大規模数値計算を支える Haskell ── Pragmatic Haskell in Large-Scale Numerical Computation──

Haskell Day 2019 での講演抄録です。

Transcript

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9. "HHSFTTJWF6TFPG()$
   

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10. "HHSFTTJWF6TFPG()$
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11. "HHSFTTJWF6TFPG()$
    TypeApplications
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    DataKinds
    TypeFamilies
    ScopedTypeVariables
    FlexibleInstances
    TypeOperators
    UndecidableInstances
    DerivingStrategies
    OverloadedStrings
    PolyKinds
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    RecordWildCards
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12. "HHSFTTJWF6TFPG()$
    TypeApplications
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    DataKinds
    TypeFamilies
    ScopedTypeVariables
    FlexibleInstances
    TypeOperators
    UndecidableInstances
    DerivingStrategies
    OverloadedStrings
    PolyKinds
    TemplateHaskell
    RecordWildCards
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    QuantifiedConstraints, DerivingVia, Source Plugins
    

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13. )PX$BO)BTLFMM)FMQUP
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14. 0VS(PBMTBOE)BTLFMM
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15. 0VS(PBMTBOE)BTLFMM
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16. &YQSFTTJWJUZBOE4BGFUZ
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17. &YBNQMFT#PVOEBSZ4BOJUZ
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18. &YBNQMFT#PVOEBSZ4BOJUZ
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19. &YBNQMFT#PVOEBSZ4BOJUZ
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20. &YBNQMFT#PVOEBSZ4BOJUZ
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21. &YBNQMFT#PVOEBSZ4BOJUZ
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22. &YBNQMFT#PVOEBSZ4BOJUZ
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23. &YBNQMFT#PVOEBSZ4BOJUZ
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24. 5BHHJOHXJUI2VBOUJUZ/BNFBOE
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    data Sanity = Yet | Done
    newtype TagQty name (s  Sanity)
    = TQty { unTagQty  PhysQty }
    unproc  TagQty k t 'Done  TagQty t 'Yet
    class Processable env k name where
    process  env  PhysQty  TagQty name 'Done
    instance s ~ 'Yet  Num (TagQty k name s)
    

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25. 5ZQFDIFDLFS1MVHJO
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    .
    {-# OPTIONS_GHC -fplugin GHC.TypeLits.Normalise #-}

    {-# OPTIONS_GHC -fplugin-opt ( ):allow-negated-numbers #-}
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26. 4VNNBSZ-FU5ZQFT
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27. 4VNNBSZ-FU5ZQFT
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32. 0VS(PBMTBOE)BTLFMM
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33. 0VS(PBMTBOE)BTLFMM
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34. .PEVMBSJUZ

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35. $&0T5XFFU
    

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36. $&0T5XFFU
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37. $&0T5XFFU
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38. .POBEEFMJNJUTUBTLT
    

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39. .POBEEFMJNJUTUBTLT
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40. .POBEEFMJNJUTUBTLT
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41. .POBEEFMJNJUTUBTLT
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42. .POBEEFMJNJUTUBTLT
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45. 5BHMFTT'JOBM4UZMF<>
    data family PhysQty m
    class Monad m  MonadDiff m where
    grad  PhysQty m  m (PhysQty m)
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    w "CTUSBDUDPNNPOPQFSBUJPOBTBNPOBEJDGVODUJPO
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46. 0VUDPNFNVMUJQMF
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47. 0VUDPNFNVMUJQMF
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48. 0VUDPNFNVMUJQMF
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49. 0VUDPNFNVMUJQMF
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    w $VSSFOUMZXFIBWF4PMWFSTJTPNPSQIJDUPQVSFReader
    envBOEReaderT env IO
    

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50. 0VUDPNFNVMUJQMF
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    w $VSSFOUMZXFIBWF4PMWFSTJTPNPSQIJDUPQVSFReader
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51. 0VUDPNFNVMUJQMF
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    w $VSSFOUMZXFIBWF4PMWFSTJTPNPSQIJDUPQVSFReader
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53. 1SPCMFN5PP.VDI#JOET
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54. 1SPCMFN5PP.VDI#JOET
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55. 1SPCMFN5PP.VDI#JOET
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56. 1SPCMFN5PP.VDI#JOET
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    1SPCMFN)BWFUPXSJUF( )UPDPNQPTFGVODUJPOT
    

