% % (c) The University of Glasgow 2006 % (c) The AQUA Project, Glasgow University, 1994-1998 % Core-syntax unfoldings Unfoldings (which can travel across module boundaries) are in Core syntax (namely @CoreExpr@s). The type @Unfolding@ sits ``above'' simply-Core-expressions unfoldings, capturing ``higher-level'' things we know about a binding, usually things that the simplifier found out (e.g., ``it's a literal''). In the corner of a @CoreUnfolding@ unfolding, you will find, unsurprisingly, a Core expression. \begin{code}

    module CoreUnfold (
    	Unfolding, UnfoldingGuidance,	-- Abstract types

    	noUnfolding, mkImplicitUnfolding,
            mkUnfolding, mkCoreUnfolding,
    	mkTopUnfolding, mkSimpleUnfolding,
    	mkInlineUnfolding, mkInlinableUnfolding, mkWwInlineRule,
    	mkCompulsoryUnfolding, mkDFunUnfolding,

    	interestingArg, ArgSummary(..),

    	couldBeSmallEnoughToInline,
    	certainlyWillInline, smallEnoughToInline,

    	callSiteInline, CallCtxt(..),

    	exprIsConApp_maybe

        ) where

    #include "HsVersions.h"

    import StaticFlags
    import DynFlags
    import CoreSyn
    import PprCore		()	-- Instances
    import TcType	 	( tcSplitSigmaTy, tcSplitDFunHead )
    import OccurAnal
    import CoreSubst hiding( substTy )
    import CoreFVs         ( exprFreeVars )
    import CoreArity       ( manifestArity, exprBotStrictness_maybe )
    import CoreUtils
    import Id
    import DataCon
    import TyCon
    import Literal
    import PrimOp
    import IdInfo
    import BasicTypes	( Arity )
    import TcType		( tcSplitDFunTy )
    import Type
    import Coercion
    import PrelNames
    import VarEnv           ( mkInScopeSet )
    import Bag
    import Util
    import FastTypes
    import FastString
    import Outputable
    import Data.Maybe

\end{code} %************************************************************************ %* * \subsection{Making unfoldings} %* * %************************************************************************ \begin{code}

    mkTopUnfolding :: Bool -> CoreExpr -> Unfolding
    mkTopUnfolding = mkUnfolding InlineRhs True {- Top level -}

    mkImplicitUnfolding :: CoreExpr -> Unfolding
    -- For implicit Ids, do a tiny bit of optimising first
    mkImplicitUnfolding expr = mkTopUnfolding False (simpleOptExpr expr)

    -- Note [Top-level flag on inline rules]
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    -- Slight hack: note that mk_inline_rules conservatively sets the
    -- top-level flag to True.  It gets set more accurately by the simplifier
    -- Simplify.simplUnfolding.

    mkSimpleUnfolding :: CoreExpr -> Unfolding
    mkSimpleUnfolding = mkUnfolding InlineRhs False False

    mkDFunUnfolding :: Type -> [DFunArg CoreExpr] -> Unfolding
    mkDFunUnfolding dfun_ty ops
      = DFunUnfolding dfun_nargs data_con ops
      where
        (tvs, theta, head_ty) = tcSplitSigmaTy dfun_ty
        	  -- NB: tcSplitSigmaTy: do not look through a newtype
    	  --     when the dictionary type is a newtype
        (cls, _)   = tcSplitDFunHead head_ty
        dfun_nargs = length tvs + length theta
        data_con   = classDataCon cls

    mkWwInlineRule :: Id -> CoreExpr -> Arity -> Unfolding
    mkWwInlineRule id expr arity
      = mkCoreUnfolding (InlineWrapper id) True
                       (simpleOptExpr expr) arity
                       (UnfWhen unSaturatedOk boringCxtNotOk)

    mkCompulsoryUnfolding :: CoreExpr -> Unfolding
    mkCompulsoryUnfolding expr	   -- Used for things that absolutely must be unfolded
      = mkCoreUnfolding InlineCompulsory True
                        expr 0    -- Arity of unfolding doesn't matter
                        (UnfWhen unSaturatedOk boringCxtOk)

    mkInlineUnfolding :: Maybe Arity -> CoreExpr -> Unfolding
    mkInlineUnfolding mb_arity expr
      = mkCoreUnfolding InlineStable
        		    True 	 -- Note [Top-level flag on inline rules]
                        expr' arity
    		    (UnfWhen unsat_ok boring_ok)
      where
        expr' = simpleOptExpr expr
        (unsat_ok, arity) = case mb_arity of
                              Nothing -> (unSaturatedOk, manifestArity expr')
                              Just ar -> (needSaturated, ar)

        boring_ok = case calcUnfoldingGuidance True    -- Treat as cheap
        	      	     			   False   -- But not bottoming
                                               (arity+1) expr' of
                  	  (_, UnfWhen _ boring_ok) -> boring_ok
                  	  _other                   -> boringCxtNotOk
         -- See Note [INLINE for small functions]

    mkInlinableUnfolding :: CoreExpr -> Unfolding
    mkInlinableUnfolding expr
      = mkUnfolding InlineStable True is_bot expr'
      where
        expr' = simpleOptExpr expr
        is_bot = isJust (exprBotStrictness_maybe expr')

\end{code} Internal functions \begin{code}

    mkCoreUnfolding :: UnfoldingSource -> Bool -> CoreExpr
                    -> Arity -> UnfoldingGuidance -> Unfolding
    -- Occurrence-analyses the expression before capturing it
    mkCoreUnfolding src top_lvl expr arity guidance
      = CoreUnfolding { uf_tmpl   	  = occurAnalyseExpr expr,
        		    uf_src        = src,
        		    uf_arity      = arity,
    		    uf_is_top 	  = top_lvl,
    		    uf_is_value   = exprIsHNF        expr,
                        uf_is_conlike = exprIsConLike    expr,
    		    uf_is_cheap   = exprIsCheap      expr,
    		    uf_expandable = exprIsExpandable expr,
    		    uf_guidance   = guidance }

    mkUnfolding :: UnfoldingSource -> Bool -> Bool -> CoreExpr -> Unfolding
    -- Calculates unfolding guidance
    -- Occurrence-analyses the expression before capturing it
    mkUnfolding src top_lvl is_bottoming expr
      = CoreUnfolding { uf_tmpl   	  = occurAnalyseExpr expr,
        		    uf_src        = src,
        		    uf_arity      = arity,
    		    uf_is_top 	  = top_lvl,
    		    uf_is_value   = exprIsHNF        expr,
                        uf_is_conlike = exprIsConLike    expr,
    		    uf_expandable = exprIsExpandable expr,
    		    uf_is_cheap   = is_cheap,
    		    uf_guidance   = guidance }
      where
        is_cheap = exprIsCheap expr
        (arity, guidance) = calcUnfoldingGuidance is_cheap (top_lvl && is_bottoming)
                                                  opt_UF_CreationThreshold expr
    	-- Sometimes during simplification, there's a large let-bound thing
    	-- which has been substituted, and so is now dead; so 'expr' contains
    	-- two copies of the thing while the occurrence-analysed expression doesn't
    	-- Nevertheless, we *don't* occ-analyse before computing the size because the
    	-- size computation bales out after a while, whereas occurrence analysis does not.
    	--
    	-- This can occasionally mean that the guidance is very pessimistic;
    	-- it gets fixed up next round.  And it should be rare, because large
    	-- let-bound things that are dead are usually caught by preInlineUnconditionally

