Summary: Syntactic Metatheory of
Higher­Order Subtyping
Andreas Abel and Dulma Rodriguez
Department of Computer Science, University of Munich
Oettingenstr. 67, D­80538 M˜unchen, Germany
{andreas.abel|dulma.rodriguez}@ifi.lmu.de
Abstract. We present a new proof of decidability of higher­order sub­
typing in the presence of bounded quantification. The algorithm is for­
mulated as a judgement which operates on beta­eta­normal forms. Tran­
sitivity and closure under application are proven directly and syntacti­
cally, without the need for a model construction or reasoning on longest
beta­reduction 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 normal­form 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: Higher­order subtyping, bounded quantification, algorith­

Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universität München

Collections: Computer Technologies and Information Sciences