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Optimal Representations of Polymorphic Types with Subtyping

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Higher-Order and Symbolic Computation

Abstract

Many type inference and program analysis systems include notions of subtyping and parametric polymorphism. When used together, these two features induce equivalences that allow types to be simplified by eliminating quantified variables. Eliminating variables both improves the readability of types and the performance of algorithms whose complexity depends on the number of type variables. We present an algorithm for simplifying quantified types in the presence of subtyping and prove it is sound and complete for non-recursive and recursive types. We also show that an extension of the algorithm is sound but not complete for a type language with intersection and union types, as well as for a language of constrained types.

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Authors and Affiliations

  1. EECS Department, University of California, Berkeley, CA, 94720-1776

    Alexander Aiken

  2. IBM Almaden Research Center, 650 Harry Rd., San Jose, CA, 95120-6099

    Edward L. Wimmers

  3. Department of Computer Science, Purdue University, West lafayette, IN, 47907

    Jens Palsberg

Authors
  1. Alexander Aiken
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  2. Edward L. Wimmers
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  3. Jens Palsberg
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Aiken, A., Wimmers, E.L. & Palsberg, J. Optimal Representations of Polymorphic Types with Subtyping. Higher-Order and Symbolic Computation 12, 237–282 (1999). https://doi.org/10.1023/A:1010056315933

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