systematic development of programs for parallel and cloud ... · joint work with (alphabetical...

Systematic Development of Programsfor Parallel and Cloud Computing:

Towards a FrameworkNII Lectures Series

Frederic Loulergue

Universite d’Orleans – LIFO – PaMDA Team

October-November 2013

F. Loulergue SyDPaCC – Towards a Framework – Lecture 1 October-November 2013 1 / 63

Joint Work with (alphabetical order)

I Dr. Wadoud Bousdira (Universite d’Orleans)I Dr. Frederic Dabrowski (Universite d’Orleans)I Sylvain Dailler (KUT & Universite d’Orleans)I Dr. Kento Emoto (Kyushu University of Technology)I Pr. Zhenjiang Hu (National Institute of Informatics)I Dr. Sylvain Jubertie (Universite d’Orleans)I Dr. Hab. Frederic Gava (Universite Paris-Est Creteil)I Dr. Louis Gesbert (OCamlPro)I Hideki Hashimoto (The University of Tokyo)I Joeffrey Legaux (Universite d’Orleans)I Dr. Kiminori Matsuzaki (Kochi University of Technology)I Dr. Virginia Niculescu (Babes-Bolyai University of Cluj-Napoca)I Thomas Pinsard (Universite d’Orleans)I Simon Robillard (Universite d’Orleans)I Pr. Masato Takeichi (The University of Tokyo)I Dr. Julien Tesson (Universite Paris-Est Creteil)

Universite d’Orleans, LIFO

Outline

1 Motivations and BackgroundOur GoalParallel ProgrammingProgram Correctness

2 Systematic Development of Programs for Parallel and Cloud Computing3 An Overview of Next Lectures

Lecture 2: Program Verification with the Coq Proof AssistantLecture 3: Parallel Programming in CoqLecture 4: Constructive Algorithms in CoqLecture 5: PowerLists in CoqLecture 6: Bulk Synchronous Parallel HomomorphismsLecture 7: Generate-Test-Aggregate in Coq

4 Summary5 Bibliography

Outline

Our Goal

To ease the development of correctand verified parallel programs

with predictable performances

using theories and tools to allowa user to develop an application

by using building blocks andimplementing short programs satisfying

conditions easily or automatically proved

Our Goal

To ease the development of correctand verified parallel programs

with predictable performances

using theories and tools to allowa user to develop an application

by using building blocks andimplementing short programs satisfying

conditions easily or automatically proved

Outline

Parallel Programming

AutomaticParallelization

Structured Parallelism

I Algorithmic Skeletons

I Bridging Models

I Declarative Parallel Programming

I . . .

Concurrent &Distributed

Programming

I Bridging Models

I . . .

Programming

I Bridging Models

I . . .

Programming

I Bridging Models

I . . .

Programming

Parallel Programming – Bridging Models I

Bridging Model

I Leslie Valiant in his 1990 CACM paper“A Bridging Model for Parallel Computation”http://dx.doi.org/10.1145/79173.79181

The von Neumann model is the connecting bridgethat enables programs from the diverse and chaoticworld of software to run efficientby on machinesfrom the diverse and chaotic world of hardware

I Valiant’s proposal: Bulk Synchronous Parallelism (BSP)

I Other models: LogP and variants, BSP variants, . . .

Parallel Programming – Bridging Models II

Research on BSP90’ by Valiant & McColl

Three models

I abstract architecture

I execution model

I cost model

BSP computerI p processor / memory pairs

(of speed r)I a communication network

(of speed g)I a global synchronisation unit

(of speed L)

Execution model

Cost modelT (s) = max0≤i<p wi + h × g + L

where h = max0≤i<p{h+i , h

−i }

Parallel Programming – Bridging Models III

Applications

I scientific computation [3]

I genetic algorithms [4]

I genetic programming [7]

I neural networks [18]

I parallel databases [1]

I parallel constraints solvers [10]

I . . .

