A Bibliography of Combinators

Foundational Documents M. Schönfinkel (1924), “Über die Bausteine der mathematischen Logik” (in German) [“On the Building Blocks of Mathematical Logic”], Mathematische Annalen 92, 305–316. doi: 10.1007/BF01448013. (Translated by S. Bauer-Mengelberg (1967), as “On the Building Blocks of Mathematical Logic”, in From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, J. van Heijenoort, Harvard University Press, 357–366.) H. B. Curry (1929), “An Analysis of Logical Substitution”, American Journal of Mathematics 51, 363–384. doi: 10.2307/2370728. H. B. Curry (1930), “Grundlagen der kombinatorischen Logik” (in German) [“Foundations of Combinatory Logic”], American Journal of Mathematics 52, 509–536. doi: 10.2307/2370619. (Translated by F. Kamareddine and J. Seldin (2016), as Foundations of Combinatory Logic, Logic PhDs vol. 1, College Publications.)

[1]  Michael Stay,et al.  Very Simple Chaitin Machines for Concrete AIT , 2005, Fundam. Informaticae.

[2]  R. Canal,et al.  Complexité de la réduction en logique combinatoire , 1978, RAIRO Theor. Informatics Appl..

[3]  Yohji Akama Limiting partial combinatory algebras , 2004, Theor. Comput. Sci..

[4]  Corrado Böhm,et al.  Combinatory foundation of functional programming , 1982, LFP '82.

[5]  Sachio Hirokawa Complexity of the Combinator Reduction Machine , 1985, Theor. Comput. Sci..

[6]  Simon H. Lavington,et al.  Parallel Associative Combinator Evaluation , 1991, PARLE.

[7]  Jean-Pierre Desclés,et al.  Korean Parsing Based on the Applicative Combinatory Categorial Grammar , 2008, PACLIC.

[8]  Rafael Dueire Lins On the efficiency of categorical combinators as a rewriting system , 1987, Softw. Pract. Exp..

[9]  Sabine Broda,et al.  On principal types of combinators , 2000, Theor. Comput. Sci..

[10]  Pierre-Louis Curien Categorical Combinators, Sequential Algorithms, and Functional Programming , 1993, Progress in Theoretical Computer Science.

[11]  Katalin Bimbó,et al.  Semantics for Dual and Symmetric Combinatory Calculi , 2004, J. Philos. Log..

[12]  Silvio Romero de Lemos Meira,et al.  Strict Combinators , 1987, Inf. Process. Lett..

[13]  Olivier Danvy,et al.  Three syntactic theories for combinatory graph reduction , 2010, TOCL.

[14]  Martin W. Bunder Various systems of set theory based on combinatory logic , 1974, Notre Dame J. Formal Log..

[15]  J. Roger Hindley Combinatory Reductions and Lambda Reductions Compared , 1977, Math. Log. Q..

[16]  H. B. Curry Some Properties of Equality and Implication in Combinatory Logic , 1934 .

[17]  Jakob Rehof,et al.  Finite Combinatory Logic with Intersection Types , 2011, TLCA.

[18]  Mariangiola Dezani-Ciancaglini,et al.  Combinatorial Problems, Combinator Equations and Normal Forms , 1974, ICALP.

[19]  Frederic Brenton Fitch A Consistent Combinatory Logic with an Inverse to Equality , 1980, J. Symb. Log..

[20]  William M. Farmer,et al.  A correctness proof for combinator reduction with cycles , 1990, TOPL.

[21]  Simon L. Peyton Jones,et al.  Termination combinators forever , 2012, Haskell '11.

[22]  Brian F. Redmond Bounded Combinatory Logic and lower complexity , 2016, Inf. Comput..

[23]  Pieter H. Hartel Performance of lazy combinator graph reduction , 1991, Softw. Pract. Exp..

[24]  Jan Willem Klop,et al.  Collapsing Partial Combinatory Algebras , 1995, HOA.

[25]  Pierluigi Minari A solution to Curry and Hindley’s problem on combinatory strong reduction , 2009, Arch. Math. Log..

[26]  G. Longo On the problem of deciding equality in partial combinatory algebras and in a formal system , 1976 .

