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, MultiWayIf #-}

    module OccurAnal (
            occurAnalysePgm, occurAnalyseExpr, occurAnalyseExpr_NoBinderSwap
        ) where

    #include "HsVersions.h"

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

    import VarSet
    import VarEnv
    import Var
    import Demand           ( argOneShots, argsOneShots )
    import Digraph          ( SCC(..), Node
                            , stronglyConnCompFromEdgedVerticesUniq
                            , stronglyConnCompFromEdgedVerticesUniqR )
    import Unique
    import UniqFM
    import UniqSet
    import Util
    import Outputable
    import Data.List
    import Control.Arrow    ( second )

    {-
    ************************************************************************
    *                                                                      *
        occurAnalysePgm, occurAnalyseExpr, occurAnalyseExpr_NoBinderSwap
    *                                                                      *
    ************************************************************************

    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
      | isEmptyDetails 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 TopLevel
                                                        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 = addManyOccsSet 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) $
                                    getUniqSet (exprFreeIds arg `delVarSetList` ru_bndrs imp_rule)
                                | imp_rule <- imp_rules
                                , not (isBuiltinRule imp_rule)  -- See Note [Plugin 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 TopLevel 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

    {- Note [Plugin rules]
    ~~~~~~~~~~~~~~~~~~~~~~
    Conal Elliott (Trac #11651) built a GHC plugin that added some
    BuiltinRules (for imported Ids) to the mg_rules field of ModGuts, to
    do some domain-specific transformations that could not be expressed
    with an ordinary pattern-matching CoreRule.  But then we can't extract
    the dependencies (in imp_rule_edges) from ru_rhs etc, because a
    BuiltinRule doesn't have any of that stuff.

    So we simply assume that BuiltinRules have no dependencies, and filter
    them out from the imp_rule_edges comprehension.
    -}

    {-
    ************************************************************************
    *                                                                      *
                    Bindings
    *                                                                      *
    ************************************************************************

    Note [Recursive bindings: the grand plan]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    When we come across a binding group
      Rec { x1 = r1; ...; xn = rn }
    we treat it like this (occAnalRecBind):

    1. Occurrence-analyse each right hand side, and build a
       "Details" for each binding to capture the results.

       Wrap the details in a Node (details, node-id, dep-node-ids),
       where node-id is just the unique of the binder, and
       dep-node-ids lists all binders on which this binding depends.
       We'll call these the "scope edges".
       See Note [Forming the Rec groups].

       All this is done by makeNode.

    2. Do SCC-analysis on these Nodes.  Each SCC will become a new Rec or
       NonRec.  The key property is that every free variable of a binding
       is accounted for by the scope edges, so that when we are done
       everything is still in scope.

    3. For each Cyclic SCC of the scope-edge SCC-analysis in (2), we
       identify suitable loop-breakers to ensure that inlining terminates.
       This is done by occAnalRec.

    4. To do so we form a new set of Nodes, with the same details, but
       different edges, the "loop-breaker nodes". The loop-breaker nodes
       have both more and fewer depedencies than the scope edges
       (see Note [Choosing loop breakers])

       More edges: if f calls g, and g has an active rule that mentions h
                   then we add an edge from f -> h

       Fewer edges: we only include dependencies on active rules, on rule
                    RHSs (not LHSs) and if there is an INLINE pragma only
                    on the stable unfolding (and vice versa).  The scope
                    edges must be much more inclusive.

    5.  The "weak fvs" of a node are, by definition:
           the scope fvs - the loop-breaker fvs
        See Note [Weak loop breakers], and the nd_weak field of Details

    6.  Having formed the loop-breaker nodes

    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.

    See also Note [Inlining and hs-boot files] in ToIface, which deals
    with a closely related source of infinite loops.

    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_nodes 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_nodes (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] (referred to from Specialise)
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    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.

    ------------------------------------------------------------
    Note [Finding join points]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    It's the occurrence analyser's job to find bindings that we can turn into join
    points, but it doesn't perform that transformation right away. Rather, it marks
    the eligible bindings as part of their occurrence data, leaving it to the
    simplifier (or to simpleOptPgm) to actually change the binder's 'IdDetails'.
    The simplifier then eta-expands the RHS if needed and then updates the
    occurrence sites. Dividing the work this way means that the occurrence analyser
    still only takes one pass, yet one can always tell the difference between a
    function call and a jump by looking at the occurrence (because the same pass
    changes the 'IdDetails' and propagates the binders to their occurrence sites).