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57. 1SPCMFN5PP.VDI#JOET
    w 8FVTF("%5T JOJUJBMSFQS
    UPQSPWJEFTNBSU
    DPOTUSVDUPST
    w 5IFZBMTPUBLFTDBSFPGBEEJUJPOBMQSFQPTU
    QSPDFTTFTGPSFBDIEJ⒎FSFOUJBMPQFSBUPST
    ν △ u −
    1
    ρ
    grad P
    (-)  ((nu *)  laplacian u)
     ((/rho)  grad u)
    
    1SPCMFN)BWFUPXSJUF( )UPDPNQPTFGVODUJPOT
    

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58. *OJUJBM3FQSFTFOUBUJPO
    w 'SFF 0QFSBUJPOBM
    .POBEBOETNBSUDPOT VTJOH("%5T
    w %J⒎FSFOUJBMPQFSBUPSTDBOBDDFQUBOZUFSNXIJDIDBOCF
    DBTUFEUPUIFJSJOUFOEFEBSHVNFOUT
    data Expr m a where
    Join  Expr m (Expr m a)  Expr m a
    Grad  (ToPhysQty m qty)
     Expr m qty  Expr m (PhysQty m)
    grad'  (ToPhysQty m a)
     a  Expr m (PhysQty m)
    grad' = Grad . toExpr -- pre-process for conversion
    

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59. &YBNQMF
    stokesEqn u ρ p = eval $
    (1 /: ρ) .*: (eta .*: laplace' u -: grad' p)
    ∂u
    ∂t
    =
    1
    ρ
    (η ▵ u − grad P)
    "MNPTU-JUFSBM5SBOTMBUJPOJOUPUIF$PEF
    㾎0OFEPFTOUIBWFUPLOPXBCPVUBOZ
    JNQMFNFOUBUJPOEFUBJMUPXSJUFFRVBUJPOT
    

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60. 5BHMFTTpOBM4VNNBSZ
    

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61. 5BHMFTTpOBM4VNNBSZ
    w 4FQBSBUFTBSFBPGUBTLTCZNPOBEJDPQFSBUJPOT
    FOBCMJOHUPDPODFOUSBUFPOUIFJSPXOCVTJOFTT
    

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62. 5BHMFTTpOBM4VNNBSZ
    w 4FQBSBUFTBSFBPGUBTLTCZNPOBEJDPQFSBUJPOT
    FOBCMJOHUPDPODFOUSBUFPOUIFJSPXOCVTJOFTT
    w &RVBUJPOXSJUFSTEPOUIBWFUPDBSFBCPVUJNQM
    EFUBJM
    

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63. 5BHMFTTpOBM4VNNBSZ
    w 4FQBSBUFTBSFBPGUBTLTCZNPOBEJDPQFSBUJPOT
    FOBCMJOHUPDPODFOUSBUFPOUIFJSPXOCVTJOFTT
    w &RVBUJPOXSJUFSTEPOUIBWFUPDBSFBCPVUJNQM
    EFUBJM
    w 8FFYQMPJUTJNJMBSUFDITUPEFMJNJUNBOZPUIFS
    UBTLTFRVBUJPO PQFSBUJPOJNQM DBDIJOH JOUFS
    QSPDFTTDPNNVOJDBUJPO
    

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64. 5BHMFTTpOBM4VNNBSZ
    w 4FQBSBUFTBSFBPGUBTLTCZNPOBEJDPQFSBUJPOT
    FOBCMJOHUPDPODFOUSBUFPOUIFJSPXOCVTJOFTT
    w &RVBUJPOXSJUFSTEPOUIBWFUPDBSFBCPVUJNQM
    EFUBJM
    w 8FFYQMPJUTJNJMBSUFDITUPEFMJNJUNBOZPUIFS
    UBTLTFRVBUJPO PQFSBUJPOJNQM DBDIJOH JOUFS
    QSPDFTTDPNNVOJDBUJPO
    w 8FDBOVTFJOJUJBMSFQSFTFOUBUJPOUPFMJNJOBUF
    CJOEIFMMJOUBHMFTTpOBMTUZMF
    

