[1] |
Alexandre Moine, Arthur Charguéraud, and François Pottier.
Specification and verification of a
transient stack.
In ACM SIGPLAN Conference on Certified Programs and Proofs
(CPP), January 2022.
[ bib |
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A transient data structure is a package of an ephemeral data structure, a persistent data structure, and fast conversions between them. We describe the specification and proof of a transient stack and its iterators. This data structure is a scaled-down version of the general-purpose transient sequence data structure implemented in the OCaml library Sek. Internally, it relies on fixed-capacity arrays, or chunks, which can be shared between several ephemeral and persistent stacks. Dynamic tests are used to determine whether a chunk can be updated in place or must be copied: a chunk can be updated if it is uniquely owned or if the update is monotonic. Using CFML, which implements Separation Logic with Time Credits inside Coq, we verify the functional correctness and the amortized time complexity of this data structure. Our verification effort covers iterators, which involve direct pointers to internal chunks. The specification of iterators describes what the operations on iterators do, how much they cost, and under what circumstances an iterator is invalidated. |
[2] |
Jean-Marie Madiot and François Pottier.
A separation logic for heap space under
garbage collection.
Proceedings of the ACM on Programming Languages, 6(POPL),
January 2022.
[ bib |
Software |
PDF |
At publisher's ]
We present SL♢, a Separation Logic that allows controlling the heap space consumption of a program in the presence of dynamic memory allocation and garbage collection. A user of the logic works with space credits, a resource that is consumed when an object is allocated and produced when a group of objects is logically deallocated, that is, when the user is able to prove that it has become unreachable and therefore can be collected. To prove such a fact, the user maintains pointed-by assertions that record the immediate predecessors of every object. Our calculus, SpaceLang, has mutable state, shared-memory concurrency, and code pointers. We prove that SL♢ is sound and present several simple examples of its use. |
[3] | Paulo Emílio de Vilhena and François Pottier. Verifying a minimalist reverse-mode AD library. Submitted, December 2021. [ bib | PDF ] |
[4] |
Frédéric Bour and François Pottier.
Faster reachability analysis for LR(1)
parsers.
In ACM SIGPLAN International Conference on Software Language
Engineering (SLE), pages 113--125, October 2021.
[ bib |
DOI |
PDF ]
We present a novel algorithm for reachability in an LR(1) automaton. For each transition in the automaton, the problem is to determine under what conditions this transition can be taken, that is, which (minimal) input fragment and which lookahead symbol allow taking this transition. Our algorithm outperforms Pottier's algorithm (2016) by up to three orders of magnitude on real-world grammars. Among other applications, this vastly improves the scalability of Jeffery's error reporting technique (2003), where a mapping of (reachable) error states to messages must be created and maintained. |
[5] |
François Pottier.
Strong automated testing of OCaml
libraries.
In Journées Francophones des Langages Applicatifs (JFLA),
February 2021.
[ bib |
PDF ]
We present Monolith, a programmable tool that helps apply random testing or fuzz testing to an OCaml library. Monolith provides a rich specification language, which allows the user to describe her library's API, and an engine, which generates clients of this API and executes them. This reduces the problem of testing a library to the problem of testing a complete program, one that is effectively addressed by off-the-shelf fuzzers such as AFL. Keywords: national |
[6] |
Paulo Emílio de Vilhena and François Pottier.
A separation logic for effect handlers.
Proceedings of the ACM on Programming Languages, 5(POPL),
January 2021.
