simplCore/OccurAnal.hs

    {-
    (c) The GRASP/AQUA Project, Glasgow University, 1992-1998

    ************************************************************************
    *                                                                      *
    \section[OccurAnal]{Occurrence analysis pass}
    *                                                                      *
    ************************************************************************

    The occurrence analyser re-typechecks a core expression, returning a new
    core expression with (hopefully) improved usage information.
    -}

    {-# LANGUAGE CPP, BangPatterns #-}

    module OccurAnal (
            occurAnalysePgm, occurAnalyseExpr, occurAnalyseExpr_NoBinderSwap
        ) where

    #include "HsVersions.h"

    import CoreSyn
    import CoreFVs
    import CoreUtils        ( exprIsTrivial, isDefaultAlt, isExpandableApp,
                              stripTicksTopE, mkTicks )
    import Id
    import Name( localiseName )
    import BasicTypes
    import Module( Module )
    import Coercion

    import VarSet
    import VarEnv
    import Var
    import Demand           ( argOneShots, argsOneShots )
    import Maybes           ( orElse )
    import Digraph          ( SCC(..), stronglyConnCompFromEdgedVerticesR )
    import Unique
    import UniqFM
    import Util
    import Outputable
    import Data.List
    import Control.Arrow    ( second )

    {-
    ************************************************************************
    *                                                                      *
    \subsection[OccurAnal-main]{Counting occurrences: main function}
    *                                                                      *
    ************************************************************************

    Here's the externally-callable interface:
    -}

    occurAnalysePgm :: Module       -- Used only in debug output
                    -> (Activation -> Bool)
                    -> [CoreRule] -> [CoreVect] -> VarSet
                    -> CoreProgram -> CoreProgram
    occurAnalysePgm this_mod active_rule imp_rules vects vectVars binds
      | isEmptyVarEnv final_usage
      = occ_anald_binds

      | otherwise   -- See Note [Glomming]
      = WARN( True, hang (text "Glomming in" <+> ppr this_mod <> colon)
                       2 (ppr final_usage ) )
        occ_anald_glommed_binds
      where
        init_env = initOccEnv active_rule
        (final_usage, occ_anald_binds) = go init_env binds
        (_, occ_anald_glommed_binds)   = occAnalRecBind init_env imp_rule_edges
                                                        (flattenBinds occ_anald_binds)
                                                        initial_uds
              -- It's crucial to re-analyse the glommed-together bindings
              -- so that we establish the right loop breakers. Otherwise
              -- we can easily create an infinite loop (Trac #9583 is an example)

        initial_uds = addIdOccs emptyDetails
                                (rulesFreeVars imp_rules `unionVarSet`
                                 vectsFreeVars vects `unionVarSet`
                                 vectVars)
        -- The RULES and VECTORISE declarations keep things alive! (For VECTORISE declarations,
        -- we only get them *until* the vectoriser runs. Afterwards, these dependencies are
        -- reflected in 'vectors' — see Note [Vectorisation declarations and occurrences].)

        -- Note [Preventing loops due to imported functions rules]
        imp_rule_edges = foldr (plusVarEnv_C unionVarSet) emptyVarEnv
                                [ mapVarEnv (const maps_to) (exprFreeIds arg `delVarSetList` ru_bndrs imp_rule)
                                | imp_rule <- imp_rules
                                , let maps_to = exprFreeIds (ru_rhs imp_rule)
                                                 `delVarSetList` ru_bndrs imp_rule
                                , arg <- ru_args imp_rule ]

        go :: OccEnv -> [CoreBind] -> (UsageDetails, [CoreBind])
        go _ []
            = (initial_uds, [])
        go env (bind:binds)
            = (final_usage, bind' ++ binds')
            where
               (bs_usage, binds')   = go env binds
               (final_usage, bind') = occAnalBind env imp_rule_edges bind bs_usage

    occurAnalyseExpr :: CoreExpr -> CoreExpr
            -- Do occurrence analysis, and discard occurrence info returned
    occurAnalyseExpr = occurAnalyseExpr' True -- do binder swap

    occurAnalyseExpr_NoBinderSwap :: CoreExpr -> CoreExpr
    occurAnalyseExpr_NoBinderSwap = occurAnalyseExpr' False -- do not do binder swap

    occurAnalyseExpr' :: Bool -> CoreExpr -> CoreExpr
    occurAnalyseExpr' enable_binder_swap expr
      = snd (occAnal env expr)
      where
        env = (initOccEnv all_active_rules) {occ_binder_swap = enable_binder_swap}
        -- To be conservative, we say that all inlines and rules are active
        all_active_rules = \_ -> True

    {-
    ************************************************************************
    *                                                                      *
    \subsection[OccurAnal-main]{Counting occurrences: main function}
    *                                                                      *
    ************************************************************************

    Bindings
    ~~~~~~~~
    -}

    type ImpRuleEdges = IdEnv IdSet     -- Mapping from FVs of imported RULE LHSs to RHS FVs

    noImpRuleEdges :: ImpRuleEdges
    noImpRuleEdges = emptyVarEnv

    occAnalBind :: OccEnv           -- The incoming OccEnv
                -> ImpRuleEdges
                -> CoreBind
                -> UsageDetails             -- Usage details of scope
                -> (UsageDetails,           -- Of the whole let(rec)
                    [CoreBind])

    occAnalBind env top_env (NonRec binder rhs) body_usage
      = occAnalNonRecBind env top_env binder rhs body_usage
    occAnalBind env top_env (Rec pairs) body_usage
      = occAnalRecBind env top_env pairs body_usage

    -----------------
    occAnalNonRecBind :: OccEnv -> ImpRuleEdges -> Var -> CoreExpr
                      -> UsageDetails -> (UsageDetails, [CoreBind])
    occAnalNonRecBind env imp_rule_edges binder rhs body_usage
      | isTyVar binder      -- A type let; we don't gather usage info
      = (body_usage, [NonRec binder rhs])

      | not (binder `usedIn` body_usage)    -- It's not mentioned
      = (body_usage, [])

      | otherwise                   -- It's mentioned in the body
      = (body_usage' +++ rhs_usage4, [NonRec tagged_binder rhs'])
      where
        (body_usage', tagged_binder) = tagBinder body_usage binder
        (rhs_usage1, rhs')           = occAnalNonRecRhs env tagged_binder rhs
        rhs_usage2 = addIdOccs rhs_usage1 (idUnfoldingVars binder)

        rhs_usage3 = addIdOccs rhs_usage2 (idRuleVars binder)
           -- See Note [Rules are extra RHSs] and Note [Rule dependency info]

        rhs_usage4 = maybe rhs_usage3 (addIdOccs rhs_usage3) $
                     lookupVarEnv imp_rule_edges binder
           -- See Note [Preventing loops due to imported functions rules]

    -----------------
    occAnalRecBind :: OccEnv -> ImpRuleEdges -> [(Var,CoreExpr)]
                   -> UsageDetails -> (UsageDetails, [CoreBind])
    occAnalRecBind env imp_rule_edges pairs body_usage
      = foldr occAnalRec (body_usage, []) sccs
            -- For a recursive group, we
            --      * occ-analyse all the RHSs
            --      * compute strongly-connected components
            --      * feed those components to occAnalRec
      where
        bndr_set = mkVarSet (map fst pairs)

        sccs :: [SCC (Node Details)]
        sccs = {-# SCC "occAnalBind.scc" #-} stronglyConnCompFromEdgedVerticesR nodes

        nodes :: [Node Details]
        nodes = {-# SCC "occAnalBind.assoc" #-} map (makeNode env imp_rule_edges bndr_set) pairs

    {-
    Note [Dead code]
    ~~~~~~~~~~~~~~~~
    Dropping dead code for a cyclic Strongly Connected Component is done
    in a very simple way:

            the entire SCC is dropped if none of its binders are mentioned
            in the body; otherwise the whole thing is kept.

    The key observation is that dead code elimination happens after
    dependency analysis: so 'occAnalBind' processes SCCs instead of the
    original term's binding groups.

    Thus 'occAnalBind' does indeed drop 'f' in an example like

            letrec f = ...g...
                   g = ...(...g...)...
            in
               ...g...

    when 'g' no longer uses 'f' at all (eg 'f' does not occur in a RULE in
    'g'). 'occAnalBind' first consumes 'CyclicSCC g' and then it consumes
    'AcyclicSCC f', where 'body_usage' won't contain 'f'.

    ------------------------------------------------------------
    Note [Forming Rec groups]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    We put bindings {f = ef; g = eg } in a Rec group if "f uses g"
    and "g uses f", no matter how indirectly.  We do a SCC analysis
    with an edge f -> g if "f uses g".

    More precisely, "f uses g" iff g should be in scope wherever f is.
    That is, g is free in:
      a) the rhs 'ef'
      b) or the RHS of a rule for f (Note [Rules are extra RHSs])
      c) or the LHS or a rule for f (Note [Rule dependency info])

    These conditions apply regardless of the activation of the RULE (eg it might be
    inactive in this phase but become active later).  Once a Rec is broken up
    it can never be put back together, so we must be conservative.

    The principle is that, regardless of rule firings, every variable is
    always in scope.

      * Note [Rules are extra RHSs]
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~
        A RULE for 'f' is like an extra RHS for 'f'. That way the "parent"
        keeps the specialised "children" alive.  If the parent dies
        (because it isn't referenced any more), then the children will die
        too (unless they are already referenced directly).

        To that end, we build a Rec group for each cyclic strongly
        connected component,
            *treating f's rules as extra RHSs for 'f'*.
        More concretely, the SCC analysis runs on a graph with an edge
        from f -> g iff g is mentioned in
            (a) f's rhs
            (b) f's RULES
        These are rec_edges.