    To track potential join points, we use the 'occ_tail' field of OccInfo. A value
    of `AlwaysTailCalled n` indicates that every occurrence of the variable is a
    tail call with `n` arguments (counting both value and type arguments). Otherwise
    'occ_tail' will be 'NoTailCallInfo'. The tail call info flows bottom-up with the
    rest of 'OccInfo' until it goes on the binder.

    Note [Rules and join points]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    Things get fiddly with rules. Suppose we have:

      let j :: Int -> Int
          j y = 2 * y
          k :: Int -> Int -> Int
          {-# RULES "SPEC k 0" k 0 = j #-}
          k x y = x + 2 * y
      in ...

    Now suppose that both j and k appear only as saturated tail calls in the body.
    Thus we would like to make them both join points. The rule complicates matters,
    though, as its RHS has an unapplied occurrence of j. *However*, if we were to
    eta-expand the rule, all would be well:

      {-# RULES "SPEC k 0" forall a. k 0 a = j a #-}

    So conceivably we could notice that a potential join point would have an
    "undersaturated" rule and account for it. This would mean we could make
    something that's been specialised a join point, for instance. But local bindings
    are rarely specialised, and being overly cautious about rules only
    costs us anything when, for some `j`:

      * Before specialisation, `j` has non-tail calls, so it can't be a join point.
      * During specialisation, `j` gets specialised and thus acquires rules.
      * Sometime afterward, the non-tail calls to `j` disappear (as dead code, say),
        and so now `j` *could* become a join point.

    This appears to be very rare in practice. TODO Perhaps we should gather
    statistics to be sure.

    Note [Excess polymorphism and join points]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    In principle, if a function would be a join point except that it fails
    the polymorphism rule (see Note [The polymorphism rule of join points] in
    CoreSyn), it can still be made a join point with some effort. This is because
    all tail calls must return the same type (they return to the same context!), and
    thus if the return type depends on an argument, that argument must always be the
    same.

    For instance, consider:

      let f :: forall a. a -> Char -> [a]
          f @a x c = ... f @a x 'a' ...
      in ... f @Int 1 'b' ... f @Int 2 'c' ...

    (where the calls are tail calls). `f` fails the polymorphism rule because its
    return type is [a], where [a] is bound. But since the type argument is always
    'Int', we can rewrite it as:

      let f' :: Int -> Char -> [Int]
          f' x c = ... f' x 'a' ...
      in ... f' 1 'b' ... f 2 'c' ...

    and now we can make f' a join point:

      join f' :: Int -> Char -> [Int]
           f' x c = ... jump f' x 'a' ...
      in ... jump f' 1 'b' ... jump f' 2 'c' ...

    It's not clear that this comes up often, however. TODO: Measure how often and
    add this analysis if necessary.

    ------------------------------------------------------------
    Note [Adjusting for lambdas]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    There's a bit of a dance we need to do after analysing a lambda expression or
    a right-hand side. In particular, we need to

      a) call 'markAllInsideLam' *unless* the binding is for a thunk, a one-shot
         lambda, or a non-recursive join point; and
      b) call 'markAllNonTailCalled' *unless* the binding is for a join point.

    Some examples, with how the free occurrences in e (assumed not to be a value
    lambda) get marked:

                                 inside lam    non-tail-called
      ------------------------------------------------------------
      let x = e                  No            Yes
      let f = \x -> e            Yes           Yes
      let f = \x{OneShot} -> e   No            Yes
      \x -> e                    Yes           Yes
      join j x = e               No            No
      joinrec j x = e            Yes           No

    There are a few other caveats; most importantly, if we're marking a binding as
    'AlwaysTailCalled', it's *going* to be a join point, so we treat it as one so
    that the effect cascades properly. Consequently, at the time the RHS is
    analysed, we won't know what adjustments to make; thus 'occAnalLamOrRhs' must
    return the unadjusted 'UsageDetails', to be adjusted by 'adjustRhsUsage' once
    join-point-hood has been decided.

    Thus the overall sequence taking place in 'occAnalNonRecBind' and
    'occAnalRecBind' is as follows:

      1. Call 'occAnalLamOrRhs' to find usage information for the RHS.
      2. Call 'tagNonRecBinder' or 'tagRecBinders', which decides whether to make
         the binding a join point.
      3. Call 'adjustRhsUsage' accordingly. (Done as part of 'tagRecBinders' when
         recursive.)

