Concrete type information is invaluable for program optimization. The determination of concrete types in object-oriented languages is a flow sensitive global data flow problem. It is made difficult by dynamic dispatch (virtual function invocation) and first class functions (and selectors) -- the very program structures for whose optimization its results are most critical. Previous work has shown that constraint-based type inference systems can be used to safely approximate concrete types [15], but their use can be expensive and their results imprecise. We present an incremental constraint-based type inference which produces precise concrete type information for a much larger class of programs at lower cost. Our algorithm extends the analysis in response to discovered imprecisions, guiding the analysis' effort to where it is most productive. This produces precise information at a cost proportional to the type complexity of the program. Many programs untypable by previous approaches or ...

PolyTOIL is a new statically-typed polymorphic object-oriented programming language that is provably type-safe. By separating the de nitions of subtyping and inheritance, providing a name for the type of self, and carefully de ning the type-checking rules, we have obtained a language that is very expressive while supporting modular type-checking of classes. The matching relation on types, which is related to F-bounded quanti cation, is used both in stating type-checking rules and expressing the bounds on type parameters for polymorphism. The design of PolyTOIL is based on a careful formal de nition of type-checking rules and semantics.

In order to illuminate the fundamental concepts involved in object-oriented programming languages, we describe the design of TOOPL, a paradigmatic, statically-typed, functional, object-oriented programming language which supports classes, objects, methods, hidden instance variables, subtypes, and inheritance. It has proven to be quite difficult to design such a language which has a secure type system. A particular problem with statically type checking object-oriented languages is designing type-checking rules which ensure that methods provided in a superclass will continue to be type correct when inherited in a subclass. The type-checking rules for TOOPL have this feature, enabling library suppliers to provide only the interfaces of classes with actual executable code, while still allowing users to safely create subclasses. In order to achieve greater expressibility while retaining type-safety, we choose to separate the inheritance and subtyping hierarchy in the language. The design of...

A polymorphic, constraint-based type inference algorithm for an object-oriented language is defined. A generalized form of type, polymorphic recursively constrained types, are inferred. These types are expressive enough for typing objects, since they generalize recursive types and F-bounded polymorphism. The well-known tradeoff between inheritance and subtyping is mitigated by the type inference mechanism. Soundness and completeness of type inference are established. 1 Introduction Type inference, the process of automatically inferring type information from untyped programs, is originally due to Hindley and Milner [16]. These ideas have found their way into some recent innovative programming languages, including Standard ML [17]. The type inference problem for object-oriented languages is a challenging one: even simple object-oriented programs require quite advanced features to be present in the type system. One of the main sources of difficulty lies with binary methods, such as an a...

Two major obstacles hindering the wider acceptance of multi-methods are concerns over the lack of encapsulation and modularity and the absence of static typechecking in existing multi-method-based languages. This paper addresses both of these problems. We present a polynomial-time static typechecking algorithm that checks the conformance, completeness, and consistency of a group of method implementations with respect to declared message signatures. This algorithm improves on previous algorithms by handling separate type and inheritance hierarchies, abstract classes, and graph-based method lookup semantics. We also present a module system that enables independently-developed code to be fully encapsulated and statically typechecked on a per-module basis. To guarantee that potential conflicts between independently-developed modules have been resolved, a simple well-formedness condition on the modules comprising a program is checked at link-time. The typechecking algorithm and module system are applicable to a range of multi-method-based languages, but the paper uses the Cecil language as a concrete example of how they can be applied.

Cecil is a purely object-oriented language intended to support rapid construction of high-quality, extensible software. Cecil combines multi-methods with a simple classless object model, a kind of dynamic inheritance, modules, and optional static type checking. Instance variables in Cecil are accessed solely through messages, allowing instance variables to be replaced or overridden by methods and vice versa. Cecil’s predicate objects mechanism allows an object to be classified automatically based on its run-time (mutable) state. Cecil’s static type system distinguishes between subtyping and code inheritance, but Cecil enables these two graphs to be described with a single set of declarations, streamlining the common case where the two graphs are parallel. Cecil includes a fairly flexible form of parameterization, including explicitly parameterized objects, types, and methods, as well as implicitly parameterized methods related to the polymorphic functions commonly found in functional languages. By making type declarations optional, Cecil aims to allow mixing of and migration between exploratory and production programming styles. Cecil supports a module mechanism that enables independently-developed subsystems to be encapsulated, allowing them to be type-checked and reasoned about in isolation despite the presence of multi-methods and subclassing. Objects can be extended externally with additional

Java `ight is a large sequential sublanguage of Java. We formalize its abstract syntax, type system, well-formedness conditions, and an operational evaluation semantics. Based on this formalization, we can express and prove type soundness. All definitions and proofs have been done formally in the theorem prover Isabelle/HOL. Thus this paper demonstrates that machine-checking the design of non-trivial programming languages has become a reality. 1 Introduction Java `ight is a large subset of the sequential part of Java [12]. This paper presents its formalization and a proof of type soundness --- specified and verified in the theorem prover Isabelle/HOL [18]. In the sequel, `Java `ight ' is abbreviated to `Bali'. On the face of it, this paper is mostly about Bali, its abstract syntax, type system, well-formedness conditions, and operational semantics, formalized as a hierarchy of Isabelle theories, and the structure of the machine-checked proof of type soundness. Although these technica...

We present a static type system for object-oriented languages which strives to provide static typechecking without resorting to dynamic "type casts," restricting what code the programmer can write, or being too verbose or difficult to use in practice. The type system supports bounded parametric polymorphism where the bounds on type variables can be expressed using general recursive subtype or signature constraints, with F-bounded polymorphism and covariant type parameters being special cases. We implemented this type system in the Cecil language and used it to successfully typecheck a 100,000-line Cecil program, the Vortex optimizing compiler. Our experience was very good: dynamically-typed code needed very little rewriting. We also observed several common programming situations that presented a challenge for our type system. We discuss these situations and ways to typecheck them statically. Keywords: Language design, static type systems, F-bounded polymorphism, where clauses, type constraints, type inference, binary methods, Cecil

. In this paper we give semantics to Loop, an expressive typed object-oriented programming language with updatable instance variables. Loop has a rich type system that allows for the typing of methods operating over an open-ended "self " type. We prove the type system given is sound; i.e., well-typed programs do not experience "message not understood" errors. The semantics of Loop is given by a translation into a state-based language, Soop, that contains reference cells, records, and a form of F-bounded polymorphic type. Keywords: Object-oriented programming, type systems, state in programming 1. Introduction Developing full and faithful type systems for object-oriented programming languages is a well-known and difficult research problem. To frame the problem we desire a static type system that preserves all of the classic features of (untyped) class-based OOP, including treatment of two particularly difficult issues: binary methods and object subsumption. Significant steps have rece...

Important strides toward developing expressive yet semantically sound type systems for object-oriented programming languages have recently been made by Cook, Bruce, Mitchell, and others. This paper focusses on how the theoretical work using F-bounded quantification may be brought more into the realm of actual language implementations while preserving rigorous soundness properties. We simultaneously address three of the more significant problems: adding a notion of global state, proving type-checking is decidable, and integrating the more widely implemented view that subclasses correspond to subtypes with the F-bounded view. 1 Introduction Developing expressive yet semantically sound type systems for object-oriented programming languages is a well-known and difficult research problem. Many workable solutions are possible, but there has as of yet been no universally accepted solution to the problem. To frame the problem we desire a static type system that preserves all of the classic ...