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65. 0VS(PBMTBOE)BTLFMM
    w (FOFSBM1VSQPTF4PMWFS
    w %FQFOEFOU)BTLFMM
    w 5BHMFTT'JOBMBOE*OJUJBM3FQSFTFOUBUJPO
    w 4QFFEBOE4DBMF
    w 1SJNJUJWF.POBET 3FXSJUJOH3VMFT 4QFDJBMJTBUJPO *OUFSQSPDFTT
    DPNNVOJDBUJPO
    w .POBEJD4FRVFODF"CTUSBDUJPOUPNBLFVTFPGUIFTF
    w 1MVHJOTVTJOH&YUFOTJCMF3FDPSET
    w "OENBOZPUIFSUFDIOJRVFTOPUNFOUJPOFEUIJTUBML
    .PEVMBSJUZ
    

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66. 0VS(PBMTBOE)BTLFMM
    w (FOFSBM1VSQPTF4PMWFS
    w %FQFOEFOU)BTLFMM
    w 5BHMFTT'JOBMBOE*OJUJBM3FQSFTFOUBUJPO
    w 4QFFEBOE4DBMF
    w 1SJNJUJWF.POBET 3FXSJUJOH3VMFT 4QFDJBMJTBUJPO *OUFSQSPDFTT
    DPNNVOJDBUJPO
    w .POBEJD4FRVFODF"CTUSBDUJPOUPNBLFVTFPGUIFTF
    w 1MVHJOTVTJOH&YUFOTJCMF3FDPSET
    w "OENBOZPUIFSUFDIOJRVFTOPUNFOUJPOFEUIJTUBML
    

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67. 4QFFEBOE&YQSFTTJWJUZ
    1SJNJUJWF.POBETBOE
    .POBEJD4FRVFODF
    

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68. 4FRVFOUJBMUZQFTJO)BTLFMM
    w 1IZTJDBMWBMVFTBSFFYQSFTTFEBTTFRVFODFTPGSFBMT
    w 8IJDI4FRVFODFUZQFNVTUXFVTF
    w -JTUTHJWFOJO1SFMVEF TJNQMFBOEEFDMBSBUJWF*'CVU4-08
    JOEFYJOH BENJUT'VTJPO
    w 7FDUPST'BTU 0
    
    JOEFYJOHXJUIEFDMBSBUJWF*' F⒏DJFOU
    TUPSBHFGPS6OCPYFEUZQFT BENJUT'VTJPO
    5FNQFSBUVSFT
    Cell #0 #1 #2 #3
    ʜʜ
    273K 273K 300K 450K
    

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69. 4USFBN'VTJPO< >
    f z ∘ g ≡ (f ∘ g) z
    

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70. 4USFBN'VTJPO< >
    w 'VODUJPOTPOTFRVFODFTBUJTpFTTPNFBMHFCSBJDMBXT XIJDIGVTFT
    NVMUJQMFMPPQJOUPPOFQBTT
    f z ∘ g ≡ (f ∘ g) z
    

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71. 4USFBN'VTJPO< >
    w 'VODUJPOTPOTFRVFODFTBUJTpFTTPNFBMHFCSBJDMBXT XIJDIGVTFT
    NVMUJQMFMPPQJOUPPOFQBTT
    w VectorsFYQMPJUTVDISFMBUJPOTUPPQUJNJTFGVODUJPOT
    f z ∘ g ≡ (f ∘ g) z
    

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72. 4USFBN'VTJPO< >
    w 'VODUJPOTPOTFRVFODFTBUJTpFTTPNFBMHFCSBJDMBXT XIJDIGVTFT
    NVMUJQMFMPPQJOUPPOFQBTT
    w VectorsFYQMPJUTVDISFMBUJPOTUPPQUJNJTFGVODUJPOT
    w 5IFZPODFDPOWFSUWFDUPSTUPBCTUSBDUStreamTBOEBundleT
    f z ∘ g ≡ (f ∘ g) z
    

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73. 4USFBN'VTJPO< >
    w 'VODUJPOTPOTFRVFODFTBUJTpFTTPNFBMHFCSBJDMBXT XIJDIGVTFT
    NVMUJQMFMPPQJOUPPOFQBTT
    w VectorsFYQMPJUTVDISFMBUJPOTUPPQUJNJTFGVODUJPOT
    w 5IFZPODFDPOWFSUWFDUPSTUPBCTUSBDUStreamTBOEBundleT
    w 4USFBNBNPOBEJDHFOFSBUJOHGVODUJPO
    f z ∘ g ≡ (f ∘ g) z
    

