{-# LANGUAGE StandaloneDeriving        #-}
{-# LANGUAGE ScopedTypeVariables       #-}
{-# LANGUAGE NoMonomorphismRestriction #-}
{-# LANGUAGE TypeSynonymInstances      #-}
{-# LANGUAGE FlexibleInstances         #-}
{-# LANGUAGE TupleSections             #-}
{-# LANGUAGE DeriveDataTypeable        #-}
{-# LANGUAGE BangPatterns              #-}
{-# LANGUAGE PatternGuards             #-}
{-# LANGUAGE DeriveFunctor             #-}
{-# LANGUAGE MultiParamTypeClasses     #-}
{-# LANGUAGE OverloadedStrings         #-}

-- | This module defines the representation of Subtyping and WF Constraints, and 
-- the code for syntax-directed constraint generation. 

module Language.Haskell.Liquid.Constraint (
    
    -- * Constraint information output by generator 
    CGInfo (..)
  
    -- * Function that does the actual generation
  , generateConstraints
    
    -- * Project Constraints to Fixpoint Format
  , cgInfoFInfo , cgInfoFInfoBot, cgInfoFInfoKvars
  
  -- * KVars in constraints, for debug/profile purposes
  -- , kvars, kvars'
  ) where

import CoreSyn
import SrcLoc           
import Type             -- (coreEqType)
import PrelNames
import qualified TyCon   as TC
import qualified DataCon as DC

import TypeRep 
import Class            (Class, className)
import Var
import Id
import Name            
import NameSet
import Text.PrettyPrint.HughesPJ hiding (first)

import Control.Monad.State

import Control.Applicative      ((<$>))
import Control.Exception.Base

import Data.Monoid              (mconcat, mempty, mappend)
import Data.Maybe               (fromJust, isJust, fromMaybe, catMaybes)
import qualified Data.HashMap.Strict as M
import qualified Data.HashSet        as S
import qualified Data.List           as L
import qualified Data.Text           as T
import Data.Bifunctor
import Data.List (foldl')

import Text.Printf

import qualified Language.Haskell.Liquid.CTags      as Tg
import qualified Language.Fixpoint.Types            as F
import Language.Fixpoint.Names (dropModuleNames)
import Language.Fixpoint.Sort (pruneUnsortedReft)

import Language.Haskell.Liquid.Fresh

import Language.Haskell.Liquid.Types            hiding (binds, Loc, loc, freeTyVars, Def)
import Language.Haskell.Liquid.Bare
import Language.Haskell.Liquid.Strata
import Language.Haskell.Liquid.Annotate
import Language.Haskell.Liquid.GhcInterface
import Language.Haskell.Liquid.RefType
import Language.Haskell.Liquid.PredType         hiding (freeTyVars)          
import Language.Haskell.Liquid.PrettyPrint
import Language.Haskell.Liquid.GhcMisc          (isInternal, collectArguments, getSourcePos, pprDoc, tickSrcSpan, hasBaseTypeVar, showPpr)
import Language.Haskell.Liquid.Misc
import Language.Fixpoint.Misc
import Language.Haskell.Liquid.Qualifier
import Control.DeepSeq

import Debug.Trace (trace)
import IdInfo
-----------------------------------------------------------------------
------------- Constraint Generation: Toplevel -------------------------
-----------------------------------------------------------------------

generateConstraints      :: GhcInfo -> CGInfo
generateConstraints info = {-# SCC "ConsGen" #-} execState act $ initCGI cfg info
  where 
    act                  = consAct info
    cfg                  = config $ spec info


consAct info
  = do γ     <- initEnv info
       sflag <- scheck <$> get
       tflag <- trustghc <$> get
       let trustBinding x = if tflag 
                             then (x `elem` (derVars info) || isInternal x) 
                             else False 
       foldM_ (consCBTop trustBinding) γ (cbs info)
       hcs <- hsCs  <$> get 
       hws <- hsWfs <$> get
       scss <- sCs <$> get
       annot <- annotMap <$> get
       scs <- if sflag then concat <$> mapM splitS (hcs ++ scss)
                       else return []
       let smap = if sflag then solveStrata scs else []
       let hcs' = if sflag then subsS smap hcs else hcs
       fcs <- concat <$> mapM splitC (subsS smap hcs') 
       fws <- concat <$> mapM splitW hws
       let annot' = if sflag then (\t -> subsS smap t) <$> annot else annot
       modify $ \st -> st { fixCs = fcs } { fixWfs = fws } {annotMap = annot'}

------------------------------------------------------------------------------------
initEnv :: GhcInfo -> CG CGEnv  
------------------------------------------------------------------------------------
initEnv info 
  = do let tce   = tcEmbeds sp
       let fVars = impVars info ++ filter isConLikeId (snd <$> freeSyms sp)
       defaults <- forM fVars $ \x -> liftM (x,) (trueTy $ varType x)
       tyi      <- tyConInfo <$> get 
       (hs,f0)  <- refreshHoles $ grty info -- asserted refinements     (for defined vars)
       f0''     <- refreshArgs' =<< grtyTop info     -- default TOP reftype      (for exported vars without spec)
       let f0'   = if notruetypes $ config sp then [] else f0''
       f1       <- refreshArgs' $ defaults           -- default TOP reftype      (for all vars)
       f2       <- refreshArgs' $ assm info          -- assumed refinements      (for imported vars)
       f3       <- refreshArgs' $ vals asmSigs sp    -- assumed refinedments     (with `assume`)
       f4       <- refreshArgs' $ vals ctors   sp    -- constructor refinements  (for measures)
       sflag    <- scheck <$> get
       let senv  = if sflag then f2 else []
       let tx    = mapFst F.symbol . addRInv ialias . strataUnify senv . predsUnify sp
       let bs    = (tx <$> ) <$> [f0 ++ f0', f1, f2, f3, f4]
       lts      <- lits <$> get
       let tcb   = mapSnd (rTypeSort tce) <$> concat bs
       let γ0    = measEnv sp (head bs) (cbs info) (tcb ++ lts) (bs!!3) hs
       foldM (++=) γ0 [("initEnv", x, y) | (x, y) <- concat $ tail bs]
  where
    sp           = spec info
    ialias       = mkRTyConIAl $ ialiases sp 
    vals f       = map (mapSnd val) . f

refreshHoles vts = first catMaybes . unzip . map extract <$> mapM refreshHoles' vts
refreshHoles' (x,t)
  | noHoles t = return (Nothing,x,t)
  | otherwise = (Just $ F.symbol x,x,) <$> mapReftM tx t
  where
    tx r | hasHole r = refresh r
         | otherwise = return r
extract (a,b,c) = (a,(b,c))
    
refreshArgs' = mapM (mapSndM refreshArgs)

strataUnify :: [(Var, SpecType)] -> (Var, SpecType) -> (Var, SpecType)
strataUnify senv (x, t) = (x, maybe t (mappend t) pt)
  where
    pt                  = (fmap (\(U r p l) -> U mempty mempty l)) <$> L.lookup x senv


-- | TODO: All this *should* happen inside @Bare@ but appears
--   to happen after certain are signatures are @fresh@-ed,
--   which is why they are here.
predsUnify sp      = second (addTyConInfo tce tyi) -- needed to eliminate some @RPropH@
                   . unifyts penv                  -- needed to match up some  @TyVars@
  where
    tce            = tcEmbeds sp 
    tyi            = tyconEnv sp
    penv           = predEnv  sp
    
predEnv            ::  GhcSpec -> F.SEnv PrType
predEnv sp         = F.fromListSEnv bs
  where
    bs             = mapFst F.symbol <$> (dcs ++ assms)
    dcs            = concatMap mkDataConIdsTy pcs
    pcs            = [(x, dcPtoPredTy x y) | (x, y) <- dconsP sp]
    assms          = mapSnd (mapReft ur_pred . val) <$> tySigs sp
    dcPtoPredTy    :: DC.DataCon -> DataConP -> PrType
    dcPtoPredTy dc = fmap ur_pred . dataConPSpecType dc

unifyts penv (x, t)     = (x, unify pt t)
 where
   pt                   = F.lookupSEnv x' penv
   x'                   = F.symbol x
---------------------------------------------------------------------------------------

measEnv sp xts cbs lts asms hs
  = CGE { loc   = noSrcSpan
        , renv  = fromListREnv $ second val <$> meas sp
        , syenv = F.fromListSEnv $ freeSyms sp
        , fenv  = initFEnv $ lts ++ (second (rTypeSort tce . val) <$> meas sp)
        , recs  = S.empty 
        , invs  = mkRTyConInv    $ invariants sp
        , ial   = mkRTyConIAl    $ ialiases   sp
        , grtys = fromListREnv xts
        , assms = fromListREnv asms
        , emb   = tce 
        , tgEnv = Tg.makeTagEnv cbs
        , tgKey = Nothing
        , trec  = Nothing
        , lcb   = M.empty
        , holes = fromListHEnv hs
        } 
    where
      tce = tcEmbeds sp

assm = assm_grty impVars
grty = assm_grty defVars

assm_grty f info = [ (x, val t) | (x, t) <- sigs, x `S.member` xs ] 
  where 
    xs           = S.fromList $ f info 
    sigs         = tySigs     $ spec info  

grtyTop info     = forM topVs $ \v -> (v,) <$> (trueTy $ varType v) -- val $ varSpecType v) | v <- defVars info, isTop v]
  where
    topVs        = filter isTop $ defVars info
    isTop v      = isExportedId v && not (v `S.member` sigVs)
    isExportedId = flip elemNameSet (exports $ spec info) . getName
    sigVs        = S.fromList $ [v | (v,_) <- (tySigs $ spec info)
                                           ++ (asmSigs $ spec info)]