[ bib |
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At publisher's ]
User-defined effects and effect handlers are advertised and advocated as a relatively easy-to-understand and modular approach to delimited control. They offer the ability of suspending and resuming a computation and allow information to be transmitted both ways between the computation, which requests a certain service, and the handler, which provides this service. Yet, a key question remains, to this day, largely unanswered: how does one modularly specify and verify programs in the presence of both user-defined effect handlers and primitive effects, such as heap-allocated mutable state? We answer this question by presenting a Separation Logic with built-in support for effect handlers, both shallow and deep. The specification of a program fragment includes a protocol that describes the effects that the program may perform as well as the replies that it can expect to receive. The logic allows local reasoning via a frame rule and a bind rule. It is based on Iris and inherits all of its advanced features, including support for higher-order functions, user-defined ghost state, and invariants. We illustrate its power via several case studies, including (1) a generic formulation of control inversion, which turns a producer that “pushes” elements towards a consumer into a producer from which one can “pull” elements on demand, and (2) a simple system for cooperative concurrency, where several threads execute concurrently, can spawn new threads, and communicate via promises. |
[7] |
Glen Mével, Jacques-Henri Jourdan, and François Pottier.
Cosmo: A concurrent separation logic for
Multicore OCaml.
Proceedings of the ACM on Programming Languages, 4(ICFP),
August 2020.
[ bib |
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At publisher's ]
Multicore OCaml extends OCaml with support for shared-memory concurrency. It is equipped with a weak memory model, for which an operational semantics has been published. This begs the question: what reasoning rules can one rely upon while writing or verifying Multicore OCaml code? To answer it, we instantiate Iris, a modern descendant of Concurrent Separation Logic, for Multicore OCaml. This yields a low-level program logic whose reasoning rules expose the details of the memory model. On top of it, we build a higher-level logic, Cosmo, which trades off some expressive power in return for a simple set of reasoning rules that allow accessing nonatomic locations in a data-race-free manner, exploiting the sequentially-consistent behavior of atomic locations, and exploiting the release/acquire behavior of atomic locations. Cosmo allows both low-level reasoning, where the details of the Multicore OCaml memory model are apparent, and high-level reasoning, which is independent of this memory model. We illustrate this claim via a number of case studies: we verify several implementations of locks with respect to a classic, memory-model-independent specification. Thus, a coarse-grained application that uses locks as the sole means of synchronization can be verified in the Concurrent-Separation-Logic fragment of Cosmo, without any knowledge of the weak memory model. |
[8] |
Paulo Emílio de Vilhena, François Pottier, and Jacques-Henri Jourdan.
Spy game: Verifying a local generic solver
in Iris.
Proceedings of the ACM on Programming Languages, 4(POPL),
January 2020.
[ bib |
PDF |
At publisher's ]
We verify the partial correctness of a “local generic solver”, that is, an on-demand, incremental, memoizing least fixed point computation algorithm. The verification is carried out in Iris, a modern breed of concurrent separation logic. The specification is simple: the solver computes the optimal least fixed point of a system of monotone equations. Although the solver relies on mutable internal state for memoization and for “spying”, a form of dynamic dependency discovery, it is apparently pure: no side effects are mentioned in its specification. As auxiliary contributions, we provide several illustrations of the use of prophecy variables, a novel feature of Iris; we establish a restricted form of the infinitary conjunction rule; and we provide a specification and proof of Longley's modulus function, an archetypical example of spying. |
[9] | Armaël Guéneau, Jacques-Henri Jourdan, Arthur Charguéraud, and François Pottier. Formal proof and analysis of an incremental cycle detection algorithm. In John Harrison, John O'Leary, and Andrew Tolmach, editors, Interactive Theorem Proving (ITP), volume 141 of Leibniz International Proceedings in Informatics, pages 18:1--18:20, Dagstuhl, Germany, September 2019. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik. [ bib | PDF | At publisher's ] |
[10] |
Glen Mével, Jacques-Henri Jourdan, and François Pottier.
Time credits and time receipts in
Iris.
In Luis Caires, editor, European Symposium on Programming
(ESOP), volume 11423 of Lecture Notes in Computer Science, pages
1--27. Springer, April 2019.
