System L is a linear λ-calculus with numbers and an iterator, which, although imposing linearity restrictions on terms, has all the computational power of Gödel’s System T. System L owes its power to two features: the use of a closed reduction strategy (which permits the construction of an iterator on an open function, but only iterates the function after it becomes closed), and the use of a liberal typing rule for iterators based on iterative types. In this paper, we study these new types, and show how they relate to intersection types. We also give a sound and complete type reconstruction algorithm for System L.

We show that typability for a natural form of polymorphic recursive typing for rank-2 intersection types is undecidable. Our proof involves characterizing typability as a context free language (CFL) graph problem, which may be of independent interest, and reduction from the boundedness problem for Turing machines. We also show a property of the type system which, in conjunction with the undecidability result, disproves a misconception about the Milner-Mycroft type system. We also show undecidability of a related program analysis problem. 1

this paper we show how they can be recast into algorithmic inference rules by applying a combination of standard techniques, among which constraint handling plays a central role. We then analyse the generated constraint sets and show that they share a common structure which can be simplified with a specialised algorithm we present. As the constraint simplification procedure is mainly based on unification, we implemented the whole inference algorithm in a Prolog program which we will comment upon