------------------------------------------------------------------------
-- | Helpers: Reading/Extending Environment Bindings -------------------
------------------------------------------------------------------------

data FEnv = FE { fe_binds :: !F.IBindEnv      -- ^ Integer Keys for Fixpoint Environment
               , fe_env   :: !(F.SEnv F.Sort) -- ^ Fixpoint Environment
               }

insertFEnv (FE benv env) ((x, t), i)
  = FE (F.insertsIBindEnv [i] benv) (F.insertSEnv x t env)

insertsFEnv = L.foldl' insertFEnv

initFEnv init = FE F.emptyIBindEnv $ F.fromListSEnv (wiredSortedSyms ++ init)

data CGEnv 
  = CGE { loc    :: !SrcSpan           -- ^ Location in original source file
        , renv   :: !REnv              -- ^ SpecTypes for Bindings in scope
        , syenv  :: !(F.SEnv Var)      -- ^ Map from free Symbols (e.g. datacons) to Var
        -- , penv   :: !(F.SEnv PrType)   -- ^ PrTypes for top-level bindings (merge with renv) 
        , fenv   :: !FEnv              -- ^ Fixpoint Environment
        , recs   :: !(S.HashSet Var)   -- ^ recursive defs being processed (for annotations)
        , invs   :: !RTyConInv         -- ^ Datatype invariants 
        , ial    :: !RTyConIAl         -- ^ Datatype checkable invariants 
        , grtys  :: !REnv              -- ^ Top-level variables with (assert)-guarantees to verify
        , assms  :: !REnv              -- ^ Top-level variables with assumed types
        , emb    :: F.TCEmb TC.TyCon   -- ^ How to embed GHC Tycons into fixpoint sorts
        , tgEnv :: !Tg.TagEnv          -- ^ Map from top-level binders to fixpoint tag
        , tgKey :: !(Maybe Tg.TagKey)  -- ^ Current top-level binder
        , trec  :: !(Maybe (M.HashMap F.Symbol SpecType)) -- ^ Type of recursive function with decreasing constraints
        , lcb   :: !(M.HashMap F.Symbol CoreExpr) -- ^ Let binding that have not been checked
        , holes :: !HEnv               -- ^ Types with holes, will need refreshing
        } -- deriving (Data, Typeable)

instance PPrint CGEnv where
  pprint = pprint . renv

instance Show CGEnv where
  show = showpp

getTag :: CGEnv -> F.Tag
getTag γ = maybe Tg.defaultTag (`Tg.getTag` (tgEnv γ)) (tgKey γ)

setLoc :: CGEnv -> SrcSpan -> CGEnv
γ `setLoc` src 
  | isGoodSrcSpan src = γ { loc = src } 
  | otherwise         = γ

withRecs :: CGEnv -> [Var] -> CGEnv 
withRecs γ xs  = γ { recs = foldl' (flip S.insert) (recs γ) xs }

withTRec γ xts = γ' {trec = Just $ M.fromList xts' `M.union` trec'}
  where γ'    = γ `withRecs` (fst <$> xts)
        trec' = fromMaybe M.empty $ trec γ
        xts'  = mapFst F.symbol <$> xts

setBind :: CGEnv -> Tg.TagKey -> CGEnv  
setBind γ k 
  | Tg.memTagEnv k (tgEnv γ) = γ { tgKey = Just k }
  | otherwise                = γ


isGeneric :: RTyVar -> SpecType -> Bool
isGeneric α t =  all (\(c, α') -> (α'/=α) || isOrd c || isEq c ) (classConstrs t)
  where classConstrs t = [(c, α') | (c, ts) <- tyClasses t
                                  , t'      <- ts
                                  , α'      <- freeTyVars t']
        isOrd          = (ordClassName ==) . className
        isEq           = (eqClassName ==) . className


-----------------------------------------------------------------
------------------- Constraints: Types --------------------------
-----------------------------------------------------------------

data SubC     = SubC { senv  :: !CGEnv
                     , lhs   :: !SpecType
                     , rhs   :: !SpecType 
                     }
              | SubR { senv  :: !CGEnv
                     , oblig :: !Oblig
                     , ref   :: !RReft
                     }

data WfC      = WfC  !CGEnv !SpecType 
              -- deriving (Data, Typeable)

type FixSubC  = F.SubC Cinfo
type FixWfC   = F.WfC Cinfo

instance PPrint SubC where
  pprint c = pprint (senv c)
           $+$ ((text " |- ") <+> ( (pprint (lhs c)) 
                             $+$ text "<:" 
                             $+$ (pprint (rhs c))))

instance PPrint WfC where
  pprint (WfC w r) = pprint w <> text " |- " <> pprint r 

instance SubStratum SubC where
  subS su (SubC γ t1 t2) = SubC γ (subS su t1) (subS su t2)
  subS _  c              = c

------------------------------------------------------------
------------------- Constraint Splitting -------------------
------------------------------------------------------------

splitW ::  WfC -> CG [FixWfC]

splitW (WfC γ t@(RFun x t1 t2 _)) 
  =  do ws   <- bsplitW γ t
        ws'  <- splitW (WfC γ t1) 
        γ'   <- (γ, "splitW") += (x, t1)
        ws'' <- splitW (WfC γ' t2)
        return $ ws ++ ws' ++ ws''

splitW (WfC γ t@(RAppTy t1 t2 _)) 
  =  do ws   <- bsplitW γ t
        ws'  <- splitW (WfC γ t1) 
        ws'' <- splitW (WfC γ t2)
        return $ ws ++ ws' ++ ws''

splitW (WfC γ (RAllT _ r)) 
  = splitW (WfC γ r)

splitW (WfC γ (RAllP _ r)) 
  = splitW (WfC γ r)

splitW (WfC γ t@(RVar _ _))
  = bsplitW γ t 

splitW (WfC γ t@(RApp _ ts rs _))
  =  do ws    <- bsplitW γ t 
        γ'    <- γ `extendEnvWithVV` t 
        ws'   <- concat <$> mapM splitW (map (WfC γ') ts)
        ws''  <- concat <$> mapM (rsplitW γ) rs
        return $ ws ++ ws' ++ ws''

splitW (WfC γ (RAllE x tx t))
  = do  ws  <- splitW (WfC γ tx) 
        γ'  <- (γ, "splitW") += (x, tx)
        ws' <- splitW (WfC γ' t)
        return $ ws ++ ws'

splitW (WfC γ (REx x tx t))
  = do  ws  <- splitW (WfC γ tx) 
        γ'  <- (γ, "splitW") += (x, tx)
        ws' <- splitW (WfC γ' t)
        return $ ws ++ ws'

splitW (WfC _ t) 
  = errorstar $ "splitW cannot handle: " ++ showpp t

rsplitW _ (RPropP _ _)  
  = errorstar "Constrains: rsplitW for RPropP"
rsplitW γ (RProp ss t0) 
  = do γ' <- foldM (++=) γ [("rsplitC", x, ofRSort s) | (x, s) <- ss]
       splitW $ WfC γ' t0

bsplitW :: CGEnv -> SpecType -> CG [FixWfC]
bsplitW γ t = pruneRefs <$> get >>= return . bsplitW' γ t

bsplitW' γ t pflag
  | F.isNonTrivialSortedReft r' = [F.wfC (fe_binds $ fenv γ) r' Nothing ci] 
  | otherwise                   = []
  where 
    r'                          = rTypeSortedReft' pflag γ t
    ci                          = Ci (loc γ) Nothing

mkSortedReft tce = F.RR . rTypeSort tce

------------------------------------------------------------
splitS  :: SubC -> CG [([Stratum], [Stratum])]
bsplitS :: SpecType -> SpecType -> CG [([Stratum], [Stratum])]
------------------------------------------------------------

splitS (SubC γ (REx x tx t1) (REx x2 _ t2)) | x == x2
  = splitS (SubC γ t1 t2)

splitS (SubC γ t1 (REx x tx t2)) 
  = splitS (SubC γ t1 t2)

splitS (SubC γ (REx x tx t1) t2) 
  = splitS (SubC γ t1 t2)

splitS (SubC γ (RAllE x tx t1) (RAllE x2 _ t2)) | x == x2
  = splitS (SubC γ t1 t2)

splitS (SubC γ (RAllE x tx t1) t2)
  = splitS (SubC γ t1 t2)

splitS (SubC γ t1 (RAllE x tx t2))
  = splitS (SubC γ t1 t2)

splitS (SubC γ (RRTy e r o t1) t2) 
  = do γ' <- foldM (\γ (x, t) -> γ `addSEnv` ("splitS", x,t)) γ e 
       c1 <- splitS (SubR γ' o r)
       c2 <- splitS (SubC γ t1 t2)
       return $ c1 ++ c2

splitS (SubC γ t1@(RFun x1 r1 r1' _) t2@(RFun x2 r2 r2' _)) 
  =  do cs       <- bsplitS t1 t2 
        cs'      <- splitS  (SubC γ r2 r1) 
        γ'       <- (γ, "splitC") += (x2, r2) 
        let r1x2' = r1' `F.subst1` (x1, F.EVar x2) 
        cs''     <- splitS  (SubC γ' r1x2' r2') 
        return    $ cs ++ cs' ++ cs''

splitS (SubC γ t1@(RAppTy r1 r1' _) t2@(RAppTy r2 r2' _)) 
  =  do cs    <- bsplitS t1 t2 
        cs'   <- splitS  (SubC γ r1 r2) 
        cs''  <- splitS  (SubC γ r1' r2') 
        cs''' <- splitS  (SubC γ r2' r1') 
        return $ cs ++ cs' ++ cs'' ++ cs'''

splitS (SubC γ t1 (RAllP p t))
  = splitS $ SubC γ t1 t'
  where t' = fmap (replacePredsWithRefs su) t
        su = (uPVar p, pVartoRConc p)

splitS (SubC _ t1@(RAllP _ _) t2) 
  = errorstar $ "Predicate in lhs of constrain:" ++ showpp t1 ++ "\n<:\n" ++ showpp t2

splitS (SubC γ (RAllT α1 t1) (RAllT α2 t2))
  |  α1 ==  α2 
  = splitS $ SubC γ t1 t2
  | otherwise   
  = splitS $ SubC γ t1 t2' 
  where t2' = subsTyVar_meet' (α2, RVar α1 mempty) t2

splitS (SubC γ (RApp c1 _ _ _) (RApp c2 _ _ _)) | isClass c1 && c1 == c2 
  = return []


splitS (SubC γ t1@(RApp _ _ _ _) t2@(RApp _ _ _ _))
  = do (t1',t2') <- unifyVV t1 t2
       cs    <- bsplitS t1' t2'
       γ'    <- γ `extendEnvWithVV` t1' 
       let RApp c  t1s r1s _ = t1'
       let RApp c' t2s r2s _ = t2'
       let tyInfo = rtc_info c
       cscov  <- splitSIndexed  γ' t1s t2s $ covariantTyArgs     tyInfo
       cscon  <- splitSIndexed  γ' t2s t1s $ contravariantTyArgs tyInfo
       cscov' <- rsplitSIndexed γ' r1s r2s $ covariantPsArgs     tyInfo
       cscon' <- rsplitSIndexed γ' r2s r1s $ contravariantPsArgs tyInfo
       return $ cs ++ cscov ++ cscon ++ cscov' ++ cscon'

splitS (SubC γ t1@(RVar a1 _) t2@(RVar a2 _)) 
  | a1 == a2
  = bsplitS t1 t2

splitS c@(SubC _ t1 t2) 
  = errorstar $ "(Another Broken Test!!!) splitS unexpected: " ++ showpp t1 ++ "\n\n" ++ showpp t2

splitS (SubR _ _ _)
  = return []

splitSIndexed γ t1s t2s indexes 
  = concatMapM splitS (zipWith (SubC γ) t1s' t2s')
  where t1s' = catMaybes $ (!?) t1s <$> indexes
        t2s' = catMaybes $ (!?) t2s <$> indexes

rsplitSIndexed γ t1s t2s indexes 
  = concatMapM (rsplitS γ) (safeZip "rsplitC" t1s' t2s')
  where t1s' = catMaybes $ (!?) t1s <$> indexes
        t2s' = catMaybes $ (!?) t2s <$> indexes

bsplitS t1 t2 
  = return $ [(s1, s2)] 
  where [s1, s2]   = getStrata <$> [t1, t2]

rsplitCS _ (RPropP _ _, RPropP _ _) 
  = errorstar "RefTypes.rsplitC on RPropP"

rsplitS γ (t1@(RProp s1 r1), t2@(RProp s2 r2))
  = splitS (SubC γ (F.subst su r1) r2)
  where su = F.mkSubst [(x, F.EVar y) | ((x,_), (y,_)) <- zip s1 s2]

rsplitS _ _  
  = errorstar "rspliS Rpoly - RPropP"

