Publications by François Pottier

[1] François Pottier. Depth-first search and strong connectivity in Coq. Submitted for publication, September 2014. [ bib | PDF ]
Using Coq, we mechanize Wegener's proof of Kosaraju's linear-time algorithm for computing the strongly connected components of a directed graph. Furthermore, also in Coq, we define an executable and terminating depth-first search algorithm.

[2] François Pottier. Hindley-Milner elaboration in applicative style. In Proceedings of the 2014 ACM SIGPLAN International Conference on Functional Programming (ICFP'14), September 2014. [ bib | PDF | At publisher's ]
Type inference-the problem of determining whether a program is well-typed-is well-understood. In contrast, elaboration-the task of constructing an explicitly-typed representation of the program-seems to have received relatively little attention, even though, in a non-local type inference system, it is non-trivial. We show that the constraint-based presentation of Hindley-Milner type inference can be extended to deal with elaboration, while preserving its elegance. This involves introducing a new notion of “constraint with a value”, which forms an applicative functor.

[3] Thibaut Balabonski, François Pottier, and Jonathan Protzenko. The design and formalization of Mezzo, a permission-based programming language. Submitted for publication, July 2014. [ bib | PDF ]
The programming language Mezzo is equipped with a rich type system that controls aliasing and access to mutable memory. We present the language at large, via an introduction along with some motivating examples. We then present a modular formalization of Mezzo's core type system, in the form of a concurrent lambda-calculus, which we extend with references and locks. We prove that well-typed programs do not go wrong and are data-race free. Our definitions and proofs are machine-checked.

[4] Thibaut Balabonski, François Pottier, and Jonathan Protzenko. Type soundness and race freedom for Mezzo. In Proceedings of the 12th International Symposium on Functional and Logic Programming (FLOPS 2014), volume 8475, pages 253-269, June 2014. [ bib | PDF | At publisher's ]
The programming language Mezzo is equipped with a rich type system that controls aliasing and access to mutable memory. We incorporate shared-memory concurrency into Mezzo and present a modular formalization of Mezzo's core type system, in the form of a concurrent lambda-calculus, which we extend with references and locks. We prove that well-typed programs do not go wrong and are data-race free. Our definitions and proofs are machine-checked.

[5] François Pottier and Jonathan Protzenko. Programming with permissions in Mezzo. In Proceedings of the 2013 ACM SIGPLAN International Conference on Functional Programming (ICFP'13), pages 173-184, September 2013. [ bib | PDF | Long PDF | At publisher's ]
We present Mezzo, a typed programming language of ML lineage. Mezzo is equipped with a novel static discipline of duplicable and affine permissions, which controls aliasing and ownership. This rules out certain mistakes, including representation exposure and data races, and enables new idioms, such as gradual initialization, memory re-use, and (type)state changes. Although the core static discipline disallows sharing a mutable data structure, Mezzo offers several ways of working around this restriction, including a novel dynamic ownership control mechanism which we dub “adoption and abandon”.

[6] Armaël Guéneau, François Pottier, and Jonathan Protzenko. The ins and outs of iteration in Mezzo. Talk proposal for HOPE 2013, July 2013. [ bib | PDF ]
This is a talk proposal for HOPE 2013. Using iteration over a collection as a case study, we wish to illustrate the strengths and weaknesses of the prototype programming language Mezzo.

[7] Jan Schwinghammer, Lars Birkedal, François Pottier, Bernhard Reus, Kristian Støvring, and Hongseok Yang. A step-indexed Kripke model of hidden state. Mathematical Structures in Computer Science, 23(1):1-54, February 2013. [ bib | PDF | At publisher's ]
[8] François Pottier. Syntactic soundness proof of a type-and-capability system with hidden state. Journal of Functional Programming, 23(1):38-144, January 2013. [ bib | PDF | At publisher's ]
This paper presents a formal definition and machine-checked soundness proof for a very expressive type-and-capability system, that is, a low-level type system that keeps precise track of ownership and side effects.

The programming language has first-class functions and references. The type system's features include: universal, existential, and recursive types; subtyping; a distinction between affine and unrestricted data; support for strong updates; support for naming values and heap fragments, via singleton and group regions; a distinction between ordinary values (which exist at runtime) and capabilities (which don't); support for dynamic re-organizations of the ownership hierarchy, by dis-assembling and re-assembling capabilities; support for temporarily or permanently hiding a capability, via frame and anti-frame rules.

One contribution of the paper is the definition of the type-and-capability system itself. We present the system as modularly as possible. In particular, at the core of the system, the treatment of affinity, in the style of dual intuitionistic linear logic, is formulated in terms of an arbitrary monotonic separation algebra, a novel axiomatization of resources, ownership, and the manner in which they evolve with time. Only the peripheral layers of the system are aware that we are dealing with a specific monotonic separation algebra, whose resources are references and regions. This semi-abstract organization should facilitate further extensions of the system with new forms of resources.

