We observe that the principal typing property of a type system is the enabling technology for modularity and separate compilation [10]. We use this technology to formulate a modular and polyvariant closure analysis, based on the rank 2 intersection types annotated with control-flow information. Modularity manifests itself in a syntax-directed, annotated-type inference algorithm that can analyse program fragments containing free variables: a principal typing property is used to formalise it. Polyvariance manifests itself in the separation of different behaviours of the same function at its different uses: this is formalised via the rank 2 intersection types. As the rank 2 intersection type discipline types at least all (core) ML programs, our analysis can be used in the separate compilation of such programs. 1

Effect systems extend classical type systems with effect information. Just as types describe the possible values of expressions, effects describe their possible evaluation behaviors. Effects, which appear in function types, introduce new constraints on the typability of expressions. To increase the exibility and accuracy of e ect systems, we present a new effect system based on subtyping. The subtype relation is induced by a subsumption relation on effects. This subtyping effect system avoids merging effect information together, thus collecting more precise effect information. We introduce a reconstruction algorithm which for any expression already typed with classical types, reconstructs its type and effect based on the subtype relation. The reconstruction algorithm is sound and complete w.r.t. the static semantics.

Optimizing compilers for function-oriented and object-oriented languages exploit type and flow information for efficient implementation. Although type and flow information (both control and data flow) are inseparably intertwined, compilers usually compute and represent them separately. Partially, 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. This integration facilitates the preservation of flow and type information through program transformations. In this paper we describe CIL, an intermediate language supporting polymorphic types and polyvariant flow information and describe its application in program optimiziation. We are experimenting with this intermediate language in a flow and typedirected compiler for a functional language. ...

Binding time analysis aims at determining which identifiers can be bound to their values at compile time. This binding time information is of utmost importance when performing partial evaluation or constant folding on programs. Existing binding time analyses are global in that they require complete program texts and descriptions of which of their inputs are available at compile time. As a consequence, such analyses cannot be used in programming languages that support modules or separate compilation. Libraries have to be analyzed every time they are used in some program. This is particularly limiting when considering programming in-the-large; any modification of an application results in the reprocessing of all the modules. This paper presents a new static analysis for higher-order typed functional languages that relies on a type and e#ect system to obtain polyvariant and separate binding time information. By allowing function types to be parametrized over the binding times of their arg...