## Design, study and implementation of languages for proofs and programs (2009)

### BibTeX

@MISC{π.r²09design,study,

author = {Project-Team π.r²},

title = {Design, study and implementation of languages for proofs and programs},

year = {2009}

}

### OpenURL

### Abstract

### Citations

2346 | Computational Complexity
- Papadimitriou
- 1994
(Show Context)
Citation Context ...arly november [21]. Connections with algorithmic complexity are discussed since focalization in the framework of computational ludics can be connected with proof methods of the linear-speedup theorem =-=[56]-=-. In the two months he has been here, Noam Zeilberger worked on different aspects of computational duality and the Curry-Howard interpretation of polarized logic. With Paul-André Melliès and Jonas Fre... |

1118 |
The Lambda Calculus: Its Syntax and Semantics
- Barendregt
(Show Context)
Citation Context ...possible semantics referred to as call-by-name and call-by-value evaluations. Of these two semantics, the first one, which is the simplest to characterize, has been deeply studied in the last decades =-=[25]-=-. For explaining the Curry-Howard correspondence, it is important to distinguish between intuitionistic and classical logic: following Brouwer at the beginning of the 20 th century, classical logic is... |

754 | publications by the team in recent years - Major |

567 |
Untersuchungen über das logische Schließen
- Gentzen
- 1935
(Show Context)
Citation Context ...ry and the Curry-Howard correspondence 3.1.1. Proofs as programs Proof theory is the branch of logic devoted to the study of the structure of proofs. An essential contributor to this field is Gentzen =-=[40]-=- who developed in 1935 two logical formalisms that are now central to the study of proofs. These are the so-called “natural deduction”, a syntax that is particularly well-suited to simulate the intuit... |

469 |
Interactive Theorem Proving and Program Development, Coq’Art: The Calculus of Inductive Constructions
- Bertot, Castéran
- 2004
(Show Context)
Citation Context ... model and commercial applets certification). All in all, it is difficult to evaluate how much Coq is used. Two indicators are the readership of the textbook on Coq by Yves Bertot and Pierre Castéran =-=[26]-=- and the number of subscribers to the Coq-club mailing list. More than 1200 copies of the book have been sold. There has been a second printing , and a Chinese translation of the book has been publish... |

332 |
The mechanical evaluation of expressions
- Landin
- 1964
(Show Context)
Citation Context ... an intermediate evaluation device, between high-level programming languages and the computer microprocessor. The typical reference for call-by-value evaluation of λ-calculus is Landin’s SECD machine =-=[48]-=- and Krivine’s abstract machine for call-by-name evaluation [47], [46]. A typical abstract machine manipulates a state that consists of a program in some environment of bindings and some evaluation co... |

320 |
λµ–calculus: an algorithmic interpretation of classical natural deduction
- Parigot
- 1992
(Show Context)
Citation Context ...trol 6.1.2.1. Delimited control and Λµ-calculus10 Activity Report INRIA 2009 In the continuation of his work with Silvia Ghilezan [4] on showing that Saurin’s variant Λµ [7] of Parigot’s λµ-calculus =-=[58]-=- for classical logic was a canonical call-by-name version of Danvy-Filinski’s call-by-value calculus of delimited control, Hugo Herbelin studied with Alexis Saurin and Silvia Ghilezan another variant ... |

300 | Definitional interpreters for higher-order programming languages
- Reynolds
- 1972
(Show Context)
Citation Context ...principle which provides classical logic. Control operators are operators used to jump from one place of a program to another place. They were first considered in the 60’s by Landin [49] and Reynolds =-=[60]-=- and started to be studied in an abstract way in the 80’s by Felleisen et al [37], culminating in Parigot’s λµ-calculus [57], a reference calculus that is in fine CurryHoward correspondence with class... |

235 | A formulae-as-types notion of control
- Griffin
- 1990
(Show Context)
Citation Context ...1. Control operators and classical logic Indeed, a significant extension of the Curry-Howard correspondence has been obtained at the beginning of the 90’s thanks to the seminal observation by Griffin =-=[43]-=- that some operators known as control operators were typable by the principle of double negation elimination (¬¬A ⇒ A), a principle which provides classical logic. Control operators are operators used... |

