{-|
  Copyright   :  (C) 2013-2016, University of Twente
  License     :  BSD2 (see the file LICENSE)
  Maintainer  :  Christiaan Baaij <christiaan.baaij@gmail.com>
-}

{-# LANGUAGE CPP              #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE TemplateHaskell  #-}
{-# LANGUAGE TupleSections    #-}
{-# LANGUAGE ViewPatterns     #-}

{-# OPTIONS_GHC -fno-warn-orphans #-}

module CLaSH.GHC.GHC2Core
  ( GHC2CoreState
  , tyConMap
  , coreToTerm
  , coreToId
  , coreToName
  , qualfiedNameString
  , makeAllTyCons
  , emptyGHC2CoreState
  )
where

-- External Modules
import           Control.Exception           (throw)
import           Control.Lens                ((^.), (%~), (&), (%=))
import           Control.Monad.Trans.Class   (lift)
import           Control.Monad.Trans.Reader  (ReaderT)
import qualified Control.Monad.Trans.Reader  as Reader
import           Control.Monad.State         (State)
import qualified Control.Monad.State.Lazy    as State
import qualified Data.ByteString.Char8       as Char8
import           Data.Hashable               (Hashable (..))
import           Data.HashMap.Lazy           (HashMap)
import qualified Data.HashMap.Lazy           as HashMap
import qualified Data.HashMap.Strict         as HSM
import           Data.Maybe                  (catMaybes,fromMaybe,listToMaybe)
import           Data.Text                   (isInfixOf,pack)
import qualified Data.Traversable            as T
import           Unbound.Generics.LocallyNameless     (bind, embed, rebind, rec,
                                              runFreshM, string2Name, unbind,
                                              unembed)
import qualified Unbound.Generics.LocallyNameless     as Unbound

-- GHC API
import CoAxiom    (CoAxiom (co_ax_branches), CoAxBranch (cab_lhs,cab_rhs), brListMapM)
import Coercion   (Coercion (..),Role(..),coercionType,coercionKind,mkCoercionType)
import CoreFVs    (exprSomeFreeVars)
import CoreSyn    (AltCon (..), Bind (..), CoreExpr,
                   Expr (..), rhssOfAlts)
import DataCon    (DataCon, dataConExTyVars,
                   dataConName, dataConRepArgTys,
                   dataConTag, dataConTyCon,
                   dataConUnivTyVars, dataConWorkId,
                   dataConWrapId_maybe)
import DynFlags   (unsafeGlobalDynFlags)
import FamInstEnv (FamInst (..), FamInstEnvs,
                   familyInstances)
import FastString (unpackFS)
import Id         (isDataConId_maybe)
import IdInfo     (IdDetails (..))
import Kind       (isSuperKindTyCon)
import Literal    (Literal (..))
import Module     (moduleName, moduleNameString)
import Name       (Name, nameModule_maybe,
                   nameOccName, nameUnique, getSrcSpan)
import OccName    (occNameString)
import Outputable (showPpr, showSDocUnsafe)
import Pair       (Pair (..))
import PprCore    (pprCoreExpr)
import SrcLoc     (isGoodSrcSpan)
import TyCon      (AlgTyConRhs (..), TyCon,
                   algTyConRhs, isAlgTyCon, isFamilyTyCon,
                   isFunTyCon, isNewTyCon,
                   isPrimTyCon, isTupleTyCon, isClosedSynFamilyTyCon_maybe,
#if __GLASGOW_HASKELL__ >= 711
                   expandSynTyCon_maybe,
#else
                   tcExpandTyCon_maybe,
#endif
                   tyConArity,
                   tyConDataCons, tyConKind,
                   tyConName, tyConUnique)
import Type       (mkTopTvSubst, substTy, tcView)
import TypeRep    (TyLit (..), Type (..))
import Unique     (Uniquable (..), Unique, getKey)
import Var        (Id, TyVar, Var, idDetails,
                   isTyVar, varName, varType,
                   varUnique)
import VarSet     (isEmptyVarSet)

