{-# OPTIONS -fno-warn-incomplete-patterns #-}
-- The above warning supression flag is a temporary kludge.
-- While working on this module you are encouraged to remove it and fix
-- any warnings in the module. See
--     http://hackage.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#Warnings
-- for details

-- | Commonly useful utilites for manipulating the Core language
module CoreUtils (
	-- * Constructing expressions
	mkSCC, mkCoerce,
	bindNonRec, needsCaseBinding,
	mkAltExpr, mkPiType, mkPiTypes,

	-- * Taking expressions apart
	findDefault, findAlt, isDefaultAlt, mergeAlts, trimConArgs,

	-- * Properties of expressions
	exprType, coreAltType, coreAltsType,
	exprIsDupable, exprIsTrivial, exprIsBottom,
        exprIsCheap, exprIsExpandable, exprIsCheap', CheapAppFun,
	exprIsHNF, exprOkForSpeculation, exprIsBig, exprIsConLike,
	rhsIsStatic, isCheapApp, isExpandableApp,

	-- * Expression and bindings size
	coreBindsSize, exprSize,
        CoreStats(..), coreBindsStats, 

	-- * Hashing
	hashExpr,

	-- * Equality
	cheapEqExpr, eqExpr, eqExprX,

	-- * Eta reduction
	tryEtaReduce,

	-- * Manipulating data constructors and types
	applyTypeToArgs, applyTypeToArg,
        dataConRepInstPat, dataConRepFSInstPat
    ) where

#include "HsVersions.h"

import CoreSyn
import PprCore
import Var
import SrcLoc
import VarEnv
import VarSet
import Name
import Literal
import DataCon
import PrimOp
import Id
import IdInfo
import Type
import Coercion
import TyCon
import CostCentre
import Unique
import Outputable
import TysPrim
import FastString
import Maybes
import Util
import Pair
import Data.Word
import Data.Bits

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 _ body)	     = exprType body
exprType (Case _ _ ty _)     = ty
exprType (Cast _ co)         = pSnd (coercionKind co)
exprType (Note _ 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"

mkPiType  :: Var -> Type -> Type
-- ^ Makes a @(->)@ type or a forall type, depending
-- on whether it is given a type variable or a term variable.
mkPiTypes :: [Var] -> Type -> Type
-- ^ 'mkPiType' for multiple type or value arguments

mkPiType v ty
   | isId v    = mkFunTy (idType v) ty
   | otherwise = mkForAllTy v ty

mkPiTypes vs ty = foldr mkPiType ty vs

applyTypeToArg :: Type -> CoreExpr -> Type
-- ^ Determines the type resulting from applying an expression to a function with the given type
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 _ op_ty [] = op_ty

applyTypeToArgs e op_ty (Type ty : args)
  =	-- Accumulate type arguments so we can instantiate all at once
    go [ty] args
  where
    go rev_tys (Type ty : args) = go (ty:rev_tys) args
    go rev_tys rest_args         = applyTypeToArgs e op_ty' rest_args
	                         where
			 	   op_ty' = applyTysD msg op_ty (reverse rev_tys)
				   msg = ptext (sLit "applyTypeToArgs") <+> 
		    		 	 panic_msg e op_ty

applyTypeToArgs e op_ty (_ : args)
  = case (splitFunTy_maybe op_ty) of
	Just (_, res_ty) -> applyTypeToArgs e res_ty args
	Nothing -> pprPanic "applyTypeToArgs" (panic_msg e op_ty)

panic_msg :: CoreExpr -> Type -> SDoc
panic_msg e op_ty = pprCoreExpr e $$ ppr op_ty

-- | Wrap the given expression in the coercion safely, dropping
-- identity coercions and coalescing nested coercions
mkCoerce :: Coercion -> CoreExpr -> CoreExpr
mkCoerce co e | isReflCo co = e
mkCoerce co (Cast expr co2)
  = ASSERT(let { Pair  from_ty  _to_ty  = coercionKind co; 
                 Pair _from_ty2  to_ty2 = coercionKind co2} in
           from_ty `eqType` to_ty2 )
    mkCoerce (mkTransCo co2 co) expr

mkCoerce co expr 
  = 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 $$ pprEqPred (coercionKind co))
         (Cast expr co)

-- | Wraps the given expression in the cost centre unless
-- in a way that maximises their utility to the user
mkSCC :: CostCentre -> Expr b -> Expr b
	-- Note: Nested SCC's *are* preserved for the benefit of
	--       cost centre stack profiling
mkSCC _  (Lit lit)          = Lit lit
mkSCC cc (Lam x e)  	    = Lam x (mkSCC cc e)  -- Move _scc_ inside lambda
mkSCC cc (Note (SCC cc') e) = Note (SCC cc) (Note (SCC cc') e)
mkSCC cc (Note n e) 	    = Note n (mkSCC cc e) -- Move _scc_ inside notes
mkSCC cc (Cast e co)        = Cast (mkSCC cc e) co -- Move _scc_ inside cast
mkSCC cc expr	    	    = Note (SCC cc) expr

