Summary: Under consideration for publication in Math. Struct. in Comp. Science
Polarized Subtyping for Sized Types
Department of Computer Science, University of Munich
Oettingenstr. 67, D-80538 M®unchen, Germany
Received March 15, 2006
We present an algorithm for deciding polarized higher-order subtyping without bounded
quantification. Constructors are identified not only modulo , but also . We give a direct proof of
completeness, without constructing a model or establishing a strong normalization theorem.
Inductive and coinductive types are enriched with a notion of size and the subtyping calculus is
extended to account for the arising inclusions between the sized types.
Polarized kinding and subtyping has recently received interest in two contexts. First, in the analy-
sis of container types in object-oriented programming languages (Duggan & Compagnoni, 1998).
If List A is a functional (meaning: read-only) collection of objects of type A and A is a subtype
(subclass) of B then List A should be a subtype of List B. However, for read-write collections, as
for instance Array, such a subtyping relation is unsound
, hence these two collection constructors
must be kept apart. The conventional modelling language for object types, System F