        Under (b) we include variables free in *either* LHS *or* RHS of
        the rule.  The former might seems silly, but see Note [Rule
        dependency info].  So in Example [eftInt], eftInt and eftIntFB
        will be put in the same Rec, even though their 'main' RHSs are
        both non-recursive.

      * Note [Rule dependency info]
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~
        The VarSet in a RuleInfo is used for dependency analysis in the
        occurrence analyser.  We must track free vars in *both* lhs and rhs.
        Hence use of idRuleVars, rather than idRuleRhsVars in occAnalBind.
        Why both? Consider
            x = y
            RULE f x = v+4
        Then if we substitute y for x, we'd better do so in the
        rule's LHS too, so we'd better ensure the RULE appears to mention 'x'
        as well as 'v'

      * Note [Rules are visible in their own rec group]
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        We want the rules for 'f' to be visible in f's right-hand side.
        And we'd like them to be visible in other functions in f's Rec
        group.  E.g. in Note [Specialisation rules] we want f' rule
        to be visible in both f's RHS, and fs's RHS.

        This means that we must simplify the RULEs first, before looking
        at any of the definitions.  This is done by Simplify.simplRecBind,
        when it calls addLetIdInfo.

    ------------------------------------------------------------
    Note [Choosing loop breakers]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Loop breaking is surprisingly subtle.  First read the section 4 of
    "Secrets of the GHC inliner".  This describes our basic plan.
    We avoid infinite inlinings by choosing loop breakers, and
    ensuring that a loop breaker cuts each loop.

    Fundamentally, we do SCC analysis on a graph.  For each recursive
    group we choose a loop breaker, delete all edges to that node,
    re-analyse the SCC, and iterate.

    But what is the graph?  NOT the same graph as was used for Note
    [Forming Rec groups]!  In particular, a RULE is like an equation for
    'f' that is *always* inlined if it is applicable.  We do *not* disable
    rules for loop-breakers.  It's up to whoever makes the rules to make
    sure that the rules themselves always terminate.  See Note [Rules for
    recursive functions] in Simplify.hs

    Hence, if
        f's RHS (or its INLINE template if it has one) mentions g, and
        g has a RULE that mentions h, and
        h has a RULE that mentions f

    then we *must* choose f to be a loop breaker.  Example: see Note
    [Specialisation rules].

    In general, take the free variables of f's RHS, and augment it with
    all the variables reachable by RULES from those starting points.  That
    is the whole reason for computing rule_fv_env in occAnalBind.  (Of
    course we only consider free vars that are also binders in this Rec
    group.)  See also Note [Finding rule RHS free vars]

    Note that when we compute this rule_fv_env, we only consider variables
    free in the *RHS* of the rule, in contrast to the way we build the
    Rec group in the first place (Note [Rule dependency info])

    Note that if 'g' has RHS that mentions 'w', we should add w to
    g's loop-breaker edges.  More concretely there is an edge from f -> g
    iff
            (a) g is mentioned in f's RHS `xor` f's INLINE rhs
                (see Note [Inline rules])
            (b) or h is mentioned in f's RHS, and
                g appears in the RHS of an active RULE of h
                or a transitive sequence of active rules starting with h

    Why "active rules"?  See Note [Finding rule RHS free vars]

    Note that in Example [eftInt], *neither* eftInt *nor* eftIntFB is
    chosen as a loop breaker, because their RHSs don't mention each other.
    And indeed both can be inlined safely.

    Note again that the edges of the graph we use for computing loop breakers
    are not the same as the edges we use for computing the Rec blocks.
    That's why we compute

    - rec_edges          for the Rec block analysis
    - loop_breaker_edges for the loop breaker analysis

      * Note [Finding rule RHS free vars]
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        Consider this real example from Data Parallel Haskell
             tagZero :: Array Int -> Array Tag
             {-# INLINE [1] tagZeroes #-}
             tagZero xs = pmap (\x -> fromBool (x==0)) xs

             {-# RULES "tagZero" [~1] forall xs n.
                 pmap fromBool <blah blah> = tagZero xs #-}
        So tagZero's RHS mentions pmap, and pmap's RULE mentions tagZero.
        However, tagZero can only be inlined in phase 1 and later, while
        the RULE is only active *before* phase 1.  So there's no problem.

        To make this work, we look for the RHS free vars only for
        *active* rules. That's the reason for the occ_rule_act field
        of the OccEnv.

      * Note [Weak loop breakers]
        ~~~~~~~~~~~~~~~~~~~~~~~~~
        There is a last nasty wrinkle.  Suppose we have

            Rec { f = f_rhs
                  RULE f [] = g

                  h = h_rhs
                  g = h
                  ...more...
            }

        Remember that we simplify the RULES before any RHS (see Note
        [Rules are visible in their own rec group] above).

        So we must *not* postInlineUnconditionally 'g', even though
        its RHS turns out to be trivial.  (I'm assuming that 'g' is
        not choosen as a loop breaker.)  Why not?  Because then we
        drop the binding for 'g', which leaves it out of scope in the
        RULE!

        Here's a somewhat different example of the same thing
            Rec { g = h
                ; h = ...f...
                ; f = f_rhs
                  RULE f [] = g }
        Here the RULE is "below" g, but we *still* can't postInlineUnconditionally
        g, because the RULE for f is active throughout.  So the RHS of h
        might rewrite to     h = ...g...
        So g must remain in scope in the output program!

        We "solve" this by:

            Make g a "weak" loop breaker (OccInfo = IAmLoopBreaker True)
            iff g is a "missing free variable" of the Rec group

        A "missing free variable" x is one that is mentioned in an RHS or
        INLINE or RULE of a binding in the Rec group, but where the
        dependency on x may not show up in the loop_breaker_edges (see
        note [Choosing loop breakers} above).

        A normal "strong" loop breaker has IAmLoopBreaker False.  So

                                        Inline  postInlineUnconditionally
       strong   IAmLoopBreaker False    no      no
       weak     IAmLoopBreaker True     yes     no
                other                   yes     yes

        The **sole** reason for this kind of loop breaker is so that
        postInlineUnconditionally does not fire.  Ugh.  (Typically it'll
        inline via the usual callSiteInline stuff, so it'll be dead in the
        next pass, so the main Ugh is the tiresome complication.)

    Note [Rules for imported functions]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider this
       f = /\a. B.g a
       RULE B.g Int = 1 + f Int
    Note that
      * The RULE is for an imported function.
      * f is non-recursive
    Now we
    can get
       f Int --> B.g Int      Inlining f
             --> 1 + f Int    Firing RULE
    and so the simplifier goes into an infinite loop. This
    would not happen if the RULE was for a local function,
    because we keep track of dependencies through rules.  But
    that is pretty much impossible to do for imported Ids.  Suppose
    f's definition had been
       f = /\a. C.h a
    where (by some long and devious process), C.h eventually inlines to
    B.g.  We could only spot such loops by exhaustively following
    unfoldings of C.h etc, in case we reach B.g, and hence (via the RULE)
    f.

    Note that RULES for imported functions are important in practice; they
    occur a lot in the libraries.

    We regard this potential infinite loop as a *programmer* error.
    It's up the programmer not to write silly rules like
         RULE f x = f x
    and the example above is just a more complicated version.

    Note [Preventing loops due to imported functions rules]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider:
      import GHC.Base (foldr)

      {-# RULES "filterList" forall p. foldr (filterFB (:) p) [] = filter p #-}
      filter p xs = build (\c n -> foldr (filterFB c p) n xs)
      filterFB c p = ...

      f = filter p xs

    Note that filter is not a loop-breaker, so what happens is:
      f =          filter p xs
        = {inline} build (\c n -> foldr (filterFB c p) n xs)
        = {inline} foldr (filterFB (:) p) [] xs
        = {RULE}   filter p xs

    We are in an infinite loop.

    A more elaborate example (that I actually saw in practice when I went to
    mark GHC.List.filter as INLINABLE) is as follows. Say I have this module:
      {-# LANGUAGE RankNTypes #-}
      module GHCList where

      import Prelude hiding (filter)
      import GHC.Base (build)

      {-# INLINABLE filter #-}
      filter :: (a -> Bool) -> [a] -> [a]
      filter p [] = []
      filter p (x:xs) = if p x then x : filter p xs else filter p xs

      {-# NOINLINE [0] filterFB #-}
      filterFB :: (a -> b -> b) -> (a -> Bool) -> a -> b -> b
      filterFB c p x r | p x       = x `c` r
                       | otherwise = r

      {-# RULES
      "filter"     [~1] forall p xs.  filter p xs = build (\c n -> foldr
      (filterFB c p) n xs)
      "filterList" [1]  forall p.     foldr (filterFB (:) p) [] = filter p
       #-}

    Then (because RULES are applied inside INLINABLE unfoldings, but inlinings
    are not), the unfolding given to "filter" in the interface file will be:
      filter p []     = []
      filter p (x:xs) = if p x then x : build (\c n -> foldr (filterFB c p) n xs)
                               else     build (\c n -> foldr (filterFB c p) n xs

    Note that because this unfolding does not mention "filter", filter is not
    marked as a strong loop breaker. Therefore at a use site in another module:
      filter p xs
        = {inline}
          case xs of []     -> []
                     (x:xs) -> if p x then x : build (\c n -> foldr (filterFB c p) n xs)
                                      else     build (\c n -> foldr (filterFB c p) n xs)

      build (\c n -> foldr (filterFB c p) n xs)
        = {inline} foldr (filterFB (:) p) [] xs
        = {RULE}   filter p xs

    And we are in an infinite loop again, except that this time the loop is producing an
    infinitely large *term* (an unrolling of filter) and so the simplifier finally
    dies with "ticks exhausted"

    Because of this problem, we make a small change in the occurrence analyser
    designed to mark functions like "filter" as strong loop breakers on the basis that:
      1. The RHS of filter mentions the local function "filterFB"
      2. We have a rule which mentions "filterFB" on the LHS and "filter" on the RHS

    So for each RULE for an *imported* function we are going to add
    dependency edges between the *local* FVS of the rule LHS and the
    *local* FVS of the rule RHS. We don't do anything special for RULES on
    local functions because the standard occurrence analysis stuff is
    pretty good at getting loop-breakerness correct there.

