% % (c) The GRASP/AQUA Project, Glasgow University, 1992-1998 % \section{SetLevels} *************************** Overview *************************** 1. We attach binding levels to Core bindings, in preparation for floating outwards (@FloatOut@). 2. We also let-ify many expressions (notably case scrutinees), so they will have a fighting chance of being floated sensible. 3. We clone the binders of any floatable let-binding, so that when it is floated out it will be unique. (This used to be done by the simplifier but the latter now only ensures that there's no shadowing; indeed, even that may not be true.) NOTE: this can't be done using the uniqAway idea, because the variable must be unique in the whole program, not just its current scope, because two variables in different scopes may float out to the same top level place NOTE: Very tiresomely, we must apply this substitution to the rules stored inside a variable too. We do *not* clone top-level bindings, because some of them must not change, but we *do* clone bindings that are heading for the top level 4. In the expression case x of wild { p -> ...wild... } we substitute x for wild in the RHS of the case alternatives: case x of wild { p -> ...x... } This means that a sub-expression involving x is not "trapped" inside the RHS. And it's not inconvenient because we already have a substitution. Note that this is EXACTLY BACKWARDS from the what the simplifier does. The simplifier tries to get rid of occurrences of x, in favour of wild, in the hope that there will only be one remaining occurrence of x, namely the scrutinee of the case, and we can inline it. \begin{code}

    module SetLevels (
    	setLevels,

    	Level(..), tOP_LEVEL,
    	LevelledBind, LevelledExpr,

    	incMinorLvl, ltMajLvl, ltLvl, isTopLvl
        ) where

    #include "HsVersions.h"

    import CoreSyn
    import CoreMonad	( FloatOutSwitches(..) )
    import CoreUtils	( exprType, mkPiTypes )
    import CoreArity	( exprBotStrictness_maybe )
    import CoreFVs		-- all of it
    import CoreSubst	( Subst, emptySubst, extendInScope, extendInScopeList,
    			  extendIdSubst, cloneIdBndr, cloneRecIdBndrs )
    import Id
    import IdInfo
    import Var
    import VarSet
    import VarEnv
    import Demand		( StrictSig, increaseStrictSigArity )
    import Name		( getOccName, mkSystemVarName )
    import OccName		( occNameString )
    import Type		( isUnLiftedType, Type )
    import BasicTypes	( TopLevelFlag(..), Arity )
    import UniqSupply
    import Util
    import Outputable
    import FastString

\end{code} %************************************************************************ %* * \subsection{Level numbers} %* * %************************************************************************ \begin{code}

    data Level = Level Int	-- Level number of enclosing lambdas
    	  	   Int	-- Number of big-lambda and/or case expressions between
    			-- here and the nearest enclosing lambda

\end{code} The {\em level number} on a (type-)lambda-bound variable is the nesting depth of the (type-)lambda which binds it. The outermost lambda has level 1, so (Level 0 0) means that the variable is bound outside any lambda. On an expression, it's the maximum level number of its free (type-)variables. On a let(rec)-bound variable, it's the level of its RHS. On a case-bound variable, it's the number of enclosing lambdas. Top-level variables: level~0. Those bound on the RHS of a top-level definition but ``before'' a lambda; e.g., the \tr{x} in (levels shown as ``subscripts'')... \begin{verbatim} a_0 = let b_? = ... in x_1 = ... b ... in ... \end{verbatim} The main function @lvlExpr@ carries a ``context level'' (@ctxt_lvl@). That's meant to be the level number of the enclosing binder in the final (floated) program. If the level number of a sub-expression is less than that of the context, then it might be worth let-binding the sub-expression so that it will indeed float. If you can float to level @Level 0 0@ worth doing so because then your allocation becomes static instead of dynamic. We always start with context @Level 0 0@. Note [FloatOut inside INLINE] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ @InlineCtxt@ very similar to @Level 0 0@, but is used for one purpose: to say "don't float anything out of here". That's exactly what we want for the body of an INLINE, where we don't want to float anything out at all. See notes with lvlMFE below. But, check this out: -- At one time I tried the effect of not float anything out of an InlineMe, -- but it sometimes works badly. For example, consider PrelArr.done. It -- has the form __inline (\d. e) -- where e doesn't mention d. If we float this to -- __inline (let x = e in \d. x) -- things are bad. The inliner doesn't even inline it because it doesn't look -- like a head-normal form. So it seems a lesser evil to let things float. -- In SetLevels we do set the context to (Level 0 0) when we get to an InlineMe -- which discourages floating out. So the conclusion is: don't do any floating at all inside an InlineMe. (In the above example, don't float the {x=e} out of the \d.) One particular case is that of workers: we don't want to float the call to the worker outside the wrapper, otherwise the worker might get inlined into the floated expression, and an importing module won't see the worker at all. \begin{code}

    type LevelledExpr  = TaggedExpr Level
    type LevelledBind  = TaggedBind Level

    tOP_LEVEL :: Level
    tOP_LEVEL   = Level 0 0

    incMajorLvl :: Level -> Level
    incMajorLvl (Level major _) = Level (major + 1) 0

    incMinorLvl :: Level -> Level
    incMinorLvl (Level major minor) = Level major (minor+1)

    maxLvl :: Level -> Level -> Level
    maxLvl l1@(Level maj1 min1) l2@(Level maj2 min2)
      | (maj1 > maj2) || (maj1 == maj2 && min1 > min2) = l1
      | otherwise					   = l2

    ltLvl :: Level -> Level -> Bool
    ltLvl (Level maj1 min1) (Level maj2 min2)
      = (maj1 < maj2) || (maj1 == maj2 && min1 < min2)

    ltMajLvl :: Level -> Level -> Bool
        -- Tells if one level belongs to a difft *lambda* level to another
    ltMajLvl (Level maj1 _) (Level maj2 _) = maj1 < maj2

    isTopLvl :: Level -> Bool
    isTopLvl (Level 0 0) = True
    isTopLvl _           = False

    instance Outputable Level where
      ppr (Level maj min) = hcat [ char '<', int maj, char ',', int min, char '>' ]

    instance Eq Level where
      (Level maj1 min1) == (Level maj2 min2) = maj1 == maj2 && min1 == min2

