Abstract. In this paper, we describe the key principles of a dependent type system for low-level imperative languages. The major contributions of this work are (1) a sound type system that combines dependent types and mutation for variables and for heap-allocated structures in a more flexible way than before and (2) a technique for automatically inferring dependent types for local variables. We have applied these general principles to design Deputy, a dependent type system for C that allows the user to describe bounded pointers and tagged unions. Deputy has been used to annotate and check a number of real-world C programs. 1

Static and dynamic type systems have well-known strengths and weaknesses, and each is better suited for different programming tasks. There have been many efforts to integrate static and dynamic typing and thereby combine the benefits of both typing disciplines in the same language. The flexibility of static typing can be improved by adding a type Dynamic and a typecase form. The safety and performance of dynamic typing can be improved by adding optional type annotations or by performing type inference (as in soft typing). However, there has been little formal work on type systems that allow a programmer-controlled migration between dynamic and static typing. Thatte proposed Quasi-Static Typing, but it does not statically catch all type errors in completely annotated programs. Anderson and Drossopoulou defined a nominal type system for an object-oriented language with optional type annotations. However, developing a sound, gradual type system for functional languages with structural types is an open problem. In this paper

Abstract. Static and dynamic type systems have well-known strengths and weaknesses. In previous work we developed a gradual type system for a functional calculus named λ? →. Gradual typing provides the benefits of both static and dynamic checking in a single language by allowing the programmer to control whether a portion of the program is type checked at compile-time or run-time by adding or removing type annotations on variables. Several object-oriented scripting languages are preparing to add static checking. To support that work this paper develops Ob? <:, a gradual type system for object-based languages, extending the Ob<: calculus of Abadi and Cardelli. Our primary contribution is to show that gradual typing and subtyping are orthogonal and can be combined in a principled fashion. We also develop a small-step semantics, provide a machine-checked proof of type safety, and improve the space efficiency of higher-order casts. 1

Abstract not found

Inter-language interoperability is big business, as the success of Microsoft’s.NET and COM and Sun’s JVM show. Programming language designers are designing programming languages that reflect that fact — SML#, Mondrian, and Scala, to name just a few examples, all treat interoperability with other languages as a central design feature. Still, current multi-language research tends not to focus on the semantics of interoperation features, but only on how to implement them efficiently. In this paper, we take first steps toward higher-level models of interoperating systems. Our technique abstracts away the low-level details of interoperability like garbage collection and representation coherence, and lets us focus on semantic properties like type-safety and observable equivalence. Beyond giving simple expressive models that are natural compositions of single-language models, our studies have uncovered several interesting facts about interoperability. For example, higherorder contracts naturally emerge as the glue to ensure that interoperating languages respect each other’s type systems. While we present our results in an abstract setting, they shed light on real multi-language systems and tools such as the JNI, SWIG, and Haskell’s stable pointers.

We present Logically Qualified Data Types, abbreviated to Liquid Types, a system that combines Hindley-Milner type inference with Predicate Abstraction to automatically infer dependent types precise enough to prove a variety of safety properties. Liquid types allow programmers to reap many of the benefits of dependent types, namely static verification of critical properties and the elimination of expensive run-time checks, without the heavy price of manual annotation. We have implemented liquid type inference in DSOLVE, which takes as input an OCAML program and a set of logical qualifiers and infers dependent types for the expressions in the OCAML program. To demonstrate the utility of our approach, we describe experiments using DSOLVE to statically verify the safety of array accesses on a set of OCAML benchmarks that were previously annotated with dependent types as part of the DML project. We show that when used in conjunction with a fixed set of array bounds checking qualifiers, DSOLVE reduces the amount of manual annotation required for proving safety from 31 % of program text to under 1%.

We describe an axiomatic extension to the Coq proof assistant, that supports writing, reasoning about, and extracting higher-order, dependently-typed programs with side-effects. Coq already includes a powerful functional language that supports dependent types, but that language is limited to pure, total functions. The key contribution of our extension, which we call Ynot, is the added support for computations that may have effects such as non-termination, accessing a mutable store, and throwing/catching exceptions. The axioms of Ynot form a small trusted computing base which has been formally justified in our previous work on Hoare Type Theory (HTT). We show how these axioms can be combined with the powerful type and abstraction mechanisms of Coq to build higher-level reasoning mechanisms which in turn can be used to build realistic, verified software components. To substantiate this claim, we describe here a representative series of modules that implement imperative finite maps, including support for a higherorder (effectful) iterator. The implementations range from simple (e.g., association lists) to complex (e.g., hash tables) but share a common interface which abstracts the implementation details and ensures that the modules properly implement the finite map abstraction.

Gradual type systems offer a smooth continuum between static and dynamic typing by permitting the free mixture of typed and untyped code. The runtime systems for these languages–and other languages with hybrid type checking–typically enforce function types by dynamically generating function proxies. This approach can result in unbounded growth in the number of proxies, however, which drastically impacts space efficiency and destroys tail recursion. We present an implementation strategy for gradual typing that is based on coercions instead of function proxies, and which combines adjacent coercions to limit their space consumption. We prove bounds on the space consumed by coercions as well as soundness of the type system, demonstrating that programmers can safely mix typing disciplines without incurring unreasonable overheads. Our approach also detects certain errors earlier than prior work. 1 GRADUAL TYPING FOR SOFTWARE EVOLUTION Dynamically typed languages have always excelled at exploratory programming.

Abstract. Proving software free of security bugs is hard. Languages that ensure that programs correctly enforce their security policies would help, but, to date, no security-typed language has the ability to verify the enforcement of the kinds of policies used in practice—dynamic, stateful policies which address a range of concerns including forms of access control and information flow tracking. This paper presents FINE, a new source-level security-typed language that, through the use of a simple module system and dependent, refinement, and affine types, checks the enforcement of dynamic security policies applied to real software. FINE is proven sound. A prototype implementation of the compiler and several example programs are available from

... title. It includes the ESOP version verbatim, followed by an appendix containing proofs.