The other main contribution is a machine-checked proof of type soundness. The proof is carried out in Wright and Felleisen's syntactic style. This offers evidence that this relatively simple-minded proof technique can scale up to systems of this complexity, and constitutes a viable alternative to more sophisticated semantic proof techniques. We do not claim that the syntactic technique is superior: we simply illustrate how it is used and highlight its strengths and shortcomings.

[9] Nicolas Pouillard and François Pottier. A unified treatment of syntax with binders. Journal of Functional Programming, 22(4-5):614-704, September 2012. [ bib | PDF | At publisher's ]
Atoms 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.

[10] Jacques-Henri Jourdan, François Pottier, and Xavier Leroy. Validating LR(1) parsers. In Proceedings of the 21st European Symposium on Programming (ESOP 2012), volume 7211 of Lecture Notes in Computer Science, pages 397-416. Springer, March 2012. [ bib | PDF | At publisher's ]
An LR(1) parser is a finite-state automaton, equipped with a stack, which uses a combination of its current state and one lookahead symbol in order to determine which action to perform next. We present a validator which, when applied to a context-free grammar G and an automaton A, checks that A and G agree. Validating the parser provides the correctness guarantees required by verified compilers and other high-assurance software that involves parsing. The validation process is independent of which technique was used to construct A. The validator is implemented and proved correct using the Coq proof assistant. As an application, we build a formally-verified parser for the C99 language.

[11] Alexandre Pilkiewicz and François Pottier. The essence of monotonic state. In Proceedings of the Sixth ACM SIGPLAN Workshop on Types in Language Design and Implementation (TLDI'11), Austin, Texas, January 2011. [ bib | PDF | At publisher's ]
We extend a static type-and-capability system with new mechanisms for expressing the promise that a certain abstract value evolves monotonically with time; for enforcing this promise; and for taking advantage of this promise to establish non-trivial properties of programs. These mechanisms are independent of the treatment of mutable state, but combine with it to offer a flexible account of “monotonic state”.

We apply these mechanisms to solve two reasoning challenges that involve mutable state. First, we show how an implementation of thunks in terms of references can be assigned types that reflect time complexity properties, in the style of Danielsson (2008). Second, we show how an implementation of hash-consing can be assigned a specification that conceals the existence of an internal state yet guarantees that two pieces of input data receive the same code if and only if they are equal.

[12] François Pottier. A typed store-passing translation for general references. In Proceedings of the 38th ACM Symposium on Principles of Programming Languages (POPL'11), Austin, Texas, January 2011. Supplementary material. [ bib | PDF | Long PDF | At publisher's ]
We present a store-passing translation of System F with general references into an extension of System Fω with certain well-behaved recursive kinds. This seems to be the first type-preserving store-passing translation for general references. It can be viewed as a purely syntactic account of a possible worlds model.

[13] Nicolas Pouillard and François Pottier. A fresh look at programming with names and binders. In Proceedings of the fifteenth ACM SIGPLAN International Conference on Functional Programming (ICFP 2010), pages 217-228, September 2010. [ bib | PDF | Long PDF | At publisher's ]
A wide range of computer programs, including compilers and theorem provers, manipulate data structures that involve names and binding. However, the design of programming idioms which allow performing these manipulations in a safe and natural style has, to a large extent, remained elusive.

In this paper, we present a novel approach to the problem. Our proposal can be viewed either as a programming language design or as a library: in fact, it is currently implemented within Agda. It provides a safe and expressive means of programming with names and binders. It is abstract enough to support multiple concrete implementations: we present one in nominal style and one in de Bruijn style. We use logical relations to prove that “well-typed programs do not mix names with different scope”. We exhibit an adequate encoding of Pitts-style nominal terms into our system.

[14] Jan Schwinghammer, Hongseok Yang, Lars Birkedal, François Pottier, and Bernhard Reus. A semantic foundation for hidden state. In C.-H. L. Ong, editor, Proceedings of the 13th International Conference on Foundations of Software Science and Computational Structures (FOSSACS 2010), volume 6014 of Lecture Notes in Computer Science, pages 2-17. Springer, March 2010. [ bib | PDF | At publisher's ]
We present the first complete soundness proof of the anti-frame rule, a recently proposed proof rule for capturing information hiding in the presence of higher-order store. Our proof involves solving a non-trivial recursive domain equation. It helps identify some of the key ingredients for soundness, and thereby suggests how one might hope to relax some of the restrictions imposed by the rule.

[15] François Pottier. Lazy least fixed points in ML. Unpublished, December 2009. [ bib | PDF ]
This “not quite functional” pearl describes an algorithm for computing the least solution of a system of monotone equations. It is implemented in imperative ocaml code, but presents a purely functional, lazy interface. It is simple, useful, and has good asymptotic complexity. Furthermore, it presents a challenge to researchers interested in modular formal proofs of ML programs.

