    {-
    (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.
    -}

    {-# LANGUAGE CPP #-}
    module SetLevels (
            setLevels,

            Level(..), tOP_LEVEL,
            LevelledBind, LevelledExpr, LevelledBndr,
            FloatSpec(..), floatSpecLevel,

            incMinorLvl, ltMajLvl, ltLvl, isTopLvl
        ) where

    #include "HsVersions.h"

    import CoreSyn
    import CoreMonad        ( FloatOutSwitches(..) )
    import CoreUtils        ( exprType, exprOkForSpeculation, exprIsBottom )
    import CoreArity        ( exprBotStrictness_maybe )
    import CoreFVs          -- all of it
    import Coercion         ( isCoVar )
    import CoreSubst        ( Subst, emptySubst, substBndrs, substRecBndrs,
                              extendIdSubst, extendSubstWithVar, cloneBndrs,
                              cloneRecIdBndrs, substTy, substCo, substVarSet )
    import MkCore           ( sortQuantVars )
    import Id
    import IdInfo
    import Var
    import VarSet
    import VarEnv
    import Literal          ( litIsTrivial )
    import Demand           ( StrictSig )
    import Name             ( getOccName, mkSystemVarName )
    import OccName          ( occNameString )
    import Type             ( isUnLiftedType, Type, mkPiTypes )
    import BasicTypes       ( Arity, RecFlag(..) )
    import UniqSupply
    import Util
    import Outputable
    import FastString

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Level numbers}
    *                                                                      *
    ************************************************************************
    -}

    type LevelledExpr = TaggedExpr FloatSpec
    type LevelledBind = TaggedBind FloatSpec
    type LevelledBndr = TaggedBndr FloatSpec

    data Level = Level Int  -- Major level: number of enclosing value lambdas
                       Int  -- Minor level: number of big-lambda and/or case
                            -- expressions between here and the nearest
                            -- enclosing value lambda

    data FloatSpec
      = FloatMe Level       -- Float to just inside the binding
                            --    tagged with this level
      | StayPut Level       -- Stay where it is; binding is
                            --     tagged with tihs level

    floatSpecLevel :: FloatSpec -> Level
    floatSpecLevel (FloatMe l) = l
    floatSpecLevel (StayPut l) = l

    {-
    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.
    -}

    instance Outputable FloatSpec where
      ppr (FloatMe l) = char 'F' <> ppr l
      ppr (StayPut l) = ppr l

    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

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Main level-setting code}
    *                                                                      *
    ************************************************************************
    -}

    setLevels :: FloatOutSwitches
              -> CoreProgram
              -> 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 bndr rhs)
      = do { rhs' <- lvlExpr env (freeVars rhs)
           ; let (env', [bndr']) = substAndLvlBndrs NonRecursive env tOP_LEVEL [bndr]
           ; return (NonRec bndr' rhs', env') }

    lvlTopBind env (Rec pairs)
      = do let (bndrs,rhss) = unzip pairs
               (env', bndrs') = substAndLvlBndrs Recursive env tOP_LEVEL bndrs
           rhss' <- mapM (lvlExpr env' . freeVars) rhss
           return (Rec (bndrs' `zip` rhss'), env')

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Setting expression levels}
    *                                                                      *
    ************************************************************************

    Note [Floating over-saturated applications]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    If we see (f x y), and (f x) is a redex (ie f's arity is 1),
    we call (f x) an "over-saturated application"

    Should we float out an over-sat app, if can escape a value lambda?
    It is sometimes very beneficial (-7% runtime -4% alloc over nofib -O2).
    But we don't want to do it for class selectors, because the work saved
    is minimal, and the extra local thunks allocated cost money.