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74. 4USFBN'VTJPO< >
    w 'VODUJPOTPOTFRVFODFTBUJTpFTTPNFBMHFCSBJDMBXT XIJDIGVTFT
    NVMUJQMFMPPQJOUPPOFQBTT
    w VectorsFYQMPJUTVDISFMBUJPOTUPPQUJNJTFGVODUJPOT
    w 5IFZPODFDPOWFSUWFDUPSTUPBCTUSBDUStreamTBOEBundleT
    w 4USFBNBNPOBEJDHFOFSBUJOHGVODUJPO
    w #VOEMF4USFBNPQUJPOBMDPODSFUFWFDUPSWBMVFBOEMFOHUI
    JOGPSNBUJPO
    f z ∘ g ≡ (f ∘ g) z
    

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75. 4USFBN'VTJPO< >
    w 'VODUJPOTPOTFRVFODFTBUJTpFTTPNFBMHFCSBJDMBXT XIJDIGVTFT
    NVMUJQMFMPPQJOUPPOFQBTT
    w VectorsFYQMPJUTVDISFMBUJPOTUPPQUJNJTFGVODUJPOT
    w 5IFZPODFDPOWFSUWFDUPSTUPBCTUSBDUStreamTBOEBundleT
    w 4USFBNBNPOBEJDHFOFSBUJOHGVODUJPO
    w #VOEMF4USFBNPQUJPOBMDPODSFUFWFDUPSWBMVFBOEMFOHUI
    JOGPSNBUJPO
    w TUSFBNVOTUSFBNGVODUJPOTDPOWFSUT7FDUPSTUPGSPN#VOEMFT
    f z ∘ g ≡ (f ∘ g) z
    

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76. 1SPCMFN.BOZLJOETPG
    WFDUPS
    w #PYFEDBOTUPSFBOZUZQFT
    w 6OCPYFEDBOTUPSF TVNPGQSPEVDUTPG
    VOCPYFE
    UZQFTFH*OU %PVCMF #PPM
    w 4UPSBCMFGPSDPNNVOJDBUJPOTXJUI$MJCSBSZ
    w BOENPOPNPSQIJDOFXUZQFXSBQQFSTBSPVOEUIFN
    w 1SPCMFN8FXBOUUPUSFBUUIFNVOJGPSNMZ
    w $BOXFEPUIJTSFUBJOJOHF⒏DJFODZPGWFDUPST
    

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77. 'JSTU"UUFNQU
    type family Elem seq
    type family Key seq
    class Monad m  MSeq m seq where
    imap  (Key seq  Elem seq  Elem seq)
     seq m seq
    index  Index seq  seq  m (Elem seq)
    ifoldr  (Key seq  Elem seq  Elem seq)  
    accum  
    instance Monad m  MSeq m (Vector a)
    instance Monad m  MSeq m (VecMap k a)
    .POBEJDSFTVMU
    w 1SPCMFN.POBEJDSFTVMUNJHIUTBDSJpDFTUSFBNGVTJPO
    w 1SPCMFN)BWFUPJNQMFNFOUWFDUPSPQFSBUJPOTBMMCZIBOET
    .BOZPUIFSPQT
    

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78. "OTXFSTUSFBNVOTUSFBN
    

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79. "OTXFSTUSFBNVOTUSFBN
    w "MNPTUBMMWFDUPSPQFSBUJPOTBSFJOEFFEJNQMEBT
    DPNQPTJUJPOTPGTUSFBNVOTUSFBNXJUI4USFBN
    #VOEMFPQFSBUJPOT
    

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80. "OTXFSTUSFBNVOTUSFBN
    w "MNPTUBMMWFDUPSPQFSBUJPOTBSFJOEFFEJNQMEBT
    DPNQPTJUJPOTPGTUSFBNVOTUSFBNXJUI4USFBN
    #VOEMFPQFSBUJPOT
    w 4JODF4USFBN#VOEMFTBSFNPOBEJDCZEFGBVMUBOE
    UIFZGVTFTXFMM XFDBOHFUF⒏DJFODZGPSGSFF
    