\end{code} %************************************************************************ %* * \subsection{The UnfoldingGuidance type} %* * %************************************************************************ \begin{code}

    calcUnfoldingGuidance
    	:: Bool		-- True <=> the rhs is cheap, or we want to treat it
    	   		--          as cheap (INLINE things)
            -> Bool		-- True <=> this is a top-level unfolding for a
    	                --          diverging function; don't inline this
            -> Int		-- Bomb out if size gets bigger than this
    	-> CoreExpr    	-- Expression to look at
    	-> (Arity, UnfoldingGuidance)
    calcUnfoldingGuidance expr_is_cheap top_bot bOMB_OUT_SIZE expr
      = case collectBinders expr of { (bndrs, body) ->
        let
            val_bndrs   = filter isId bndrs
    	n_val_bndrs = length val_bndrs

        	guidance
              = case (sizeExpr (iUnbox bOMB_OUT_SIZE) val_bndrs body) of
          	      TooBig -> UnfNever
          	      SizeIs size cased_bndrs scrut_discount
          	        | uncondInline n_val_bndrs (iBox size)
                    , expr_is_cheap
          	        -> UnfWhen unSaturatedOk boringCxtOk   -- Note [INLINE for small functions]
    		| top_bot  -- See Note [Do not inline top-level bottoming functions]
    		-> UnfNever

    	        | otherwise
          	        -> UnfIfGoodArgs { ug_args  = map (discount cased_bndrs) val_bndrs
          	                         , ug_size  = iBox size
          	        	  	 , ug_res   = iBox scrut_discount }

            discount cbs bndr
               = foldlBag (\acc (b',n) -> if bndr==b' then acc+n else acc)
    		      0 cbs
        in
        (n_val_bndrs, guidance) }

\end{code} Note [Computing the size of an expression] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The basic idea of sizeExpr is obvious enough: count nodes. But getting the heuristics right has taken a long time. Here's the basic strategy: * Variables, literals: 0 (Exception for string literals, see litSize.) * Function applications (f e1 .. en): 1 + #value args * Constructor applications: 1, regardless of #args * Let(rec): 1 + size of components * Note, cast: 0 Examples Size Term -------------- 0 42# 0 x 0 True 2 f x 1 Just x 4 f (g x) Notice that 'x' counts 0, while (f x) counts 2. That's deliberate: there's a function call to account for. Notice also that constructor applications are very cheap, because exposing them to a caller is so valuable. Note [Do not inline top-level bottoming functions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The FloatOut pass has gone to some trouble to float out calls to 'error' and similar friends. See Note [Bottoming floats] in SetLevels. Do not re-inline them! But we *do* still inline if they are very small (the uncondInline stuff). Note [INLINE for small functions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider {-# INLINE f #-} f x = Just x g y = f y Then f's RHS is no larger than its LHS, so we should inline it into even the most boring context. In general, f the function is sufficiently small that its body is as small as the call itself, the inline unconditionally, regardless of how boring the context is. Things to note: * We inline *unconditionally* if inlined thing is smaller (using sizeExpr) than the thing it's replacing. Notice that (f x) --> (g 3) -- YES, unconditionally (f x) --> x : [] -- YES, *even though* there are two -- arguments to the cons x --> g 3 -- NO x --> Just v -- NO It's very important not to unconditionally replace a variable by a non-atomic term. * We do this even if the thing isn't saturated, else we end up with the silly situation that f x y = x ...map (f 3)... doesn't inline. Even in a boring context, inlining without being saturated will give a lambda instead of a PAP, and will be more efficient at runtime. * However, when the function's arity > 0, we do insist that it has at least one value argument at the call site. Otherwise we find this: f = /\a \x:a. x d = /\b. MkD (f b) If we inline f here we get d = /\b. MkD (\x:b. x) and then prepareRhs floats out the argument, abstracting the type variables, so we end up with the original again! \begin{code}

    uncondInline :: Arity -> Int -> Bool
    -- Inline unconditionally if there no size increase
    -- Size of call is arity (+1 for the function)
    -- See Note [INLINE for small functions]
    uncondInline arity size
      | arity == 0 = size == 0
      | otherwise  = size <= arity + 1

\end{code} \begin{code}

    sizeExpr :: FastInt 	    -- Bomb out if it gets bigger than this
    	 -> [Id]	    -- Arguments; we're interested in which of these
    			    -- get case'd
    	 -> CoreExpr
    	 -> ExprSize

    -- Note [Computing the size of an expression]

    sizeExpr bOMB_OUT_SIZE top_args expr
      = size_up expr
      where
        size_up (Cast e _) = size_up e
        size_up (Note _ e) = size_up e
        size_up (Type _)   = sizeZero           -- Types cost nothing
        size_up (Lit lit)  = sizeN (litSize lit)
        size_up (Var f)    = size_up_call f []  -- Make sure we get constructor
        	    	       	 	      	    -- discounts even on nullary constructors

        size_up (App fun (Type _)) = size_up fun
        size_up (App fun arg)      = size_up arg  `addSizeNSD`
                                     size_up_app fun [arg]

        size_up (Lam b e) | isId b    = lamScrutDiscount (size_up e `addSizeN` 1)
    		      | otherwise = size_up e

        size_up (Let (NonRec binder rhs) body)
          = size_up rhs		`addSizeNSD`
    	size_up body		`addSizeN`
    	(if isUnLiftedType (idType binder) then 0 else 1)
    		-- For the allocation
    		-- If the binder has an unlifted type there is no allocation

        size_up (Let (Rec pairs) body)
          = foldr (addSizeNSD . size_up . snd)
                  (size_up body `addSizeN` length pairs)	-- (length pairs) for the allocation
                  pairs

        size_up (Case (Var v) _ _ alts)
    	| v `elem` top_args		-- We are scrutinising an argument variable
    	= alts_size (foldr1 addAltSize alt_sizes)
    		    (foldr1 maxSize alt_sizes)
    		-- Good to inline if an arg is scrutinised, because
    		-- that may eliminate allocation in the caller
    		-- And it eliminates the case itself
    	where
    	  alt_sizes = map size_up_alt alts