[16] François Pottier. Three comments on the anti-frame rule. Unpublished, July 2009. [ bib | PDF ]
This informal note presents three comments about the anti-frame rule, which respectively regard: its interaction with polymorphism; its interaction with the higher-order frame axiom; and a problematic lack of modularity.

[17] François Pottier. Generalizing the higher-order frame and anti-frame rules. Unpublished, July 2009. [ bib | PDF ]
This informal note presents generalized versions of the higher-order frame and anti-frame rules. The main insights reside in two successive generalizations of the “tensor” operator . In the first step, a form of “local invariant”, which allows implicit reasoning about “well-bracketed state changes”, is introduced. In the second step, a form of “local monotonicity” is added.

[18] Arthur Charguéraud and François Pottier. Functional translation of a calculus of capabilities. In Proceedings of the 2008 ACM SIGPLAN International Conference on Functional Programming (ICFP'08), pages 213-224, September 2008. [ bib | PDF | PostScript | At publisher's ]
Reasoning about imperative programs requires the ability to track aliasing and ownership properties. We present a type system that provides this ability, by using regions, capabilities, and singleton types. It is designed for a high-level calculus with higher-order functions, algebraic data structures, and references (mutable memory cells). The type system has polymorphism, yet does not require a value restriction, because capabilities act as explicit store typings.

We exhibit a type-directed, type-preserving, and meaning-preserving translation of this imperative calculus into a pure calculus. Like the monadic translation, this is a store-passing translation. Here, however, the store is partitioned into multiple fragments, which are threaded through a computation only if they are relevant to it. Furthermore, the decomposition of the store into fragments can evolve dynamically to reflect ownership transfers.

The translation offers deep insight about the inner workings and soundness of the type system. If coupled with a semantic model of its target calculus, it leads to a semantic model of its imperative source calculus. Furthermore, it provides a foundation for our long-term objective of designing a system for specifying and certifying imperative programs with dynamic memory allocation.

[19] Yann Régis-Gianas and François Pottier. A Hoare logic for call-by-value functional programs. In Proceedings of the Ninth International Conference on Mathematics of Program Construction (MPC'08), volume 5133 of Lecture Notes in Computer Science, pages 305-335. Springer, July 2008. [ bib | PDF | PostScript | At publisher's ]
We present a Hoare logic for a call-by-value programming language equipped with recursive, higher-order functions, algebraic data types, and a polymorphic type system in the style of Hindley and Milner. It is the theoretical basis for a tool that extracts proof obligations out of programs annotated with logical assertions. These proof obligations, expressed in a typed, higher-order logic, are discharged using off-the-shelf automated or interactive theorem provers. Although the technical apparatus that we exploit is by now standard, its application to functional programming languages appears to be new, and (we claim) deserves attention. As a sample application, we check the partial correctness of a balanced binary search tree implementation.

[20] François Pottier. Hiding local state in direct style: a higher-order anti-frame rule. In Twenty-Third Annual IEEE Symposium on Logic In Computer Science (LICS'08), pages 331-340, Pittsburgh, Pennsylvania, June 2008. [ bib | PDF | At publisher's ]
Separation logic involves two dual forms of modularity: local reasoning makes part of the store invisible within a static scope, whereas hiding local state makes part of the store invisible outside a static scope. In the recent literature, both idioms are explained in terms of a higher-order frame rule. I point out that this approach to hiding local state imposes continuation-passing style, which is impractical. Instead, I introduce a higher-order anti-frame rule, which permits hiding local state in direct style. I formalize this rule in the setting of a type system, equipped with linear capabilities, for an ML-like programming language, and prove type soundness via a syntactic argument. Several applications illustrate the expressive power of the new rule.

[21] François Pottier. Static name control for FreshML. In Twenty-Second Annual IEEE Symposium on Logic In Computer Science (LICS'07), pages 356-365, Wroclaw, Poland, July 2007. [ bib | PDF | PostScript | Long PDF | Long PostScript | At publisher's ]
FreshML extends ML with constructs for declaring and manipulating abstract syntax trees that involve names and statically scoped binders. It is impure: name generation is an observable side effect. In practice, this means that FreshML allows writing programs that create fresh names and unintentionally fail to bind them. Following in the steps of early work by Pitts and Gabbay, this paper defines Pure FreshML, a subset of FreshML equipped with a static proof system that guarantees purity. Pure FreshML relies on a rich binding specification language, on user-provided assertions, expressed in a logic that allows reasoning about values and about the names that they contain, and on a conservative, automatic decision procedure for this logic. It is argued that Pure FreshML can express non-trivial syntax-manipulating algorithms.

