Abstract
We propose a novel definition of binders using matching logic, where the binding behavior of object-level binders is directly inherited from the built-in exists binder of matching logic. We show that the behavior of binders in various logical systems such as lambda-calculus, System F, pi-calculus, pure type systems, can be axiomatically defined in matching logic as notations and logical theories. We show the correctness of our definitions by proving conservative extension theorems, which state that a sequent/judgment is provable in the original system if and only if it is provable in matching logic, in the corresponding theory. Our matching logic definition of binders also yields models to all binders, which are deductively complete with respect to formal reasoning in the original systems. For lambda-calculus, we further show that the yielded models are representationally complete, a desired property that is not enjoyed by many existing lambda-calculus semantics. This work is part of a larger effort to develop a logical foundation for the programming language semantics framework K (http://kframework.org).
Supplemental Material
- M. Abadi, L. Cardelli, P.-L. Curien, and J.-J. Lévy. 1991. Explicit substitutions. Journal of Functional Programming 1, 4 ( 1991 ), 375-416. https://doi.org/10.1017/S0956796800000186 Google Scholar
Cross Ref
- Areski Nait Abdallah. 1995. Partial first-order logic. In The Logic of Partial Information. Springer, Berlin, Heidelberg, Chapter 14, 425-452. https://doi.org/10.1007/978-3-642-78160-5_14 Google Scholar
Cross Ref
- Mauricio Ayala-Rincón, Washington de Carvalho-Segundo, Maribel Fernández, and Daniele Nantes-Sobrinho. 2018. Nominal C-unification. In Proceedings of the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR'17) (Lecture Notes in Computer Science), Vol. 10855. Springer International Publishing, Namur, Belgium, 235-251.Google Scholar
- Mauricio Ayala-Rincón, Maribel Fernández, and Daniele Nantes-Sobrinho. 2016. Nominal narrowing. In Proceedings of the 1st International Conference on Formal Structures for Computation and Deduction (FSCD'16) (Leibniz International Proceedings in Informatics (LIPIcs)), Vol. 52. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 11 : 1-11 : 17. https://doi.org/10.4230/LIPIcs.FSCD. 2016.11 Google Scholar
Cross Ref
- Brian Aydemir, Arthur Charguéraud, Benjamin C. Pierce, Randy Pollack, and Stephanie Weirich. 2008. Engineering formal metatheory. In Proceedings of the 35th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL'08) (San Francisco, California, USA). ACM, New York, NY, USA, 3-15. https://doi.org/10.1145/1328438.1328443 Google Scholar
Digital Library
- Henk Barendregt. 1984. The lambda calculus, its syntax and semantics. College Publications, King's College London, Strand, London WC2R 2LS, UK. https://doi.org/10.2307/2274112 Google Scholar
Cross Ref
- Henk Barendregt. 1993. Lambda calculi with types. In Handbook of Logic in Computer Science. Vol. 2, background: computational structures. Oxford University Press, UK, Chapter 2, 117-309. https://doi.org/10.5555/162552.162561 Google Scholar
Digital Library
- John Bell and Moshe Machover. 1977. A course in mathematical logic. North Holland, Amsterdam, Netherlands.Google Scholar
- Chantal Berline. 2000. From computation to foundations via functions and application: the-calculus and its webbed models. Theoretical Computer Science 249, 1 ( 2000 ), 81-161. https://doi.org/10.1016/S0304-3975 ( 00 ) 00057-8 Google Scholar
Digital Library