    		-- alts_size tries to compute a good discount for
    		-- the case when we are scrutinising an argument variable
    	  alts_size (SizeIs tot tot_disc tot_scrut)  -- Size of all alternatives
    		    (SizeIs max _        _)          -- Size of biggest alternative
    	 	= SizeIs tot (unitBag (v, iBox (_ILIT(2) +# tot -# max)) `unionBags` tot_disc) tot_scrut
    			-- If the variable is known, we produce a discount that
    			-- will take us back to 'max', the size of the largest alternative
    			-- The 1+ is a little discount for reduced allocation in the caller
    			--
    			-- Notice though, that we return tot_disc, the total discount from
    			-- all branches.  I think that's right.

    	  alts_size tot_size _ = tot_size

        size_up (Case e _ _ alts) = size_up e  `addSizeNSD`
                                    foldr (addAltSize . size_up_alt) sizeZero alts
    	  	-- We don't charge for the case itself
    		-- It's a strict thing, and the price of the call
    		-- is paid by scrut.  Also consider
    		--	case f x of DEFAULT -> e
    		-- This is just ';'!  Don't charge for it.
    		--
    		-- Moreover, we charge one per alternative.

        ------------
        -- size_up_app is used when there's ONE OR MORE value args
        size_up_app (App fun arg) args
    	| isTypeArg arg		   = size_up_app fun args
    	| otherwise		   = size_up arg  `addSizeNSD`
                                         size_up_app fun (arg:args)
        size_up_app (Var fun)     args = size_up_call fun args
        size_up_app other         args = size_up other `addSizeN` length args

        ------------
        size_up_call :: Id -> [CoreExpr] -> ExprSize
        size_up_call fun val_args
           = case idDetails fun of
               FCallId _        -> sizeN opt_UF_DearOp
               DataConWorkId dc -> conSize    dc (length val_args)
               PrimOpId op      -> primOpSize op (length val_args)
    	   ClassOpId _ 	    -> classOpSize top_args val_args
    	   _     	    -> funSize top_args fun (length val_args)

        ------------
        size_up_alt (_con, _bndrs, rhs) = size_up rhs `addSizeN` 1
     	-- Don't charge for args, so that wrappers look cheap
    	-- (See comments about wrappers with Case)
    	--
    	-- IMPORATANT: *do* charge 1 for the alternative, else we
    	-- find that giant case nests are treated as practically free
    	-- A good example is Foreign.C.Error.errrnoToIOError

        ------------
    	-- These addSize things have to be here because
    	-- I don't want to give them bOMB_OUT_SIZE as an argument
        addSizeN TooBig          _  = TooBig
        addSizeN (SizeIs n xs d) m 	= mkSizeIs bOMB_OUT_SIZE (n +# iUnbox m) xs d

            -- addAltSize is used to add the sizes of case alternatives
        addAltSize TooBig	         _	= TooBig
        addAltSize _		 TooBig	= TooBig
        addAltSize (SizeIs n1 xs d1) (SizeIs n2 ys d2)
    	= mkSizeIs bOMB_OUT_SIZE (n1 +# n2)
                                     (xs `unionBags` ys)
                                     (d1 +# d2)   -- Note [addAltSize result discounts]

            -- This variant ignores the result discount from its LEFT argument
    	-- It's used when the second argument isn't part of the result
        addSizeNSD TooBig	         _	= TooBig
        addSizeNSD _		 TooBig	= TooBig
        addSizeNSD (SizeIs n1 xs _) (SizeIs n2 ys d2)
    	= mkSizeIs bOMB_OUT_SIZE (n1 +# n2)
                                     (xs `unionBags` ys)
                                     d2  -- Ignore d1

\end{code} \begin{code}

    -- | Finds a nominal size of a string literal.
    litSize :: Literal -> Int
    -- Used by CoreUnfold.sizeExpr
    litSize (MachStr str) = 1 + ((lengthFS str + 3) `div` 4)
    	-- If size could be 0 then @f "x"@ might be too small
    	-- [Sept03: make literal strings a bit bigger to avoid fruitless
    	--  duplication of little strings]
    litSize _other = 0    -- Must match size of nullary constructors
    	       	      -- Key point: if  x |-> 4, then x must inline unconditionally
    		      --     	    (eg via case binding)

    classOpSize :: [Id] -> [CoreExpr] -> ExprSize
    -- See Note [Conlike is interesting]
    classOpSize _ []
      = sizeZero
    classOpSize top_args (arg1 : other_args)
      = SizeIs (iUnbox size) arg_discount (_ILIT(0))
      where
        size = 2 + length other_args
        -- If the class op is scrutinising a lambda bound dictionary then
        -- give it a discount, to encourage the inlining of this function
        -- The actual discount is rather arbitrarily chosen
        arg_discount = case arg1 of
        		     Var dict | dict `elem` top_args
    		     	      -> unitBag (dict, opt_UF_DictDiscount)
    		     _other   -> emptyBag

    funSize :: [Id] -> Id -> Int -> ExprSize
    -- Size for functions that are not constructors or primops
    -- Note [Function applications]
    funSize top_args fun n_val_args
      | fun `hasKey` buildIdKey   = buildSize
      | fun `hasKey` augmentIdKey = augmentSize
      | otherwise = SizeIs (iUnbox size) arg_discount (iUnbox res_discount)
      where
        some_val_args = n_val_args > 0

        arg_discount | some_val_args && fun `elem` top_args
        		 = unitBag (fun, opt_UF_FunAppDiscount)
    		 | otherwise = emptyBag
    	-- If the function is an argument and is applied
    	-- to some values, give it an arg-discount

        res_discount | idArity fun > n_val_args = opt_UF_FunAppDiscount
        		 | otherwise   	 	    = 0
            -- If the function is partially applied, show a result discount

        size | some_val_args = 1 + n_val_args
             | otherwise     = 0
    	-- The 1+ is for the function itself
    	-- Add 1 for each non-trivial arg;
    	-- the allocation cost, as in let(rec)

    conSize :: DataCon -> Int -> ExprSize
    conSize dc n_val_args
      | n_val_args == 0 = SizeIs (_ILIT(0)) emptyBag (_ILIT(1))	-- Like variables