[27]  A. Ciabattoni,et al.  On Completability of Partial Combinatory Algebras , 2011 .

[28]  Kohei Noshita,et al.  The BC-chain method for representing combinators in linear space , 2009, New Generation Computing.

[29]  James A. Davis,et al.  New families of combinators for efficient list manipulation , 1994, J. Syst. Softw..

[30]  Keisuke Nakano,et al.  On repetitive right application of B-terms , 2018, FSCD.

[31]  Daan Leijen,et al.  Parsec, a fast combinator parser , 2001 .

[32]  Rafael Dueire Lins,et al.  The Categorical Multi-Combinator Machine: CMCM , 1992, Comput. J..

[33]  Ján Kollár,et al.  Supercombinator driven grammar reconstruction , 2017, 2017 IEEE 14th International Scientific Conference on Informatics.

[34]  Sven-Bodo Scholz,et al.  Implementation and Application of Functional Languages , 2009, Lecture Notes in Computer Science.

[35]  João Saraiva,et al.  A Combinator Language for Software Quality Reports , 2013 .

[36]  Benedetto Intrigila,et al.  On the number of fixed points of a combinator in lambda calculus , 2000, Math. Struct. Comput. Sci..

[37]  Simon L. Peyton Jones,et al.  A Safe Approach to Parallel Combinator Reduction (Extended Abstract) , 1986, ESOP.

[38]  Albert R. Meyer,et al.  What is a Model of the Lambda Calculus? , 1982, Inf. Control..

[39]  Da Xiao,et al.  Improving the Universality and Learnability of Neural Programmer-Interpreters with Combinator Abstraction , 2018, ICLR.

[40]  Jørgen Fischer Nilsson A Case Study in Knowledge Representation and Reasoning with Higher-Order Combinators , 1989, SCAI.

[41]  Nicolas D. Goodman A simplification of combinatory Logic , 1972, J. Symb. Log..

[42]  M. Goldberg On the Recursive Enumerability of Fixed-Point Combinators , 2004 .

[43]  Hendrik Pieter Barendregt,et al.  Systems of illative combinatory logic complete for first-order propositional and predicate calculus , 1993, Journal of Symbolic Logic.

[44]  Larry Wos,et al.  Challenge Problems Focusing on Equality and Combinatory Logic: Evaluating Automated Theorem-Proving Programs , 1988, CADE.

[45]  Alessandro Berarducci Innite -calculus and non-sensible models , 1994 .

[46]  Hirofumi Yokouchi Church-Rosser Theorem for a Rewriting System on Categorical Combinators , 1989, Theor. Comput. Sci..

[47]  Yohji Akama SN Combinators and Partial Combinatory Algebras , 1998, RTA.

[48]  Benjamin C. Pierce,et al.  Combinators for bidirectional tree transformations: A linguistic approach to the view-update problem , 2007, TOPL.

[49]  Teruo Hikita On the Average Size of Turner's Translation to Combinator Programs , 1984 .

[50]  Colin Runciman,et al.  Adapting combinator and SECD machines to display snapshots of functional computations , 2009, New Generation Computing.

[51]  S. Kamal Abdali,et al.  An abstraction algorithm for combinatory logic , 1976, Journal of Symbolic Logic.

[52]  John Staples Combinator realizability of constructive finite type analysis , 1973 .

[53]  Daniel J. Dougherty Higher-Order Unification via Combinators , 1993, Theor. Comput. Sci..

[54]  A. Dickinson,et al.  A simple machine (based on the SK-combinator reduction mechanism) , 1992, TENCON'92 - Technology Enabling Tomorrow.

[55]  Jonathan P. Seldin,et al.  Set Theory based on Combinatory Logic. , 1970 .

[56]  Tom Ridge,et al.  Simple, Efficient, Sound and Complete Combinator Parsing for All Context-Free Grammars, Using an Oracle , 2014, SLE.

[57]  Jan Bessai A type-theoretic framework for software component synthesis , 2019 .

[58]  E. Engeler Algebras and combinators , 1981 .

[59]  Dana S. Scott,et al.  Some philosophical issues concerning theories of combinators , 1975, Lambda-Calculus and Computer Science Theory.

[60]  Karel Lambert,et al.  The logical way of doing things , 1969 .