------------------------------------------------------------
splitC :: SubC -> CG [FixSubC]
------------------------------------------------------------

splitC (SubC γ (REx x tx t1) (REx x2 _ t2)) | x == x2
  = do γ' <- (γ, "addExBind 0") += (x, forallExprRefType γ tx)
       splitC (SubC γ' t1 t2)

splitC (SubC γ t1 (REx x tx t2)) 
  = do γ' <- (γ, "addExBind 1") += (x, forallExprRefType γ tx)
       let xs  = grapBindsWithType tx γ
       let t2' = splitExistsCases x xs tx t2
       splitC (SubC γ' t1 t2')

-- existential at the left hand side is treated like forall
splitC z@(SubC γ (REx x tx t1) t2) 
  = do -- let tx' = traceShow ("splitC: " ++ showpp z) tx 
       γ' <- (γ, "addExBind 1") += (x, forallExprRefType γ tx)
       splitC (SubC γ' t1 t2)

splitC (SubC γ (RAllE x tx t1) (RAllE x2 _ t2)) | x == x2
  = do γ' <- (γ, "addExBind 0") += (x, forallExprRefType γ tx)
       splitC (SubC γ' t1 t2)


splitC (SubC γ (RAllE x tx t1) t2)
  = do γ' <- (γ, "addExBind 2") += (x, forallExprRefType γ tx)
       splitC (SubC γ' t1 t2)

splitC (SubC γ t1 (RAllE x tx t2))
  = do γ' <- (γ, "addExBind 2") += (x, forallExprRefType γ tx)
       splitC (SubC γ' t1 t2)

splitC (SubC γ (RRTy e r o t1) t2) 
  = do γ' <- foldM (\γ (x, t) -> γ `addSEnv` ("splitS", x,t)) γ e 
       c1 <- splitC (SubR γ' o  r )
       c2 <- splitC (SubC γ t1 t2)
       return $ c1 ++ c2

splitC (SubC γ t1@(RFun x1 r1 r1' _) t2@(RFun x2 r2 r2' _)) 
  =  do cs       <- bsplitC γ t1 t2 
        cs'      <- splitC  (SubC γ r2 r1) 
        γ'       <- (γ, "splitC") += (x2, r2) 
        let r1x2' = r1' `F.subst1` (x1, F.EVar x2) 
        cs''     <- splitC  (SubC γ' r1x2' r2') 
        return    $ cs ++ cs' ++ cs''

splitC (SubC γ t1@(RAppTy r1 r1' _) t2@(RAppTy r2 r2' _)) 
  =  do cs    <- bsplitC γ t1 t2 
        cs'   <- splitC  (SubC γ r1 r2) 
        cs''  <- splitC  (SubC γ r1' r2') 
        cs''' <- splitC  (SubC γ r2' r1') 
        return $ cs ++ cs' ++ cs'' ++ cs'''

splitC (SubC γ t1 (RAllP p t))
  = splitC $ SubC γ t1 t'
  where t' = fmap (replacePredsWithRefs su) t
        su = (uPVar p, pVartoRConc p)

splitC (SubC _ t1@(RAllP _ _) t2) 
  = errorstar $ "Predicate in lhs of constraint:" ++ showpp t1 ++ "\n<:\n" ++ showpp t2

splitC (SubC γ (RAllT α1 t1) (RAllT α2 t2))
  |  α1 ==  α2 
  = splitC $ SubC γ t1 t2
  | otherwise   
  = splitC $ SubC γ t1 t2' 
  where t2' = subsTyVar_meet' (α2, RVar α1 mempty) t2


splitC (SubC γ t1@(RApp c1 _ _ _) t2@(RApp c2 _ _ _)) | isClass c1 && c1 == c2
  = return []

splitC (SubC γ t1@(RApp _ _ _ _) t2@(RApp _ _ _ _))
  = do (t1',t2') <- unifyVV t1 t2
       cs    <- bsplitC γ t1' t2'
       γ'    <- γ `extendEnvWithVV` t1' 
       let RApp c  t1s r1s _ = t1'
       let RApp c' t2s r2s _ = t2'
       let tyInfo = rtc_info c
       cscov  <- splitCIndexed  γ' t1s t2s $ covariantTyArgs     tyInfo
       cscon  <- splitCIndexed  γ' t2s t1s $ contravariantTyArgs tyInfo
       cscov' <- rsplitCIndexed γ' r1s r2s $ covariantPsArgs     tyInfo
       cscon' <- rsplitCIndexed γ' r2s r1s $ contravariantPsArgs tyInfo
       return $ cs ++ cscov ++ cscon ++ cscov' ++ cscon'

splitC (SubC γ t1@(RVar a1 _) t2@(RVar a2 _)) 
  | a1 == a2
  = bsplitC γ t1 t2

splitC c@(SubC _ t1 t2) 
  = errorstar $ "(Another Broken Test!!!) splitc unexpected: " ++ showpp t1 ++ "\n\n" ++ showpp t2

splitC (SubR γ o r)
  = do fg     <- pruneRefs <$> get 
       let r1' = if fg then pruneUnsortedReft γ'' r1 else r1
       return $ F.subC γ' F.PTrue r1' r2 Nothing tag ci
  where
    γ'' = fe_env $ fenv γ
    γ'  = fe_binds $ fenv γ
    r1  = F.RR s $ F.toReft r
    r2  = F.RR s $ F.Reft (vv, [F.RConc $ F.PBexp $ F.EVar vv])
    vv  = "vvRec"
    s   = F.FApp F.boolFTyCon []
    ci  = Ci src err
    err = Just $ ErrAssType src o (text $ show o ++ "type error") r
    tag = getTag γ
    src = loc γ 

splitCIndexed γ t1s t2s indexes 
  = concatMapM splitC (zipWith (SubC γ) t1s' t2s')
  where
    t1s' = catMaybes $ (!?) t1s <$> indexes
    t2s' = catMaybes $ (!?) t2s <$> indexes

rsplitCIndexed γ t1s t2s indexes 
  = concatMapM (rsplitC γ) (safeZip "rsplitC" t1s'' t2s'')
  where
    t1s'           = catMaybes $ (!?) t1s <$> indexes
    t2s'           = catMaybes $ (!?) t2s <$> indexes
    (t1s'', t2s'') = pad "rsplitCIndexed" F.top t1s' t2s'


bsplitC γ t1 t2
  = checkStratum γ t1 t2 >> pruneRefs <$> get >>= return . bsplitC' γ t1 t2

checkStratum γ t1 t2
  | s1 <:= s2 = return ()
  | otherwise = addWarning wrn
  where [s1, s2]   = getStrata <$> [t1, t2]
        wrn        =  ErrOther (loc γ) (text $ "Stratum Error : " ++ show s1 ++ " > " ++ show s2) 

bsplitC' γ t1 t2 pflag
  | F.isFunctionSortedReft r1' && F.isNonTrivialSortedReft r2'
  = F.subC γ' F.PTrue (r1' {F.sr_reft = mempty}) r2' Nothing tag ci
  | F.isNonTrivialSortedReft r2'
  = F.subC γ' F.PTrue r1'  r2' Nothing tag ci
  | otherwise
  = []
  where 
    γ'     = fe_binds $ fenv γ
    r1'    = rTypeSortedReft' pflag γ t1
    r2'    = rTypeSortedReft' pflag γ t2
    ci     = Ci src err
    tag    = getTag γ
    err    = Just $ ErrSubType src (text "subtype") g t1 t2 
    src    = loc γ
    REnv g = renv γ 



unifyVV t1@(RApp c1 _ _ _) t2@(RApp c2 _ _ _)
  = do vv     <- (F.vv . Just) <$> fresh
       return  $ (shiftVV t1 vv,  (shiftVV t2 vv) ) -- {rt_pargs = r2s'})

rsplitC _ (RPropP _ _, RPropP _ _) 
  = errorstar "RefTypes.rsplitC on RPropP"

rsplitC γ (t1@(RProp s1 r1), t2@(RProp s2 r2))
  = do γ'  <-  foldM (++=) γ [("rsplitC1", x, ofRSort s) | (x, s) <- s2]
       splitC (SubC γ' (F.subst su r1) r2)
  where su = F.mkSubst [(x, F.EVar y) | ((x,_), (y,_)) <- zip s1 s2]

rsplitC _ _  
  = errorstar "rsplit Rpoly - RPropP"


-----------------------------------------------------------
-------------------- Generation: Types --------------------
-----------------------------------------------------------

data CGInfo = CGInfo { hsCs       :: ![SubC]                      -- ^ subtyping constraints over RType
                     , hsWfs      :: ![WfC]                       -- ^ wellformedness constraints over RType
                     , sCs        :: ![SubC]                      -- ^ additional stratum constrains for let bindings
                     , fixCs      :: ![FixSubC]                   -- ^ subtyping over Sort (post-splitting)
                     , isBind     :: ![Bool]                      -- ^ tracks constraints that come from let-bindings 
                     , fixWfs     :: ![FixWfC]                    -- ^ wellformedness constraints over Sort (post-splitting)
                     , globals    :: !F.FEnv                      -- ^ ? global measures
                     , freshIndex :: !Integer                     -- ^ counter for generating fresh KVars
                     , binds      :: !F.BindEnv                   -- ^ set of environment binders
                     , annotMap   :: !(AnnInfo (Annot SpecType))  -- ^ source-position annotation map
                     , tyConInfo  :: !(M.HashMap TC.TyCon RTyCon) -- ^ information about type-constructors
                     , specQuals  :: ![F.Qualifier]               -- ^ ? qualifiers in source files
                     , specDecr   :: ![(Var, [Int])]              -- ^ ? FIX THIS
                     , termExprs  :: !(M.HashMap Var [F.Expr])    -- ^ Terminating Metrics for Recursive functions
                     , specLVars  :: !(S.HashSet Var)             -- ^ Set of variables to ignore for termination checking
                     , specLazy   :: !(S.HashSet Var)             -- ^ ? FIX THIS
                     , tyConEmbed :: !(F.TCEmb TC.TyCon)          -- ^ primitive Sorts into which TyCons should be embedded
                     , kuts       :: !(F.Kuts)                    -- ^ Fixpoint Kut variables (denoting "back-edges"/recursive KVars)
                     , lits       :: ![(F.Symbol, F.Sort)]        -- ^ ? FIX THIS 
                     , tcheck     :: !Bool                        -- ^ Check Termination (?) 
                     , scheck     :: !Bool                        -- ^ Check Strata (?)
                     , trustghc   :: !Bool                        -- ^ Trust ghc auto generated bindings
                     , pruneRefs  :: !Bool                        -- ^ prune unsorted refinements
                     , logErrors  :: ![TError SpecType]           -- ^ Errors during coontraint generation
                     , kvProf     :: !KVProf                      -- ^ Profiling distribution of KVars 
                     , recCount   :: !Int                         -- ^ number of recursive functions seen (for benchmarks)
                     } -- deriving (Data, Typeable)