Parallel Programming – Algorithmic Skeletons

Algorithmic Skeletons

I Coined by Murray Cole inAlgorithmic Skeletons: Structured Managementof Parallel Computation, MIT Press, 1989http://homepages.inf.ed.ac.uk/mic/Pubs/skeletonbook.ps.gz

I Popular skeletons: Google’s MapReduce

Skeletal Parallelism

I Skeleton = pattern of a parallel algorithmfamiliar sequential semantics

I Program = composition of skeletons

Algorithmic Skeletons

I Coined by Murray Cole inAlgorithmic Skeletons: Structured Managementof Parallel Computation, MIT Press, 1989http://homepages.inf.ed.ac.uk/mic/Pubs/skeletonbook.ps.gz

I Popular skeletons: Google’s MapReduce

Skeletal Parallelism

I Skeleton = higher-order function implemented in parallelfamiliar sequential semantics

I Program = composition of skeletons

Libraries of Algorithmic Skeletons

I For C++: SkeTo1, OSL2, Muesli, QUAFF, . . .

I For C: eSkel, SKElib

I For Java: Lithium, Muskel, Calcium, . . .I For functional languages:

I OCaml: OCamlP3L, ParmapI Erlang: SkelI Haskell: HaskSkel, Edenskeletons

Algorithmic Skeletons Theory

I List homomorphisms for parallel programming (Cole 1993)

I Many further developments in particular in Tokyo

1http://sketo.ipl-lab.org2http://traclifo.univ-orleans.fr/OSL

An Example: Variance

n−1∑k=0

(xk −1

n−1∑k=0

Variance as an OSL Program

double avg = reduce(plus<double>(), x) / x.getSize();

double variance =

reduce(plus<double>(),

map(bind(minus<double>(),avg, _2), x));

Outline

Program Correctness?

Program Verification I

Verification MethodsSome properties:

I Model checking

I Static analysis in particular abstract interpretation

Functional correctness {P} c {Q}:I interactive provers:

I CoqI Isabelle/HOL

I deductive program verification:verification condition generator + (SMT) solvers

I Why3I Boogie

Program Verification II

The seL4 operating system kernel Klein et al. [12]

Design Cycle

Haskell Prototype

Design

Formal Executable Spec

High-Performance C ImplementationUser Programs

Hardware Simulator

ProofManual

Implementation

Figure 1: The seL4 design process

prototype in a near-to-realistic setting, we link itwith software (derived from QEMU) that simulatesthe hardware platform. Normal user-level executionis enabled by the simulator, while traps are passedto the kernel model which computes the result ofthe trap. The prototype modifies the user-level stateof the simulator to appear as if a real kernel hadexecuted in privileged mode.

This arrangement provides a prototyping environ-ment that enables low-level design evaluation fromboth the user and kernel perspective, including low-level physical and virtual memory management. Italso provides a realistic execution environment that isbinary-compatible with the real kernel. For example,we ran a subset of the Iguana embedded OS [37] onthe simulator-Haskell combination. The alternativeof producing the executable specification directlyin the theorem prover would have meant a steeplearning curve for the design team and a much lesssophisticated tool chain for execution and simulation.

We restrict ourselves to a subset of Haskell thatcan be automatically translated into the languageof the theorem prover we use. For instance, we donot make any substantial use of laziness, make onlyrestricted use of type classes, and we prove that allfunctions terminate. The details of this subset aredescribed elsewhere [19,41].

While the Haskell prototype is an executable modeland implementation of the final design, it is not thefinal production kernel. We manually re-implementthe model in the C programming language for severalreasons. Firstly, the Haskell runtime is a significantbody of code (much bigger than our kernel) whichwould be hard to verify for correctness. Secondly, theHaskell runtime relies on garbage collection which isunsuitable for real-time environments. Incidentally,the same arguments apply to other systems based ontype-safe languages, such as SPIN [7] and Singular-ity [23]. Additionally, using C enables optimisation ofthe low-level implementation for performance. Whilean automated translation from Haskell to C wouldhave simplified verification, we would have lost most

Abstract Specification

Executable Specification

High-Performance C Implementation

Haskell Prototype

Isabelle/HOL

Automatic Translation

Refinement Proof

Figure 2: The refinement layers in the verification ofseL4

opportunities to micro-optimise the kernel, which isrequired for adequate microkernel performance.

