  Expansion is an operation on typings (i.e., pairs of typing environments and
result types) defined originally in type systems for the lambda-calculus with
intersection types in order to obtain principal (i.e., most informative,
strongest) typings. In a type inference scenario, expansion allows postponing
choices for whether and how to use non-syntax-driven typing rules (e.g.,
intersection introduction) until enough information has been gathered to make
the right decision. Furthermore, these choices can be equivalent to inserting
uses of such typing rules at deeply nested positions in a typing derivation,
without needing to actually inspect or modify (or even have) the typing
derivation. Expansion has in recent years become simpler due to the use of
expansion variables (e.g., in System E).
  This paper extends expansion and expansion variables to systems with
forall-quantifiers. We present System Fs, an extension of System F with
expansion, and prove its main properties. This system turns type inference into
a constraint solving problem; this could be helpful to design a modular type
inference algorithm for System F types in the future.