    -- See Note [Constructor size]
      | isUnboxedTupleCon dc = SizeIs (_ILIT(0)) emptyBag (iUnbox n_val_args +# _ILIT(1))

    -- See Note [Unboxed tuple result discount]
    --  | isUnboxedTupleCon dc = SizeIs (_ILIT(0)) emptyBag (_ILIT(0))

    -- See Note [Constructor size]
      | otherwise = SizeIs (_ILIT(1)) emptyBag (iUnbox n_val_args +# _ILIT(1))

\end{code} Note [Constructor size] ~~~~~~~~~~~~~~~~~~~~~~~ Treat a constructors application as size 1, regardless of how many arguments it has; we are keen to expose them (and we charge separately for their args). We can't treat them as size zero, else we find that (Just x) has size 0, which is the same as a lone variable; and hence 'v' will always be replaced by (Just x), where v is bound to Just x. However, unboxed tuples count as size zero. I found occasions where we had f x y z = case op# x y z of { s -> (# s, () #) } and f wasn't getting inlined. Note [Unboxed tuple result discount] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I tried giving unboxed tuples a *result discount* of zero (see the commented-out line). Why? When returned as a result they do not allocate, so maybe we don't want to charge so much for them If you have a non-zero discount here, we find that workers often get inlined back into wrappers, because it look like f x = case $wf x of (# a,b #) -> (a,b) and we are keener because of the case. However while this change shrank binary sizes by 0.5% it also made spectral/boyer allocate 5% more. All other changes were very small. So it's not a big deal but I didn't adopt the idea. \begin{code}

    primOpSize :: PrimOp -> Int -> ExprSize
    primOpSize op n_val_args
     | not (primOpIsDupable op) = sizeN opt_UF_DearOp
     | not (primOpOutOfLine op) = sizeN 1
    	-- Be very keen to inline simple primops.
    	-- We give a discount of 1 for each arg so that (op# x y z) costs 2.
    	-- We can't make it cost 1, else we'll inline let v = (op# x y z)
    	-- at every use of v, which is excessive.
    	--
    	-- A good example is:
    	--	let x = +# p q in C {x}
    	-- Even though x get's an occurrence of 'many', its RHS looks cheap,
    	-- and there's a good chance it'll get inlined back into C's RHS. Urgh!

     | otherwise = sizeN n_val_args

    buildSize :: ExprSize
    buildSize = SizeIs (_ILIT(0)) emptyBag (_ILIT(4))
    	-- We really want to inline applications of build
    	-- build t (\cn -> e) should cost only the cost of e (because build will be inlined later)
    	-- Indeed, we should add a result_discount becuause build is
    	-- very like a constructor.  We don't bother to check that the
    	-- build is saturated (it usually is).  The "-2" discounts for the \c n,
    	-- The "4" is rather arbitrary.

    augmentSize :: ExprSize
    augmentSize = SizeIs (_ILIT(0)) emptyBag (_ILIT(4))
    	-- Ditto (augment t (\cn -> e) ys) should cost only the cost of
    	-- e plus ys. The -2 accounts for the \cn

    -- When we return a lambda, give a discount if it's used (applied)
    lamScrutDiscount :: ExprSize -> ExprSize
    lamScrutDiscount (SizeIs n vs _) = SizeIs n vs (iUnbox opt_UF_FunAppDiscount)
    lamScrutDiscount TooBig          = TooBig

\end{code} Note [addAltSize result discounts] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ When adding the size of alternatives, we *add* the result discounts too, rather than take the *maximum*. For a multi-branch case, this gives a discount for each branch that returns a constructor, making us keener to inline. I did try using 'max' instead, but it makes nofib 'rewrite' and 'puzzle' allocate significantly more, and didn't make binary sizes shrink significantly either. Note [Discounts and thresholds] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Constants for discounts and thesholds are defined in main/StaticFlags, all of form opt_UF_xxxx. They are: opt_UF_CreationThreshold (45) At a definition site, if the unfolding is bigger than this, we may discard it altogether opt_UF_UseThreshold (6) At a call site, if the unfolding, less discounts, is smaller than this, then it's small enough inline opt_UF_KeennessFactor (1.5) Factor by which the discounts are multiplied before subtracting from size opt_UF_DictDiscount (1) The discount for each occurrence of a dictionary argument as an argument of a class method. Should be pretty small else big functions may get inlined opt_UF_FunAppDiscount (6) Discount for a function argument that is applied. Quite large, because if we inline we avoid the higher-order call. opt_UF_DearOp (4) The size of a foreign call or not-dupable PrimOp Note [Function applications] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In a function application (f a b) - If 'f' is an argument to the function being analysed, and there's at least one value arg, record a FunAppDiscount for f - If the application if a PAP (arity > 2 in this example) record a *result* discount (because inlining with "extra" args in the call may mean that we now get a saturated application) Code for manipulating sizes \begin{code}

    data ExprSize = TooBig
    	      | SizeIs FastInt		-- Size found
    		       (Bag (Id,Int))	-- Arguments cased herein, and discount for each such
    		       FastInt		-- Size to subtract if result is scrutinised
    					-- by a case expression

    instance Outputable ExprSize where
      ppr TooBig         = ptext (sLit "TooBig")
      ppr (SizeIs a _ c) = brackets (int (iBox a) <+> int (iBox c))

    -- subtract the discount before deciding whether to bale out. eg. we
    -- want to inline a large constructor application into a selector:
    --  	tup = (a_1, ..., a_99)
    --  	x = case tup of ...
    --
    mkSizeIs :: FastInt -> FastInt -> Bag (Id, Int) -> FastInt -> ExprSize
    mkSizeIs max n xs d | (n -# d) ># max = TooBig
    		    | otherwise	      = SizeIs n xs d

    maxSize :: ExprSize -> ExprSize -> ExprSize
    maxSize TooBig         _ 				  = TooBig
    maxSize _              TooBig				  = TooBig
    maxSize s1@(SizeIs n1 _ _) s2@(SizeIs n2 _ _) | n1 ># n2  = s1
    					      | otherwise = s2

    sizeZero :: ExprSize
    sizeN :: Int -> ExprSize

    sizeZero = SizeIs (_ILIT(0))  emptyBag (_ILIT(0))
    sizeN n  = SizeIs (iUnbox n) emptyBag (_ILIT(0))

\end{code} %************************************************************************ %* * \subsection[considerUnfolding]{Given all the info, do (not) do the unfolding} %* * %************************************************************************ We use 'couldBeSmallEnoughToInline' to avoid exporting inlinings that we ``couldn't possibly use'' on the other side. Can be overridden w/ flaggery. Just the same as smallEnoughToInline, except that it has no actual arguments. \begin{code}

    couldBeSmallEnoughToInline :: Int -> CoreExpr -> Bool
    couldBeSmallEnoughToInline threshold rhs
      = case sizeExpr (iUnbox threshold) [] body of
           TooBig -> False
           _      -> True
      where
        (_, body) = collectBinders rhs

