Properties of a Type Abstract Interpreter

In a previous paper, we have developed a type abstract interpreter which was shown to be more precise then the classical ML type inference algorithm in inferring monomorphic types, represented as Herbrand terms with variables à la Hindley. In order to deal with recursive functions, we introduce a new abstract fixpoint operator which generalizes the one used in the Hindley and ML inference algorithms by performing k fixpoint computation steps (as done in the case of polymorphic types). Our abstract interpreter has many interesting properties. It is possible to reconstruct the ML result by just one fixpoint computation step (k = 1) and to show that for every k ≥ 1, either we reach the least fixpoint (which is in general more precise than the ML result), or we get exactly the same result as ML. One important result is that our type interpreter turns out to correspond to a type system, which lies between monomorphism and polymorphic recursio