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 _ _)       = False  -- See Note [Tick trivial]
exprIsTrivial (Cast e _)       = exprIsTrivial e
exprIsTrivial (Lam b body)     = not (isRuntimeVar b) && exprIsTrivial body
exprIsTrivial _                = False

getIdFromTrivialExpr :: CoreExpr -> Id
getIdFromTrivialExpr e = go e
  where go (Var v) = v
        go (App f t) | not (isRuntimeArg t) = go f
        go (Cast e _) = go e
        go (Lam b e) | not (isRuntimeVar b) = go e
        go e = pprPanic "getIdFromTrivialExpr" (ppr e)

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 :: 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.

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

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 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 _ _ = 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

-----------------------------
-- | '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:
--
--  * The expression guarantees to terminate,
--  * soon,
--  * without raising an exception,
--  * without causing a side effect (e.g. writing a mutable variable)
--
-- Note that if @exprIsHNF e@, then @exprOkForSpecuation e@.
-- 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
        (Var f, args) -> 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 [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.
-}

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

    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 = zipWith3 mk_id_var id_uniqs id_fss arg_tys
    mk_id_var uniq fs ty = mkUserLocal (mkVarOccFS fs) uniq 
                                       (Type.substTy full_subst ty) noSrcSpan

-- | 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 (Var v1)   (Var v2)   = v1==v2
cheapEqExpr (Lit lit1) (Lit lit2) = lit1 == lit2
cheapEqExpr (Type t1) (Type t2) = t1 `eqType` t2
cheapEqExpr (Coercion c1) (Coercion c2) = c1 `coreEqCoercion` c2

cheapEqExpr (App f1 a1) (App f2 a2)
  = f1 `cheapEqExpr` f2 && a1 `cheapEqExpr` a2

cheapEqExpr (Cast e1 t1) (Cast e2 t2)
  = e1 `cheapEqExpr` e2 && t1 `coreEqCoercion` t2

cheapEqExpr _ _ = False

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 _            = 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)  = go_tickish 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)
      = 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

    -----------
    go_tickish env (Breakpoint lid lids) (Breakpoint rid rids)
      = lid == rid  &&  map (rnOccL env) lids == map (rnOccR env) rids
    go_tickish _ l r = l == r

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

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 (b : bs) (App fun arg) co
      | Just co' <- ok_arg b arg co
      = go bs fun co'

    go _ _ _  = Nothing         -- Failure!

    ---------------
    -- Note [Eta reduction conditions]
    ok_fun (App fun (Type {})) = ok_fun fun
    ok_fun (Cast fun _)        = ok_fun fun
    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)
    -- 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   = Just (mkFunCo Representational
                                     (mkReflCo Representational (idType bndr)) co)
    ok_arg bndr (Cast (Var v) co_arg) co
       | bndr == v  = Just (mkFunCo Representational (mkSymCo co_arg) co)
       -- The simplifier combines multiple casts into one,
       -- so we can have a simple-minded pattern match here
    ok_arg _ _ _ = Nothing

-- | 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) -> 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 platform is_dynamic_name 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 _      (Lit (LitInteger {})) = False
  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) ||
          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