[22] Vincent Simonet and François Pottier. A constraint-based approach to guarded algebraic data types. ACM Transactions on Programming Languages and Systems, 29(1), January 2007. [ bib | PDF | PostScript | At publisher's ]
We study HMG(X), an extension of the constraint-based type system HM(X) with deep pattern matching, polymorphic recursion, and guarded algebraic data types. Guarded algebraic data types subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, (first-class) phantom types, and equality qualified types, and are closely related to inductive types. Their characteristic property is to allow every branch of a case construct to be typechecked under different assumptions about the type variables in scope. We prove that HMG(X) is sound and that, provided recursive definitions carry a type annotation, type inference can be reduced to constraint solving. Constraint solving is decidable, at least for some instances of X, but prohibitively expensive. Effective type inference for guarded algebraic data types is left as an issue for future research.

[23] François Pottier. An overview of Cαml. In ACM Workshop on ML, volume 148(2) of Electronic Notes in Theoretical Computer Science, pages 27-52, March 2006. [ bib | PDF | PostScript | At publisher's ]
Cαml is a tool that turns a so-called “binding specification” into an Objective Caml compilation unit. A binding specification resembles an algebraic data type declaration, but also includes information about names and binding. Cαml is meant to help writers of interpreters, compilers, or other programs-that-manipulate-programs deal with α-conversion in a safe and concise style. This paper presents an overview of Cαml's binding specification language and of the code that Cαml produces.

[24] François Pottier and Nadji Gauthier. Polymorphic typed defunctionalization and concretization. Higher-Order and Symbolic Computation, 19:125-162, March 2006. [ bib | PDF | PostScript | At publisher's ]
Defunctionalization is a program transformation that eliminates functions as first-class values. We show that defunctionalization can be viewed as a type-preserving transformation of an extension of with guarded algebraic data types into itself. We also suggest that defunctionalization is an instance of concretization, a more general technique that allows eliminating constructs other than functions. We illustrate this point by presenting two new type-preserving transformations that can be viewed as instances of concretization. One eliminates Rémy-style polymorphic records; the other eliminates the dictionary records introduced by the standard compilation scheme for Haskell's type classes.

[25] François Pottier and Yann Régis-Gianas. Towards efficient, typed LR parsers. In ACM Workshop on ML, volume 148(2) of Electronic Notes in Theoretical Computer Science, pages 155-180, March 2006. [ bib | PDF | PostScript | At publisher's ]
The LR parser generators that are bundled with many functional programming language implementations produce code that is untyped, needlessly inefficient, or both. We show that, using generalized algebraic data types, it is possible to produce parsers that are well-typed (so they cannot unexpectedly crash or fail) and nevertheless efficient. This is a pleasing result as well as an illustration of the new expressiveness offered by generalized algebraic data types.

[26] François Pottier and Yann Régis-Gianas. Stratified type inference for generalized algebraic data types. In Proceedings of the 33rd ACM Symposium on Principles of Programming Languages (POPL'06), pages 232-244, Charleston, South Carolina, January 2006. [ bib | PDF | PostScript | At publisher's ]
We offer a solution to the type inference problem for an extension of Hindley and Milner's type system with generalized algebraic data types. Our approach is in two strata. The bottom stratum is a core language that marries type inference in the style of Hindley and Milner with type checking for generalized algebraic data types. This results in an extremely simple specification, where case constructs must carry an explicit type annotation and type conversions must be made explicit. The top stratum consists of (two variants of) an independent shape inference algorithm. This algorithm accepts a source term that contains some explicit type information, propagates this information in a local, predictable way, and produces a new source term that carries more explicit type information. It can be viewed as a preprocessor that helps produce some of the type annotations required by the bottom stratum. It is proven sound in the sense that it never inserts annotations that could contradict the type derivation that the programmer has in mind.

[27] François Pottier and Yann Régis-Gianas. Menhir, December 2005. [ bib | Software ]
[28] François Pottier. A modern eye on ML type inference: old techniques and recent developments. Lecture notes for the APPSEM Summer School, September 2005. [ bib | PDF | PostScript ]
[29] François Pottier. Cαml, June 2005. [ bib | Software ]
[30] Roberto Di Cosmo, François Pottier, and Didier Rémy. Subtyping recursive types modulo associative commutative products. In Seventh International Conference on Typed Lambda Calculi and Applications (TLCA'05), volume 3461 of Lecture Notes in Computer Science, pages 179-193, Nara, Japan, April 2005. Springer. [ bib | PDF | PostScript | Long PDF | Long PostScript | At publisher's ]
This work sets the formal bases for building tools that help retrieve classes in object-oriented libraries. In such systems, the user provides a query, formulated as a set of class interfaces. The tool returns classes in the library that can be used to implement the user's request and automatically builds the required glue code. We propose subtyping of recursive types in the presence of associative and commutative products-that is, subtyping modulo a restricted form of type isomorphisms-as a model of the relation that exists between the user's query and the tool's answers. We show that this relation is a composition of the standard subtyping relation with equality up to associativity and commutativity of products and we present an efficient decision algorithm for it. We also provide an automatic way of constructing coercions between related types.