2.3 Formal verification

The technique we use for formal verification is inter-active, machine-assisted and machine-checked proof.Specifically, we use the theorem prover Isabelle/HOL[50]. Interactive theorem proving requires humanintervention and creativity to construct and guidethe proof. However, it has the advantage that it isnot constrained to specific properties or finite, feasi-ble state spaces, unlike more automated methods ofverification such as static analysis or model checking.

The property we are proving is functional correct-ness in the strongest sense. Formally, we are showingrefinement [18]: A refinement proof establishes acorrespondence between a high-level (abstract) anda low-level (concrete, or refined) representation of asystem.

The correspondence established by the refinementproof ensures that all Hoare logic properties of theabstract model also hold for the refined model. Thismeans that if a security property is proved in Hoarelogic about the abstract model (not all security prop-erties can be), refinement guarantees that the sameproperty holds for the kernel source code. In thispaper, we concentrate on the general functional cor-rectness property. We have also modelled and provedthe security of seL4’s access-control system in Is-abelle/HOL on a high level. This is described else-where [11,21], and we have not yet connected it tothe proof presented here.

Fig. 2 shows the specification layers used in theverification of seL4; they are related by formal proof.Sect. 4 explains the proof and each of these layers indetail; here we give a short summary.

The top-most layer in the picture is the abstractspecification: an operational model that is the main,complete specification of system behaviour. Theabstract level contains enough detail to specify theouter interface of the kernel, e.g., how system-callarguments are encoded in binary form, and it de-

from [12]

I Proof assistant: Isabelle/HOL

I Memory model: Sequential Consistency

Program Verification III

Verified compilation

Target Language

Syntax:

OperationalSemantics:

Source Language

Syntax:

OperationalSemantics:

ProgramAST

Programexecution

Proof of SemanticPreservation

Compilation Pass

Program Verification IV

The Compcert [13] and CompcertTSO Compilers [19]

from http://compcert.inria.fr

I Proof assistant: CoqI Transformation passes are proved to preserve semanticsI The compiler is extracted from the formal developmentI CompcertTSO: a first step towards parallelism

Program Refinement & Program Calculation

B Method

Abstract Model(B language)

⇓Refined Model

(B language)⇓...

Concrete Model(B language)

⇓Programming Language

Source Code

Program Calculation

Problem Specification⇓

Derivation based onTransformation Theory

⇓Optimised Algorithm

⇓Programming Language

Source Code

Verification of Parallel Programs?

I Functional correctness:I concurrent extension of CI BSP-Why

I Some properties:I MPI in TLA+I . . .

Outline

SyDPaCC – Systematic Development of Programsfor Parallel and Cloud Computing

SyDPaCC: Program Development

Past and Ongoing Projects

SDPP (J. Tesson PhD) PAPDAS

Task 1ALGORITHMIC SKELETONS

BASED ON CONSTRUCTIVE ALGORITHMS

Task 3A VERIFIED COMPILER

FOR ATOMIC SECTIONS C

Program generation: Atomic Sections C

Certified Compiler in Coq

Certified Parallel Programsassembly code

+ system calls for parallelism and/or communications

Derivation based on proved transformation theory

Problem specification

Algorithm as composition ofAlgorithmic Skeletons

Task 2EFFICIENT C++ALGORITHMIC

SKELETON LIBRARIES

SkeTo(C++)

OSLPrototype(Coq&BSML)

OSL(C++)

Algorithmic Skeletons Verified in Coq

BSMLAxiomatisation

Parallel Programsassembly code

Certified Parallel Programsassembly code

OCaml Source Code

BSMLImplemention

Outline

The Coq Proof Assistant I

ACM SIGPLAN Software Award 2013The Coq proof assistant provides a rich environment forinteractive development of machine-checked formalreasoning. Coq is having a profound impact on research onprogramming languages and systems [. . . ] It has beenwidely adopted as a research tool by the programminglanguage research community [. . . ] Last but not least,these successes have helped to spark a wave of widespreadinterest in dependent type theory, the richly expressivecore logic on which Coq is based.