-- Local imports
import qualified CLaSH.Core.DataCon          as C
import qualified CLaSH.Core.Literal          as C
import qualified CLaSH.Core.Term             as C
import qualified CLaSH.Core.TyCon            as C
import qualified CLaSH.Core.Type             as C
import qualified CLaSH.Core.Var              as C
import           CLaSH.Driver.Types
import           CLaSH.Primitives.Types
import           CLaSH.Util

instance Hashable Name where
  hashWithSalt s = hashWithSalt s . getKey . nameUnique

data GHC2CoreState
  = GHC2CoreState
  { _tyConMap :: HashMap C.TyConName TyCon
  , _nameMap  :: HashMap Name String
  }

makeLenses ''GHC2CoreState

emptyGHC2CoreState :: GHC2CoreState
emptyGHC2CoreState = GHC2CoreState HSM.empty HSM.empty

makeAllTyCons :: GHC2CoreState
              -> FamInstEnvs
              -> HashMap C.TyConName C.TyCon
makeAllTyCons hm fiEnvs = go hm hm
  where
    go old new
        | HSM.null (new ^. tyConMap) = HSM.empty
        | otherwise                  = tcm `HSM.union` tcm'
      where
        (tcm,old') = State.runState (T.mapM (makeTyCon fiEnvs) (new ^. tyConMap)) old
        tcm'       = go old' (old' & tyConMap %~ (`HSM.difference` (old ^. tyConMap)))

makeTyCon :: FamInstEnvs
          -> TyCon
          -> State GHC2CoreState C.TyCon
makeTyCon fiEnvs tc = tycon
  where
    tycon
      | isFamilyTyCon tc    = mkFunTyCon
      | isTupleTyCon tc     = mkTupleTyCon
      | isAlgTyCon tc       = mkAlgTyCon
      | isPrimTyCon tc      = mkPrimTyCon
      | isSuperKindTyCon tc = mkSuperKindTyCon
      | otherwise           = mkVoidTyCon
      where
        tcArity = tyConArity tc

        mkAlgTyCon = do
          tcName <- coreToName tyConName tyConUnique qualfiedNameString tc
          tcKind <- coreToType (tyConKind tc)
          tcRhsM <- makeAlgTyConRhs $ algTyConRhs tc
          case tcRhsM of
            Just tcRhs ->
              return
                C.AlgTyCon
                { C.tyConName   = tcName
                , C.tyConKind   = tcKind
                , C.tyConArity  = tcArity
                , C.algTcRhs    = tcRhs
                }
            Nothing -> return (C.PrimTyCon tcName tcKind tcArity)

        mkFunTyCon = do
          tcName <- coreToName tyConName tyConUnique qualfiedNameString tc
          tcKind <- coreToType (tyConKind tc)
          substs <- case isClosedSynFamilyTyCon_maybe tc of
            Nothing -> let instances = familyInstances fiEnvs tc
                       in  mapM famInstToSubst instances
            Just cx -> let bx = co_ax_branches cx
                       in  brListMapM (\b -> (,) <$> mapM coreToType (cab_lhs b)
                                                 <*> coreToType (cab_rhs b)) bx
          return
            C.FunTyCon
            { C.tyConName  = tcName
            , C.tyConKind  = tcKind
            , C.tyConArity = tcArity
            , C.tyConSubst = substs
            }

        mkTupleTyCon = do
          tcName <- coreToName tyConName tyConUnique qualfiedNameString tc
          tcKind <- coreToType (tyConKind tc)
          tcDc   <- fmap (C.DataTyCon . (:[])) . coreToDataCon False . head . tyConDataCons $ tc
          return
            C.AlgTyCon
            { C.tyConName   = tcName
            , C.tyConKind   = tcKind
            , C.tyConArity  = tcArity
            , C.algTcRhs    = tcDc
            }

        mkPrimTyCon = do
          tcName <- coreToName tyConName tyConUnique qualfiedNameString tc
          tcKind <- coreToType (tyConKind tc)
          return
            C.PrimTyCon
            { C.tyConName    = tcName
            , C.tyConKind    = tcKind
            , C.tyConArity   = tcArity
            }

