content: {-
  (c) The University of Glasgow 2006
  (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
  
  
  Utility functions on @Core@ syntax
  -}
  
  {-# LANGUAGE CPP #-}
  
  -- | Commonly useful utilites for manipulating the Core language
  module Eta.Core.CoreUtils (
          -- * Constructing expressions
          mkCast,
          mkTick, mkTicks, mkTickNoHNF, tickHNFArgs,
          bindNonRec, needsCaseBinding,
          mkAltExpr,
  
          -- * Taking expressions apart
          findDefault, addDefault, findAlt, isDefaultAlt,
          mergeAlts, trimConArgs, filterAlts,
  
          -- * Properties of expressions
          exprType, coreAltType, coreAltsType,
          exprIsDupable, exprIsTrivial, getIdFromTrivialExpr, exprIsBottom,
          getIdFromTrivialExpr_maybe,
          exprIsCheap, exprIsExpandable, exprIsCheap', CheapAppFun,
          exprIsHNF, exprOkForSpeculation, exprOkForSideEffects, exprIsWorkFree,
          exprIsBig, exprIsConLike,
          rhsIsStatic, isCheapApp, isExpandableApp,
          altsAreExhaustive,
  
          -- * Expression and bindings size
          coreBindsSize, exprSize,
          CoreStats(..), coreBindsStats,
  
          -- * Equality
          cheapEqExpr, cheapEqExpr', eqExpr,
          diffExpr, diffBinds,
  
          -- * Eta reduction
          tryEtaReduce,
  
          -- * Manipulating data constructors and types
          applyTypeToArgs, applyTypeToArg,
          dataConRepInstPat, dataConRepFSInstPat,
  
          -- * Working with ticks
          stripTicksTop, stripTicksTopE, stripTicksTopT,
          stripTicksE, stripTicksT
      ) where
  
  #include "HsVersions.h"
  
  import Eta.Core.CoreSyn
  import Eta.Core.CoreSeq
  import Eta.Core.PprCore
  import Eta.Core.CoreFVs( exprFreeVars )
  import Eta.BasicTypes.Var
  import Eta.BasicTypes.SrcLoc
  import Eta.BasicTypes.VarEnv
  import Eta.BasicTypes.VarSet
  import Eta.BasicTypes.Name
  import Eta.BasicTypes.Literal
  import Eta.BasicTypes.DataCon
  import Eta.Prelude.PrimOp
  import Eta.BasicTypes.Id
  import Eta.BasicTypes.IdInfo
  import Eta.Types.Type
  import qualified Eta.Types.Type as Type
  import Eta.Types.Coercion
  import Eta.Types.TyCon
  import Eta.BasicTypes.Unique
  import Eta.Utils.Outputable
  import Eta.Prelude.TysPrim
  import Eta.Main.DynFlags
  import Eta.Utils.FastString
  import Eta.Utils.Maybes
  import Eta.Utils.Platform
  import Eta.Utils.Util
  import Eta.Utils.Pair
  import Data.Function       ( on )
  import Data.List
  import Data.Ord            ( comparing )
  import Eta.Utils.OrdList
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Find the type of a Core atom/expression}
  *                                                                      *
  ************************************************************************
  -}
  
  exprType :: CoreExpr -> Type
  -- ^ Recover the type of a well-typed Core expression. Fails when
  -- applied to the actual 'CoreSyn.Type' expression as it cannot
  -- really be said to have a type
  exprType (Var var)           = idType var
  exprType (Lit lit)           = literalType lit
  exprType (Coercion co)       = coercionType co
  exprType (Let bind body)
    | NonRec tv rhs <- bind    -- See Note [Type bindings]
    , Type ty <- rhs           = substTyWith [tv] [ty] (exprType body)
    | otherwise                = exprType body
  exprType (Case _ _ ty _)     = ty
  exprType (Cast _ co)         = pSnd (coercionKind co)
  exprType (Tick _ e)          = exprType e
  exprType (Lam binder expr)   = mkPiType binder (exprType expr)
  exprType e@(App _ _)
    = case collectArgs e of
          (fun, args) -> applyTypeToArgs e (exprType fun) args
  
  exprType other = pprTrace "exprType" (pprCoreExpr other) alphaTy
  
  coreAltType :: CoreAlt -> Type
  -- ^ Returns the type of the alternatives right hand side
  coreAltType (_,bs,rhs)
    | any bad_binder bs = expandTypeSynonyms ty
    | otherwise         = ty    -- Note [Existential variables and silly type synonyms]
    where
      ty           = exprType rhs
      free_tvs     = tyVarsOfType ty
      bad_binder b = isTyVar b && b `elemVarSet` free_tvs
  
  coreAltsType :: [CoreAlt] -> Type
  -- ^ Returns the type of the first alternative, which should be the same as for all alternatives
  coreAltsType (alt:_) = coreAltType alt
  coreAltsType []      = panic "corAltsType"
  