- Chantal Berline. 2006. Graph models of-calculus at work, and variations. Mathematical Structures in Computer Science 16, 2 ( 2006 ), 185-221. https://doi.org/10.1017/S0960129506005123 Google Scholar
Digital Library
- Gilles Bernot, Michel Bidoit, and Christine Choppy. 1986. Abstract data types with exception handling: An initial approach based on a distinction between exceptions and errors. Theoretical Computer Science 46 ( 1986 ), 13-45. https://doi.org/10. 1016/ 0304-3975 ( 86 ) 90019-8 Google Scholar
Cross Ref
- Gérard Berry. 1978. Stable models of typed-calculi. In Automata, Languages and Programming. Springer, Berlin, Heidelberg, 72-89. https://doi.org/10.5555/646232.682069 Google Scholar
Digital Library
- Patrick Blackburn, Maarten de Rijke, and Yde Venema. 2001. Modal logic. Cambridge University Press, One Liberty Plaza, New York, NY.Google Scholar
- C. J. Bloo. 1997. Preservation of termination for explicit substitution. Ph.D. Dissertation. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR499858 Google Scholar
Cross Ref
- Denis Bogdănaş and Grigore Roşu. 2015. K-Java: A complete semantics of Java. In Proceedings of the 42nd Symposium on Principles of Programming Languages (POPL'15). ACM, Mumbai, India, 445-456.Google Scholar
Digital Library
- Antonio Bucciarelli and Thomas Ehrhard. 1993. A theory of sequentiality. Theoretical Computer Science 113, 2 ( 1993 ), 273-291. https://doi.org/10.1016/ 0304-3975% 2893 % 2990005-E Google Scholar
Cross Ref
- Antonio Bucciarelli and Antonino Salibra. 2004. The sensible graph theories of lambda calculus. In Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS'04). IEEE, Turku, Finland, 276-285. https://doi.org/10.1109/ LICS. 2004.1319622 Google Scholar
Cross Ref
- Peter Burmeister. 1993. Partial algebras-an introductory survey. In Algebras and orders. NATO ASI Series, Vol. 389. Springer, Dordrecht, Netherlands, 1-70. https://doi.org/10.1007/ 978-94-017-0697-1_1 Google Scholar
Cross Ref
- Luca Cardelli. 1996. Type systems. ACM Computing Surveys (CSUR) 28, 1 ( 1996 ), 263-264.Google Scholar
- Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. 1994. An extension of system F with subtyping. Information and Computation 109, 1 ( 1994 ), 4-56. https://doi.org/10.1006/inco. 1994.1013 Google Scholar
Digital Library
- Xiaohong Chen and Grigore Roşu. 2019. Matching-logic. In Proceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS'19). IEEE, Vancouver, Canada, 1-13. https://doi.org/10.1109/LICS. 2019.8785675 Google Scholar
Cross Ref
- Xiaohong Chen and Grigore Roşu. 2020. A general approach to define binders using matching logic. Technical Report. University of Illinois at Urbana-Champaign. http://hdl.handle. net/2142/106608Google Scholar
- James Cheney. 2006. Completeness and Herbrand theorems for nominal logic. Journal of Symbolic Logic 71, 1 ( 2006 ), 299-320.Google Scholar
Cross Ref
- James Cheney. 2014. A simple sequent calculus for nominal logic. Journal of Logic and Computation 26, 2 ( 2014 ), 699-726. https://doi.org/10.1093/logcom/exu024 Google Scholar
Cross Ref
- James Cheney, Michael Norrish, and René Vestergaard. 2012. Formalizing adequacy: a case study for higher-order abstract syntax. Journal of Automated Reasoning 49, 2 ( 2012 ), 209-239. https://doi.org/10.1007/s10817-011-9221-6 Google Scholar
Digital Library
- Adam Chlipala. 2008. Parametric higher-order abstract syntax for mechanized semantics. In Proceedings of the 13th ACM SIGPLAN International Conference on Functional Programming (ICFP'08). ACM, British Columbia, Canada, 143-156.Google Scholar
Digital Library