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"

-- | Extract the default case alternative
findDefault :: [CoreAlt] -> ([CoreAlt], Maybe CoreExpr)
findDefault ((DEFAULT,args,rhs) : alts) = ASSERT( null args ) (alts, Just rhs)
findDefault alts			= 		      (alts, Nothing)

isDefaultAlt :: CoreAlt -> Bool
isDefaultAlt (DEFAULT, _, _) = True
isDefaultAlt _               = False


-- | Find the case alternative corresponding to a particular 
-- constructor: panics if no such constructor exists
findAlt :: AltCon -> [CoreAlt] -> Maybe CoreAlt
    -- 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 :: [CoreAlt] -> [CoreAlt] -> [CoreAlt]
-- ^ 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

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

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 (Note _ e) 		 = go n e     
    go n (Cast e _) 		 = go n e
    go n (Let _ e)  		 = go n e
    go _ _          		 = False

exprIsDupable :: CoreExpr -> Bool
exprIsDupable 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 (Note _ 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 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 :: CoreExpr -> Bool
exprIsCheap = exprIsCheap' isCheapApp

exprIsExpandable :: CoreExpr -> Bool
exprIsExpandable = exprIsCheap' isExpandableApp	-- See Note [CONLIKE pragma] in BasicTypes

type CheapAppFun = Id -> Int -> Bool
exprIsCheap' :: CheapAppFun -> CoreExpr -> Bool
exprIsCheap' _        (Lit _)      = True
exprIsCheap' _        (Type _)    = True
exprIsCheap' _        (Coercion _) = True
exprIsCheap' _        (Var _)      = True
exprIsCheap' good_app (Note _ e)   = exprIsCheap' good_app e
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 (Let (NonRec x _) e)  
  | isUnLiftedType (idType x) = exprIsCheap' good_app e
  | otherwise		      = False
	-- Strict lets always have cheap right hand sides,
	-- and do no allocation, so just look at the body
	-- Non-strict lets do allocation so we don't treat them as cheap
	-- See also 

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
    go (Var f) args
        = case idDetails f of
		RecSelId {}  	    	     -> go_sel args
		ClassOpId {} 	    	     -> go_sel args
		PrimOpId op  	    	     -> go_primop op args
		_ | good_app f (length args) -> go_pap 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)

isCheapApp :: CheapAppFun
isCheapApp fn n_val_args
  = isDataConWorkId fn 
  || 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]
     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 :: Expr b -> Bool
  -- Polymorphic in binder type
  -- There is one call at a non-Id binder type, in SetLevels
exprOkForSpeculation (Lit _)      = True
exprOkForSpeculation (Type _)     = True
exprOkForSpeculation (Coercion _) = True

exprOkForSpeculation (Var v)     
  | isTickBoxOp v = False     -- Tick boxes are *not* suitable for speculation
  | otherwise     =  isUnLiftedType (idType v)	-- c.f. the Var case of exprIsHNF
    		  || isDataConWorkId v	    	-- Nullary constructors
    		  || idArity v > 0   		-- Functions
    		  || isEvaldUnfolding (idUnfolding v)	-- Let-bound values

exprOkForSpeculation (Note _ e)  = exprOkForSpeculation e
exprOkForSpeculation (Cast e _)  = exprOkForSpeculation e

exprOkForSpeculation (Case e _ _ alts) 
  =  exprOkForSpeculation e  -- Note [exprOkForSpeculation: case expressions]
  && all (\(_,_,rhs) -> exprOkForSpeculation rhs) alts
  && altsAreExhaustive alts     -- Note [exprOkForSpeculation: exhaustive alts]

exprOkForSpeculation other_expr
  = case collectArgs other_expr of
	(Var f, args) -> spec_ok (idDetails f) args
        _             -> False
 
  where
    spec_ok (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

    spec_ok (PrimOpId op) args
      | isDivOp op,		-- Special case for dividing operations that fail
	[arg1, Lit lit] <- args	-- only if the divisor is zero
      = not (isZeroLit lit) && exprOkForSpeculation 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
      = primOpOkForSpeculation op && 
	all exprOkForSpeculation args
				-- A bit conservative: we don't really need
				-- to care about lazy arguments, but this is easy

    spec_ok (DFunId new_type) _ = not new_type
         -- DFuns terminate, unless the dict is implemented with a newtype
	 -- in which case they may not

    spec_ok _ _ = False

altsAreExhaustive :: [Alt b] -> Bool
-- True  <=> the case alterantives 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 (Note _ e)       = is_hnf_like e
    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 (Note _ 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

