Typing rule-based transformations over topological collections

TL;DR

This paper extends pattern-matching rule-based programming to topological collections in a typed functional language, maintaining type inference and broadening application scope beyond algebraic data-types.

Contribution

It introduces a polytypic extension of mini-ML that supports rule-based transformations over topological collections with preserved type inference.

Findings

Topological collections enable rule-based programming beyond algebraic data-types.

Type inference remains feasible in the extended mini-ML language.

The extension retains the benefits of typed functional programming.

Abstract

Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits the field of application. However, as shown by Giavitto and Michel at RULE'02, case-based function definitions can be extended to more general data structures called topological collections. We show in this paper that this extension retains the benefits of the typed discipline of the functional languages. More precisely, we show that topological collections and the rule-based definition of functions associated with them fit in a polytypic extension of mini-ML where type inference is still possible.