227 |
Une extension de l’interprétation de Gödel à l’analyse, et son application à l’elimination des coupures dans l’analyse et la théorie des types
- Girard
- 1971
(Show Context)
Citation Context ...gical system and a (typed) programming language [52]. In 1985, Coquand and Huet [30], [31] in the Formel team of INRIA-Rocquencourt explored an alternative approach based on Girard-Reynolds’ system F =-=[41]-=-, [61]. This formalism, called the Calculus of Constructions, served as logical foundation of the first implementation of Coq in 1984. Coq was called CoC at this time. 3.1.3. The Calculus of Inductive... |

161 | The duality of computation
- Curien, Herbelin
- 2000
(Show Context)
Citation Context ...eory of refinement type systems (intersection and union types, subtyping, etc.) in the presence of effects. 6.1.1.3. Focalisation and classical realizability Following the work of Curien and Herbelin =-=[3]-=- and Girard [42], Guillaume Munch–Maccagnoni gave a term syntax (Lfoc) for polarised classical logic (LKpol) and linear logic with strategies of reduction based on Girard’s classical logic LC. This ’f... |

160 |
A new constructive logic: Classical Logic
- Girard
- 1991
(Show Context)
Citation Context ...ent type systems (intersection and union types, subtyping, etc.) in the presence of effects. 6.1.1.3. Focalisation and classical realizability Following the work of Curien and Herbelin [3] and Girard =-=[42]-=-, Guillaume Munch–Maccagnoni gave a term syntax (Lfoc) for polarised classical logic (LKpol) and linear logic with strategies of reduction based on Girard’s classical logic LC. This ’focalising’ strat... |

129 | Representing monads
- Filinski
- 1994
(Show Context)
Citation Context ...nally encoded into a “stack”. 3.4.4. Delimited control Delimited control extends the expressiveness of control operators with effects: the fundamental result here is a completeness result by Filinski =-=[38]-=-: any side-effect expressible in monadic style (and this covers references, exceptions, states, dynamic bindings, ...) can be simulated in λ-calculus equipped with delimited control. 4. Application Do... |

108 |
Inductively defined types
- Coquand, Paulin-Mohring
(Show Context)
Citation Context ...ata types (a paragon of it being the type of list). In CoC, it was possible to simulate algebraic data types, but only through a not-so-natural not-so-convenient encoding. In 1989, Coquand and Paulin =-=[32]-=- designed an extension of the Calculus of Constructions with a generalisation of algebraic types called inductive types, leading to the Calculus of Inductive Constructions (CIC) that started to serve ... |

101 |
A set of postulates for the foundation of logic
- Church
- 1932
(Show Context)
Citation Context ...mmed out – a formalism that is both a logic and a programming language and that is at the source of the Coq system [29]. 3.1.2. Towards the calculus of constructions The λ-calculus, defined by Church =-=[28]-=-, is a remarkably succinct model of computation that is defined via only three constructions (abstraction of a program with respect to one of its parameters, reference to such a parameter, application... |

80 | The Why/Krakatoa/Caduceus platform for deductive program verification
- Filliâtre, Marché
- 2007
(Show Context)
Citation Context ...on. In collaboration with Philippe Audebaud (Plume/ENS-Lyon) and Christine Paulin-Mohring (LRI/INRIA Proval/UPS), Yann Régis-Gianas worked on proofs of probabilistic programs. He has extended the Why =-=[39]-=- proof system with randomized primitives in the programming language and predicates over random distributions in the specification language. Yann Régis-Gianas started some investigations about semanti... |

72 |
Constructions: A higher order proof system for mechanizing mathematics
- Coquand, Huet
(Show Context)
Citation Context ...accomplished by Martin-Löf who designed in 1971 a formalism, referred to as modern type theory, that was both a logical system and a (typed) programming language [52]. In 1985, Coquand and Huet [30], =-=[31]-=- in the Formel team of INRIA-Rocquencourt explored an alternative approach based on Girard-Reynolds’ system F [41], [61]. This formalism, called the Calculus of Constructions, served as logical founda... |

