% % (c) The University of Glasgow 2006 % (c) The GRASP/AQUA Project, Glasgow University, 1992-1998 % Utility functions on @Core@ syntax \begin{code}

    {-# 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, mkCoerceI,
    	bindNonRec, needsCaseBinding,
    	mkAltExpr, mkPiType, mkPiTypes,

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

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

    	-- * Expression and bindings size
    	coreBindsSize, exprSize,

    	-- * Hashing
    	hashExpr,

    	-- * Equality
    	cheapEqExpr, eqExpr, eqExprX,

    	-- * Eta reduction
    	tryEtaReduce,

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

    #include "HsVersions.h"

    import CoreSyn
    import PprCore
    import Var
    import SrcLoc
    import VarEnv
    import VarSet
    import Name
    #if mingw32_TARGET_OS
    import Packages
    #endif
    import Literal
    import DataCon
    import PrimOp
    import Id
    import IdInfo
    import TcType	( isPredTy )
    import Type
    import Coercion
    import TyCon
    import CostCentre
    import Unique
    import Outputable
    import TysPrim
    import PrelNames( absentErrorIdKey )
    import FastString
    import Maybes
    import Util
    import Data.Word
    import Data.Bits

\end{code} %************************************************************************ %* * \subsection{Find the type of a Core atom/expression} %* * %************************************************************************ \begin{code}

    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 (Let _ body)	     = exprType body
    exprType (Case _ _ ty _)     = ty
    exprType (Cast _ co)         = snd (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 = isTyCoVar 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"

\end{code} 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. \begin{code}

    mkPiType  :: EvVar -> Type -> Type
    -- ^ Makes a @(->)@ type or a forall type, depending
    -- on whether it is given a type variable or a term variable.
    mkPiTypes :: [EvVar] -> 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

\end{code} \begin{code}

    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

\end{code} %************************************************************************ %* * \subsection{Attaching notes} %* * %************************************************************************ \begin{code}

    -- | Wrap the given expression in the coercion, dropping identity coercions and coalescing nested coercions
    mkCoerceI :: CoercionI -> CoreExpr -> CoreExpr
    mkCoerceI (IdCo _) e = e
    mkCoerceI (ACo co) e = mkCoerce co e

    -- | Wrap the given expression in the coercion safely, coalescing nested coercions
    mkCoerce :: Coercion -> CoreExpr -> CoreExpr
    mkCoerce co (Cast expr co2)
      = ASSERT(let { (from_ty, _to_ty) = coercionKind co;
                     (_from_ty2, to_ty2) = coercionKind co2} in
               from_ty `coreEqType` to_ty2 )
        mkCoerce (mkTransCoercion co2 co) expr

    mkCoerce co expr
      = let (from_ty, _to_ty) = coercionKind co in
    --    if to_ty `coreEqType` from_ty
    --    then expr
    --    else
            WARN(not (from_ty `coreEqType` exprType expr), text "Trying to coerce" <+> text "(" <> ppr expr $$ text "::" <+> ppr (exprType expr) <> text ")" $$ ppr co $$ pprEqPred (coercionKind co))
             (Cast expr co)

\end{code} \begin{code}

    -- | 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

\end{code} %************************************************************************ %* * \subsection{Other expression construction} %* * %************************************************************************ \begin{code}

    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)

\end{code} \begin{code}

    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"

\end{code} %************************************************************************ %* * \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. \begin{code}

    -- | 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

\end{code} 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), becuase \$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 [SCCs are trivial] ~~~~~~~~~~~~~~~~~~~~~~~ We used not to treat (_scc_ "foo" x) as trivial, because it really generates code, (and a heap object when it's a function arg) to capture the cost centre. However, the profiling system discounts the allocation costs for such "boxing thunks" whereas the extra costs of *not* inlining otherwise-trivial bindings can be high, and are hard to discount. \begin{code}

    exprIsTrivial :: CoreExpr -> Bool
    exprIsTrivial (Var _)          = True        -- See Note [Variables are trivial]
    exprIsTrivial (Type _)         = 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

