Hidden Type Variables and Conditional Extension for More Expressive Generic Programs

Generic object-oriented programming languages combine parametric polymorphism and nominal subtype polymorphism, thereby providing better data abstraction, greater code reuse, and fewer run-time errors. However, most generic object-oriented languages provide a straightforward combination of the two kinds of polymorphism, which prevents the expression of advanced type relationships. Furthermore, most generic object-oriented languages have a type-erasure semantics: instantiations of type parameters are not available at run time, and thus may not be used by type-dependent operations. This dissertation shows that two features, which allow the expression of many advanced type relationships, can be added to a generic object-oriented programming language without type erasure: 1. type variables that are not parameters of the class that declares them, and 2. extension that is dependent on the satisfiability of one or more constraints. We refer to the first feature as hidden type variables and the second feature as conditional extension. Hidden type variables allow: covariance and contravariance without variance annotations or special type arguments such as wildcards; a single type to extend, and inherit methods from, infinitely many instantiations of another type; a limited capacity to augment the set of superclasses after that class is defined; and the omission of redundant type arguments. Conditional extension allows the properties of a collection type to be dependent on the properties of its element type. This dissertation describes the semantics and implementation of hidden type variables and conditional extension. A sound type system is presented. In addition, a sound and terminating type checking algorithm is presented. Although designed for the Fortress programming language, hidden type variables and conditional extension can be incorporated into other generic object-oriented languages. Many of the same problems would arise, and solutions analogous to those we present would apply.

A Type System For Safe SN Resource Allocation

snBench is a platform on which novice users compose and deploy distributed Sense and Respond programs for simultaneous execution on a shared, distributed infrastructure. It is a natural imperative that we have the ability to (1) verify the safety/correctness of newly submitted tasks and (2) derive the resource requirements for these tasks such that correct allocation may occur. To achieve these goals we have established a multi-dimensional sized type system for our functional-style Domain Specific Language (DSL) called Sensor Task Execution Plan (STEP). In such a type system data types are annotated with a vector of size attributes (e.g., upper and lower size bounds). Tracking multiple size aspects proves essential in a system in which Images are manipulated as a first class data type, as image manipulation functions may have specific minimum and/or maximum resolution restrictions on the input they can correctly process. Through static analysis of STEP instances we not only verify basic type safety and establish upper computational resource bounds (i.e., time and space), but we also derive and solve data and resource sizing constraints (e.g., Image resolution, camera capabilities) from the implicit constraints embedded in program instances. In fact, the static methods presented here have benefit beyond their application to Image data, and may be extended to other data types that require tracking multiple dimensions (e.g., image "quality", video frame-rate or aspect ratio, audio sampling rate). In this paper we present the syntax and semantics of our functional language, our type system that builds costs and resource/data constraints, and (through both formalism and specific details of our implementation) provide concrete examples of how the constraints and sizing information are used in practice.

Type Inference For Recursive Definitions

We consider type systems that combine universal types, recursive types, and object types. We study type inference in these systems under a rank restriction, following Leivant's notion of rank. To motivate our work, we present several examples showing how our systems can be used to type programs encountered in practice. We show that type inference in the rank-k system is decidable for k ≤ 2 and undecidable for k ≥ 3. (Similar results based on different techniques are known to hold for System F, without recursive types and object types.) Our undecidability result is obtained by a reduction from a particular adaptation (which we call "regular") of the semi-unification problem and whose undecidability is, interestingly, obtained by methods totally different from those used in the case of standard (or finite) semi-unification.

Type Inference for Variant Object Types

Existing type systems for object calculi are based on invariant subtyping. Subtyping invariance is required for soundness of static typing in the presence of method overrides, but it is often in the way of the expressive power of the type system. Flexibility of static typing can be recovered in different ways: in first-order systems, by the adoption of object types with variance annotations, in second-order systems by resorting to Self types. Type inference is known to be P-complete for first-order systems of finite and recursive object types, and NP-complete for a restricted version of Self types. The complexity of type inference for systems with variance annotations is yet unknown. This paper presents a new object type system based on the notion of Split types, a form of object types where every method is assigned two types, namely, an update type and a select type. The subtyping relation that arises for Split types is variant and, as a result, subtyping can be performed both in width and in depth. The new type system generalizes all the existing first-order type systems for objects, including systems based on variance annotations. Interestingly, the additional expressive power does not affect the complexity of the type inference problem, as we show by presenting an O(n^3) inference algorithm.