        mkSuperKindTyCon = do
          tcName <- coreToName tyConName tyConUnique qualfiedNameString tc
          return C.SuperKindTyCon
                   { C.tyConName = tcName
                   }

        mkVoidTyCon = do
          tcName <- coreToName tyConName tyConUnique qualfiedNameString tc
          tcKind <- coreToType (tyConKind tc)
          return (C.PrimTyCon tcName tcKind tcArity)

        famInstToSubst :: FamInst -> State GHC2CoreState ([C.Type],C.Type)
        famInstToSubst fi = do
          tys <- mapM coreToType  (fi_tys fi)
          ty  <- coreToType (fi_rhs fi)
          return (tys,ty)

makeAlgTyConRhs :: AlgTyConRhs
                -> State GHC2CoreState (Maybe C.AlgTyConRhs)
makeAlgTyConRhs algTcRhs = case algTcRhs of
  DataTyCon dcs _ -> Just <$> C.DataTyCon <$> mapM (coreToDataCon False) dcs
  NewTyCon dc _ (rhsTvs,rhsEtad) _ -> Just <$> (C.NewTyCon <$> coreToDataCon False dc
                                                           <*> ((,) <$> mapM coreToVar rhsTvs
                                                                    <*> coreToType rhsEtad
                                                               )
                                               )
  AbstractTyCon _ -> return Nothing
  DataFamilyTyCon -> return Nothing

coreToTerm :: PrimMap a
           -> [Var]
           -> SrcSpan
           -> CoreExpr
           -> State GHC2CoreState C.Term
coreToTerm primMap unlocs srcsp coreExpr = Reader.runReaderT (term coreExpr) srcsp
  where
    term :: CoreExpr -> ReaderT SrcSpan (State GHC2CoreState) C.Term
    term (Var x)                 = lift (var x)
    term (Lit l)                 = return $ C.Literal (coreToLiteral l)
    term (App eFun (Type tyArg)) = C.TyApp <$> term eFun <*> lift (coreToType tyArg)
    term (App eFun eArg)         = C.App   <$> term eFun <*> term eArg
    term (Lam x e) | isTyVar x   = C.TyLam <$> (bind <$> lift (coreToTyVar x) <*> addUsefull (getSrcSpan x) (term e))
                   | otherwise   = C.Lam   <$> (bind <$> lift (coreToId x) <*> addUsefull (getSrcSpan x) (term e))
    term (Let (NonRec x e1) e2)  = do
      x' <- lift (coreToId x)
      e1' <- addUsefull (getSrcSpan x) (term e1)
      e2' <- term e2
      return $ C.Letrec $ bind (rec [(x', embed e1')]) e2'

    term (Let (Rec xes) e) = do
      xes' <- mapM (\(x,b) -> (,) <$> lift (coreToId x)
                                  <*> addUsefull (getSrcSpan x)
                                                 (embed <$> term b))
                   xes
      e' <- term e
      return $ C.Letrec $ bind (rec xes') e'

    term (Case _ _ ty [])  = C.Prim (pack "EmptyCase") <$> lift (coreToType ty)
    term (Case e b ty alts) = do
     let usesBndr = any ( not . isEmptyVarSet . exprSomeFreeVars (`elem` [b]))
                  $ rhssOfAlts alts
     b' <- lift (coreToId b)
     e' <- addUsefull (getSrcSpan b) (term e)
     ty' <- lift (coreToType ty)
     let caseTerm v = C.Case v ty' <$> mapM (addUsefull (getSrcSpan b) . alt) alts
     if usesBndr
      then do
        ct <- caseTerm (C.Var (unembed $ C.varType b') (C.varName b'))
        return $ C.Letrec $ bind (rec [(b',embed e')]) ct
      else caseTerm e'