[ bib |
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At publisher's ]
We present a machine-checked extension of the program logic Iris with time credits and time receipts, two dual means of reasoning about time. Whereas time credits are used to establish an upper bound on a program's execution time, time receipts can be used to establish a lower bound. More strikingly, time receipts can be used to prove that certain undesirable events---such as integer overflows---cannot occur until a very long time has elapsed. We present several machine-checked applications of time credits and time receipts, including an application where both concepts are exploited. |
[11] |
Arthur Charguéraud and François Pottier.
Verifying the correctness and amortized
complexity of a union-find implementation in separation logic with time
credits.
Journal of Automated Reasoning, 62(3):331--365, March 2019.
[ bib |
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At publisher's ]
Union-Find is a famous example of a simple data structure whose amortized asymptotic time complexity analysis is nontrivial. We present a Coq formalization of this analysis, following Alstrup et al.'s recent proof (2014). Moreover, we implement Union-Find as an OCaml library and formally endow it with a modular specification that offers a full functional correctness guarantee as well as an amortized complexity bound. In order to reason in Coq about imperative OCaml code, we use the CFML tool, which implements Separation Logic for a subset of OCaml, and which we extend with time credits. Although it was known in principle that amortized analysis can be explained in terms of time credits and that time credits can be viewed as resources in Separation Logic, we believe our work is the first practical demonstration of this approach. Finally, in order to explain the meta-theoretical foundations of our approach, we define a Separation Logic with time credits for an untyped call-by-value lambda-calculus, and formally verify its soundness. |
[12] |
Armaël Guéneau, Arthur Charguéraud, and François Pottier.
A fistful of dollars: Formalizing
asymptotic complexity claims via deductive program verification.
In Amal Ahmed, editor, European Symposium on Programming
(ESOP), volume 10801 of Lecture Notes in Computer Science, pages
533--560. Springer, April 2018.
[ bib |
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At publisher's ]
We present a framework for simultaneously verifying the functional correctness and the worst-case asymptotic time complexity of higher-order imperative programs. We build on top of Separation Logic with Time Credits, embedded in an interactive proof assistant. We formalize the O notation, which is key to enabling modular specifications and proofs. We cover the subtleties of the multivariate case, where the complexity of a program fragment depends on multiple parameters. We propose a way of integrating complexity bounds into specifications, present lemmas and tactics that support a natural reasoning style, and illustrate their use with a collection of examples. |
[13] |
François Pottier.
Visitors unchained.
In ACM SIGPLAN International Conference on Functional
Programming (ICFP), September 2017.
[ bib |
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At publisher's ]
Traversing and transforming abstract syntax trees that involve name binding is notoriously difficult to do in a correct, concise, modular, customizable manner. We address this problem in the setting of OCaml, a functional programming language equipped with powerful object-oriented features. We use visitor classes as partial, composable descriptions of the operations that we wish to perform on abstract syntax trees. We introduce visitors, a simple type-directed facility for generating visitor classes that have no knowledge of binding. Separately, we present alphaLib, a library of small hand-written visitor classes, each of which knows about a specific binding construct, a specific representation of names, and/or a specific operation on abstract syntax trees. By combining these components, a wide range of operations can be defined. Multiple representations of names can be supported, as well as conversions between representations. Binding structure can be described either in a programmatic style, by writing visitor methods, or in a declarative style, via preprogrammed binding combinators. |
[14] | Jacques-Henri Jourdan and François Pottier. A simple, possibly correct LR parser for C11. ACM Transactions on Programming Languages and Systems, 39(4):14:1--14:36, August 2017. [ bib | Software | PDF | At publisher's ] |
[15] | François Pottier. Revisiting the CPS transformation and its implementation. Unpublished, July 2017. [ bib | PDF ] |
[16] |
Arthur Charguéraud and François Pottier.
Temporary read-only permissions for
separation logic.
In Hongseok Yang, editor, European Symposium on Programming
(ESOP), volume 10201 of Lecture Notes in Computer Science, pages
260--286. Springer, April 2017.