[. . . ] The Coq team continues to develop the system,bringing significant improvements in expressiveness andusability with each new release.

In short, Coq is playing an essential role in our transitionto a new era of formal assurance in mathematics,semantics, and program verification.

The Coq Proof Assistant II

Foundations

I Calculus ofinductiveconstructions

I Curry-Howardcorrespondance

The Coq Proof Assistant III

Natural Deduction

(v)A ∈ Γ

Γ ` A

(l)Γ,A ` B

Γ ` A→ B

(a)Γ ` A→ B Γ ` A

Γ ` B

Simply Typed λ-Calculus

(V )x : A ∈ Γ

Γ ` x : A

(L)Γ, x : A ` e : B

Γ ` (λx :A.e) : A→ B

(A)Γ ` e : A→ B Γ ` e′ : A

Γ ` (e e′) : B

The Coq Proof Assistant IV

Curry-Howard IsomomorphismFor all formula there exists a proof of this formula in natural deduction ifand only if there exists a λ-term that has this formula as type.

I Theorem statement ⇔ Type

I Proof ⇔ Program

Coq in practice

I Functional programming language

I Rich type system: allow to express logical properties

I Language for building proofs (ie proof terms)

I Program extraction

The Coq Proof Assistant V

The Lecture

I Functional programming in Coq

I Writing specifications

I Proving correctness

I Program extraction

Outline

Parallel Programming in Coq I

High-level Building Blocks

I Candidates: algorithmic skeletons

I How to implement them?

with Bulk Synchronous Parallel ML (BSML)a dialect/library for OCaml

I How to prove the correctness of the implementation?

using the Coq Proof Assistant

Parallel Programming in Coq I

High-level Building Blocks

I Candidates: algorithmic skeletons

I How to implement them?with Bulk Synchronous Parallel ML (BSML)a dialect/library for OCaml

I How to prove the correctness of the implementation?using the Coq Proof Assistant

Parallel Programming in Coq II

The Bulk Synchronous Parallel ML Approach

I an efficient functional programming language with formalsemantics and easy reasoning about the performance ofprograms (strict evaluation):

ML (Objective Caml flavor)

I a restricted model of parallelism with no deadlock, verylimited cases of non-determinism, a simple cost model:

Bulk Synchronous Parallelism

The result is:Bulk Synchronous Parallel ML (BSML)

Parallel Programming in Coq III

Bulk Synchronous Parallel ML

Design principles:

I Small set of parallel primitives

I Universal for bulk synchronous parallelism

I Global view of programs

I Simple formal semantics

a sequential functional language

+ a parallel data structure (non nestable)

+ parallel operations on this data structure

Papers and software

I http://traclifo.univ-orleans.fr/BSML

Parallel Programming in Coq IV

The Lecture

I Tutorial on programming with BSML

I BSML in Coq

I Reasoning about BSML programs in Coq

I Applications and experiments

Based on [21, 20]

Outline

Constructive Algorithms in Coq IProgram calculation

maximum = hd � sort.

if law :8 f,f (if a then b else c)= if a then f b else f c

maximum (a :: x)= { def. of maximum }

hd (sort (a :: x))= { def. of sort }

hd (if a > hd(sort x) then a :: sort xelse hd(sort x) :: insert a (tail(sort x)))

= { by if law }if a > hd(sort x) then hd(a : sort x)else hd(hd(sort x) :: insert a (tail(sort x)))

= { def. of hd }if a > hd(sort x) then a else hd(sort x)

= { def. of maximum }if a > maximum x then a else maximum x

= { define x " y = if x > y then x else y }a " (maximum x)

Tesson, Hashimoto, Hu, Loulergue, Takeichi Program Calculation in Coq AMAST, June 2010 4 / 30

Constructive Algorithms in Coq IIExample

Lemma maximum over list :8 a x d ,

maximum d (a::x) = if a ?> (maximum a x) then a else maximum a x .Proof.Begin.LHS

= { by def maximum}(hd d (sort (a::x)) ).