  {-
  Note [Type bindings]
  ~~~~~~~~~~~~~~~~~~~~
  Core does allow type bindings, although such bindings are
  not much used, except in the output of the desuguarer.
  Example:
       let a = Int in (\x:a. x)
  Given this, exprType must be careful to substitute 'a' in the
  result type (Trac #8522).
  
  Note [Existential variables and silly type synonyms]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Consider
          data T = forall a. T (Funny a)
          type Funny a = Bool
          f :: T -> Bool
          f (T x) = x
  
  Now, the type of 'x' is (Funny a), where 'a' is existentially quantified.
  That means that 'exprType' and 'coreAltsType' may give a result that *appears*
  to mention an out-of-scope type variable.  See Trac #3409 for a more real-world
  example.
  
  Various possibilities suggest themselves:
  
   - Ignore the problem, and make Lint not complain about such variables
  
   - Expand all type synonyms (or at least all those that discard arguments)
        This is tricky, because at least for top-level things we want to
        retain the type the user originally specified.
  
   - Expand synonyms on the fly, when the problem arises. That is what
     we are doing here.  It's not too expensive, I think.
  -}
  
  applyTypeToArg :: Type -> CoreExpr -> Type
  -- ^ Determines the type resulting from applying an expression with given type
  -- to a given argument expression
  applyTypeToArg fun_ty (Type arg_ty) = applyTy fun_ty arg_ty
  applyTypeToArg fun_ty _             = funResultTy fun_ty
  
  applyTypeToArgs :: CoreExpr -> Type -> [CoreExpr] -> Type
  -- ^ A more efficient version of 'applyTypeToArg' when we have several arguments.
  -- The first argument is just for debugging, and gives some context
  applyTypeToArgs e op_ty args
    = go op_ty args
    where
      go op_ty []               = op_ty
      go op_ty (Type ty : args) = go_ty_args op_ty [ty] args
      go op_ty (_ : args)       | Just (_, res_ty) <- splitFunTy_maybe op_ty
                                = go res_ty args
      go _ _ = pprPanic "applyTypeToArgs" panic_msg
  
      -- go_ty_args: accumulate type arguments so we can instantiate all at once
      go_ty_args op_ty rev_tys (Type ty : args)
         = go_ty_args op_ty (ty:rev_tys) args
      go_ty_args op_ty rev_tys args
         = go (applyTysD panic_msg_w_hdr op_ty (reverse rev_tys)) args
  
      panic_msg_w_hdr = hang (ptext (sLit "applyTypeToArgs")) 2 panic_msg
      panic_msg = vcat [ ptext (sLit "Expression:") <+> pprCoreExpr e
                       , ptext (sLit "Type:") <+> ppr op_ty
                       , ptext (sLit "Args:") <+> ppr args ]
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Attaching notes}
  *                                                                      *
  ************************************************************************
  -}
  
  -- | Wrap the given expression in the coercion safely, dropping
  -- identity coercions and coalescing nested coercions
  mkCast :: CoreExpr -> Coercion -> CoreExpr
  mkCast e co | ASSERT2( coercionRole co == Representational
                       , ptext (sLit "coercion") <+> ppr co <+> ptext (sLit "passed to mkCast") <+> ppr e <+> ptext (sLit "has wrong role") <+> ppr (coercionRole co) )
                isReflCo co = e
  
  mkCast (Coercion e_co) co
    | isCoVarType (pSnd (coercionKind co))
         -- The guard here checks that g has a (~#) on both sides,
         -- otherwise decomposeCo fails.  Can in principle happen
         -- with unsafeCoerce
    = Coercion (mkCoCast e_co co)
  
  mkCast (Cast expr co2) co
    = WARN(let { Pair  from_ty  _to_ty  = coercionKind co;
                 Pair _from_ty2  to_ty2 = coercionKind co2} in
              not (from_ty `eqType` to_ty2),
               vcat ([ ptext (sLit "expr:") <+> ppr expr
                     , ptext (sLit "co2:") <+> ppr co2
                     , ptext (sLit "co:") <+> ppr co ]) )
      mkCast expr (mkTransCo co2 co)
  
  mkCast (Tick t expr) co
     = Tick t (mkCast expr co)
  
  mkCast expr co
    = let Pair from_ty _to_ty = coercionKind co in
  --    if to_ty `eqType` from_ty
  --    then expr
  --    else
          WARN(not (from_ty `eqType` exprType expr), text "Trying to coerce" <+> text "(" <> ppr expr $$ text "::" <+> ppr (exprType expr) <> text ")" $$ ppr co $$ ppr (coercionType co))
           (Cast expr co)
  
  -- | Wraps the given expression in the source annotation, dropping the
  -- annotation if possible.
  mkTick :: Tickish Id -> CoreExpr -> CoreExpr
  mkTick t orig_expr = mkTick' id id orig_expr
   where
    -- Some ticks (cost-centres) can be split in two, with the
    -- non-counting part having laxer placement properties.
    canSplit = tickishCanSplit t && tickishPlace (mkNoCount t) /= tickishPlace t
  
    mkTick' :: (CoreExpr -> CoreExpr) -- ^ apply after adding tick (float through)
            -> (CoreExpr -> CoreExpr) -- ^ apply before adding tick (float with)
            -> CoreExpr               -- ^ current expression
            -> CoreExpr
    mkTick' top rest expr = case expr of
  
      -- Cost centre ticks should never be reordered relative to each
      -- other. Therefore we can stop whenever two collide.
      Tick t2 e
        | ProfNote{} <- t2, ProfNote{} <- t -> top $ Tick t $ rest expr
  
      -- Otherwise we assume that ticks of different placements float
      -- through each other.
        | tickishPlace t2 /= tickishPlace t -> mkTick' (top . Tick t2) rest e
  
      -- For annotations this is where we make sure to not introduce
      -- redundant ticks.
        | tickishContains t t2              -> mkTick' top rest e
        | tickishContains t2 t              -> orig_expr
        | otherwise                         -> mkTick' top (rest . Tick t2) e
  
      -- Ticks don't care about types, so we just float all ticks
      -- through them. Note that it's not enough to check for these
      -- cases top-level. While mkTick will never produce Core with type
      -- expressions below ticks, such constructs can be the result of
      -- unfoldings. We therefore make an effort to put everything into
      -- the right place no matter what we start with.
      Cast e co   -> mkTick' (top . flip Cast co) rest e
      Coercion co -> Coercion co
  
      Lam x e
        -- Always float through type lambdas. Even for non-type lambdas,
        -- floating is allowed for all but the most strict placement rule.
        | not (isRuntimeVar x) || tickishPlace t /= PlaceRuntime
        -> mkTick' (top . Lam x) rest e
  
        -- If it is both counting and scoped, we split the tick into its
        -- two components, often allowing us to keep the counting tick on
        -- the outside of the lambda and push the scoped tick inside.
        -- The point of this is that the counting tick can probably be
        -- floated, and the lambda may then be in a position to be
        -- beta-reduced.
        | canSplit
        -> top $ Tick (mkNoScope t) $ rest $ Lam x $ mkTick (mkNoCount t) e
  
      App f arg
        -- Always float through type applications.
        | not (isRuntimeArg arg)
        -> mkTick' (top . flip App arg) rest f
  
        -- We can also float through constructor applications, placement
        -- permitting. Again we can split.
        | isSaturatedConApp expr && (tickishPlace t==PlaceCostCentre || canSplit)
        -> if tickishPlace t == PlaceCostCentre
           then top $ rest $ tickHNFArgs t expr
           else top $ Tick (mkNoScope t) $ rest $ tickHNFArgs (mkNoCount t) expr
  
      Var x
        | notFunction && tickishPlace t == PlaceCostCentre
        -> orig_expr
        | notFunction && canSplit
        -> top $ Tick (mkNoScope t) $ rest expr
        where
          -- SCCs can be eliminated on variables provided the variable
          -- is not a function.  In these cases the SCC makes no difference:
          -- the cost of evaluating the variable will be attributed to its
          -- definition site.  When the variable refers to a function, however,
          -- an SCC annotation on the variable affects the cost-centre stack
          -- when the function is called, so we must retain those.
          notFunction = not (isFunTy (idType x))
  
      Lit{}
        | tickishPlace t == PlaceCostCentre
        -> orig_expr
  
      -- Catch-all: Annotate where we stand
      _any -> top $ Tick t $ rest expr
  
  mkTicks :: [Tickish Id] -> CoreExpr -> CoreExpr
  mkTicks ticks expr = foldr mkTick expr ticks
  
  isSaturatedConApp :: CoreExpr -> Bool
  isSaturatedConApp e = go e []
    where go (App f a) as = go f (a:as)
          go (Var fun) args
             = isConLikeId fun && idArity fun == valArgCount args
          go (Cast f _) as = go f as
          go _ _ = False
  
  mkTickNoHNF :: Tickish Id -> CoreExpr -> CoreExpr
  mkTickNoHNF t e
    | exprIsHNF e = tickHNFArgs t e
    | otherwise   = mkTick t e
  
  -- push a tick into the arguments of a HNF (call or constructor app)
  tickHNFArgs :: Tickish Id -> CoreExpr -> CoreExpr
  tickHNFArgs t e = push t e
   where
    push t (App f (Type u)) = App (push t f) (Type u)
    push t (App f arg) = App (push t f) (mkTick t arg)
    push _t e = e
  
  -- | Strip ticks satisfying a predicate from top of an expression
  stripTicksTop :: (Tickish Id -> Bool) -> Expr b -> ([Tickish Id], Expr b)
  stripTicksTop p = go []
    where go ts (Tick t e) | p t = go (t:ts) e
          go ts other            = (reverse ts, other)
  
  -- | Strip ticks satisfying a predicate from top of an expression,
  -- returning the remaining expresion
  stripTicksTopE :: (Tickish Id -> Bool) -> Expr b -> Expr b
  stripTicksTopE p = go
    where go (Tick t e) | p t = go e
          go other            = other
  
  -- | Strip ticks satisfying a predicate from top of an expression,
  -- returning the ticks
  stripTicksTopT :: (Tickish Id -> Bool) -> Expr b -> [Tickish Id]
  stripTicksTopT p = go []
    where go ts (Tick t e) | p t = go (t:ts) e
          go ts _                = ts
  
  -- | Completely strip ticks satisfying a predicate from an
  -- expression. Note this is O(n) in the size of the expression!
  stripTicksE :: (Tickish Id -> Bool) -> Expr b -> Expr b
  stripTicksE p expr = go expr
    where go (App e a)        = App (go e) (go a)
          go (Lam b e)        = Lam b (go e)
          go (Let b e)        = Let (go_bs b) (go e)
          go (Case e b t as)  = Case (go e) b t (map go_a as)
          go (Cast e c)       = Cast (go e) c
          go (Tick t e)
            | p t             = go e
            | otherwise       = Tick t (go e)
          go other            = other
          go_bs (NonRec b e)  = NonRec b (go e)
          go_bs (Rec bs)      = Rec (map go_b bs)
          go_b (b, e)         = (b, go e)
          go_a (c,bs,e)       = (c,bs, go e)
  
  stripTicksT :: (Tickish Id -> Bool) -> Expr b -> [Tickish Id]
  stripTicksT p expr = fromOL $ go expr
    where go (App e a)        = go e `appOL` go a
          go (Lam _ e)        = go e
          go (Let b e)        = go_bs b `appOL` go e
          go (Case e _ _ as)  = go e `appOL` concatOL (map go_a as)
          go (Cast e _)       = go e
          go (Tick t e)
            | p t             = t `consOL` go e
            | otherwise       = go e
          go _                = nilOL
          go_bs (NonRec _ e)  = go e
          go_bs (Rec bs)      = concatOL (map go_b bs)
          go_b (_, e)         = go e
          go_a (_, _, e)      = go e
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Other expression construction}
  *                                                                      *
  ************************************************************************
  -}
  
  bindNonRec :: Id -> CoreExpr -> CoreExpr -> CoreExpr
  -- ^ @bindNonRec x r b@ produces either:
  --
  -- > let x = r in b
  --
  -- or:
  --
  -- > case r of x { _DEFAULT_ -> b }
  --
  -- depending on whether we have to use a @case@ or @let@
  -- binding for the expression (see 'needsCaseBinding').
  -- It's used by the desugarer to avoid building bindings
  -- that give Core Lint a heart attack, although actually
  -- the simplifier deals with them perfectly well. See
  -- also 'MkCore.mkCoreLet'
  bindNonRec bndr rhs body
    | needsCaseBinding (idType bndr) rhs = Case rhs bndr (exprType body) [(DEFAULT, [], body)]
    | otherwise                          = Let (NonRec bndr rhs) body
  
  -- | Tests whether we have to use a @case@ rather than @let@ binding for this expression
  -- as per the invariants of 'CoreExpr': see "CoreSyn#let_app_invariant"
  needsCaseBinding :: Type -> CoreExpr -> Bool
  needsCaseBinding ty rhs = isUnLiftedType ty && not (exprOkForSpeculation rhs)
          -- Make a case expression instead of a let
          -- These can arise either from the desugarer,
          -- or from beta reductions: (\x.e) (x +# y)
  
  mkAltExpr :: AltCon     -- ^ Case alternative constructor
            -> [CoreBndr] -- ^ Things bound by the pattern match
            -> [Type]     -- ^ The type arguments to the case alternative
            -> CoreExpr
  -- ^ This guy constructs the value that the scrutinee must have
  -- given that you are in one particular branch of a case
  mkAltExpr (DataAlt con) args inst_tys
    = mkConApp con (map Type inst_tys ++ varsToCoreExprs args)
  mkAltExpr (LitAlt lit) [] []
    = Lit lit
  mkAltExpr (LitAlt _) _ _ = panic "mkAltExpr LitAlt"
  mkAltExpr DEFAULT _ _ = panic "mkAltExpr DEFAULT"
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Taking expressions apart}
  *                                                                      *
  ************************************************************************
  
  The default alternative must be first, if it exists at all.
  This makes it easy to find, though it makes matching marginally harder.
  -}
  
  -- | Extract the default case alternative
  findDefault :: [(AltCon, [a], b)] -> ([(AltCon, [a], b)], Maybe b)
  findDefault ((DEFAULT,args,rhs) : alts) = ASSERT( null args ) (alts, Just rhs)
  findDefault alts                        =                     (alts, Nothing)
  
  addDefault :: [(AltCon, [a], b)] -> Maybe b -> [(AltCon, [a], b)]
  addDefault alts Nothing    = alts
  addDefault alts (Just rhs) = (DEFAULT, [], rhs) : alts
  
  isDefaultAlt :: (AltCon, a, b) -> Bool
  isDefaultAlt (DEFAULT, _, _) = True
  isDefaultAlt _               = False
  
  
  -- | Find the case alternative corresponding to a particular
  -- constructor: panics if no such constructor exists
  findAlt :: AltCon -> [(AltCon, a, b)] -> Maybe (AltCon, a, b)
      -- A "Nothing" result *is* legitmiate
      -- See Note [Unreachable code]
  findAlt con alts
    = case alts of
          (deflt@(DEFAULT,_,_):alts) -> go alts (Just deflt)
          _                          -> go alts Nothing
    where
      go []                     deflt = deflt
      go (alt@(con1,_,_) : alts) deflt
        = case con `cmpAltCon` con1 of
            LT -> deflt   -- Missed it already; the alts are in increasing order
            EQ -> Just alt
            GT -> ASSERT( not (con1 == DEFAULT) ) go alts deflt
  
  ---------------------------------
  mergeAlts :: [(AltCon, a, b)] -> [(AltCon, a, b)] -> [(AltCon, a, b)]
  -- ^ Merge alternatives preserving order; alternatives in
  -- the first argument shadow ones in the second
  mergeAlts [] as2 = as2
  mergeAlts as1 [] = as1
  mergeAlts (a1:as1) (a2:as2)
    = case a1 `cmpAlt` a2 of
          LT -> a1 : mergeAlts as1      (a2:as2)
          EQ -> a1 : mergeAlts as1      as2       -- Discard a2
          GT -> a2 : mergeAlts (a1:as1) as2
  
  
  ---------------------------------
  trimConArgs :: AltCon -> [CoreArg] -> [CoreArg]
  -- ^ Given:
  --
  -- > case (C a b x y) of
  -- >        C b x y -> ...
  --
  -- We want to drop the leading type argument of the scrutinee
  -- leaving the arguments to match agains the pattern
  
  trimConArgs DEFAULT      args = ASSERT( null args ) []
  trimConArgs (LitAlt _)   args = ASSERT( null args ) []
  trimConArgs (DataAlt dc) args = dropList (dataConUnivTyVars dc) args
  
  filterAlts :: [Unique]             -- ^ Supply of uniques used in case we have to manufacture a new AltCon
             -> Type                 -- ^ Type of scrutinee (used to prune possibilities)
             -> [AltCon]             -- ^ 'imposs_cons': constructors known to be impossible due to the form of the scrutinee
             -> [(AltCon, [Var], a)] -- ^ Alternatives
             -> ([AltCon], Bool, [(AltCon, [Var], a)])
               -- Returns:
               --  1. Constructors that will never be encountered by the
               --     *default* case (if any).  A superset of imposs_cons
               --  2. Whether we managed to refine the default alternative into a specific constructor (for statistics only)
               --  3. The new alternatives, trimmed by
               --        a) remove imposs_cons
               --        b) remove constructors which can't match because of GADTs
               --      and with the DEFAULT expanded to a DataAlt if there is exactly
               --      remaining constructor that can match
               --
               -- NB: the final list of alternatives may be empty:
               -- This is a tricky corner case.  If the data type has no constructors,
               -- which GHC allows, or if the imposs_cons covers all constructors (after taking
               -- account of GADTs), then no alternatives can match.
               --
               -- If callers need to preserve the invariant that there is always at least one branch
               -- in a "case" statement then they will need to manually add a dummy case branch that just
               -- calls "error" or similar.
  filterAlts us ty imposs_cons alts
    | Just (tycon, inst_tys) <- splitTyConApp_maybe ty
    = filter_alts tycon inst_tys
    | otherwise
    = (imposs_cons, False, alts)
    where
      (alts_wo_default, maybe_deflt) = findDefault alts
      alt_cons = [con | (con,_,_) <- alts_wo_default]
  
      filter_alts tycon inst_tys
        = (imposs_deflt_cons, refined_deflt, merged_alts)
       where
         trimmed_alts = filterOut (impossible_alt inst_tys) alts_wo_default
  
         imposs_deflt_cons = nub (imposs_cons ++ alt_cons)
           -- "imposs_deflt_cons" are handled
           --   EITHER by the context,
           --   OR by a non-DEFAULT branch in this case expression.
  
         merged_alts  = mergeAlts trimmed_alts (maybeToList maybe_deflt')
           -- We need the mergeAlts in case the new default_alt
           -- has turned into a constructor alternative.
           -- The merge keeps the inner DEFAULT at the front, if there is one
           -- and interleaves the alternatives in the right order
  
         (refined_deflt, maybe_deflt') = case maybe_deflt of
            Nothing -> (False, Nothing)
            Just deflt_rhs
               | isAlgTyCon tycon            -- It's a data type, tuple, or unboxed tuples.
               , not (isNewTyCon tycon)      -- We can have a newtype, if we are just doing an eval:
                                             --      case x of { DEFAULT -> e }
                                             -- and we don't want to fill in a default for them!
               , Just all_cons <- tyConDataCons_maybe tycon
               , let imposs_data_cons = [con | DataAlt con <- imposs_deflt_cons]   -- We now know it's a data type
                     impossible con   = con `elem` imposs_data_cons || dataConCannotMatch inst_tys con
               -> case filterOut impossible all_cons of
                    -- Eliminate the default alternative
                    -- altogether if it can't match:
                    []    -> (False, Nothing)
                    -- It matches exactly one constructor, so fill it in:
                    [con] -> (True, Just (DataAlt con, ex_tvs ++ arg_ids, deflt_rhs))
                      where (ex_tvs, arg_ids) = dataConRepInstPat us con inst_tys
                    _     -> (False, Just (DEFAULT, [], deflt_rhs))
  
               | debugIsOn, isAlgTyCon tycon
               , null (tyConDataCons tycon)
               , not (isFamilyTyCon tycon || isAbstractTyCon tycon)
                     -- Check for no data constructors
                     -- This can legitimately happen for abstract types and type families,
                     -- so don't report that
               -> pprTrace "prepareDefault" (ppr tycon)
                  (False, Just (DEFAULT, [], deflt_rhs))
  
               | otherwise -> (False, Just (DEFAULT, [], deflt_rhs))
  
      impossible_alt :: [Type] -> (AltCon, a, b) -> Bool
      impossible_alt _ (con, _, _) | con `elem` imposs_cons = True
      impossible_alt inst_tys (DataAlt con, _, _) = dataConCannotMatch inst_tys con
      impossible_alt _  _                         = False
  
  {-
  Note [Unreachable code]
  ~~~~~~~~~~~~~~~~~~~~~~~
  It is possible (although unusual) for GHC to find a case expression
  that cannot match.  For example:
  
