We present # CIL , a typed #-calculus which serves as the foundation for a typed intermediate language for optimizing compilers for higher-order polymorphic programming languages. The key innovation of # CIL is a novel formulation of intersection and union types and flow labels on both terms

polymorphism, in a constraint based formulation. The type system is "soft" in the sense that it does not reject programs. It is also not decidable, but there is a broad spectrum of sound and terminating, though incomplete, algorithms whose precision can be characterized by restricting

in terms of polyvariant flow information. We use the theorem as basis for a new flow-type system in the spirit of the CIL -calculus of Wells, Dimock, Muller, and Turbak, in which types are annotated with flow information. A flow-type system is useful as an interface between a owanalysis algorithm and a

, this has been a result of the usual polymorphic type systems using 8 and 9 quantifiers, which are difficult to use in combination with flow annotations. In the Church Project, we are experimenting with intermediate languages that integrate type and flow information into a single flow type framework

. The basic idea behind improving the quality of a monovariant control flow analysis such as 0CFA is the concept of polyvariant analyses such as Agesen's Cartesian Product Algorithm (CPA) and Shivers' nCFA. In this paper we develop a novel framework for polyvariant flow analysis based

. Building on t h work of Nielson Nielson and of Palsberg Pavlopoulou, we present t h firstfaithT# translations between a class of finitary polyvariant flow analyses and a type system supporting polymorph@@ in th form of intersection and union types. Additionally, our flow/type correspondence solves several

. However, versions of the algorithm previously described [19] do not handle data polymorphism well, conservatively merging separate data flows that go through distinct instantiations of a collection type. In this paper, we describe a new extension to DDP that helps to disentangle these flows, permitting

(x) is called once with dynamic data, no reductions on x can be performed in the body of f even when f is called with static data. There is currently great interest in polyvariant binding time analysis. Gengler and Rytz [Gengler & Rytz 1992a, Gengler & Rytz 1992b] use a kind of repeated abstract

polymorphism and (in combination with the labels) polyvariant flow analysis. Accurate flow types expose opportunities for a wide range of optimizing program transformations. This paper is organized as follows. In section 1, we explain the background of the use of types and flow information in compilation