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+monad-ran-0.0.6: Implementations of common monads and monad transformers as right Kan extensions (Index)
monad-ran-0.0.6: Implementations of common monads and monad transformers as right Kan extensions
-- Finding the right Kan extension
+
+moduleControl.Monad.Ran
+(Yoneda(..)
+,Codensity(..)
+,Ran(..)
+,RMonad
+,G
+,H
+,toRan
+,fromRan
+)where
+
+importData.Monoid
+importControl.Applicative
+importControl.Monad
+importControl.Monad.Identity
+importControl.Monad.Cont
+importControl.Monad.State
+importControl.Monad.Error
+importControl.Monad.Reader
+importControl.Monad.Writer
+importControl.Monad.RWS
+
+dataYonedafa=Yoneda{getYoneda::forallb.(a->b)->fb}
+
+instanceFunctor(Yonedaf)where
+fmapfm=Yoneda(\k->getYonedam(k.f))
+
+instanceApplicativef=>Applicative(Yonedaf)where
+purea=Yoneda(\f->pure(fa))
+m<*>n=Yoneda(\f->getYonedam(f.)<*>getYonedanid)
+
+instanceMonadf=>Monad(Yonedaf)where
+returna=Yoneda(\f->return(fa))
+m>>=k=Yoneda(\f->getYonedamid>>=\a->getYoneda(ka)f)
+
+instanceMonadTransYonedawhere
+liftm=Yoneda(\f->liftMfm)
+
+dataCodensityfa=Codensity{getCodensity::forallb.(a->fb)->fb}
+
+instanceFunctor(Codensityk)where
+fmapfm=Codensity(\k->getCodensitym(k.f))
+
+instanceApplicative(Codensityf)where
+pure=return
+(<*>)=ap
+
+instanceMonad(Codensityf)where
+returnx=Codensity(\k->kx)
+m>>=k=Codensity(\c->getCodensitym(\a->getCodensity(ka)c))
+
+instanceMonadTransCodensitywhere
+liftm=Codensity(m>>=)
+
+runCodensity::Monadm=>Codensityma->ma
+runCodensity=flipgetCodensityreturn
+
+runCodensityApp::Applicativef=>Codensityfa->fa
+runCodensityApp=flipgetCodensitypure
+
+-- .. Pointed
+
+dataRanma=Ran{getRan::forallb.(a->Gmb)->Hmb}
+
+classMonadf=>RMonadfwhere
+typeGf::*->*
+typeHf::*->*
+toRan::fa->Ranfa
+fromRan::Ranfa->fa
+
+--class RMonadTrans t where
+-- liftR :: RMonad m => RanT m a -> RanT (t m) a
+
+-- utility bifunctors for definitions below
+typeHom=(->)
+type(:->)=ReaderT
+
+dataErrorHbr=ErrorH{getErrorH::(b->r)->r}
+dataErrorTHbmr=ErrorTH{getErrorTH::(b->Gmr)->Hmr}
+
+-- Yoneda Identity
+-- forall o. (a -> o) -> o
+instanceRMonadIdentitywhere
+typeGIdentity=Identity
+typeHIdentity=Identity
+toRanm=Ran(m>>=)
+fromRan=flipgetRanIdentity
+
+-- Yoneda Endo
+-- forall o. (a -> o) -> o -> o
+instanceRMonadMaybewhere
+typeGMaybe=Identity
+typeHMaybe=Endo
+toRan(Justx)=Ran(\k->Endo(\_->runIdentity(kx)))
+toRanNothing=Ran(\_->Endoid)
+fromRan(Ranf)=appEndo(f(Identity.Just))Nothing
+
+-- Yoneda (ErrorH b)
+-- forall o. (a -> o) -> (b -> o) -> o
+instanceErrorb=>RMonad(Eitherb)where
+typeG(Eitherb)=Identity
+typeH(Eitherb)=ErrorHb
+
+-- Yoneda (ErrorTH b m)
+-- forall o. (a -> G m o) -> (b -> G m o) -> H m o
+instance(RMonadm,Errorb)=>RMonad(ErrorTbm)where
+typeG(ErrorTbm)=Gm
+typeH(ErrorTbm)=ErrorTHbm
+
+-- Yoneda f
+-- forall o. (a -> o) -> f o
+instanceMonadf=>RMonad(Yonedaf)where
+typeG(Yonedaf)=Identity
+typeH(Yonedaf)=f
+
+-- Codensity f
+-- forall o. (a -> f o) -> f o
+instanceRMonad(Codensityf)where
+typeG(Codensityf)=f
+typeH(Codensityf)=f
+
+-- Yoneda (Reader r)
+-- forall o. (a -> o) -> r -> o
+instanceRMonad(Readere)where
+typeG(Readere)=Identity
+typeH(Readere)=Home
+
+-- embedded as CPS'd State to avoid superfluous 'mappend mempty' calls
+-- specialized Codensity (Reader w)
+-- forall o. (a -> w -> o) -> w -> o
+instanceMonoidw=>RMonad(Writerw)where
+typeG(Writerw)=Homw
+typeH(Writerw)=Homw
+-- forall o. (a -> w -> o) -> o
+-- type H (Writer w) = Identity
+
+-- Codensity (Reader s)
+-- forall o. (a -> s -> o) -> s -> o
+instanceRMonad(States)where
+typeG(States)=Homs
+typeH(States)=Homs
+
+-- Codensity (Const r)
+-- (a -> r) -> r
+instanceRMonad(Contr)where
+typeG(Contr)=Constr
+typeH(Contr)=Constr
+
+-- forall o. (a -> G m o) -> r -> H m o
+instanceRMonadm=>RMonad(ReaderTem)where
+typeG(ReaderTem)=Gm
+typeH(ReaderTem)=e:->Hm
+
+-- forall o. (a -> w -> G m o) -> H m o
+instance(Monoidw,RMonadm)=>RMonad(WriterTwm)where
+typeG(WriterTwm)=w:->Gm
+typeH(WriterTwm)=Hm
+
+-- forall o. (a -> s -> G m o) -> s -> H m o
+instanceRMonadm=>RMonad(StateTsm)where
+typeG(StateTsm)=s:->Gm
+typeH(StateTsm)=s:->Hm
+
+-- (a -> G m r) -> H m r
+dataConstTrfa=ConstT{getConstT::fr}
+instanceRMonadm=>RMonad(ContTrm)where
+typeG(ContTrm)=ConstTr(Gm)
+typeH(ContTrm)=ConstTr(Hm)
+
Instances