       data Col = Red | Green | Blue
       x = Red
       f v = case x of
                Red -> ...
                _ -> ...(case x of { Green -> e1; Blue -> e2 })...
  
  Suppose that for some silly reason, x isn't substituted in the case
  expression.  (Perhaps there's a NOINLINE on it, or profiling SCC stuff
  gets in the way; cf Trac #3118.)  Then the full-lazines pass might produce
  this
  
       x = Red
       lvl = case x of { Green -> e1; Blue -> e2 })
       f v = case x of
               Red -> ...
               _ -> ...lvl...
  
  Now if x gets inlined, we won't be able to find a matching alternative
  for 'Red'.  That's because 'lvl' is unreachable.  So rather than crashing
  we generate (error "Inaccessible alternative").
  
  Similar things can happen (augmented by GADTs) when the Simplifier
  filters down the matching alternatives in Simplify.rebuildCase.
  
  
  ************************************************************************
  *                                                                      *
               exprIsTrivial
  *                                                                      *
  ************************************************************************
  
  Note [exprIsTrivial]
  ~~~~~~~~~~~~~~~~~~~~
  @exprIsTrivial@ is true of expressions we are unconditionally happy to
                  duplicate; simple variables and constants, and type
                  applications.  Note that primop Ids aren't considered
                  trivial unless
  
  Note [Variable are trivial]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~
  There used to be a gruesome test for (hasNoBinding v) in the
  Var case:
          exprIsTrivial (Var v) | hasNoBinding v = idArity v == 0
  The idea here is that a constructor worker, like \$wJust, is
  really short for (\x -> \$wJust x), because \$wJust has no binding.
  So it should be treated like a lambda.  Ditto unsaturated primops.
  But now constructor workers are not "have-no-binding" Ids.  And
  completely un-applied primops and foreign-call Ids are sufficiently
  rare that I plan to allow them to be duplicated and put up with
  saturating them.
  
  Note [Tick trivial]
  ~~~~~~~~~~~~~~~~~~~
  
  Ticks are only trivial if they are pure annotations. If we treat
  "tick<n> x" as trivial, it will be inlined inside lambdas and the
  entry count will be skewed, for example.  Furthermore "scc<n> x" will
  turn into just "x" in mkTick.
  -}
  
  exprIsTrivial :: CoreExpr -> Bool
  exprIsTrivial (Var _)          = True        -- See Note [Variables are trivial]
  exprIsTrivial (Type _)         = True
  exprIsTrivial (Coercion _)     = True
  exprIsTrivial (Lit lit)        = litIsTrivial lit
  exprIsTrivial (App e arg)      = not (isRuntimeArg arg) && exprIsTrivial e
  exprIsTrivial (Tick t e)       = not (tickishIsCode t) && exprIsTrivial e
                                   -- See Note [Tick trivial]
  exprIsTrivial (Cast e _)       = exprIsTrivial e
  exprIsTrivial (Lam b body)     = not (isRuntimeVar b) && exprIsTrivial body
  exprIsTrivial _                = False
  
  {-
  Note [getIdFromTrivialExpr]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~
  When substituting in a breakpoint we need to strip away the type cruft
  from a trivial expression and get back to the Id.  The invariant is
  that the expression we're substituting was originally trivial
  according to exprIsTrivial, AND the expression is not a literal.
  See Note [substTickish] for how breakpoint substitution preserves
  this extra invariant.
  
  We also need this functionality in CorePrep to extract out Id of a
  function which we are saturating.  However, in this case we don't know
  if the variable actually refers to a literal; thus we use
  'getIdFromTrivialExpr_maybe' to handle this case.  See test
  T12076lit for an example where this matters.
  -}
  
  getIdFromTrivialExpr :: CoreExpr -> Id
  getIdFromTrivialExpr e
      = fromMaybe (pprPanic "getIdFromTrivialExpr" (ppr e))
                  (getIdFromTrivialExpr_maybe e)
  
  getIdFromTrivialExpr_maybe :: CoreExpr -> Maybe Id
  -- See Note [getIdFromTrivialExpr]
  getIdFromTrivialExpr_maybe e = go e
    where go (Var v) = Just v
          go (App f t) | not (isRuntimeArg t) = go f
          go (Tick t e) | not (tickishIsCode t) = go e
          go (Cast e _) = go e
          go (Lam b e) | not (isRuntimeVar b) = go e
          go _ = Nothing
  
  {-
  exprIsBottom is a very cheap and cheerful function; it may return
  False for bottoming expressions, but it never costs much to ask.  See
  also CoreArity.exprBotStrictness_maybe, but that's a bit more
  expensive.
  -}
  
  exprIsBottom :: CoreExpr -> Bool
  exprIsBottom e
    = go 0 e
    where
      go n (Var v) = isBottomingId v &&  n >= idArity v
      go n (App e a) | isTypeArg a = go n e
                     | otherwise   = go (n+1) e
      go n (Tick _ e)              = go n e
      go n (Cast e _)              = go n e
      go n (Let _ e)               = go n e
      go _ _                       = False
  
  {-
  ************************************************************************
  *                                                                      *
               exprIsDupable
  *                                                                      *
  ************************************************************************
  
  Note [exprIsDupable]
  ~~~~~~~~~~~~~~~~~~~~
  @exprIsDupable@ is true of expressions that can be duplicated at a modest
                  cost in code size.  This will only happen in different case
                  branches, so there's no issue about duplicating work.
  
                  That is, exprIsDupable returns True of (f x) even if
                  f is very very expensive to call.
  
                  Its only purpose is to avoid fruitless let-binding
                  and then inlining of case join points
  -}
  
  exprIsDupable :: DynFlags -> CoreExpr -> Bool
  exprIsDupable dflags e
    = isJust (go dupAppSize e)
    where
      go :: Int -> CoreExpr -> Maybe Int
      go n (Type {})     = Just n
      go n (Coercion {}) = Just n
      go n (Var {})      = decrement n
      go n (Tick _ e)    = go n e
      go n (Cast e _)    = go n e
      go n (App f a) | Just n' <- go n a = go n' f
      go n (Lit lit) | litIsDupable dflags lit = decrement n
      go _ _ = Nothing
  
      decrement :: Int -> Maybe Int
      decrement 0 = Nothing
      decrement n = Just (n-1)
  
  dupAppSize :: Int
  dupAppSize = 8   -- Size of term we are prepared to duplicate
                   -- This is *just* big enough to make test MethSharing
                   -- inline enough join points.  Really it should be
                   -- smaller, and could be if we fixed Trac #4960.
  
  {-
  ************************************************************************
  *                                                                      *
               exprIsCheap, exprIsExpandable
  *                                                                      *
  ************************************************************************
  
  Note [exprIsWorkFree]
  ~~~~~~~~~~~~~~~~~~~~~
  exprIsWorkFree is used when deciding whether to inline something; we
  don't inline it if doing so might duplicate work, by peeling off a
  complete copy of the expression.  Here we do not want even to
  duplicate a primop (Trac #5623):
     eg   let x = a #+ b in x +# x
     we do not want to inline/duplicate x
  
  Previously we were a bit more liberal, which led to the primop-duplicating
  problem.  However, being more conservative did lead to a big regression in
  one nofib benchmark, wheel-sieve1.  The situation looks like this:
  
     let noFactor_sZ3 :: GHC.Types.Int -> GHC.Types.Bool
         noFactor_sZ3 = case s_adJ of _ { GHC.Types.I# x_aRs ->
           case GHC.Prim.<=# x_aRs 2 of _ {
             GHC.Types.False -> notDivBy ps_adM qs_adN;
             GHC.Types.True -> lvl_r2Eb }}
         go = \x. ...(noFactor (I# y))....(go x')...
  