    Arguably we could float even class-op applications if they were going to
    top level -- but then they must be applied to a constant dictionary and
    will almost certainly be optimised away anyway.
    -}

    lvlExpr :: LevelEnv             -- Context
            -> CoreExprWithFVs      -- Input expression
            -> LvlM LevelledExpr    -- Result expression

    {-
    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.
    -}

    lvlExpr env (_, AnnType ty)     = return (Type (substTy (le_subst env) ty))
    lvlExpr env (_, AnnCoercion co) = return (Coercion (substCo (le_subst env) co))
    lvlExpr env (_, AnnVar v)       = return (lookupVar env v)
    lvlExpr _   (_, AnnLit lit)     = return (Lit lit)

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

    lvlExpr env (_, AnnTick tickish expr) = do
        expr' <- lvlExpr env expr
        return (Tick tickish expr')

    lvlExpr env expr@(_, AnnApp _ _) = do
        let
          (fun, args) = collectAnnArgs expr
        --
        case fun of
          (_, AnnVar f) | floatOverSat env   -- See Note [Floating over-saturated applications]
                        , arity > 0
                        , arity < n_val_args
                        , Nothing <- isClassOpId_maybe f ->
            do
             let (lapp, rargs) = left (n_val_args - arity) expr []
             rargs' <- mapM (lvlMFE False env) rargs
             lapp' <- lvlMFE False 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 env) args
             fun'  <- lvlExpr env fun
             return (foldl App fun' args')

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

    lvlExpr env expr@(_, AnnLam {})
      = do { new_body <- lvlMFE True new_env body
           ; return (mkLams new_bndrs new_body) }
      where
        (bndrs, body)        = collectAnnBndrs expr
        (env1, bndrs1)       = substBndrsSL NonRecursive env bndrs
        (new_env, new_bndrs) = lvlLamBndrs env1 (le_ctxt_lvl env) bndrs1
            -- 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 env (_, AnnLet bind body)
      = do { (bind', new_env) <- lvlBind env bind
           ; body' <- lvlExpr new_env body
               -- No point in going via lvlMFE here.  If the binding is alive
               -- (mentioned in body), and the whole let-expression doesn't
               -- float, then neither will the body
           ; return (Let bind' body') }

    lvlExpr env (_, AnnCase scrut@(scrut_fvs,_) case_bndr ty alts)
      = do { scrut' <- lvlMFE True env scrut
           ; lvlCase env scrut_fvs scrut' case_bndr ty alts }

    -------------------------------------------
    lvlCase :: LevelEnv             -- Level of in-scope names/tyvars
            -> VarSet               -- Free vars of input scrutinee
            -> LevelledExpr         -- Processed scrutinee
            -> Id -> Type           -- Case binder and result type
            -> [AnnAlt Id VarSet]   -- Input alternatives
            -> LvlM LevelledExpr    -- Result expression
    lvlCase env scrut_fvs scrut' case_bndr ty alts
      | [(con@(DataAlt {}), bs, body)] <- alts
      , exprOkForSpeculation scrut'   -- See Note [Check the output scrutinee for okForSpec]
      , not (isTopLvl dest_lvl)       -- Can't have top-level cases
      =     -- See Note [Floating cases]
            -- Always float the case if possible
            -- Unlike lets we don't insist that it escapes a value lambda
        do { (rhs_env, (case_bndr':bs')) <- cloneVars NonRecursive env dest_lvl (case_bndr:bs)
                       -- We don't need to use extendCaseBndrLvlEnv here
                       -- because we are floating the case outwards so
                       -- no need to do the binder-swap thing
           ; body' <- lvlMFE True rhs_env body
           ; let alt' = (con, [TB b (StayPut dest_lvl) | b <- bs'], body')
           ; return (Case scrut' (TB case_bndr' (FloatMe dest_lvl)) ty [alt']) }

      | otherwise     -- Stays put
      = do { let (alts_env1, [case_bndr']) = substAndLvlBndrs NonRecursive env incd_lvl [case_bndr]
                 alts_env = extendCaseBndrEnv alts_env1 case_bndr scrut'
           ; alts' <- mapM (lvl_alt alts_env) alts
           ; return (Case scrut' case_bndr' ty alts') }
      where
          incd_lvl = incMinorLvl (le_ctxt_lvl env)
          dest_lvl = maxFvLevel (const True) env scrut_fvs
                  -- Don't abstact over type variables, hence const True

          lvl_alt alts_env (con, bs, rhs)
            = do { rhs' <- lvlMFE True new_env rhs
                 ; return (con, bs', rhs') }
            where
              (new_env, bs') = substAndLvlBndrs NonRecursive alts_env incd_lvl bs