    It is important to note that even with this extra hack we aren't always going to get
    things right. For example, it might be that the rule LHS mentions an imported Id,
    and another module has a RULE that can rewrite that imported Id to one of our local
    Ids.

    Note [Specialising imported functions]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    BUT for *automatically-generated* rules, the programmer can't be
    responsible for the "programmer error" in Note [Rules for imported
    functions].  In paricular, consider specialising a recursive function
    defined in another module.  If we specialise a recursive function B.g,
    we get
             g_spec = .....(B.g Int).....
             RULE B.g Int = g_spec
    Here, g_spec doesn't look recursive, but when the rule fires, it
    becomes so.  And if B.g was mutually recursive, the loop might
    not be as obvious as it is here.

    To avoid this,
     * When specialising a function that is a loop breaker,
       give a NOINLINE pragma to the specialised function

    Note [Glomming]
    ~~~~~~~~~~~~~~~
    RULES for imported Ids can make something at the top refer to something at the bottom:
            f = \x -> B.g (q x)
            h = \y -> 3

            RULE:  B.g (q x) = h x

    Applying this rule makes f refer to h, although f doesn't appear to
    depend on h.  (And, as in Note [Rules for imported functions], the
    dependency might be more indirect. For example, f might mention C.t
    rather than B.g, where C.t eventually inlines to B.g.)

    NOTICE that this cannot happen for rules whose head is a
    locally-defined function, because we accurately track dependencies
    through RULES.  It only happens for rules whose head is an imported
    function (B.g in the example above).

    Solution:
      - When simplifying, bring all top level identifiers into
        scope at the start, ignoring the Rec/NonRec structure, so
        that when 'h' pops up in f's rhs, we find it in the in-scope set
        (as the simplifier generally expects). This happens in simplTopBinds.

      - In the occurrence analyser, if there are any out-of-scope
        occurrences that pop out of the top, which will happen after
        firing the rule:      f = \x -> h x
                              h = \y -> 3
        then just glom all the bindings into a single Rec, so that
        the *next* iteration of the occurrence analyser will sort
        them all out.   This part happens in occurAnalysePgm.

    ------------------------------------------------------------
    Note [Inline rules]
    ~~~~~~~~~~~~~~~~~~~
    None of the above stuff about RULES applies to Inline Rules,
    stored in a CoreUnfolding.  The unfolding, if any, is simplified
    at the same time as the regular RHS of the function (ie *not* like
    Note [Rules are visible in their own rec group]), so it should be
    treated *exactly* like an extra RHS.

    Or, rather, when computing loop-breaker edges,
      * If f has an INLINE pragma, and it is active, we treat the
        INLINE rhs as f's rhs
      * If it's inactive, we treat f as having no rhs
      * If it has no INLINE pragma, we look at f's actual rhs

    There is a danger that we'll be sub-optimal if we see this
         f = ...f...
         [INLINE f = ..no f...]
    where f is recursive, but the INLINE is not. This can just about
    happen with a sufficiently odd set of rules; eg

            foo :: Int -> Int
            {-# INLINE [1] foo #-}
            foo x = x+1

            bar :: Int -> Int
            {-# INLINE [1] bar #-}
            bar x = foo x + 1

            {-# RULES "foo" [~1] forall x. foo x = bar x #-}

    Here the RULE makes bar recursive; but it's INLINE pragma remains
    non-recursive. It's tempting to then say that 'bar' should not be
    a loop breaker, but an attempt to do so goes wrong in two ways:
       a) We may get
             $df = ...$cfoo...
             $cfoo = ...$df....
             [INLINE $cfoo = ...no-$df...]
          But we want $cfoo to depend on $df explicitly so that we
          put the bindings in the right order to inline $df in $cfoo
          and perhaps break the loop altogether.  (Maybe this
       b)

    Example [eftInt]
    ~~~~~~~~~~~~~~~
    Example (from GHC.Enum):

      eftInt :: Int# -> Int# -> [Int]
      eftInt x y = ...(non-recursive)...

      {-# INLINE [0] eftIntFB #-}
      eftIntFB :: (Int -> r -> r) -> r -> Int# -> Int# -> r
      eftIntFB c n x y = ...(non-recursive)...

      {-# RULES
      "eftInt"  [~1] forall x y. eftInt x y = build (\ c n -> eftIntFB c n x y)
      "eftIntList"  [1] eftIntFB  (:) [] = eftInt
       #-}

    Note [Specialisation rules]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider this group, which is typical of what SpecConstr builds:

       fs a = ....f (C a)....
       f  x = ....f (C a)....
       {-# RULE f (C a) = fs a #-}

    So 'f' and 'fs' are in the same Rec group (since f refers to fs via its RULE).

    But watch out!  If 'fs' is not chosen as a loop breaker, we may get an infinite loop:
      - the RULE is applied in f's RHS (see Note [Self-recursive rules] in Simplify
      - fs is inlined (say it's small)
      - now there's another opportunity to apply the RULE

    This showed up when compiling Control.Concurrent.Chan.getChanContents.
    -}

    type Node details = (details, Unique, [Unique]) -- The Ints are gotten from the Unique,
                                                    -- which is gotten from the Id.
    data Details
      = ND { nd_bndr :: Id          -- Binder
           , nd_rhs  :: CoreExpr    -- RHS, already occ-analysed

           , nd_uds  :: UsageDetails  -- Usage from RHS, and RULES, and stable unfoldings
                                      -- ignoring phase (ie assuming all are active)
                                      -- See Note [Forming Rec groups]

           , nd_inl  :: IdSet       -- Free variables of
                                    --   the stable unfolding (if present and active)
                                    --   or the RHS (if not)
                                    -- but excluding any RULES
                                    -- This is the IdSet that may be used if the Id is inlined

           , nd_weak :: IdSet       -- Binders of this Rec that are mentioned in nd_uds
                                    -- but are *not* in nd_inl.  These are the ones whose
                                    -- dependencies might not be respected by loop_breaker_edges
                                    -- See Note [Weak loop breakers]

           , nd_active_rule_fvs :: IdSet   -- Free variables of the RHS of active RULES
      }

    instance Outputable Details where
       ppr nd = text "ND" <> braces
                 (sep [ text "bndr =" <+> ppr (nd_bndr nd)
                      , text "uds =" <+> ppr (nd_uds nd)
                      , text "inl =" <+> ppr (nd_inl nd)
                      , text "weak =" <+> ppr (nd_weak nd)
                      , text "rule =" <+> ppr (nd_active_rule_fvs nd)
                 ])

    makeNode :: OccEnv -> ImpRuleEdges -> VarSet -> (Var, CoreExpr) -> Node Details
    makeNode env imp_rule_edges bndr_set (bndr, rhs)
      = (details, varUnique bndr, keysUFM node_fvs)
      where
        details = ND { nd_bndr = bndr
                     , nd_rhs  = rhs'
                     , nd_uds  = rhs_usage3
                     , nd_weak = node_fvs `minusVarSet` inl_fvs
                     , nd_inl  = inl_fvs
                     , nd_active_rule_fvs = active_rule_fvs }

        -- Constructing the edges for the main Rec computation
        -- See Note [Forming Rec groups]
        (rhs_usage1, rhs') = occAnalRecRhs env rhs
        rhs_usage2 = addIdOccs rhs_usage1 all_rule_fvs   -- Note [Rules are extra RHSs]
                                                         -- Note [Rule dependency info]
        rhs_usage3 = case mb_unf_fvs of
                       Just unf_fvs -> addIdOccs rhs_usage2 unf_fvs
                       Nothing      -> rhs_usage2
        node_fvs = udFreeVars bndr_set rhs_usage3

        -- Finding the free variables of the rules
        is_active = occ_rule_act env :: Activation -> Bool
        rules = filterOut isBuiltinRule (idCoreRules bndr)
        rules_w_fvs :: [(Activation, VarSet)]    -- Find the RHS fvs
        rules_w_fvs = maybe id (\ids -> ((AlwaysActive, ids):)) (lookupVarEnv imp_rule_edges bndr)
                       -- See Note [Preventing loops due to imported functions rules]
                      [ (ru_act rule, fvs)
                      | rule <- rules
                      , let fvs = exprFreeVars (ru_rhs rule)
                                  `delVarSetList` ru_bndrs rule
                      , not (isEmptyVarSet fvs) ]
        all_rule_fvs = rule_lhs_fvs `unionVarSet` rule_rhs_fvs
        rule_rhs_fvs = mapUnionVarSet snd rules_w_fvs
        rule_lhs_fvs = mapUnionVarSet (\ru -> exprsFreeVars (ru_args ru)
                                              `delVarSetList` ru_bndrs ru) rules
        active_rule_fvs = unionVarSets [fvs | (a,fvs) <- rules_w_fvs, is_active a]

        -- Finding the free variables of the INLINE pragma (if any)
        unf        = realIdUnfolding bndr     -- Ignore any current loop-breaker flag
        mb_unf_fvs = stableUnfoldingVars unf

        -- Find the "nd_inl" free vars; for the loop-breaker phase
        inl_fvs = case mb_unf_fvs of
                    Nothing -> udFreeVars bndr_set rhs_usage1 -- No INLINE, use RHS
                    Just unf_fvs -> unf_fvs
                          -- We could check for an *active* INLINE (returning
                          -- emptyVarSet for an inactive one), but is_active
                          -- isn't the right thing (it tells about
                          -- RULE activation), so we'd need more plumbing