    ----------------
    smallEnoughToInline :: Unfolding -> Bool
    smallEnoughToInline (CoreUnfolding {uf_guidance = UnfIfGoodArgs {ug_size = size}})
      = size <= opt_UF_UseThreshold
    smallEnoughToInline _
      = False

    ----------------
    certainlyWillInline :: Unfolding -> Bool
      -- Sees if the unfolding is pretty certain to inline
    certainlyWillInline (CoreUnfolding { uf_is_cheap = is_cheap, uf_arity = n_vals, uf_guidance = guidance })
      = case guidance of
          UnfNever      -> False
          UnfWhen {}    -> True
          UnfIfGoodArgs { ug_size = size}
                        -> is_cheap && size - (n_vals +1) <= opt_UF_UseThreshold

    certainlyWillInline _
      = False

\end{code} %************************************************************************ %* * \subsection{callSiteInline} %* * %************************************************************************ This is the key function. It decides whether to inline a variable at a call site callSiteInline is used at call sites, so it is a bit more generous. It's a very important function that embodies lots of heuristics. A non-WHNF can be inlined if it doesn't occur inside a lambda, and occurs exactly once or occurs once in each branch of a case and is small If the thing is in WHNF, there's no danger of duplicating work, so we can inline if it occurs once, or is small NOTE: we don't want to inline top-level functions that always diverge. It just makes the code bigger. Tt turns out that the convenient way to prevent them inlining is to give them a NOINLINE pragma, which we do in StrictAnal.addStrictnessInfoToTopId \begin{code}

    callSiteInline :: DynFlags
    	       -> Id			-- The Id
    	       -> Bool			-- True <=> unfolding is active
    	       -> Bool			-- True if there are are no arguments at all (incl type args)
    	       -> [ArgSummary]		-- One for each value arg; True if it is interesting
    	       -> CallCtxt		-- True <=> continuation is interesting
    	       -> Maybe CoreExpr	-- Unfolding, if any

    instance Outputable ArgSummary where
      ppr TrivArg    = ptext (sLit "TrivArg")
      ppr NonTrivArg = ptext (sLit "NonTrivArg")
      ppr ValueArg   = ptext (sLit "ValueArg")

    data CallCtxt = BoringCtxt

    	      | ArgCtxt		-- We are somewhere in the argument of a function
                            Bool	-- True  <=> we're somewhere in the RHS of function with rules
    				-- False <=> we *are* the argument of a function with non-zero
    				-- 	     arg discount
                                    --        OR
                                    --           we *are* the RHS of a let  Note [RHS of lets]
                                    -- In both cases, be a little keener to inline

    	      | ValAppCtxt 	-- We're applied to at least one value arg
    				-- This arises when we have ((f x |> co) y)
    				-- Then the (f x) has argument 'x' but in a ValAppCtxt

    	      | CaseCtxt	-- We're the scrutinee of a case
    				-- that decomposes its scrutinee

    instance Outputable CallCtxt where
      ppr BoringCtxt      = ptext (sLit "BoringCtxt")
      ppr (ArgCtxt rules) = ptext (sLit "ArgCtxt") <+> ppr rules
      ppr CaseCtxt 	      = ptext (sLit "CaseCtxt")
      ppr ValAppCtxt      = ptext (sLit "ValAppCtxt")

    callSiteInline dflags id active_unfolding lone_variable arg_infos cont_info
      = case idUnfolding id of
          -- idUnfolding checks for loop-breakers, returning NoUnfolding
          -- Things with an INLINE pragma may have an unfolding *and*
          -- be a loop breaker  (maybe the knot is not yet untied)
    	CoreUnfolding { uf_tmpl = unf_template, uf_is_top = is_top
    		      , uf_is_cheap = is_cheap, uf_arity = uf_arity
                          , uf_guidance = guidance }
              | active_unfolding -> tryUnfolding dflags id lone_variable
                                        arg_infos cont_info unf_template is_top
                                        is_cheap uf_arity guidance
              | otherwise    -> Nothing
    	NoUnfolding 	 -> Nothing
    	OtherCon {} 	 -> Nothing
    	DFunUnfolding {} -> Nothing 	-- Never unfold a DFun

    tryUnfolding :: DynFlags -> Id -> Bool -> [ArgSummary] -> CallCtxt
                 -> CoreExpr -> Bool -> Bool -> Arity -> UnfoldingGuidance
    	     -> Maybe CoreExpr
    tryUnfolding dflags id lone_variable
                 arg_infos cont_info unf_template is_top
                 is_cheap uf_arity guidance
    			-- uf_arity will typically be equal to (idArity id),
    			-- but may be less for InlineRules
     | dopt Opt_D_dump_inlinings dflags && dopt Opt_D_verbose_core2core dflags
     = pprTrace ("Considering inlining: " ++ showSDoc (ppr id))
    		 (vcat [text "arg infos" <+> ppr arg_infos,
    			text "uf arity" <+> ppr uf_arity,
    			text "interesting continuation" <+> ppr cont_info,
    			text "some_benefit" <+> ppr some_benefit,
                            text "is cheap:" <+> ppr is_cheap,
    			text "guidance" <+> ppr guidance,
    			extra_doc,
    			text "ANSWER =" <+> if yes_or_no then text "YES" else text "NO"])
    	         result
      | otherwise  = result

      where
        n_val_args = length arg_infos
        saturated  = n_val_args >= uf_arity

        result | yes_or_no = Just unf_template
               | otherwise = Nothing

        interesting_args = any nonTriv arg_infos
        	-- NB: (any nonTriv arg_infos) looks at the
        	-- over-saturated args too which is "wrong";
        	-- but if over-saturated we inline anyway.