[ bib |
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We present an extension of Separation Logic with a general mechanism for temporarily converting any assertion (or “permission”) to a read-only form. No accounting is required: our read-only permissions can be freely duplicated and discarded. We argue that, in circumstances where mutable data structures are temporarily accessed only for reading, our read-only permissions enable more concise specifications and proofs. The metatheory of our proposal is verified in Coq. |
[17] |
François Pottier.
Verifying a hash table and its iterators
in higher-order separation logic.
In ACM SIGPLAN Conference on Certified Programs and Proofs
(CPP), pages 3--16, January 2017.
[ bib |
DOI |
Software |
PDF |
At publisher's ]
We describe the specification and proof of an (imperative, sequential) hash table implementation. The usual dictionary operations (insertion, lookup, and so on) are supported, as well as iteration via folds and iterators. The code is written in OCaml and verified using higher-order separation logic, embedded in Coq, via the CFML tool and library. This case study is part of a larger project that aims to build a verified OCaml library of basic data structures. |
[18] |
Thibaut Balabonski, François Pottier, and Jonathan Protzenko.
The design and formalization of Mezzo, a
permission-based programming language.
ACM Transactions on Programming Languages and Systems,
38(4):14:1--14:94, August 2016.
[ bib |
DOI |
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At publisher's ]
The programming language Mezzo is equipped with a rich type system that controls aliasing and access to mutable memory. We give a comprehensive tutorial overview of the language. Then, we present a modular formalization of Mezzo's core type system, in the form of a concurrent λ-calculus, which we successively extend with references, locks, and adoption and abandon, a novel mechanism that marries Mezzo's static ownership discipline with dynamic ownership tests. We prove that well-typed programs do not go wrong and are data-race free. Our definitions and proofs are machine-checked. |
[19] |
François Pottier.
Reachability and error diagnosis in
LR(1) parsers.
In International Conference on Compiler Construction (CC),
pages 88--98, March 2016.
[ bib |
DOI |
PDF |
At publisher's ]
Given an LR(1) automaton, what are the states in which an error can be detected? For each such “error state”, what is a minimal input sentence that causes an error in this state? We propose an algorithm that answers these questions. This allows building a collection of pairs of an erroneous input sentence and a (handwritten) diagnostic message, ensuring that this collection covers every error state, and maintaining this property as the grammar evolves. We report on an application of this technique to the CompCert ISO C99 parser, and discuss its strengths and limitations. |
[20] |
François Pottier.
Reachability and error diagnosis in
LR(1) automata.
In Journées Francophones des Langages Applicatifs (JFLA),
January 2016.
[ bib |
PDF |
At publisher's ]
Given an LR(1) automaton, what are the states in which an error can be detected? For each such “error state”, what is a minimal input sentence that causes an error in this state? We propose an algorithm that answers these questions. Such an algorithm allows building a collection of pairs of an erroneous input sentence and a diagnostic message, ensuring that this collection covers every error state, and maintaining this property as the grammar evolves. We report on an application of this technique to the CompCert ISO C99 parser, and discuss its strengths and limitations. Keywords: national |
[21] |
Arthur Charguéraud and François Pottier.
Machine-checked verification of the
correctness and amortized complexity of an efficient union-find
implementation.
In Interactive Theorem Proving (ITP), volume 9236 of
Lecture Notes in Computer Science, pages 137--153. Springer, August 2015.
[ bib |
Software |
PDF |
At publisher's ]
Union-Find is a famous example of a simple data structure whose amortized asymptotic time complexity analysis is non-trivial. We present a Coq formalization of this analysis. Moreover, we implement Union-Find as an OCaml library and formally endow it with a modular specification that offers a full functional correctness guarantee as well as an amortized complexity bound. Reasoning in Coq about imperative OCaml code relies on the CFML tool, which is based on characteristic formulae and Separation Logic, and which we extend with time credits. Although it was known in principle that amortized analysis can be explained in terms of time credits and that time credits can be viewed as resources in Separation Logic, we believe our work is the first practical demonstration of this approach. |
[22] |
François Pottier and Jonathan Protzenko.
