Path Polymorphism

Abstract

Typing terms that act uniformly on all data structures is challenging because the type of a compound does not determine the types of its components, so that direct attempts to type car or cdr produce ill formed types. The query calculus can be seen as a typed version of the compound calculus, in which the operators car and cdr are replaced by folds built from functions that are polymorphic enough to handle whatever components may arise. Such folds are expressive enough to represent many path polymorphic functions including the usual generic queries. Further, by constraining the types of constructors to avoid higher types, reduction becomes strongly normalising. When typing the static pattern calculus, the challenges are met by careful characterisation of the local type symbols that are implicitly bound in a case.