    -----------------------------
    occAnalRec :: SCC (Node Details)
               -> (UsageDetails, [CoreBind])
               -> (UsageDetails, [CoreBind])

            -- The NonRec case is just like a Let (NonRec ...) above
    occAnalRec (AcyclicSCC (ND { nd_bndr = bndr, nd_rhs = rhs, nd_uds = rhs_uds}, _, _))
               (body_uds, binds)
      | not (bndr `usedIn` body_uds)
      = (body_uds, binds)           -- See Note [Dead code]

      | otherwise                   -- It's mentioned in the body
      = (body_uds' +++ rhs_uds,
         NonRec tagged_bndr rhs : binds)
      where
        (body_uds', tagged_bndr) = tagBinder body_uds bndr

            -- The Rec case is the interesting one
            -- See Note [Loop breaking]
    occAnalRec (CyclicSCC nodes) (body_uds, binds)
      | not (any (`usedIn` body_uds) bndrs) -- NB: look at body_uds, not total_uds
      = (body_uds, binds)                   -- See Note [Dead code]

      | otherwise   -- At this point we always build a single Rec
      = -- pprTrace "occAnalRec" (vcat
        --   [ text "tagged nodes" <+> ppr tagged_nodes
        --   , text "lb edges" <+> ppr loop_breaker_edges])
        (final_uds, Rec pairs : binds)

      where
        bndrs    = [b | (ND { nd_bndr = b }, _, _) <- nodes]
        bndr_set = mkVarSet bndrs

            ----------------------------
            -- Tag the binders with their occurrence info
        tagged_nodes = map tag_node nodes
        total_uds = foldl add_uds body_uds nodes
        final_uds = total_uds `minusVarEnv` bndr_set
        add_uds usage_so_far (nd, _, _) = usage_so_far +++ nd_uds nd

        tag_node :: Node Details -> Node Details
        tag_node (details@ND { nd_bndr = bndr }, k, ks)
          | let bndr1 = setBinderOcc total_uds bndr
          = (details { nd_bndr = bndr1 }, k, ks)

        ---------------------------
        -- Now reconstruct the cycle
        pairs :: [(Id,CoreExpr)]
        pairs | isEmptyVarSet weak_fvs = reOrderNodes   0 bndr_set weak_fvs tagged_nodes       []
              | otherwise              = loopBreakNodes 0 bndr_set weak_fvs loop_breaker_edges []
              -- If weak_fvs is empty, the loop_breaker_edges will include all
              -- the edges in tagged_nodes, so there isn't any point in doing
              -- a fresh SCC computation that will yield a single CyclicSCC result.

        weak_fvs :: VarSet
        weak_fvs = mapUnionVarSet (nd_weak . fstOf3) nodes

            -- See Note [Choosing loop breakers] for loop_breaker_edges
        loop_breaker_edges = map mk_node tagged_nodes
        mk_node (details@(ND { nd_inl = inl_fvs }), k, _)
          = (details, k, keysUFM (extendFvs_ rule_fv_env inl_fvs))

        ------------------------------------
        rule_fv_env :: IdEnv IdSet
            -- Maps a variable f to the variables from this group
            --      mentioned in RHS of active rules for f
            -- Domain is *subset* of bound vars (others have no rule fvs)
        rule_fv_env = transClosureFV (mkVarEnv init_rule_fvs)
        init_rule_fvs   -- See Note [Finding rule RHS free vars]
          = [ (b, trimmed_rule_fvs)
            | (ND { nd_bndr = b, nd_active_rule_fvs = rule_fvs },_,_) <- nodes
            , let trimmed_rule_fvs = rule_fvs `intersectVarSet` bndr_set
            , not (isEmptyVarSet trimmed_rule_fvs)]

    {-
    @loopBreakSCC@ is applied to the list of (binder,rhs) pairs for a cyclic
    strongly connected component (there's guaranteed to be a cycle).  It returns the
    same pairs, but
            a) in a better order,
            b) with some of the Ids having a IAmALoopBreaker pragma

    The "loop-breaker" Ids are sufficient to break all cycles in the SCC.  This means
    that the simplifier can guarantee not to loop provided it never records an inlining
    for these no-inline guys.

    Furthermore, the order of the binds is such that if we neglect dependencies
    on the no-inline Ids then the binds are topologically sorted.  This means
    that the simplifier will generally do a good job if it works from top bottom,
    recording inlinings for any Ids which aren't marked as "no-inline" as it goes.
    -}

    type Binding = (Id,CoreExpr)

    mk_loop_breaker :: Node Details -> Binding
    mk_loop_breaker (ND { nd_bndr = bndr, nd_rhs = rhs}, _, _)
      = (setIdOccInfo bndr strongLoopBreaker, rhs)

    mk_non_loop_breaker :: VarSet -> Node Details -> Binding
    -- See Note [Weak loop breakers]
    mk_non_loop_breaker used_in_rules (ND { nd_bndr = bndr, nd_rhs = rhs}, _, _)
      | bndr `elemVarSet` used_in_rules = (setIdOccInfo bndr weakLoopBreaker, rhs)
      | otherwise                       = (bndr, rhs)

    udFreeVars :: VarSet -> UsageDetails -> VarSet
    -- Find the subset of bndrs that are mentioned in uds
    udFreeVars bndrs uds = intersectUFM_C (\b _ -> b) bndrs uds

    loopBreakNodes :: Int
                   -> VarSet        -- All binders
                   -> VarSet        -- Binders whose dependencies may be "missing"
                                    -- See Note [Weak loop breakers]
                   -> [Node Details]
                   -> [Binding]             -- Append these to the end
                   -> [Binding]
    -- Return the bindings sorted into a plausible order, and marked with loop breakers.
    loopBreakNodes depth bndr_set weak_fvs nodes binds
      = go (stronglyConnCompFromEdgedVerticesR nodes) binds
      where
        go []         binds = binds
        go (scc:sccs) binds = loop_break_scc scc (go sccs binds)

        loop_break_scc scc binds
          = case scc of
              AcyclicSCC node  -> mk_non_loop_breaker weak_fvs node : binds
              CyclicSCC [node] -> mk_loop_breaker node : binds
              CyclicSCC nodes  -> reOrderNodes depth bndr_set weak_fvs nodes binds

    reOrderNodes :: Int -> VarSet -> VarSet -> [Node Details] -> [Binding] -> [Binding]
        -- Choose a loop breaker, mark it no-inline,
        -- do SCC analysis on the rest, and recursively sort them out
    reOrderNodes _ _ _ [] _  = panic "reOrderNodes"
    reOrderNodes depth bndr_set weak_fvs (node : nodes) binds
      = -- pprTrace "reOrderNodes" (text "unchosen" <+> ppr unchosen $$
        --                           text "chosen" <+> ppr chosen_nodes) $
        loopBreakNodes new_depth bndr_set weak_fvs unchosen $
        (map mk_loop_breaker chosen_nodes ++ binds)
      where
        (chosen_nodes, unchosen) = choose_loop_breaker (score node) [node] [] nodes

        approximate_loop_breaker = depth >= 2
        new_depth | approximate_loop_breaker = 0
                  | otherwise                = depth+1
            -- After two iterations (d=0, d=1) give up
            -- and approximate, returning to d=0

        choose_loop_breaker :: Int                  -- Best score so far
                            -> [Node Details]       -- Nodes with this score
                            -> [Node Details]       -- Nodes with higher scores
                            -> [Node Details]       -- Unprocessed nodes
                            -> ([Node Details], [Node Details])
            -- This loop looks for the bind with the lowest score
            -- to pick as the loop  breaker.  The rest accumulate in
        choose_loop_breaker _ loop_nodes acc []
            = (loop_nodes, acc)        -- Done

            -- If approximate_loop_breaker is True, we pick *all*
            -- nodes with lowest score, else just one
            -- See Note [Complexity of loop breaking]
        choose_loop_breaker loop_sc loop_nodes acc (node : nodes)
            | sc < loop_sc  -- Lower score so pick this new one
            = choose_loop_breaker sc [node] (loop_nodes ++ acc) nodes

            | approximate_loop_breaker && sc == loop_sc
            = choose_loop_breaker loop_sc (node : loop_nodes) acc nodes

            | otherwise     -- Higher score so don't pick it
            = choose_loop_breaker loop_sc loop_nodes (node : acc) nodes
            where
              sc = score node

        score :: Node Details -> Int        -- Higher score => less likely to be picked as loop breaker
        score (ND { nd_bndr = bndr, nd_rhs = rhs }, _, _)
            | not (isId bndr) = 100     -- A type or cercion variable is never a loop breaker

            | isDFunId bndr = 9   -- Never choose a DFun as a loop breaker
                                  -- Note [DFuns should not be loop breakers]

            | Just be_very_keen <- hasStableCoreUnfolding_maybe (idUnfolding bndr)
            = if be_very_keen then 6    -- Note [Loop breakers and INLINE/INLINEABLE pragmas]
                              else 3
                   -- Data structures are more important than INLINE pragmas
                   -- so that dictionary/method recursion unravels
                   -- Note that this case hits all stable unfoldings, so we
                   -- never look at 'rhs' for stable unfoldings. That's right, because
                   -- 'rhs' is irrelevant for inlining things with a stable unfolding

            | is_con_app rhs = 5  -- Data types help with cases: Note [Constructor applications]

            | exprIsTrivial rhs = 10  -- Practically certain to be inlined
                    -- Used to have also: && not (isExportedId bndr)
                    -- But I found this sometimes cost an extra iteration when we have
                    --      rec { d = (a,b); a = ...df...; b = ...df...; df = d }
                    -- where df is the exported dictionary. Then df makes a really
                    -- bad choice for loop breaker