    {-
    Note [Floating cases]
    ~~~~~~~~~~~~~~~~~~~~~
    Consider this:
      data T a = MkT !a
      f :: T Int -> blah
      f x vs = case x of { MkT y ->
                 let f vs = ...(case y of I# w -> e)...f..
                 in f vs
    Here we can float the (case y ...) out , because y is sure
    to be evaluated, to give
      f x vs = case x of { MkT y ->
               caes y of I# w ->
                 let f vs = ...(e)...f..
                 in f vs

    That saves unboxing it every time round the loop.  It's important in
    some DPH stuff where we really want to avoid that repeated unboxing in
    the inner loop.

    Things to note
     * We can't float a case to top level
     * It's worth doing this float even if we don't float
       the case outside a value lambda.  Example
         case x of {
           MkT y -> (case y of I# w2 -> ..., case y of I# w2 -> ...)
       If we floated the cases out we could eliminate one of them.
     * We only do this with a single-alternative case

    Note [Check the output scrutinee for okForSpec]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider this:
      case x of y {
        A -> ....(case y of alts)....
      }
    Because of the binder-swap, the inner case will get substituted to
    (case x of ..).  So when testing whether the scrutinee is
    okForSpecuation we must be careful to test the *result* scrutinee ('x'
    in this case), not the *input* one 'y'.  The latter *is* ok for
    speculation here, but the former is not -- and indeed we can't float
    the inner case out, at least not unless x is also evaluated at its
    binding site.

    That's why we apply exprOkForSpeculation to scrut' and not to scrut.
    -}

    lvlMFE ::  Bool                 -- True <=> strict context [body of case or let]
            -> LevelEnv             -- Level of in-scope names/tyvars
            -> CoreExprWithFVs      -- input expression
            -> LvlM LevelledExpr    -- Result expression
    -- lvlMFE is just like lvlExpr, except that it might let-bind
    -- the expression, so that it can itself be floated.

    lvlMFE _ env (_, AnnType ty)
      = return (Type (substTy (le_subst env) 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 env (_, AnnTick t e)
      = do { e' <- lvlMFE strict_ctxt env e
           ; return (Tick t e') }

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

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

    lvlMFE strict_ctxt env ann_expr@(fvs, _)
      |  isUnLiftedType (exprType expr)
             -- Can't let-bind it; see Note [Unlifted MFEs]
             -- This includes coercions, which we don't want to float anyway
             -- NB: no need to substitute cos isUnLiftedType doesn't change
      || notWorthFloating ann_expr abs_vars
      || not float_me
      =     -- Don't float it out
        lvlExpr env ann_expr

      | otherwise   -- Float it out!
      = do { expr' <- lvlFloatRhs abs_vars dest_lvl env ann_expr
           ; var   <- newLvlVar expr' is_bot
           ; return (Let (NonRec (TB var (FloatMe dest_lvl)) expr')
                         (mkVarApps (Var var) abs_vars)) }
      where
        expr     = deAnnotate ann_expr
        is_bot   = exprIsBottom expr      -- Note [Bottoming floats]
        dest_lvl = destLevel env fvs (isFunction ann_expr) is_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.
        float_me = dest_lvl `ltMajLvl` (le_ctxt_lvl env)    -- Escapes a value lambda
                    -- OLD CODE: not (exprIsCheap expr) || isTopLvl dest_lvl
                    --           see Note [Escaping 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
              --    lvl    = /\ a -> foldr ..a.. (++) []
              --    concat = /\ a -> lvl a
              -- which is pretty stupid.  Hence the strict_ctxt test
              --
              -- Also a strict contxt includes uboxed values, and they
              -- can't be bound at top level