[31] François Pottier, Christian Skalka, and Scott Smith. A systematic approach to static access control. ACM Transactions on Programming Languages and Systems, 27(2):344-382, March 2005. [ bib | PostScript | At publisher's ]
The Java Security Architecture includes a dynamic mechanism for enforcing access control checks, the so-called stack inspection process. While the architecture has several appealing features, access control checks are all implemented via dynamic method calls. This is a highly non-declarative form of specification which is hard to read, and which leads to additional run-time overhead. This paper develops type systems which can statically guarantee the success of these checks. Our systems allow security properties of programs to be clearly expressed within the types themselves, which thus serve as static declarations of the security policy. We develop these systems using a systematic methodology: we show that the security-passing style translation, proposed by Wallach, Appel and Felten as a dynamic implementation technique, also gives rise to static security-aware type systems, by composition with conventional type systems. To define the latter, we use the general HM(X) framework, and easily construct several constraint- and unification-based type systems.

[32] François Pottier and Didier Rémy. The essence of ML type inference. In Benjamin C. Pierce, editor, Advanced Topics in Types and Programming Languages, chapter 10, pages 389-489. MIT Press, 2005. A draft extended version is also available. [ bib | PDF | At publisher's ]
[33] Vincent Simonet and François Pottier. Constraint-based type inference for guarded algebraic data types. Research Report 5462, INRIA, January 2005. [ bib | PDF | PostScript | At publisher's ]
Guarded algebraic data types subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, and first-class phantom types, and are closely related to inductive types. They have the distinguishing feature that, when typechecking a function defined by cases, every branch may be checked under different assumptions about the type variables in scope. This mechanism allows exploiting the presence of dynamic tests in the code to produce extra static type information.

We propose an extension of the constraint-based type system HM(X) with deep pattern matching, guarded algebraic data types, and polymorphic recursion. We prove that the type system is sound and that, provided recursive function definitions carry a type annotation, type inference may be reduced to constraint solving. Then, because solving arbitrary constraints is expensive, we further restrict the form of type annotations and prove that this allows producing so-called tractable constraints. Last, in the specific setting of equality, we explain how to solve tractable constraints.

To the best of our knowledge, this is the first generic and comprehensive account of type inference in the presence of guarded algebraic data types.

[34] François Pottier. Types et contraintes. Mémoire d'habilitation à diriger des recherches, Université Paris 7, December 2004. [ bib | PDF | PostScript ]
[35] Nadji Gauthier and François Pottier. Numbering matters: First-order canonical forms for second-order recursive types. In Proceedings of the 2004 ACM SIGPLAN International Conference on Functional Programming (ICFP'04), pages 150-161, September 2004. [ bib | PDF | PostScript | At publisher's ]
We study a type system equipped with universal types and equirecursive types, which we refer to as Fmu. We show that type equality may be decided in time O(nlogn), an improvement over the previous known bound of O(n2). In fact, we show that two more general problems, namely entailment of type equations and type unification, may be decided in time O(nlog n), a new result. To achieve this bound, we associate, with every Fmu type, a first-order canonical form, which may be computed in time O(nlogn). By exploiting this notion, we reduce all three problems to equality and unification of first-order recursive terms, for which efficient algorithms are known.

[36] François Pottier and Nadji Gauthier. Polymorphic typed defunctionalization. In Proceedings of the 31st ACM Symposium on Principles of Programming Languages (POPL'04), pages 89-98, Venice, Italy, January 2004. Superseded by [24]. [ bib | PDF | PostScript | At publisher's ]
Defunctionalization is a program transformation that aims to turn a higher-order functional program into a first-order one, that is, to eliminate the use of functions as first-class values. Its purpose is thus identical to that of closure conversion. It differs from closure conversion, however, by storing a tag, instead of a code pointer, within every closure. Defunctionalization has been used both as a reasoning tool and as a compilation technique.

Defunctionalization is commonly defined and studied in the setting of a simply-typed λ-calculus, where it is shown that semantics and well-typedness are preserved. It has been observed that, in the setting of a polymorphic type system, such as ML or System F, defunctionalization is not type-preserving. In this paper, we show that extending System F with guarded algebraic data types allows recovering type preservation. This result allows adding defunctionalization to the toolbox of type-preserving compiler writers.

[37] Jean-Christophe Filliâtre and François Pottier. Producing all ideals of a forest, functionally. Journal of Functional Programming, 13(5):945-956, September 2003. [ bib | PostScript | At publisher's ]
We present functional implementations of Koda and Ruskey's algorithm for generating all ideals of a forest poset as a Gray code. Using a continuation-based approach, we give an extremely concise formulation of the algorithm's core. Then, in a number of steps, we derive a first-order version whose efficiency is comparable to that of a C implementation given by Knuth.