    -- If an Id is marked "never inline" then it makes a great loop breaker
    -- The only reason for not checking that here is that it is rare
    -- and I've never seen a situation where it makes a difference,
    -- so it probably isn't worth the time to test on every binder
    --      | isNeverActive (idInlinePragma bndr) = -10

            | isOneOcc (idOccInfo bndr) = 2  -- Likely to be inlined

            | canUnfold (realIdUnfolding bndr) = 1
                    -- The Id has some kind of unfolding
                    -- Ignore loop-breaker-ness here because that is what we are setting!

            | otherwise = 0

            -- Checking for a constructor application
            -- Cheap and cheerful; the simplifer moves casts out of the way
            -- The lambda case is important to spot x = /\a. C (f a)
            -- which comes up when C is a dictionary constructor and
            -- f is a default method.
            -- Example: the instance for Show (ST s a) in GHC.ST
            --
            -- However we *also* treat (\x. C p q) as a con-app-like thing,
            --      Note [Closure conversion]
        is_con_app (Var v)    = isConLikeId v
        is_con_app (App f _)  = is_con_app f
        is_con_app (Lam _ e)  = is_con_app e
        is_con_app (Tick _ e) = is_con_app e
        is_con_app _          = False

    {-
    Note [Complexity of loop breaking]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The loop-breaking algorithm knocks out one binder at a time, and
    performs a new SCC analysis on the remaining binders.  That can
    behave very badly in tightly-coupled groups of bindings; in the
    worst case it can be (N**2)*log N, because it does a full SCC
    on N, then N-1, then N-2 and so on.

    To avoid this, we switch plans after 2 (or whatever) attempts:
      Plan A: pick one binder with the lowest score, make it
              a loop breaker, and try again
      Plan B: pick *all* binders with the lowest score, make them
              all loop breakers, and try again
    Since there are only a small finite number of scores, this will
    terminate in a constant number of iterations, rather than O(N)
    iterations.

    You might thing that it's very unlikely, but RULES make it much
    more likely.  Here's a real example from Trac #1969:
      Rec { $dm = \d.\x. op d
            {-# RULES forall d. $dm Int d  = $s$dm1
                      forall d. $dm Bool d = $s$dm2 #-}

            dInt = MkD .... opInt ...
            dInt = MkD .... opBool ...
            opInt  = $dm dInt
            opBool = $dm dBool

            $s$dm1 = \x. op dInt
            $s$dm2 = \x. op dBool }
    The RULES stuff means that we can't choose $dm as a loop breaker
    (Note [Choosing loop breakers]), so we must choose at least (say)
    opInt *and* opBool, and so on.  The number of loop breakders is
    linear in the number of instance declarations.

    Note [Loop breakers and INLINE/INLINEABLE pragmas]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Avoid choosing a function with an INLINE pramga as the loop breaker!
    If such a function is mutually-recursive with a non-INLINE thing,
    then the latter should be the loop-breaker.

    It's vital to distinguish between INLINE and INLINEABLE (the
    Bool returned by hasStableCoreUnfolding_maybe).  If we start with
       Rec { {-# INLINEABLE f #-}
             f x = ...f... }
    and then worker/wrapper it through strictness analysis, we'll get
       Rec { {-# INLINEABLE $wf #-}
             $wf p q = let x = (p,q) in ...f...

             {-# INLINE f #-}
             f x = case x of (p,q) -> $wf p q }

    Now it is vital that we choose $wf as the loop breaker, so we can
    inline 'f' in '$wf'.

    Note [DFuns should not be loop breakers]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    It's particularly bad to make a DFun into a loop breaker.  See
    Note [How instance declarations are translated] in TcInstDcls

    We give DFuns a higher score than ordinary CONLIKE things because
    if there's a choice we want the DFun to be the non-looop breker. Eg

    rec { sc = /\ a \$dC. $fBWrap (T a) ($fCT @ a $dC)

          $fCT :: forall a_afE. (Roman.C a_afE) => Roman.C (Roman.T a_afE)
          {-# DFUN #-}
          $fCT = /\a \$dC. MkD (T a) ((sc @ a $dC) |> blah) ($ctoF @ a $dC)
        }

    Here 'sc' (the superclass) looks CONLIKE, but we'll never get to it
    if we can't unravel the DFun first.

    Note [Constructor applications]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    It's really really important to inline dictionaries.  Real
    example (the Enum Ordering instance from GHC.Base):

         rec     f = \ x -> case d of (p,q,r) -> p x
                 g = \ x -> case d of (p,q,r) -> q x
                 d = (v, f, g)

    Here, f and g occur just once; but we can't inline them into d.
    On the other hand we *could* simplify those case expressions if
    we didn't stupidly choose d as the loop breaker.
    But we won't because constructor args are marked "Many".
    Inlining dictionaries is really essential to unravelling
    the loops in static numeric dictionaries, see GHC.Float.

    Note [Closure conversion]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    We treat (\x. C p q) as a high-score candidate in the letrec scoring algorithm.
    The immediate motivation came from the result of a closure-conversion transformation
    which generated code like this:

        data Clo a b = forall c. Clo (c -> a -> b) c

        ($:) :: Clo a b -> a -> b
        Clo f env $: x = f env x

        rec { plus = Clo plus1 ()

            ; plus1 _ n = Clo plus2 n

            ; plus2 Zero     n = n
            ; plus2 (Succ m) n = Succ (plus $: m $: n) }

    If we inline 'plus' and 'plus1', everything unravels nicely.  But if
    we choose 'plus1' as the loop breaker (which is entirely possible
    otherwise), the loop does not unravel nicely.

    @occAnalRhs@ deals with the question of bindings where the Id is marked
    by an INLINE pragma.  For these we record that anything which occurs
    in its RHS occurs many times.  This pessimistically assumes that ths
    inlined binder also occurs many times in its scope, but if it doesn't
    we'll catch it next time round.  At worst this costs an extra simplifier pass.
    ToDo: try using the occurrence info for the inline'd binder.

    [March 97] We do the same for atomic RHSs.  Reason: see notes with loopBreakSCC.
    [June 98, SLPJ]  I've undone this change; I don't understand it.  See notes with loopBreakSCC.
    -}

    occAnalRecRhs :: OccEnv -> CoreExpr    -- Rhs
               -> (UsageDetails, CoreExpr)
                  -- Returned usage details covers only the RHS,
                  -- and *not* the RULE or INLINE template for the Id
    occAnalRecRhs env rhs = occAnal (rhsCtxt env) rhs

    occAnalNonRecRhs :: OccEnv
                     -> Id -> CoreExpr    -- Binder and rhs
                         -- Binder is already tagged with occurrence info
                     -> (UsageDetails, CoreExpr)
                  -- Returned usage details covers only the RHS,
                  -- and *not* the RULE or INLINE template for the Id
    occAnalNonRecRhs env bndr rhs
      = occAnal rhs_env rhs
      where
        -- See Note [Use one-shot info]
        env1 = env { occ_one_shots = argOneShots OneShotLam dmd }

        -- See Note [Cascading inlines]
        rhs_env | certainly_inline = env1
                | otherwise        = rhsCtxt env1

        certainly_inline -- See Note [Cascading inlines]
          = case idOccInfo bndr of
              OneOcc in_lam one_br _ -> not in_lam && one_br && active && not_stable
              _                      -> False

        dmd        = idDemandInfo bndr
        active     = isAlwaysActive (idInlineActivation bndr)
        not_stable = not (isStableUnfolding (idUnfolding bndr))

    addIdOccs :: UsageDetails -> VarSet -> UsageDetails
    addIdOccs usage id_set = foldVarSet addIdOcc usage id_set

    addIdOcc :: Id -> UsageDetails -> UsageDetails
    addIdOcc v u | isId v    = addOneOcc u v NoOccInfo
                 | otherwise = u
            -- Give a non-committal binder info (i.e NoOccInfo) because
            --   a) Many copies of the specialised thing can appear
            --   b) We don't want to substitute a BIG expression inside a RULE
            --      even if that's the only occurrence of the thing
            --      (Same goes for INLINE.)

    {-
    Note [Cascading inlines]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    By default we use an rhsCtxt for the RHS of a binding.  This tells the
    occ anal n that it's looking at an RHS, which has an effect in
    occAnalApp.  In particular, for constructor applications, it makes
    the arguments appear to have NoOccInfo, so that we don't inline into
    them. Thus    x = f y
                  k = Just x
    we do not want to inline x.

    But there's a problem.  Consider
         x1 = a0 : []
         x2 = a1 : x1
         x3 = a2 : x2
         g  = f x3
    First time round, it looks as if x1 and x2 occur as an arg of a
    let-bound constructor ==> give them a many-occurrence.
    But then x3 is inlined (unconditionally as it happens) and
    next time round, x2 will be, and the next time round x1 will be
    Result: multiple simplifier iterations.  Sigh.

    So, when analysing the RHS of x3 we notice that x3 will itself
    definitely inline the next time round, and so we analyse x3's rhs in
    an ordinary context, not rhsCtxt.  Hence the "certainly_inline" stuff.

    Annoyingly, we have to approximate SimplUtils.preInlineUnconditionally.
    If we say "yes" when preInlineUnconditionally says "no" the simplifier iterates
    indefinitely:
            x = f y
            k = Just x
    inline ==>
            k = Just (f y)
    float ==>
            x1 = f y
            k = Just x1

    This is worse than the slow cascade, so we only want to say "certainly_inline"
    if it really is certain.  Look at the note with preInlineUnconditionally
    for the various clauses.