  The function 'noFactor' is heap-allocated and then called.  Turns out
  that 'notDivBy' is strict in its THIRD arg, but that is invisible to
  the caller of noFactor, which therefore cannot do w/w and
  heap-allocates noFactor's argument.  At the moment (May 12) we are just
  going to put up with this, because the previous more aggressive inlining
  (which treated 'noFactor' as work-free) was duplicating primops, which
  in turn was making inner loops of array calculations runs slow (#5623)
  -}
  
  exprIsWorkFree :: CoreExpr -> Bool
  -- See Note [exprIsWorkFree]
  exprIsWorkFree e = go 0 e
    where    -- n is the number of value arguments
      go _ (Lit {})                     = True
      go _ (Type {})                    = True
      go _ (Coercion {})                = True
      go n (Cast e _)                   = go n e
      go n (Case scrut _ _ alts)        = foldl (&&) (exprIsWorkFree scrut)
                                                [ go n rhs | (_,_,rhs) <- alts ]
           -- See Note [Case expressions are work-free]
      go _ (Let {})                     = False
      go n (Var v)                      = isCheapApp v n
      go n (Tick t e) | tickishCounts t = False
                      | otherwise       = go n e
      go n (Lam x e)  | isRuntimeVar x = n==0 || go (n-1) e
                      | otherwise      = go n e
      go n (App f e)  | isRuntimeArg e = exprIsWorkFree e && go (n+1) f
                      | otherwise      = go n f
  
  {-
  Note [Case expressions are work-free]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Are case-expressions work-free?  Consider
      let v = case x of (p,q) -> p
          go = \y -> ...case v of ...
  Should we inline 'v' at its use site inside the loop?  At the moment
  we do.  I experimented with saying that case are *not* work-free, but
  that increased allocation slightly.  It's a fairly small effect, and at
  the moment we go for the slightly more aggressive version which treats
  (case x of ....) as work-free if the alternatives are.
  
  
  Note [exprIsCheap]   See also Note [Interaction of exprIsCheap and lone variables]
  ~~~~~~~~~~~~~~~~~~   in CoreUnfold.lhs
  @exprIsCheap@ looks at a Core expression and returns \tr{True} if
  it is obviously in weak head normal form, or is cheap to get to WHNF.
  [Note that that's not the same as exprIsDupable; an expression might be
  big, and hence not dupable, but still cheap.]
  
  By ``cheap'' we mean a computation we're willing to:
          push inside a lambda, or
          inline at more than one place
  That might mean it gets evaluated more than once, instead of being
  shared.  The main examples of things which aren't WHNF but are
  ``cheap'' are:
  
    *     case e of
            pi -> ei
          (where e, and all the ei are cheap)
  
    *     let x = e in b
          (where e and b are cheap)
  
    *     op x1 ... xn
          (where op is a cheap primitive operator)
  
    *     error "foo"
          (because we are happy to substitute it inside a lambda)
  
  Notice that a variable is considered 'cheap': we can push it inside a lambda,
  because sharing will make sure it is only evaluated once.
  
  Note [exprIsCheap and exprIsHNF]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Note that exprIsHNF does not imply exprIsCheap.  Eg
          let x = fac 20 in Just x
  This responds True to exprIsHNF (you can discard a seq), but
  False to exprIsCheap.
  -}
  
  exprIsCheap :: CoreExpr -> Bool
  exprIsCheap = exprIsCheap' isCheapApp
  
  exprIsExpandable :: CoreExpr -> Bool
  exprIsExpandable = exprIsCheap' isExpandableApp -- See Note [CONLIKE pragma] in BasicTypes
  
  exprIsCheap' :: CheapAppFun -> CoreExpr -> Bool
  exprIsCheap' _        (Lit _)      = True
  exprIsCheap' _        (Type _)    = True
  exprIsCheap' _        (Coercion _) = True
  exprIsCheap' _        (Var _)      = True
  exprIsCheap' good_app (Cast e _)   = exprIsCheap' good_app e
  exprIsCheap' good_app (Lam x e)    = isRuntimeVar x
                                    || exprIsCheap' good_app e
  
  exprIsCheap' good_app (Case e _ _ alts) = exprIsCheap' good_app e &&
                                            and [exprIsCheap' good_app rhs | (_,_,rhs) <- alts]
          -- Experimentally, treat (case x of ...) as cheap
          -- (and case __coerce x etc.)
          -- This improves arities of overloaded functions where
          -- there is only dictionary selection (no construction) involved
  
  exprIsCheap' good_app (Tick t e)
    | tickishCounts t = False
    | otherwise       = exprIsCheap' good_app e
       -- never duplicate counting ticks.  If we get this wrong, then
       -- HPC's entry counts will be off (check test in
       -- libraries/hpc/tests/raytrace)
  
  exprIsCheap' good_app (Let (NonRec _ b) e)
    = exprIsCheap' good_app b && exprIsCheap' good_app e
  exprIsCheap' good_app (Let (Rec prs) e)
    = all (exprIsCheap' good_app . snd) prs && exprIsCheap' good_app e
  
  exprIsCheap' good_app other_expr        -- Applications and variables
    = go other_expr []
    where
          -- Accumulate value arguments, then decide
      go (Cast e _) val_args                 = go e val_args
      go (App f a) val_args | isRuntimeArg a = go f (a:val_args)
                            | otherwise      = go f val_args
  
      go (Var _) [] = True
           -- Just a type application of a variable
           -- (f t1 t2 t3) counts as WHNF
           -- This case is probably handeld by the good_app case
           -- below, which should have a case for n=0, but putting
           -- it here too is belt and braces; and it's such a common
           -- case that checking for null directly seems like a
           -- good plan
  
      go (Var f) args
         | good_app f (length args)
         = go_pap args
  
         | otherwise
          = case idDetails f of
                  RecSelId {}         -> go_sel args
                  ClassOpId {}        -> go_sel args
                  PrimOpId op         -> go_primop op args
                  _ | isBottomingId f -> True
                    | otherwise       -> False
                          -- Application of a function which
                          -- always gives bottom; we treat this as cheap
                          -- because it certainly doesn't need to be shared!
  
      go (Tick t e) args
        | not (tickishCounts t) -- don't duplicate counting ticks, see above
        = go e args
  
      go _ _ = False
  
      --------------
      go_pap args = all (exprIsCheap' good_app) args
          -- Used to be "all exprIsTrivial args" due to concerns about
          -- duplicating nested constructor applications, but see #4978.
          -- The principle here is that
          --    let x = a +# b in c *# x
          -- should behave equivalently to
          --    c *# (a +# b)
          -- Since lets with cheap RHSs are accepted,
          -- so should paps with cheap arguments
  
      --------------
      go_primop op args = primOpIsCheap op && all (exprIsCheap' good_app) args
          -- In principle we should worry about primops
          -- that return a type variable, since the result
          -- might be applied to something, but I'm not going
          -- to bother to check the number of args
  
      --------------
      go_sel [arg] = exprIsCheap' good_app arg    -- I'm experimenting with making record selection
      go_sel _     = False                -- look cheap, so we will substitute it inside a
                                          -- lambda.  Particularly for dictionary field selection.
                  -- BUT: Take care with (sel d x)!  The (sel d) might be cheap, but
                  --      there's no guarantee that (sel d x) will be too.  Hence (n_val_args == 1)
  
  -------------------------------------
  type CheapAppFun = Id -> Int -> Bool
    -- Is an application of this function to n *value* args
    -- always cheap, assuming the arguments are cheap?
    -- Mainly true of partial applications, data constructors,
    -- and of course true if the number of args is zero
  
  isCheapApp :: CheapAppFun
  isCheapApp fn n_val_args
    =  isDataConWorkId fn
    || n_val_args == 0
    || n_val_args < idArity fn
  
  isExpandableApp :: CheapAppFun
  isExpandableApp fn n_val_args
    =  isConLikeId fn
    || n_val_args < idArity fn
    || go n_val_args (idType fn)
    where
    -- See if all the arguments are PredTys (implicit params or classes)
    -- If so we'll regard it as expandable; see Note [Expandable overloadings]
    -- This incidentally picks up the (n_val_args = 0) case
       go 0 _ = True
       go n_val_args ty
         | Just (_, ty) <- splitForAllTy_maybe ty   = go n_val_args ty
         | Just (arg, ty) <- splitFunTy_maybe ty
         , isPredTy arg                             = go (n_val_args-1) ty
         | otherwise                                = False
  
  {-
  Note [Expandable overloadings]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Suppose the user wrote this
     {-# RULE  forall x. foo (negate x) = h x #-}
     f x = ....(foo (negate x))....
  He'd expect the rule to fire. But since negate is overloaded, we might
  get this:
      f = \d -> let n = negate d in \x -> ...foo (n x)...
  So we treat the application of a function (negate in this case) to a
  *dictionary* as expandable.  In effect, every function is CONLIKE when
  it's applied only to dictionaries.
  
  
  ************************************************************************
  *                                                                      *
               exprOkForSpeculation
  *                                                                      *
  ************************************************************************
  -}
  
  -----------------------------
  -- | 'exprOkForSpeculation' returns True of an expression that is:
  --
  --  * Safe to evaluate even if normal order eval might not
  --    evaluate the expression at all, or
  --
  --  * Safe /not/ to evaluate even if normal order would do so
  --
  -- It is usually called on arguments of unlifted type, but not always
  -- In particular, Simplify.rebuildCase calls it on lifted types
  -- when a 'case' is a plain 'seq'. See the example in
  -- Note [exprOkForSpeculation: case expressions] below
  --
  -- Precisely, it returns @True@ iff:
  --  a) The expression guarantees to terminate,
  --  b) soon,
  --  c) without causing a write side effect (e.g. writing a mutable variable)
  --  d) without throwing a Haskell exception
  --  e) without risking an unchecked runtime exception (array out of bounds,
  --     divide by zero)
  --
  -- For @exprOkForSideEffects@ the list is the same, but omitting (e).
  --
  -- Note that
  --    exprIsHNF            implies exprOkForSpeculation
  --    exprOkForSpeculation implies exprOkForSideEffects
  --
  -- See Note [PrimOp can_fail and has_side_effects] in PrimOp
  -- and Note [Implementation: how can_fail/has_side_effects affect transformations]
  --
  -- As an example of the considerations in this test, consider:
  --
  -- > let x = case y# +# 1# of { r# -> I# r# }
  -- > in E
  --
  -- being translated to:
  --
  -- > case y# +# 1# of { r# ->
  -- >    let x = I# r#
  -- >    in E
  -- > }
  --
  -- We can only do this if the @y + 1@ is ok for speculation: it has no
  -- side effects, and can't diverge or raise an exception.
  exprOkForSpeculation, exprOkForSideEffects :: Expr b -> Bool
  exprOkForSpeculation = expr_ok primOpOkForSpeculation
  exprOkForSideEffects = expr_ok primOpOkForSideEffects
    -- Polymorphic in binder type
    -- There is one call at a non-Id binder type, in SetLevels
  
  expr_ok :: (PrimOp -> Bool) -> Expr b -> Bool
  expr_ok _ (Lit _)      = True
  expr_ok _ (Type _)     = True
  expr_ok _ (Coercion _) = True
  expr_ok primop_ok (Var v)      = app_ok primop_ok v []
  expr_ok primop_ok (Cast e _)   = expr_ok primop_ok e
  
  -- Tick annotations that *tick* cannot be speculated, because these
  -- are meant to identify whether or not (and how often) the particular
  -- source expression was evaluated at runtime.
  expr_ok primop_ok (Tick tickish e)
     | tickishCounts tickish = False
     | otherwise             = expr_ok primop_ok e
  
  expr_ok primop_ok (Case e _ _ alts)
    =  expr_ok primop_ok e  -- Note [exprOkForSpeculation: case expressions]
    && all (\(_,_,rhs) -> expr_ok primop_ok rhs) alts
    && altsAreExhaustive alts     -- Note [Exhaustive alts]
  
  expr_ok primop_ok other_expr
    = case collectArgs other_expr of
          (expr, args) | Var f <- stripTicksTopE (not . tickishCounts) expr
                       -> app_ok primop_ok f args
          _            -> False
  
  -----------------------------
  app_ok :: (PrimOp -> Bool) -> Id -> [Expr b] -> Bool
  app_ok primop_ok fun args
    = case idDetails fun of
        DFunId _ new_type ->  not new_type
           -- DFuns terminate, unless the dict is implemented
           -- with a newtype in which case they may not
  
        DataConWorkId {} -> True
                  -- The strictness of the constructor has already
                  -- been expressed by its "wrapper", so we don't need
                  -- to take the arguments into account
  
        PrimOpId op
          | isDivOp op              -- Special case for dividing operations that fail
          , [arg1, Lit lit] <- args -- only if the divisor is zero
          -> not (isZeroLit lit) && expr_ok primop_ok arg1
                    -- Often there is a literal divisor, and this
                    -- can get rid of a thunk in an inner looop
  
          | DataToTagOp <- op      -- See Note [dataToTag speculation]
          -> True
  
          | otherwise
          -> primop_ok op                   -- A bit conservative: we don't really need
          && all (expr_ok primop_ok) args   -- to care about lazy arguments, but this is easy
  
        _other -> isUnLiftedType (idType fun)          -- c.f. the Var case of exprIsHNF
               || idArity fun > n_val_args             -- Partial apps
               || (n_val_args == 0 &&
                   isEvaldUnfolding (idUnfolding fun)) -- Let-bound values
               where
                 n_val_args = valArgCount args
  
  -----------------------------
  altsAreExhaustive :: [Alt b] -> Bool
  -- True  <=> the case alternatives are definiely exhaustive
  -- False <=> they may or may not be
  altsAreExhaustive []
    = False    -- Should not happen
  altsAreExhaustive ((con1,_,_) : alts)
    = case con1 of
        DEFAULT   -> True
        LitAlt {} -> False
        DataAlt c -> 1 + length alts == tyConFamilySize (dataConTyCon c)
        -- It is possible to have an exhaustive case that does not
        -- enumerate all constructors, notably in a GADT match, but
        -- we behave conservatively here -- I don't think it's important
        -- enough to deserve special treatment
  
  -- | True of dyadic operators that can fail only if the second arg is zero!
  isDivOp :: PrimOp -> Bool
  -- This function probably belongs in PrimOp, or even in
  -- an automagically generated file.. but it's such a
  -- special case I thought I'd leave it here for now.
  isDivOp IntQuotOp        = True
  isDivOp IntRemOp         = True
  isDivOp WordQuotOp       = True
  isDivOp WordRemOp        = True
  isDivOp FloatDivOp       = True
  isDivOp DoubleDivOp      = True
  isDivOp _                = False
  
  {-
  Note [exprOkForSpeculation: case expressions]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  It's always sound for exprOkForSpeculation to return False, and we
  don't want it to take too long, so it bales out on complicated-looking
  terms.  Notably lets, which can be stacked very deeply; and in any
  case the argument of exprOkForSpeculation is usually in a strict context,
  so any lets will have been floated away.
  
  However, we keep going on case-expressions.  An example like this one
  showed up in DPH code (Trac #3717):
      foo :: Int -> Int
      foo 0 = 0
      foo n = (if n < 5 then 1 else 2) `seq` foo (n-1)
  
  If exprOkForSpeculation doesn't look through case expressions, you get this:
      T.$wfoo =
        \ (ww :: GHC.Prim.Int#) ->
          case ww of ds {
            __DEFAULT -> case (case <# ds 5 of _ {
                            GHC.Types.False -> lvl1;
                            GHC.Types.True -> lvl})
                         of _ { __DEFAULT ->
                         T.$wfoo (GHC.Prim.-# ds_XkE 1) };
            0 -> 0
          }
  
  The inner case is redundant, and should be nuked.
  
  Note [Exhaustive alts]
  ~~~~~~~~~~~~~~~~~~~~~~
  We might have something like
    case x of {
      A -> ...
      _ -> ...(case x of { B -> ...; C -> ... })...
  Here, the inner case is fine, because the A alternative
  can't happen, but it's not ok to float the inner case outside
  the outer one (even if we know x is evaluated outside), because
  then it would be non-exhaustive. See Trac #5453.
  