    {-
    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, *immediately*, for two reasons:

      * To prevent the abstracted thing being immediately inlined back in again
        via preInlineUnconditionally.  The latter has a test for bottoming Ids
        to stop inlining them, so we'd better make sure it *is* a 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.
    -}

    annotateBotStr :: Id -> Maybe (Arity, StrictSig) -> Id
    -- See Note [Bottoming floats] for why we want to add
    -- bottoming information right now
    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 lit) n   = ASSERT( n==0 )
                                 litIsTrivial lit   -- Note [Floating literals]
        go (_, AnnTick t e) n  = not (tickishIsCode t) && go e n
        go (_, AnnCast e _)  n = go e n
        go (_, AnnApp e arg) n
           | (_, AnnType {}) <- arg = go e n
           | (_, AnnCoercion {}) <- 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 (_, AnnApp e (_, AnnCoercion {})) = is_triv e
        is_triv (_, AnnTick t e)              = not (tickishIsCode t) && is_triv e
        is_triv _                             = False

    {-
    Note [Floating literals]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    It's important to float Integer literals, so that they get shared,
    rather than being allocated every time round the loop.
    Hence the litIsTrivial.

    We'd *like* to share MachStr literal strings too, mainly so we could
    CSE them, but alas can't do so directly because they are unlifted.

    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.
    -}

    lvlBind :: LevelEnv
            -> CoreBindWithFVs
            -> LvlM (LevelledBind, LevelEnv)

    lvlBind env (AnnNonRec bndr rhs@(rhs_fvs,_))
      | isTyVar bndr    -- Don't do anything for TyVar binders
                        --   (simplifier gets rid of them pronto)
      || isCoVar bndr   -- Difficult to fix up CoVar occurrences (see extendPolyLvlEnv)
                        -- so we will ignore this case for now
      || not (profitableFloat env dest_lvl)
      || (isTopLvl dest_lvl && isUnLiftedType (idType bndr))
              -- We can't float an unlifted binding to top level, so we don't
              -- float it at all.  It's a bit brutal, but unlifted bindings
              -- aren't expensive either
      = -- No float
        do { rhs' <- lvlExpr env rhs
           ; let  bind_lvl        = incMinorLvl (le_ctxt_lvl env)
                  (env', [bndr']) = substAndLvlBndrs NonRecursive env bind_lvl [bndr]
           ; return (NonRec bndr' rhs', env') }

      -- Otherwise we are going to float
      | null abs_vars
      = do {  -- No type abstraction; clone existing binder
             rhs' <- lvlExpr (setCtxtLvl env dest_lvl) rhs
           ; (env', [bndr']) <- cloneVars NonRecursive env dest_lvl [bndr]
           ; return (NonRec (TB bndr' (FloatMe 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]
           ; return (NonRec (TB bndr' (FloatMe 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) is_bot
        is_bot     = exprIsBottom (deAnnotate rhs)

    lvlBind env (AnnRec pairs)
      | not (profitableFloat env dest_lvl)
      = do { let bind_lvl = incMinorLvl (le_ctxt_lvl env)
                 (env', bndrs') = substAndLvlBndrs Recursive env bind_lvl bndrs
           ; rhss' <- mapM (lvlExpr env') rhss
           ; return (Rec (bndrs' `zip` rhss'), env') }

      | null abs_vars
      = do { (new_env, new_bndrs) <- cloneVars Recursive env dest_lvl bndrs
           ; new_rhss <- mapM (lvlExpr (setCtxtLvl new_env dest_lvl)) rhss
           ; return ( Rec ([TB b (FloatMe dest_lvl) | b <- new_bndrs] `zip` new_rhss)
                    , new_env) }

    -- ToDo: when enabling the floatLambda stuff,
    --       I think we want to stop doing this
      | [(bndr,rhs)] <- 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 (rhs_env, abs_vars_w_lvls) = lvlLamBndrs env dest_lvl abs_vars
            rhs_lvl = le_ctxt_lvl rhs_env