    Expressions
    ~~~~~~~~~~~
    -}

    occAnal :: OccEnv
            -> CoreExpr
            -> (UsageDetails,       -- Gives info only about the "interesting" Ids
                CoreExpr)

    occAnal _   expr@(Type _) = (emptyDetails,         expr)
    occAnal _   expr@(Lit _)  = (emptyDetails,         expr)
    occAnal env expr@(Var v)  = (mkOneOcc env v False, expr)
        -- At one stage, I gathered the idRuleVars for v here too,
        -- which in a way is the right thing to do.
        -- But that went wrong right after specialisation, when
        -- the *occurrences* of the overloaded function didn't have any
        -- rules in them, so the *specialised* versions looked as if they
        -- weren't used at all.

    occAnal _ (Coercion co)
      = (addIdOccs emptyDetails (coVarsOfCo co), Coercion co)
            -- See Note [Gather occurrences of coercion variables]

    {-
    Note [Gather occurrences of coercion variables]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We need to gather info about what coercion variables appear, so that
    we can sort them into the right place when doing dependency analysis.
    -}

    occAnal env (Tick tickish body)
      | tickish `tickishScopesLike` SoftScope
      = (usage, Tick tickish body')

      | Breakpoint _ ids <- tickish
      = (usage_lam +++ mkVarEnv (zip ids (repeat NoOccInfo)), Tick tickish body')
        -- never substitute for any of the Ids in a Breakpoint

      | otherwise
      = (usage_lam, Tick tickish body')
      where
        !(usage,body') = occAnal env body
        -- for a non-soft tick scope, we can inline lambdas only
        usage_lam = mapVarEnv markInsideLam usage

    occAnal env (Cast expr co)
      = case occAnal env expr of { (usage, expr') ->
        let usage1 = markManyIf (isRhsEnv env) usage
            usage2 = addIdOccs usage1 (coVarsOfCo co)
              -- See Note [Gather occurrences of coercion variables]
        in (usage2, Cast expr' co)
            -- If we see let x = y `cast` co
            -- then mark y as 'Many' so that we don't
            -- immediately inline y again.
        }

    occAnal env app@(App _ _)
      = occAnalApp env (collectArgsTicks tickishFloatable app)

    -- Ignore type variables altogether
    --   (a) occurrences inside type lambdas only not marked as InsideLam
    --   (b) type variables not in environment

    occAnal env (Lam x body) | isTyVar x
      = case occAnal env body of { (body_usage, body') ->
        (body_usage, Lam x body')
        }

    -- For value lambdas we do a special hack.  Consider
    --      (\x. \y. ...x...)
    -- If we did nothing, x is used inside the \y, so would be marked
    -- as dangerous to dup.  But in the common case where the abstraction
    -- is applied to two arguments this is over-pessimistic.
    -- So instead, we just mark each binder with its occurrence
    -- info in the *body* of the multiple lambda.
    -- Then, the simplifier is careful when partially applying lambdas.

    occAnal env expr@(Lam _ _)
      = case occAnal env_body body of { (body_usage, body') ->
        let
            (final_usage, tagged_binders) = tagLamBinders body_usage binders'
                          -- Use binders' to put one-shot info on the lambdas

            really_final_usage
              | all isOneShotBndr binders' = final_usage
              | otherwise = mapVarEnv markInsideLam final_usage
        in
        (really_final_usage, mkLams tagged_binders body') }
      where
        (binders, body)      = collectBinders expr
        (env_body, binders') = oneShotGroup env binders

    occAnal env (Case scrut bndr ty alts)
      = case occ_anal_scrut scrut alts     of { (scrut_usage, scrut') ->
        case mapAndUnzip occ_anal_alt alts of { (alts_usage_s, alts')   ->
        let
            alts_usage  = foldr combineAltsUsageDetails emptyDetails alts_usage_s
            (alts_usage1, tagged_bndr) = tag_case_bndr alts_usage bndr
            total_usage = scrut_usage +++ alts_usage1
        in
        total_usage `seq` (total_usage, Case scrut' tagged_bndr ty alts') }}
      where
            -- Note [Case binder usage]
            -- ~~~~~~~~~~~~~~~~~~~~~~~~
            -- The case binder gets a usage of either "many" or "dead", never "one".
            -- Reason: we like to inline single occurrences, to eliminate a binding,
            -- but inlining a case binder *doesn't* eliminate a binding.
            -- We *don't* want to transform
            --      case x of w { (p,q) -> f w }
            -- into
            --      case x of w { (p,q) -> f (p,q) }
        tag_case_bndr usage bndr
          = case lookupVarEnv usage bndr of
              Nothing -> (usage,                  setIdOccInfo bndr IAmDead)
              Just _  -> (usage `delVarEnv` bndr, setIdOccInfo bndr NoOccInfo)

        alt_env = mkAltEnv env scrut bndr
        occ_anal_alt = occAnalAlt alt_env

        occ_anal_scrut (Var v) (alt1 : other_alts)
            | not (null other_alts) || not (isDefaultAlt alt1)
            = (mkOneOcc env v True, Var v)  -- The 'True' says that the variable occurs
                                            -- in an interesting context; the case has
                                            -- at least one non-default alternative
        occ_anal_scrut (Tick t e) alts
            | t `tickishScopesLike` SoftScope
              -- No reason to not look through all ticks here, but only
              -- for soft-scoped ticks we can do so without having to
              -- update returned occurance info (see occAnal)
            = second (Tick t) $ occ_anal_scrut e alts

        occ_anal_scrut scrut _alts
            = occAnal (vanillaCtxt env) scrut    -- No need for rhsCtxt

    occAnal env (Let bind body)
      = case occAnal env body                               of { (body_usage, body') ->
        case occAnalBind env noImpRuleEdges bind body_usage of { (final_usage, new_binds) ->
           (final_usage, mkLets new_binds body') }}

    occAnalArgs :: OccEnv -> [CoreExpr] -> [OneShots] -> (UsageDetails, [CoreExpr])
    occAnalArgs _ [] _
      = (emptyDetails, [])

    occAnalArgs env (arg:args) one_shots
      | isTypeArg arg
      = case occAnalArgs env args one_shots of { (uds, args') ->
        (uds, arg:args') }

      | otherwise
      = case argCtxt env one_shots           of { (arg_env, one_shots') ->
        case occAnal arg_env arg             of { (uds1, arg') ->
        case occAnalArgs env args one_shots' of { (uds2, args') ->
        (uds1 +++ uds2, arg':args') }}}

    {-
    Applications are dealt with specially because we want
    the "build hack" to work.

    Note [Arguments of let-bound constructors]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider
        f x = let y = expensive x in
              let z = (True,y) in
              (case z of {(p,q)->q}, case z of {(p,q)->q})
    We feel free to duplicate the WHNF (True,y), but that means
    that y may be duplicated thereby.

    If we aren't careful we duplicate the (expensive x) call!
    Constructors are rather like lambdas in this way.
    -}

    occAnalApp :: OccEnv
               -> (Expr CoreBndr, [Arg CoreBndr], [Tickish Id])
               -> (UsageDetails, Expr CoreBndr)
    occAnalApp env (Var fun, args, ticks)
      | null ticks = (uds, mkApps (Var fun) args')
      | otherwise  = (uds, mkTicks ticks $ mkApps (Var fun) args')
      where
        uds = fun_uds +++ final_args_uds

        !(args_uds, args') = occAnalArgs env args one_shots
        !final_args_uds = markManyIf (isRhsEnv env && is_exp) args_uds
           -- We mark the free vars of the argument of a constructor or PAP
           -- as "many", if it is the RHS of a let(rec).
           -- This means that nothing gets inlined into a constructor argument
           -- position, which is what we want.  Typically those constructor
           -- arguments are just variables, or trivial expressions.
           --
           -- This is the *whole point* of the isRhsEnv predicate
           -- See Note [Arguments of let-bound constructors]

        n_val_args = valArgCount args
        fun_uds    = mkOneOcc env fun (n_val_args > 0)
        is_exp     = isExpandableApp fun n_val_args
               -- See Note [CONLIKE pragma] in BasicTypes
               -- The definition of is_exp should match that in
               -- Simplify.prepareRhs

        one_shots  = argsOneShots (idStrictness fun) n_val_args
                     -- See Note [Use one-shot info]

    occAnalApp env (fun, args, ticks)
      = (fun_uds +++ args_uds, mkTicks ticks $ mkApps fun' args')
      where
        !(fun_uds, fun') = occAnal (addAppCtxt env args) fun
            -- The addAppCtxt is a bit cunning.  One iteration of the simplifier
            -- often leaves behind beta redexs like
            --      (\x y -> e) a1 a2
            -- Here we would like to mark x,y as one-shot, and treat the whole
            -- thing much like a let.  We do this by pushing some True items
            -- onto the context stack.
        !(args_uds, args') = occAnalArgs env args []

    markManyIf :: Bool              -- If this is true
               -> UsageDetails      -- Then do markMany on this
               -> UsageDetails
    markManyIf True  uds = mapVarEnv markMany uds
    markManyIf False uds = uds

    {-
    Note [Use one-shot information]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The occurrrence analyser propagates one-shot-lambda information in two situation
      * Applications:  eg   build (\cn -> blah)
        Propagate one-shot info from the strictness signature of 'build' to
        the \cn

      * Let-bindings:  eg   let f = \c. let ... in \n -> blah
                            in (build f, build f)
        Propagate one-shot info from the demanand-info on 'f' to the
        lambdas in its RHS (which may not be syntactically at the top)

    Some of this is done by the demand analyser, but this way it happens
    much earlier, taking advantage of the strictness signature of
    imported functions.

