Optimal Representations of Polymorphic Types with Subtyping

Authors:
Alexander Aiken;Edward L. Wimmers;Jens Palsberg
Affiliations:
EECS Department, University of California, Berkeley, CA 94720-1776. aiken@cs.berkeley.edu;IBM Almaden Research Center, 650 Harry Rd., San Jose, CA 95120-6099. wimmers@almaden.ibm.com;Department of Computer Science, Purdue University, West lafayette, IN 47907. palsberg@cs.purdue.edu
Venue:
Higher-Order and Symbolic Computation
Year:
1999

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Abstract

Many type inference and program analysis systems include notions ofsubtyping and parametric polymorphism. When used together, these two featuresinduce equivalences that allow types to be simplified by eliminatingquantified variables. Eliminating variables both improves thereadability of types and the performance of algorithms whosecomplexity depends on the number of type variables. We present analgorithm for simplifying quantified types in the presence ofsubtyping and prove it is sound and complete for non-recursive and recursivetypes. We also show that an extension of the algorithm is sound butnot complete for a type language with intersection and union types, as well asfor a language of constrained types.