- Alonzo Church. 1941. The calculi of lambda-conversion. Princeton University Press, Princeton, New Jersey, USA. https: //doi.org/10.2307/2267126 Google Scholar
Cross Ref
- Bruno Courcelle and Joost Engelfriet. 2012. Graph structure and monadic second-order logic: a language-theoretic approach. Vol. 138. Cambridge University Press, England, UK. https://doi.org/10.1017/CBO9780511977619 Google Scholar
Cross Ref
- Sandeep Dasgupta, Daejun Park, Theodoros Kasampalis, Vikram S. Adve, and Grigore Roşu. 2019. A complete formal semantics of x86-64 user-level instruction set architecture. In Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI'19). ACM, Phoenix, Arizona, USA, 1133-1148.Google Scholar
Digital Library
- Nicolaas Govert de Bruijn. 1972. Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem. Indagationes Mathematicae 75, 5 ( 1972 ), 381-392. https://doi.org/10.1016/ 1385-7258 ( 72 ) 90034-0 Google Scholar
Cross Ref
- Joëlle Despeyroux, Amy Felty, and André Hirschowitz. 1995. Higher-order abstract syntax in Coq. In Typed Lambda Calculi and Applications. Springer, Berlin, Heidelberg, 124-138. https://doi.org/10.1007/BFb0014049 Google Scholar
Cross Ref
- Erwin Engeler. 1981. Algebras and combinators. Algebra Universalis 13, 1 ( 1981 ), 389-392. https://doi.org/10.1007/BF02483849 Google Scholar
Cross Ref
- Amy Felty and Alberto Momigliano. 2012. Hybrid, a definitional two-level approach to reasoning with higher-order abstract syntax. Journal of Automated Reasoning 48, 1 ( 2012 ), 43-105. https://doi.org/10.1007/s10817-010-9194-x Google Scholar
Digital Library
- Marcelo Fiore and Chung-Kil Hur. 2010. Second-order equational logic (extended abstract). In Computer Science Logic, Anuj Dawar and Helmut Veith (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 320-335.Google Scholar
- Marcelo Fiore and Ola Mahmoud. 2010. Second-order algebraic theories. In Mathematical Foundations of Computer Science 2010, Petr Hliněný and Antonín Kučera (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 368-380.Google Scholar
- M. Fiore, G. Plotkin, and D. Turi. 1999. Abstract syntax and variable binding. In Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158). IEEE, Trento, Italy, 193-202.Google Scholar
- Murdoch Gabbay and James Cheney. 2004. A sequent calculus for nominal logic. In Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS'04). IEEE, Washington, DC, USA, 139-148. https://doi.org/10.5555/ 1018438.1021850 Google Scholar
Digital Library
- Murdoch J. Gabbay and Michael J. Gabbay. 2017. Representation and duality of the untyped-calculus in nominal lattice and topological semantics, with a proof of topological completeness. Annals of Pure and Applied Logic Volume 168, 3 (Oct. 2017 ), 501-621. https://doi.org/10.1016/j.apal. 2016. 10.001 Google Scholar
Cross Ref
- M. Gabbay and A. Pitts. 1999. A new approach to abstract syntax involving binders. In Proceedings of the 14th Symposium on Logic in Computer Science (LICS'19). IEEE, Trento, Italy, 214-224. https://doi.org/10.1109/LICS. 1999.782617 Google Scholar
Cross Ref
- Murdoch J. Gabbay. 2000. A theory of inductive definitions with-equivalence: semantics, implementation, programming language. Ph.D. Dissertation. DPMMS and Trinity College, Cambridge University.Google Scholar
- Andrew Gacek, Dale Miller, and Gopalan Nadathur. 2012. A two-level logic approach to reasoning about computations. Journal of Automated Reasoning 49, 2 ( 2012 ), 241-273. https://doi.org/10.1007/s10817-011-9218-1 Google Scholar
Digital Library