    Note [Binders in case alternatives]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider
        case x of y { (a,b) -> f y }
    We treat 'a', 'b' as dead, because they don't physically occur in the
    case alternative.  (Indeed, a variable is dead iff it doesn't occur in
    its scope in the output of OccAnal.)  It really helps to know when
    binders are unused.  See esp the call to isDeadBinder in
    Simplify.mkDupableAlt

    In this example, though, the Simplifier will bring 'a' and 'b' back to
    life, beause it binds 'y' to (a,b) (imagine got inlined and
    scrutinised y).
    -}

    occAnalAlt :: (OccEnv, Maybe (Id, CoreExpr))
               -> CoreAlt
               -> (UsageDetails, Alt IdWithOccInfo)
    occAnalAlt (env, scrut_bind) (con, bndrs, rhs)
      = case occAnal env rhs of { (rhs_usage1, rhs1) ->
        let
            (alt_usg, tagged_bndrs) = tagLamBinders rhs_usage1 bndrs
                                      -- See Note [Binders in case alternatives]
            (alt_usg', rhs2) =
              wrapAltRHS env scrut_bind alt_usg tagged_bndrs rhs1
        in
        (alt_usg', (con, tagged_bndrs, rhs2)) }

    wrapAltRHS :: OccEnv
               -> Maybe (Id, CoreExpr)      -- proxy mapping generated by mkAltEnv
               -> UsageDetails              -- usage for entire alt (p -> rhs)
               -> [Var]                     -- alt binders
               -> CoreExpr                  -- alt RHS
               -> (UsageDetails, CoreExpr)
    wrapAltRHS env (Just (scrut_var, let_rhs)) alt_usg bndrs alt_rhs
      | occ_binder_swap env
      , scrut_var `usedIn` alt_usg -- bndrs are not be present in alt_usg so this
                                   -- handles condition (a) in Note [Binder swap]
      , not captured               -- See condition (b) in Note [Binder swap]
      = ( alt_usg' +++ let_rhs_usg
        , Let (NonRec tagged_scrut_var let_rhs') alt_rhs )
      where
        captured = any (`usedIn` let_rhs_usg) bndrs
        -- The rhs of the let may include coercion variables
        -- if the scrutinee was a cast, so we must gather their
        -- usage. See Note [Gather occurrences of coercion variables]
        (let_rhs_usg, let_rhs') = occAnal env let_rhs
        (alt_usg', tagged_scrut_var) = tagBinder alt_usg scrut_var

    wrapAltRHS _ _ alt_usg _ alt_rhs
      = (alt_usg, alt_rhs)

    {-
    ************************************************************************
    *                                                                      *
                        OccEnv
    *                                                                      *
    ************************************************************************
    -}

    data OccEnv
      = OccEnv { occ_encl       :: !OccEncl      -- Enclosing context information
               , occ_one_shots  :: !OneShots     -- Tells about linearity
               , occ_gbl_scrut  :: GlobalScruts
               , occ_rule_act   :: Activation -> Bool   -- Which rules are active
                 -- See Note [Finding rule RHS free vars]
               , occ_binder_swap :: !Bool -- enable the binder_swap
                 -- See CorePrep Note [Dead code in CorePrep]
        }

    type GlobalScruts = IdSet   -- See Note [Binder swap on GlobalId scrutinees]

    -----------------------------
    -- OccEncl is used to control whether to inline into constructor arguments
    -- For example:
    --      x = (p,q)               -- Don't inline p or q
    --      y = /\a -> (p a, q a)   -- Still don't inline p or q
    --      z = f (p,q)             -- Do inline p,q; it may make a rule fire
    -- So OccEncl tells enought about the context to know what to do when
    -- we encounter a contructor application or PAP.

    data OccEncl
      = OccRhs              -- RHS of let(rec), albeit perhaps inside a type lambda
                            -- Don't inline into constructor args here
      | OccVanilla          -- Argument of function, body of lambda, scruintee of case etc.
                            -- Do inline into constructor args here

    instance Outputable OccEncl where
      ppr OccRhs     = text "occRhs"
      ppr OccVanilla = text "occVanilla"

    type OneShots = [OneShotInfo]
            -- []           No info
            --
            -- one_shot_info:ctxt    Analysing a function-valued expression that
            --                       will be applied as described by one_shot_info

    initOccEnv :: (Activation -> Bool) -> OccEnv
    initOccEnv active_rule
      = OccEnv { occ_encl      = OccVanilla
               , occ_one_shots = []
               , occ_gbl_scrut = emptyVarSet
               , occ_rule_act  = active_rule
               , occ_binder_swap = True }

    vanillaCtxt :: OccEnv -> OccEnv
    vanillaCtxt env = env { occ_encl = OccVanilla, occ_one_shots = [] }

    rhsCtxt :: OccEnv -> OccEnv
    rhsCtxt env = env { occ_encl = OccRhs, occ_one_shots = [] }

    argCtxt :: OccEnv -> [OneShots] -> (OccEnv, [OneShots])
    argCtxt env []
      = (env { occ_encl = OccVanilla, occ_one_shots = [] }, [])
    argCtxt env (one_shots:one_shots_s)
      = (env { occ_encl = OccVanilla, occ_one_shots = one_shots }, one_shots_s)

    isRhsEnv :: OccEnv -> Bool
    isRhsEnv (OccEnv { occ_encl = OccRhs })     = True
    isRhsEnv (OccEnv { occ_encl = OccVanilla }) = False

    oneShotGroup :: OccEnv -> [CoreBndr]
                 -> ( OccEnv
                    , [CoreBndr] )
            -- The result binders have one-shot-ness set that they might not have had originally.
            -- This happens in (build (\cn -> e)).  Here the occurrence analyser
            -- linearity context knows that c,n are one-shot, and it records that fact in
            -- the binder. This is useful to guide subsequent float-in/float-out tranformations

    oneShotGroup env@(OccEnv { occ_one_shots = ctxt }) bndrs
      = go ctxt bndrs []
      where
        go ctxt [] rev_bndrs
          = ( env { occ_one_shots = ctxt, occ_encl = OccVanilla }
            , reverse rev_bndrs )

        go [] bndrs rev_bndrs
          = ( env { occ_one_shots = [], occ_encl = OccVanilla }
            , reverse rev_bndrs ++ bndrs )

        go ctxt (bndr:bndrs) rev_bndrs
          | isId bndr

          = case ctxt of
              []                -> go []   bndrs (bndr : rev_bndrs)
              (one_shot : ctxt) -> go ctxt bndrs (bndr': rev_bndrs)
                                where
                                   bndr' = updOneShotInfo bndr one_shot
           | otherwise
          = go ctxt bndrs (bndr:rev_bndrs)

    addAppCtxt :: OccEnv -> [Arg CoreBndr] -> OccEnv
    addAppCtxt env@(OccEnv { occ_one_shots = ctxt }) args
      = env { occ_one_shots = replicate (valArgCount args) OneShotLam ++ ctxt }

    transClosureFV :: UniqFM VarSet -> UniqFM VarSet
    -- If (f,g), (g,h) are in the input, then (f,h) is in the output
    --                                   as well as (f,g), (g,h)
    transClosureFV env
      | no_change = env
      | otherwise = transClosureFV (listToUFM new_fv_list)
      where
        (no_change, new_fv_list) = mapAccumL bump True (ufmToList env)
        bump no_change (b,fvs)
          | no_change_here = (no_change, (b,fvs))
          | otherwise      = (False,     (b,new_fvs))
          where
            (new_fvs, no_change_here) = extendFvs env fvs

    -------------
    extendFvs_ :: UniqFM VarSet -> VarSet -> VarSet
    extendFvs_ env s = fst (extendFvs env s)   -- Discard the Bool flag

    extendFvs :: UniqFM VarSet -> VarSet -> (VarSet, Bool)
    -- (extendFVs env s) returns
    --     (s `union` env(s), env(s) `subset` s)
    extendFvs env s
      | isNullUFM env
      = (s, True)
      | otherwise
      = (s `unionVarSet` extras, extras `subVarSet` s)
      where
        extras :: VarSet    -- env(s)
        extras = foldUFM unionVarSet emptyVarSet $
                 intersectUFM_C (\x _ -> x) env s

    {-
    ************************************************************************
    *                                                                      *
                        Binder swap
    *                                                                      *
    ************************************************************************

    Note [Binder swap]
    ~~~~~~~~~~~~~~~~~~
    We do these two transformations right here:

     (1)   case x of b { pi -> ri }
        ==>
          case x of b { pi -> let x=b in ri }

     (2)  case (x |> co) of b { pi -> ri }
        ==>
          case (x |> co) of b { pi -> let x = b |> sym co in ri }

        Why (2)?  See Note [Case of cast]

    In both cases, in a particular alternative (pi -> ri), we only
    add the binding if
      (a) x occurs free in (pi -> ri)
            (ie it occurs in ri, but is not bound in pi)
      (b) the pi does not bind b (or the free vars of co)
    We need (a) and (b) for the inserted binding to be correct.

    For the alternatives where we inject the binding, we can transfer
    all x's OccInfo to b.  And that is the point.

    Notice that
      * The deliberate shadowing of 'x'.
      * That (a) rapidly becomes false, so no bindings are injected.

    The reason for doing these transformations here is because it allows
    us to adjust the OccInfo for 'x' and 'b' as we go.

      * Suppose the only occurrences of 'x' are the scrutinee and in the
        ri; then this transformation makes it occur just once, and hence
        get inlined right away.

      * If we do this in the Simplifier, we don't know whether 'x' is used
        in ri, so we are forced to pessimistically zap b's OccInfo even
        though it is typically dead (ie neither it nor x appear in the
        ri).  There's nothing actually wrong with zapping it, except that
        it's kind of nice to know which variables are dead.  My nose
        tells me to keep this information as robustly as possible.

    The Maybe (Id,CoreExpr) passed to occAnalAlt is the extra let-binding
    {x=b}; it's Nothing if the binder-swap doesn't happen.

