionist combinatory logic." In 1990 IJCNN International Joint Conference on Neural Networks. IEEE, 1990. http://dx.doi.org/10.1109/ijcnn.1990.137921.

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Fehlmann, Thomas, and Eberhard Kranich. "The Neural Algebra and its Impact on Design and Test of Intelligent Systems." In Intelligent Human Systems Integration (IHSI 2024) Integrating People and Intelligent Systems. AHFE International, 2024. http://dx.doi.org/10.54941/ahfe1004475.

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The Graph Model of Combinatory Logic (Engeler, 1981) is also a mathematical model for "how does the brain think". It attempts to explain how complex scripts of behavior and conceptual content can reside in, combine, and interact on large neural networks (Engeler 2019). This has an impact on building intelligent systems that interact with humans. Intelligent systems should employ the same kind of concepts humans do; otherwise, their actions remain incomprehensible and erratic to human users, concepts can be represented in the Graph Model by using the "Lambda-Theorem" found be Barendregt in 1977

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Hasegawa, Masahito, and Serge Lechenne. "Braids, Twists, Trace and Duality in Combinatory Algebras." In LICS '24: 39th Annual ACM/IEEE Symposium on Logic in Computer Science. ACM, 2024. http://dx.doi.org/10.1145/3661814.3662098.

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Alur, Rajeev, Adam Freilich, and Mukund Raghothaman. "Regular combinators for string transformations." In CSL-LICS '14: JOINT MEETING OF the Twenty-Third EACSL Annual Conference on COMPUTER SCIENCE LOGIC. ACM, 2014. http://dx.doi.org/10.1145/2603088.2603151.

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Endrullis, Jörg, Dimitri Hendriks, and Jan Willem Klop. "Modular Construction of Fixed Point Combinators and Clocked Böhm Trees." In 2010 25th Annual IEEE Symposium on Logic in Computer Science (LICS 2010). IEEE, 2010. http://dx.doi.org/10.1109/lics.2010.8.

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