[61]  Jean-Pierre Desclés,et al.  Combinatory Logic, Language, and Cognitive Representations , 2004 .

[62]  Richard S. Bird A Formal Development of an Efficient Subercombinator Compiler , 1987, Sci. Comput. Program..

[63]  Edward Cherlin,et al.  Pure functions in APL and J , 1991, APL '91.

[64]  Michel Lemaître,et al.  A Set of Combinators for Abstraction in Linear Space , 1987, Inf. Process. Lett..

[65]  Alberto Pettorossi,et al.  A property which guarantees termination in weak combinatory logic and subtree replacement systems , 1981, Notre Dame J. Formal Log..

[66]  Guy Durrieu,et al.  MaRS, a Combinator Graph Reduction Multiprocessor , 1989, PARLE.

[67]  E. V. Krishnamurthy,et al.  Compact Numeral Representation with Combinators , 1987, J. Symb. Log..

[68]  The Elimination of Variables by Regular Combinators 1 , 2018, Critical Approaches to Science & Philosophy with a new introduction.

[69]  John T. Kearns Combinatory Logic with Discriminators , 1969, J. Symb. Log..

[70]  Andrew Kennedy,et al.  Pickler combinators , 2004, J. Funct. Program..

[71]  Marinus J. Plasmeijer,et al.  Efficient Combinator Parsers , 1998, IFL.

[72]  M. Takeichi An Alternative Scheme for Evaluating Combinator Expressions , 1984 .

[73]  D. A. Turner Another Algorithm for Bracket Abstraction , 1979, J. Symb. Log..

[74]  Peter Lee,et al.  A Fresh Look at Combinator Graph Reduction (Or, Having a TIGRE by the Tail) , 1989 .

[75]  Peter M. Maurer,et al.  The Use of Combinators in Translating A Purely Functional Language to Low-Level Data-Flow Graphs , 1983, Comput. Lang..

[76]  Adolfo Piperno,et al.  Abstraction Problems in Combinatory Logic a Compositive Approach , 1989, Theor. Comput. Sci..

[77]  Jan Willem Klop,et al.  Clocked lambda calculus , 2017, Math. Struct. Comput. Sci..

[78]  Haskell B. Curry Some Additions to the Theory of Combinators , 1932 .

[79]  H. B. Curry Combinatory recursive objects of all finite types , 1964 .

[80]  John Tromp Kolmogorov Complexity in Combinatory Logic , 2007 .

[81]  E. Cogan A formalization of the theory of sets from the point of view of combinatory logic , 1955 .

[82]  Maciej Bendkowski,et al.  Asymptotic Properties of Combinatory Logic , 2015, TAMC.

[83]  Mark Steedman,et al.  Combinatory grammars and parasitic gaps , 1987 .

[84]  Jakob Rehof,et al.  Bounded Combinatory Logic , 2012, CSL.

[85]  Vincent van Oostrom,et al.  Combinatory Reduction Systems: Introduction and Survey , 1993, Theor. Comput. Sci..

[86]  Mike S. Joy,et al.  NP-Completeness of a Combinator Optimization Problem , 1995, Notre Dame J. Formal Log..

[87]  Yves Lafont Interaction Combinators , 1997, Inf. Comput..

[88]  William W. Tait,et al.  Intensional interpretations of functionals of finite type I , 1967, Journal of Symbolic Logic.

[89]  Luis E. Sanchis,et al.  Types in combinatory logic , 1964, Notre Dame J. Formal Log..

[90]  Mark Steedman,et al.  Combinators and Grammars , 1988 .

[91]  Roger Hindley,et al.  Some remarks about the connections between Combinatory Logic and axiomatic recursion theory , 1977, Arch. Math. Log..

[92]  Richard Statman Effective Reduction and Conversion Strategies for Combinators , 1997, RTA.

[93]  Jørgen Fischer Nilsson,et al.  Inductive Synthesis of Logic Programs by Composition of Combinatory Program Schemes , 1998, LOPSTR.

[94]  Arthur Charguéraud The Optimal Fixed Point Combinator , 2010, ITP.

[95]  Albert Hoogewijs,et al.  Combinatory logic, a bridge to verified programs , 2003 .