  Similarly, this is a valid program (albeit a slightly dodgy one)
     let v = case x of { B -> ...; C -> ... }
     in case x of
           A -> ...
           _ ->  ...v...v....
  But we don't want to speculate the v binding.
  
  One could try to be clever, but the easy fix is simpy to regard
  a non-exhaustive case as *not* okForSpeculation.
  
  
  Note [dataToTag speculation]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Is this OK?
     f x = let v::Int# = dataToTag# x
           in ...
  We say "yes", even though 'x' may not be evaluated.  Reasons
  
    * dataToTag#'s strictness means that its argument often will be
      evaluated, but FloatOut makes that temporarily untrue
           case x of y -> let v = dataToTag# y in ...
      -->
           case x of y -> let v = dataToTag# x in ...
      Note that we look at 'x' instead of 'y' (this is to improve
      floating in FloatOut).  So Lint complains.
  
      Moreover, it really *might* improve floating to let the
      v-binding float out
  
    * CorePrep makes sure dataToTag#'s argument is evaluated, just
      before code gen.  Until then, it's not guaranteed
  
  
  ************************************************************************
  *                                                                      *
               exprIsHNF, exprIsConLike
  *                                                                      *
  ************************************************************************
  -}
  
  -- Note [exprIsHNF]             See also Note [exprIsCheap and exprIsHNF]
  -- ~~~~~~~~~~~~~~~~
  -- | exprIsHNF returns true for expressions that are certainly /already/
  -- evaluated to /head/ normal form.  This is used to decide whether it's ok
  -- to change:
  --
  -- > case x of _ -> e
  --
  --    into:
  --
  -- > e
  --
  -- and to decide whether it's safe to discard a 'seq'.
  --
  -- So, it does /not/ treat variables as evaluated, unless they say they are.
  -- However, it /does/ treat partial applications and constructor applications
  -- as values, even if their arguments are non-trivial, provided the argument
  -- type is lifted. For example, both of these are values:
  --
  -- > (:) (f x) (map f xs)
  -- > map (...redex...)
  --
  -- because 'seq' on such things completes immediately.
  --
  -- For unlifted argument types, we have to be careful:
  --
  -- > C (f x :: Int#)
  --
  -- Suppose @f x@ diverges; then @C (f x)@ is not a value. However this can't
  -- happen: see "CoreSyn#let_app_invariant". This invariant states that arguments of
  -- unboxed type must be ok-for-speculation (or trivial).
  exprIsHNF :: CoreExpr -> Bool           -- True => Value-lambda, constructor, PAP
  exprIsHNF = exprIsHNFlike isDataConWorkId isEvaldUnfolding
  
  -- | Similar to 'exprIsHNF' but includes CONLIKE functions as well as
  -- data constructors. Conlike arguments are considered interesting by the
  -- inliner.
  exprIsConLike :: CoreExpr -> Bool       -- True => lambda, conlike, PAP
  exprIsConLike = exprIsHNFlike isConLikeId isConLikeUnfolding
  
  -- | Returns true for values or value-like expressions. These are lambdas,
  -- constructors / CONLIKE functions (as determined by the function argument)
  -- or PAPs.
  --
  exprIsHNFlike :: (Var -> Bool) -> (Unfolding -> Bool) -> CoreExpr -> Bool
  exprIsHNFlike is_con is_con_unf = is_hnf_like
    where
      is_hnf_like (Var v) -- NB: There are no value args at this point
        =  is_con v       -- Catches nullary constructors,
                          --      so that [] and () are values, for example
        || idArity v > 0  -- Catches (e.g.) primops that don't have unfoldings
        || is_con_unf (idUnfolding v)
          -- Check the thing's unfolding; it might be bound to a value
          -- We don't look through loop breakers here, which is a bit conservative
          -- but otherwise I worry that if an Id's unfolding is just itself,
          -- we could get an infinite loop
  
      is_hnf_like (Lit _)          = True
      is_hnf_like (Type _)         = True       -- Types are honorary Values;
                                                -- we don't mind copying them
      is_hnf_like (Coercion _)     = True       -- Same for coercions
      is_hnf_like (Lam b e)        = isRuntimeVar b || is_hnf_like e
      is_hnf_like (Tick tickish e) = not (tickishCounts tickish)
                                        && is_hnf_like e
                                        -- See Note [exprIsHNF Tick]
      is_hnf_like (Cast e _)           = is_hnf_like e
      is_hnf_like (App e (Type _))     = is_hnf_like e
      is_hnf_like (App e (Coercion _)) = is_hnf_like e
      is_hnf_like (App e a)            = app_is_value e [a]
      is_hnf_like (Let _ e)            = is_hnf_like e  -- Lazy let(rec)s don't affect us
      is_hnf_like _                    = False
  
      -- There is at least one value argument
      app_is_value :: CoreExpr -> [CoreArg] -> Bool
      app_is_value (Var fun) args
        = idArity fun > valArgCount args    -- Under-applied function
          || is_con fun                     --  or constructor-like
      app_is_value (Tick _ f) as = app_is_value f as
      app_is_value (Cast f _) as = app_is_value f as
      app_is_value (App f a)  as = app_is_value f (a:as)
      app_is_value _          _  = False
  
  {-
  Note [exprIsHNF Tick]
  
  We can discard source annotations on HNFs as long as they aren't
  tick-like:
  
    scc c (\x . e)    =>  \x . e
    scc c (C x1..xn)  =>  C x1..xn
  
  So we regard these as HNFs.  Tick annotations that tick are not
  regarded as HNF if the expression they surround is HNF, because the
  tick is there to tell us that the expression was evaluated, so we
  don't want to discard a seq on it.
  -}
  
  {-
  ************************************************************************
  *                                                                      *
               Instantiating data constructors
  *                                                                      *
  ************************************************************************
  
  These InstPat functions go here to avoid circularity between DataCon and Id
  -}
  
  dataConRepInstPat   ::                 [Unique] -> DataCon -> [Type] -> ([TyVar], [Id])
  dataConRepFSInstPat :: [FastString] -> [Unique] -> DataCon -> [Type] -> ([TyVar], [Id])
  
  dataConRepInstPat   = dataConInstPat (repeat ((fsLit "ipv")))
  dataConRepFSInstPat = dataConInstPat
  
  dataConInstPat :: [FastString]          -- A long enough list of FSs to use for names
                 -> [Unique]              -- An equally long list of uniques, at least one for each binder
                 -> DataCon
                 -> [Type]                -- Types to instantiate the universally quantified tyvars
                 -> ([TyVar], [Id])       -- Return instantiated variables
  -- dataConInstPat arg_fun fss us con inst_tys returns a triple
  -- (ex_tvs, arg_ids),
  --
  --   ex_tvs are intended to be used as binders for existential type args
  --
  --   arg_ids are indended to be used as binders for value arguments,
  --     and their types have been instantiated with inst_tys and ex_tys
  --     The arg_ids include both evidence and
  --     programmer-specified arguments (both after rep-ing)
  --
  -- Example.
  --  The following constructor T1
  --
  --  data T a where
  --    T1 :: forall b. Int -> b -> T(a,b)
  --    ...
  --
  --  has representation type
  --   forall a. forall a1. forall b. (a ~ (a1,b)) =>
  --     Int -> b -> T a
  --
  --  dataConInstPat fss us T1 (a1',b') will return
  --
  --  ([a1'', b''], [c :: (a1', b')~(a1'', b''), x :: Int, y :: b''])
  --
  --  where the double-primed variables are created with the FastStrings and
  --  Uniques given as fss and us
  dataConInstPat fss uniqs con inst_tys
    = ASSERT( univ_tvs `equalLength` inst_tys )
      (ex_bndrs, arg_ids)
    where
      univ_tvs = dataConUnivTyVars con
      ex_tvs   = dataConExTyVars con
      arg_tys  = dataConRepArgTys con
      arg_strs = dataConRepStrictness con  -- 1-1 with arg_tys
      n_ex = length ex_tvs
  