\end{code} %************************************************************************ %* * \subsection{Main level-setting code} %* * %************************************************************************ \begin{code}

    setLevels :: FloatOutSwitches
    	  -> [CoreBind]
    	  -> UniqSupply
    	  -> [LevelledBind]

    setLevels float_lams binds us
      = initLvl us (do_them init_env binds)
      where
        init_env = initialEnv float_lams

        do_them :: LevelEnv -> [CoreBind] -> LvlM [LevelledBind]
        do_them _ [] = return []
        do_them env (b:bs)
          = do { (lvld_bind, env') <- lvlTopBind env b
               ; lvld_binds <- do_them env' bs
               ; return (lvld_bind : lvld_binds) }

    lvlTopBind :: LevelEnv -> Bind Id -> LvlM (LevelledBind, LevelEnv)
    lvlTopBind env (NonRec binder rhs)
      = lvlBind TopLevel tOP_LEVEL env (AnnNonRec binder (freeVars rhs))
    					-- Rhs can have no free vars!

    lvlTopBind env (Rec pairs)
      = lvlBind TopLevel tOP_LEVEL env (AnnRec [(b,freeVars rhs) | (b,rhs) <- pairs])

\end{code} %************************************************************************ %* * \subsection{Setting expression levels} %* * %************************************************************************ \begin{code}

    lvlExpr :: Level		-- ctxt_lvl: Level of enclosing expression
    	-> LevelEnv		-- Level of in-scope names/tyvars
    	-> CoreExprWithFVs	-- input expression
    	-> LvlM LevelledExpr	-- Result expression

\end{code} The @ctxt_lvl@ is, roughly, the level of the innermost enclosing binder. Here's an example v = \x -> ...\y -> let r = case (..x..) of ..x.. in .. When looking at the rhs of @r@, @ctxt_lvl@ will be 1 because that's the level of @r@, even though it's inside a level-2 @\y@. It's important that @ctxt_lvl@ is 1 and not 2 in @r@'s rhs, because we don't want @lvlExpr@ to turn the scrutinee of the @case@ into an MFE --- because it isn't a *maximal* free expression. If there were another lambda in @r@'s rhs, it would get level-2 as well. \begin{code}

    lvlExpr _ _ (  _, AnnType ty) = return (Type ty)
    lvlExpr _ env (_, AnnVar v)   = return (lookupVar env v)
    lvlExpr _ _   (_, AnnLit lit) = return (Lit lit)

    lvlExpr ctxt_lvl env expr@(_, AnnApp _ _) = do
        let
          (fun, args) = collectAnnArgs expr
        --
        case fun of
             -- float out partial applications.  This is very beneficial
             -- in some cases (-7% runtime -4% alloc over nofib -O2).
             -- In order to float a PAP, there must be a function at the
             -- head of the application, and the application must be
             -- over-saturated with respect to the function's arity.
          (_, AnnVar f) | floatPAPs env &&
                          arity > 0 && arity < n_val_args ->
            do
             let (lapp, rargs) = left (n_val_args - arity) expr []
             rargs' <- mapM (lvlMFE False ctxt_lvl env) rargs
             lapp' <- lvlMFE False ctxt_lvl env lapp
             return (foldl App lapp' rargs')
            where
             n_val_args = count (isValArg . deAnnotate) args
             arity = idArity f

             -- separate out the PAP that we are floating from the extra
             -- arguments, by traversing the spine until we have collected
             -- (n_val_args - arity) value arguments.
             left 0 e               rargs = (e, rargs)
             left n (_, AnnApp f a) rargs
                | isValArg (deAnnotate a) = left (n-1) f (a:rargs)
                | otherwise               = left n     f (a:rargs)
             left _ _ _                   = panic "SetLevels.lvlExpr.left"

             -- No PAPs that we can float: just carry on with the
             -- arguments and the function.
          _otherwise -> do
             args' <- mapM (lvlMFE False ctxt_lvl env) args
             fun'  <- lvlExpr ctxt_lvl env fun
             return (foldl App fun' args')

    lvlExpr ctxt_lvl env (_, AnnNote note expr) = do
        expr' <- lvlExpr ctxt_lvl env expr
        return (Note note expr')

    lvlExpr ctxt_lvl env (_, AnnCast expr co) = do
        expr' <- lvlExpr ctxt_lvl env expr
        return (Cast expr' co)

    -- We don't split adjacent lambdas.  That is, given
    --	\x y -> (x+1,y)
    -- we don't float to give
    --	\x -> let v = x+y in \y -> (v,y)
    -- Why not?  Because partial applications are fairly rare, and splitting
    -- lambdas makes them more expensive.