    (In the recursive case, this logic is spread between 'makeNode' and
    'occAnalRec'.)
    -}

    ------------------------------------------------------------------
    --                 occAnalBind
    ------------------------------------------------------------------

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

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

    -----------------
    occAnalNonRecBind :: OccEnv -> TopLevelFlag -> ImpRuleEdges -> Var -> CoreExpr
                      -> UsageDetails -> (UsageDetails, [CoreBind])
    occAnalNonRecBind env lvl 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_usage', [NonRec tagged_binder rhs'])
      where
        (body_usage', tagged_binder) = tagNonRecBinder lvl body_usage binder
        mb_join_arity = willBeJoinId_maybe tagged_binder

        (bndrs, body) = collectBinders rhs

        (rhs_usage1, bndrs', body') = occAnalNonRecRhs env tagged_binder bndrs body
        rhs' = mkLams (markJoinOneShots mb_join_arity bndrs') body'
               -- For a /non-recursive/ join point we can mark all
               -- its join-lambda as one-shot; and it's a good idea to do so

        -- Unfoldings
        -- See Note [Unfoldings and join points]
        rhs_usage2 = case occAnalUnfolding env NonRecursive binder of
                       Just unf_usage -> rhs_usage1 +++ unf_usage
                       Nothing        -> rhs_usage1

        -- Rules
        -- See Note [Rules are extra RHSs] and Note [Rule dependency info]
        rules_w_uds = occAnalRules env mb_join_arity NonRecursive tagged_binder
        rhs_usage3 = rhs_usage2 +++ combineUsageDetailsList
                                      (map (\(_, l, r) -> l +++ r) rules_w_uds)
        rhs_usage4 = maybe rhs_usage3 (addManyOccsSet rhs_usage3) $
                     lookupVarEnv imp_rule_edges binder
           -- See Note [Preventing loops due to imported functions rules]

        -- Final adjustment
        rhs_usage' = adjustRhsUsage mb_join_arity NonRecursive bndrs' rhs_usage4

    -----------------
    occAnalRecBind :: OccEnv -> TopLevelFlag -> ImpRuleEdges -> [(Var,CoreExpr)]
                   -> UsageDetails -> (UsageDetails, [CoreBind])
    occAnalRecBind env lvl imp_rule_edges pairs body_usage
      = foldr (occAnalRec lvl) (body_usage, []) sccs
            -- For a recursive group, we
            --      * occ-analyse all the RHSs
            --      * compute strongly-connected components
            --      * feed those components to occAnalRec
            -- See Note [Recursive bindings: the grand plan]
      where
        sccs :: [SCC Details]
        sccs = {-# SCC "occAnalBind.scc" #-}
               stronglyConnCompFromEdgedVerticesUniq nodes

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

        bndr_set = mkVarSet (map fst pairs)

    {-
    Note [Unfoldings and join points]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    We assume that anything in an unfolding occurs multiple times, since unfoldings
    are often copied (that's the whole point!). But we still need to track tail
    calls for the purpose of finding join points.
    -}

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

            -- The NonRec case is just like a Let (NonRec ...) above
    occAnalRec lvl (AcyclicSCC (ND { nd_bndr = bndr, nd_rhs = rhs
                                   , nd_uds = rhs_uds, nd_rhs_bndrs = rhs_bndrs }))
               (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) = tagNonRecBinder lvl body_uds bndr
        rhs_uds' = adjustRhsUsage (willBeJoinId_maybe tagged_bndr) NonRecursive
                                  rhs_bndrs rhs_uds

            -- The Rec case is the interesting one
            -- See Note [Recursive bindings: the grand plan]
            -- See Note [Loop breaking]
    occAnalRec lvl (CyclicSCC details_s) (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 "weak_fvs" <+> ppr weak_fvs
        --  , text "tagged details" <+> ppr tagged_details_s
        --  , text "lb nodes" <+> ppr loop_breaker_nodes])
        (final_uds, Rec pairs : binds)

      where
        bndrs    = map nd_bndr details_s
        bndr_set = mkVarSet bndrs

        ------------------------------
            -- See Note [Choosing loop breakers] for loop_breaker_nodes
        final_uds :: UsageDetails
        loop_breaker_nodes :: [LetrecNode]
        (final_uds, loop_breaker_nodes)
          = mkLoopBreakerNodes lvl bndr_set body_uds details_s

        ------------------------------
        weak_fvs :: VarSet
        weak_fvs = mapUnionVarSet nd_weak details_s