\end{code} %************************************************************************ %* * 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 \begin{code}

    exprIsDupable :: CoreExpr -> Bool
    exprIsDupable (Type _)   = True
    exprIsDupable (Var _)    = True
    exprIsDupable (Lit lit)  = litIsDupable lit
    exprIsDupable (Note _ e) = exprIsDupable e
    exprIsDupable (Cast e _) = exprIsDupable e
    exprIsDupable expr
      = go expr 0
      where
        go (Var _)   _      = True
        go (App f a) n_args =  n_args < dupAppSize
    			&& exprIsDupable a
    			&& go f (n_args+1)
        go _         _      = False

    dupAppSize :: Int
    dupAppSize = 4		-- Size of application we are prepared to duplicate

\end{code} %************************************************************************ %* * exprIsCheap, exprIsExpandable %* * %************************************************************************ 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. \begin{code}

    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' _          (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 exprIsTrivial args
     	-- For constructor applications and primops, check that all
     	-- the args are trivial.  We don't want to treat as cheap, say,
     	-- 	(1:2:3:4:5:[])
     	-- We'll put up with one constructor application, but not dozens

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

\end{code} 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 %* * %************************************************************************ \begin{code}

    -- | '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
    --
    -- 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 :: CoreExpr -> Bool
    exprOkForSpeculation (Lit _)     = True
    exprOkForSpeculation (Type _)    = True
        -- Tick boxes are *not* suitable for speculation
    exprOkForSpeculation (Var v)     = isUnLiftedType (idType v)
    				 && not (isTickBoxOp v)
    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

    exprOkForSpeculation other_expr
      = case collectArgs other_expr of
    	(Var f, args) | f `hasKey` absentErrorIdKey	-- Note [Absent error Id]
                          -> all exprOkForSpeculation args  --    in WwLib
                          | otherwise
                          -> 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

          | 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

    -- | 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

\end{code} 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: 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.$wfoo = \ (ww :: GHC.Prim.Int#) -> case ww of ds { __DEFAULT -> case (case <# ds 5 of _ { GHC.Bool.False -> lvl1; GHC.Bool.True -> lvl}) of _ { __DEFAULT -> T.$wfoo (GHC.Prim.-# ds_XkE 1) }; 0 -> 0 } The inner case is redundant, and should be nuked. %************************************************************************ %* * exprIsHNF, exprIsConLike %* * %************************************************************************ \begin{code}

    -- 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

\end{code} \begin{code}

    -- | 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 (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 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

\end{code} %************************************************************************ %* * Instantiating data constructors %* * %************************************************************************ These InstPat functions go here to avoid circularity between DataCon and Id \begin{code}

    dataConRepInstPat, dataConOrigInstPat :: [Unique] -> DataCon -> [Type] -> ([TyVar], [CoVar], [Id])
    dataConRepFSInstPat :: [FastString] -> [Unique] -> DataCon -> [Type] -> ([TyVar], [CoVar], [Id])

    dataConRepInstPat   = dataConInstPat dataConRepArgTys (repeat ((fsLit "ipv")))
    dataConRepFSInstPat = dataConInstPat dataConRepArgTys
    dataConOrigInstPat  = dataConInstPat dc_arg_tys       (repeat ((fsLit "ipv")))
      where
        dc_arg_tys dc = map mkPredTy (dataConEqTheta dc) ++ map mkPredTy (dataConDictTheta dc) ++ dataConOrigArgTys dc
    	-- Remember to include the existential dictionaries

