Types and automata

A hierarchical type system for imperative programming languages gives rise to various computational problems, such as type equivalence, type ordering, etc. We present a particular class of finite automata which are shown to be isomorphic to type equations. All the relevant type concepts turn out to have well-known automata analogues, such as language equality, language inclusion, etc. This provides optimal or best known algorithms for the type system, by a process of translating type equations to automata, solving the analogous problem, and translating the result back to type equations. Apart from suggesting an implementation, this connection lends a certain naturality to our type system. We also introduce a very general form of extended (recursive) type equations which are explained in terms of (monotone) alternating automata. Since types are simply equationally defined trees, these results may have wider applications