Graphical and incremental type inference: a graph transformation approach

Abstract

We present a graph grammar based type inference system for a totally graphic development language. NiMo (Nets in Motion) can be seen as a graphic equivalent to Haskell that acts as an on-line tracer and debugger. Programs are process networks that evolve giving total visibility of the execution state, and can be interactively completed, changed or stored at any step. In such a context, type inference must be incremental. During the net construction or modification only type safe connections are allowed. The user visualises the type information evolution and, in case of conflict, can easily identify the causes. Though based on the same ideas, the type inference system has significant differences with its analogous in functional languages. Process types are a non-trivial generalization of functional types to handle multiple outputs, partial application in any order, and curried-uncurried coercion. Here we present the elements to model graphical inference, the notion of structural and non-structural equivalence of type graphs, and a graph unification and composition calculus for typing nets in an incremental way.