Jacob Burton Matthews

Revised6 report on the algorithmic language scheme

Programming languages should be designed not by piling feature on top of feature, but by removing the weaknesses and restrictions that make additional features appear necessary. Scheme demonstrates that a very small number of rules for forming expressions, with no restrictions on how they are composed, suffice to form a practical and efficient programming language that is flexible enough to support most of the major programming paradigms in use today. Scheme was one of the first programming languages to incorporate first-class procedures as in the lambda calculus, thereby proving the usefulness of static scope rules and block structure in a dynamically typed language. Scheme was the first major dialect of Lisp to distinguish procedures from lambda expressions and symbols, to use a single lexical environment for all variables, and to evaluate the operator position of a procedure call in the same way as an operand position. By relying entirely on procedure calls to express iteration, Scheme emphasized the fact that tail-recursive procedure calls are essentially gotos that pass arguments. Scheme was the first widely used programming language to embrace first-class escape procedures, from which all previously known sequential control structures can be synthesized. A subsequent version of Scheme introduced the concept of exact and inexact number objects, an extension of Common Lisps generic arithmetic. More recently, Scheme became the first programming language to support hygienic macros, which permit the syntax of a block-structured language to be extended in a consistent and reliable manner.

Operational semantics for multi-language programs

Inter-language interoperability is big business, as the success of Microsofts .NET and COM and Suns 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, higher-order contracts naturally emerge as the glue to ensure that interoperating languages respect each others 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 Haskells stable pointers.

Blame for all

We present a language that integrates statically and dynamically typed components, similar to the gradual types of Siek and Taha (2006), and extend it to incorporate parametric polymorphism. Our system permits a dynamically typed value to be cast to a polymorphic type, with the type enforced by dynamic sealing along the lines proposed by Pierce and Sumii (2000), Matthews and Ahmed (2008), and Neis, Dreyer, and Rossberg (2009), in a way that ensures all terms satisfy relational parametricity. Our system includes a notion of blame, which allows us to show that when more-typed and less-typed portions of a program interact, that any type failures are due to the less-typed portion.

Parametric polymorphism through run-time sealing or, theorems for low, low prices!

We show how to extend System Fs parametricity guarantee to a Matthews-Findler-style multi-language system that combines System F with an untyped language by use of dynamic sealing. While the use of sealing for this purpose has been suggested before, it has never been proven to preserve parametricity. In this paper we prove that it does using step-indexed logical relations. Using this result we show a scheme for implementing parametric higher-order contracts in an untyped setting which corresponds to a translation given by Sumii and Pierce. These contracts satisfy rich enough guarantees that we can extract analogues to Wadlers free theorems that rely on run-time enforcement of dynamic seals.

Relationally-parametric polymorphic contracts

The analogy between types and contracts raises the question of how many features of static type systems can be expressed as dynamic contracts. An important feature missing in prior work on contracts is parametricity, as represented by the polymorphic types in languages like Standard ML. We present a contract counterpart to parametricity. We explore multiple designs for such a system and present one that is simple and incurs minimal execution overhead. We show how to extend the notion of contract blame to our definition. We present a form of inference that can often save programmers from having to explicitly instantiate many parametric contracts. Finally, we present several examples that illustrate how this system mimics the feel and properties of parametric polymorphism in typed languages.

An operational semantics for scheme1

This paper presents an operational semantics for the core of Scheme. Our specification improves over the denotational semantics from the Revised5 Report on Scheme specification in four ways. First, it covers a larger part of the language, specifically eval, quote, dynamic-wind, and the top level. Second, it models multiple values in a way that does not require changes to unrelated parts of the language. Third, it provides a faithful model of Schemes undefined order of evaluation. Finally, we have implemented our specification in PLT Redex, a domain-specific language for writing operational semantics. The implementation allows others to experiment with our specification and allows us to build a specification test suite, which improves our confidence that our system is a faithful model of Scheme. In addition to a specification of Scheme, this paper contributes three novel modeling techniques for Felleisen Hieb-style rewriting semantics. All three techniques are applicable to a wider range of problems than modeling Scheme, and they combine seamlessly in our model, suggesting that they would scale to complete models of other languages.