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 
  = (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 existential type variables
    ex_bndrs = zipWith3 mk_ex_var ex_uniqs ex_fss ex_tvs
    mk_ex_var uniq fs var = mkTyVar new_name kind
      where
        new_name = mkSysTvName uniq fs
        kind     = tyVarKind var

      -- Make the instantiating substitution
    subst = zipOpenTvSubst (univ_tvs ++ ex_tvs) (inst_tys ++ map mkTyVarTy ex_bndrs)

      -- Make value vars, instantiating types
    mk_id_var uniq fs ty = mkUserLocal (mkVarOccFS fs) uniq (Type.substTy subst ty) noSrcSpan
    arg_ids = zipWith3 mk_id_var id_uniqs id_fss arg_tys

-- | 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
  = eqExprX id_unf (mkRnEnv2 in_scope) e1 e2
  where
    id_unf _ = noUnfolding	-- Don't expand

eqExprX :: IdUnfoldingFun -> RnEnv2 -> CoreExpr -> CoreExpr -> Bool
-- ^ Compares expressions for equality, modulo alpha.
-- Does /not/ look through newtypes or predicate types
-- Used in rule matching, and also CSE

eqExprX id_unfolding_fun env e1 e2
  = go env e1 e2
  where
    go env (Var v1) (Var v2)
      | rnOccL env v1 == rnOccR env v2
      = True

    -- The next two rules expand non-local variables
    -- C.f. Note [Expanding variables] in Rules.lhs
    -- and  Note [Do not expand locally-bound variables] in Rules.lhs
    go env (Var v1) e2
      | not (locallyBoundL env v1)
      , Just e1' <- expandUnfolding_maybe (id_unfolding_fun (lookupRnInScope env v1))
      = go (nukeRnEnvL env) e1' e2

    go env e1 (Var v2)
      | not (locallyBoundR env v2)
      , Just e2' <- expandUnfolding_maybe (id_unfolding_fun (lookupRnInScope env v2))
      = go (nukeRnEnvR env) e1 e2'

    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 (Note n1 e1)  (Note n2 e2)  = go_note 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 _ a1) (Case e2 b2 _ a2)
      =  go env e1 e2
      && eqTypeX env (idType b1) (idType b2)
      && 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_note (SCC cc1)     (SCC cc2)      = cc1 == cc2
    go_note (CoreNote s1) (CoreNote s2)  = s1 == s2
    go_note _             _              = False

locallyBoundL, locallyBoundR :: RnEnv2 -> Var -> Bool
locallyBoundL rn_env v = inRnEnvL rn_env v
locallyBoundR rn_env v = inRnEnvR rn_env v

coreBindsSize :: [CoreBind] -> Int
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)       = varSize b + exprSize e
exprSize (Let b e)       = bindSize b + exprSize e
exprSize (Case e b t as) = seqType t `seq` exprSize e + varSize b + 1 + foldr ((+) . altSize) 0 as
exprSize (Cast e co)     = (seqCo co `seq` 1) + exprSize e
exprSize (Note n e)      = noteSize n + exprSize e
exprSize (Type t)       = seqType t `seq` 1
exprSize (Coercion co)   = seqCo co `seq` 1

noteSize :: Note -> Int
noteSize (SCC cc)       = cc `seq` 1
noteSize (CoreNote s)   = s `seq` 1  -- hdaume: core annotations
 
varSize :: Var -> Int
varSize b  | isTyVar b = 1
	   | otherwise = seqType (idType b)		`seq`
			 megaSeqIdInfo (idInfo b) 	`seq`
			 1

varsSize :: [Var] -> Int
varsSize = sum . map varSize

bindSize :: CoreBind -> Int
bindSize (NonRec b e) = varSize b + exprSize e
bindSize (Rec prs)    = foldr ((+) . pairSize) 0 prs

pairSize :: (Var, CoreExpr) -> Int
pairSize (b,e) = varSize b + exprSize e

altSize :: CoreAlt -> Int
altSize (c,bs,e) = c `seq` varsSize bs + exprSize e

data CoreStats = CS { cs_tm, cs_ty, cs_co :: Int }

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 (Note _ e)      = exprStats e

altStats :: CoreAlt -> CoreStats
altStats (_, bs, r) = sumCS bndrStats bs `plusCS` exprStats r

tyStats :: Type -> CoreStats
tyStats ty = zeroCS { cs_ty = typeSize ty }

coStats :: Coercion -> CoreStats
coStats co = zeroCS { cs_co = coercionSize co }

hashExpr :: CoreExpr -> Int
-- ^ Two expressions that hash to the same @Int@ may be equal (but may not be)
-- Two expressions that hash to the different Ints are definitely unequal.
--
-- The emphasis is on a crude, fast hash, rather than on high precision.
-- 
-- But unequal here means \"not identical\"; two alpha-equivalent 
-- expressions may hash to the different Ints.
--
-- We must be careful that @\\x.x@ and @\\y.y@ map to the same hash code,
-- (at least if we want the above invariant to be true).