69 |
A lambda calculus structure isomorphic to Gentzen-style sequent calculus structure
- Herbelin
- 1995
(Show Context)
Citation Context ....1.4. Pure type systems in sequent calculus Hugo Herbelin and Vincent Siles investigated different formulations of pure type systems in sequent calculus building up on previous works by Hugo Herbelin =-=[5]-=- and Stéphane Lengrand [50], especially in connection to the problem of Expansion Postponement (see below). Vincent Siles summarised these investigations in a paper under consideration for submission.... |

58 |
Reasoning with continuations
- Felleisen, Friedman, et al.
- 1986
(Show Context)
Citation Context ... jump from one place of a program to another place. They were first considered in the 60’s by Landin [49] and Reynolds [60] and started to be studied in an abstract way in the 80’s by Felleisen et al =-=[37]-=-, culminating in Parigot’s λµ-calculus [57], a reference calculus that is in fine CurryHoward correspondence with classical natural deduction. In this respect, control operators are fundamental pieces... |

42 | Boomerang: resourceful lenses for string data
- Bohannon, Foster, et al.
- 2008
(Show Context)
Citation Context ...n collaboration with Hugo Heuzard (Master student, UPD), Yann Régis-Gianas worked on the mixing of two programming paradigms, namely functional reactive programming [55] and bidirectional programming =-=[27]-=-, to develop user interfaces with built-in operators working on interaction history. (For instance, the standard "undo" action is such an operator.) 6.3. Coq as a functional programming language Parti... |

41 |
Une Théorie des Constructions
- Coquand
- 1985
(Show Context)
Citation Context ...ing point to a large spectrum of researches and results contributing to deeply connect logic and computer science. In particular, it is from this line of work that Coquand’s Calculus of Constructions =-=[30]-=- stemmed out – a formalism that is both a logic and a programming language and that is at the source of the Coq system [29]. 3.1.2. Towards the calculus of constructions The λ-calculus, defined by Chu... |

29 | The Implicit Calculus of Constructions as a Programming Language with Dependent Types
- Barras, Bernardo
- 2008
(Show Context)
Citation Context ...c information (types and proof objects) is transparent and does not affect the computational behavior. Bruno Bernardo has already defined a formalism and studied an Implicit Calculus of Constructions =-=[1]-=-. Next step is to add Σ-types to the system by extending Alexandre Miquel’s models based on coherence spaces [54] in order to prove the consistency and the strong normalisation property of the system.... |

25 | A call-by-name lambda calculus machine
- Krivine
- 2007
(Show Context)
Citation Context ...guages and the computer microprocessor. The typical reference for call-by-value evaluation of λ-calculus is Landin’s SECD machine [48] and Krivine’s abstract machine for call-by-name evaluation [47], =-=[46]-=-. A typical abstract machine manipulates a state that consists of a program in some environment of bindings and some evaluation context traditionally encoded into a “stack”. 3.4.4. Delimited control D... |

22 | Recursive polymorphic types and parametricity in an operational framework
- Melliès, Vouillon
- 2005
(Show Context)
Citation Context ...ty could further be seen as a tool (looking like Pitts’ logical relations [59]) for the study of programming languages: • Provided one accepts the Adequacy Lemma as an argument for type safety (as in =-=[53]-=-), it gives concise and modular proofs of type safety in the presence of polymorphism, sub-typing and inductive algebraic types, including in CBV. • It can be used to derive certain parametricity resu... |

19 |
Le Calcul des Constructions Implicite: Syntaxe et Sémantique. Theèses de Doctorat, Université
- Miquel
- 2001
(Show Context)
Citation Context ...nardo has already defined a formalism and studied an Implicit Calculus of Constructions [1]. Next step is to add Σ-types to the system by extending Alexandre Miquel’s models based on coherence spaces =-=[54]-=- in order to prove the consistency and the strong normalisation property of the system. This is joint work with Bruno Barras, researcher of the Typical team and PhD advisor of Bruno Bernardo. 6.2.3. P... |

14 | A Hoare logic for call-by-value functional programs
- Régis-Gianas, Pottier
- 2008
(Show Context)
Citation Context ...ion with François Pottier (INRIA Gallium) about proofs of higherorder programs using Hoare Logic. They have submitted a long version of the paper “A Hoare Logic for Call-By-Value Functional Programs” =-=[6]-=- to a journal. An extension of this system with generalized algebraic datatypes and a machine-checked proof of its metatheory are in preparation. In collaboration with Philippe Audebaud (Plume/ENS-Lyo... |

