Untyped Functional Language Research Articles

A verified compiler for an impure functional language

We present a verified compiler to an idealized assembly language from a small, untyped functional language with mutable references and exceptions. The compiler is programmed in the Coq proof assistant and has a proof of total correctness with respect to big-step operational semantics for the source and target languages. Compilation is staged and includes standard phases like translation to continuation-passing style and closure conversion, as well as a common subexpression elimination optimization. In this work, our focus has been on discovering and using techniques that make our proofs easy to engineer and maintain. While most programming language work with proof assistants uses very manual proof styles, all of our proofs are implemented as adaptive programs in Coq's tactic language, making it possible to reuse proofs unchanged as new language features are added. In this paper, we focus especially on phases of compilation that rearrange the structure of syntax with nested variable binders. That aspect has been a key challenge area in past compiler verification projects, with much more effort expended in the statement and proof of binder-related lemmas than is found in standard pencil-and-paper proofs. We show how to exploit the representation technique of parametric higher-order abstract syntax to avoid the need to prove any of the usual lemmas about binder manipulation, often leading to proofs that are actually shorter than their pencil-and-paper analogues. Our strategy is based on a new approach to encoding operational semantics which delegates all concerns about substitution to the meta language, without using features incompatible with general-purpose type theories like Coq's logic.

On the relations between monadic semantics

We present a simple computational metalanguage with general recursive types and multiple notions of effects, through which a variety of concrete denotational semantics can be conveniently factored, by suitably interpreting the effects as monads. We then propose a methodology for relating two such interpretations of the metalanguage, with the aim of showing that the semantics they induce agree for complete programs. As a prototypical instance of such a relation, we use the framework to show agreement between a direct and a continuation semantics of the simple, untyped functional language from Reynolds’s original paper on the subject.

The hierarchical development of a generic type mechanism for functional languages

Adoption of a scientific approach to language design, featuring the identification of language design with programming, leads to the advocacy of an explicitly hierarchical approach to language development. Choice of the lambda-calculus as basis of the linguistic hierarchy is determined when “elegance” is the predominant criterion for assessing the quality of designs. The consequence is that the hierarchy is primarily comprised of a family of untyped functional languages. We embark upon the hierarchical development of a quality data type system for such languages, including a powerful mechanism for generic data abstraction, in five stages. We show that the expressiveness of the system, in comparison with the widespread “polymorphic” typing approach, is well worth the price of the necessarily dynamic checking for type conformance.