instance PPrint CGInfo where 
  pprint cgi =  {-# SCC "ppr_CGI" #-} ppr_CGInfo cgi

ppr_CGInfo cgi 
  =  (text "*********** Constraint Information ***********")
  -- -$$ (text "*********** Haskell SubConstraints ***********")
  -- -$$ (pprintLongList $ hsCs  cgi)
  -- -$$ (text "*********** Haskell WFConstraints ************")
  -- -$$ (pprintLongList $ hsWfs cgi)
  -- -$$ (text "*********** Fixpoint SubConstraints **********")
  -- -$$ (F.toFix  $ fixCs cgi)
  -- -$$ (text "*********** Fixpoint WFConstraints ************")
  -- -$$ (F.toFix  $ fixWfs cgi)
  -- -$$ (text "*********** Fixpoint Kut Variables ************")
  -- -$$ (F.toFix  $ kuts cgi)
  -- -$$ (text "*********** Literals in Source     ************")
  -- -$$ (pprint $ lits cgi)
  -- -$$ (text "*********** KVar Distribution *****************")
  -- -$$ (pprint $ kvProf cgi)
  -- -$$ (text "Recursive binders:" <+> pprint (recCount cgi))

type CG = State CGInfo

initCGI cfg info = CGInfo {
    hsCs       = [] 
  , sCs        = [] 
  , hsWfs      = [] 
  , fixCs      = []
  , isBind     = []
  , fixWfs     = [] 
  , globals    = globs
  , freshIndex = 0
  , binds      = F.emptyBindEnv
  , annotMap   = AI M.empty
  , tyConInfo  = tyi
  , specQuals  =  qualifiers spc ++ specificationQualifiers (maxParams cfg) (info {spec = spec'})
  , tyConEmbed = tce  
  , kuts       = F.ksEmpty 
  , lits       = coreBindLits tce info 
  , termExprs  = M.fromList $ texprs spc
  , specDecr   = decr spc
  , specLVars  = lvars spc
  , specLazy   = lazy spc
  , tcheck     = not $ notermination cfg
  , scheck     = strata cfg
  , trustghc   = trustinternals cfg
  , pruneRefs  = not $ noPrune cfg
  , logErrors  = []
  , kvProf     = emptyKVProf
  , recCount   = 0
  } 
  where 
    tce        = tcEmbeds spc 
    spc        = spec info
    spec'      = spc { tySigs  = [ (x, addTyConInfo tce tyi <$> t) | (x, t) <- tySigs spc]
                     , asmSigs = [ (x, addTyConInfo tce tyi <$> t) | (x, t) <- asmSigs spc]}
    tyi        = tyconEnv spc -- EFFECTS HEREHEREHERE makeTyConInfo (tconsP spc)
    globs      = F.fromListSEnv . map mkSort $ meas spc
    mkSort     = mapSnd (rTypeSortedReft tce . val)

coreBindLits tce info
  = sortNub      $ [ (val x, so) | (_, Just (F.ELit x so)) <- lconsts]
                ++ [ (dconToSym dc, dconToSort dc) | dc <- dcons]
  where 
    lconsts      = literalConst tce <$> literals (cbs info)
    dcons        = filter isDCon $ impVars info
    dconToSort   = typeSort tce . expandTypeSynonyms . varType 
    dconToSym    = dataConSymbol . idDataCon
    isDCon x     = isDataConWorkId x && not (hasBaseTypeVar x)

extendEnvWithVV γ t 
  | F.isNontrivialVV vv
  = (γ, "extVV") += (vv, t)
  | otherwise
  = return γ
  where vv = rTypeValueVar t

{- see tests/pos/polyfun for why you need everything in fixenv -} 
addCGEnv :: (SpecType -> SpecType) -> CGEnv -> (String, F.Symbol, SpecType) -> CG CGEnv
addCGEnv tx γ (_, x, t') 
  = do idx   <- fresh
       let t  = tx $ normalize γ {-x-} idx t'  
       let γ' = γ { renv = insertREnv x t (renv γ) }  
       pflag <- pruneRefs <$> get
       is    <- if isBase t 
                  then liftM2 (++) (liftM single $ addBind x $ rTypeSortedReft' pflag γ' t) (addClassBind t)
                  else return [] -- addClassBind t 
       return $ γ' { fenv = insertsFEnv (fenv γ) is }

(++=) :: CGEnv -> (String, F.Symbol, SpecType) -> CG CGEnv
(++=) γ = addCGEnv (addRTyConInv (M.unionWith mappend (invs γ) (ial γ))) γ  

addSEnv :: CGEnv -> (String, F.Symbol, SpecType) -> CG CGEnv
addSEnv γ = addCGEnv (addRTyConInv (invs γ)) γ

rTypeSortedReft' pflag γ 
  | pflag
  = pruneUnsortedReft (fe_env $ fenv γ) . f
  | otherwise
  = f 
  where f = rTypeSortedReft (emb γ)

(+++=) :: (CGEnv, String) -> (F.Symbol, CoreExpr, SpecType) -> CG CGEnv

(γ, msg) +++= (x, e, t) = (γ{lcb = M.insert x e (lcb γ)}, "+++=") += (x, t)

(+=) :: (CGEnv, String) -> (F.Symbol, SpecType) -> CG CGEnv
(γ, msg) += (x, r)
  | x == F.dummySymbol
  = return γ
  | x `memberREnv` (renv γ)
  = err 
  | otherwise
  =  γ ++= (msg, x, r) 
  where err = errorstar $ msg ++ " Duplicate binding for " 
                              ++ F.symbolString x 
                              ++ "\n New: " ++ showpp r
                              ++ "\n Old: " ++ showpp (x `lookupREnv` (renv γ))
                        
γ -= x =  γ {renv = deleteREnv x (renv γ), lcb  = M.delete x (lcb γ)}

(??=) :: CGEnv -> F.Symbol -> CG SpecType
γ ??= x 
  = case M.lookup x (lcb γ) of
    Just e  -> consE (γ-=x) e
    Nothing -> refreshTy $ γ ?= x

(?=) ::  CGEnv -> F.Symbol -> SpecType 
γ ?= x = fromMaybe err $ lookupREnv x (renv γ)
         where err = errorstar $ "EnvLookup: unknown " 
                               ++ showpp x 
                               ++ " in renv " 
                               ++ showpp (renv γ)

normalize' γ x idx t = addRTyConInv (M.unionWith mappend (invs γ) (ial γ)) $ normalize γ idx t

normalize γ idx 
  = normalizeVV idx 
  . normalizePds

normalizeVV idx t@(RApp _ _ _ _)
  | not (F.isNontrivialVV (rTypeValueVar t))
  = shiftVV t (F.vv $ Just idx)

normalizeVV _ t 
  = t 


addBind :: F.Symbol -> F.SortedReft -> CG ((F.Symbol, F.Sort), F.BindId)
addBind x r 
  = do st          <- get
       let (i, bs') = F.insertBindEnv x r (binds st)
       put          $ st { binds = bs' }
       return ((x, F.sr_sort r), i) -- traceShow ("addBind: " ++ showpp x) i

addClassBind :: SpecType -> CG [((F.Symbol, F.Sort), F.BindId)]
addClassBind = mapM (uncurry addBind) . classBinds

-- RJ: What is this `isBind` business?
pushConsBind act
  = do modify $ \s -> s { isBind = False : isBind s }
       z <- act
       modify $ \s -> s { isBind = tail (isBind s) }
       return z

addC :: SubC -> String -> CG ()  
addC !c@(SubC γ t1 t2) _msg 
  = do -- trace ("addC at " ++ show (loc γ) ++ _msg++ showpp t1 ++ "\n <: \n" ++ showpp t2 ) $
       modify $ \s -> s { hsCs  = c : (hsCs s) }
       bflag <- safeHead True . isBind <$> get
       sflag <- scheck                 <$> get 
       if bflag && sflag
         then modify $ \s -> s {sCs = (SubC γ t2 t1) : (sCs s) }
         else return ()
  where 
    safeHead a []     = a
    safeHead _ (x:xs) = x


addC !c _msg 
  = modify $ \s -> s { hsCs  = c : (hsCs s) }

addPost γ (RRTy e r OInv t) 
  = do γ' <- foldM (\γ (x, t) -> γ `addSEnv` ("addPost", x,t)) γ e 
       addC (SubR γ' OInv r) "precondition" >> return t

addPost γ (RRTy e r o t) 
  = do γ' <- foldM (\γ (x, t) -> γ ++= ("addPost", x,t)) γ e 
       addC (SubR γ' o r) "precondition" >> return t
addPost _ t  
  = return t

addW   :: WfC -> CG ()  
addW !w = modify $ \s -> s { hsWfs = w : (hsWfs s) }

addWarning   :: TError SpecType -> CG ()  
addWarning w = modify $ \s -> s { logErrors = w : (logErrors s) }

-- | Used for annotation binders (i.e. at binder sites)

addIdA            :: Var -> Annot SpecType -> CG ()
addIdA !x !t      = modify $ \s -> s { annotMap = upd $ annotMap s }
  where 
    loc           = getSrcSpan x
    upd m@(AI z)  = if boundRecVar loc m then m else addA loc (Just x) t m
    -- loc        = traceShow ("addIdA: " ++ show x ++ " :: " ++ showpp t ++ " at ") $ getSrcSpan x

boundRecVar l (AI m) = not $ null [t | (_, AnnRDf t) <- M.lookupDefault [] l m]


-- | Used for annotating reads (i.e. at Var x sites) 

addLocA :: Maybe Var -> SrcSpan -> Annot SpecType -> CG ()
addLocA !xo !l !t 
  = modify $ \s -> s { annotMap = addA l xo t $ annotMap s }

-- | Used to update annotations for a location, due to (ghost) predicate applications

updateLocA (_:_)  (Just l) t = addLocA Nothing l (AnnUse t)
updateLocA _      _        _ = return () 

addA !l xo@(Just _) !t (AI m)
  | isGoodSrcSpan l 
  = AI $ inserts l (T.pack . showPpr <$> xo, t) m
addA !l xo@Nothing  !t (AI m)
  | l `M.member` m                  -- only spans known to be variables
  = AI $ inserts l (T.pack . showPpr <$> xo, t) m
addA _ _ _ !a 
  = a

-------------------------------------------------------------------
------------------------ Generation: Freshness --------------------
-------------------------------------------------------------------

