Type Inference for Intersection Types with Expansion Variables Principality of typings is the property that, for each typable term, there is a typing from which all other typings are obtained via some set of operations.
Type inference is the problem of finding a typing for a given term, if possible.
We define an intersection type system which has principal typings and types exactly the strongly normalizable lambda-terms. This is in contrast to System F where the finite rank restriction for every finite rank at 3 and above has neither principal typings nor decidable type inference. In our system the earlier notion of expansion is integrated in the form of expansion variables , which are subject to substitution as are ordinary variables.