This paper presents a type-based information flow analysis for a call-by-value λ-calculus equipped with references, exceptions and let-polymorphism, which we refer to as Core ML. The type system is constraint-based and has decidable type inference. Its noninterference proof is reasonably light-weight, thanks to the use of a number of orthogonal techniques. First, a syntactic segregation between values and expressions allows a lighter formulation of the type system. Second, noninterference is reduced to subject reduction for a nonstandard language extension. Lastly, a semi-syntactic approach to type soundness allows dealing with constraint-based polymorphism separately.

This paper shows how to systematically extend an arbitrary type system with dependency information, and how soundness and non-interference proofs for the new system may rely upon, rather than duplicate, the soundness proof of the original system. This allows enriching virtually any of the type systems known today with information ow analysis, while requiring only a minimal proof eort.

... This paper develops type systems which can statically guarantee the success of these checks. Our systems allow security properties of programs to be clearly expressed within the types themselves, which thus serve as static declarations of the security policy. We develop these systems using a systematic methodology: we show that the security-passing style translation, proposed by Wallach, Appel and Felten as a dynamic implementation technique, also gives rise to static security-aware type systems, by composition with conventional type systems. To de ne the latter, we use the general HM(X) framework, and easily construct several constraint- and unification-based type systems.

In this paper, we explore an extension to Haskell type classes that allows a type class declaration to define data types as well as values (or methods). Similarly, an instance declaration gives a witness for such data types, as well as a witness for each method. It turns out that this extension directly supports the idea of a type-indexed type, and is useful in many applications, especially for self-optimising libraries that adapt their data representations and algorithms in a type-directed manner.

Abstract We introduce a novel approach for debugging ill-typed programs in the Hindley/Milner system. We map the typing problem for a program to a system of constraints each attached to program code that generates the constraints. We use reasoning about constraint satisfiability and implication to find minimal justifications of type errors, and to explain unexpected types that arise. Through an interactive process akin to declarative debugging, a user can track down exactly where a type error occurs. We are able to capture various extensions of the Hindley/Milner system such as type annotations and Haskell-style type class overloading. The approach has been implemented as part of the Chameleon system.

Many program optimizations and analyses, such as array-bounds checking, termination analysis, etc, depend on knowing the size of a function's input and output. However, size information can be dicult to compute. Firstly, accurate size computation requires detecting a size relation between different inputs of a function. Secondly, different optimizations and analyses may require slightly different size information, and thus slightly different computation. Literature in size computation has mainly concentrated on size checking, instead of size inference. In this paper, we provide a generic framework on which di erent size variants can be expressed and computed. We also describe an effective algorithm for inferring, instead of checking, size information. Size information are expressed in terms of Presburger formulae, and our algorithm utilizes the Omega Calculator to compute as exact a size information as possible, within the linear arithmetic capability.

Record calculi use labels to distinguish between the elements of products and sums. This paper presents a novel variation, type-indexed rows, in which labels are discarded and the types of the elements themselves serve as indices. The calculus, TIR , can express tuples, recursive datatypes, monomophic records, polymorphic extensible records, and closed-world style type-based overloading. Our key application of TIR , however, is to encode the \choice" types of XML, and the \unordered sequence" types of SGML. Indeed, TIR is the kernel of the language XM, a lazy functional language extending XML with polymorphism and higher-order functions. The system is built from rows, equality constraints, membership constraints and constrained parametric polymorphism. The constraint domain enjoys decidable entailment and satisfaction (in EXP). We present a type checking algorithm, and show how TIR may be implemented by a typedirected translation which replaces type-indexing by conven...

with constraints. The basic idea is to factor out the common core of previous extensions of the Hindley/Milner system. I present a Hindley/Milner system where the constraint part is a parameter. Speci c applications can be obtained by providing speci c constraint systems which capture the application in mind. For instance, the Hindley/Milner system can be recovered by instantiating the constraint part to the standard Herbrand constraint system. Type system instances of the general framework are sound if the underlying constraint system is sound. Furthermore, I give a generic type inference algorithm for the general framework, under sucient conditions on the speci c constraint system type inference yields principal types.

Guarded algebraic data types, which subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, and phantom types, and are closely related to inductive types, have the distinguishing feature that, when typechecking a function defined by cases, every branch must be checked under di#erent typing assumptions. This mechanism allows exploiting the presence of dynamic tests in the code to produce extra static type information.

Abstract. There are a number of extended forms of algebraic data types such as type classes with existential types and generalized algebraic data types. Such extensions are highly useful but their interaction has not been studied formally so far. Here, we present a unifying framework for these extensions. We show that the combination of type classes and generalized algebraic data types allows us to express a number of interesting properties which are desired by programmers. We support type checking based on a novel constraint solver. Our results show that our system is practical and greatly extends the expressive power of languages such as Haskell and ML. 1