    lvlExpr ctxt_lvl env expr@(_, AnnLam {}) = do
        new_body <- lvlMFE True new_lvl new_env body
        return (mkLams new_bndrs new_body)
      where
        (bndrs, body)	 = collectAnnBndrs expr
        (new_lvl, new_bndrs) = lvlLamBndrs ctxt_lvl bndrs
        new_env 		 = extendLvlEnv env new_bndrs
    	-- At one time we called a special verion of collectBinders,
    	-- which ignored coercions, because we don't want to split
    	-- a lambda like this (\x -> coerce t (\s -> ...))
    	-- This used to happen quite a bit in state-transformer programs,
    	-- but not nearly so much now non-recursive newtypes are transparent.
    	-- [See SetLevels rev 1.50 for a version with this approach.]

    lvlExpr ctxt_lvl env (_, AnnLet (AnnNonRec bndr rhs) body)
      | isUnLiftedType (idType bndr) = do
    	-- Treat unlifted let-bindings (let x = b in e) just like (case b of x -> e)
    	-- That is, leave it exactly where it is
    	-- We used to float unlifted bindings too (e.g. to get a cheap primop
    	-- outside a lambda (to see how, look at lvlBind in rev 1.58)
    	-- but an unrelated change meant that these unlifed bindings
    	-- could get to the top level which is bad.  And there's not much point;
    	-- unlifted bindings are always cheap, and so hardly worth floating.
        rhs'  <- lvlExpr ctxt_lvl env rhs
        body' <- lvlExpr incd_lvl env' body
        return (Let (NonRec bndr' rhs') body')
      where
        incd_lvl = incMinorLvl ctxt_lvl
        bndr' = TB bndr incd_lvl
        env'  = extendLvlEnv env [bndr']

    lvlExpr ctxt_lvl env (_, AnnLet bind body) = do
        (bind', new_env) <- lvlBind NotTopLevel ctxt_lvl env bind
        body' <- lvlExpr ctxt_lvl new_env body
        return (Let bind' body')

    lvlExpr ctxt_lvl env (_, AnnCase expr case_bndr ty alts) = do
        expr' <- lvlMFE True ctxt_lvl env expr
        let alts_env = extendCaseBndrLvlEnv env expr' case_bndr incd_lvl
        alts' <- mapM (lvl_alt alts_env) alts
        return (Case expr' (TB case_bndr incd_lvl) ty alts')
      where
          incd_lvl  = incMinorLvl ctxt_lvl

          lvl_alt alts_env (con, bs, rhs) = do
              rhs' <- lvlMFE True incd_lvl new_env rhs
              return (con, bs', rhs')
            where
              bs'     = [ TB b incd_lvl | b <- bs ]
              new_env = extendLvlEnv alts_env bs'

\end{code} @lvlMFE@ is just like @lvlExpr@, except that it might let-bind the expression, so that it can itself be floated. Note [Unlifted MFEs] ~~~~~~~~~~~~~~~~~~~~ We don't float unlifted MFEs, which potentially loses big opportunites. For example: \x -> f (h y) where h :: Int -> Int# is expensive. We'd like to float the (h y) outside the \x, but we don't because it's unboxed. Possible solution: box it. Note [Bottoming floats] ~~~~~~~~~~~~~~~~~~~~~~~ If we see f = \x. g (error "urk") we'd like to float the call to error, to get lvl = error "urk" f = \x. g lvl Furthermore, we want to float a bottoming expression even if it has free variables: f = \x. g (let v = h x in error ("urk" ++ v)) Then we'd like to abstact over 'x' can float the whole arg of g: lvl = \x. let v = h x in error ("urk" ++ v) f = \x. g (lvl x) See Maessen's paper 1999 "Bottom extraction: factoring error handling out of functional programs" (unpublished I think). When we do this, we set the strictness and arity of the new bottoming Id, so that it's properly exposed as such in the interface file, even if this is all happening after strictness analysis. Note [Bottoming floats: eta expansion] c.f Note [Bottoming floats] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Tiresomely, though, the simplifier has an invariant that the manifest arity of the RHS should be the same as the arity; but we can't call etaExpand during SetLevels because it works over a decorated form of CoreExpr. So we do the eta expansion later, in FloatOut. Note [Case MFEs] ~~~~~~~~~~~~~~~~ We don't float a case expression as an MFE from a strict context. Why not? Because in doing so we share a tiny bit of computation (the switch) but in exchange we build a thunk, which is bad. This case reduces allocation by 7% in spectral/puzzle (a rather strange benchmark) and 1.2% in real/fem. Doesn't change any other allocation at all. \begin{code}

    lvlMFE ::  Bool			-- True <=> strict context [body of case or let]
    	-> Level		-- Level of innermost enclosing lambda/tylam
    	-> LevelEnv		-- Level of in-scope names/tyvars
    	-> CoreExprWithFVs	-- input expression
    	-> LvlM LevelledExpr	-- Result expression

    lvlMFE _ _ _ (_, AnnType ty)
      = return (Type ty)

    -- No point in floating out an expression wrapped in a coercion or note
    -- If we do we'll transform  lvl = e |> co
    --			 to  lvl' = e; lvl = lvl' |> co
    -- and then inline lvl.  Better just to float out the payload.
    lvlMFE strict_ctxt ctxt_lvl env (_, AnnNote n e)
      = do { e' <- lvlMFE strict_ctxt ctxt_lvl env e
           ; return (Note n e') }

    lvlMFE strict_ctxt ctxt_lvl env (_, AnnCast e co)
      = do	{ e' <- lvlMFE strict_ctxt ctxt_lvl env e
    	; return (Cast e' co) }