        (rhs_env', [new_bndr]) <- cloneVars Recursive rhs_env rhs_lvl [bndr]
        let
            (lam_bndrs, rhs_body)   = collectAnnBndrs rhs
            (body_env1, lam_bndrs1) = substBndrsSL NonRecursive rhs_env' lam_bndrs
            (body_env2, lam_bndrs2) = lvlLamBndrs body_env1 rhs_lvl lam_bndrs1
        new_rhs_body <- lvlExpr body_env2 rhs_body
        (poly_env, [poly_bndr]) <- newPolyBndrs dest_lvl env abs_vars [bndr]
        return (Rec [(TB poly_bndr (FloatMe dest_lvl)
                     , mkLams abs_vars_w_lvls $
                       mkLams lam_bndrs2 $
                       Let (Rec [( TB new_bndr (StayPut rhs_lvl)
                                 , mkLams lam_bndrs2 new_rhs_body)])
                           (mkVarApps (Var new_bndr) lam_bndrs1))]
               , poly_env)

      | otherwise  -- Non-null abs_vars
      = do { (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 (FloatMe 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) False
        abs_vars = abstractVars dest_lvl env bind_fvs

    profitableFloat :: LevelEnv -> Level -> Bool
    profitableFloat env dest_lvl
      =  (dest_lvl `ltMajLvl` le_ctxt_lvl env)  -- Escapes a value lambda
      || isTopLvl dest_lvl                      -- Going all the way to top level

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

    lvlFloatRhs :: [OutVar] -> Level -> LevelEnv -> CoreExprWithFVs
                -> UniqSM (Expr LevelledBndr)
    lvlFloatRhs abs_vars dest_lvl env rhs
      = do { rhs' <- lvlExpr rhs_env rhs
           ; return (mkLams abs_vars_w_lvls rhs') }
      where
        (rhs_env, abs_vars_w_lvls) = lvlLamBndrs env dest_lvl abs_vars

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Deciding floatability}
    *                                                                      *
    ************************************************************************
    -}

    substAndLvlBndrs :: RecFlag -> LevelEnv -> Level -> [InVar] -> (LevelEnv, [LevelledBndr])
    substAndLvlBndrs is_rec env lvl bndrs
      = lvlBndrs subst_env lvl subst_bndrs
      where
        (subst_env, subst_bndrs) = substBndrsSL is_rec env bndrs

    substBndrsSL :: RecFlag -> LevelEnv -> [InVar] -> (LevelEnv, [OutVar])
    -- So named only to avoid the name clash with CoreSubst.substBndrs
    substBndrsSL is_rec env@(LE { le_subst = subst, le_env = id_env }) bndrs
      = ( env { le_subst    = subst'
              , le_env      = foldl add_id  id_env (bndrs `zip` bndrs') }
        , bndrs')
      where
        (subst', bndrs') = case is_rec of
                             NonRecursive -> substBndrs    subst bndrs
                             Recursive    -> substRecBndrs subst bndrs

    lvlLamBndrs :: LevelEnv -> Level -> [OutVar] -> (LevelEnv, [LevelledBndr])
    -- Compute the levels for the binders of a lambda group
    lvlLamBndrs env lvl bndrs
      = lvlBndrs env new_lvl bndrs
      where
        new_lvl | any is_major bndrs = incMajorLvl lvl
                | otherwise          = incMinorLvl lvl

        is_major bndr = isId bndr && not (isProbablyOneShotLambda bndr)
           -- The "probably" part says "don't float things out of a
           -- probable one-shot lambda"
           -- See Note [Computing one-shot info] in Demand.lhs

    lvlBndrs :: LevelEnv -> Level -> [CoreBndr] -> (LevelEnv, [LevelledBndr])
    -- The binders returned are exactly the same as the ones passed,
    -- apart from applying the substitution, but they are now paired
    -- with a (StayPut level)
    --
    -- The returned envt has ctxt_lvl updated to the new_lvl
    --
    -- All the new binders get the same level, because
    -- any floating binding is either going to float past
    -- all or none.  We never separate binders.
    lvlBndrs env@(LE { le_lvl_env = lvl_env }) new_lvl bndrs
      = ( env { le_ctxt_lvl = new_lvl
              , le_lvl_env  = foldl add_lvl lvl_env bndrs }
        , lvld_bndrs)
      where
        lvld_bndrs    = [TB bndr (StayPut new_lvl) | bndr <- bndrs]
        add_lvl env v = extendVarEnv env v new_lvl