= { unfold sort }(hd d (if a ?> (hd a (sort x)) then a::(sort x)else (hd a (sort x))::(insert a (tail (sort x))))).

={ rewrite (if law (hd d))}(if a ?> hd a (sort x) then hd d (a :: (sort x))else hd d (hd a (sort x) :: insert a (tail (sort x)))) .

={ by def hd ; simpl if }(if a ?> hd a (sort x) then a else hd a (sort x)) .

={by def maximum}(if a ?> (maximum a x) then a else maximum a x).

[].Qed.

Tesson, Hashimoto, Hu, Loulergue, Takeichi Program Calculation in Coq AMAST, June 2010 9 / 30

Constructive Algorithms in Coq III

Correct ParallelisationParallelisation correcte

Parallelisation correcte composable

J. Tesson, Developpement et preuve de correction de programmes paralleles fonctionnels. soutenance, 2011 23 / 52

Constructive Algorithms in Coq IV

The Lecture

I Program calculation in Coq

I Examples

I Correct parallelisation

I Application to BSML skeletons/applications

Based on [21, 20]

Outline

Powerlists in Coq I

Powerlists J. Misra

I singleton powerlistI p, q powerlists of the same length:

I tie: p|q concatenation of p and q,I zip: p 1 q alternating items from p and q

Powerlists in Coq II

Powerlist laws

I L0 (identical base cases): 〈x〉|〈y〉 = 〈x〉 1 〈y〉I L1 (dual deconstruction): P a non-singleton powerlist there exist

r , s, u, v such that:(a) P = r | s(b) P = u 1 v

I L2 (unique deconstruction):(a) (〈x〉 = 〈y〉) ≡ (x = y)(b) (p | q = u|v) ≡ (p = u ∧ q = v)(c) (p 1 q = u 1 v) ≡ (p = u ∧ q = v)

I L3 (commutativity):(p | q) 1 (u | v) = (p 1 u) | (q 1 v)

Powerlists in Coq III

The Lecture

I Powerlist axiomatisation in Coq

I Programming with powerlists in Coq

I Reasoning about powerlists in Coq

I Applications

Based on [15, 14]

Outline

Bulk Synchronous Parallel Homomorphisms I

BSP Homomorphism

118 Chapitre 7. Parallélisation correcte avec l’homomorphisme BSP

la fonction au résultat de son application sur un ensemble de sous-listes correspondprécisément à la définition d’un homomorphisme.

La dernière étape consiste finalement en l’application du calcul local décrit pré-cédemment, en utilisant les résumés globaux obtenus après les calculs précédentscomme éléments l et r. Le lien entre BH et le modèle BSP devient explicite à la vuede ce schéma : dans ce calcul nous avons une première phase de calculs locaux, suivied’une phase de communication globale, puis d’une dernière phase de calculs locaux,ce schéma peut donc directement s’exprimer sous la forme de super-étapes BSP.

0 i p � 1

BHseq BHseq BHseq

BHSteps

Calculdes résuméspar g1 et g2

Communications

Fusion des résuméspar � et ⌦

Calcul de BHlocal

Figure 7.2 – Calcul de BH en parallèle

7.1.2 Transformation d’une fonction mapAround en BH

Les homomorphismes BSP sont très puissants car ils permettent de paralléliser uncalcul de manière correcte, cependant il est difficile de transformer la spécificationd’un programme en un BH. Au lieu de vérifier directement qu’une fonction donnéepuisse être exprimée sous la forme d’un BH, nous pouvons utiliser une représenta-tion intermédiaire beaucoup plus facile à manipuler intuitivement faisant appel ausquelette mapAround.