        -- split the Uniques and FastStrings
      (ex_uniqs, id_uniqs) = splitAt n_ex uniqs
      (ex_fss,   id_fss)   = splitAt n_ex fss
  
        -- Make the instantiating substitution for universals
      univ_subst = zipOpenTvSubst univ_tvs inst_tys
  
        -- Make existential type variables, applyingn and extending the substitution
      (full_subst, ex_bndrs) = mapAccumL mk_ex_var univ_subst
                                         (zip3 ex_tvs ex_fss ex_uniqs)
  
      mk_ex_var :: TvSubst -> (TyVar, FastString, Unique) -> (TvSubst, TyVar)
      mk_ex_var subst (tv, fs, uniq) = (Type.extendTvSubst subst tv (mkTyVarTy new_tv)
                                       , new_tv)
        where
          new_tv   = mkTyVar new_name kind
          new_name = mkSysTvName uniq fs
          kind     = Type.substTy subst (tyVarKind tv)
  
        -- Make value vars, instantiating types
      arg_ids = zipWith4 mk_id_var id_uniqs id_fss arg_tys arg_strs
      mk_id_var uniq fs ty str
        = mkLocalIdWithInfo name (Type.substTy full_subst ty) info
        where
          name = mkInternalName uniq (mkVarOccFS fs) noSrcSpan
          info | isMarkedStrict str = vanillaIdInfo `setUnfoldingInfo` evaldUnfolding
               | otherwise          = vanillaIdInfo
               -- See Note [Mark evaluated arguments]
  
  {-
  Note [Mark evaluated arguments]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  When pattern matching on a constructor with strict fields, the binder
  can have an 'evaldUnfolding'.  Moreover, it *should* have one, so that
  when loading an interface file unfolding like:
    data T = MkT !Int
    f x = case x of { MkT y -> let v::Int# = case y of I# n -> n+1
                               in ... }
  we don't want Lint to complain.  The 'y' is evaluated, so the
  case in the RHS of the binding for 'v' is fine.  But only if we
  *know* that 'y' is evaluated.
  
  c.f. add_evals in Simplify.simplAlt
  
  ************************************************************************
  *                                                                      *
           Equality
  *                                                                      *
  ************************************************************************
  -}
  
  -- | A cheap equality test which bales out fast!
  --      If it returns @True@ the arguments are definitely equal,
  --      otherwise, they may or may not be equal.
  --
  -- See also 'exprIsBig'
  cheapEqExpr :: Expr b -> Expr b -> Bool
  cheapEqExpr = cheapEqExpr' (const False)
  
  -- | Cheap expression equality test, can ignore ticks by type.
  cheapEqExpr' :: (Tickish Id -> Bool) -> Expr b -> Expr b -> Bool
  cheapEqExpr' ignoreTick = go_s
    where go_s = go `on` stripTicksTopE ignoreTick
          go (Var v1)   (Var v2)   = v1 == v2
          go (Lit lit1) (Lit lit2) = lit1 == lit2
          go (Type t1)  (Type t2)  = t1 `eqType` t2
          go (Coercion c1) (Coercion c2) = c1 `coreEqCoercion` c2
  
          go (App f1 a1) (App f2 a2)
            = f1 `go_s` f2 && a1 `go_s` a2
  
          go (Cast e1 t1) (Cast e2 t2)
            = e1 `go_s` e2 && t1 `coreEqCoercion` t2
  
          go (Tick t1 e1) (Tick t2 e2)
            = t1 == t2 && e1 `go_s` e2
  
          go _ _ = False
          {-# INLINE go #-}
  {-# INLINE cheapEqExpr' #-}
  
  exprIsBig :: Expr b -> Bool
  -- ^ Returns @True@ of expressions that are too big to be compared by 'cheapEqExpr'
  exprIsBig (Lit _)      = False
  exprIsBig (Var _)      = False
  exprIsBig (Type _)     = False
  exprIsBig (Coercion _) = False
  exprIsBig (Lam _ e)    = exprIsBig e
  exprIsBig (App f a)    = exprIsBig f || exprIsBig a
  exprIsBig (Cast e _)   = exprIsBig e    -- Hopefully coercions are not too big!
  exprIsBig (Tick _ e)   = exprIsBig e
  exprIsBig _            = True
  
  eqExpr :: InScopeSet -> CoreExpr -> CoreExpr -> Bool
  -- Compares for equality, modulo alpha
  eqExpr in_scope e1 e2
    = go (mkRnEnv2 in_scope) e1 e2
    where
      go env (Var v1) (Var v2)
        | rnOccL env v1 == rnOccR env v2
        = True
  
      go _   (Lit lit1)    (Lit lit2)      = lit1 == lit2
      go env (Type t1)    (Type t2)        = eqTypeX env t1 t2
      go env (Coercion co1) (Coercion co2) = coreEqCoercion2 env co1 co2
      go env (Cast e1 co1) (Cast e2 co2) = coreEqCoercion2 env co1 co2 && go env e1 e2
      go env (App f1 a1)   (App f2 a2)   = go env f1 f2 && go env a1 a2
      go env (Tick n1 e1)  (Tick n2 e2)  = eqTickish env n1 n2 && go env e1 e2
  
      go env (Lam b1 e1)  (Lam b2 e2)
        =  eqTypeX env (varType b1) (varType b2)   -- False for Id/TyVar combination
        && go (rnBndr2 env b1 b2) e1 e2
  
      go env (Let (NonRec v1 r1) e1) (Let (NonRec v2 r2) e2)
        =  go env r1 r2  -- No need to check binder types, since RHSs match
        && go (rnBndr2 env v1 v2) e1 e2
  
      go env (Let (Rec ps1) e1) (Let (Rec ps2) e2)
        = length ps1 == length ps2
        && all2 (go env') rs1 rs2 && go env' e1 e2
        where
          (bs1,rs1) = unzip ps1
          (bs2,rs2) = unzip ps2
          env' = rnBndrs2 env bs1 bs2
  
      go env (Case e1 b1 t1 a1) (Case e2 b2 t2 a2)
        | null a1   -- See Note [Empty case alternatives] in TrieMap
        = null a2 && go env e1 e2 && eqTypeX env t1 t2
        | otherwise
        =  go env e1 e2 && all2 (go_alt (rnBndr2 env b1 b2)) a1 a2
  
      go _ _ _ = False
  
      -----------
      go_alt env (c1, bs1, e1) (c2, bs2, e2)
        = c1 == c2 && go (rnBndrs2 env bs1 bs2) e1 e2
  
  eqTickish :: RnEnv2 -> Tickish Id -> Tickish Id -> Bool
  eqTickish env (Breakpoint lid lids) (Breakpoint rid rids)
        = lid == rid  &&  map (rnOccL env) lids == map (rnOccR env) rids
  eqTickish _ l r = l == r
  
  -- | Finds differences between core expressions, modulo alpha and
  -- renaming. Setting @top@ means that the @IdInfo@ of bindings will be
  -- checked for differences as well.
  diffExpr :: Bool -> RnEnv2 -> CoreExpr -> CoreExpr -> [SDoc]
  diffExpr _   env (Var v1)   (Var v2)   | rnOccL env v1 == rnOccR env v2 = []
  diffExpr _   _   (Lit lit1) (Lit lit2) | lit1 == lit2                   = []
  diffExpr _   env (Type t1)  (Type t2)  | eqTypeX env t1 t2              = []
  diffExpr _   env (Coercion co1) (Coercion co2)
                                         | coreEqCoercion2 env co1 co2    = []
  diffExpr top env (Cast e1 co1)  (Cast e2 co2)
    | coreEqCoercion2 env co1 co2            = diffExpr top env e1 e2
  diffExpr top env (Tick n1 e1)   e2
    | not (tickishIsCode n1)                 = diffExpr top env e1 e2
  diffExpr top env e1             (Tick n2 e2)
    | not (tickishIsCode n2)                 = diffExpr top env e1 e2
  diffExpr top env (Tick n1 e1)   (Tick n2 e2)
    | eqTickish env n1 n2                    = diffExpr top env e1 e2
   -- The error message of failed pattern matches will contain
   -- generated names, which are allowed to differ.
  diffExpr _   _   (App (App (Var absent) _) _)
                   (App (App (Var absent2) _) _)
    | isBottomingId absent && isBottomingId absent2 = []
  diffExpr top env (App f1 a1)    (App f2 a2)
    = diffExpr top env f1 f2 ++ diffExpr top env a1 a2
  diffExpr top env (Lam b1 e1)  (Lam b2 e2)
    | eqTypeX env (varType b1) (varType b2)   -- False for Id/TyVar combination
    = diffExpr top (rnBndr2 env b1 b2) e1 e2
  diffExpr top env (Let bs1 e1) (Let bs2 e2)
    = let (ds, env') = diffBinds top env (flattenBinds [bs1]) (flattenBinds [bs2])
      in ds ++ diffExpr top env' e1 e2
  diffExpr top env (Case e1 b1 t1 a1) (Case e2 b2 t2 a2)
    | length a1 == length a2 && not (null a1) || eqTypeX env t1 t2
      -- See Note [Empty case alternatives] in TrieMap
    = diffExpr top env e1 e2 ++ concat (zipWith diffAlt a1 a2)
    where env' = rnBndr2 env b1 b2
          diffAlt (c1, bs1, e1) (c2, bs2, e2)
            | c1 /= c2  = [text "alt-cons " <> ppr c1 <> text " /= " <> ppr c2]
            | otherwise = diffExpr top (rnBndrs2 env' bs1 bs2) e1 e2
  diffExpr _  _ e1 e2
    = [fsep [ppr e1, text "/=", ppr e2]]
  
  -- | Finds differences between core bindings, see @diffExpr@.
  --
  -- The main problem here is that while we expect the binds to have the
  -- same order in both lists, this is not guaranteed. To do this
  -- properly we'd either have to do some sort of unification or check
  -- all possible mappings, which would be seriously expensive. So
  -- instead we simply match single bindings as far as we can. This
  -- leaves us just with mutually recursive and/or mismatching bindings,
  -- which we then specuatively match by ordering them. It's by no means
  -- perfect, but gets the job done well enough.
  diffBinds :: Bool -> RnEnv2 -> [(Var, CoreExpr)] -> [(Var, CoreExpr)]
            -> ([SDoc], RnEnv2)
  diffBinds top env binds1 = go (length binds1) env binds1
   where go _    env []     []
            = ([], env)
         go fuel env binds1 binds2
            -- No binds left to compare? Bail out early.
            | null binds1 || null binds2
            = (warn env binds1 binds2, env)
            -- Iterated over all binds without finding a match? Then
            -- try speculatively matching binders by order.
            | fuel == 0
            = if not $ env `inRnEnvL` fst (head binds1)
              then let env' = uncurry (rnBndrs2 env) $ unzip $
                              zip (sort $ map fst binds1) (sort $ map fst binds2)
                   in go (length binds1) env' binds1 binds2
              -- If we have already tried that, give up
              else (warn env binds1 binds2, env)
         go fuel env ((bndr1,expr1):binds1) binds2
            | let matchExpr (bndr,expr) =
                    (not top || null (diffIdInfo env bndr bndr1)) &&
                    null (diffExpr top (rnBndr2 env bndr1 bndr) expr1 expr)
            , (binds2l, (bndr2,_):binds2r) <- break matchExpr binds2
            = go (length binds1) (rnBndr2 env bndr1 bndr2)
                  binds1 (binds2l ++ binds2r)
            | otherwise -- No match, so push back (FIXME O(n^2))
            = go (fuel-1) env (binds1++[(bndr1,expr1)]) binds2
         go _ _ _ _ = panic "diffBinds: impossible" -- GHC isn't smart enough
  
