From a scalar type system
90 pages

Découvre YouScribe en t'inscrivant gratuitement

Je m'inscris

From a scalar type system

-

Découvre YouScribe en t'inscrivant gratuitement

Je m'inscris
Obtenez un accès à la bibliothèque pour le consulter en ligne
En savoir plus
90 pages
Obtenez un accès à la bibliothèque pour le consulter en ligne
En savoir plus

Description

Niveau: Supérieur
From a scalar type system to a vectorial type system Work in progress Alejandro Díaz-Caro Joint work with Pablo Arrighi Université de Grenoble Laboratoire d'Informatique de Grenoble May 4th, 2009. LIX (Paris)

  • linear-algebraic ?-calculus

  • curry-howard correspondence

  • defined quantum

  • ad hoc before

  • quantum programs

  • correspondence


Sujets

Informations

Publié par
Nombre de lectures 33

Extrait

oFtiqueromUniversit?aLIXscalaablorotMaypJointewithsystemgtoGrenoblead'InfovectoGrenoblri4th,aalwtrkypPeArrisystemhideWLaboratoirerkrmaindeperogressy2009.Alejandro(PD?az-Caris)roλ
rMotivationeLinearogressr-AlgebWraicinRoadmaputureo-CalculussystemSystemoFkThepscalaFrwtrkypI
I
I
823843.Logicl1ondence).wvonasedevelosteppcoed,adstudyhoacrkbrdsefoCurry-HoreBirkho,quantumlogiccomputing37(nofromcleatr(Curry-Horelationcowithwquantumapwrograms).foQuantumaviaThereaisondenceaandneedmann,foquantumrofapplogiclogicthatthecouldofaidypussystemstowisolatingrdtherrespreasoningThisboehindissomerstquantumtoalgoarithms.aMotivationrmally-denedquantumphysicalUsuallyogictherisingreasoningthebwehindrdarrespp1rogramG.canJ.bNeueThemadeoftomechanicsaAnnalsriseMathematicsvia(1936),a.formally-denedI
I
I
logicLogicl1Thiswmann,assystemsdevelotopondenceedofadofhordcisbaefoareandquantumquantumcomputingpp(nothecleayprwrelationrrespwithoquantumrstparograms).rmally-denedQuantumaviaCurry-HoTherecoisBirkho,avonneedlogicfo,r37a823843.logicfromthatstudycouldtaideus(Curry-Hotoaisolatingcotheondence).reasoningwbrkehindasomestepquantumwalgordsrithms.foMotivationquantumphysicalUsuallyogictherisingreasoningthebwehindrdarrespp1rogramG.canJ.bNeueThemadeoftomechanicsaAnnalsriseMathematicsvia(1936),a.formally-denedI
I
I
ppLogicrmally-dened1rrespwandasypdevelorstpaedquantumadthehowcobaefoviareondencequantummann,computingof(nologiccleaofrsystemsrelationrdwithThisquantumisptorograms).aQuantumaThereCurry-HoiscoaBirkho,needvonfologicr,a37logic823843.thatfromcouldstudyaidtuseto(Curry-Hoisolatingathecoreasoningondence).bwehindrksomeaquantumstepalgowrithms.rdsMotivationfoquantumlphysicalUsuallyogictherisingreasoningthebwehindrdarrespp1rogramG.canJ.bNeueThemadeoftomechanicsaAnnalsriseMathematicsvia(1936),a.formally-denedI
I
I
ppLogicrmally-dened1rrespwandasypdevelorstpaedquantumadthehowcobaefoviareondencequantummann,computingof(nologiccleaofrsystemsrelationrdwithThisquantumisptorograms).aQuantumaThereCurry-HoiscoaBirkho,needvonfologicr,a37logic823843.thatfromcouldstudyaidtuseto(Curry-Hoisolatingathecoreasoningondence).bwehindrksomeaquantumstepalgowrithms.rdsMotivationfoquantumlphysicalUsuallyogictherisingreasoningthebwehindrdarrespp1rogramG.canJ.bNeueThemadeoftomechanicsaAnnalsriseMathematicsvia(1936),a.formally-denedλ
tMotivationrogressLineaWr-AlgeboraiceRoadmaprin-CalculusutureTherlanguageypWhysystemtheorkestrictionspSystemFFwTherkscala+ |α. |
I Iλ . → [ / ](∗)
+ →
α.( + )→α. +α.
I
α. +β. → (α+β).
+
I
( + )→ ( )+( )
λ
::= |λ . |( ) |
λ
(**)rmal.ek.Lineatrriable.algebvraArrighi,titotsuchcomputationxrderbHigher-oG.thigher-olanguageu0aTheuElementaApplicationryuruleswsuchvasuu(***)2.0o-Calculusr-algebnouencoandgsv(**)raicvar-AlgebruabstractionLinea.1731.anurulesxasandbt(*)uxclosedxuubandt.wNotes.Computer2(RTPactoandrisationDruleswsuchLineaasraic(***)-calculus:rmal.rder,udnoncloseduconuencetLecture5117inppSciencetA'08),F(2008),v..vI Iλ . → [ / ](∗)
+ →
α.( + )→α. +α.
I
α. +β. → (α+β).
+
I
( + )→ ( )+( )
λ
::= |λ . |( ) | + |α. |
λ
xrmal.languageLineagsrrulesalgebG.noraSciencet.closedttArrighi,vek.uencouLecturet(2008),andrderascomputationtxx0bThevElementaury(***)rules.suchoasr-algebuhigher-o2i0conuence-CalculusinuA'08),and(*)(***)Higher-oraicur-Algeb(**)uApplicationLineasuch1731.urmal.vtwttnouubclosedxtwu.v2.P(**)and.DactowrisationLinearulesraicsuch-calculus:asrder,riable.dvanuanda.rNotesoComputeru(RTabstraction5117anppbFvI
+ →
α.( + )→α. +α.
I
α. +β. → (α+β).
+
I
( + )→ ( )+( )
λ
::= |λ . |( ) | + |α. |
I λ . → [ / ](∗)
λ
.rmal.raicLineavrxalgebanraandtbandotrulesub(***)urmal.wt(**)noriable.0aThetElementaabstractionryasrulestsuch(*)asxuP2D0Linea-CalculustuuandtnouencovairgstconuenceuLecture(**)inApplicationSciencesuchA'08),u(2008),v.wxxcloseduclosedvwu.2thigher-o(***).Arrighi,u.FG.actoorisationek.rulesr-algebsuchas-calculus:brder,vdraicnr-Algebandu.LineaNotes1731.Computerrder(RTHigher-o5117languageppcomputationuv

  • Accueil Accueil
  • Univers Univers
  • Ebooks Ebooks
  • Livres audio Livres audio
  • Presse Presse
  • BD BD
  • Documents Documents