14 |
Pure type systems with judgemental equality
- Adams
(Show Context)
Citation Context ...d main kind of way in which type theory can be presented. The connection between the “declarative” and “typed equality” presentations has been open for many years before being proved in 2006 by Adams =-=[24]-=- for a large set of type theories, called “functional”. Unfortunately, the CIC is not functional and the result of Adams does not apply to Coq. Unfortunately also, the only known set-theoretical model... |

13 |
The formulae-as-types notion of construction. To HB Curry: essays on combinatory logic, lambda calculus and formalism
- Howard
- 1980
(Show Context)
Citation Context ...tion. Proof theory gained a remarkable importance in computer science when it became clear, after genuine observations first by Curry in 1958 [34], then by Howard and de Bruijn at the end of the 60’s =-=[44]-=-, [63], that proofs had the very same structure as programs: for instance, natural deduction proofs can be identified as typed programs of the ideal programming language known as λ-calculus. This proo... |

12 | A Simple Proof Technique for Certain Parametricity Results, in "ICFP
- CRARY
- 1999
(Show Context)
Citation Context ...ular proofs of type safety in the presence of polymorphism, sub-typing and inductive algebraic types, including in CBV. • It can be used to derive certain parametricity results in the manner of Crary =-=[33]-=-. • Properties of ’internal completeness’ allow one to prove additional equalities of types (such as the ’shocking equalities’ of polymorphism). Paul-André Melliès (from PPS) and Guillaume Munch–Macca... |

9 | Normalisation & Equivalence in Proof Theory & Type Theory
- Lengrand
- 2006
(Show Context)
Citation Context ... sequent calculus Hugo Herbelin and Vincent Siles investigated different formulations of pure type systems in sequent calculus building up on previous works by Hugo Herbelin [5] and Stéphane Lengrand =-=[50]-=-, especially in connection to the problem of Expansion Postponement (see below). Vincent Siles summarised these investigations in a paper under consideration for submission. 6.1.2. On the logical cont... |

9 |
Free Deduction: An Analysis of ”Computations
- Parigot
- 1990
(Show Context)
Citation Context ...r place. They were first considered in the 60’s by Landin [49] and Reynolds [60] and started to be studied in an abstract way in the 80’s by Felleisen et al [37], culminating in Parigot’s λµ-calculus =-=[57]-=-, a reference calculus that is in fine CurryHoward correspondence with classical natural deduction. In this respect, control operators are fundamental pieces of the full connection between proofs and ... |

8 |
An approach to call-by-name delimited continuations
- Herbelin, Ghilezan
- 2008
(Show Context)
Citation Context ...ation for submission. 6.1.2. On the logical contents of delimited control 6.1.2.1. Delimited control and Λµ-calculus10 Activity Report INRIA 2009 In the continuation of his work with Silvia Ghilezan =-=[4]-=- on showing that Saurin’s variant Λµ [7] of Parigot’s λµ-calculus [58] for classical logic was a canonical call-by-name version of Danvy-Filinski’s call-by-value calculus of delimited control, Hugo He... |

8 |
Une étude logique du contrôle (appliquée à la programmation fonctionnelle et logique
- Saurin
- 2008
(Show Context)
Citation Context ... establishes a standardization theorem and characterizes solvability for the Λµ-calculus [7] and introduces Böhm trees for Λµ-calculus. Those two works develop previous works by the author alone [7], =-=[10]-=-, [8], [11]. Other current research work of Alexis Saurin, besides the on-going one mentioned above with Ghilezan and Herbelin, concerns a calculus for streams (in collaboration with Marco Gaboardi fr... |

7 |
Vèrification formelle d’un compilateur pour langages fonctionnels
- Dargaye
- 2009
(Show Context)
Citation Context ...t Coq system, similar to the existing one, but that would also generate correctness proofs of the generated programs. The target language is ML, which is a source language considered by Z. Dargaye in =-=[35]-=-. The semantics of the target language is formalized in Coq, but the semantics of the source language—in which correctness proofs are stated—is left implicit. Stéphane Glondu investigated several ways... |