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81. "OTXFSTUSFBNVOTUSFBN
    w "MNPTUBMMWFDUPSPQFSBUJPOTBSFJOEFFEJNQMEBT
    DPNQPTJUJPOTPGTUSFBNVOTUSFBNXJUI4USFBN
    #VOEMFPQFSBUJPOT
    w 4JODF4USFBN#VOEMFTBSFNPOBEJDCZEFGBVMUBOE
    UIFZGVTFTXFMM XFDBOHFUF⒏DJFODZGPSGSFF
    w 5IFSVMFstream ○ unstream ≡ returnSFEVDFT
    JOUFSOBMUFSNTFWFOJGUIFSFTVMUJTNPOBEJD
    

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82. "OTXFSTUSFBNVOTUSFBN
    w "MNPTUBMMWFDUPSPQFSBUJPOTBSFJOEFFEJNQMEBT
    DPNQPTJUJPOTPGTUSFBNVOTUSFBNXJUI4USFBN
    #VOEMFPQFSBUJPOT
    w 4JODF4USFBN#VOEMFTBSFNPOBEJDCZEFGBVMUBOE
    UIFZGVTFTXFMM XFDBOHFUF⒏DJFODZGPSGSFF
    w 5IFSVMFstream ○ unstream ≡ returnSFEVDFT
    JOUFSOBMUFSNTFWFOJGUIFSFTVMUJTNPOBEJD
    w 0OFDBOBMTPQSPWJEFBO*'UPGVTFEJ⒎FSFOULJOEPG
    WFDUPSTJOUPPOF
    

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83. 3FTVMU
    type family VecRep seq  Type  Type
    class (Monad m)  MSequence m seq where
    unfoldrM  (s  m (Maybe (Elem seq, s)))
     s  m seq
    indexM'  seq  Int  m (Elem seq)
    stream'  seq  B.Bundle m (VecRep seq) (Elem seq)
    unstream'  B.Bundle m (VecRep seq) (Elem seq)  m seq
    

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84. 3FTVMU
    type family VecRep seq  Type  Type
    class (Monad m)  MSequence m seq where
    unfoldrM  (s  m (Maybe (Elem seq, s)))
     s  m seq
    indexM'  seq  Int  m (Elem seq)
    stream'  seq  B.Bundle m (VecRep seq) (Elem seq)
    unstream'  B.Bundle m (VecRep seq) (Elem seq)  m seq
    w "MMPUIFSPQFSBUJPOTBSFEFSJWFEGSPNUIFTFQSJNJUJWFTXJUI
    Data.Vector.Fusion.Bundle.MonadicNPEVMF
    

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85. 3FTVMU
    type family VecRep seq  Type  Type
    class (Monad m)  MSequence m seq where
    unfoldrM  (s  m (Maybe (Elem seq, s)))
     s  m seq
    indexM'  seq  Int  m (Elem seq)
    stream'  seq  B.Bundle m (VecRep seq) (Elem seq)
    unstream'  B.Bundle m (VecRep seq) (Elem seq)  m seq
    w "MMPUIFSPQFSBUJPOTBSFEFSJWFEGSPNUIFTFQSJNJUJWFTXJUI
    Data.Vector.Fusion.Bundle.MonadicNPEVMF
    w 0OFDBOFYQMPJUGVTJPOSVMFTQSPWJEFECZWFDUPSQBDLBHFGPSGSFF
    

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86. 3FTVMU
    type family VecRep seq  Type  Type
    class (Monad m)  MSequence m seq where
    unfoldrM  (s  m (Maybe (Elem seq, s)))
     s  m seq
    indexM'  seq  Int  m (Elem seq)
    stream'  seq  B.Bundle m (VecRep seq) (Elem seq)
    unstream'  B.Bundle m (VecRep seq) (Elem seq)  m seq
    w "MMPUIFSPQFSBUJPOTBSFEFSJWFEGSPNUIFTFQSJNJUJWFTXJUI
    Data.Vector.Fusion.Bundle.MonadicNPEVMF
    w 0OFDBOFYQMPJUGVTJPOSVMFTQSPWJEFECZWFDUPSQBDLBHFGPSGSFF
    w #POVT)FUFSPHFOFPVT$PNCJOBUPSTBOE1SJN.POBEPQUJNJTBUJPO
    