               -- some_benefit is used when the RHS is small enough
               -- and the call has enough (or too many) value
               -- arguments (ie n_val_args >= arity). But there must
               -- be *something* interesting about some argument, or the
               -- result context, to make it worth inlining
        some_benefit
           | not saturated = interesting_args	-- Under-saturated
        	   	      		     	-- Note [Unsaturated applications]
           | n_val_args > uf_arity = True	-- Over-saturated
           | otherwise = interesting_args	-- Saturated
                      || interesting_saturated_call

        interesting_saturated_call
          = case cont_info of
              BoringCtxt -> not is_top && uf_arity > 0	      -- Note [Nested functions]
              CaseCtxt   -> not (lone_variable && is_cheap)   -- Note [Lone variables]
              ArgCtxt {} -> uf_arity > 0     		      -- Note [Inlining in ArgCtxt]
              ValAppCtxt -> True			      -- Note [Cast then apply]

        (yes_or_no, extra_doc)
          = case guidance of
              UnfNever -> (False, empty)

              UnfWhen unsat_ok boring_ok
                 -> (enough_args && (boring_ok || some_benefit), empty )
                 where      -- See Note [INLINE for small functions]
                   enough_args = saturated || (unsat_ok && n_val_args > 0)

              UnfIfGoodArgs { ug_args = arg_discounts, ug_res = res_discount, ug_size = size }
          	     -> ( is_cheap && some_benefit && small_enough
                    , (text "discounted size =" <+> int discounted_size) )
        	     where
        	       discounted_size = size - discount
        	       small_enough = discounted_size <= opt_UF_UseThreshold
        	       discount = computeDiscount uf_arity arg_discounts
        	         		          res_discount arg_infos cont_info

\end{code} Note [RHS of lets] ~~~~~~~~~~~~~~~~~~ Be a tiny bit keener to inline in the RHS of a let, because that might lead to good thing later f y = (y,y,y) g y = let x = f y in ...(case x of (a,b,c) -> ...) ... We'd inline 'f' if the call was in a case context, and it kind-of-is, only we can't see it. So we treat the RHS of a let as not-totally-boring. Note [Unsaturated applications] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ When a call is not saturated, we *still* inline if one of the arguments has interesting structure. That's sometimes very important. A good example is the Ord instance for Bool in Base: Rec { $fOrdBool =GHC.Classes.D:Ord @ Bool ... $cmin_ajX $cmin_ajX [Occ=LoopBreaker] :: Bool -> Bool -> Bool $cmin_ajX = GHC.Classes.$dmmin @ Bool $fOrdBool } But the defn of GHC.Classes.$dmmin is: $dmmin :: forall a. GHC.Classes.Ord a => a -> a -> a {- Arity: 3, HasNoCafRefs, Strictness: SLL, Unfolding: (\ @ a $dOrd :: GHC.Classes.Ord a x :: a y :: a -> case @ a GHC.Classes.<= @ a $dOrd x y of wild { GHC.Bool.False -> y GHC.Bool.True -> x }) -} We *really* want to inline $dmmin, even though it has arity 3, in order to unravel the recursion. Note [Things to watch] ~~~~~~~~~~~~~~~~~~~~~~ * { y = I# 3; x = y `cast` co; ...case (x `cast` co) of ... } Assume x is exported, so not inlined unconditionally. Then we want x to inline unconditionally; no reason for it not to, and doing so avoids an indirection. * { x = I# 3; ....f x.... } Make sure that x does not inline unconditionally! Lest we get extra allocation. Note [Inlining an InlineRule] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ An InlineRules is used for (a) programmer INLINE pragmas (b) inlinings from worker/wrapper For (a) the RHS may be large, and our contract is that we *only* inline when the function is applied to all the arguments on the LHS of the source-code defn. (The uf_arity in the rule.) However for worker/wrapper it may be worth inlining even if the arity is not satisfied (as we do in the CoreUnfolding case) so we don't require saturation. Note [Nested functions] ~~~~~~~~~~~~~~~~~~~~~~~ If a function has a nested defn we also record some-benefit, on the grounds that we are often able to eliminate the binding, and hence the allocation, for the function altogether; this is good for join points. But this only makes sense for *functions*; inlining a constructor doesn't help allocation unless the result is scrutinised. UNLESS the constructor occurs just once, albeit possibly in multiple case branches. Then inlining it doesn't increase allocation, but it does increase the chance that the constructor won't be allocated at all in the branches that don't use it. Note [Cast then apply] ~~~~~~~~~~~~~~~~~~~~~~ Consider myIndex = __inline_me ( (/\a. <blah>) |> co ) co :: (forall a. a -> a) ~ (forall a. T a) ... /\a.\x. case ((myIndex a) |> sym co) x of { ... } ... We need to inline myIndex to unravel this; but the actual call (myIndex a) has no value arguments. The ValAppCtxt gives it enough incentive to inline. Note [Inlining in ArgCtxt] ~~~~~~~~~~~~~~~~~~~~~~~~~~ The condition (arity > 0) here is very important, because otherwise we end up inlining top-level stuff into useless places; eg x = I# 3# f = \y. g x This can make a very big difference: it adds 16% to nofib 'integer' allocs, and 20% to 'power'. At one stage I replaced this condition by 'True' (leading to the above slow-down). The motivation was test eyeball/inline1.hs; but that seems to work ok now. NOTE: arguably, we should inline in ArgCtxt only if the result of the call is at least CONLIKE. At least for the cases where we use ArgCtxt for the RHS of a 'let', we only profit from the inlining if we get a CONLIKE thing (modulo lets). Note [Lone variables] See also Note [Interaction of exprIsCheap and lone variables] ~~~~~~~~~~~~~~~~~~~~~ which appears below The "lone-variable" case is important. I spent ages messing about with unsatisfactory varaints, but this is nice. The idea is that if a variable appears all alone as an arg of lazy fn, or rhs BoringCtxt as scrutinee of a case CaseCtxt as arg of a fn ArgCtxt AND it is bound to a cheap expression then we should not inline it (unless there is some other reason, e.g. is is the sole occurrence). That is what is happening at the use of 'lone_variable' in 'interesting_saturated_call'. Why? At least in the case-scrutinee situation, turning let x = (a,b) in case x of y -> ... into let x = (a,b) in case (a,b) of y -> ... and thence to let x = (a,b) in let y = (a,b) in ... is bad if the binding for x will remain. Another example: I discovered that strings were getting inlined straight back into applications of 'error' because the latter is strict. s = "foo" f = \x -> ...(error s)... Fundamentally such contexts should not encourage inlining because the context can ``see'' the unfolding of the variable (e.g. case or a RULE) so there's no gain. If the thing is bound to a value. However, watch out: * Consider this: foo = _inline_ (\n. [n]) bar = _inline_ (foo 20) baz = \n. case bar of { (m:_) -> m + n } Here we really want to inline 'bar' so that we can inline 'foo' and the whole thing unravels as it should obviously do. This is important: in the NDP project, 'bar' generates a closure data structure rather than a list. So the non-inlining of lone_variables should only apply if the unfolding is regarded as cheap; because that is when exprIsConApp_maybe looks through the unfolding. Hence the "&& is_cheap" in the InlineRule branch. * Even a type application or coercion isn't a lone variable. Consider case $fMonadST @ RealWorld of { :DMonad a b c -> c } We had better inline that sucker! The case won't see through it. For now, I'm treating treating a variable applied to types in a *lazy* context "lone". The motivating example was f = /\a. \x. BIG g = /\a. \y. h (f a) There's no advantage in inlining f here, and perhaps a significant disadvantage. Hence some_val_args in the Stop case Note [Interaction of exprIsCheap and lone variables] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The lone-variable test says "don't inline if a case expression scrutines a lone variable whose unfolding is cheap". It's very important that, under these circumstances, exprIsConApp_maybe can spot a constructor application. So, for example, we don't consider let x = e in (x,x) to be cheap, and that's good because exprIsConApp_maybe doesn't think that expression is a constructor application. I used to test is_value rather than is_cheap, which was utterly wrong, because the above expression responds True to exprIsHNF. This kind of thing can occur if you have {-# INLINE foo #-} foo = let x = e in (x,x) which Roman did. \begin{code}