         -- We have tried everything, but couldn't find a good match. So
         -- now we just return the comparison results when we pair up
         -- the binds in a pseudo-random order.
         warn env binds1 binds2 =
           concatMap (uncurry (diffBind env)) (zip binds1' binds2') ++
           unmatched "unmatched left-hand:" (drop l binds1') ++
           unmatched "unmatched right-hand:" (drop l binds2')
          where binds1' = sortBy (comparing fst) binds1
                binds2' = sortBy (comparing fst) binds2
                l = min (length binds1') (length binds2')
         unmatched _   [] = []
         unmatched txt bs = [text txt $$ ppr (Rec bs)]
         diffBind env (bndr1,expr1) (bndr2,expr2)
           | ds@(_:_) <- diffExpr top env expr1 expr2
           = locBind "in binding" bndr1 bndr2 ds
           | otherwise
           = diffIdInfo env bndr1 bndr2
  
  -- | Find differences in @IdInfo@. We will especially check whether
  -- the unfoldings match, if present (see @diffUnfold@).
  diffIdInfo :: RnEnv2 -> Var -> Var -> [SDoc]
  diffIdInfo env bndr1 bndr2
    | arityInfo info1 == arityInfo info2
      && cafInfo info1 == cafInfo info2
      && oneShotInfo info1 == oneShotInfo info2
      && inlinePragInfo info1 == inlinePragInfo info2
      && occInfo info1 == occInfo info2
      && demandInfo info1 == demandInfo info2
      && callArityInfo info1 == callArityInfo info2
    = locBind "in unfolding of" bndr1 bndr2 $
      diffUnfold env (unfoldingInfo info1) (unfoldingInfo info2)
    | otherwise
    = locBind "in Id info of" bndr1 bndr2
      [fsep [pprBndr LetBind bndr1, text "/=", pprBndr LetBind bndr2]]
    where info1 = idInfo bndr1; info2 = idInfo bndr2
  
  -- | Find differences in unfoldings. Note that we will not check for
  -- differences of @IdInfo@ in unfoldings, as this is generally
  -- redundant, and can lead to an exponential blow-up in complexity.
  diffUnfold :: RnEnv2 -> Unfolding -> Unfolding -> [SDoc]
  diffUnfold _   NoUnfolding    NoUnfolding                 = []
  diffUnfold _   (OtherCon cs1) (OtherCon cs2) | cs1 == cs2 = []
  diffUnfold env (DFunUnfolding bs1 c1 a1)
                 (DFunUnfolding bs2 c2 a2)
    | c1 == c2 && length bs1 == length bs2
    = concatMap (uncurry (diffExpr False env')) (zip a1 a2)
    where env' = rnBndrs2 env bs1 bs2
  diffUnfold env (CoreUnfolding t1 _ _ v1 cl1 wf1 x1 g1)
                 (CoreUnfolding t2 _ _ v2 cl2 wf2 x2 g2)
    | v1 == v2 && cl1 == cl2
      && wf1 == wf2 && x1 == x2 && g1 == g2
    = diffExpr False env t1 t2
  diffUnfold _   uf1 uf2
    = [fsep [ppr uf1, text "/=", ppr uf2]]
  
  -- | Add location information to diff messages
  locBind :: String -> Var -> Var -> [SDoc] -> [SDoc]
  locBind loc b1 b2 diffs = map addLoc diffs
    where addLoc d            = d $$ nest 2 (parens (text loc <+> bindLoc))
          bindLoc | b1 == b2  = ppr b1
                  | otherwise = ppr b1 <> char '/' <> ppr b2
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{The size of an expression}
  *                                                                      *
  ************************************************************************
  -}
  
  data CoreStats = CS { cs_tm :: Int    -- Terms
                      , cs_ty :: Int    -- Types
                      , cs_co :: Int }  -- Coercions
  
  
  instance Outputable CoreStats where
   ppr (CS { cs_tm = i1, cs_ty = i2, cs_co = i3 })
     = braces (sep [ptext (sLit "terms:")     <+> intWithCommas i1 <> comma,
                    ptext (sLit "types:")     <+> intWithCommas i2 <> comma,
                    ptext (sLit "coercions:") <+> intWithCommas i3])
  
  plusCS :: CoreStats -> CoreStats -> CoreStats
  plusCS (CS { cs_tm = p1, cs_ty = q1, cs_co = r1 })
         (CS { cs_tm = p2, cs_ty = q2, cs_co = r2 })
    = CS { cs_tm = p1+p2, cs_ty = q1+q2, cs_co = r1+r2 }
  
  zeroCS, oneTM :: CoreStats
  zeroCS = CS { cs_tm = 0, cs_ty = 0, cs_co = 0 }
  oneTM  = zeroCS { cs_tm = 1 }
  
  sumCS :: (a -> CoreStats) -> [a] -> CoreStats
  sumCS f = foldr (plusCS . f) zeroCS
  
  coreBindsStats :: [CoreBind] -> CoreStats
  coreBindsStats = sumCS bindStats
  
  bindStats :: CoreBind -> CoreStats
  bindStats (NonRec v r) = bindingStats v r
  bindStats (Rec prs)    = sumCS (\(v,r) -> bindingStats v r) prs
  
  bindingStats :: Var -> CoreExpr -> CoreStats
  bindingStats v r = bndrStats v `plusCS` exprStats r
  
  bndrStats :: Var -> CoreStats
  bndrStats v = oneTM `plusCS` tyStats (varType v)
  
  exprStats :: CoreExpr -> CoreStats
  exprStats (Var {})        = oneTM
  exprStats (Lit {})        = oneTM
  exprStats (Type t)        = tyStats t
  exprStats (Coercion c)    = coStats c
  exprStats (App f a)       = exprStats f `plusCS` exprStats a
  exprStats (Lam b e)       = bndrStats b `plusCS` exprStats e
  exprStats (Let b e)       = bindStats b `plusCS` exprStats e
  exprStats (Case e b _ as) = exprStats e `plusCS` bndrStats b `plusCS` sumCS altStats as
  exprStats (Cast e co)     = coStats co `plusCS` exprStats e
  exprStats (Tick _ e)      = exprStats e
  
  altStats :: CoreAlt -> CoreStats
  altStats (_, bs, r) = altBndrStats bs `plusCS` exprStats r
  
  altBndrStats :: [Var] -> CoreStats
  -- Charge one for the alternative, not for each binder
  altBndrStats vs = oneTM `plusCS` sumCS (tyStats . varType) vs
  
  tyStats :: Type -> CoreStats
  tyStats ty = zeroCS { cs_ty = typeSize ty }
  
  coStats :: Coercion -> CoreStats
  coStats co = zeroCS { cs_co = coercionSize co }
  
  coreBindsSize :: [CoreBind] -> Int
  -- We use coreBindStats for user printout
  -- but this one is a quick and dirty basis for
  -- the simplifier's tick limit
  coreBindsSize bs = foldr ((+) . bindSize) 0 bs
  
  exprSize :: CoreExpr -> Int
  -- ^ A measure of the size of the expressions, strictly greater than 0
  -- It also forces the expression pretty drastically as a side effect
  -- Counts *leaves*, not internal nodes. Types and coercions are not counted.
  exprSize (Var v)         = v `seq` 1
  exprSize (Lit lit)       = lit `seq` 1
  exprSize (App f a)       = exprSize f + exprSize a
  exprSize (Lam b e)       = bndrSize b + exprSize e
  exprSize (Let b e)       = bindSize b + exprSize e
  exprSize (Case e b t as) = seqType t `seq` exprSize e + bndrSize b + 1 + foldr ((+) . altSize) 0 as
  exprSize (Cast e co)     = (seqCo co `seq` 1) + exprSize e
  exprSize (Tick n e)      = tickSize n + exprSize e
  exprSize (Type t)        = seqType t `seq` 1
  exprSize (Coercion co)   = seqCo co `seq` 1
  
  tickSize :: Tickish Id -> Int
  tickSize (ProfNote cc _ _) = cc `seq` 1
  tickSize _ = 1 -- the rest are strict
  
  bndrSize :: Var -> Int
  bndrSize b | isTyVar b = seqType (tyVarKind b) `seq` 1
             | otherwise = seqType (idType b)             `seq`
                           megaSeqIdInfo (idInfo b)       `seq`
                           1
  
  bndrsSize :: [Var] -> Int
  bndrsSize = sum . map bndrSize
  
  bindSize :: CoreBind -> Int
  bindSize (NonRec b e) = bndrSize b + exprSize e
  bindSize (Rec prs)    = foldr ((+) . pairSize) 0 prs
  
  pairSize :: (Var, CoreExpr) -> Int
  pairSize (b,e) = bndrSize b + exprSize e
  
  altSize :: CoreAlt -> Int
  altSize (c,bs,e) = c `seq` bndrsSize bs + exprSize e
  
  {-
  ************************************************************************
  *                                                                      *
                  Eta reduction
  *                                                                      *
  ************************************************************************
  
  Note [Eta reduction conditions]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  We try for eta reduction here, but *only* if we get all the way to an
  trivial expression.  We don't want to remove extra lambdas unless we
  are going to avoid allocating this thing altogether.
  
  There are some particularly delicate points here:
  
  * We want to eta-reduce if doing so leaves a trivial expression,
    *including* a cast.  For example
         \x. f |> co  -->  f |> co
    (provided co doesn't mention x)
  
  * Eta reduction is not valid in general:
          \x. bot  /=  bot
    This matters, partly for old-fashioned correctness reasons but,
    worse, getting it wrong can yield a seg fault. Consider
          f = \x.f x
          h y = case (case y of { True -> f `seq` True; False -> False }) of
                  True -> ...; False -> ...
  
    If we (unsoundly) eta-reduce f to get f=f, the strictness analyser
    says f=bottom, and replaces the (f `seq` True) with just
    (f `cast` unsafe-co).  BUT, as thing stand, 'f' got arity 1, and it
    *keeps* arity 1 (perhaps also wrongly).  So CorePrep eta-expands
    the definition again, so that it does not termninate after all.
    Result: seg-fault because the boolean case actually gets a function value.
    See Trac #1947.
  
    So it's important to do the right thing.
  
  * Note [Arity care]: we need to be careful if we just look at f's
    arity. Currently (Dec07), f's arity is visible in its own RHS (see
    Note [Arity robustness] in SimplEnv) so we must *not* trust the
    arity when checking that 'f' is a value.  Otherwise we will
    eta-reduce
        f = \x. f x
    to
        f = f
    Which might change a terminating program (think (f `seq` e)) to a
    non-terminating one.  So we check for being a loop breaker first.
  
