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Summary: Syntactic Metatheory of
Higher-Order Subtyping
Andreas Abel and Dulma Rodriguez
Department of Computer Science, University of Munich
Oettingenstr. 67, D-80538 M¨unchen, Germany
{andreas.abel|dulma.rodriguez}@ifi.lmu.de
Abstract. We present a new proof of decidability of higher-order sub-
typing in the presence of bounded quantification. The algorithm is for-
mulated as a judgement which operates on beta-eta-normal forms. Tran-
sitivity and closure under application are proven directly and syntacti-
cally, without the need for a model construction or reasoning on longest
beta-reduction sequences. The main technical tool is hereditary substi-
tution, i.e., substitution of one normal form into another, resolving all
freshly generated redexes on the fly. Hereditary substitutions are used to
keep types in normal-form during execution of the subtyping algorithm.
Termination of hereditary substitutions can be proven in an elementary
way, by a lexicographic induction on the kind of the substituted variable
and the size of the expression substituted into--this is what enables a
purely syntactic metatheory.
Keywords: Higher-order subtyping, bounded quantification, algorith-
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