    dataConInstPat :: (DataCon -> [Type])      -- function used to find arg tys
                      -> [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], [CoVar], [Id]) -- Return instantiated variables
    -- dataConInstPat arg_fun fss us con inst_tys returns a triple
    -- (ex_tvs, co_tvs, arg_ids),
    --
    --   ex_tvs are intended to be used as binders for existential type args
    --
    --   co_tvs are intended to be used as binders for coercion args and the kinds
    --     of these vars have been instantiated by the inst_tys and the ex_tys
    --     The co_tvs include both GADT equalities (dcEqSpec) and
    --     programmer-specified equalities (dcEqTheta)
    --
    --   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 dicts (dcDictTheta) and
    --     programmer-specified arguments (after rep-ing) (deRepArgTys)
    --
    -- 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 arg_fun fss uniqs con inst_tys
      = (ex_bndrs, co_bndrs, arg_ids)
      where
        univ_tvs = dataConUnivTyVars con
        ex_tvs   = dataConExTyVars con
        arg_tys  = arg_fun con
        eq_spec  = dataConEqSpec con
        eq_theta = dataConEqTheta con
        eq_preds = eqSpecPreds eq_spec ++ eq_theta

        n_ex = length ex_tvs
        n_co = length eq_preds

          -- split the Uniques and FastStrings
        (ex_uniqs, uniqs')   = splitAt n_ex uniqs
        (co_uniqs, id_uniqs) = splitAt n_co uniqs'

        (ex_fss, fss')     = splitAt n_ex fss
        (co_fss, id_fss)   = splitAt n_co 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 new coercion vars, instantiating kind
        co_bndrs = zipWith3 mk_co_var co_uniqs co_fss eq_preds
        mk_co_var uniq fs eq_pred = mkCoVar new_name co_kind
           where
             new_name = mkSysTvName uniq fs
             co_kind  = substTy subst (mkPredTy eq_pred)

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

\end{code} %************************************************************************ %* * Equality %* * %************************************************************************ \begin{code}

    -- | 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 `coreEqType` t2

    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

\end{code} \begin{code}

    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 (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

\end{code} \begin{code}

    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

\end{code} \begin{code}

    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)     = tcEqTypeX env t1 t2
        go env (Cast e1 co1) (Cast e2 co2) = tcEqTypeX 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)
          =  tcEqTypeX 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
          && tcEqTypeX 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

\end{code} Auxiliary functions \begin{code}

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

\end{code} %************************************************************************ %* * \subsection{The size of an expression} %* * %************************************************************************ \begin{code}

    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
    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)     = (seqType co `seq` 1) + exprSize e
    exprSize (Note n e)      = noteSize n + exprSize e
    exprSize (Type t)        = seqType t `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  | isTyCoVar 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

\end{code} %************************************************************************ %* * \subsection{Hashing} %* * %************************************************************************ \begin{code}

    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.

    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 _   (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

    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))

\end{code} %************************************************************************ %* * 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: * 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 to 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 terminiating 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. \begin{code}

    tryEtaReduce :: [Var] -> CoreExpr -> Maybe CoreExpr
    tryEtaReduce bndrs body
      = go (reverse bndrs) body (IdCo (exprType body))
      where
        incoming_arity = count isId bndrs

        go :: [Var]	           -- Binders, innermost first, types [a3,a2,a1]
           -> CoreExpr         -- Of type tr
           -> CoercionI        -- 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 (mkCoerceI 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 && isLoopBreaker (idOccInfo fun) = 0
           | otherwise = idArity fun

        ---------------
        ok_lam v = isTyCoVar v || isDictId v

        ---------------
        ok_arg :: Var 	        -- Of type bndr_t
               -> CoreExpr          -- Of type arg_t
               -> CoercionI         -- Of kind (t1~t2)
               -> Maybe CoercionI   -- 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 (mkForAllTyCoI tv co)
        ok_arg bndr (Var v) co
           | bndr == v   = Just (mkFunTyCoI (IdCo (idType bndr)) co)
        ok_arg bndr (Cast (Var v) co_arg) co
           | bndr == v  = Just (mkFunTyCoI (ACo (mkSymCoercion co_arg)) co)
           -- The simplifier combines multiple casts into one,
           -- so we can have a simple-minded pattern match here
        ok_arg _ _ _ = Nothing

\end{code} %************************************************************************ %* * \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. \begin{code}

    -- | 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 _      (Lit lit)
        = case lit of
      	MachLabel _ _ _ -> False
            _             -> 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

\end{code}