    term (Cast e co) = do
      let (Pair ty1 ty2) = coercionKind co
      hasPrimCoM <- lift (hasPrimCo co)
      ty1_I <- lift (isIntegerTy ty1)
      ty2_I <- lift (isIntegerTy ty2)
      case hasPrimCoM of
        Just ty | ty1_I || ty2_I -> do
          sp <- Reader.ask
          throw (CLaSHException sp
                  (unlines [ "CLaSH cannot translate the following cast:\n"
                           , showSDocUnsafe (pprCoreExpr (Cast e co))
                           , "\nbecause it contains the following coercion:\n"
                           , showPpr unsafeGlobalDynFlags (if ty1_I then mkCoercionType Representational ty1 ty
                                                                    else mkCoercionType Representational ty ty2)
                           , "\nthat exposes the internal structure of the CLaSH primitive type: " ++ showPpr unsafeGlobalDynFlags ty
                           , "This is most likely due to the use of 'seq' or BangPatterns on values of (newtype wrappers of) types: {BitVector,Index,Signed,Unsigned}"
                           ])
                  (Just (unlines ["The cast occurs in the following core expression:\n"
                                 , showSDocUnsafe (pprCoreExpr coreExpr)]))
                  )

        _ -> term e
    term (Tick _ e)        = term e
    term (Type t)          = C.Prim (pack "_TY_") <$> lift (coreToType t)
    term (Coercion co)     = C.Prim (pack "_CO_") <$> lift (coreToType (coercionType co))

    var x = do
        xVar   <- coreToVar x
        xPrim  <- coreToPrimVar x
        let xNameS = pack $ Unbound.name2String xPrim
        xType  <- coreToType (varType x)
        case isDataConId_maybe x of
          Just dc -> case HashMap.lookup xNameS primMap of
                      Just _  -> return $ C.Prim xNameS xType
                      Nothing -> C.Data <$> coreToDataCon (isDataConWrapId x && not (isNewTyCon (dataConTyCon dc))) dc
          Nothing -> case HashMap.lookup xNameS primMap of
            Just (Primitive f _)
              | f == pack "CLaSH.Signal.Internal.mapSignal#" -> return (mapSignalTerm xType)
              | f == pack "CLaSH.Signal.Internal.signal#"    -> return (signalTerm xType)
              | f == pack "CLaSH.Signal.Internal.appSignal#" -> return (appSignalTerm xType)
              | f == pack "CLaSH.Signal.Internal.traverse#"  -> return (traverseTerm xType)
              | f == pack "CLaSH.Signal.Internal.joinSignal#" -> return (joinTerm xType)
              | f == pack "CLaSH.Signal.Bundle.vecBundle#"   -> return (vecUnwrapTerm xType)
              | f == pack "GHC.Base.$"                       -> return (dollarTerm xType)
              | otherwise                                    -> return (C.Prim xNameS xType)
            Just (BlackBox {}) ->
              return (C.Prim xNameS xType)
            Nothing
              | x `elem` unlocs -> return (C.Prim xNameS xType)
              | pack "$cshow" `isInfixOf` xNameS -> return (C.Prim xNameS xType)
              | otherwise       -> return  (C.Var xType xVar)

    alt (DEFAULT   , _ , e) = bind C.DefaultPat <$> term e
    alt (LitAlt l  , _ , e) = bind (C.LitPat . embed $ coreToLiteral l) <$> term e
    alt (DataAlt dc, xs, e) = case span isTyVar xs of
      (tyvs,tmvs) -> bind <$> (C.DataPat . embed <$>
                                lift (coreToDataCon False dc) <*>
                                (rebind <$>
                                  lift (mapM coreToTyVar tyvs) <*>
                                  lift (mapM coreToId tmvs))) <*>
                              term e

    coreToLiteral :: Literal
                  -> C.Literal
    coreToLiteral l = case l of
      MachStr    fs  -> C.StringLiteral (Char8.unpack fs)
      MachChar   c   -> C.CharLiteral c
      MachInt    i   -> C.IntLiteral i
      MachInt64  i   -> C.IntLiteral i
      MachWord   i   -> C.WordLiteral i
      MachWord64 i   -> C.WordLiteral i
      LitInteger i _ -> C.IntegerLiteral i
      MachFloat r    -> C.RationalLiteral r
      MachDouble r   -> C.RationalLiteral r
      MachNullAddr   -> C.StringLiteral []
      MachLabel fs _ _ -> C.StringLiteral (unpackFS fs)