    -- Note [Case MFEs]
    lvlMFE True ctxt_lvl env e@(_, AnnCase {})
      = lvlExpr ctxt_lvl env e     -- Don't share cases

    lvlMFE strict_ctxt ctxt_lvl env ann_expr@(fvs, _)
      |  isUnLiftedType ty			-- Can't let-bind it; see Note [Unlifted MFEs]
      || notWorthFloating ann_expr abs_vars
      || not good_destination
      = 	-- Don't float it out
        lvlExpr ctxt_lvl env ann_expr

      | otherwise	-- Float it out!
      = do expr' <- lvlFloatRhs abs_vars dest_lvl env ann_expr
           var <- newLvlVar abs_vars ty mb_bot
           return (Let (NonRec (TB var dest_lvl) expr')
                       (mkVarApps (Var var) abs_vars))
      where
        expr     = deAnnotate ann_expr
        ty       = exprType expr
        mb_bot   = exprBotStrictness_maybe expr
        dest_lvl = destLevel env fvs (isFunction ann_expr) mb_bot
        abs_vars = abstractVars dest_lvl env fvs

    	-- A decision to float entails let-binding this thing, and we only do
    	-- that if we'll escape a value lambda, or will go to the top level.
        good_destination
    	| dest_lvl `ltMajLvl` ctxt_lvl		-- Escapes a value lambda
    	= True
    	-- OLD CODE: not (exprIsCheap expr) || isTopLvl dest_lvl
    	-- 	     see Note [Escaping a value lambda]

    	| otherwise		-- Does not escape a value lambda
    	= isTopLvl dest_lvl 	-- Only float if we are going to the top level
    	&& floatConsts env	--   and the floatConsts flag is on
    	&& not strict_ctxt	-- Don't float from a strict context
    	  -- We are keen to float something to the top level, even if it does not
    	  -- escape a lambda, because then it needs no allocation.  But it's controlled
    	  -- by a flag, because doing this too early loses opportunities for RULES
    	  -- which (needless to say) are important in some nofib programs
    	  -- (gcd is an example).
    	  --
    	  -- Beware:
    	  --	concat = /\ a -> foldr ..a.. (++) []
    	  -- was getting turned into
    	  --	concat = /\ a -> lvl a
    	  --	lvl    = /\ a -> foldr ..a.. (++) []
    	  -- which is pretty stupid.  Hence the strict_ctxt test

    annotateBotStr :: Id -> Maybe (Arity, StrictSig) -> Id
    annotateBotStr id Nothing            = id
    annotateBotStr id (Just (arity,sig)) = id `setIdArity` arity
    				          `setIdStrictness` sig

    notWorthFloating :: CoreExprWithFVs -> [Var] -> Bool
    -- Returns True if the expression would be replaced by
    -- something bigger than it is now.  For example:
    --   abs_vars = tvars only:  return True if e is trivial,
    --                           but False for anything bigger
    --   abs_vars = [x] (an Id): return True for trivial, or an application (f x)
    --   	      	    	     but False for (f x x)
    --
    -- One big goal is that floating should be idempotent.  Eg if
    -- we replace e with (lvl79 x y) and then run FloatOut again, don't want
    -- to replace (lvl79 x y) with (lvl83 x y)!

    notWorthFloating e abs_vars
      = go e (count isId abs_vars)
      where
        go (_, AnnVar {}) n    = n >= 0
        go (_, AnnLit {}) n    = n >= 0
        go (_, AnnCast e _)  n = go e n
        go (_, AnnApp e arg) n
           | (_, AnnType {}) <- arg = go e n
           | n==0                   = False
           | is_triv arg       	= go e (n-1)
           | otherwise         	= False
        go _ _                 	= False

        is_triv (_, AnnLit {})   	       	  = True	-- Treat all literals as trivial
        is_triv (_, AnnVar {})   	       	  = True	-- (ie not worth floating)
        is_triv (_, AnnCast e _) 	       	  = is_triv e
        is_triv (_, AnnApp e (_, AnnType {})) = is_triv e
        is_triv _                             = False

\end{code} Note [Escaping a value lambda] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We want to float even cheap expressions out of value lambdas, because that saves allocation. Consider f = \x. .. (\y.e) ... Then we'd like to avoid allocating the (\y.e) every time we call f, (assuming e does not mention x). An example where this really makes a difference is simplrun009. Another reason it's good is because it makes SpecContr fire on functions. Consider f = \x. ....(f (\y.e)).... After floating we get lvl = \y.e f = \x. ....(f lvl)... and that is much easier for SpecConstr to generate a robust specialisation for. The OLD CODE (given where this Note is referred to) prevents floating of the example above, so I just don't understand the old code. I don't understand the old comment either (which appears below). I measured the effect on nofib of changing OLD CODE to 'True', and got zeros everywhere, but a 4% win for 'puzzle'. Very small 0.5% loss for 'cse'; turns out to be because our arity analysis isn't good enough yet (mentioned in Simon-nofib-notes). OLD comment was: Even if it escapes a value lambda, we only float if it's not cheap (unless it'll get all the way to the top). I've seen cases where we float dozens of tiny free expressions, which cost more to allocate than to evaluate. NB: exprIsCheap is also true of bottom expressions, which is good; we don't want to share them It's only Really Bad to float a cheap expression out of a strict context, because that builds a thunk that otherwise would never be built. So another alternative would be to add || (strict_ctxt && not (exprIsBottom expr)) to the condition above. We should really try this out. %************************************************************************ %* * \subsection{Bindings} %* * %************************************************************************ The binding stuff works for top level too. \begin{code}

