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

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"HHSFTTJWF6TFPG()$ TypeApplications FlexibleContexts MPTC DataKinds TypeFamilies ScopedTypeVariables FlexibleInstances TypeOperators UndecidableInstances DerivingStrategies OverloadedStrings PolyKinds TemplateHaskell RecordWildCards GND 0 50 100 150 200 5PUBM.PEVMFT &YUFOTJPOT 0O()$

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5BHMFTT'JOBM4UZMF<> data family PhysQty m class Monad m  MonadDiff m where grad  PhysQty m  m (PhysQty m) div  PhysQty m  m (PhysQty m) w "CTUSBDUDPNNPOPQFSBUJPOBTBNPOBEJDGVODUJPO w "DUVBMMZ diffOFFETTPNFHFPNFUSJDJOGPBTBOFYUSBBSHVNFOU CVUJUJTIJEEFOJOMonadic value m w 5IJTIJEFTUIFJNQMEFUBJMPGEJ⒎PQTBOEFOBCMFTVTUPTFQBSBUFJNQM GSPNBCTUSBDUFRVBUJPOT5IJTFODPVSBHFTNPEVMBSJUZBOEHFOFSBMJUZ

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1SPCMFN5PP.VDI#JOET ν △ u − 1 ρ grad P 1SPCMFN)BWFUPXSJUF( )UPDPNQPTFGVODUJPOT

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1SPCMFN5PP.VDI#JOET ν △ u − 1 ρ grad P (-)  ((nu *)  laplacian u)  ((/rho)  grad u) 1SPCMFN)BWFUPXSJUF( )UPDPNQPTFGVODUJPOT

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

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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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#FGPSF5D1MVHJO (&%~)  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 $ gcastWith (takeMapApply @Entry' @(Index l (Labels xs)) @xs) $ gcastWith (dropMapApply @Entry' @(Index l (Labels xs) + 1) @xs) $ gcastWith (mapApplyAppend @Entry' @(Take (Index l (Labels xs)) xs) @((l  a) ': Drop (Index l (Labels xs) + 1) xs) ) $ hmodify' (Proxy @(Index l (Labels xs))) f hl 5SJWJBMIBOEXSJUUFOQSPPGT .BQI YTZT .BQIYT.BQIZT

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"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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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 = () } 8JUIPVU4PVSDF1MVHJO 8JUI4PVSDF1MVHJO w 0WFSMPBEJOHGPS3FDPSEVQEBUFBOEBDDFTTPSTZOUBYDBOOPUCF JNQMFNFOUFEXJUIUIFDVSSFOU()$4PVSDF1MVHJO.FDIBOJTN

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#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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