hashExpr e = fromIntegral (hash_expr (1,emptyVarEnv) e .&. 0x7fffffff)
             -- UniqFM doesn't like negative Ints

type HashEnv = (Int, VarEnv Int)  -- Hash code for bound variables

hash_expr :: HashEnv -> CoreExpr -> Word32
-- Word32, because we're expecting overflows here, and overflowing
-- signed types just isn't cool.  In C it's even undefined.
hash_expr env (Note _ e)   	      = hash_expr env e
hash_expr env (Cast e _)              = hash_expr env e
hash_expr env (Var v)     	      = hashVar env v
hash_expr _   (Lit lit)               = fromIntegral (hashLiteral lit)
hash_expr env (App f e)   	      = hash_expr env f * fast_hash_expr env e
hash_expr env (Let (NonRec b r) e)    = hash_expr (extend_env env b) e * fast_hash_expr env r
hash_expr env (Let (Rec ((b,_):_)) e) = hash_expr (extend_env env b) e
hash_expr env (Case e _ _ _)	      = hash_expr env e
hash_expr env (Lam b e)	              = hash_expr (extend_env env b) e
hash_expr _   (Type _)                = WARN(True, text "hash_expr: type") 1
-- Shouldn't happen.  Better to use WARN than trace, because trace
-- prevents the CPR optimisation kicking in for hash_expr.
hash_expr _   (Coercion _)            = WARN(True, text "hash_expr: coercion") 1

fast_hash_expr :: HashEnv -> CoreExpr -> Word32
fast_hash_expr env (Var v)     	 = hashVar env v
fast_hash_expr env (Type t)	 = fast_hash_type env t
fast_hash_expr env (Coercion co) = fast_hash_co env co
fast_hash_expr _   (Lit lit)     = fromIntegral (hashLiteral lit)
fast_hash_expr env (Cast e _)    = fast_hash_expr env e
fast_hash_expr env (Note _ e)    = fast_hash_expr env e
fast_hash_expr env (App _ a)     = fast_hash_expr env a	-- A bit idiosyncratic ('a' not 'f')!
fast_hash_expr _   _             = 1

fast_hash_type :: HashEnv -> Type -> Word32
fast_hash_type env ty 
  | Just tv <- getTyVar_maybe ty            = hashVar env tv
  | Just (tc,tys) <- splitTyConApp_maybe ty = let hash_tc = fromIntegral (hashName (tyConName tc))
					      in foldr (\t n -> fast_hash_type env t + n) hash_tc tys
  | otherwise				    = 1

fast_hash_co :: HashEnv -> Coercion -> Word32
fast_hash_co env co
  | Just cv <- getCoVar_maybe co              = hashVar env cv
  | Just (tc,cos) <- splitTyConAppCo_maybe co = let hash_tc = fromIntegral (hashName (tyConName tc))
                                                in foldr (\c n -> fast_hash_co env c + n) hash_tc cos
  | otherwise                                 = 1

extend_env :: HashEnv -> Var -> (Int, VarEnv Int)
extend_env (n,env) b = (n+1, extendVarEnv env b n)

hashVar :: HashEnv -> Var -> Word32
hashVar (_,env) v
 = fromIntegral (lookupVarEnv env v `orElse` hashName (idName v))

tryEtaReduce :: [Var] -> CoreExpr -> Maybe CoreExpr
tryEtaReduce bndrs body 
  = go (reverse bndrs) body (mkReflCo (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 = Just (mkCoerce co fun)

    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 ty)) 
        | not (any (`elemVarSet` tyVarsOfType ty) bndrs)
	=  ok_fun fun
    ok_fun (Var fun_id)
	=  not (fun_id `elem` bndrs)
	&& (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
       | otherwise = 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 (mkReflCo (idType bndr)) co)
    ok_arg bndr (Cast (Var v) co_arg) co
       | bndr == v  = Just (mkFunCo (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 :: (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 _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 (Note n e) 		= notSccNote 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 (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
#if mingw32_TARGET_OS
        | not (_is_dynamic_name (idName f))
#endif
	=  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 (Note n f) n_val_args = notSccNote 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