Decidability of Higher-Order Subtyping with Intersection Types

The combination of higher-order subtyping with intersection types yields a typed model of object-oriented programming with multiple inheritance [11]. The target calculus, F ⋀ ω , a natural generalization of Girard's system Fω with intersection types and bounded polymorphism, is of independent interest, and is our subject of study.

[1]  Benjamin C. Pierce,et al.  Simple type-theoretic foundations for object-oriented programming , 1994, Journal of Functional Programming.

[2]  B. Pierce Programming with intersection types and bounded polymorphism , 1992 .

[3]  John C. Mitchell,et al.  F-bounded quantification for object-oriented programming , 1989 .

[4]  F. Cardone,et al.  Two extensions of Curry's type inference system , 1990 .

[5]  John C. Mitchell,et al.  F-bounded polymorphism for object-oriented programming , 1989, FPCA.

[6]  Benjamin C. Pierce,et al.  Higher-Order Subtyping , 1994, Theor. Comput. Sci..

[7]  Adriana B. Compagnoni,et al.  Higher-order subtyping with intersection types , 1995 .

[8]  Luca Cardelli,et al.  On understanding types, data abstraction, and polymorphism , 1985, CSUR.

[9]  Giuseppe Castagna,et al.  Decidable bounded quantification , 1994, POPL '94.

[10]  John C. Mitchell,et al.  Theoretical aspects of object-oriented programming: types, semantics, and language design , 1994, Choice Reviews Online.

[11]  Piergiorgio Odifreddi,et al.  Logic and computer science , 1990 .

[12]  Benjamin C. PierceyLFCS Decidable Bounded Quantiication , 1994 .

[13]  John C. Mitchell,et al.  PER models of subtyping, recursive types and higher-order polymorphism , 1992, POPL '92.

[14]  John C. Mitchell Toward a typed foundation for method specialization and inheritance , 1989, POPL '90.

[15]  William R. Cook,et al.  Canning: inheritance is not subtyping , 1990 .

[16]  Giorgio Ghelli,et al.  Coherence of Subsumption, Minimum Typing and Type-Checking in F<= , 1992, Math. Struct. Comput. Sci..

[17]  William R. Cook,et al.  Inheritance is not subtyping , 1989, POPL '90.

[18]  Mariangiola Dezani-Ciancaglini,et al.  A new type assignment for λ-terms , 1978, Arch. Math. Log..

[19]  Luca Cardelli,et al.  A Semantics of Multiple Inheritance , 1984, Information and Computation.

[20]  Mariangiola Dezani-Ciancaglini,et al.  A filter lambda model and the completeness of type assignment , 1983, Journal of Symbolic Logic.