- Jean-Yves Girard. 1972. Interprétation fonctionnelle et élimination des coupures de l'arithmétique d'ordre supérieur. Ph.D. Dissertation. Paris Diderot University, Paris, France.Google Scholar
- Jean-Yves Girard. 1986. The system F of variable types, fifteen years later. Theoretical Computer Science 45 ( 1986 ), 159-192. https://doi.org/10.1016/ 0304-3975 ( 86 ) 90044-7 Google Scholar
Digital Library
- Jean-Yves Girard. 1987. Linear logic. Theoretical Computer Science 50, 1 ( 1987 ), 1-101. https://doi.org/10.1016/ 0304-3975 ( 87 ) 90045-4 Google Scholar
Digital Library
- M. Gogolla, K. Drosten, U. Lipeck, and H.-D. Ehrich. 1984. Algebraic and operational semantics of specifications allowing exceptions and errors. Theoretical Computer Science 34, 3 ( 1984 ), 289-313. https://doi.org/10.1016/ 0304-3975 ( 84 ) 90056-2 Google Scholar
Cross Ref
- Joseph Goguen and José Meseguer. 1992. Order-sorted algebra, part I: equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theoretical Computer Science 105, 2 ( 1992 ), 217-273. https://doi.org/10. 1016/ 0304-3975 ( 92 ) 90302-V Google Scholar
Digital Library
- Robert Harper, Furio Honsell, and Gordon Plotkin. 1993. A framework for defining logics. J. ACM 40, 1 ( 1993 ), 143-184. https://doi.org/10.1145/138027.138060 Google Scholar
Digital Library
- Gisbert Hasenjaeger. 1953. Eine bemerkung zu Henkin's beweis für die vollständigkeit des prädikatenkalküls der ersten stufe. The Journal of Symbolic Logic 18, 1 ( 1953 ), 42-48. https://doi.org/10.2307/2266326 Google Scholar
Cross Ref
- Chris Hathhorn, Chucky Ellison, and Grigore Roşu. 2015. Defining the undefinedness of C. In Proceedings of the 36th annual ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI'15). ACM, Portland, OR, 336-345.Google Scholar
Digital Library
- Everett Hildenbrandt, Manasvi Saxena, Xiaoran Zhu, Nishant Rodrigues, Philip Daian, Dwight Guth, Brandon Moore, Yi Zhang, Daejun Park, Andrei Ştefănescu, and Grigore Roşu. 2018. KEVM: A complete semantics of the Ethereum virtual machine. In Proceedings of the 2018 IEEE Computer Security Foundations Symposium (CSF'18). IEEE, Oxford, UK, 204-217. http://jellopaper.org.Google Scholar
Cross Ref
- Roger Hindley and Giuseppe Longo. 1980. Lambda-calculus models and extensionality. Mathematical Logic Quarterly 26, 4 ( 1980 ), 289-310. https://doi.org/10.1002/malq.19800261902 Google Scholar
Cross Ref
- K Team. 2020. K tutorials--calculus. https://github.com/kframework/k/tree/master/k-distribution/tutorial/1_k/1_lambda/ lesson_2.Google Scholar
- Delia Kesner. 2009. A theory of explicit substitutions with safe and full composition. Logical Methods in Computer Science 5, 3 ( 2009 ), 1-29.Google Scholar
- Jan Willem Klop. 1993. Term rewriting systems. In Handbook of Logic in Computer Science. Vol. 2, Background : computational structures. Oxford University Press, Inc., USA, Chapter 1, 1-116.Google Scholar
- C. P. J. Koymans. 1982. Models of the lambda calculus. Information and Control 52 ( 1982 ), 306-332.Google Scholar
- Jean Louis Krivine. 1993. Lambda-calculus, types and models. Ellis Horwood, USA.Google Scholar
- Patrick Lincoln and John Mitchell. 1992. Operational aspects of linear lambda calculus. In Proceedings of the 7th Annual IEEE Symposium on Logic in Computer Science (LICS'92). IEEE, California, USA, 235-246. https://doi.org/10.1109/LICS. 1992. 185536 Google Scholar
Cross Ref
- Leopold Löwenheim. 1915. Über möglichkeiten im relativkalkül. Math. Ann. 76, 4 ( 1915 ), 447-470.Google Scholar