[38] François Pottier. A constraint-based presentation and generalization of rows. In Eighteenth Annual IEEE Symposium on Logic In Computer Science (LICS'03), pages 331-340, Ottawa, Canada, June 2003. [ bib | PostScript | Long PostScript | At publisher's ]
We study the combination of possibly conditional non-structural subtyping constraints with rows. We give a new presentation of rows, where row terms disappear; instead, we annotate constraints with filters. We argue that, in the presence of subtyping, this approach is simpler and more general. In the case where filters are finite or cofinite sets of row labels, we give a constraint solving algorithm whose complexity is O(n3mlogm), where n is the size of the constraint and m is the number of row labels that appear in it. We point out that this allows efficient type inference for record concatenation. Furthermore, by varying the nature of filters, we obtain several natural generalizations of rows.

[39] François Pottier and Vincent Simonet. Information flow inference for ML. ACM Transactions on Programming Languages and Systems, 25(1):117-158, January 2003. [ bib | PostScript | At publisher's ]
This paper presents a type-based information flow analysis for a call-by-value lambda-calculus equipped with references, exceptions and let-polymorphism, which we refer to as Core ML. The type system is constraint-based and has decidable type inference. Its non-interference proof is reasonably light-weight, thanks to the use of a number of orthogonal techniques. First, a syntactic segregation between values and expressions allows a lighter formulation of the type system. Second, non-interference is reduced to subject reduction for a non-standard language extension. Lastly, a semi-syntactic approach to type soundness allows dealing with constraint-based polymorphism separately.

[40] Christian Skalka and François Pottier. Syntactic type soundness for HM(X). In Proceedings of the Workshop on Types in Programming (TIP'02), volume 75 of Electronic Notes in Theoretical Computer Science, Dagstuhl, Germany, July 2002. [ bib | PostScript ]
The HM(X) framework is a constraint-based type framework with built-in let-polymorphism. This paper establishes purely syntactic type soundness for the framework, treating an extended version of the language containing state and recursive binding. These results demonstrate that any instance of HM(X), comprising a specialized constraint system and possibly additional functional constants and their types, enjoys syntactic type soundness.

[41] François Pottier. A simple view of type-secure information flow in the π-calculus. In Proceedings of the 15th IEEE Computer Security Foundations Workshop, pages 320-330, Cape Breton, Nova Scotia, June 2002. [ bib | PostScript | Long PostScript | At publisher's ]
One way of enforcing an information flow control policy is to use a static type system capable of guaranteeing a noninterference property. Noninterference requires that two processes with distinct “high”-level components, but common “low”-level structure, cannot be distinguished by “low”-level observers. We state this property in terms of a rather strict notion of process equivalence, namely weak barbed reduction congruence.

Because noninterference is not a safety property, it is often regarded as more difficult to establish than a conventional type safety result. This paper aims to provide an elementary noninterference proof in the setting of the π-calculus. This is done by reducing the problem to subject reduction - a safety property - for a nonstandard, but fairly natural, extension of the π-calculus, baptized the <π>-calculus.

[42] François Pottier and Vincent Simonet. Information flow inference for ML. In Proceedings of the 29th ACM Symposium on Principles of Programming Languages (POPL'02), pages 319-330, Portland, Oregon, January 2002. Superseded by [39]. [ bib | PostScript | Long PostScript | At publisher's ]
This paper presents a type-based information flow analysis for a call-by-value lambda-calculus equipped with references, exceptions and let-polymorphism, which we refer to as Core ML. The type system is constraint-based and has decidable type inference. Its non-interference proof is reasonably light-weight, thanks to the use of a number of orthogonal techniques. First, a syntactic segregation between values and expressions allows a lighter formulation of the type system. Second, non-interference is reduced to subject reduction for a non-standard language extension. Lastly, a semi-syntactic approach to type soundness allows dealing with constraint-based polymorphism separately.

[43] François Pottier. Simplifying subtyping constraints: a theory. Information & Computation, 170(2):153-183, November 2001. [ bib | PostScript | At publisher's ]
This paper offers a theoretical study of constraint simplification, a fundamental issue for the designer of a practical type inference system with subtyping.

In the simpler case where constraints are equations, a simple isomorphism between constrained type schemes and finite state automata yields a complete constraint simplification method. Using it as a guide for the intuition, we move on to the case of subtyping, and describe several simplification algorithms. Although no longer complete, they are conceptually simple, efficient, and very effective in practice.

Overall, this paper gives a concise theoretical account of the techniques found at the core of our type inference system. Our study is restricted to the case where constraints are interpreted in a non-structural lattice of regular terms. Nevertheless, we highlight a small number of general ideas, which explain our algorithms at a high level and may be applicable to a variety of other systems.