addUsefull :: SrcSpan -> ReaderT SrcSpan (State GHC2CoreState) a
            -> ReaderT SrcSpan (State GHC2CoreState) a
addUsefull x = Reader.local (\r -> if isGoodSrcSpan x then x else r)

isIntegerTy :: Type -> State GHC2CoreState Bool
isIntegerTy (TyConApp tc []) = do
  tcNm <- qualfiedNameString (tyConName tc)
  return (tcNm == "GHC.Integer.Type.Integer")
isIntegerTy _ = return False

hasPrimCo :: Coercion -> State GHC2CoreState (Maybe Type)
hasPrimCo (TyConAppCo _ _ coers) = do
  tcs <- catMaybes <$> mapM hasPrimCo coers
  return (listToMaybe tcs)

hasPrimCo (AppCo co1 co2) = do
  tc1M <- hasPrimCo co1
  case tc1M of
    Just _ -> return tc1M
    _ -> hasPrimCo co2
hasPrimCo (ForAllCo _ co) = hasPrimCo co

hasPrimCo co@(AxiomInstCo _ _ coers) = do
    let (Pair ty1 _) = coercionKind co
    ty1PM <- isPrimTc ty1
    if ty1PM
       then return (Just ty1)
       else do
         tcs <- catMaybes <$> mapM hasPrimCo coers
         return (listToMaybe tcs)
  where
    isPrimTc (TyConApp tc _) = do
      tcNm <- qualfiedNameString (tyConName tc)
      return (tcNm `elem` ["CLaSH.Sized.Internal.BitVector.BitVector"
                          ,"CLaSH.Sized.Internal.Index.Index"
                          ,"CLaSH.Sized.Internal.Signed.Signed"
                          ,"CLaSH.Sized.Internal.Unsigned.Unsigned"
                          ])
    isPrimTc _ = return False

hasPrimCo (SymCo co) = hasPrimCo co

hasPrimCo (TransCo co1 co2) = do
  tc1M <- hasPrimCo co1
  case tc1M of
    Just _ -> return tc1M
    _ -> hasPrimCo co2

hasPrimCo (AxiomRuleCo _ _ coers) = do
  tcs <- catMaybes <$> mapM hasPrimCo coers
  return (listToMaybe tcs)

hasPrimCo (NthCo _ co)  = hasPrimCo co
hasPrimCo (LRCo _ co)   = hasPrimCo co
hasPrimCo (InstCo co _) = hasPrimCo co
hasPrimCo (SubCo co)    = hasPrimCo co

hasPrimCo _ = return Nothing

coreToDataCon :: Bool
              -> DataCon
              -> State GHC2CoreState C.DataCon
coreToDataCon mkWrap dc = do
    repTys <- mapM coreToType (dataConRepArgTys dc)
    dcTy   <- if mkWrap
                then case dataConWrapId_maybe dc of
                        Just wrapId -> coreToType (varType wrapId)
                        Nothing     -> error $ concat [ $(curLoc)
                                                      , "DataCon Wrapper: "
                                                      , showPpr unsafeGlobalDynFlags dc
                                                      , " not found"
                                                      ]
                else coreToType (varType $ dataConWorkId dc)
    mkDc dcTy repTys
  where
    mkDc dcTy repTys = do
      nm   <- coreToName dataConName getUnique qualfiedNameString dc
      uTvs <- mapM coreToVar (dataConUnivTyVars dc)
      eTvs <- mapM coreToVar (dataConExTyVars dc)
      return $ C.MkData
             { C.dcName       = nm
             , C.dcTag        = dataConTag dc
             , C.dcType       = dcTy
             , C.dcArgTys     = repTys
             , C.dcUnivTyVars = uTvs
             , C.dcExtTyVars  = eTvs
             }

coreToType :: Type
           -> State GHC2CoreState C.Type
coreToType ty = coreToType' $ fromMaybe ty (tcView ty)