    However for GlobalIds we can look at the arity; and for primops we
    must, since they have no unfolding.
  
  * Regardless of whether 'f' is a value, we always want to
    reduce (/\a -> f a) to f
    This came up in a RULE: foldr (build (/\a -> g a))
    did not match           foldr (build (/\b -> ...something complex...))
    The type checker can insert these eta-expanded versions,
    with both type and dictionary lambdas; hence the slightly
    ad-hoc isDictId
  
  * Never *reduce* arity. For example
        f = \xy. g x y
    Then if h has arity 1 we don't want to eta-reduce because then
    f's arity would decrease, and that is bad
  
  These delicacies are why we don't use exprIsTrivial and exprIsHNF here.
  Alas.
  
  Note [Eta reduction with casted arguments]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Consider
      (\(x:t3). f (x |> g)) :: t3 -> t2
    where
      f :: t1 -> t2
      g :: t3 ~ t1
  This should be eta-reduced to
  
      f |> (sym g -> t2)
  
  So we need to accumulate a coercion, pushing it inward (past
  variable arguments only) thus:
     f (x |> co_arg) |> co  -->  (f |> (sym co_arg -> co)) x
     f (x:t)         |> co  -->  (f |> (t -> co)) x
     f @ a           |> co  -->  (f |> (forall a.co)) @ a
     f @ (g:t1~t2)   |> co  -->  (f |> (t1~t2 => co)) @ (g:t1~t2)
  These are the equations for ok_arg.
  
  It's true that we could also hope to eta reduce these:
      (\xy. (f x |> g) y)
      (\xy. (f x y) |> g)
  But the simplifier pushes those casts outwards, so we don't
  need to address that here.
  -}
  
  tryEtaReduce :: [Var] -> CoreExpr -> Maybe CoreExpr
  tryEtaReduce bndrs body
    = go (reverse bndrs) body (mkReflCo Representational (exprType body))
    where
      incoming_arity = count isId bndrs
  
      go :: [Var]            -- Binders, innermost first, types [a3,a2,a1]
         -> CoreExpr         -- Of type tr
         -> Coercion         -- Of type tr ~ ts
         -> Maybe CoreExpr   -- Of type a1 -> a2 -> a3 -> ts
      -- See Note [Eta reduction with casted arguments]
      -- for why we have an accumulating coercion
      go [] fun co
        | ok_fun fun
        , let used_vars = exprFreeVars fun `unionVarSet` tyCoVarsOfCo co
        , not (any (`elemVarSet` used_vars) bndrs)
        = Just (mkCast fun co)   -- Check for any of the binders free in the result
                                 -- including the accumulated coercion
  
      go bs (Tick t e) co
        | tickishFloatable t
        = fmap (Tick t) $ go bs e co
        -- Float app ticks: \x -> Tick t (e x) ==> Tick t e
  
      go (b : bs) (App fun arg) co
        | Just (co', ticks) <- ok_arg b arg co
        = fmap (flip (foldr mkTick) ticks) $ go bs fun co'
              -- Float arg ticks: \x -> e (Tick t x) ==> Tick t e
  
      go _ _ _  = Nothing         -- Failure!
  
      ---------------
      -- Note [Eta reduction conditions]
      ok_fun (App fun (Type {})) = ok_fun fun
      ok_fun (Cast fun _)        = ok_fun fun
      ok_fun (Tick _ expr)       = ok_fun expr
      ok_fun (Var fun_id)        = ok_fun_id fun_id || all ok_lam bndrs
      ok_fun _fun                = False
  
      ---------------
      ok_fun_id fun = fun_arity fun >= incoming_arity
  
      ---------------
      fun_arity fun             -- See Note [Arity care]
         | isLocalId fun
         , isStrongLoopBreaker (idOccInfo fun) = 0
         | arity > 0                           = arity
         | isEvaldUnfolding (idUnfolding fun)  = 1
              -- See Note [Eta reduction of an eval'd function]
         | otherwise                           = 0
         where
           arity = idArity fun
  
      ---------------
      ok_lam v = isTyVar v || isEvVar v
  
      ---------------
      ok_arg :: Var              -- Of type bndr_t
             -> CoreExpr         -- Of type arg_t
             -> Coercion         -- Of kind (t1~t2)
             -> Maybe (Coercion  -- Of type (arg_t -> t1 ~  bndr_t -> t2)
                                 --   (and similarly for tyvars, coercion args)
                      , [Tickish Var])
      -- See Note [Eta reduction with casted arguments]
      ok_arg bndr (Type ty) co
         | Just tv <- getTyVar_maybe ty
         , bndr == tv  = Just (mkForAllCo tv co, [])
      ok_arg bndr (Var v) co
         | bndr == v   = let reflCo = mkReflCo Representational (idType bndr)
                         in Just (mkFunCo Representational reflCo co, [])
      ok_arg bndr (Cast e co_arg) co
         | (ticks, Var v) <- stripTicksTop tickishFloatable e
         , bndr == v
         = Just (mkFunCo Representational (mkSymCo co_arg) co, ticks)
         -- The simplifier combines multiple casts into one,
         -- so we can have a simple-minded pattern match here
      ok_arg bndr (Tick t arg) co
         | tickishFloatable t, Just (co', ticks) <- ok_arg bndr arg co
         = Just (co', t:ticks)
  
      ok_arg _ _ _ = Nothing
  
  {-
  Note [Eta reduction of an eval'd function]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  In Haskell is is not true that    f = \x. f x
  because f might be bottom, and 'seq' can distinguish them.
  
  But it *is* true that   f = f `seq` \x. f x
  and we'd like to simplify the latter to the former.  This amounts
  to the rule that
    * when there is just *one* value argument,
    * f is not bottom
  we can eta-reduce    \x. f x  ===>  f
  
  This turned up in Trac #7542.
  
  
  ************************************************************************
  *                                                                      *
  \subsection{Determining non-updatable right-hand-sides}
  *                                                                      *
  ************************************************************************
  
  Top-level constructor applications can usually be allocated
  statically, but they can't if the constructor, or any of the
  arguments, come from another DLL (because we can't refer to static
  labels in other DLLs).
  
  If this happens we simply make the RHS into an updatable thunk,
  and 'execute' it rather than allocating it statically.
  -}
  
  -- | This function is called only on *top-level* right-hand sides.
  -- Returns @True@ if the RHS can be allocated statically in the output,
  -- with no thunks involved at all.
  rhsIsStatic :: Platform
              -> (Name -> Bool)         -- Which names are dynamic
              -> (Integer -> CoreExpr)  -- Desugaring for integer literals (disgusting)
                                        -- C.f. Note [Disgusting computation of CafRefs]
                                        --      in TidyPgm
              -> CoreExpr -> Bool
  -- It's called (i) in TidyPgm.hasCafRefs to decide if the rhs is, or
  -- refers to, CAFs; (ii) in CoreToStg to decide whether to put an
  -- update flag on it and (iii) in DsExpr to decide how to expand
  -- list literals
  --
  -- The basic idea is that rhsIsStatic returns True only if the RHS is
  --      (a) a value lambda
  --      (b) a saturated constructor application with static args
  --
  -- BUT watch out for
  --  (i) Any cross-DLL references kill static-ness completely
  --      because they must be 'executed' not statically allocated
  --      ("DLL" here really only refers to Windows DLLs, on other platforms,
  --      this is not necessary)
  --
  -- (ii) We treat partial applications as redexes, because in fact we
  --      make a thunk for them that runs and builds a PAP
  --      at run-time.  The only appliations that are treated as
  --      static are *saturated* applications of constructors.
  
  -- We used to try to be clever with nested structures like this:
  --              ys = (:) w ((:) w [])
  -- on the grounds that CorePrep will flatten ANF-ise it later.
  -- But supporting this special case made the function much more
  -- complicated, because the special case only applies if there are no
  -- enclosing type lambdas:
  --              ys = /\ a -> Foo (Baz ([] a))
  -- Here the nested (Baz []) won't float out to top level in CorePrep.
  --
  -- But in fact, even without -O, nested structures at top level are
  -- flattened by the simplifier, so we don't need to be super-clever here.
  --
  -- Examples
  --
  --      f = \x::Int. x+7        TRUE
  --      p = (True,False)        TRUE
  --
  --      d = (fst p, False)      FALSE because there's a redex inside
  --                              (this particular one doesn't happen but...)
  --
  --      h = D# (1.0## /## 2.0##)        FALSE (redex again)
  --      n = /\a. Nil a                  TRUE
  --
  --      t = /\a. (:) (case w a of ...) (Nil a)  FALSE (redex)
  --
  --
  -- This is a bit like CoreUtils.exprIsHNF, with the following differences:
  --    a) scc "foo" (\x -> ...) is updatable (so we catch the right SCC)
  --
  --    b) (C x xs), where C is a contructor is updatable if the application is
  --         dynamic
  --
  --    c) don't look through unfolding of f in (f x).
  
  rhsIsStatic _ is_dynamic_name cvt_integer rhs = is_static False rhs
    where
    is_static :: Bool     -- True <=> in a constructor argument; must be atomic
              -> CoreExpr -> Bool
  
    is_static False  (Lam b e)              = isRuntimeVar b || is_static False e
    is_static in_arg (Tick n e)             = not (tickishIsCode n)
                                                && is_static in_arg e
    is_static in_arg (Cast e _)             = is_static in_arg e
    is_static _      (Coercion {})          = True   -- Behaves just like a literal
    is_static in_arg (Lit (LitInteger i _)) = is_static in_arg (cvt_integer i)
    is_static _      (Lit (MachLabel {}))   = False
    is_static _      (Lit _)                = True
          -- A MachLabel (foreign import "&foo") in an argument
          -- prevents a constructor application from being static.  The
          -- reason is that it might give rise to unresolvable symbols
          -- in the object file: under Linux, references to "weak"
          -- symbols from the data segment give rise to "unresolvable
          -- relocation" errors at link time This might be due to a bug
          -- in the linker, but we'll work around it here anyway.
          -- SDM 24/2/2004
  
    is_static in_arg other_expr = go other_expr 0
     where
      go (Var f) n_val_args
          | -- (platformOS platform /= OSMinGW32) ||
            -- WARNING: Commenting the above line
            --          may cause some issues.
            not (is_dynamic_name (idName f))
          =  saturated_data_con f n_val_args
          || (in_arg && n_val_args == 0)
                  -- A naked un-applied variable is *not* deemed a static RHS
                  -- E.g.         f = g
                  -- Reason: better to update so that the indirection gets shorted
                  --         out, and the true value will be seen
                  -- NB: if you change this, you'll break the invariant that THUNK_STATICs
                  --     are always updatable.  If you do so, make sure that non-updatable
                  --     ones have enough space for their static link field!
  
      go (App f a) n_val_args
          | isTypeArg a                    = go f n_val_args
          | not in_arg && is_static True a = go f (n_val_args + 1)
          -- The (not in_arg) checks that we aren't in a constructor argument;
          -- if we are, we don't allow (value) applications of any sort
          --
          -- NB. In case you wonder, args are sometimes not atomic.  eg.
          --   x = D# (1.0## /## 2.0##)
          -- can't float because /## can fail.
  
      go (Tick n f) n_val_args = not (tickishIsCode n) && go f n_val_args
      go (Cast e _) n_val_args = go e n_val_args
      go _          _          = False
  
      saturated_data_con f n_val_args
          = case isDataConWorkId_maybe f of
              Just dc -> n_val_args == dataConRepArity dc
              Nothing -> False
  