[44] Sylvain Conchon and François Pottier. JOIN(X): Constraint-based type inference for the join-calculus. In David Sands, editor, Proceedings of the 10th European Symposium on Programming (ESOP'01), volume 2028 of Lecture Notes in Computer Science, pages 221-236. Springer, April 2001. [ bib | PostScript | Long PostScript | At publisher's ]
We present a generic constraint-based type system for the join-calculus. The key issue is type generalization, which, in the presence of concurrency, must be restricted. We first define a liberal generalization criterion, and prove it correct. Then, we find that it hinders type inference, and propose a cruder one, reminiscent of ML's value restriction.

We establish type safety using a semi-syntactic technique, which we believe is of independent interest. It consists in interpreting typing judgements as (sets of) judgements in an underlying system, which itself is given a syntactic soundness proof. This hybrid approach allows giving pleasant logical meaning to high-level notions such as type variables, constraints and generalization, and clearly separating them from low-level aspects (substitution lemmas, etc.), which are dealt with in a simple, standard way.

[45] François Pottier, Christian Skalka, and Scott Smith. A systematic approach to static access control. In David Sands, editor, Proceedings of the 10th European Symposium on Programming (ESOP'01), volume 2028 of Lecture Notes in Computer Science, pages 30-45. Springer, April 2001. Superseded by [31]. [ bib | PostScript | At publisher's ]
The Java JDK 1.2 Security Architecture includes a dynamic mechanism for enforcing access control checks, so-called stack inspection. This paper studies type systems which can statically guarantee the success of these checks. We develop these systems using a new, systematic methodology: we show that the security-passing style translation, proposed by Wallach and Felten as a dynamic implementation technique, also gives rise to static security-aware type systems, by composition with conventional type systems. To define the latter, we use the general HM(X) framework, and easily construct several constraint- and unification-based type systems. They offer significant improvements on a previous type system for JDK access control, both in terms of expressiveness and in terms of readability of type specifications.

[46] François Pottier. A semi-syntactic soundness proof for HM(X). Research Report 4150, INRIA, March 2001. [ bib | PDF ]
This document gives a soundness proof for the generic constraint-based type inference framework HM(X). Our proof is semi-syntactic. It consists of two steps. The first step is to define a ground type system, where polymorphism is extensional, and prove its correctness in a syntactic way. The second step is to interpret HM(X) judgements as (sets of) judgements in the underlying system, which gives a logical view of polymorphism and constraints. Overall, the approach may be seen as more modular than a purely syntactic approach: because polymorphism and constraints are dealt with separately, they do not clutter the subject reduction proof. However, it yields a slightly weaker result: it only establishes type soundness, rather than subject reduction, for HM(X).

[47] François Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4):312-347, November 2000. [ bib | PostScript ]
The combination of subtyping, conditional constraints and rows yields a powerful constraint-based type inference system. We illustrate this claim by proposing solutions to three delicate type inference problems: “accurate” pattern matchings, record concatenation, and first-class messages. Previously known solutions involved a different technique in each case; our theoretical contribution is in using only a single set of tools. On the practical side, this allows all three problems to benefit from a common set of constraint simplification techniques, a formal description of which is given in an appendix.

[48] François Pottier and Sylvain Conchon. Information flow inference for free. In Proceedings of the Fifth ACM SIGPLAN International Conference on Functional Programming (ICFP'00), pages 46-57, Montréal, Canada, September 2000. [ bib | PostScript | At publisher's ]
This paper shows how to systematically extend an arbitrary type system with dependency information, and how the new system's soundness and non-interference proofs may rely upon, rather than duplicate, the original system's soundness proof. This allows enriching virtually any of the type systems known today with information flow analysis, while requiring only a minimal proof effort.

Our approach is based on an untyped operational semantics for a labelled calculus akin to core ML. Thus, it is simple, and should be applicable to other computing paradigms, such as object or process calculi.

The paper also discusses access control, and shows it may be viewed as entirely independent of information flow control. Letting the two mechanisms coexist, without interacting, yields a simple and expressive type system, which allows, in particular, “selective” declassification.

[49] François Pottier. A 3-part type inference engine. In Gert Smolka, editor, Proceedings of the 2000 European Symposium on Programming (ESOP'00), volume 1782 of Lecture Notes in Computer Science, pages 320-335. Springer, March 2000. Superseded by [47]. [ bib | PostScript | At publisher's ]
Extending a subtyping-constraint-based type inference framework with conditional constraints and rows yields a powerful type inference engine. We illustrate this claim by proposing solutions to three delicate type inference problems: “accurate” pattern matchings, record concatenation, and “dynamic” messages. Until now, known solutions required significantly different techniques; our theoretical contribution is in using only a single (and simple) set of tools. On the practical side, this allows all three problems to benefit from a common set of constraint simplification techniques, leading to efficient solutions.

[50] François Pottier. Wallace: an efficient implementation of type inference with subtyping, February 2000. [ bib | Software ]
[51] François Pottier. A framework for type inference with subtyping. In Proceedings of the third ACM SIGPLAN International Conference on Functional Programming (ICFP'98), pages 228-238, September 1998. [ bib | PostScript | At publisher's ]
This paper describes a full framework for type inference and simplification in the presence of subtyping. We give a clean, simple presentation of the system and show that it leads to an efficient implementation. Previous inference systems had severe efficiency problems, mainly by lack of a systematic substitution algorithm, but also because the issue of data representation was not settled. We explain how to solve these problems and obtain a fully integrated framework.