coreToType' :: Type
            -> State GHC2CoreState C.Type
coreToType' (TyVarTy tv) = C.VarTy <$> coreToType (varType tv) <*> (coreToVar tv)
coreToType' (TyConApp tc args)
  | isFunTyCon tc = foldl C.AppTy (C.ConstTy C.Arrow) <$> mapM coreToType args
#if __GLASGOW_HASKELL__ >= 711
  | otherwise     = case expandSynTyCon_maybe tc args of
#else
  | otherwise     = case tcExpandTyCon_maybe tc args of
#endif
                      Just (substs,synTy,remArgs) -> do
                        let substs' = mkTopTvSubst substs
                            synTy'  = substTy substs' synTy
                        foldl C.AppTy <$> coreToType synTy' <*> mapM coreToType remArgs
                      _ -> do
                        tcName <- coreToName tyConName tyConUnique qualfiedNameString tc
                        tyConMap %= (HSM.insert tcName tc)
                        C.mkTyConApp <$> (pure tcName) <*> mapM coreToType args
coreToType' (FunTy ty1 ty2)  = C.mkFunTy <$> coreToType ty1 <*> coreToType ty2
coreToType' (ForAllTy tv ty) = C.ForAllTy <$>
                               (bind <$> coreToTyVar tv <*> coreToType ty)
coreToType' (LitTy tyLit)    = return $ C.LitTy (coreToTyLit tyLit)
coreToType' (AppTy ty1 ty2)  = C.AppTy <$> coreToType ty1 <*> coreToType' ty2

coreToTyLit :: TyLit
            -> C.LitTy
coreToTyLit (NumTyLit i) = C.NumTy (fromInteger i)
coreToTyLit (StrTyLit s) = C.SymTy (unpackFS s)

coreToTyVar :: TyVar
            -> State GHC2CoreState C.TyVar
coreToTyVar tv =
  C.TyVar <$> (coreToVar tv) <*> (embed <$> coreToType (varType tv))

coreToId :: Id
         -> State GHC2CoreState C.Id
coreToId i =
  C.Id <$> (coreToVar i) <*> (embed <$> coreToType (varType i))

coreToVar :: Var
          -> State GHC2CoreState (Unbound.Name a)
coreToVar = coreToName varName varUnique qualfiedNameStringM

coreToPrimVar :: Var
              -> State GHC2CoreState (Unbound.Name C.Term)
coreToPrimVar = coreToName varName varUnique qualfiedNameString

coreToName :: (b -> Name)
           -> (b -> Unique)
           -> (Name -> State GHC2CoreState String)
           -> b
           -> State GHC2CoreState (Unbound.Name a)
coreToName toName toUnique toString v = do
  ns <- toString (toName v)
  return (Unbound.makeName ns (toInteger . getKey . toUnique $ v))

qualfiedNameString :: Name
                   -> State GHC2CoreState String
qualfiedNameString n = makeCached n nameMap
                     $ return (fromMaybe "_INTERNAL_" (modNameM n) ++ ('.':occName))
  where
    occName = occNameString $ nameOccName n

qualfiedNameStringM :: Name
                    -> State GHC2CoreState String
qualfiedNameStringM n = makeCached n nameMap
                      $ return (maybe occName (\modName -> modName ++ ('.':occName)) (modNameM n))
  where
    occName = occNameString $ nameOccName n

modNameM :: Name
         -> Maybe String
modNameM n = do
      module_ <- nameModule_maybe n
      let moduleNm = moduleName module_
      return (moduleNameString moduleNm)

-- | Given the type:
--
-- @forall a. forall b. forall clk. (a -> b) -> Signal' clk a -> Signal' clk b@
--
-- Generate the term:
--
-- @
-- /\(a:*)./\(b:*)./\(clk:Clock).\(f : (Signal' clk a -> Signal' clk b)).
-- \(x : Signal' clk a).f x
-- @
mapSignalTerm :: C.Type
              -> C.Term
mapSignalTerm (C.ForAllTy tvATy) =
    C.TyLam (bind aTV (
    C.TyLam (bind bTV (
    C.TyLam (bind clkTV (
    C.Lam   (bind fId (
    C.Lam   (bind xId (
    C.App (C.Var fTy fName) (C.Var aTy xName)))))))))))
  where
    (aTV,bTV,clkTV,funTy) = runFreshM $ do
      { (aTV',C.ForAllTy tvBTy)   <- unbind tvATy
      ; (bTV',C.ForAllTy tvClkTy) <- unbind tvBTy
      ; (clkTV',funTy')           <- unbind tvClkTy
      ; return (aTV',bTV',clkTV',funTy')
      }
    (C.FunTy _ funTy'') = C.tyView funTy
    (C.FunTy aTy bTy)   = C.tyView funTy''
    fName = string2Name "f"
    xName = string2Name "x"
    fTy   = C.mkFunTy aTy bTy
    fId   = C.Id fName (embed fTy)
    xId   = C.Id xName (embed aTy)