      -- Destination level is the max Id level of the expression
      -- (We'll abstract the type variables, if any.)
    destLevel :: LevelEnv -> VarSet
              -> Bool   -- True <=> is function
              -> Bool   -- True <=> is bottom
              -> Level
    destLevel env fvs is_function is_bot
      | is_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 = maxFvLevel isId env fvs  -- Max over Ids only; the tyvars
                                             -- will be abstracted

    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 (_, AnnTick _ e)          = isFunction e  -- dubious
    isFunction _                           = False

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

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Free-To-Level Monad}
    *                                                                      *
    ************************************************************************
    -}

    type InVar  = Var   -- Pre  cloning
    type InId   = Id    -- Pre  cloning
    type OutVar = Var   -- Post cloning
    type OutId  = Id    -- Post cloning

    data LevelEnv
      = LE { le_switches :: FloatOutSwitches
           , le_ctxt_lvl :: Level           -- The current level
           , le_lvl_env  :: VarEnv Level    -- Domain is *post-cloned* TyVars and Ids
           , le_subst    :: Subst           -- Domain is pre-cloned TyVars and Ids
                                            -- The Id -> CoreExpr in the Subst is ignored
                                            -- (since we want to substitute a LevelledExpr for
                                            -- an Id via le_env) but we do use the Co/TyVar substs
           , le_env      :: IdEnv ([OutVar], LevelledExpr)  -- Domain is pre-cloned Ids
        }
            -- We clone let- and case-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_ctxt_lvl = tOP_LEVEL
           , 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)

    floatOverSat :: LevelEnv -> Bool
    floatOverSat le = floatOutOverSatApps (le_switches le)

    setCtxtLvl :: LevelEnv -> Level -> LevelEnv
    setCtxtLvl env lvl = env { le_ctxt_lvl = lvl }

    -- extendCaseBndrLvlEnv adds the mapping case-bndr->scrut-var if it can
    -- (see point 4 of the module overview comment)
    extendCaseBndrEnv :: LevelEnv
                      -> Id                 -- Pre-cloned case binder
                      -> Expr LevelledBndr  -- Post-cloned scrutinee
                      -> LevelEnv
    extendCaseBndrEnv le@(LE { le_subst = subst, le_env = id_env })
                      case_bndr (Var scrut_var)
      = le { le_subst   = extendSubstWithVar subst case_bndr scrut_var
           , le_env     = add_id id_env (case_bndr, scrut_var) }
    extendCaseBndrEnv env _ _ = env

    maxFvLevel :: (Var -> Bool) -> LevelEnv -> VarSet -> Level
    maxFvLevel max_me (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
            | max_me out_var = case lookupVarEnv lvl_env out_var of
                                    Just lvl' -> maxLvl lvl' lvl
                                    Nothing   -> lvl
            | otherwise = lvl       -- Ignore some vars depending on max_me

