Type Soundness for Path Polymorphism

Abstract

Path polymorphism is the ability to define functions that can operate uniformly over arbitrary recursively specified data structures. Its essence is captured by patterns of the form x y which decompose a compound data structure into its parts. Typing these kinds of patterns is challenging since the type of a compound should determine the type of its components. We propose a static type system (i.e. no run-time analysis) for a pattern calculus that captures this feature. Our solution combines type application, constants as types, union types and recursive types. We address the fundamental properties of Subject Reduction and Progress that guarantee a well-behaved dynamics. Both these results rely crucially on a notion of pattern compatibility and also on a coinductive characterisation of subtyping.

Pure Pattern Calculus à la de Bruijn

“…Developing such a calculus implies numerous technical challenges to guarantee well-behaved operational semantics in the untyped framework. Recently, a static type system has been introduced for a restriction of PPC called Calculus of Applicative Patterns (CAP) [VBA15], which is able to capture the path polymorphic aspect of PPC. Moreover, type-checking algorithms for such a formalism has also been studied [EVB15], as a first step towards an implementation of a prototype for a typed functional programming language capturing such features.…”