6 | An operational account of call-by-value minimal and classical lambda-calculus in “natural deduction” form
- Herbelin, Zimmermann
- 2009
(Show Context)
Citation Context ...h and without control) that is both complete with respect to the continuation-passingstyle semantics of call-by-value and confluent. This has been presented to the 2009 edition of the TLCA conference =-=[14]-=-.Project-Team π.r 2 9 6.1.1.2. Focalisation Alexis Saurin has investigated how the focalization theorem of linear logic can be proved by interactive means in Girard’s Ludics (in Terui’s Computational... |

5 |
The differential lambda-calculus. Theor
- Ehrhard, Regnier
(Show Context)
Citation Context ...h that A(t) holds. 6.1.2.3. Differential linear logic and a logical interpretation of statically bound exceptions Guillaume Munch–Maccagnoni developed a symmetric syntax for Differential Linear Logic =-=[36]-=- inspired by the linear-non-linear adjunction of linear logic. This syntax allowed him to give a logical interpretation of statically bound exceptions using primitives from differential linear logic. ... |

4 | Forcing-based cut-elimination for gentzen-style intuitionistic sequent calculus
- Herbelin, Lee
- 2009
(Show Context)
Citation Context ... and Gyesik Lee (ROPAS Center, Seoul University) presented their work on a simple proof of Kripke completeness for the negative fragment of intuitionistic logic to the 2009 edition of WOLLIC workshop =-=[13]-=-. This work provides an interesting case study on the representation of binders in Coq. This resulted in a paper submitted to the Special Issue on Binding, Substitution and Naming edited by C. Urban a... |

4 |
Un interpréteur du lambda-calcul
- Krivine
- 1985
(Show Context)
Citation Context ...ng languages and the computer microprocessor. The typical reference for call-by-value evaluation of λ-calculus is Landin’s SECD machine [48] and Krivine’s abstract machine for call-by-name evaluation =-=[47]-=-, [46]. A typical abstract machine manipulates a state that consists of a program in some environment of bindings and some evaluation context traditionally encoded into a “stack”. 3.4.4. Delimited con... |

3 |
On the Relations between the Syntactic Theories of λµ-Calculi
- Saurin
- 2008
(Show Context)
Citation Context ...lishes a standardization theorem and characterizes solvability for the Λµ-calculus [7] and introduces Böhm trees for Λµ-calculus. Those two works develop previous works by the author alone [7], [10], =-=[8]-=-, [11]. Other current research work of Alexis Saurin, besides the on-going one mentioned above with Ghilezan and Herbelin, concerns a calculus for streams (in collaboration with Marco Gaboardi from To... |

3 |
Kripke models for classical logic
- Ilik, Lee, et al.
(Show Context)
Citation Context ... and Gyesik Lee gave a new kind of direct semantics for classical logic, similar to Kripke models, and proved constructively that it is sound and complete for first-order logic. They submitted a paper=-=[18]-=-, which was conditionally accepted.Project-Team π.r 2 11 They also formalised the proofs in the Coq proof assistant, allowing them to do experiments on the operational behaviour of the semantics, con... |

3 |
λµ-calculus and Λµ-calculus: a Capital Difference
- Herbelin, Saurin
- 2010
(Show Context)
Citation Context ...variant of λµ-calculus by de Groote has been conducted by Hugo Herbelin and Alexis Saurin resulting in a conditional acceptance to a special issue of the APAL journal on Computational Classical logic =-=[20]-=-. Alexis Saurin submitted two articles to international conferences since he joined the team: the first one [22] introduces a hierarchy of calculi for delimited control in call-by-name (that is a CBN ... |

2 |
Towards Ludics Programming: Interactive Proof Search, in "ICLP 2008
- SAURIN
(Show Context)
Citation Context ...s the on-going one mentioned above with Ghilezan and Herbelin, concerns a calculus for streams (in collaboration with Marco Gaboardi from Torino), an interactive approach to proof search using ludics =-=[9]-=-, and the logical understanding of intersection types with Simona Ronchi della Rocca. 6.1.2.2. Control delimiters and Markov’s principle In the last months, Hugo Herbelin discovered a relation between... |