    lvlBind :: TopLevelFlag		-- Used solely to decide whether to clone
    	-> Level		-- Context level; might be Top even for bindings nested in the RHS
    				-- of a top level binding
    	-> LevelEnv
    	-> CoreBindWithFVs
    	-> LvlM (LevelledBind, LevelEnv)

    lvlBind top_lvl ctxt_lvl env (AnnNonRec bndr rhs@(rhs_fvs,_))
      |  isTyCoVar bndr 		-- Don't do anything for TyVar binders
    				--   (simplifier gets rid of them pronto)
      = do rhs' <- lvlExpr ctxt_lvl env rhs
           return (NonRec (TB bndr ctxt_lvl) rhs', env)

      | null abs_vars
      = do  -- No type abstraction; clone existing binder
           rhs' <- lvlExpr dest_lvl env rhs
           (env', bndr') <- cloneVar top_lvl env bndr ctxt_lvl dest_lvl
           return (NonRec (TB bndr' dest_lvl) rhs', env')

      | otherwise
      = do  -- Yes, type abstraction; create a new binder, extend substitution, etc
           rhs' <- lvlFloatRhs abs_vars dest_lvl env rhs
           (env', [bndr']) <- newPolyBndrs dest_lvl env abs_vars [bndr_w_str]
           return (NonRec (TB bndr' dest_lvl) rhs', env')

      where
        bind_fvs   = rhs_fvs `unionVarSet` idFreeVars bndr
        abs_vars   = abstractVars dest_lvl env bind_fvs
        dest_lvl   = destLevel env bind_fvs (isFunction rhs) mb_bot
        mb_bot     = exprBotStrictness_maybe (deAnnotate rhs)
        bndr_w_str = annotateBotStr bndr mb_bot

\end{code} \begin{code}

    lvlBind top_lvl ctxt_lvl env (AnnRec pairs)
      | null abs_vars
      = do (new_env, new_bndrs) <- cloneRecVars top_lvl env bndrs ctxt_lvl dest_lvl
           new_rhss <- mapM (lvlExpr ctxt_lvl new_env) rhss
           return (Rec ([TB b dest_lvl | b <- new_bndrs] `zip` new_rhss), new_env)

    -- ToDo: when enabling the floatLambda stuff,
    --       I think we want to stop doing this
      | isSingleton pairs && count isId abs_vars > 1
      = do	-- Special case for self recursion where there are
    	-- several variables carried around: build a local loop:
    	--	poly_f = \abs_vars. \lam_vars . letrec f = \lam_vars. rhs in f lam_vars
    	-- This just makes the closures a bit smaller.  If we don't do
    	-- this, allocation rises significantly on some programs
    	--
    	-- We could elaborate it for the case where there are several
    	-- mutually functions, but it's quite a bit more complicated
    	--
    	-- This all seems a bit ad hoc -- sigh
        let
            (bndr,rhs) = head pairs
            (rhs_lvl, abs_vars_w_lvls) = lvlLamBndrs dest_lvl abs_vars
            rhs_env = extendLvlEnv env abs_vars_w_lvls
        (rhs_env', new_bndr) <- cloneVar NotTopLevel rhs_env bndr rhs_lvl rhs_lvl
        let
            (lam_bndrs, rhs_body)     = collectAnnBndrs rhs
            (body_lvl, new_lam_bndrs) = lvlLamBndrs rhs_lvl lam_bndrs
            body_env                  = extendLvlEnv rhs_env' new_lam_bndrs
        new_rhs_body <- lvlExpr body_lvl body_env rhs_body
        (poly_env, [poly_bndr]) <- newPolyBndrs dest_lvl env abs_vars [bndr]
        return (Rec [(TB poly_bndr dest_lvl,
                   mkLams abs_vars_w_lvls $
                   mkLams new_lam_bndrs $
                   Let (Rec [(TB new_bndr rhs_lvl, mkLams new_lam_bndrs new_rhs_body)])
                       (mkVarApps (Var new_bndr) lam_bndrs))],
                   poly_env)

      | otherwise = do  -- Non-null abs_vars
        (new_env, new_bndrs) <- newPolyBndrs dest_lvl env abs_vars bndrs
        new_rhss <- mapM (lvlFloatRhs abs_vars dest_lvl new_env) rhss
        return (Rec ([TB b dest_lvl | b <- new_bndrs] `zip` new_rhss), new_env)

      where
        (bndrs,rhss) = unzip pairs

    	-- Finding the free vars of the binding group is annoying
        bind_fvs	    = (unionVarSets [ idFreeVars bndr `unionVarSet` rhs_fvs
    				    | (bndr, (rhs_fvs,_)) <- pairs])
    		      `minusVarSet`
    		      mkVarSet bndrs

        dest_lvl = destLevel env bind_fvs (all isFunction rhss) Nothing
        abs_vars = abstractVars dest_lvl env bind_fvs

    ----------------------------------------------------
    -- Three help functions for the type-abstraction case

    lvlFloatRhs :: [CoreBndr] -> Level -> LevelEnv -> CoreExprWithFVs
                -> UniqSM (Expr (TaggedBndr Level))
    lvlFloatRhs abs_vars dest_lvl env rhs = do
        rhs' <- lvlExpr rhs_lvl rhs_env rhs
        return (mkLams abs_vars_w_lvls rhs')
      where
        (rhs_lvl, abs_vars_w_lvls) = lvlLamBndrs dest_lvl abs_vars
        rhs_env = extendLvlEnv env abs_vars_w_lvls