    computeDiscount :: Int -> [Int] -> Int -> [ArgSummary] -> CallCtxt -> Int
    computeDiscount n_vals_wanted arg_discounts res_discount arg_infos cont_info
     	-- We multiple the raw discounts (args_discount and result_discount)
    	-- ty opt_UnfoldingKeenessFactor because the former have to do with
    	--  *size* whereas the discounts imply that there's some extra
    	--  *efficiency* to be gained (e.g. beta reductions, case reductions)
    	-- by inlining.

      = 1 		-- Discount of 1 because the result replaces the call
    		-- so we count 1 for the function itself

        + length (take n_vals_wanted arg_infos)
          	       -- Discount of (un-scaled) 1 for each arg supplied,
       	       -- because the result replaces the call

        + round (opt_UF_KeenessFactor *
    	     fromIntegral (arg_discount + res_discount'))
      where
        arg_discount = sum (zipWith mk_arg_discount arg_discounts arg_infos)

        mk_arg_discount _ 	     TrivArg    = 0
        mk_arg_discount _ 	     NonTrivArg = 1
        mk_arg_discount discount ValueArg   = discount

        res_discount' = case cont_info of
    			BoringCtxt  -> 0
    			CaseCtxt    -> res_discount
    			_other      -> 4 `min` res_discount
    		-- res_discount can be very large when a function returns
    		-- constructors; but we only want to invoke that large discount
    		-- when there's a case continuation.
    		-- Otherwise we, rather arbitrarily, threshold it.  Yuk.
    		-- But we want to aovid inlining large functions that return
    		-- constructors into contexts that are simply "interesting"

\end{code} %************************************************************************ %* * Interesting arguments %* * %************************************************************************ Note [Interesting arguments] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ An argument is interesting if it deserves a discount for unfoldings with a discount in that argument position. The idea is to avoid unfolding a function that is applied only to variables that have no unfolding (i.e. they are probably lambda bound): f x y z There is little point in inlining f here. Generally, *values* (like (C a b) and (\x.e)) deserve discounts. But we must look through lets, eg (let x = e in C a b), because the let will float, exposing the value, if we inline. That makes it different to exprIsHNF. Before 2009 we said it was interesting if the argument had *any* structure at all; i.e. (hasSomeUnfolding v). But does too much inlining; see Trac #3016. But we don't regard (f x y) as interesting, unless f is unsaturated. If it's saturated and f hasn't inlined, then it's probably not going to now! Note [Conlike is interesting] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider f d = ...((*) d x y)... ... f (df d')... where df is con-like. Then we'd really like to inline 'f' so that the rule for (*) (df d) can fire. To do this a) we give a discount for being an argument of a class-op (eg (*) d) b) we say that a con-like argument (eg (df d)) is interesting \begin{code}

    data ArgSummary = TrivArg	-- Nothing interesting
         		| NonTrivArg	-- Arg has structure
    		| ValueArg	-- Arg is a con-app or PAP
    		  		-- ..or con-like. Note [Conlike is interesting]

    interestingArg :: CoreExpr -> ArgSummary
    -- See Note [Interesting arguments]
    interestingArg e = go e 0
      where
        -- n is # value args to which the expression is applied
        go (Lit {}) _   	   = ValueArg
        go (Var v)  n
           | isConLikeId v     = ValueArg	-- Experimenting with 'conlike' rather that
           	 	     	     		--    data constructors here
           | idArity v > n	   = ValueArg	-- Catches (eg) primops with arity but no unfolding
           | n > 0	           = NonTrivArg	-- Saturated or unknown call
           | conlike_unfolding = ValueArg	-- n==0; look for an interesting unfolding
                                            -- See Note [Conlike is interesting]
           | otherwise	   = TrivArg	-- n==0, no useful unfolding
           where
             conlike_unfolding = isConLikeUnfolding (idUnfolding v)

        go (Type _)          _ = TrivArg
        go (App fn (Type _)) n = go fn n
        go (App fn _)        n = go fn (n+1)
        go (Note _ a) 	 n = go a n
        go (Cast e _) 	 n = go e n
        go (Lam v e)  	 n
           | isTyCoVar v	   = go e n
           | n>0	 	   = go e (n-1)
           | otherwise	   = ValueArg
        go (Let _ e)  	 n = case go e n of { ValueArg -> ValueArg; _ -> NonTrivArg }
        go (Case {})  	 _ = NonTrivArg

    nonTriv ::  ArgSummary -> Bool
    nonTriv TrivArg = False
    nonTriv _       = True

\end{code} %************************************************************************ %* * exprIsConApp_maybe %* * %************************************************************************ Note [exprIsConApp_maybe] ~~~~~~~~~~~~~~~~~~~~~~~~~ exprIsConApp_maybe is a very important function. There are two principal uses: * case e of { .... } * cls_op e, where cls_op is a class operation In both cases you want to know if e is of form (C e1..en) where C is a data constructor. However e might not *look* as if \begin{code}

    -- | Returns @Just (dc, [t1..tk], [x1..xn])@ if the argument expression is
    -- a *saturated* constructor application of the form @dc t1..tk x1 .. xn@,
    -- where t1..tk are the *universally-qantified* type args of 'dc'
    exprIsConApp_maybe :: IdUnfoldingFun -> CoreExpr -> Maybe (DataCon, [Type], [CoreExpr])

    exprIsConApp_maybe id_unf (Note note expr)
      | notSccNote note
      = exprIsConApp_maybe id_unf expr
    	-- We ignore all notes except SCCs.  For example,
    	--  	case _scc_ "foo" (C a b) of
    	--			C a b -> e
    	-- should not be optimised away, because we'll lose the
    	-- entry count on 'foo'; see Trac #4414

    exprIsConApp_maybe id_unf (Cast expr co)
      =     -- Here we do the KPush reduction rule as described in the FC paper
    	-- The transformation applies iff we have
    	--	(C e1 ... en) `cast` co
    	-- where co :: (T t1 .. tn) ~ to_ty
    	-- The left-hand one must be a T, because exprIsConApp returned True
    	-- but the right-hand one might not be.  (Though it usually will.)