mapSignalTerm ty = error $ $(curLoc) ++ show ty

-- | Given the type:
--
-- @forall a. forall clk. a -> Signal' clk a@
--
-- Generate the term
--
-- @/\(a:*)./\(clk:Clock).\(x:Signal' clk a).x@
signalTerm :: C.Type
           -> C.Term
signalTerm (C.ForAllTy tvATy) =
    C.TyLam (bind aTV (
    C.TyLam (bind clkTV (
    C.Lam   (bind xId (
    C.Var   aTy xName))))))
  where
    (aTV,clkTV,funTy) = runFreshM $ do
      { (aTV', C.ForAllTy tvClkTy) <- unbind tvATy
      ; (clkTV', funTy')           <- unbind tvClkTy
      ; return (aTV',clkTV',funTy')
      }
    (C.FunTy _ aTy) = C.tyView funTy
    xName = string2Name "x"
    xId   = C.Id xName (embed aTy)

signalTerm ty = error $ $(curLoc) ++ show ty

-- | Given the type:
--
-- @
-- forall clk. forall a. forall b. Signal' clk (a -> b) -> Signal' clk a ->
-- Signal' clk b
-- @
--
-- Generate the term:
--
-- @
-- /\(clk:Clock)./\(a:*)./\(b:*).\(f : (Signal' clk a -> Signal' clk b)).
-- \(x : Signal' clk a).f x
-- @
appSignalTerm :: C.Type
              -> C.Term
appSignalTerm (C.ForAllTy tvClkTy) =
    C.TyLam (bind clkTV (
    C.TyLam (bind aTV (
    C.TyLam (bind bTV (
    C.Lam   (bind fId (
    C.Lam   (bind xId (
    C.App (C.Var fTy fName) (C.Var aTy xName)))))))))))
  where
    (clkTV,aTV,bTV,funTy) = runFreshM $ do
      { (clkTV',C.ForAllTy tvATy) <- unbind tvClkTy
      ; (aTV',C.ForAllTy tvBTy)   <- unbind tvATy
      ; (bTV',funTy')           <- unbind tvBTy
      ; return (clkTV',aTV',bTV',funTy')
      }
    (C.FunTy _ funTy'') = C.tyView funTy
    (C.FunTy aTy bTy)   = C.tyView funTy''
    fName = string2Name "f"
    xName = string2Name "x"
    fTy   = C.mkFunTy aTy bTy
    fId   = C.Id fName (embed fTy)
    xId   = C.Id xName (embed aTy)

appSignalTerm ty = error $ $(curLoc) ++ show ty

-- | Given the type:
--
-- @
-- forall t.forall n.forall a.SClock t -> Vec n (Signal' t a) ->
-- Signal' t (Vec n a)
-- @
--
-- Generate the term:
--
-- @
-- /\(t:Clock)./\(n:Nat)./\(a:*).\(sclk:SClock t).\(vs:Signal' (Vec n a)).vs
-- @
vecUnwrapTerm :: C.Type
              -> C.Term
vecUnwrapTerm (C.ForAllTy tvTTy) =
    C.TyLam (bind tTV (
    C.TyLam (bind nTV (
    C.TyLam (bind aTV (
    C.Lam   (bind sclkId (
    C.Lam   (bind vsId (
    C.Var vsTy vsName))))))))))
  where
    (tTV,nTV,aTV,funTy) = runFreshM $ do
      { (tTV',C.ForAllTy tvNTy) <- unbind tvTTy
      ; (nTV',C.ForAllTy tvATy) <- unbind tvNTy
      ; (aTV',funTy')           <- unbind tvATy
      ; return (tTV',nTV',aTV',funTy')
      }
    (C.FunTy sclkTy funTy'') = C.tyView funTy
    (C.FunTy _ vsTy)         = C.tyView funTy''
    sclkName = string2Name "sclk"
    vsName   = string2Name "vs"
    sclkId   = C.Id sclkName (embed sclkTy)
    vsId     = C.Id vsName   (embed vsTy)