\end{code} %************************************************************************ %* * \subsection{Deciding floatability} %* * %************************************************************************ \begin{code}

    lvlLamBndrs :: Level -> [CoreBndr] -> (Level, [TaggedBndr Level])
    -- Compute the levels for the binders of a lambda group
    -- The binders returned are exactly the same as the ones passed,
    -- but they are now paired with a level
    lvlLamBndrs lvl []
      = (lvl, [])

    lvlLamBndrs lvl bndrs
      = go  (incMinorLvl lvl)
    	False 	-- Havn't bumped major level in this group
    	[] bndrs
      where
        go old_lvl bumped_major rev_lvld_bndrs (bndr:bndrs)
    	| isId bndr &&	    		-- Go to the next major level if this is a value binder,
    	  not bumped_major && 		-- and we havn't already gone to the next level (one jump per group)
    	  not (isOneShotLambda bndr)	-- and it isn't a one-shot lambda
    	= go new_lvl True (TB bndr new_lvl : rev_lvld_bndrs) bndrs

    	| otherwise
    	= go old_lvl bumped_major (TB bndr old_lvl : rev_lvld_bndrs) bndrs

    	where
    	  new_lvl = incMajorLvl old_lvl

        go old_lvl _ rev_lvld_bndrs []
    	= (old_lvl, reverse rev_lvld_bndrs)
    	-- a lambda like this (\x -> coerce t (\s -> ...))
    	-- This happens quite a bit in state-transformer programs

\end{code} \begin{code}

      -- Destintion level is the max Id level of the expression
      -- (We'll abstract the type variables, if any.)
    destLevel :: LevelEnv -> VarSet -> Bool -> Maybe (Arity, StrictSig) -> Level
    destLevel env fvs is_function mb_bot
      | Just {} <- mb_bot = tOP_LEVEL	-- Send bottoming bindings to the top
    					-- regardless; see Note [Bottoming floats]
      | Just n_args <- floatLams env
      , n_args > 0	-- n=0 case handled uniformly by the 'otherwise' case
      , is_function
      , countFreeIds fvs <= n_args
      = tOP_LEVEL	-- Send functions to top level; see
    					-- the comments with isFunction
      | otherwise         = maxIdLevel env fvs

    isFunction :: CoreExprWithFVs -> Bool
    -- The idea here is that we want to float *functions* to
    -- the top level.  This saves no work, but
    --	(a) it can make the host function body a lot smaller,
    --		and hence inlinable.
    --	(b) it can also save allocation when the function is recursive:
    --	    h = \x -> letrec f = \y -> ...f...y...x...
    --		      in f x
    --     becomes
    --	    f = \x y -> ...(f x)...y...x...
    --	    h = \x -> f x x
    --     No allocation for f now.
    -- We may only want to do this if there are sufficiently few free
    -- variables.  We certainly only want to do it for values, and not for
    -- constructors.  So the simple thing is just to look for lambdas
    isFunction (_, AnnLam b e) | isId b    = True
                               | otherwise = isFunction e
    isFunction (_, AnnNote _ e)            = isFunction e
    isFunction _                           = False

    countFreeIds :: VarSet -> Int
    countFreeIds = foldVarSet add 0
      where
        add :: Var -> Int -> Int
        add v n | isId v    = n+1
                | otherwise = n

\end{code} %************************************************************************ %* * \subsection{Free-To-Level Monad} %* * %************************************************************************ \begin{code}

    data LevelEnv
      = LE { le_switches :: FloatOutSwitches
           , le_lvl_env  :: VarEnv Level	-- Domain is *post-cloned* TyVars and Ids
           , le_subst    :: Subst 		-- Domain is pre-cloned Ids; tracks the in-scope set
    					-- 	so that subtitution is capture-avoiding
           , le_env      :: IdEnv ([Var], LevelledExpr)	-- Domain is pre-cloned Ids
        }
    	-- We clone let-bound variables so that they are still
    	-- distinct when floated out; hence the le_subst/le_env.
            -- (see point 3 of the module overview comment).
    	-- We also use these envs when making a variable polymorphic
    	-- because we want to float it out past a big lambda.
    	--
    	-- The le_subst and le_env always implement the same mapping, but the
    	-- le_subst maps to CoreExpr and the le_env to LevelledExpr
    	-- Since the range is always a variable or type application,
    	-- there is never any difference between the two, but sadly
    	-- the types differ.  The le_subst is used when substituting in
    	-- a variable's IdInfo; the le_env when we find a Var.
    	--
    	-- In addition the le_env records a list of tyvars free in the
    	-- type application, just so we don't have to call freeVars on
    	-- the type application repeatedly.
    	--
    	-- The domain of the both envs is *pre-cloned* Ids, though
    	--
    	-- The domain of the le_lvl_env is the *post-cloned* Ids

    initialEnv :: FloatOutSwitches -> LevelEnv
    initialEnv float_lams
      = LE { le_switches = float_lams, le_lvl_env = emptyVarEnv
           , le_subst = emptySubst, le_env = emptyVarEnv }

    floatLams :: LevelEnv -> Maybe Int
    floatLams le = floatOutLambdas (le_switches le)

    floatConsts :: LevelEnv -> Bool
    floatConsts le = floatOutConstants (le_switches le)

    floatPAPs :: LevelEnv -> Bool
    floatPAPs le = floatOutPartialApplications (le_switches le)