-- | Right now, we generate NO new pvars. Rather than clutter code 
--   with `uRType` calls, put it in one place where the above 
--   invariant is /obviously/ enforced.
--   Constraint generation should ONLY use @freshTy_type@ and @freshTy_expr@

freshTy_type        :: KVKind -> CoreExpr -> Type -> CG SpecType 
freshTy_type k e τ  = freshTy_reftype k $ ofType τ

freshTy_expr        :: KVKind -> CoreExpr -> Type -> CG SpecType 
freshTy_expr k e _  = freshTy_reftype k $ exprRefType e

freshTy_reftype     :: KVKind -> SpecType -> CG SpecType 
-- freshTy_reftype k t = do t <- refresh =<< fixTy t 
--                          addKVars k t
--                          return t
                       
freshTy_reftype k t = (fixTy t >>= refresh) =>> addKVars k

-- | Used to generate "cut" kvars for fixpoint. Typically, KVars for recursive
--   definitions, and also to update the KVar profile.

addKVars        :: KVKind -> SpecType -> CG ()
addKVars !k !t  = do when (True)    $ modify $ \s -> s { kvProf = updKVProf k kvars (kvProf s) }
                     when (isKut k) $ modify $ \s -> s { kuts   = F.ksUnion kvars   (kuts s)   }
  where
     kvars      = sortNub $ specTypeKVars t

isKut          :: KVKind -> Bool
isKut RecBindE = True
isKut _        = False

specTypeKVars :: SpecType -> [F.Symbol]
specTypeKVars = foldReft ((++) . (F.reftKVars . ur_reft)) []

trueTy  :: Type -> CG SpecType
trueTy = ofType' >=> true

ofType' :: Type -> CG SpecType
ofType' = fixTy . ofType
  
fixTy :: SpecType -> CG SpecType
fixTy t = do tyi   <- tyConInfo  <$> get
             tce   <- tyConEmbed <$> get
             return $ addTyConInfo tce tyi t

refreshArgsTop :: (Var, SpecType) -> CG SpecType
refreshArgsTop (x, t) 
  = do (t', su) <- refreshArgsSub t
       modify $ \s -> s {termExprs = M.adjust (F.subst su <$>) x $ termExprs s}
       return t'
  
refreshArgs :: SpecType -> CG SpecType
refreshArgs t 
  = fst <$> refreshArgsSub t

refreshArgsSub :: SpecType -> CG (SpecType, F.Subst)
refreshArgsSub t 
  = do ts     <- mapM refreshArgs ts_u
       xs'    <- mapM (\_ -> fresh) xs
       let sus = F.mkSubst <$> (L.inits $ zip xs (F.EVar <$> xs'))
       let su  = last sus 
       let ts' = zipWith F.subst sus ts
       let t'  = fromRTypeRep $ trep {ty_binds = xs', ty_args = ts', ty_res = F.subst su tbd}
       return (t', su)
    where
       trep    = toRTypeRep t
       xs      = ty_binds trep
       ts_u    = ty_args  trep
       tbd     = ty_res   trep

instance Freshable CG Integer where
  fresh = do s <- get
             let n = freshIndex s
             put $ s { freshIndex = n + 1 }
             return n
  	

-------------------------------------------------------------------------------
----------------------- TERMINATION TYPE --------------------------------------
-------------------------------------------------------------------------------

makeDecrIndex :: (Var, SpecType)-> CG [Int]
makeDecrIndex (x, t) 
  = do spDecr <- specDecr <$> get
       hint   <- checkHint' (L.lookup x $ spDecr)
       case dindex of
         Nothing -> addWarning msg >> return []
         Just i  -> return $ fromMaybe [i] hint
    where
       ts         = ty_args $ toRTypeRep t
       checkHint' = checkHint x ts isDecreasing
       dindex     = L.findIndex isDecreasing ts
       msg        = ErrTermin [x] (getSrcSpan x) (text "No decreasing parameter") 

recType ((_, []), (_, [], t))
  = t

recType ((vs, indexc), (x, index, t))
  = makeRecType t v dxt index       
  where v    = (vs !!)  <$> indexc
        dxt  = (xts !!) <$> index
        loc  = showPpr (getSrcSpan x)
        xts  = zip (ty_binds trep) (ty_args trep) 
        trep = toRTypeRep t
        msg' = printf "%s: No decreasing argument on %s with %s" 
        msg  = printf "%s: No decreasing parameter" loc
                  loc (showPpr x) (showPpr vs)

checkIndex (x, vs, t, index)
  = do mapM_ (safeLogIndex msg' vs) index
       mapM  (safeLogIndex msg  ts) index
    where
       loc   = getSrcSpan x
       ts    = ty_args $ toRTypeRep t
       msg'  = ErrTermin [x] loc (text $ "No decreasing argument on " ++ (showPpr x) ++ " with " ++ (showPpr vs))
       msg   = ErrTermin [x] loc (text "No decreasing parameter")

makeRecType t vs dxs is
  = fromRTypeRep $ trep {ty_binds = xs', ty_args = ts'}
  where
    (xs', ts') = unzip $ replaceN (last is) (makeDecrType vdxs) xts
    vdxs       = zip vs dxs
    xts        = zip (ty_binds trep) (ty_args trep)
    trep       = toRTypeRep t

safeLogIndex err ls n
  | n >= length ls = addWarning err >> return Nothing
  | otherwise      = return $ Just $ ls !! n

checkHint _ _ _ Nothing 
  = return Nothing

checkHint x ts f (Just ns) | L.sort ns /= ns
  = addWarning (ErrTermin [x] loc (text "The hints should be increasing")) >> return Nothing
  where loc = getSrcSpan x

checkHint x ts f (Just ns) 
  = (mapM (checkValidHint x ts f) ns) >>= (return . Just . catMaybes)

checkValidHint x ts f n
  | n < 0 || n >= length ts = addWarning err >> return Nothing
  | f (ts L.!! n)           = return $ Just n
  | otherwise               = addWarning err >> return Nothing
  where err = ErrTermin [x] loc (text $ "Invalid Hint " ++ show (n+1) ++ " for " ++ (showPpr x) ++  "\nin\n" ++ show (ts))
        loc = getSrcSpan x

-------------------------------------------------------------------
-------------------- Generation: Corebind -------------------------
-------------------------------------------------------------------
consCBTop :: (Var -> Bool) -> CGEnv -> CoreBind -> CG CGEnv 
consCBLet :: CGEnv -> CoreBind -> CG CGEnv 
-------------------------------------------------------------------

consCBLet γ cb
  = do oldtcheck <- tcheck <$> get
       strict    <- specLazy <$> get
       let tflag  = oldtcheck
       let isStr  = tcond cb strict
       modify $ \s -> s{tcheck = tflag && isStr}
       γ' <- consCB (tflag && isStr) isStr γ cb
       modify $ \s -> s{tcheck = oldtcheck}
       return γ'

consCBTop trustBinding γ cb | all trustBinding xs
  = do ts <- mapM trueTy (varType <$> xs)
       foldM (\γ xt -> (γ, "derived") += xt) γ (zip xs' ts)
  where xs             = bindersOf cb
        xs'            = F.symbol <$> xs

consCBTop _ γ cb
  = do oldtcheck <- tcheck <$> get
       strict    <- specLazy <$> get
       let tflag  = oldtcheck
       let isStr  = tcond cb strict
       modify $ \s -> s{tcheck = tflag && isStr}
       γ' <- consCB (tflag && isStr) isStr γ cb
       modify $ \s -> s{tcheck = oldtcheck}
       return γ'

tcond cb strict
  = not $ any (\x -> S.member x strict || isInternal x) (binds cb)
  where binds (NonRec x _) = [x]
        binds (Rec xes)    = fst $ unzip xes

-------------------------------------------------------------------
consCB :: Bool -> Bool -> CGEnv -> CoreBind -> CG CGEnv 
-------------------------------------------------------------------

consCBSizedTys tflag γ (Rec xes)
  = do xets''    <- forM xes $ \(x, e) -> liftM (x, e,) (varTemplate γ (x, Just e))
       sflag     <- scheck <$> get
       let cmakeFinType = if sflag then makeFinType else id
       let cmakeFinTy   = if sflag then makeFinTy   else snd
       let xets = mapThd3 (fmap cmakeFinType) <$> xets''
       ts'      <- mapM refreshArgs $ (fromAsserted . thd3 <$> xets)
       let vs    = zipWith collectArgs ts' es
       is       <- mapM makeDecrIndex (zip xs ts') >>= checkSameLens
       let ts = cmakeFinTy  <$> zip is ts'
       let xeets = (\vis -> [(vis, x) | x <- zip3 xs is ts]) <$> (zip vs is)
       (L.transpose <$> mapM checkIndex (zip4 xs vs ts is)) >>= checkEqTypes
       let rts   = (recType <$>) <$> xeets
       let xts   = zip xs (Asserted <$> ts)
       γ'       <- foldM extender γ xts
       let γs    = [γ' `withTRec` (zip xs rts') | rts' <- rts]
       let xets' = zip3 xs es (Asserted <$> ts)
       mapM_ (uncurry $ consBind True) (zip γs xets')
       return γ'
  where
       dmapM f  = sequence . (mapM f <$>)
       (xs, es) = unzip xes
       collectArgs    = collectArguments . length . ty_binds . toRTypeRep
       checkEqTypes :: [[Maybe SpecType]] -> CG [[SpecType]]
       checkEqTypes x = mapM (checkAll err1 toRSort) (catMaybes <$> x)
       checkSameLens  = checkAll err2 length
       err1           = ErrTermin xs loc $ text "The decreasing parameters should be of same type"
       err2           = ErrTermin xs loc $ text "All Recursive functions should have the same number of decreasing parameters"
       loc            = getSrcSpan (head xs)

       checkAll _   _ []            = return []
       checkAll err f (x:xs) 
         | all (==(f x)) (f <$> xs) = return (x:xs)
         | otherwise                = addWarning err >> return [] 

consCBWithExprs γ (Rec xes) 
  = do xets'     <- forM xes $ \(x, e) -> liftM (x, e,) (varTemplate γ (x, Just e))
       texprs <- termExprs <$> get
       let xtes = catMaybes $ (`lookup` texprs) <$> xs
       sflag     <- scheck <$> get
       let cmakeFinType = if sflag then makeFinType else id
       let cmakeFinTy   = if sflag then makeFinTy   else snd
       let xets  = mapThd3 (fmap cmakeFinType) <$> xets'
       let ts    = safeFromAsserted err . thd3 <$> xets
       ts'      <- mapM refreshArgs ts
       let xts   = zip xs (Asserted <$> ts')
       γ'       <- foldM extender γ xts
       let γs    = makeTermEnvs γ' xtes xes ts ts'
       let xets' = zip3 xs es (Asserted <$> ts')
       mapM_ (uncurry $ consBind True) (zip γs xets')
       return γ'
  where (xs, es) = unzip xes
        lookup k m | Just x <- M.lookup k m = Just (k, x)
                   | otherwise              = Nothing
        err      = "Constant: consCBWithExprs"

makeFinTy (ns, t) = fromRTypeRep $ trep {ty_args = args'}
  where trep = toRTypeRep t
        args' = mapNs ns makeFinType $ ty_args trep


