    -- Apply the vectorisation transformation to types. This is the \mathcal{L}_t scheme in HtM.

    module Vectorise.Type.Type
      ( vectTyCon
      , vectAndLiftType
      , vectType
      )
    where

    import Vectorise.Utils
    import Vectorise.Monad
    import Vectorise.Builtins
    import TcType
    import Type
    import TypeRep
    import TyCon
    import Control.Monad
    import Control.Applicative
    import Data.Maybe
    import Prelude -- avoid redundant import warning due to AMP

    -- |Vectorise a type constructor. Unless there is a vectorised version (stripped of embedded
    -- parallel arrays), the vectorised version is the same as the original.
    --
    vectTyCon :: TyCon -> VM TyCon
    vectTyCon tc = maybe tc id <$> lookupTyCon tc

    -- |Produce the vectorised and lifted versions of a type.
    --
    -- NB: Here we are limited to properly handle predicates at the toplevel only.  Anything embedded
    --     in what is called the 'body_ty' below will end up as an argument to the type family 'PData'.
    --
    vectAndLiftType :: Type -> VM (Type, Type)
    vectAndLiftType ty | Just ty' <- coreView ty = vectAndLiftType ty'
    vectAndLiftType ty
      = do { padicts  <- liftM catMaybes $ mapM paDictArgType tyvars
           ; vmono_ty <- vectType mono_ty
           ; lmono_ty <- mkPDataType vmono_ty
           ; return (abstractType tyvars (padicts ++ theta) vmono_ty,
                     abstractType tyvars (padicts ++ theta) lmono_ty)
           }
      where
        (tyvars, phiTy)  = splitForAllTys ty
        (theta, mono_ty) = tcSplitPhiTy phiTy

    -- |Vectorise a type.
    --
    -- For each quantified var we need to add a PA dictionary out the front of the type.
    -- So          forall a.         C  a => a -> a
    -- turns into  forall a. PA a => Cv a => a :-> a
    --
    vectType :: Type -> VM Type
    vectType ty
      | Just ty'  <- coreView ty
      = vectType ty'
    vectType (TyVarTy tv)      = return $ TyVarTy tv
    vectType (LitTy l)         = return $ LitTy l
    vectType (AppTy ty1 ty2)   = AppTy <$> vectType ty1 <*> vectType ty2
    vectType (TyConApp tc tys) = TyConApp <$> vectTyCon tc <*> mapM vectType tys
    vectType (FunTy ty1 ty2)
      | isPredTy ty1
      = FunTy <$> vectType ty1 <*> vectType ty2   -- don't build a closure for dictionary abstraction
      | otherwise
      = TyConApp <$> builtin closureTyCon <*> mapM vectType [ty1, ty2]
    vectType ty@(ForAllTy _ _)
     = do {   -- strip off consecutive foralls
          ; let (tyvars, tyBody) = splitForAllTys ty

              -- vectorise the body
          ; vtyBody <- vectType tyBody

              -- make a PA dictionary for each of the type variables
          ; dictsPA <- liftM catMaybes $ mapM paDictArgType tyvars

              -- add the PA dictionaries after the foralls
          ; return $ abstractType tyvars dictsPA vtyBody
          }

    -- |Add quantified vars and dictionary parameters to the front of a type.
    --
    abstractType :: [TyVar] -> [Type] -> Type -> Type
    abstractType tyvars dicts = mkForAllTys tyvars . mkFunTys dicts