- Francisca Lucio-Carrasco and Antonio Gavilanes-Franco. 1989. A first order logic for partial functions. In Proceedings of the 6th Annual Symposium on Theoretical Aspects of Computer Science (STACS'89). Springer, Paderborn, Germany, 47-58. https://doi.org/10.1007/BFb0028972 Google Scholar
Cross Ref
- Giulio Manzonetto. 2008. Models and theories of lambda calculus. Ph.D. Dissertation. Università Ca' Foscari di Venezia. https://tel.archives-ouvertes.fr/tel-00715207Google Scholar
- Per Martin-Löf. 1998. Twenty five years of constructive type theory. Oxford Logic Guides Book, Vol. 36. Oxford University Press, Oxford, UK, Chapter An intuitionistic theory of types, 127-172. http://www.cse.chalmers.se/~peterd/papers/ MartinLöf1972.pdfGoogle Scholar
- Raymond C. McDowell and Dale A. Miller. 2002. Reasoning with higher-order abstract syntax in a logical framework. ACM Transactions on Computational Logic 3, 1 ( 2002 ), 80-136. https://doi.org/10.1145/504077.504080 Google Scholar
Digital Library
- James McKinna and Robert Pollack. 1993. Pure type systems formalized. In Typed Lambda Calculi and Applications, Marc Bezem and Jan Friso Groote (Eds.). Springer, Berlin, Heidelberg, 289-305. https://doi.org/10.1007/BFb0037113 Google Scholar
Cross Ref
- José Meseguer and Grigore Roşu. 2013. The rewriting logic semantics project: a progress report. Information and Computation 231 (Oct. 2013 ), 38-69. https://doi.org/10.1016/j.ic. 2013. 08.004 Invited paper at FCT 2011. Google Scholar
Cross Ref
- Robin Milner, Joachim Parrow, and David Walker. 1992. A calculus of mobile processes (part 1). Information and Computation 100, 1 ( 1992 ), 1-40. https://doi.org/10.1016/ 0890-5401 ( 92 ) 90008-4 Google Scholar
Digital Library
- Timothy Nelson, Daniel Dougherty, Kathi Fisler, and Shriram Krishnamurthi. 2010. On the finite model property in order-sorted logic. Technical Report. Worcester Polytechnic Institute, Brown University.Google Scholar
- Daejun Park, Andrei Ştefănescu, and Grigore Roşu. 2015. KJS: A complete formal semantics of JavaScript. In Proceedings of the 36th annual ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI'15). ACM, Portland, OR, 346-356.Google Scholar
Digital Library
- Lawrence C. Paulson. 1989. The foundation of a generic theorem prover. Journal of Automated Reasoning 5, 3 ( 1989 ), 363-397. https://doi.org/10.1007/BF00248324 Google Scholar
Digital Library
- Frank Pfenning and Conal Elliott. 1988. Higher-order abstract syntax. In Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI'88). ACM, New York, NY, USA, 199-208. https://doi.org/10. 1145/53990.54010 Google Scholar
Digital Library
- Frank Pfenning and Carsten Schürmann. 1999. System description: Twelf-a meta-logical framework for deductive systems. In Proceedings of the 16th International Conference on Automated Deduction (CADE 99). Springer, Trento, Italy, 202-206. https://doi.org/10.1007/3-540-48660-7_14 Google Scholar
Cross Ref
- Andrew M. Pitts. 2003. Nominal logic, a first order theory of names and binding. Information and Computation 186, 2 ( 2003 ), 165-193. https://doi.org/10.1016/S0890-5401 ( 03 ) 00138-X Google Scholar
Digital Library
- Andrew M. Pitts. 2005. Alpha-structural recursion and induction. In Theorem Proving in Higher Order Logics, Joe Hurd and Tom Melham (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 17-34.Google Scholar
- Andrew M. Pitts. 2013. Nominal sets: names and symmetry in computer science. Cambridge University Press, New York, NY, USA. https://doi.org/10.1017/CBO9781139084673 Google Scholar
Cross Ref
- Gordon Plotkin. 1972. A set-theoretical definition of application. Technical Report. University of Edinburgh.Google Scholar