makeTermEnvs γ xtes xes ts ts' = withTRec γ . zip xs <$> rts
  where
    vs   = zipWith collectArgs ts es
    ys   = (fst3 . bkArrowDeep) <$> ts 
    ys'  = (fst3 . bkArrowDeep) <$> ts'
    sus' = zipWith mkSub ys ys'
    sus  = zipWith mkSub ys ((F.symbol <$>) <$> vs)
    ess  = (\x -> (safeFromJust (err x) $ (x `L.lookup` xtes))) <$> xs
    tes  = zipWith (\su es -> F.subst su <$> es)  sus ess 
    tes' = zipWith (\su es -> F.subst su <$> es)  sus' ess 
    rss  = zipWith makeLexRefa tes' <$> (repeat <$> tes)
    rts  = zipWith addTermCond ts' <$> rss
    (xs, es)     = unzip xes
    mkSub ys ys' = F.mkSubst [(x, F.EVar y) | (x, y) <- zip ys ys']
    collectArgs  = collectArguments . length . ty_binds . toRTypeRep
    err x        = "Constant: makeTermEnvs: no terminating expression for " ++ showPpr x 


                   
consCB tflag _ γ (Rec xes) | tflag 
  = do texprs <- termExprs <$> get
       modify $ \i -> i { recCount = recCount i + length xes }
       let xxes = catMaybes $ (`lookup` texprs) <$> xs
       if null xxes 
         then consCBSizedTys tflag γ (Rec xes)
         else check xxes <$> consCBWithExprs γ (Rec xes)
  where xs = fst $ unzip xes
        check ys r | length ys == length xs = r
                   | otherwise              = errorstar err
        err = printf "%s: Termination expressions should be provided for ALL mutual recursive functions" loc
        loc = showPpr $ getSrcSpan (head xs)
        lookup k m | Just x <- M.lookup k m = Just (k, x)
                   | otherwise              = Nothing

consCB _ str γ (Rec xes) | not str
  = do xets'   <- forM xes $ \(x, e) -> liftM (x, e,) (varTemplate γ (x, Just e))
       sflag     <- scheck <$> get
       let cmakeDivType = if sflag then makeDivType else id
       let xets = mapThd3 (fmap cmakeDivType) <$> xets'
       modify $ \i -> i { recCount = recCount i + length xes }
       let xts = [(x, to) | (x, _, to) <- xets]
       γ'     <- foldM extender (γ `withRecs` (fst <$> xts)) xts
       mapM_ (consBind True γ') xets
       return γ' 

consCB _ _ γ (Rec xes) 
  = do xets   <- forM xes $ \(x, e) -> liftM (x, e,) (varTemplate γ (x, Just e))
       modify $ \i -> i { recCount = recCount i + length xes }
       let xts = [(x, to) | (x, _, to) <- xets]
       γ'     <- foldM extender (γ `withRecs` (fst <$> xts)) xts
       mapM_ (consBind True γ') xets
       return γ' 

consCB _ _ γ (NonRec x e)
  = do to  <- varTemplate γ (x, Nothing) 
       to' <- consBind False γ (x, e, to) >>= (addPostTemplate γ)
       extender γ (x, to')

consBind isRec γ (x, e, Asserted spect) 
  = do let γ'         = (γ `setLoc` getSrcSpan x) `setBind` x
           (_,πs,_,_) = bkUniv spect
       γπ    <- foldM addPToEnv γ' πs
       cconsE γπ e spect
       when (F.symbol x `elemHEnv` holes γ) $
         -- have to add the wf constraint here for HOLEs so we have the proper env
         addW $ WfC γπ $ fmap killSubst spect
       addIdA x (defAnn isRec spect)
       return $ Asserted spect -- Nothing

consBind isRec γ (x, e, Assumed spect) 
  = do let γ' = (γ `setLoc` getSrcSpan x) `setBind` x
       γπ    <- foldM addPToEnv γ' πs
       cconsE γπ e =<< true spect
       addIdA x (defAnn isRec spect)
       return $ Asserted spect -- Nothing
  where πs   = ty_preds $ toRTypeRep spect

consBind isRec γ (x, e, Unknown)
  = do t     <- consE (γ `setBind` x) e
       addIdA x (defAnn isRec t)
       return $ Asserted t

noHoles = and . foldReft (\r bs -> not (hasHole r) : bs) []

killSubst :: RReft -> RReft
killSubst = fmap tx
  where
    tx (F.Reft (s, rs)) = F.Reft (s, map f rs)
    f (F.RKvar k _) = F.RKvar k mempty
    f (F.RConc p)   = F.RConc p

defAnn True  = AnnRDf
defAnn False = AnnDef

addPToEnv γ π
  = do γπ <- γ ++= ("addSpec1", pname π, pvarRType π)
       foldM (++=) γπ [("addSpec2", x, ofRSort t) | (t, x, _) <- pargs π]

extender γ (x, Asserted t) = γ ++= ("extender", F.symbol x, t)
extender γ (x, Assumed t)  = γ ++= ("extender", F.symbol x, t)
extender γ _               = return γ

addBinders γ0 x' cbs   = foldM (++=) (γ0 -= x') [("addBinders", x, t) | (x, t) <- cbs]

data Template a = Asserted a | Assumed a | Unknown deriving (Functor)

deriving instance (Show a) => (Show (Template a))


addPostTemplate γ (Asserted t) = Asserted <$> addPost γ t
addPostTemplate γ (Assumed  t) = Assumed  <$> addPost γ t
addPostTemplate γ Unknown      = return Unknown 

fromAsserted (Asserted t) = t
safeFromAsserted msg (Asserted t) = t

-- | @varTemplate@ is only called with a `Just e` argument when the `e`
-- corresponds to the body of a @Rec@ binder.
varTemplate :: CGEnv -> (Var, Maybe CoreExpr) -> CG (Template SpecType)
varTemplate γ (x, eo)
  = case (eo, lookupREnv (F.symbol x) (grtys γ), lookupREnv (F.symbol x) (assms γ)) of
      (_, Just t, _) -> Asserted <$> refreshArgsTop (x, t)
      (_, _, Just t) -> Assumed  <$> refreshArgsTop (x, t)
      (Just e, _, _) -> do t  <- freshTy_expr RecBindE e (exprType e)
                           addW (WfC γ t)
                           Asserted <$> refreshArgsTop (x, t)
      (_,      _, _) -> return Unknown

-------------------------------------------------------------------
-------------------- Generation: Expression -----------------------
-------------------------------------------------------------------

----------------------- Type Checking -----------------------------
cconsE :: CGEnv -> Expr Var -> SpecType -> CG () 
-------------------------------------------------------------------
cconsE γ e@(Let b@(NonRec x _) ee) t
  = do sp <- specLVars <$> get
       if (x `S.member` sp) || isDefLazyVar x  
        then cconsLazyLet γ e t 
        else do γ'  <- consCBLet γ b
                cconsE γ' ee t
  where
       isDefLazyVar = L.isPrefixOf "fail" . showPpr

cconsE γ (Let b e) t    
  = do γ'  <- consCBLet γ b
       cconsE γ' e t 

cconsE γ (Case e x _ cases) t 
  = do γ'  <- consCBLet γ (NonRec x e)
       forM_ cases $ cconsCase γ' x t nonDefAlts 
    where 
       nonDefAlts = [a | (a, _, _) <- cases, a /= DEFAULT]

cconsE γ (Lam α e) (RAllT α' t) | isTyVar α 
  = cconsE γ e $ subsTyVar_meet' (α', rVar α) t 

cconsE γ (Lam x e) (RFun y ty t _) 
  | not (isTyVar x) 
  = do γ' <- (γ, "cconsE") += (F.symbol x, ty)
       cconsE γ' e (t `F.subst1` (y, F.EVar $ F.symbol x))
       addIdA x (AnnDef ty) 

cconsE γ (Tick tt e) t   
  = cconsE (γ `setLoc` tickSrcSpan tt) e t

cconsE γ e@(Cast e' _) t     
  = do t' <- castTy γ (exprType e) e'
       addC (SubC γ t' t) ("cconsE Cast" ++ showPpr e) 

cconsE γ e (RAllP p t)
  = cconsE γ e t'
  where
    t' = replacePredsWithRefs su <$> t
    su = (uPVar p, pVartoRConc p)

cconsE γ e t
  = do te  <- consE γ e
       te' <- instantiatePreds γ e te >>= addPost γ
       addC (SubC γ te' t) ("cconsE" ++ showPpr e)


-------------------------------------------------------------------
-- | @instantiatePreds@ peels away the universally quantified @PVars@
--   of a @RType@, generates fresh @Ref@ for them and substitutes them
--   in the body.
       
instantiatePreds γ e t0@(RAllP π t)
  = do r     <- freshPredRef γ e π
       let πZZ = {- traceShow ("instantiatePreds 1") -} π
       let tZZ = {- traceShow ("instantiatePreds 2") -} t
       let rZZ = {- traceShow ("instantiatePreds 3") -} r
       let t'  = replacePreds "consE" tZZ [(πZZ, rZZ)]
       instantiatePreds γ e t'

instantiatePreds _ _ t0
  = return t0

-------------------------------------------------------------------
-- | @instantiateStrata@ generates fresh @Strata@ vars and substitutes
--   them inside the body of the type.

instantiateStrata ls t = substStrata t ls <$> mapM (\_ -> fresh) ls

substStrata t ls ls'   = F.substa f t
  where
    f x                = fromMaybe x $ L.lookup x su
    su                 = zip ls ls'

-------------------------------------------------------------------

cconsLazyLet γ (Let (NonRec x ex) e) t
  = do tx <- trueTy (varType x)
       γ' <- (γ, "Let NonRec") +++= (x', ex, tx)
       cconsE γ' e t
    where
       xr = singletonReft x
       x' = F.symbol x


-------------------------------------------------------------------
-- | Type Synthesis -----------------------------------------------
-------------------------------------------------------------------
consE :: CGEnv -> Expr Var -> CG SpecType 
-------------------------------------------------------------------

consE γ (Var x)   
  = do t <- varRefType γ x
       addLocA (Just x) (loc γ) (varAnn γ x t)
       return t

consE γ (Lit c) 
  = refreshVV $ uRType $ literalFRefType (emb γ) c

consE γ e'@(App e (Type τ)) 
  = do RAllT α te <- checkAll ("Non-all TyApp with expr", e) <$> consE γ e
       t          <- if isGeneric α te then freshTy_type TypeInstE e τ else trueTy τ
       addW        $ WfC γ t
       t'         <- refreshVV t
       instantiatePreds γ e' $ subsTyVar_meet' (α, t') te

consE γ e'@(App e a)               
  = do ([], πs, ls, te) <- bkUniv <$> consE γ e
       te0              <- instantiatePreds γ e' $ foldr RAllP te πs 
       te'              <- instantiateStrata ls te0
       (γ', te'')       <- dropExists γ te'
       updateLocA πs (exprLoc e) te'' 
       let RFun x tx t _ = checkFun ("Non-fun App with caller ", e') te''
       pushConsBind      $ cconsE γ' a tx 
       addPost γ'        $ maybe (checkUnbound γ' e' x t) (F.subst1 t . (x,)) (argExpr γ a)

consE γ (Lam α e) | isTyVar α 
  = liftM (RAllT (rTyVar α)) (consE γ e) 

consE γ  e@(Lam x e1) 
  = do tx      <- freshTy_type LamE (Var x) τx 
       γ'      <- ((γ, "consE") += (F.symbol x, tx))
       t1      <- consE γ' e1
       addIdA x $ AnnDef tx 
       addW     $ WfC γ tx 
       return   $ rFun (F.symbol x) tx t1
    where
      FunTy τx _ = exprType e 