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87. #POVT)FUFSPHFOFPVT
    $PNCJOBUPST
    w 0OFDBONBQ[JQEJ⒎FSFOULJOEPGTUSFBNTJOPOFQBTT
    w 8FQSPWJEF3FXSJUF3VMFTUPFMJNJOBUFDPOWFSTJPOPWFSIFBET
    XIFOTPNFPGBSHVNFOUTIBWFUIFTBNFWFDUPSSFQSFTFOUBUJPO
    hzipWith  (MSeq m s, MSeq m t, MSeq m u,
    Key s ~ Key t, Key s ~ Key u)
     (Elem s  Elem t  Elem u)
     s  t  m u
    hzipWithM f = \as bs 
    unstream $ B.zipWithM f (B.reVector $ stream as)
    (B.reVector $ stream bs)
    

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88. #POVT%FTUSVDUJWF
    "TTJHONFOUTBSF:PVS'SJFOET
    

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89. #POVT%FTUSVDUJWF
    "TTJHONFOUTBSF:PVS'SJFOET
    w MSeqBTTVNFTUIFJSSFUVSOUZQFUPCFNPOBEJD
    

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90. #POVT%FTUSVDUJWF
    "TTJHONFOUTBSF:PVS'SJFOET
    w MSeqBTTVNFTUIFJSSFUVSOUZQFUPCFNPOBEJD
    w 5IFSFJTBDMBTTPG.POBETBENJUUJOHEFTUSVDUJWF
    BTTJHONFOUT PrimMonad GSPNprimitiveQBDLBHF
    
    

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91. #POVT%FTUSVDUJWF
    "TTJHONFOUTBSF:PVS'SJFOET
    w MSeqBTTVNFTUIFJSSFUVSOUZQFUPCFNPOBEJD
    w 5IFSFJTBDMBTTPG.POBETBENJUUJOHEFTUSVDUJWF
    BTTJHONFOUT PrimMonad GSPNprimitiveQBDLBHF
    
    w 1SPWJEFTBDPNNPO*'GPSSTBOEIONPOBETBOE
    NPOBEUSBOTGPSNFSTBSPVOEUIFN
    

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92. #POVT%FTUSVDUJWF
    "TTJHONFOUTBSF:PVS'SJFOET
    w MSeqBTTVNFTUIFJSSFUVSOUZQFUPCFNPOBEJD
    w 5IFSFJTBDMBTTPG.POBETBENJUUJOHEFTUSVDUJWF
    BTTJHONFOUT PrimMonad GSPNprimitiveQBDLBHF
    
    w 1SPWJEFTBDPNNPO*'GPSSTBOEIONPOBETBOE
    NPOBEUSBOTGPSNFSTBSPVOEUIFN
    w *GVOEFSMZJOHNPOBEmJTPrimMonad POFDBOVTFUIFJS
    BCJMJUZGPSNVUBCMFSFGFSFODFTUPHBJOQFSGPSNBODF
    

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93. VOTUSFBNXJUI1SJN.POBE
    w *GNJTPrimMonad JOQBSUJDVMBSJGIOXJUIFYUSBUSBOTGPSNFS
    MBZFSTPOUPQ
    XFDBOVTFNVUBCMFPQFSBUJPOTPOUIFNUPHFU
    WFDUPSTJOTUBOUMZ
    w 5IJTHBWFVTYTQFFEVQTJOQSBDUJDF &YBDUSFDPSETBSF
    MPTUTPSSZ
    
    ‎ $PNQPTFTXFMMXJUIUBHMFTTpOBMBQQSPBDI
    unstreamPrimM  (PrimMonad m, Vector (VRep s) (Elem s),
    VRep s (Elem seq) ~R# seq)
     B.Bundle m u (Element s)  m s
    unstreamPrimM s =
    coerce  (G.unsafeFreeze  MG.munstream s)
    {-# RULES "unstreamM[IO]" unstreamM = unstreamPrimM #-}
    

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94. .POBEJD4FRVFODFBOE
    1SJN.POBE4VNNBSZ
    

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95. .POBEJD4FRVFODFBOE
    1SJN.POBE4VNNBSZ
    w 4USFBN'VTJPOSFEVDFTDPOTUBOUPWFSIFBETJHOJpDBOUMZ
    w &YQMPJUJOHvectorT4USFBN#VOEMF'VTJPONFDIBOJTN
    XPSLTMJLFBDIBSN
    w "MTPFOBCMFTUPGVTFEJ⒎FSFOULJOEPGWFDUPST
    w 3FXSJUJOH3VMFTDBOIFMQSFEVDFPWFSIFBEIFSF
    