[52] François Pottier. Type inference in the presence of subtyping: from theory to practice. Research Report 3483, INRIA, September 1998. [ bib | PDF ]
From a purely theoretical point of view, type inference for a functional language with parametric polymorphism and subtyping poses no difficulties. Indeed, it suffices to generalize the inference algorithm used in the ML language, so as to deal with type inequalities, rather than equalities. However, the number of such inequalities is linear in the program size; whence, from a practical point of view, a serious efficiency and readability problem.

To solve this problem, one must simplify the inferred constraints. So, after studying the logical properties of subtyping constraints, this work proposes several simplification algorithms. They combine seamlessly, yielding a homogeneous, fully formal framework, which directly leads to an efficient implementation. Although this theoretical study is performed in a simplified setting, numerous extensions are possible. Thus, this framework is realistic, and should allow a practical appearance of subtyping in languages with type inference.

This is the English version of the author's PhD dissertation.

[53] François Pottier. Synthèse de types en présence de sous-typage: de la théorie à la pratique. PhD thesis, Université Paris 7, July 1998. [ bib | PostScript ]
D'un point de vue purement théorique, l'inférence de types pour un langage fonctionnel doté de polymorphisme paramétrique et de sous-typage ne pose pas de difficultés. Il suffit en effet de généraliser l'algorithme d'inférence utilisé par le langage ML, de façon à manipuler non plus des égalités, mais des inégalités entre types. Cependant, celles-ci sont engendrées en nombre proportionnel à la taille du programme, ce qui pose, d'un point de vue pratique, un grave problème d'efficacité et de lisibilité.

Pour résoudre ce problème, il est nécessaire de simplifier les contraintes inférées. Ce travail étudie donc d'abord les propriétés logiques des contraintes de sous-typage, puis propose plusieurs algorithmes de simplification. Ceux-ci se composent naturellement pour former un tout homogène, entièrement formalisé, qui conduit directement à une implémentation efficace. Bien que cette étude théorique soit effectuée dans un cadre simplifié, de nombreuses extensions sont possibles. Le système proposé est donc réaliste, et permet d'imaginer l'introduction pratique du sous-typage dans des langages dotés d'inférence de types.

[54] François Pottier. Simplifying subtyping constraints. In Proceedings of the 1996 ACM SIGPLAN International Conference on Functional Programming (ICFP'96), pages 122-133, May 1996. [ bib | PostScript | At publisher's ]
This paper studies type inference for a functional, ML-style language with subtyping, and focuses on the issue of simplifying inferred constraint sets. We propose a powerful notion of entailment between constraint sets, as well as an algorithm to check it, which we prove to be sound. The algorithm, although very powerful in practice, is not complete. We also introduce two new typing rules which allow simplifying constraint sets. These rules give very good practical results.

[55] François Pottier. Type inference and simplification for recursively constrained types. In Actes du GDR Programmation 1995 (journée du pôle Programmation Fonctionnelle), November 1995. [ bib | PostScript ]
This paper studies type inference for a functional language with subtyping, and focuses on the issue of simplifying inferred types. It does not attempt to give a fully detailed, formal framework; instead, it tries to explain the issues informally and suggest possible solutions by providing examples.

[56] François Pottier. Implémentation d'un système de modules évolué en Caml-Light. Research Report 2449, INRIA, January 1995. [ bib | PDF | PostScript ]
Ce mémoire décrit la conception et l'implémentation d'un langage de modules évolué en Caml-Light. Nous décrivons d'abord ce que nous entendons par langage de modules, et l'intérêt qu'un tel langage présente pour la programmation à moyenne ou grande échelle. Nous expliquons ensuite en quoi le précurseur en la matière, SML, souffre de limitations graves vis-à-vis de la compilation séparée. Nous exposons un système similaire mais mieux adapté à la compilation séparée, et en même temps simplifié. Enfin, certains problèmes d'implémentation inattendus sont évoqués.

[57] Michel Mauny and François Pottier. An implementation of Caml Light with existential types. Technical Report 2183, INRIA, October 1993. [ bib | PDF | PostScript ]
This work is based on a proposal by Läufer and Odersky. They show that it is possible to add existential types to an ML-like language without even modifying its syntax. ML's strong typing properties are of course retained. We implemented their proposal into Caml-Light, thus making it possible to write real-sized programs using existential types.

This paper is divided into three parts. First, we give a definition of existential types and show how to use them in our enhanced version of Caml-Light. We then give interesting examples demonstrating their usefulness. Finally, a more technical section gives an overview of the changes made to the compiler and discusses some technical issues.


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