        case exprIsConApp_maybe id_unf expr of {
    	Nothing 	                 -> Nothing ;
    	Just (dc, _dc_univ_args, dc_args) ->

        let (_from_ty, to_ty) = coercionKind co
    	dc_tc = dataConTyCon dc
        in
        case splitTyConApp_maybe to_ty of {
    	Nothing -> Nothing ;
    	Just (to_tc, to_tc_arg_tys)
    		| dc_tc /= to_tc -> Nothing
    		-- These two Nothing cases are possible; we might see
    		--	(C x y) `cast` (g :: T a ~ S [a]),
    		-- where S is a type function.  In fact, exprIsConApp
    		-- will probably not be called in such circumstances,
    		-- but there't nothing wrong with it

    	 	| otherwise  ->
        let
    	tc_arity       = tyConArity dc_tc
    	dc_univ_tyvars = dataConUnivTyVars dc
            dc_ex_tyvars   = dataConExTyVars dc
            arg_tys        = dataConRepArgTys dc

            dc_eqs :: [(Type,Type)]	  -- All equalities from the DataCon
            dc_eqs = [(mkTyVarTy tv, ty)   | (tv,ty) <- dataConEqSpec dc] ++
                     [getEqPredTys eq_pred | eq_pred <- dataConEqTheta dc]

            (ex_args, rest1)    = splitAtList dc_ex_tyvars dc_args
    	(co_args, val_args) = splitAtList dc_eqs rest1

    	-- Make the "theta" from Fig 3 of the paper
            gammas = decomposeCo tc_arity co
            theta  = zipOpenTvSubst (dc_univ_tyvars ++ dc_ex_tyvars)
                                    (gammas         ++ stripTypeArgs ex_args)

              -- Cast the existential coercion arguments
            cast_co (ty1, ty2) (Type co)
              = Type $ mkSymCoercion (substTy theta ty1)
    		   `mkTransCoercion` co
    		   `mkTransCoercion` (substTy theta ty2)
            cast_co _ other_arg = pprPanic "cast_co" (ppr other_arg)
            new_co_args = zipWith cast_co dc_eqs co_args

              -- Cast the value arguments (which include dictionaries)
    	new_val_args = zipWith cast_arg arg_tys val_args
    	cast_arg arg_ty arg = mkCoerce (substTy theta arg_ty) arg
        in
    #ifdef DEBUG
        let dump_doc = vcat [ppr dc,      ppr dc_univ_tyvars, ppr dc_ex_tyvars,
                             ppr arg_tys, ppr dc_args,        ppr _dc_univ_args,
                             ppr ex_args, ppr val_args]
        in
        ASSERT2( coreEqType _from_ty (mkTyConApp dc_tc _dc_univ_args), dump_doc )
        ASSERT2( all isTypeArg (ex_args ++ co_args), dump_doc )
        ASSERT2( equalLength val_args arg_tys, dump_doc )
    #endif

        Just (dc, to_tc_arg_tys, ex_args ++ new_co_args ++ new_val_args)
        }}

    exprIsConApp_maybe id_unf expr
      = analyse expr []
      where
        analyse (App fun arg) args = analyse fun (arg:args)
        analyse fun@(Lam {})  args = beta fun [] args

        analyse (Var fun) args
    	| Just con <- isDataConWorkId_maybe fun
            , count isValArg args == idArity fun
    	, let (univ_ty_args, rest_args) = splitAtList (dataConUnivTyVars con) args
    	= Just (con, stripTypeArgs univ_ty_args, rest_args)

    	-- Look through dictionary functions; see Note [Unfolding DFuns]
            | DFunUnfolding dfun_nargs con ops <- unfolding
            , let sat = length args == dfun_nargs    -- See Note [DFun arity check]
              in if sat then True else
                 pprTrace "Unsaturated dfun" (ppr fun <+> int dfun_nargs $$ ppr args) False
            , let (dfun_tvs, _cls, dfun_res_tys) = tcSplitDFunTy (idType fun)
                  subst    = zipOpenTvSubst dfun_tvs (stripTypeArgs (takeList dfun_tvs args))
                  mk_arg (DFunConstArg e) = e
                  mk_arg (DFunLamArg i)   = args !! i
                  mk_arg (DFunPolyArg e)  = mkApps e args
            = Just (con, substTys subst dfun_res_tys, map mk_arg ops)

    	-- Look through unfoldings, but only cheap ones, because
    	-- we are effectively duplicating the unfolding
    	| Just rhs <- expandUnfolding_maybe unfolding
    	= -- pprTrace "expanding" (ppr fun $$ ppr rhs) $
              analyse rhs args
            where
    	  unfolding = id_unf fun

        analyse _ _ = Nothing

        -----------
        beta (Lam v body) pairs (arg : args)
            | isTypeArg arg
            = beta body ((v,arg):pairs) args

        beta (Lam {}) _ _    -- Un-saturated, or not a type lambda
    	= Nothing

        beta fun pairs args
            = analyse (substExpr (text "subst-expr-is-con-app") subst fun) args
            where
              subst = mkOpenSubst (mkInScopeSet (exprFreeVars fun)) pairs
    	  -- doc = vcat [ppr fun, ppr expr, ppr pairs, ppr args]

    stripTypeArgs :: [CoreExpr] -> [Type]
    stripTypeArgs args = ASSERT2( all isTypeArg args, ppr args )
                         [ty | Type ty <- args]

\end{code} Note [Unfolding DFuns] ~~~~~~~~~~~~~~~~~~~~~~ DFuns look like df :: forall a b. (Eq a, Eq b) -> Eq (a,b) df a b d_a d_b = MkEqD (a,b) ($c1 a b d_a d_b) ($c2 a b d_a d_b) So to split it up we just need to apply the ops $c1, $c2 etc to the very same args as the dfun. It takes a little more work to compute the type arguments to the dictionary constructor. Note [DFun arity check] ~~~~~~~~~~~~~~~~~~~~~~~ Here we check that the total number of supplied arguments (inclding type args) matches what the dfun is expecting. This may be *less* than the ordinary arity of the dfun: see Note [DFun unfoldings] in CoreSyn