[96]  Maciej Bendkowski,et al.  On the likelihood of normalization in combinatory logic , 2017, J. Log. Comput..

[97]  Eric James Parfitt Patterns in Combinator Evolution , 2017, Complex Syst..

[98]  R. K. Shyamasundar,et al.  Combinatory formulations of concurrent languages , 1995, TOPL.

[99]  Peter Lee,et al.  Cache performance of combinator graph reduction , 1990, Proceedings. 1990 International Conference on Computer Languages.

[100]  David Meredith Combinatory and propositional logic , 1974, Notre Dame J. Formal Log..

[101]  Sabine Broda,et al.  A New Translation Algorithm from Lambda Calculus into Combinatory Logic , 1995, EPIA.

[102]  Joyce L. Vedral,et al.  Functional Programming Languages and Computer Architecture , 1989, Lecture Notes in Computer Science.

[103]  Giuseppe Jacopini,et al.  A condition for identifying two elements of whatever model of combinatory logic , 1975, Lambda-Calculus and Computer Science Theory.

[104]  Steven T. Piantadosi,et al.  The Computational Origin of Representation , 2020, Minds and Machines.

[105]  A. C. Norman,et al.  SKIM - The S, K, I reduction machine , 1980, LISP Conference.

[106]  D. Park,et al.  The Y-combinator in Scott''s Lambda-calculus Models , 1976 .

[107]  Andrew Cheese Combinatory code and a parallel packet-based computational model , 1987, SIGP.

[108]  Andrew Polonsky Fixed point combinators as fixed points of higher-order fixed point generators , 2020, Log. Methods Comput. Sci..

[109]  Jan Willem Klop,et al.  Extending partial combinatory algebras , 1999, Mathematical Structures in Computer Science.

[110]  Martin W. Bunder Propositional and predicate calculuses based on combinatory logic , 1974, Notre Dame J. Formal Log..

[111]  Ahmed Bhayat,et al.  A Knuth-Bendix-Like Ordering for Orienting Combinator Equations , 2020, IJCAR.

[112]  Paul Hudak,et al.  A combinator-based compiler for a functional language , 1984, POPL '84.

[113]  Phil Scott,et al.  A Combinator Language for Theorem Discovery , 2012, AISC/MKM/Calculemus.

[114]  Adolfo Piperno A Compositive Abstraction Algorithm for Combinatory Logic , 1987, TAPSOFT, Vol.2.

[115]  Matthias Fuchs,et al.  Evolving Combinators , 1997, CADE.

[116]  Karl Meinke,et al.  Equational Specification of Abstract Types and Combinators , 1991, CSL.

[117]  Haskell B. Curry The Universal Quantifier in Combinatory Logic , 1931 .

[118]  R. Hindley The Principal Type-Scheme of an Object in Combinatory Logic , 1969 .

[119]  Robert K. Meyer,et al.  Implementing the ‘Fool's model’ of combinatory logic , 1991, Journal of Automated Reasoning.

[120]  M. Randall Holmes,et al.  Systems of Combinatory Logic Related to Quine's 'New Foundations' , 1991, Ann. Pure Appl. Log..

[121]  Mark Scheevel NORMA: a graph reduction processor , 1986, LFP '86.

[122]  Robin Milner,et al.  Four combinators for concurrency , 1982, PODC '82.

[123]  Perry Alexander,et al.  Constructing language processors with algebra combinators , 2007, GPCE '07.

[124]  John Gateley,et al.  Call-by-Value Combinatory Logic and the Lambda-Value Calculus , 1991, MFPS.

[125]  Jörg Endrullis,et al.  Local Termination: theory and practice , 2010, Log. Methods Comput. Sci..

[126]  Mark Steedman,et al.  The Lost Combinator , 2018, CL.

[127]  Arch D. Robison The Illinois functional programming interpreter , 1987, PLDI.

[128]  Kohei Noshita Translation of Turner Combinators in O(n log n) Space , 1985, Inf. Process. Lett..

[129]  Robert Bruce Findler,et al.  Fair enumeration combinators , 2017, J. Funct. Program..

[130]  Gerd Mitschke,et al.  The Standardization Theorem for λ-Calculus , 1979, Math. Log. Q..

