A Graph-Based Generic Type System for Object-Oriented Programs

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References 52References[1] J. Gosling, B. Joy, G. Steele, and G. Bracha, Java Language Specification: The Java Series. Addison-Wesley Longman Publishing Co., Inc. Boston, MA, USA, 2000.[2] O. M. Group, “Omg unified modeling language (omg uml), superstructure, v2.1.2,” tech. rep., 2007.www.omg.org/spec/UML/2.1.2/Superstructure/PDF.[3] C. A. R. Hoare and J. He, “A trace model for pointers and objects,” in 13th European Conferenceon Object-Oriented Programming, LNCS 1628, pp. 1–17, Springer, 1999.[4] J. He, X. Li, and Z. Liu, “rCOS: A refinement calculus for object systems,” Theor. Comput. Sci.,vol. 365, no. 1-2, pp. 109–142, 2006.[5] G. Klein and T. Nipkow, “A machine-checked model for a Java-like language, virtual machine, andcompiler,” ACM Transactions on Programming Languages and Systems (TOPLAS), vol. 28, no. 4,pp. 619–695, 2006.[6] W. Ke, Z. Liu, S. Wang, and L. Zhao, “A Graph-based Operational Semantics of OO Programs,”Formal Methods and Software Engineering, pp. 347–366, 2009.[7] G. Bracha, “Generics in the Java programming language,” Sun Microsystems, 2004. java.sun.com/j2se/1.5/pdf/generics-tutorial.pdf.[8] B. Pierce, Types and programming languages. The MIT Press, 2002.[9] L. Zhao, X. Liu, Z. Liu, and Z. Qiu, “Graph transformations for object-oriented refinement,” Form.Asp. Comput., vol. 21, no. 1-2, pp. 103–131, 2009.[10] W. Ke, Z. Liu, S. Wang, and L. Zhao, “Graph-based type system, operational semantics and implementationof an object-oriented programming language,” Tech. Rep. 410, UNU-IIST, P.O. Box3058, Macau, 2009. www.iist.unu.edu/www/docs/techreports/reports/report410.pdf.[11] M. Abadi and L. Cardelli, A Theory of Objects. Springer, 1996.[12] A. Igarashi, B. Pierce, and P. Wadler, “Featherweight Java: A minimal core calculus for Javaand GJ,” ACM Transactions on Programming Languages and Systems (TOPLAS), vol. 23, no. 3,pp. 396–450, 2001.[13] S. Wang, Q. Long, and Z. Qiu, “Type Safety for FJ and FGJ,” Theoretical Aspects of Computing-ICTAC 2006, pp. 257–271, 2006.[14] A. P. L. Ferreira, L. Foss, and L. Ribeiro, “Formal verification of object-oriented graph grammarsspecifications,” Electronic Notes in Theoretical Computer Science, vol. 175, no. 4, pp. 101 – 114,2007.[15] A. Corradini, F. L. Dotti, L. Foss, and L. Ribeiro, “Translating Java code to graph transformationsystems,” in Graph Transformations, LNCS 3256, pp. 383–398, Springer, 2004.[16] H. Kastenberg, A. Kleppe, and A. Rensink, “Defining object-oriented execution semantics usinggraph transformations,” in Formal Methods for Open Object-Based Distributed Systems, LNCS 4037,Springer, 2006.[17] R. Heckel, J. M. Küster, and G. Taentzer, “Confluence of typed attributed graph transformationsystems,” in ICGT ’02: Proceedings of the First International Conference on Graph Transformation,pp. 161–176, Springer-Verlag, 2002.[18] M. Wermelinger and J. L. Fiadero, “A graph transformation approach to software architecture reconfiguration,”Sci. Comput. Program., vol. 44, no. 2, pp. 133–155, 2002.Report No. 448, June 2011UNU-IIST, P.O. Box 3058, Macao
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Page 1 and 2: UNU-IISTInternational Institute for
Page 3 and 4: UNU-IISTInternational Institute for
Page 5: Contents 5Contents1 Introduction 72
Page 9 and 10: An Object Oriented Language 9system
Page 11 and 12: Type Graphs 11denoted by Cc. Only c
Page 13 and 14: Type Graphs 13aa generic classa sta
Page 15 and 16: Type Graphs 15u ∼ v ∼ w ∼ ru,
Page 17 and 18: Type Operations 17Table 2: Type Equ
Page 19 and 20: Type Operations 194.2 Conjunction G
Page 21 and 22: Type Operations 211. all effective
Page 23 and 24: Type Operations 23Lemma 3 For a typ
Page 25 and 26: Type Operations 25Proof. By Definit
Page 27: Type System 27αaγPairaList⊲Pair
Page 30 and 31: Type System 30c ::= . . . other com
Page 32 and 33: Type System 32For a list x of varia
Page 34 and 35: Type System 34Table 5: Visibility o
Page 36 and 37: Type System 36Table 6: Type-Checkin
Page 38 and 39: Type System 38Table 8: Type-Checkin
Page 40 and 41: Execution Environment 40We extract
Page 42 and 43: Execution Environment 42Table 9: Co
Page 44 and 45: Operational Semantics 44RanulllnkCa
Page 46 and 47: Operational Semantics 46Table 10: O
Page 48 and 49: Operational Semantics 48- Case e is
Page 50 and 51: Operational Semantics 50push(G, (se

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