    There is a danger though.  Consider
          let v = x +# y
          in case (f v) of w -> ...v...v...
    And suppose that (f v) expands to just v.  Then we'd like to
    use 'w' instead of 'v' in the alternative.  But it may be too
    late; we may have substituted the (cheap) x+#y for v in the
    same simplifier pass that reduced (f v) to v.

    I think this is just too bad.  CSE will recover some of it.

    Note [Case of cast]
    ~~~~~~~~~~~~~~~~~~~
    Consider        case (x `cast` co) of b { I# ->
                    ... (case (x `cast` co) of {...}) ...
    We'd like to eliminate the inner case.  That is the motivation for
    equation (2) in Note [Binder swap].  When we get to the inner case, we
    inline x, cancel the casts, and away we go.

    Note [Binder swap on GlobalId scrutinees]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    When the scrutinee is a GlobalId we must take care in two ways

     i) In order to *know* whether 'x' occurs free in the RHS, we need its
        occurrence info. BUT, we don't gather occurrence info for
        GlobalIds.  That's the reason for the (small) occ_gbl_scrut env in
        OccEnv is for: it says "gather occurrence info for these".

     ii) We must call localiseId on 'x' first, in case it's a GlobalId, or
         has an External Name. See, for example, SimplEnv Note [Global Ids in
         the substitution].

    Note [Zap case binders in proxy bindings]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    From the original
         case x of cb(dead) { p -> ...x... }
    we will get
         case x of cb(live) { p -> let x = cb in ...x... }

    Core Lint never expects to find an *occurrence* of an Id marked
    as Dead, so we must zap the OccInfo on cb before making the
    binding x = cb.  See Trac #5028.

    Historical note [no-case-of-case]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We *used* to suppress the binder-swap in case expressions when
    -fno-case-of-case is on.  Old remarks:
        "This happens in the first simplifier pass,
        and enhances full laziness.  Here's the bad case:
                f = \ y -> ...(case x of I# v -> ...(case x of ...) ... )
        If we eliminate the inner case, we trap it inside the I# v -> arm,
        which might prevent some full laziness happening.  I've seen this
        in action in spectral/cichelli/Prog.hs:
                 [(m,n) | m <- [1..max], n <- [1..max]]
        Hence the check for NoCaseOfCase."
    However, now the full-laziness pass itself reverses the binder-swap, so this
    check is no longer necessary.

    Historical note [Suppressing the case binder-swap]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    This old note describes a problem that is also fixed by doing the
    binder-swap in OccAnal:

        There is another situation when it might make sense to suppress the
        case-expression binde-swap. If we have

            case x of w1 { DEFAULT -> case x of w2 { A -> e1; B -> e2 }
                           ...other cases .... }

        We'll perform the binder-swap for the outer case, giving

            case x of w1 { DEFAULT -> case w1 of w2 { A -> e1; B -> e2 }
                           ...other cases .... }

        But there is no point in doing it for the inner case, because w1 can't
        be inlined anyway.  Furthermore, doing the case-swapping involves
        zapping w2's occurrence info (see paragraphs that follow), and that
        forces us to bind w2 when doing case merging.  So we get

            case x of w1 { A -> let w2 = w1 in e1
                           B -> let w2 = w1 in e2
                           ...other cases .... }

        This is plain silly in the common case where w2 is dead.

        Even so, I can't see a good way to implement this idea.  I tried
        not doing the binder-swap if the scrutinee was already evaluated
        but that failed big-time:

                data T = MkT !Int

                case v of w  { MkT x ->
                case x of x1 { I# y1 ->
                case x of x2 { I# y2 -> ...

        Notice that because MkT is strict, x is marked "evaluated".  But to
        eliminate the last case, we must either make sure that x (as well as
        x1) has unfolding MkT y1.  The straightforward thing to do is to do
        the binder-swap.  So this whole note is a no-op.

    It's fixed by doing the binder-swap in OccAnal because we can do the
    binder-swap unconditionally and still get occurrence analysis
    information right.
    -}

    mkAltEnv :: OccEnv -> CoreExpr -> Id -> (OccEnv, Maybe (Id, CoreExpr))
    -- Does two things: a) makes the occ_one_shots = OccVanilla
    --                  b) extends the GlobalScruts if possible
    --                  c) returns a proxy mapping, binding the scrutinee
    --                     to the case binder, if possible
    mkAltEnv env@(OccEnv { occ_gbl_scrut = pe }) scrut case_bndr
      = case stripTicksTopE (const True) scrut of
          Var v           -> add_scrut v case_bndr'
          Cast (Var v) co -> add_scrut v (Cast case_bndr' (mkSymCo co))
                              -- See Note [Case of cast]
          _               -> (env { occ_encl = OccVanilla }, Nothing)

      where
        add_scrut v rhs = ( env { occ_encl = OccVanilla, occ_gbl_scrut = pe `extendVarSet` v }
                          , Just (localise v, rhs) )

        case_bndr' = Var (zapIdOccInfo case_bndr) -- See Note [Zap case binders in proxy bindings]
        localise scrut_var = mkLocalIdOrCoVar (localiseName (idName scrut_var)) (idType scrut_var)
            -- Localise the scrut_var before shadowing it; we're making a
            -- new binding for it, and it might have an External Name, or
            -- even be a GlobalId; Note [Binder swap on GlobalId scrutinees]
            -- Also we don't want any INLINE or NOINLINE pragmas!

    {-
    ************************************************************************
    *                                                                      *
    \subsection[OccurAnal-types]{OccEnv}
    *                                                                      *
    ************************************************************************
    -}

    type UsageDetails = IdEnv OccInfo       -- A finite map from ids to their usage
                    -- INVARIANT: never IAmDead
                    -- (Deadness is signalled by not being in the map at all)

    (+++), combineAltsUsageDetails
            :: UsageDetails -> UsageDetails -> UsageDetails

    (+++) usage1 usage2
      = plusVarEnv_C addOccInfo usage1 usage2

    combineAltsUsageDetails usage1 usage2
      = plusVarEnv_C orOccInfo usage1 usage2

    addOneOcc :: UsageDetails -> Id -> OccInfo -> UsageDetails
    addOneOcc usage id info
      = plusVarEnv_C addOccInfo usage (unitVarEnv id info)
            -- ToDo: make this more efficient

    emptyDetails :: UsageDetails
    emptyDetails = (emptyVarEnv :: UsageDetails)

    usedIn :: Id -> UsageDetails -> Bool
    v `usedIn` details = isExportedId v || v `elemVarEnv` details

    type IdWithOccInfo = Id

    tagLamBinders :: UsageDetails          -- Of scope
                  -> [Id]                  -- Binders
                  -> (UsageDetails,        -- Details with binders removed
                     [IdWithOccInfo])    -- Tagged binders
    -- Used for lambda and case binders
    -- It copes with the fact that lambda bindings can have a
    -- stable unfolding, used for join points
    tagLamBinders usage binders = usage' `seq` (usage', bndrs')
      where
        (usage', bndrs') = mapAccumR tag_lam usage binders
        tag_lam usage bndr = (usage2, setBinderOcc usage bndr)
          where
            usage1 = usage `delVarEnv` bndr
            usage2 | isId bndr = addIdOccs usage1 (idUnfoldingVars bndr)
                   | otherwise = usage1

    tagBinder :: UsageDetails           -- Of scope
              -> Id                     -- Binders
              -> (UsageDetails,         -- Details with binders removed
                  IdWithOccInfo)        -- Tagged binders

    tagBinder usage binder
     = let
         usage'  = usage `delVarEnv` binder
         binder' = setBinderOcc usage binder
       in
       usage' `seq` (usage', binder')

    setBinderOcc :: UsageDetails -> CoreBndr -> CoreBndr
    setBinderOcc usage bndr
      | isTyVar bndr      = bndr
      | isExportedId bndr = case idOccInfo bndr of
                              NoOccInfo -> bndr
                              _         -> setIdOccInfo bndr NoOccInfo
                -- Don't use local usage info for visible-elsewhere things
                -- BUT *do* erase any IAmALoopBreaker annotation, because we're
                -- about to re-generate it and it shouldn't be "sticky"

      | otherwise = setIdOccInfo bndr occ_info
      where
        occ_info = lookupVarEnv usage bndr `orElse` IAmDead

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Operations over OccInfo}
    *                                                                      *
    ************************************************************************
    -}

    mkOneOcc :: OccEnv -> Id -> InterestingCxt -> UsageDetails
    mkOneOcc env id int_cxt
      | isLocalId id
      = unitVarEnv id (OneOcc False True int_cxt)

      | id `elemVarEnv` occ_gbl_scrut env
      = unitVarEnv id NoOccInfo

      | otherwise
      = emptyDetails

    markMany, markInsideLam :: OccInfo -> OccInfo

    markMany _  = NoOccInfo

    markInsideLam (OneOcc _ one_br int_cxt) = OneOcc True one_br int_cxt
    markInsideLam occ                       = occ

    addOccInfo, orOccInfo :: OccInfo -> OccInfo -> OccInfo

    addOccInfo a1 a2  = ASSERT( not (isDeadOcc a1 || isDeadOcc a2) )
                        NoOccInfo   -- Both branches are at least One
                                    -- (Argument is never IAmDead)

    -- (orOccInfo orig new) is used
    -- when combining occurrence info from branches of a case

    orOccInfo (OneOcc in_lam1 _ int_cxt1)
              (OneOcc in_lam2 _ int_cxt2)
      = OneOcc (in_lam1 || in_lam2)
               False        -- False, because it occurs in both branches
               (int_cxt1 && int_cxt2)
    orOccInfo a1 a2 = ASSERT( not (isDeadOcc a1 || isDeadOcc a2) )
                      NoOccInfo