[131]  Katalin Bimbó,et al.  The Church-Rosser property in dual combinatory logic , 2003, Journal of Symbolic Logic.

[132]  Mayer Goldberg,et al.  A Variadic Extension of Curry's Fixed-Point Combinator , 2005, High. Order Symb. Comput..

[133]  Jan Willem Klop,et al.  Dance of the Starlings , 2017 .

[134]  Gerd Mitschke Ein algebraischer Beweis für das Church-Rosser-Theorem , 1972 .

[135]  Gordon Plotkin,et al.  A Set-Theoretical Definition of Application , 2003 .

[136]  John Tromp Binary Lambda Calculus and Combinatory Logic , 2006, Kolmogorov Complexity and Applications.

[137]  Michael T. A Bel An intuitionistic combinatory theory not closed under the rule of choice , 1977 .

[138]  Bertrand Meyer The Component Combinator for Enterprise Applications , 1998, J. Object Oriented Program..

[139]  Cezary Z. Janikow,et al.  A survey of modularity in genetic programming , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[140]  Richard J. Lipton,et al.  On the Halting of Tree Replacement Systems. , 1977 .

[141]  Patrick Bellot,et al.  GRAAL: A Functional Programming System with Uncurryfied Combinators and its Reduction Machine , 1986, ESOP.

[142]  P. P. Chu,et al.  Exploitation fine-grain parallelism in a combinator-based functional system , 1990, [1990 Proceedings] The Third Symposium on the Frontiers of Massively Parallel Computation.

[143]  L. V. Shabunin On the Interpretation of Combinators with Weak Reduction , 1983, J. Symb. Log..

[144]  Kenneth Loewen The Church Rosser theorem for strong reduction in combinatory logic , 1968, Notre Dame J. Formal Log..

[145]  Chris Hankin,et al.  Reversible combinatory logic , 2006, Mathematical Structures in Computer Science.

[146]  Martin W. Bunder Scott's models and illative combinatory logic , 1979, Notre Dame J. Formal Log..

[147]  N. Packard,et al.  A Less Abstract Artificial Chemistry , 2000 .

[148]  Rafael Dueire Lins,et al.  GM-C: a graph multi-combinator machine , 1991 .

[149]  Jonathan P. Seldin,et al.  The search for a reduction in combinatory logic equivalent to λβ-reduction , 2011, Theor. Comput. Sci..

[150]  William P. Worzel,et al.  SKGP: The Way of the Combinator , 2014, GPTP.

[151]  F. Warren Burton,et al.  Efficient Combinator Code , 1985, Comput. Lang..

[152]  A. Church The calculi of lambda-conversion , 1941 .

[153]  Higher-Order Algebra, Logic, and Term Rewriting , 1995, Lecture Notes in Computer Science.

[154]  Wamberto Weber Vasconcelos,et al.  Sharing Resource-Sensitive Knowledge Using Combinator Logics , 2000, IBERAMIA-SBIA.

[155]  Corrado Böhm,et al.  Functional Programming and Combinatory Algebras , 1988, International Symposium on Mathematical Foundations of Computer Science.

[156]  Bruce Lercher Strong Reduction and Normal Form in Combinatory Logic , 1967, J. Symb. Log..

[157]  Thomas Given-Wilson,et al.  A combinatory account of internal structure , 2011, The Journal of Symbolic Logic.

[158]  Hugolin Bergier How Combinatory Logic Can Limit Computing Complexity , 2020, EPJ Web of Conferences.

[159]  Hans-Georg Oberhauser On the correspondence of lambda style reduction and combinator style reduction , 1986, Graph Reduction.

[160]  Sabine Broda,et al.  Compact bracket abstraction in combinatory logic , 1997, Journal of Symbolic Logic.

[161]  Jacek Gibert,et al.  Functional Programming with Combinators , 1987, J. Symb. Comput..

[162]  Jason Baldridge,et al.  A Logical Basis for the D Combinator and Normal Form in CCG , 2008, ACL.

[163]  Jørgen Villadsen Combinatory Categorial Grammar for Intensional Fragment of Natural Language , 1991, SCAI.

[164]  Thomas Jech,et al.  Some results on combinators in the system TRC , 1998, Journal of Symbolic Logic.