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

    abstractVars :: Level -> LevelEnv -> VarSet -> [OutVar]
            -- 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_subst = subst, le_lvl_env = lvl_env }) in_fvs
      = map zap $ uniq $ sortQuantVars
        [out_var | out_fv  <- varSetElems (substVarSet subst in_fvs)
                 , out_var <- varSetElems (close out_fv)
                 , abstract_me out_var ]
            -- NB: it's important to call abstract_me only on the OutIds the
            -- come from substVarSet (not on fv, which is an InId)
      where
        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

        close :: Var -> VarSet  -- Close over variables free in the type
                                -- Result includes the input variable itself
        close v = foldVarSet (unionVarSet . close)
                             (unitVarSet v)
                             (varTypeTyVars v)

    type LvlM result = UniqSM result

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

    newPolyBndrs :: Level -> LevelEnv -> [OutVar] -> [InId] -> UniqSM (LevelEnv, [OutId])
    -- The envt is extended to bind the new bndrs to dest_lvl, but
    -- the ctxt_lvl is unaffected
    newPolyBndrs dest_lvl
                 env@(LE { le_lvl_env = lvl_env, le_subst = subst, le_env = id_env })
                 abs_vars bndrs
     = ASSERT( all (not . isCoVar) bndrs )   -- What would we add to the CoSubst in this case. No easy answer.
       do { uniqs <- getUniquesM
          ; let new_bndrs = zipWith mk_poly_bndr bndrs uniqs
                bndr_prs  = bndrs `zip` new_bndrs
                env' = env { le_lvl_env = foldl add_lvl   lvl_env new_bndrs
                           , le_subst   = foldl add_subst subst   bndr_prs
                           , le_env     = foldl add_id    id_env  bndr_prs }
          ; return (env', new_bndrs) }
      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)

        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 (substTy subst (idType bndr))

    newLvlVar :: LevelledExpr        -- The RHS of the new binding
              -> Bool                -- Whether it is bottom
              -> LvlM Id
    newLvlVar lvld_rhs is_bot
      = do { uniq <- getUniqueM
           ; return (add_bot_info (mkLocalId (mk_name uniq) rhs_ty)) }
      where
        add_bot_info var  -- We could call annotateBotStr always, but the is_bot
                          -- flag just tells us when we don't need to do so
           | is_bot    = annotateBotStr var (exprBotStrictness_maybe de_tagged_rhs)
           | otherwise = var
        de_tagged_rhs = deTagExpr lvld_rhs
        rhs_ty = exprType de_tagged_rhs
        mk_name uniq = mkSystemVarName uniq (mkFastString "lvl")

    cloneVars :: RecFlag -> LevelEnv -> Level -> [Var] -> LvlM (LevelEnv, [Var])
    -- Works for Ids, TyVars and CoVars
    -- The dest_lvl is attributed to the binders in the new env,
    -- but cloneVars doesn't affect the ctxt_lvl of the incoming env
    cloneVars is_rec
              env@(LE { le_subst = subst, le_lvl_env = lvl_env, le_env = id_env })
              dest_lvl vs
      = do { us <- getUniqueSupplyM
           ; let (subst', vs1) = case is_rec of
                                   NonRecursive -> cloneBndrs      subst us vs
                                   Recursive    -> cloneRecIdBndrs subst us vs
                 vs2  = map zap_demand_info vs1  -- See Note [Zapping the demand info]
                 prs  = vs `zip` vs2
                 env' = env { le_lvl_env = foldl add_lvl lvl_env vs2
                            , le_subst   = subst'
                            , le_env     = foldl add_id id_env prs }

           ; return (env', vs2) }
      where
         add_lvl env v_cloned = extendVarEnv env v_cloned dest_lvl

    add_id :: IdEnv ([Var], LevelledExpr) -> (Var, Var) -> IdEnv ([Var], LevelledExpr)
    add_id id_env (v, v1)
      | isTyVar v = delVarEnv    id_env v
      | otherwise = extendVarEnv id_env v ([v1], ASSERT(not (isCoVar v1)) Var v1)

    zap_demand_info :: Var -> Var
    zap_demand_info v
      | isId v    = zapIdDemandInfo v
      | otherwise = v

    {-
    Note [Zapping the demand info]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    VERY IMPORTANT: we must zap the demand info if the thing is going to
    float out, becuause it may be less demanded than at its original
    binding site.  Eg
       f :: Int -> Int
       f x = let v = 3*4 in v+x
    Here v is strict; but if we float v to top level, it isn't any more.
    -}