A few lessons from the Mezzo project.
In Thomas Ball, Rastislav Bodik, Shriram Krishnamurthi, Benjamin S.
Lerner, and Greg Morrisett, editors, Summit oN Advances in Programming
Languages (SNAPL), volume 32 of Leibniz International Proceedings in
Informatics, pages 221--237. Schloss Dagstuhl--Leibniz-Zentrum für
Informatik, May 2015.
[ bib |
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At publisher's ]
With Mezzo, we set out to design a new, better programming language. In this modest document, we recount our adventure: what worked, and what did not; the decisions that appear in hindsight to have been good, and the design mistakes that cost us; the things that we are happy with in the end, and the frustrating aspects we wish we had handled better. |
[23] |
François Pottier.
Depth-first search and strong connectivity
in Coq.
In Journées Francophones des Langages Applicatifs (JFLA),
January 2015.
[ bib |
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At publisher's ]
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. Keywords: national |
[24] |
François Pottier.
Hindley-Milner elaboration in
applicative style.
In ACM SIGPLAN International Conference on Functional
Programming (ICFP), September 2014.
[ bib |
DOI |
Software |
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. |
[25] |
Thibaut Balabonski, François Pottier, and Jonathan Protzenko.
Type soundness and race freedom for
Mezzo.
In International Symposium on Functional and Logic Programming
(FLOPS), volume 8475 of Lecture Notes in Computer Science, pages
253--269. Springer, 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. |
[26] |
François Pottier and Jonathan Protzenko.
Programming with permissions in Mezzo.
In ACM SIGPLAN International Conference on Functional
Programming (ICFP), pages 173--184, September 2013.
[ bib |
DOI |
PDF |
Long version |
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”. |
[27] |
Armaël Guéneau, François Pottier, and Jonathan Protzenko.
The ins and outs of iteration in
Mezzo.
Talk proposal for HOPE 2013, July 2013.
[ bib |
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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. |
[28] | 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 ] |
[29] |
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 |
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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. |
[30] |
Nicolas Pouillard and François Pottier.
A unified treatment of syntax with
binders.
Journal of Functional Programming, 22(4--5):614--704, September
2012.
[ bib |
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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. |
[31] |
Jacques-Henri Jourdan, François Pottier, and Xavier Leroy.
Validating LR(1) parsers.
In European Symposium on Programming (ESOP), volume 7211 of
Lecture Notes in Computer Science, pages 397--416. Springer, March
2012.
[ bib |
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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. |
[32] |
François Pottier.
A typed store-passing translation for
general references.
In ACM Symposium on Principles of Programming Languages (POPL),
Austin, Texas, January 2011.
Supplementary material.
[ bib |
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At publisher's ]
We present a store-passing translation of System F with general references into an extension of System F_{ω} 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. |
[33] |
Alexandre Pilkiewicz and François Pottier.
The essence of monotonic state.
In ACM SIGPLAN Workshop on Types in Language Design and
Implementation (TLDI), Austin, Texas, January 2011.
[ bib |
DOI |
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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”. |
[34] |
Nicolas Pouillard and François Pottier.
A fresh look at programming with names and
binders.
In ACM SIGPLAN International Conference on Functional
Programming (ICFP), pages 217--228, September 2010.
[ bib |
DOI |
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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. |
[35] |
Jan Schwinghammer, Hongseok Yang, Lars Birkedal, François Pottier, and
Bernhard Reus.
A semantic foundation for hidden state.
In C.-H. L. Ong, editor, International Conference on Foundations
of Software Science and Computational Structures (FOSSACS), volume 6014 of
Lecture Notes in Computer Science, pages 2--17. Springer, March 2010.