Cette fonction proche de map exprime elle aussi des calculs indépendants sur leséléments d’une liste, mais permet d’exprimer des calculs plus complexes faisant in-tervenir l’ensemble des éléments de la liste. Intuitivement, mapAround applique unefonction séparément pour chacun des éléments d’une liste, mais cette fonction pourraextraire des informations des sous-listes à gauche et à droite de l’élément considéré

Bulk Synchronous Parallel Homomorphisms II

Applications

I Tower building xL x1 x2 x3 xi xn−1 xn xR

hL h1h2

hn−1 hnhR

· · · · · ·

I Array packing

pack p [x0, . . . , xn]= [ xi0 , . . . , xim︸︷︷︸∀x . p x= true

, xk0 , . . . , xkm′︸︷︷︸∀x . p x= false

I All nearest smaller valuesansv [3, 1, 4, 1, 5, 9, 2]= [(⊥, 1), (⊥,⊥), (1, 1),

(⊥,⊥), (1, 2), (5, 2), (1,⊥)]

I Sparse matrix-vector multiplication

Bulk Synchronous Parallel Homomorphisms III

The Lecture

I BSP homomorphisms theory

I BSP homomorphisms in CoqI The BH skeleton:

I in CoqI in OSL

I Applications

Outline

Generate-Test-Aggregate in Coq I

Generate-Test-Aggregate K. Emoto, S. Fischer, Z. Hu

User’s perspective:

G Generator to produce all candidates

T Tester for validity check of candidates

A Aggregator to build the final result

Optimization:

I Filter embedding: G T A ⇒ G A

I Semiring Fusion: G A ⇒ D&C

Generate-Test-Aggregate in Coq II

The Lecture

I Overview of GTAI GTA in Coq:

I Data structuresI GTA optmisation theoremI Support for automatic parallelisationI Program extraction?

Based on [8, 9] and ongoing work

Outline

Bibliography I

[1] M. Bamha and M. Exbrayat. Pipelining a Skew-Insensitive ParallelJoin Algorithm. Parallel Processing Letters, 13(3):317–328, 2003.

[2] Y. Bertot and P. Casteran. Interactive Theorem Proving andProgram Development. Springer, 2004.

[3] R. Bisseling. Parallel Scientific Computation. A structured approachusing BSP and MPI. Oxford University Press, 2004.

[4] A. Braud and C. Vrain. A parallel genetic algorithm based on theBSP model. In Evolutionary Computation and Parallel ProcessingGECCO & AAAI Workshop, Orlando (Florida), USA, 1999.

[5] M. Cole. Algorithmic Skeletons: Structured Management of ParallelComputation. MIT Press, 1989. Available athttp://homepages.inf.ed.ac.uk/mic/Pubs.

[6] M. Cole. Parallel Programming with List Homomorphisms. ParallelProcessing Letters, 5(2):191–203, 1995.

Bibliography II

[7] D. C. Dracopoulos and S. Kent. Speeding up genetic programming:A parallel BSP implementation. In First Annual Conference onGenetic Programming. MIT Press, July 1996.

[8] K. Emoto, S. Fischer, and Z. Hu. Generate, Test, and Aggregate –A Calculation-based Framework for Systematic ParallelProgramming with MapReduce. In ESOP, volume 7211 of LNCS,pages 254–273. Springer, 2012. doi:10.1007/978-3-642-28869-2 13.

[9] K. Emoto, S. Fischer, and Z. Hu. Filter-embedding semiring fusionfor programming with MapReduce. Formal Asp. Comput., 24(4-6):623–645, 2012. doi:10.1007/s00165-012-0241-8.

[10] L. Granvilliers, G. Hains, Q. Miller, and N. Romero. A system forthe high-level parallelization and cooperation of constraint solvers.In Y. Pan, S. G. Akl, and K. Li, editors, Proceedings of InternationalConference on Parallel and Distributed Computing and Systems(PDCS), pages 596–601, Las Vegas, USA, 1998. IASTED/ACTAPress.

