Matthias Felleisen

A Syntactic Approach to Type Soundness

We present a new approach to proving type soundness for Hindley/Milner-style polymorphic type systems. The keys to our approach are (1) an adaptation of subject reduction theorems from combinatory logic to programming languages, and (2) the use of rewriting techniques for the specification of the language semantics. The approach easily extends from polymorphic functional languages to imperative languages that provide references, exceptions, continuations, and similar features. We illustrate the technique with a type soundness theorem for the core of Standard ML, which includes the first type soundness proof for polymorphic exceptions and continuations.

Classes and mixins

While class-based object-oriented programming languages provide a flexible mechanism for re-using and managing related pieces of code, they typically lack linguistic facilities for specifying a uniform extension of many classes with one set of fields and methods. As a result, programmers are unable to express certain abstractions over classes.In this paper we develop a model of class-to-class functions that we refer to as mixins. A mixin function maps a class to an extended class by adding or overriding fields and methods. Programming with mixins is similar to programming with single inheritance classes, but mixins more directly encourage programming to interfaces.The paper develops these ideas within the context of Java. The results are 1. an intuitive model of an essential Java subset; 2. an extension that explains and models mixins; and 3. type soundness theorems for these languages.

The essence of compiling with continuations

In order to simplify the compilation process, many compilers for higher-order languages use the continuation-passing style (CPS) transformation in a first phase to generate an intermediate representation of the source program. The salient aspect of this intermediate form is that all procedures take an argument that represents the rest of the computation (the “continuation”). Since the nai¨ve CPS transformation considerably increases the size of programs, CPS compilers perform reductions to produce a more compact intermediate representation. Although often implemented as a part of the CPS transformation, this step is conceptually a second phase. Finally, code generators for typical CPS compilers treat continuations specially in order to optimize the interpretation of continuation parameters. A thorough analysis of the abstract machine for CPS terms show that the actions of the code generator invert the nai¨ve CPS translation step. Put differently, the combined effect of the three phases is equivalent to a source-to-source transformation that simulates the compaction phase. Thus, fully developed CPS compilers do not need to employ the CPS transformation but can achieve the same results with a simple source-level transformation.

The revised report on the syntactic theories of sequential control and state

Abstract The syntactic theories of control and state are conservative extensions of the λ υ -calculus for equational reasoning about imperative programming facilities in higher-order languages. Unlike the simple λ υ -calculus, the extended theories are mixtures of equivalence relations and compatible congruence relations on the term language, which significantly complicates the reasoning process. In this paper we develop fully compatible equational theories of the same imperative higher-order programming languages. The new theories subsume the original calculi of control and state and satisfy the usual Church–Rosser and Standardization Theorems. With the new calculi, equational reasoning about imperative programs becomes as simple as reasoning about functional programs.

Hygienic macro expansion

Macro expansion in current Lisp systems is naive with respect to block structure. Every macro function can cause the capture of free user identifiers and thus corrupt intended bindings. We propose a change to the expansion algorithm so that macros will only violate the binding discipline when it is explicitly intended.

A call-by-need lambda calculus

The mismatch between the operational semantics of the lambda calculus and the actual behavior of implementations is a major obstacle for compiler writers. They cannot explain the behavior of their evaluator in terms of source level syntax, and they cannot easily compare distinct implementations of different lazy strategies. In this paper we derive an equational characterization of call-by-need and prove it correct with respect to the original lambda calculus. The theory is a strictly smaller theory than the lambda calculus. Immediate applications of the theory concern the correctness proofs of a number of implementation strategies, e.g., the call-by-need continuation passing transformation and the realization of sharing via assignments.

On the Expressive Power of Programming Languages

The literature on programming languages contains an abundance of informal claims on the relative expressive power of programming languages, but there is no framework for formalizing such statements nor for deriving interesting consequences. As a first step in this direction, we develop a formal notion of expressiveness and investigate its properties. To demonstrate the theorys closeness to published intuitions on expressiveness, we analyze the expressive power of several extensions of functional languages. Based on these results, we believe that our system correctly captures many of the informal ideas on expressiveness, and that it constitutes a good basis for further research in this direction.

Units: cool modules for HOT languages

A module system ought to enable assembly-line programming using separate compilation and an expressive linking language. Separate compilation allows programmers to develop parts of a program independently. A linking language gives programmers precise control over the assembly of parts into a whole. This paper presents models of program units, MzSchemes module language for assembly-line programming. Units support separate compilation, independent module reuse, cyclic dependencies, hierarchical structuring, and dynamic linking. The models explain how to integrate units with untyped and typed languages such as Scheme and ML.

Reasoning about programs in continuation-passing style

Plotkins λv-calculus for call-by-value programs is weaker than the λβη-calculus for the same programs in continuation-passing style (CPS). To identify the call-by-value axioms that correspond to βη on CPS terms, we define a new CPS transformation and an inverse mapping, both of which are interesting in their own right. Using the new CPS transformation, we determine the precise language of CPS terms closed under βη-transformations, as well as the call-by-value axioms that correspond to the so-called administrative βη-reductions on CPS terms. Using the inverse mapping, we map the remaining β and η equalities on CPS terms to axioms on call-by-value terms. On the pure (constant free) set of Λ-terms, the resulting set of axioms is equivalent to Moggis computational λ-calculus. If the call-by-value language includes the control operatorsabort andcall-with-current-continuation, the axioms are equivalent to an extension of Felleisenet al.s λv-C-calculus and to the equational subtheory of Talcotts logic IOCC.

DrScheme: a programming environment for Scheme

DrScheme is a programming environment for Scheme. It fully integrates a graphics-enriched editor, a parser for multiple variants of Scheme, a functional read-eval-print loop, and an algebraic printer. The environment is especially useful for students, because it has a tower of syntactically restricted variants of Scheme that are designed to catch typical student mistakes and explain them in terms the students understand. The environment is also useful for professional programmers, due to its sophisticated programming tools, such as the static debugger, and its advanced language features, such as units and mixins. Beyond the ordinary programming environment tools, DrScheme provides an algebraic stepper, a context-sensitive syntax checker, and a static debugger. The stepper reduces Scheme programs to values, according to the reduction semantics of Scheme. It is useful for explaining the semantics of linguistic facilities and for studying the behavior of small programs. The syntax checker annotates programs with font and color changes based on the syntactic structure of the program. On demand, it draws arrows that point from bound to binding occurrences of identifiers. It also supports α-renaming. Finally, the static debugger provides a type inference system that explains specific inferences in terms of a value-flow graph, selectively overlaid on the program text.