[ bib |
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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. |
[36] |
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. |
[37] |
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. |
[38] |
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. |
[39] |
Arthur Charguéraud and François Pottier.
Functional translation of a calculus of
capabilities.
In ACM SIGPLAN International Conference on Functional
Programming (ICFP), pages 213--224, September 2008.
[ bib |
DOI |
PDF |
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. |
[40] |
Yann Régis-Gianas and François Pottier.
A Hoare logic for call-by-value
functional programs.
In International Conference on Mathematics of Program
Construction (MPC), volume 5133 of Lecture Notes in Computer Science,
pages 305--335. Springer, July 2008.
[ bib |
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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. |
[41] |
François Pottier.
Hiding local state in direct style: a
higher-order anti-frame rule.
In IEEE Symposium on Logic In Computer Science (LICS), 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. |
[42] |
François Pottier.
Static name control for FreshML.
In IEEE Symposium on Logic In Computer Science (LICS), pages
356--365, Wroclaw, Poland, July 2007.
[ bib |
PDF |
Long version |
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. |
[43] |
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 |
DOI |
PDF |
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. |
[44] |
François Pottier and Yann Régis-Gianas.
Towards efficient, typed LR parsers.
In ACM Workshop on ML (ML), volume 148(2) of Electronic
Notes in Theoretical Computer Science, pages 155--180, March 2006.
[ bib |
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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. |
[45] |
François Pottier and Nadji Gauthier.
Polymorphic typed defunctionalization and
concretization.
Higher-Order and Symbolic Computation, 19:125--162, March 2006.
[ bib |
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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. |
[46] |
François Pottier.
An overview of Cαml.
In ACM Workshop on ML (ML), volume 148(2) of Electronic
Notes in Theoretical Computer Science, pages 27--52, March 2006.
[ bib |
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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. |
[47] |
François Pottier and Yann Régis-Gianas.
Stratified type inference for generalized
algebraic data types.
In ACM Symposium on Principles of Programming Languages (POPL),
pages 232--244, Charleston, South Carolina, January 2006.
[ bib |
DOI |
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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. |
[48] | 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 ] |
[49] |
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 2005), volume 3461 of Lecture Notes in Computer
Science, pages 179--193, Nara, Japan, April 2005. Springer.
[ bib |
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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. |
[50] |
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 |
DOI |
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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. |
[51] |
Vincent Simonet and François Pottier.
Constraint-based type inference for
guarded algebraic data types.
Research Report 5462, INRIA, January 2005.
[ bib |
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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. |
[52] | 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 ] |
[53] | François Pottier. Types et contraintes. Mémoire d'habilitation à diriger des recherches, Université Paris 7, December 2004. [ bib | PDF ] |
[54] |
Nadji Gauthier and François Pottier.
Numbering matters: First-order canonical
forms for second-order recursive types.
In ACM SIGPLAN International Conference on Functional
Programming (ICFP), pages 150--161, September 2004.
[ bib |
DOI |
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We study a type system equipped with universal types and equirecursive types, which we refer to as F_{mu}. We show that type equality may be decided in time O(nlogn), an improvement over the previous known bound of O(n^{2}). 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 F_{mu} 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. |
[55] |
François Pottier and Nadji Gauthier.
Polymorphic typed defunctionalization.
In ACM Symposium on Principles of Programming Languages (POPL),
pages 89--98, Venice, Italy, January 2004.
Superseded by [45].
[ bib |
DOI |
PDF |
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. |
[56] |
Jean-Christophe Filliâtre and François Pottier.
Producing all ideals of a forest,
functionally.
Journal of Functional Programming, 13(5):945--956, September
2003.
[ bib |
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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. |
[57] |
François Pottier.
A constraint-based presentation and
generalization of rows.
In IEEE Symposium on Logic In Computer Science (LICS), pages
331--340, Ottawa, Canada, June 2003.