-- EXISTS-BASED CONSTRAINTS HEREHEREHEREHERE
-- Currently suppressed because they break all sorts of invariants,
-- e.g. for `unfoldR`...
-- consE γ e@(Let b@(NonRec x _) e')
--   = do γ'    <- consCBLet γ b
--        consElimE γ' [F.symbol x] e'
-- 
-- consE γ (Case e x _ [(ac, ys, ce)]) 
--   = do γ'  <- consCBLet γ (NonRec x e)
--        γ'' <- caseEnv γ' x [] ac ys
--        consElimE γ'' (F.symbol <$> (x:ys)) ce 

consE γ e@(Let _ _) 
  = cconsFreshE LetE γ e

consE γ e@(Case _ _ _ _) 
  = cconsFreshE CaseE γ e

consE γ (Tick tt e)
  = do t <- consE (γ `setLoc` l) e
       addLocA Nothing l (AnnUse t)
       return t
    where l = tickSrcSpan tt

consE γ e@(Cast e' _)      
  = castTy γ (exprType e) e'

consE γ e@(Coercion _)
   = trueTy $ exprType e

consE _ e	    
  = errorstar $ "consE cannot handle " ++ showPpr e 

castTy _ τ (Var x)
  = do t <- trueTy τ 
       return $  t `strengthen` (uTop $ F.uexprReft $ F.expr x)

castTy γ τ e
  = do t <- trueTy (exprType e)
       cconsE γ e t
       trueTy τ 

singletonReft = uTop . F.symbolReft . F.symbol 

-- | @consElimE@ is used to *synthesize* types by **existential elimination** 
--   instead of *checking* via a fresh template. That is, assuming
--      γ |- e1 ~> t1
--   we have
--      γ |- let x = e1 in e2 ~> Ex x t1 t2 
--   where
--      γ, x:t1 |- e2 ~> t2
--   instead of the earlier case where we generate a fresh template `t` and check
--      γ, x:t1 |- e <~ t

consElimE γ xs e
  = do t     <- consE γ e
       xts   <- forM xs $ \x -> (x,) <$> (γ ??= x)
       return $ rEx xts t

-- | @consFreshE@ is used to *synthesize* types with a **fresh template** when
--   the above existential elimination is not easy (e.g. at joins, recursive binders)

cconsFreshE kvkind γ e
  = do t   <- freshTy_type kvkind e $ exprType e
       addW $ WfC γ t
       cconsE γ e t
       return t

checkUnbound γ e x t 
  | x `notElem` (F.syms t) = t
  | otherwise              = errorstar $ "consE: cannot handle App " ++ showPpr e ++ " at " ++ showPpr (loc γ)

dropExists γ (REx x tx t) = liftM (, t) $ (γ, "dropExists") += (x, tx)
dropExists γ t            = return (γ, t)

-------------------------------------------------------------------------------------
cconsCase :: CGEnv -> Var -> SpecType -> [AltCon] -> (AltCon, [Var], CoreExpr) -> CG ()
-------------------------------------------------------------------------------------
cconsCase γ x t acs (ac, ys, ce)
  = do cγ <- caseEnv γ x acs ac ys 
       cconsE cγ ce t

refreshTy t = refreshVV t >>= refreshArgs

refreshVV (RAllT a t) = liftM (RAllT a) (refreshVV t)
refreshVV (RAllP p t) = liftM (RAllP p) (refreshVV t)

refreshVV (REx x t1 t2)
  = do [t1', t2'] <- mapM refreshVV [t1, t2]
       liftM (shiftVV (REx x t1' t2')) fresh

refreshVV (RFun x t1 t2 r)
  = do [t1', t2'] <- mapM refreshVV [t1, t2]
       liftM (shiftVV (RFun x t1' t2' r)) fresh

refreshVV (RAppTy t1 t2 r)
  = do [t1', t2'] <- mapM refreshVV [t1, t2]
       liftM (shiftVV (RAppTy t1' t2' r)) fresh

refreshVV (RApp c ts rs r)
  = do ts' <- mapM refreshVV ts
       rs' <- mapM refreshVVRef rs
       liftM (shiftVV (RApp c ts' rs' r)) fresh

refreshVV t           
  = return t


refreshVVRef (RProp ss t) 
  = do xs    <- mapM (\_ -> fresh) (fst <$> ss)
       let su = F.mkSubst $ zip (fst <$> ss) (F.EVar <$> xs)
       liftM (RProp (zip xs (snd <$> ss)) . F.subst su) (refreshVV t)
refreshVVRef (RPropP ss r) 
  = return $ RPropP ss r



-------------------------------------------------------------------------------------
caseEnv   :: CGEnv -> Var -> [AltCon] -> AltCon -> [Var] -> CG CGEnv 
-------------------------------------------------------------------------------------
caseEnv γ x _   (DataAlt c) ys
  = do let (x' : ys')    = F.symbol <$> (x:ys)
       xt0              <- checkTyCon ("checkTycon cconsCase", x) <$> γ ??= x'
       tdc              <- γ ??= (dataConSymbol c) >>= refreshVV
       let (rtd, yts, _) = unfoldR c tdc (shiftVV xt0 x') ys
       let r1            = dataConReft   c   ys' 
       let r2            = dataConMsReft rtd ys'
       let xt            = xt0 `strengthen` (uTop (r1 `F.meet` r2))
       let cbs           = safeZip "cconsCase" (x':ys') (xt0:yts)
       cγ'              <- addBinders γ x' cbs
       cγ               <- addBinders cγ' x' [(x', xt)]
       return cγ 

caseEnv γ x acs a _ 
  = do let x'  = F.symbol x
       xt'    <- (`strengthen` uTop (altReft γ acs a)) <$> (γ ??= x')
       cγ     <- addBinders γ x' [(x', xt')]
       return cγ

-- cconsCase γ x t _ (DataAlt c, ys, ce) 
--  = do xt0              <- checkTyCon ("checkTycon cconsCase", x) <$> γ ??= x'
--       tdc              <- γ ??= (dataConSymbol c)
--       let (rtd, yts, _) = unfoldR c tdc (shiftVV xt0 x') ys
--       let r1            = dataConReft   c   ys' 
--       let r2            = dataConMsReft rtd ys'
--       let xt            = xt0 `strengthen` (uTop (r1 `F.meet` r2))
--       let cbs           = safeZip "cconsCase" (x':ys') (xt0:yts)
--       cγ'              <- addBinders γ x' cbs
--       cγ               <- addBinders cγ' x' [(x', xt)]
--       cconsE cγ ce t
--    where 
--       (x':ys')        = F.symbol <$> (x:ys)
-- 
-- 
-- cconsCase γ x t acs (a, _, ce) 
--        cconsE cγ ce t

altReft γ _ (LitAlt l)   = literalFReft (emb γ) l
altReft γ acs DEFAULT    = mconcat [notLiteralReft l | LitAlt l <- acs]
  where notLiteralReft   = maybe mempty F.notExprReft . snd . literalConst (emb γ)
altReft _ _ _            = error "Constraint : altReft"

unfoldR dc td (RApp _ ts rs _) ys = (t3, tvys ++ yts, ignoreOblig rt)
  where 
        tbody           = instantiatePvs (instantiateTys td ts) $ reverse rs
        (ys0, yts', rt) = safeBkArrow $ instantiateTys tbody tvs'
        yts''           = zipWith F.subst sus (yts'++[rt])
        (t3,yts)        = (last yts'', init yts'')
        sus             = F.mkSubst <$> (L.inits [(x, F.EVar y) | (x, y) <- zip ys0 ys'])
        (αs, ys')       = mapSnd (F.symbol <$>) $ L.partition isTyVar ys
        tvs'            = rVar <$> αs
        tvys            = ofType . varType <$> αs

unfoldR _ _  _                _  = error "Constraint.hs : unfoldR"

instantiateTys = foldl' go
  where go (RAllT α tbody) t = subsTyVar_meet' (α, t) tbody
        go _ _               = errorstar "Constraint.instanctiateTy" 

instantiatePvs = foldl' go 
  where go (RAllP p tbody) r = replacePreds "instantiatePv" tbody [(p, r)]
        go _ _               = errorstar "Constraint.instanctiatePv" 

instance Show CoreExpr where
  show = showPpr

checkTyCon _ t@(RApp _ _ _ _) = t
checkTyCon x t                = checkErr x t --errorstar $ showPpr x ++ "type: " ++ showPpr t

-- checkRPred _ t@(RAll _ _)     = t
-- checkRPred x t                = checkErr x t

checkFun _ t@(RFun _ _ _ _)   = t
checkFun x t                  = checkErr x t

checkAll _ t@(RAllT _ _)      = t
checkAll x t                  = checkErr x t

checkErr (msg, e) t          = errorstar $ msg ++ showPpr e ++ ", type: " ++ showpp t

varAnn γ x t 
  | x `S.member` recs γ
  = AnnLoc (getSrcSpan' x) 
  | otherwise 
  = AnnUse t

getSrcSpan' x 
  | loc == noSrcSpan
  = loc
  | otherwise
  = loc
  where loc = getSrcSpan x

-----------------------------------------------------------------------
-- | Helpers: Creating Fresh Refinement -------------------------------
-----------------------------------------------------------------------

freshPredRef :: CGEnv -> CoreExpr -> PVar RSort -> CG SpecProp
freshPredRef γ e (PV n (PVProp τ) _ as)
  = do t    <- freshTy_type PredInstE e (toType τ)
       args <- mapM (\_ -> fresh) as
       let targs = [(x, s) | (x, (s, y, z)) <- zip args as, (F.EVar y) == z ]
       γ' <- foldM (++=) γ [("freshPredRef", x, ofRSort τ) | (x, τ) <- targs]
       addW $ WfC γ' t
       return $ RProp targs t

freshPredRef _ _ (PV _ PVHProp _ _)
  = errorstar "TODO:EFFECTS:freshPredRef"

-----------------------------------------------------------------------
---------- Helpers: Creating Refinement Types For Various Things ------
-----------------------------------------------------------------------

argExpr :: CGEnv -> CoreExpr -> Maybe F.Expr
argExpr _ (Var vy)    = Just $ F.eVar vy
argExpr γ (Lit c)     = snd  $ literalConst (emb γ) c
argExpr γ (Tick _ e)  = argExpr γ e
argExpr _ e           = errorstar $ "argExpr: " ++ showPpr e


varRefType γ x = liftM (varRefType' γ x) (γ ??= F.symbol x)

varRefType' γ x t'
  | Just tys <- trec γ, Just tr <- M.lookup x' tys 
  = tr `strengthen` xr
  | otherwise
  = t
  where t  = t' `strengthen` xr
        xr = singletonReft x -- uTop $ F.symbolReft $ F.symbol x
        x' = F.symbol x

