A unified treatment of syntax with binders

International audienceAtoms and de Bruijn indices are two well-known representation techniques for data structures that involve names and binders. However, using either technique, it is all too easy to make a programming error that causes one name to be used where another was intended. We propose an abstract interface to names and binders that rules out many of these errors. This interface is implemented as a library in Agda. It allows defining and manipulating term representations in nominal style and in de Bruijn style. The programmer is not forced to choose between these styles: on the contrary, the library allows using both styles in the same program, if desired. Whereas indexing the types of names and terms with a natural number is a well-known technique to better control the use of de Bruijn indices, we index types with worlds. Worlds are at the same time more precise and more abstract than natural numbers. Via logical relations and parametricity, we are able to demonstrate in what sense our library is safe, and to obtain theorems for free about world-polymorphic functions. For instance, we prove that a world-polymorphic term transformation function must commute with any renaming of the free variables. The proof is entirely carried out in Agda

A Type-Preserving Compiler from System F to Typed Assembly Language

L'utilisation des méthodes formelles est de plus en plus courante dans le développement logiciel, et les systèmes de types sont la méthode formelle qui a le plus de succès. L'avancement des méthodes formelles présente de nouveaux défis, ainsi que de nouvelles opportunités. L'un des défis est d'assurer qu'un compilateur préserve la sémantique des programmes, de sorte que les propriétés que l'on garantit à propos de son code source s'appliquent également au code exécutable. Cette thèse présente un compilateur qui traduit un langage fonctionnel d'ordre supérieur avec polymorphisme vers un langage assembleur typé, dont la propriété principale est que la préservation des types est vérifiée de manière automatisée, à l'aide d'annotations de types sur le code du compilateur. Notre compilateur implante les transformations de code essentielles pour un langage fonctionnel d'ordre supérieur, nommément une conversion CPS, une conversion des fermetures et une génération de code. Nous présentons les détails des représentation fortement typées des langages intermédiaires, et les contraintes qu'elles imposent sur l'implantation des transformations de code. Notre objectif est de garantir la préservation des types avec un minimum d'annotations, et sans compromettre les qualités générales de modularité et de lisibilité du code du compilateur. Cet objectif est atteint en grande partie dans le traitement des fonctionnalités de base du langage (les «types simples»), contrairement au traitement du polymorphisme qui demande encore un travail substantiel pour satisfaire la vérification de type.Formal methods are rapidly improving and gaining ground in software. Type systems are the most successful and popular formal method used to develop software. As the technology of type systems progresses, new needs and new opportunities appear. One of those needs is to ensure the faithfulness of the translation from source code to machine code, so that the properties you prove about the code you write also apply to the code you run. This thesis presents a compiler from a polymorphic higher-order functional language to typed assembly language, whose main property is that type preservation is verified statically, through type annotations on the compiler's code. Our compiler implements the essential code transformations for a higher-order functional language, namely a CPS conversion and closure conversion as well as a code generation. The thesis presents the details of the strongly typed intermediate representations and the constraints they set on the implementation of code transformations. Our goal is to guarantee type preservation with a minimum of type annotations, and without compromising readability and modularity of the code. This goal is already a reality for simple types, and we discuss the problems remaining for polymorphism, which still requires substantial extra work to satisfy the type checker

Implementing Typeful Program Transformations

The notion of program transformation is ubiquitous in programming language studies on interpreters, compilers, partial evaluators, etc. In order to implement a program transformation, we need to choose a representation in the meta language, that is, the programming language in which we construct programs, for representing object programs, that is, the programs in the object language on which the program transformation is to be performed. In practice, most representations chosen for typed object programs are typeless in the sense that the type of an object program cannot be reflected in the type of its representation. This is unsatisfactory as such typeless representations make it impossible to capture in the type system of the meta language various invariants in a program transformation that are related to the types of object programs. In this paper, we propose an approach to implementing program transformations that makes use of a first-order typeful program representation formed in Dependent ML (DML), where the type of an object program as well as the types of the free variables in the object program can be reflected in the type of the representation of the object program. We introduce some programming techniques needed to handle this typeful program representation, and then present an implementation of a CPS transform function where the relation between the type of an object program and that of its CPS transform is captured in the type system of DML. In a broader context, we claim to have taken a solid step along the line of research on constructing certifying compilers