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96. .POBEJD4FRVFODFBOE
    1SJN.POBE4VNNBSZ
    w 4USFBN'VTJPOSFEVDFTDPOTUBOUPWFSIFBETJHOJpDBOUMZ
    w &YQMPJUJOHvectorT4USFBN#VOEMF'VTJPONFDIBOJTN
    XPSLTMJLFBDIBSN
    w "MTPFOBCMFTUPGVTFEJ⒎FSFOULJOEPGWFDUPST
    w 3FXSJUJOH3VMFTDBOIFMQSFEVDFPWFSIFBEIFSF
    w *GUIFSFTVMUUZQFJTNPOBEJD UIFOPOFDBOFYQMPJU1SJN.POBE
    JOTUBODFUPHBJONPSFTQFFE SFUBJOJOHEFDMBSBUJWFNBOOFS
    w 5IJTDPNQPTFTXFMMXJUIUBHMFTTpOBMTUZMFBQQSPBDI
    JNQMFNFOUFEXJUI3*0QBUUFSO
    w %FTUSVDUJWFBTTJHONFOUT EJTHVJTFEBTEFDMBSBUJWF
    DPNCJOBUPST
    BSFJOEFFEZPVSGSJFOET
    

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97. 0VS(PBMTBOE)BTLFMM
    w (FOFSBM1VSQPTF4PMWFS
    w %FQFOEFOU)BTLFMM
    w 5BHMFTT'JOBMBOE*OJUJBM3FQSFTFOUBUJPO
    w 4QFFEBOE4DBMF
    w 1SJNJUJWF.POBET 3FXSJUJOH3VMFT 4QFDJBMJTBUJPO *OUFSQSPDFTT
    DPNNVOJDBUJPO
    w .POBEJD4FRVFODF"CTUSBDUJPOUPNBLFVTFPGUIFTF
    w 1MVHJOTVTJOH&YUFOTJCMF3FDPSET
    w "OENBOZPUIFSUFDIOJRVFTOPUNFOUJPOFEUIJTUBML
    

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98. 0VS(PBMTBOE)BTLFMM
    w (FOFSBM1VSQPTF4PMWFS
    w %FQFOEFOU)BTLFMM
    w 5BHMFTT'JOBMBOE*OJUJBM3FQSFTFOUBUJPO
    w 4QFFEBOE4DBMF
    w 1SJNJUJWF.POBET 3FXSJUJOH3VMFT 4QFDJBMJTBUJPO *OUFSQSPDFTT
    DPNNVOJDBUJPO
    w .POBEJD4FRVFODF"CTUSBDUJPOUPNBLFVTFPGUIFTF
    w 1MVHJOTVTJOH&YUFOTJCMF3FDPSET
    w "OENBOZPUIFSUFDIOJRVFTOPUNFOUJPOFEUIJTUBML
    &YUFOTJCJMJUZ
    

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99. &YUFOTJCJMJUZ
    &YUFOTJCMF3FDPSET
    

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100. .PUJWBUJPO1MVHJO
     .FDIBOJTN
     

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101. .PUJWBUJPO1MVHJO
     .FDIBOJTN
     w 5BHMFTTpOBMTUZMFBMMPXFEVTUPXSJUFNVMUJQMF
     4PMWFSTOJDFMZ
     

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102. .PUJWBUJPO1MVHJO
     .FDIBOJTN
     w 5BHMFTTpOBMTUZMFBMMPXFEVTUPXSJUFNVMUJQMF
     4PMWFSTOJDFMZ
     w CVUUIFPGTPMWFSTFWFOUVBMMZJODSFBTFE BOE
     JUIBECFDPNFIBSEUPNBJOUBJOBMMPGUIFN
     