    extendLvlEnv :: LevelEnv -> [TaggedBndr Level] -> LevelEnv
    -- Used when *not* cloning
    extendLvlEnv le@(LE { le_lvl_env = lvl_env, le_subst = subst, le_env = id_env })
                 prs
      = le { le_lvl_env = foldl add_lvl lvl_env prs
           , le_subst   = foldl del_subst subst prs
           , le_env     = foldl del_id id_env prs }
      where
        add_lvl   env (TB v l) = extendVarEnv env v l
        del_subst env (TB v _) = extendInScope env v
        del_id    env (TB v _) = delVarEnv env v
      -- We must remove any clone for this variable name in case of
      -- shadowing.  This bit me in the following case
      -- (in nofib/real/gg/Spark.hs):
      --
      --   case ds of wild {
      --     ... -> case e of wild {
      --              ... -> ... wild ...
      --            }
      --   }
      --
      -- The inside occurrence of @wild@ was being replaced with @ds@,
      -- incorrectly, because the SubstEnv was still lying around.  Ouch!
      -- KSW 2000-07.

    extendInScopeEnv :: LevelEnv -> Var -> LevelEnv
    extendInScopeEnv le@(LE { le_subst = subst }) v
      = le { le_subst = extendInScope subst v }

    extendInScopeEnvList :: LevelEnv -> [Var] -> LevelEnv
    extendInScopeEnvList le@(LE { le_subst = subst }) vs
      = le { le_subst = extendInScopeList subst vs }

    -- extendCaseBndrLvlEnv adds the mapping case-bndr->scrut-var if it can
    -- (see point 4 of the module overview comment)
    extendCaseBndrLvlEnv :: LevelEnv -> Expr (TaggedBndr Level) -> Var -> Level
                         -> LevelEnv
    extendCaseBndrLvlEnv le@(LE { le_lvl_env = lvl_env, le_subst = subst, le_env = id_env })
                         (Var scrut_var) case_bndr lvl
      = le { le_lvl_env = extendVarEnv lvl_env case_bndr lvl
           , le_subst   = extendIdSubst subst case_bndr (Var scrut_var)
           , le_env     = extendVarEnv id_env case_bndr ([scrut_var], Var scrut_var) }

    extendCaseBndrLvlEnv env _scrut case_bndr lvl
      = extendLvlEnv env [TB case_bndr lvl]

    extendPolyLvlEnv :: Level -> LevelEnv -> [Var] -> [(Var, Var)] -> LevelEnv
    extendPolyLvlEnv dest_lvl
                     le@(LE { le_lvl_env = lvl_env, le_subst = subst, le_env = id_env })
                     abs_vars bndr_pairs
      = le { le_lvl_env = foldl add_lvl   lvl_env bndr_pairs
           , le_subst   = foldl add_subst subst   bndr_pairs
           , le_env     = foldl add_id    id_env  bndr_pairs }
      where
         add_lvl   env (_, v') = extendVarEnv env v' dest_lvl
         add_subst env (v, v') = extendIdSubst env v (mkVarApps (Var v') abs_vars)
         add_id    env (v, v') = extendVarEnv env v ((v':abs_vars), mkVarApps (Var v') abs_vars)

    extendCloneLvlEnv :: Level -> LevelEnv -> Subst -> [(Var, Var)] -> LevelEnv
    extendCloneLvlEnv lvl le@(LE { le_lvl_env = lvl_env, le_env = id_env })
                      new_subst bndr_pairs
      = le { le_lvl_env = foldl add_lvl   lvl_env bndr_pairs
           , le_subst   = new_subst
           , le_env     =  foldl add_id    id_env  bndr_pairs }
      where
         add_lvl env (_, v') = extendVarEnv env v' lvl
         add_id  env (v, v') = extendVarEnv env v ([v'], Var v')

    maxIdLevel :: LevelEnv -> VarSet -> Level
    maxIdLevel (LE { le_lvl_env = lvl_env, le_env = id_env }) var_set
      = foldVarSet max_in tOP_LEVEL var_set
      where
        max_in in_var lvl = foldr max_out lvl (case lookupVarEnv id_env in_var of
    						Just (abs_vars, _) -> abs_vars
    						Nothing		   -> [in_var])

        max_out out_var lvl
    	| isId out_var = case lookupVarEnv lvl_env out_var of
    				Just lvl' -> maxLvl lvl' lvl
    				Nothing   -> lvl
    	| otherwise    = lvl	-- Ignore tyvars in *maxIdLevel*

    lookupVar :: LevelEnv -> Id -> LevelledExpr
    lookupVar le v = case lookupVarEnv (le_env le) v of
    		    Just (_, expr) -> expr
    		    _              -> Var v

    abstractVars :: Level -> LevelEnv -> VarSet -> [Var]
    	-- Find the variables in fvs, free vars of the target expresion,
    	-- whose level is greater than the destination level
    	-- These are the ones we are going to abstract out
    abstractVars dest_lvl (LE { le_lvl_env = lvl_env, le_env = id_env }) fvs
      = map zap $ uniq $ sortLe le
    	[var | fv <- varSetElems fvs
    	     , var <- absVarsOf id_env fv
    	     , abstract_me var ]
    	-- NB: it's important to call abstract_me only on the OutIds the
    	-- come from absVarsOf (not on fv, which is an InId)
      where
    	-- Sort the variables so the true type variables come first;
    	-- the tyvars scope over Ids and coercion vars
        v1 `le` v2 = case (is_tv v1, is_tv v2) of
    		   (True, False) -> True
    		   (False, True) -> False
    		   _    	 -> v1 <= v2	-- Same family

        is_tv v = isTyCoVar v && not (isCoVar v)

        uniq :: [Var] -> [Var]
    	-- Remove adjacent duplicates; the sort will have brought them together
        uniq (v1:v2:vs) | v1 == v2  = uniq (v2:vs)
    		    | otherwise = v1 : uniq (v2:vs)
        uniq vs = vs

        abstract_me v = case lookupVarEnv lvl_env v of
    			Just lvl -> dest_lvl `ltLvl` lvl
    			Nothing  -> False

