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Sébastien Carlier, Jeff Polakow, J. B. Wells, and A. J. Kfoury

System E: Expansion variables for flexible typing with linear and non-linear types and intersection types

In Programming Languages & Systems, 13th European Symp. Programming, volume 2986 of LNCS, pages 294-309 Springer-Verlag, 2004


Types are often used to control and analyze computer programs. Intersection types give a type system great flexibility, but have been difficult to implement. The ! operator, used to distinguish between linear and non-linear types, has good potential for improving tracking of resource usage, but has not been as flexible as one might want and has been difficult to use in compositional analysis. We introduce System E, a type system with expansion variables, linear intersection types, and the ! type constructor for creating non-linear types. System E is designed for maximum flexibility in automatic type inference and for ease of automatic manipulation of type information. Expansion variables allow postponing the choice of which typing rules to use until later constraint solving gives enough information to allow making a good choice. System E removes many limitations and technical difficulties that expansion variables had in the earlier System I and extends expansion variables to work with ! in addition to the intersection type constructor. We present subject reduction results for call-by-need evaluation and discuss approaches for implementing program analysis in System E.


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