vecUnwrapTerm ty = error $ $(curLoc) ++ show ty

-- | Given the type:
--
-- @
-- forall f.forall a.forall b.forall clk.Applicative f => (a -> f b) ->
-- CSignal clk a -> f (Signal' clk b)
-- @
--
-- Generate the term:
--
-- @
-- /\(f:* -> *)./\(a:*)./\(b:*)./\(clk:Clock).\(dict:Applicative f).
-- \(g:a -> f b).\(x:Signal' clk a).g x
-- @
traverseTerm :: C.Type
             -> C.Term
traverseTerm (C.ForAllTy tvFTy) =
    C.TyLam (bind fTV (
    C.TyLam (bind aTV (
    C.TyLam (bind bTV (
    C.TyLam (bind clkTV (
    C.Lam   (bind dictId (
    C.Lam   (bind gId (
    C.Lam   (bind xId (
    C.App (C.Var gTy gName) (C.Var xTy xName)))))))))))))))
  where
    (fTV,aTV,bTV,clkTV,funTy) = runFreshM $ do
      { (fTV',C.ForAllTy tvATy) <- unbind tvFTy
      ; (aTV',C.ForAllTy tvBTy) <- unbind tvATy
      ; (bTV',C.ForAllTy tvClkTy) <- unbind tvBTy
      ; (clkTV',funTy') <- unbind tvClkTy
      ; return (fTV',aTV',bTV',clkTV',funTy')
      }
    (C.FunTy dictTy funTy1) = C.tyView funTy
    (C.FunTy gTy    funTy2) = C.tyView funTy1
    (C.FunTy xTy    _)      = C.tyView funTy2
    dictName = string2Name "dict"
    gName    = string2Name "g"
    xName    = string2Name "x"
    dictId   = C.Id dictName (embed dictTy)
    gId      = C.Id gName (embed gTy)
    xId      = C.Id xName (embed xTy)

traverseTerm ty = error $ $(curLoc) ++ show ty

-- | Given the type:
--
-- @forall a. forall b. (a -> b) -> a -> b@
--
-- Generate the term:
--
-- @/\(a:*)./\(b:*).\(f : (a -> b)).\(x : a).f x@
dollarTerm :: C.Type
           -> C.Term
dollarTerm (C.ForAllTy tvATy) =
    C.TyLam (bind aTV (
    C.TyLam (bind bTV (
    C.Lam   (bind fId (
    C.Lam   (bind xId (
    C.App (C.Var fTy fName) (C.Var aTy xName)))))))))
  where
    (aTV,bTV,funTy) = runFreshM $ do
      { (aTV',C.ForAllTy tvBTy) <- unbind tvATy
      ; (bTV',funTy')           <- unbind tvBTy
      ; return (aTV',bTV',funTy')
      }
    (C.FunTy fTy funTy'') = C.tyView funTy
    (C.FunTy aTy _)       = C.tyView funTy''
    fName = string2Name "f"
    xName = string2Name "x"
    fId   = C.Id fName (embed fTy)
    xId   = C.Id xName (embed aTy)

dollarTerm ty = error $ $(curLoc) ++ show ty

-- | Given the type:
--
-- @forall a. forall clk. Signal' clk (Signal' clk a) -> Signal' clk a@
--
-- Generate the term
--
-- @/\(a:*)./\(clk:Clock).\(x:Signal' clk a).x@
joinTerm :: C.Type
         -> C.Term
joinTerm ty@(C.ForAllTy _) = signalTerm ty
joinTerm ty = error $ $(curLoc) ++ show ty

isDataConWrapId :: Id -> Bool
isDataConWrapId v = case idDetails v of
                      DataConWrapId {} -> True
                      _                -> False