Bibliography III

[11] Z. Hu, H. Iwasaki, and M. Takechi. Formal derivation of efficientparallel programs by construction of list homomorphisms. ACMTrans. Program. Lang. Syst., 19(3):444–461, 1997. ISSN0164-0925. doi:10.1145/256167.256201.

[12] G. Klein, K. Elphinstone, G. Heiser, J. Andronick, D. Cock,P. Derrin, D. Elkaduwe, K. Engelhardt, R. Kolanski, M. Norrish,T. Sewell, H. Tuch, and S. Winwood. seL4: formal verification of anOS kernel. In Proceedings of the ACM SIGOPS 22nd symposium onOperating systems principles (SOSP’09), pages 207–220. ACM,2009. ISBN 978-1-60558-752-3. doi:10.1145/1629575.1629596.

[13] X. Leroy. A formally verified compiler back-end. Journal ofAutomated Reasoning, 43(4):363–446, 2009.doi:10.1007/s10817-009-9155-4.

[14] F. Loulergue, V. Niculescu, and S. Robillard. Powerlists in Coq:Programming and Reasoning. In First International Symposium onComputing and Networking (CANDAR). IEEE Computer Society,2013. to appear.

Bibliography IV

[15] J. Misra. Powerlist: A structure for parallel recursion. ACM Trans.Program. Lang. Syst., 16(6):1737–1767, November 1994.

[16] A. Morihata, K. Matsuzaki, Z. Hu, and M. Takeichi. The thirdhomomorphism theorem on trees: downward & upward lead todivide-and-conquer. In Z. Shao and B. C. Pierce, editors,Symposium on Principles of Programming Languages (POPL),pages 177–185. ACM Press, 2009. doi:10.1145/1480881.1480905.

[17] K. Morita, A. Morihata, K. Matsuzaki, Z. Hu, and M. Takeichi.Automatic Inversion Generates Divide-and-Conquer ParallelPrograms. In Conference on Programming Language Design andImplementation (PLDI), pages 146–155. ACM Press, 2007.doi:10.1145/1250734.1250752.

[18] R. O. Rogers and D. B. Skillicorn. Using the BSP cost model tooptimise parallel neural network training. Future GenerationComputer Systems, 14(5-6):409–424, 1998.

Bibliography V

[19] J. Sevcık, V. Vafeiadis, F. Z. Nardelli, S. Jagannathan, andP. Sewell. CompCertTSO: A Verified Compiler for Relaxed-MemoryConcurrency. Journal of the ACM, 60(3):22, 2013.doi:10.1145/2487241.2487248.

[20] J. Tesson. Environnement pour le developpement et la preuve decorrection systematiques de programmes paralleles fonctionnels.PhD thesis, LIFO, University of Orleans, November 2011. URLhttp://hal.archives-ouvertes.fr/tel-00660554/en/.

[21] J. Tesson, H. Hashimoto, Z. Hu, F. Loulergue, and M. Takeichi.Program Calculation in Coq. In Thirteenth International Conferenceon Algebraic Methodology And Software Technology(AMAST2010), LNCS 6486, pages 163–179. Springer, 2010.doi:10.1007/978-3-642-17796-5 10.

[22] The Coq Development Team. The Coq Proof Assistant.http://coq.inria.fr.

[23] L. G. Valiant. A bridging model for parallel computation. Commun.ACM, 33(8):103, 1990. doi:10.1145/79173.79181.

Coq Hands-On

I To try during the presentation, and/or

I For Coq hands-on after the lecture

Installing Coq

Coq website: http://coq.inria.fr

Recommended installation:

I Windows installer for Coq’s website

I Linux: Ubuntu packages (coq, coqide, proofgeneral-coq)

I MacOS: MacPorts or Homebrew

Recommended IDE: emacs + ProofGeneral

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