[ bib |
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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(n^{3}mlogm), 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. |
[58] |
François Pottier and Vincent Simonet.
Information flow inference for ML.
ACM Transactions on Programming Languages and Systems,
25(1):117--158, January 2003.
[ bib |
DOI |
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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. |
[59] |
Christian Skalka and François Pottier.
Syntactic type soundness for HM(X).
In Workshop on Types in Programming (TIP), volume 75 of
Electronic Notes in Theoretical Computer Science, Dagstuhl, Germany, July
2002.
[ bib |
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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. |
[60] |
François Pottier.
A simple view of type-secure information
flow in the π-calculus.
In IEEE Computer Security Foundations Workshop (CSFW), pages
320--330, Cape Breton, Nova Scotia, June 2002.
[ bib |
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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. |
[61] |
François Pottier and Vincent Simonet.
Information flow inference for ML.
In ACM Symposium on Principles of Programming Languages (POPL),
pages 319--330, Portland, Oregon, January 2002.
Superseded by [58].
[ bib |
DOI |
PDF |
Long version |
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. |
[62] |
François Pottier.
Simplifying subtyping constraints: a
theory.
Information & Computation, 170(2):153--183, November 2001.
[ bib |
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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. |
[63] |
François Pottier, Christian Skalka, and Scott Smith.
A systematic approach to static access
control.
In David Sands, editor, European Symposium on Programming
(ESOP), volume 2028 of Lecture Notes in Computer Science, pages
30--45. Springer, April 2001.
Superseded by [50].
[ bib |
PDF |
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. |
[64] |
Sylvain Conchon and François Pottier.
JOIN(X): Constraint-based type
inference for the join-calculus.
In David Sands, editor, European Symposium on Programming
(ESOP), volume 2028 of Lecture Notes in Computer Science, pages
221--236. Springer, April 2001.
[ bib |
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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. |
[65] |
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). |
[66] |
François Pottier.
A versatile constraint-based type
inference system.
Nordic Journal of Computing, 7(4):312--347, November 2000.
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PDF ]
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. |
[67] |
François Pottier and Sylvain Conchon.
Information flow inference for free.
In ACM SIGPLAN International Conference on Functional
Programming (ICFP), pages 46--57, Montréal, Canada, September 2000.
[ bib |
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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. |
[68] |
François Pottier.
A 3-part type inference engine.
In Gert Smolka, editor, European Symposium on Programming
(ESOP), volume 1782 of Lecture Notes in Computer Science, pages
320--335. Springer, March 2000.
Superseded by [66].
[ bib |
PDF |
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. |
[69] |
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. |
[70] |
François Pottier.
A framework for type inference with
subtyping.
In ACM SIGPLAN International Conference on Functional
Programming (ICFP), pages 228--238, September 1998.
[ bib |
DOI |
PDF |
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. |
[71] |
François Pottier.
Synthèse de types en présence de
sous-typage: de la théorie à la pratique.
PhD thesis, Université Paris 7, July 1998.
[ bib |
PDF ]
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. |
[72] |
François Pottier.
Simplifying subtyping constraints.
In ACM SIGPLAN International Conference on Functional
Programming (ICFP), pages 122--133, May 1996.
[ bib |
DOI |
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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. |
[73] |
François Pottier.
Type inference and simplification for
recursively constrained types.
In Actes du GDR Programmation (journée du pôle Programmation
Fonctionnelle), November 1995.
[ bib |
PDF ]
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. Keywords: national |
[74] |
François Pottier.
Implémentation d'un système de modules
évolué en Caml-Light.
Research Report 2449, INRIA, January 1995.
[ bib |
PDF |
At publisher's ]
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. |
[75] |
Michel Mauny and François Pottier.
An implementation of Caml Light with
existential types.
Technical Report 2183, INRIA, October 1993.
[ bib |
PDF |
At publisher's ]
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. |
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