2 |
A Hierarchy for Delimited Control in Call-by-Name
- Saurin
- 2010
(Show Context)
Citation Context ...onal acceptance to a special issue of the APAL journal on Computational Classical logic [20]. Alexis Saurin submitted two articles to international conferences since he joined the team: the first one =-=[22]-=- introduces a hierarchy of calculi for delimited control in call-by-name (that is a CBN correspondent to DanvyFilinski’s CPS hierarchy) and has been accepted to FOSSACS 2010 while the second one [23] ... |

2 |
DEVELOPMENT TEAM. The Coq Reference Manual, version 8.2
- COQ
- 2008
(Show Context)
Citation Context ...cular, it is from this line of work that Coquand’s Calculus of Constructions [30] stemmed out – a formalism that is both a logic and a programming language and that is at the source of the Coq system =-=[29]-=-. 3.1.2. Towards the calculus of constructions The λ-calculus, defined by Church [28], is a remarkably succinct model of computation that is defined via only three constructions (abstraction of a prog... |

2 |
Call-by-Push-Value: A Subsuming Paradigm, in "TLCA
- LEVY
- 1999
(Show Context)
Citation Context ...es strict (positive) and lazy (negative) programs, and thus encompasses with a single deterministic strategy both call-by-value and call-by-name, in the spirit of Paul Blain Levy’s call-by-push-value =-=[51]-=-, however in direct style. Further syntactical investigations on this theme, establishing links with Zeilberger’s work and with ludics, have been carried out in joint work between Pierre-Louis Curien ... |

1 |
On the Meaning of Focalization, in "(informal
- BASALDELLA, SAURIN, et al.
(Show Context)
Citation Context ...isation Alexis Saurin has investigated how the focalization theorem of linear logic can be proved by interactive means in Girard’s Ludics (in Terui’s Computational Ludics setting [62]) , resulting in =-=[2]-=-, which has since been improved and submitted to an international conference in early november [21]. Connections with algorithmic complexity are discussed since focalization in the framework of comput... |

1 |
Separation with Streams in the Λµ-calculus, in "Symposium on Logic
- SAURIN
- 2005
(Show Context)
Citation Context ...cal contents of delimited control 6.1.2.1. Delimited control and Λµ-calculus10 Activity Report INRIA 2009 In the continuation of his work with Silvia Ghilezan [4] on showing that Saurin’s variant Λµ =-=[7]-=- of Parigot’s λµ-calculus [58] for classical logic was a canonical call-by-name version of Danvy-Filinski’s call-by-value calculus of delimited control, Hugo Herbelin studied with Alexis Saurin and Si... |

1 |
Typing Streams in the Λµ-calculus, in "ACM
- SAURIN
(Show Context)
Citation Context ...s a standardization theorem and characterizes solvability for the Λµ-calculus [7] and introduces Böhm trees for Λµ-calculus. Those two works develop previous works by the author alone [7], [10], [8], =-=[11]-=-. Other current research work of Alexis Saurin, besides the on-going one mentioned above with Ghilezan and Herbelin, concerns a calculus for streams (in collaboration with Marco Gaboardi from Torino),... |

1 |
The duality of computation under focus, in "Higher Order and Symbolic Computation", 2010, in preparation for a special issue
- CURIEN, MUNCH-MACCAGNONI
(Show Context)
Citation Context ...th ludics, have been carried out in joint work between Pierre-Louis Curien and Guillaume Munch–Maccagnoni, and are to be written down for a special issue of the journal HOSC in honour of Peter Landin =-=[12]-=-. Guillaume Munch–Maccagnoni has extended Krivine’s classical realisability [45] to Lfoc, and therefore to CBV in particular. He showed that these tools concisely account for “imperfections” (Zeilberg... |

1 |
Focalisation and Classical Realisability, in "Computer Science Logic ’09
- MUNCH-MACCAGNONI
(Show Context)
Citation Context ...th effect such as the value restriction required for the polymorphism in CBV to be a sound principle. This work led to a paper which was accepted to the CSL’09 conference during his Master internship =-=[15]-=-. Guillaume Munch–Maccagnoni then showed during his internship how classical realizability could further be seen as a tool (looking like Pitts’ logical relations [59]) for the study of programming lan... |