-- TODO: should only expose/use subt. Not subsTyVar_meet
subsTyVar_meet' (α, t) = subsTyVar_meet (α, toRSort t, t)

-----------------------------------------------------------------------
--------------- Forcing Strictness ------------------------------------
-----------------------------------------------------------------------

instance NFData CGEnv where
  rnf (CGE x1 x2 x3 x5 x6 x7 x8 x9 _ _ x10 x11 _ _ _)
    = x1 `seq` rnf x2 `seq` seq x3 `seq` rnf x5 `seq` 
      rnf x6  `seq` x7 `seq` rnf x8 `seq` rnf x9 `seq` rnf x10

instance NFData FEnv where
  rnf (FE x1 _) = rnf x1

instance NFData SubC where
  rnf (SubC x1 x2 x3) 
    = rnf x1 `seq` rnf x2 `seq` rnf x3
  rnf (SubR x1 _ x2) 
    = rnf x1 `seq` rnf x2

instance NFData Class where
  rnf _ = ()

instance NFData RTyCon where
  rnf _ = ()

instance NFData Type where 
  rnf _ = ()

instance NFData WfC where
  rnf (WfC x1 x2)   
    = rnf x1 `seq` rnf x2

instance NFData CGInfo where
  rnf x = ({-# SCC "CGIrnf1" #-}  rnf (hsCs x))       `seq` 
          ({-# SCC "CGIrnf2" #-}  rnf (hsWfs x))      `seq` 
          ({-# SCC "CGIrnf3" #-}  rnf (fixCs x))      `seq` 
          ({-# SCC "CGIrnf4" #-}  rnf (fixWfs x))     `seq` 
          ({-# SCC "CGIrnf5" #-}  rnf (globals x))    `seq` 
          ({-# SCC "CGIrnf6" #-}  rnf (freshIndex x)) `seq`
          ({-# SCC "CGIrnf7" #-}  rnf (binds x))      `seq`
          ({-# SCC "CGIrnf8" #-}  rnf (annotMap x))   `seq`
          ({-# SCC "CGIrnf9" #-}  rnf (specQuals x))  `seq`
          ({-# SCC "CGIrnf10" #-} rnf (kuts x))       `seq`
          ({-# SCC "CGIrnf10" #-} rnf (lits x))       `seq`
          ({-# SCC "CGIrnf10" #-} rnf (kvProf x)) 

-------------------------------------------------------------------------------
--------------------- Reftypes from F.Fixpoint Expressions ----------------------
-------------------------------------------------------------------------------

forallExprRefType     :: CGEnv -> SpecType -> SpecType
forallExprRefType γ t = t `strengthen` (uTop r') 
  where r'            = fromMaybe mempty $ forallExprReft γ r 
        r             = F.sr_reft $ rTypeSortedReft (emb γ) t

forallExprReft γ r 
  = do e  <- F.isSingletonReft r
       r' <- forallExprReft_ γ e
       return r'

forallExprReft_ γ e@(F.EApp f es) 
  = case forallExprReftLookup γ (val f) of
      Just (xs,_,t) -> let su = F.mkSubst $ safeZip "fExprRefType" xs es in
                       Just $ F.subst su $ F.sr_reft $ rTypeSortedReft (emb γ) t
      Nothing       -> Nothing -- F.exprReft e

forallExprReft_ γ e@(F.EVar x) 
  = case forallExprReftLookup γ x of 
      Just (_,_,t)  -> Just $ F.sr_reft $ rTypeSortedReft (emb γ) t 
      Nothing       -> Nothing -- F.exprReft e

forallExprReft_ _ e = Nothing -- F.exprReft e 

forallExprReftLookup γ x = snap <$> F.lookupSEnv x (syenv γ)
  where 
    snap                 = mapThd3 ignoreOblig . bkArrow . fourth4 . bkUniv . (γ ?=) . F.symbol

grapBindsWithType tx γ 
  = fst <$> toListREnv (filterREnv ((== toRSort tx) . toRSort) (renv γ))

splitExistsCases z xs tx
  = fmap $ fmap (exrefAddEq z xs tx)

exrefAddEq z xs t (F.Reft(s, rs))
  = F.Reft(s, [F.RConc (F.POr [ pand x | x <- xs])])
  where tref                = fromMaybe mempty $ stripRTypeBase t
        pand x              = F.PAnd $ (substzx x) (fFromRConc <$> rs)
                                       ++ exrefToPred x tref
        substzx x           = F.subst (F.mkSubst [(z, F.EVar x)])

exrefToPred x uref
  = F.subst (F.mkSubst [(v, F.EVar x)]) ((fFromRConc <$> r))
  where (F.Reft(v, r))         = ur_reft uref
fFromRConc (F.RConc p) = p
fFromRConc _           = errorstar "can not hanlde existential type with kvars"

-------------------------------------------------------------------------------
-------------------- Cleaner Signatures For Rec-bindings ----------------------
-------------------------------------------------------------------------------

exprLoc                         :: CoreExpr -> Maybe SrcSpan

exprLoc (Tick tt _)             = Just $ tickSrcSpan tt
exprLoc (App e a) | isType a    = exprLoc e
exprLoc _                       = Nothing

isType (Type _)                 = True
isType a                        = eqType (exprType a) predType


exprRefType :: CoreExpr -> SpecType 
exprRefType = exprRefType_ M.empty 

exprRefType_ :: M.HashMap Var SpecType -> CoreExpr -> SpecType 
exprRefType_ γ (Let b e) 
  = exprRefType_ (bindRefType_ γ b) e

exprRefType_ γ (Lam α e) | isTyVar α
  = RAllT (rTyVar α) (exprRefType_ γ e)

exprRefType_ γ (Lam x e) 
  = rFun (F.symbol x) (ofType $ varType x) (exprRefType_ γ e)

exprRefType_ γ (Tick _ e)
  = exprRefType_ γ e

exprRefType_ γ (Var x) 
  = M.lookupDefault (ofType $ varType x) x γ

exprRefType_ _ e
  = ofType $ exprType e

bindRefType_ γ (Rec xes)
  = extendγ γ [(x, exprRefType_ γ e) | (x,e) <- xes]

bindRefType_ γ (NonRec x e)
  = extendγ γ [(x, exprRefType_ γ e)]

extendγ γ xts
  = foldr (\(x,t) m -> M.insert x t m) γ xts



-------------------------------------------------------------------
-- | Strengthening Binders with TyCon Invariants ------------------
-------------------------------------------------------------------

type RTyConInv = M.HashMap RTyCon [SpecType]
type RTyConIAl = M.HashMap RTyCon [SpecType]

-- mkRTyConInv    :: [Located SpecType] -> RTyConInv 
mkRTyConInv ts = group [ (c, t) | t@(RApp c _ _ _) <- strip <$> ts]
  where 
    strip      = fourth4 . bkUniv . val 

mkRTyConIAl    = mkRTyConInv . fmap snd

addRTyConInv :: RTyConInv -> SpecType -> SpecType
addRTyConInv m t@(RApp c _ _ _)
  = case M.lookup c m of
      Nothing -> t
      Just ts -> foldl' conjoinInvariant' t ts
addRTyConInv _ t 
  = t 

addRInv :: RTyConInv -> (Var, SpecType) -> (Var, SpecType)
addRInv m (x, t) 
  | x `elem` ids , (RApp c _ _ _) <- res t, Just invs <- M.lookup c m
  = (x, addInvCond t (mconcat $ catMaybes (stripRTypeBase <$> invs))) 
  | otherwise    
  = (x, t)
   where
     ids = [id | tc <- M.keys m
               , dc <- TC.tyConDataCons $ rtc_tc tc
               , id <- DC.dataConImplicitIds dc]
     res = ty_res . toRTypeRep
     xs  = ty_args $ toRTypeRep t

conjoinInvariant' t1 t2     
  = conjoinInvariantShift t1 t2

conjoinInvariantShift t1 t2 
  = conjoinInvariant t1 (shiftVV t2 (rTypeValueVar t1)) 

conjoinInvariant (RApp c ts rs r) (RApp ic its _ ir) 
  | (c == ic && length ts == length its)
  = RApp c (zipWith conjoinInvariantShift ts its) rs (r `F.meet` ir)

conjoinInvariant t@(RApp _ _ _ r) (RVar _ ir) 
  = t { rt_reft = r `F.meet` ir }

conjoinInvariant t@(RVar _ r) (RVar _ ir) 
  = t { rt_reft = r `F.meet` ir }

conjoinInvariant t _  
  = t

---------------------------------------------------------------
----- Refinement Type Environments ----------------------------
---------------------------------------------------------------

instance NFData REnv where
  rnf (REnv _) = () -- rnf m

toListREnv (REnv env)     = M.toList env
filterREnv f (REnv env)   = REnv $ M.filter f env
fromListREnv              = REnv . M.fromList
deleteREnv x (REnv env)   = REnv (M.delete x env)
insertREnv x y (REnv env) = REnv (M.insert x y env)
lookupREnv x (REnv env)   = M.lookup x env
memberREnv x (REnv env)   = M.member x env
-- domREnv (REnv env)        = M.keys env
-- emptyREnv                 = REnv M.empty

cgInfoFInfoBot cgi = cgInfoFInfo cgi { specQuals = [] }

cgInfoFInfoKvars cgi kvars = cgInfoFInfo cgi{fixCs = fixCs' ++ trueCs}
  where 
    fixCs'                 = concatMap (updateCs kvars) (fixCs cgi) 
    trueCs                 = concatMap (`F.trueSubCKvar` (Ci noSrcSpan Nothing)) kvars

cgInfoFInfo cgi
  = F.FI { F.cm    = M.fromList $ F.addIds $ fixCs cgi
         , F.ws    = fixWfs cgi  
         , F.bs    = binds cgi 
         , F.gs    = globals cgi 
         , F.lits  = lits cgi 
         , F.kuts  = kuts cgi 
         , F.quals = specQuals cgi
         }

updateCs kvars cs
  | null lhskvars || F.isFalse rhs
  = [cs] 
  | all (`elem` kvars) lhskvars && null lhsconcs
  = []
  | any (`elem` kvars) lhskvars
  = [F.removeLhsKvars cs kvars]
  | otherwise 
  = [cs]
  where lhskvars = F.reftKVars lhs
        rhskvars = F.reftKVars rhs
        lhs      = F.lhsCs cs
        rhs      = F.rhsCs cs
        F.Reft(_, lhspds) = lhs
        lhsconcs = [p | F.RConc p <- lhspds]

newtype HEnv = HEnv (S.HashSet F.Symbol)

fromListHEnv = HEnv . S.fromList
elemHEnv x (HEnv s) = x `S.member` s