- Andrei Popescu and Grigore Roşu. 2013. Term-generic logic (extended technical report). Technical Report. Technische Universitat Munchen, University of Illinois at Urbana-Champaign.Google Scholar
- Andrei Popescu and Grigore Roşu. 2015. Term-generic logic. Theoretical Computer Science 577 ( 2015 ), 1-24. https: //doi.org/10.1016/j.tcs. 2015. 01.047 Google Scholar
Digital Library
- Robert W. Quackenbush. 1988. Completeness theorems for universal and implicational logics of algebras via congruences. Proc. Amer. Math. Soc. 103, 4 ( 1988 ), 1015-1021. https://doi.org/10.2307/2047077 Google Scholar
Cross Ref
- John C. Reynolds. 1974. Towards a theory of type structure. In Programming Symposium. Springer, Berlin, Heidelberg, 408-425. https://doi.org/10.1007/3-540-06859-7_148 Google Scholar
Cross Ref
- John C. Reynolds. 2002. Separation logic: A logic for shared mutable data structures. In Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science (LICS'02). IEEE, Copenhagen, Denmark, 55-74.Google Scholar
Cross Ref
- Grigore Roşu. 2017. Matching logic. Logical Methods in Computer Science 13, 4 ( 2017 ), 1-61. https://doi.org/10.23638/ LMCS13 (4:28) 2017 Google Scholar
Cross Ref
- Grigore Roşu and Traian Florin Şerbănuţă. 2010. An overview of the K semantic framework. Journal of Logic and Algebraic Programming 79, 6 ( 2010 ), 397-434. https://doi.org/10.1016/j.jlap. 2010. 03.012 Google Scholar
Cross Ref
- Harold Schellinx. 1991. Isomorphisms and nonisomorphisms of graph models. Journal of Symbolic Logic 56, 1 (Oct. 1991 ), 227-249. https://doi.org/10.2307/2274916 Google Scholar
Digital Library
- Carsten Schürmann, Joëlle Despeyroux, and Frank Pfenning. 2001. Primitive recursion for higher-order abstract syntax. Theoretical Computer Science 266, 1 ( 2001 ), 1-57. https://doi.org/10.1016/S0304-3975 ( 00 ) 00418-7 Google Scholar
Digital Library
- Dana Scott. 1972. Continuous lattices. In Toposes, Algebraic Geometry and Logic. Springer, Berlin, Heidelberg, 97-136. https://doi.org/10.1007/BFb0073967 Google Scholar
Cross Ref
- Dana Scott. 1975a. Data types as lattices. SIAM J. Comput. 5, 3 ( 1975 ), 522-587. https://doi.org/10.1137/0205037 Google Scholar
Cross Ref
- Dana Scott. 1975b. Some philosophical issues concerning theories of combinators. In Proceedings of the International Symposium on-Calculus and Computer Science Theory. Springer, Berlin, Heidelberg, 346-366. https://doi.org/10.1007/ BFb0029537 Google Scholar
Cross Ref
- Traian Florin Şerbănuţă and Grigore Roşu. 2012. A truly concurrent semantics for the K framework based on graph transformations. In Proceedings of the 6th International Conference on Graph Transformation (ICGT'12). Springer, Bremen, Germany, 294-310.Google Scholar
- Mark-Oliver Stehr. 2000. CINNI-a generic calculus of explicit substitutions and its application to--and-calculi. Electronic Notes in Theoretical Computer Science 36 ( 2000 ), 70-92. https://doi.org/10.1016/S1571-0661 ( 05 ) 80125-2 Google Scholar
Cross Ref
- Christian Urban. 2008. Nominal techniques in Isabelle/HOL. Journal of Automated Reasoning 40, 4 ( 01 May 2008 ), 327-356. https://doi.org/10.1007/s10817-008-9097-2 Google Scholar
Digital Library
- Jonni Virtema, Jeremy Meyers, and Antti Kuusisto. 2013. Undecidable first-order theories of afine geometries. Logical Methods in Computer Science 9, 4 ( 2013 ), 1-23. https://doi.org/10.2168/LMCS-9( 4 :26) 2013 Google Scholar
Cross Ref
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A general approach to define binders using matching logic
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