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103. .PUJWBUJPO1MVHJO
     .FDIBOJTN
     w 5BHMFTTpOBMTUZMFBMMPXFEVTUPXSJUFNVMUJQMF
     4PMWFSTOJDFMZ
     w CVUUIFPGTPMWFSTFWFOUVBMMZJODSFBTFE BOE
     JUIBECFDPNFIBSEUPNBJOUBJOBMMPGUIFN
     w *UJTEFTJSBCMFGPSVTUPIBWFPOMZBMJNJUFEOVNCFS
     PG4PMWFSTBOEFYUFOEUIFNCZ1MVHJOTGPS
     NPEVMBSJUZBOENBJOUBJOBCJMJUZ
     

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104. .PUJWBUJPO1MVHJO
     .FDIBOJTN
     w 5BHMFTTpOBMTUZMFBMMPXFEVTUPXSJUFNVMUJQMF
     4PMWFSTOJDFMZ
     w CVUUIFPGTPMWFSTFWFOUVBMMZJODSFBTFE BOE
     JUIBECFDPNFIBSEUPNBJOUBJOBMMPGUIFN
     w *UJTEFTJSBCMFGPSVTUPIBWFPOMZBMJNJUFEOVNCFS
     PG4PMWFSTBOEFYUFOEUIFNCZ1MVHJOTGPS
     NPEVMBSJUZBOENBJOUBJOBCJMJUZ
     w 8IBUTOFFEFEGPSUIFN
     

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105. 1MVHJO4QFD
     class Plugin p where
     data PState p  Type
     data PConfig p  Type
     type POutput p  Type
     type PlugM p (m  *  *)  Constraint
     pluginOptionP  OptParser (PConfig p)
     setupState  MonadIO m  PConfig p  m (PState p)
     initialise  (p ∈ ps, MonadPlugins ps m, PlugM p m)
      proxy p  Info  m Info
     finalise  (p ∈ ps, MonadPlugins ps m, PlugM p m)
      proxy p  Info  m Info
     genOutput  (p ∈ ps, MonadPlugins ps m, PlugM p m)
      PConfig p  m (POutput p)
     

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106. #VOEMJOHNVMUJQMFQMVHJO
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     Solver '[] -- Solver without any Plugin 

     Solver '[A, B, C] -- Solver with Plugins A, B and C
     

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     type PBundle h ps = Record h (IdentFields ps)
     type PStateB ps = PBundle PState ps
     

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115. #FGPSF5D1MVHJO
     (&%~)  forall l xs h a. Member l (Labels xs)
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      Record h ((l  a) |< xs)
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     $ gcastWith
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     $ gcastWith
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     @Entry' @(Take (Index l (Labels xs)) xs)
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     )
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116. #FGPSF5D1MVHJO
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      l := (h (ElemAt (Idx l (Labels xs)) (Vals xs))  h a)
      Record h ((l  a) |< xs)
     Record hl &%~ (_ := f) =
     Record
     $ gcastWith
     (takeMapApply @Entry' @(Index l (Labels xs)) @xs)
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     (dropMapApply @Entry' @(Index l (Labels xs) + 1) @xs)
     $ gcastWith
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     )
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117. "GUFS5D1MVHJO
     {-# OPTIONS_GHC -fplugin Data.TypeLevel.List.Solver #-}
     (&%~)  forall l xs h a. Member l (Labels xs)
      Record h xs
      l := (h (ElemAt (Idx l (Labels xs)) (Vals xs))  h a)
      Record h ((l  a) |< xs)
     Record hl &%~ (_ := f) =
     Record
     $ hmodify' (Proxy @(Index l (Labels xs))) f hl
     
     

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118. 4PVSDF1MVHJO
     {-# LANGUAGE OverloadedLabels #-}
     record = emptyRec &+ #a := 42
     &+ #b := False &+ #c := ()
     {-# OPTIONS_GHC -fplugin Data.Record.Plugin #-}
     {-# LANGUAGE OverloadedLabels #-}
     record = MkRecord { a = 42  Int, b = False, c = () }
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126. $PODMVTJPOT
     

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128. #JCMJPHSBQIZ
     Oleg Kiselyov, Tagless-final style. http://
     okmij.org/ftp/tagless-final/index.html
     2. D. Coutts, R. Leshchinskiy and D. Stewart, Stream
     Fusion: From Lists to Streams to Nothing at All.
     3. G. Mainland, R. Leshchinskiy and SPJ, Exploiting
     Vector Instructions with Generalized Stream Fusion.
     4. ghc-typelits-natnormalise package
     

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129. 5IBOLZPV
     

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