[165]  James A. Davis,et al.  Implementing functional languages on a combinator-based reduction machine , 1988, SIGP.

[166]  Jan Willem Klop,et al.  Modular Construction of Fixed Point Combinators and Clocked Böhm Trees , 2010, 2010 25th Annual IEEE Symposium on Logic in Computer Science.

[167]  F. Warren Burton A Linear Space Translation of Functional Programs to Turner Combinators , 1982, Inf. Process. Lett..

[168]  Forrest Briggs,et al.  Functional genetic programming and exhaustive program search with combinator expressions , 2008, Int. J. Knowl. Based Intell. Eng. Syst..

[169]  Kenneth Loewen Modified strong reduction in combinatory logic , 1968, Notre Dame J. Formal Log..

[170]  Jacek Gibert The J-Machine: Functional Programming with Combinators , 1986, CADE.

[171]  S. Doaitse Swierstra,et al.  Combinator Parsing: A Short Tutorial , 2009, LerNet ALFA Summer School.

[172]  J. Roger Hindley,et al.  To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus, and Formalism , 1980 .

[173]  Robert K. Meyer,et al.  Combinators and Structurally Free Logic , 1997, Log. J. IGPL.

[174]  John Staples,et al.  Combinator Realizability of a Constructive Morse Set Theory , 1974, J. Symb. Log..

[175]  Teruo Hikita,et al.  A Rewriting System for Categorical Combinators with Multiple Arguments , 1990, SIAM J. Comput..

[176]  Paul Tarau,et al.  On a uniform representation of combinators, arithmetic, lambda terms and types , 2015, PPDP.

[177]  Martin W. Bunder,et al.  On the equivalence of systems of rules and systems of axioms in illative combinatory logic , 1979, Notre Dame J. Formal Log..

[178]  Neil D. Jones,et al.  A fixed-program machine for combinator expression evaluation , 1982, LFP '82.

[179]  Christophe Raffalli,et al.  Asymptotically almost all \lambda-terms are strongly normalizing , 2009 .

[180]  Ralf Lämmel,et al.  Scrap your boilerplate with XPath-like combinators , 2007, POPL '07.

[181]  Michael I. Jordan,et al.  Learning Programs: A Hierarchical Bayesian Approach , 2010, ICML.

[182]  Symbolic Systems , 2021 .

[183]  Jean-Pierre Desclés,et al.  Applicative and combinatiry categorical grammar (from syntax to functional semantics) , 1997 .

[184]  Ismaïl Biskri Applicative and Combinatory Categorial Grammar and Subordinate Constructions in French , 2005, Int. J. Artif. Intell. Tools.

[185]  Gordon J. Pace,et al.  The Semantics of Verilog Using Transition System Combinators , 2000, FMCAD.

[186]  James H. Andrews,et al.  An untyped higher order logic with Y combinator , 2007, Journal of Symbolic Logic.

[187]  David W. Stemple,et al.  Uniform Traversal Combinators: Definition, Use and Properties , 1992, CADE.

[188]  Kohei Noshita,et al.  A fast algorithm for translating combinator expressions with BC-chains , 2009, New Generation Computing.

[189]  Peter J. Stuckey,et al.  Search combinators , 2012, Constraints.

[190]  Peter Dybjer,et al.  Formal neighbourhoods, combinatory Böhm trees, and untyped normalization by evaluation , 2012, Ann. Pure Appl. Log..

[191]  Mitchell Wand Loops in combinator-based compilers , 1983, POPL '83.

[192]  Feng Shi,et al.  The Combinator – a computer-based tool for creative idea generation based on a simulation approach , 2018, Design Science.

[193]  Bruce J. MacLennan Preliminary Investigation of Random SKI-Combinator Trees , 1997 .

[194]  A. S. Kuzichev Deductive operators of combinatory logic , 1974 .

[195]  Syed Kamal Abdali A combinatory logic model of programming languages. , 1974 .

[196]  Nils Anders Danielsson Total parser combinators , 2010, ICFP '10.

[197]  Richard Statman Two Variables Are Not Enough , 2005, ICTCS.

[198]  Robin Milner Parallel Combinator Reduction Machine , 1983, The Analysis of Concurrent Systems.