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

We present a novel approach to scalable implementation of type-based flow analysis with polymorphic subtyping. Using a new presentation of polymorphic subtyping with instantiation constraints, we are able to apply context-free language (CFL) reachability techniques to type-based flow analysis. We develop a CFL-based algorithm for computing flow information in time O(n 3 ), where n is the size of the typed program. The algorithm substantially improves upon the best previously known algorithm for flow analysis based on polymorphic subtyping with complexity O(n 8 ). Our technique also yields the first demand-driven algorithm for polymorphic subtype-based flow-computation. It works directly on higher-order programs with structured data of finite type (unbounded data structures are incorporated via finite approximations), supports context-sensitive, global flow summarization and includes polymorphic recursion.

Many polyvariant program analyses have been studied in the 1990s, including k-CFA, polymorphic splitting, and the cartesian product algorithm. The idea of polyvariance is to analyze functions more than once and thereby obtain better precision for each call site. In this paper we present an equivalence theorem which relates a co-inductively defined family of polyvariant ow analyses and a standard type system. The proof embodies a way of understanding polyvariant flow information in terms of union and intersection types, and, conversely, a way of understanding union and intersection types 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 program optimizer. Derived systematically via our equivalence theorem, our flow-type system should be a g...

Abstract. The design and implementation of a correct system can benefit from employing static techniques for ensuring that the dynamic behaviour satisfies the specification. Many programming languages incorporate types for ensuring that certain operations are only applied to data of the appropriate form. A natural extension of type checking techniques is to enrich the types with annotations and effects that further describe intensional aspects of the dynamic behaviour.

We present a new framework for transforming data representations in a strongly typed intermediate language. Our method allows both value producers (sources) and value consumers (sinks) to support multiple representations, automatically inserting any required code. Specialized representations can be easily chosen for particular source/sink pairs. The framework is based on these techniques: 1. Flow annotated types encode the "flows-from" (source) and "flows-to" (sink) information of a flow graph. 2. Intersection and union types support (a) encoding precise flow information, (b) separating flow information so that transformations can be well typed, (c) automatically reorganizing flow paths to enable multiple representations. As an instance of our framework, we provide a function representation transformation that encompasses both closure conversion and inlining. Our framework is adaptable to data other than functions.

Type-based analysis is an approach to static analysis of programs that has been studied for more than a decade. A type-based analysis assumes that the program type checks, and the analysis takes advantage of that. This paper examines the state of the art of type-based analysis, and it surveys some of the many software tools that use type-based analysis. Most of the surveyed tools use types as discriminators, while most of the theoretical studies use type and effect systems. We conclude that type-based analysis is a promising approach to achieving both provable correctness and good performance with a reasonable effort.

We present a typed intermediate language # CIL for optimizing compilers for function-oriented and polymorphically typed programming languages (e.g., ML). The language # CIL is a typed lambda calculus with product, sum, intersection, and union types as well as function types annotated with flow labels. A novel formulation of intersection and union types supports encoding flow information in the typed program representation. This flow information can direct optimization.

We show a type-based method for useless variable elimination, i.e., transformation that eliminates variables whose values contribute nothing to the final outcome of a computation, and prove its correctness. The algorithm is a surprisingly simple extension of the usual type reconstruction algorithm. Our method seems more attractive than Wand and Siveroni's 0CFA-based method in many respects. First, it is efficient: it runs in time almost linear in the size of an input expression for a simply-typed -calculus, while the 0CFA-based method may require a cubic time. Second, our transformation can be shown to be optimal among those that preserve well-typedness, both for the simply-typed language and for an ML-style polymorphically-typed language. On the other hand, the 0CFA-based method is not optimal for the polymophically-typed language. ANY OTHER IDENTIFYING INFORMATION OF THIS REPORT Summary has been submitted for publication. Up-to-date version of this report will be available through ...

. Flow analysis is especially valuable for optimizing functional languages because control-flow information is not syntactically apparent in higher-order programs. Flow analyses typically operate on untyped languages. However, recent compilers for typed functional languages such as ML and Haskell use a typed intermediate language to expose data representations for optimization. This paper presents a polyvariant flow analysis framework for the predicative subset of system F , a common basis for typed intermediate languages. Analyses in this framework can take advantage of types to analyze programs more precisely. We study a specific analysis called SRT that uses types to control polyvariance. We prove that SRT respects types: whenever it assigns abstract value v to a variable and the type system assigns type oe to the same variable, then [[v]] ` [[oe]], where [[ \Delta ]] denotes a set of values. SRT does not terminate for some programs. We present several variants of SRT that are bett...

Type systems and model checking are two prevalent approaches to program verification. A prominent difference between them is that type systems are typically defined in a syntactic and modular style whereas model checking is usually performed in a semantic and whole-program style. This difference between the two approaches lends them complementary to each other: type systems are good at explaining why a program was accepted while model checkers are good at explaining why a program was rejected. We present a type system that is equivalent to a model checker for verifying temporal safety properties of imperative programs. The model checker is natural and may be instantiated with any finite-state abstraction scheme such as predicate abstraction. The type system, which is also parametric, type checks exactly those programs that are accepted by the model checker. It uses function types to capture flow sensitivity and intersection and union types to capture context sensitivity. Our result sheds light on the relationship between the two approaches, provides a methodology for studying their relative expressiveness, is a step towards sharing results between them, and motivates synergistic program analyses involving interplay between them.