    	-- We are going to lambda-abstract, so nuke any IdInfo,
    	-- and add the tyvars of the Id (if necessary)
        zap v | isId v = WARN( isStableUnfolding (idUnfolding v) ||
    		           not (isEmptySpecInfo (idSpecialisation v)),
    		           text "absVarsOf: discarding info on" <+> ppr v )
    		     setIdInfo v vanillaIdInfo
    	  | otherwise = v

    absVarsOf :: IdEnv ([Var], LevelledExpr) -> Var -> [Var]
    	-- If f is free in the expression, and f maps to poly_f a b c in the
    	-- current substitution, then we must report a b c as candidate type
    	-- variables
    	--
    	-- Also, if x::a is an abstracted variable, then so is a; that is,
    	--	we must look in x's type
    	-- And similarly if x is a coercion variable.
    absVarsOf id_env v
      | isId v    = [av2 | av1 <- lookup_avs v
    		     , av2 <- add_tyvars av1]
      | isCoVar v = add_tyvars v
      | otherwise = [v]

      where
        lookup_avs v = case lookupVarEnv id_env v of
    			Just (abs_vars, _) -> abs_vars
    			Nothing	           -> [v]

        add_tyvars v = v : varSetElems (varTypeTyVars v)

\end{code} \begin{code}

    type LvlM result = UniqSM result

    initLvl :: UniqSupply -> UniqSM a -> a
    initLvl = initUs_

\end{code} \begin{code}

    newPolyBndrs :: Level -> LevelEnv -> [Var] -> [Id] -> UniqSM (LevelEnv, [Id])
    newPolyBndrs dest_lvl env abs_vars bndrs = do
        uniqs <- getUniquesM
        let new_bndrs = zipWith mk_poly_bndr bndrs uniqs
        return (extendPolyLvlEnv dest_lvl env abs_vars (bndrs `zip` new_bndrs), new_bndrs)
      where
        mk_poly_bndr bndr uniq = transferPolyIdInfo bndr abs_vars $ 	-- Note [transferPolyIdInfo] in Id.lhs
    			     mkSysLocal (mkFastString str) uniq poly_ty
    			   where
    			     str     = "poly_" ++ occNameString (getOccName bndr)
    			     poly_ty = mkPiTypes abs_vars (idType bndr)

    newLvlVar :: [CoreBndr] -> Type 	-- Abstract wrt these bndrs
    	  -> Maybe (Arity, StrictSig)   -- Note [Bottoming floats]
    	  -> LvlM Id
    newLvlVar vars body_ty mb_bot
      = do { uniq <- getUniqueM
           ; return (mkLocalIdWithInfo (mk_name uniq) (mkPiTypes vars body_ty) info) }
      where
        mk_name uniq = mkSystemVarName uniq (mkFastString "lvl")
        arity = count isId vars
        info = case mb_bot of
    		Nothing               -> vanillaIdInfo
    		Just (bot_arity, sig) -> vanillaIdInfo
    					   `setArityInfo`      (arity + bot_arity)
    					   `setStrictnessInfo` Just (increaseStrictSigArity arity sig)

    -- The deeply tiresome thing is that we have to apply the substitution
    -- to the rules inside each Id.  Grr.  But it matters.

    cloneVar :: TopLevelFlag -> LevelEnv -> Id -> Level -> Level -> LvlM (LevelEnv, Id)
    cloneVar TopLevel env v _ _
      = return (extendInScopeEnv env v, v)	-- Don't clone top level things
    		-- But do extend the in-scope env, to satisfy the in-scope invariant

    cloneVar NotTopLevel env v ctxt_lvl dest_lvl
      = ASSERT( isId v ) do
        us <- getUniqueSupplyM
        let
          (subst', v1) = cloneIdBndr (le_subst env) us v
          v2	   = zap_demand ctxt_lvl dest_lvl v1
          env'	   = extendCloneLvlEnv dest_lvl env subst' [(v,v2)]
        return (env', v2)

    cloneRecVars :: TopLevelFlag -> LevelEnv -> [Id] -> Level -> Level -> LvlM (LevelEnv, [Id])
    cloneRecVars TopLevel env vs _ _
      = return (extendInScopeEnvList env vs, vs)	-- Don't clone top level things
    cloneRecVars NotTopLevel env vs ctxt_lvl dest_lvl
      = ASSERT( all isId vs ) do
        us <- getUniqueSupplyM
        let
          (subst', vs1) = cloneRecIdBndrs (le_subst env) us vs
          vs2	    = map (zap_demand ctxt_lvl dest_lvl) vs1
          env'	    = extendCloneLvlEnv dest_lvl env subst' (vs `zip` vs2)
        return (env', vs2)

    	-- VERY IMPORTANT: we must zap the demand info
    	-- if the thing is going to float out past a lambda,
    	-- or if it's going to top level (where things can't be strict)
    zap_demand :: Level -> Level -> Id -> Id
    zap_demand dest_lvl ctxt_lvl id
      | ctxt_lvl == dest_lvl,
        not (isTopLvl dest_lvl) = id	-- Stays, and not going to top level
      | otherwise		    = zapDemandIdInfo id	-- Floats out

\end{code}