        ---------------------------
        -- Now reconstruct the cycle
        pairs :: [(Id,CoreExpr)]
        pairs | isEmptyVarSet weak_fvs = reOrderNodes   0 bndr_set weak_fvs loop_breaker_nodes []
              | otherwise              = loopBreakNodes 0 bndr_set weak_fvs loop_breaker_nodes []
              -- If weak_fvs is empty, the loop_breaker_nodes will include
              -- all the edges in the original scope edges [remember,
              -- weak_fvs is the difference between scope edges and
              -- lb-edges], so a fresh SCC computation would yield a
              -- single CyclicSCC result; and reOrderNodes deals with
              -- exactly that case

    ------------------------------------------------------------------
    --                 Loop breaking
    ------------------------------------------------------------------

    type Binding = (Id,CoreExpr)

    loopBreakNodes :: Int
                   -> VarSet        -- All binders
                   -> VarSet        -- Binders whose dependencies may be "missing"
                                    -- See Note [Weak loop breakers]
                   -> [LetrecNode]
                   -> [Binding]             -- Append these to the end
                   -> [Binding]
    {-
    loopBreakNodes is applied to the list of nodes for a cyclic strongly
    connected component (there's guaranteed to be a cycle).  It returns
    the same nodes, 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.
    -}

    -- Return the bindings sorted into a plausible order, and marked with loop breakers.
    loopBreakNodes depth bndr_set weak_fvs nodes binds
      = go (stronglyConnCompFromEdgedVerticesUniqR 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 nodes  -> reOrderNodes depth bndr_set weak_fvs nodes binds

    ----------------------------------
    reOrderNodes :: Int -> VarSet -> VarSet -> [LetrecNode] -> [Binding] -> [Binding]
        -- Choose a loop breaker, mark it no-inline,
        -- and call loopBreakNodes on the rest
    reOrderNodes _ _ _ []     _     = panic "reOrderNodes"
    reOrderNodes _ _ _ [node] binds = mk_loop_breaker node : binds
    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) = chooseLoopBreaker approximate_lb
                                                     (nd_score (fstOf3 node))
                                                     [node] [] nodes

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

    mk_loop_breaker :: LetrecNode -> Binding
    mk_loop_breaker (ND { nd_bndr = bndr, nd_rhs = rhs}, _, _)
      = (bndr `setIdOccInfo` strongLoopBreaker { occ_tail = tail_info }, rhs)
      where
        tail_info = tailCallInfo (idOccInfo bndr)

    mk_non_loop_breaker :: VarSet -> LetrecNode -> Binding
    -- See Note [Weak loop breakers]
    mk_non_loop_breaker weak_fvs (ND { nd_bndr = bndr, nd_rhs = rhs}, _, _)
      | bndr `elemVarSet` weak_fvs = (setIdOccInfo bndr occ', rhs)
      | otherwise                  = (bndr, rhs)
      where
        occ' = weakLoopBreaker { occ_tail = tail_info }
        tail_info = tailCallInfo (idOccInfo bndr)

    ----------------------------------
    chooseLoopBreaker :: Bool             -- True <=> Too many iterations,
                                          --          so approximate
                      -> NodeScore            -- Best score so far
                      -> [LetrecNode]       -- Nodes with this score
                      -> [LetrecNode]       -- Nodes with higher scores
                      -> [LetrecNode]       -- Unprocessed nodes
                      -> ([LetrecNode], [LetrecNode])
        -- This loop looks for the bind with the lowest score
        -- to pick as the loop  breaker.  The rest accumulate in
    chooseLoopBreaker _ _ 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]
    chooseLoopBreaker approx_lb loop_sc loop_nodes acc (node : nodes)
      | approx_lb
      , rank sc == rank loop_sc
      = chooseLoopBreaker approx_lb loop_sc (node : loop_nodes) acc nodes

      | sc `betterLB` loop_sc  -- Better score so pick this new one
      = chooseLoopBreaker approx_lb sc [node] (loop_nodes ++ acc) nodes

      | otherwise              -- Worse score so don't pick it
      = chooseLoopBreaker approx_lb loop_sc loop_nodes (node : acc) nodes
      where
        sc = nd_score (fstOf3 node)

    {-
    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/INLINABLE 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 INLINABLE (the
    Bool returned by hasStableCoreUnfolding_maybe).  If we start with
       Rec { {-# INLINABLE f #-}
             f x = ...f... }
    and then worker/wrapper it through strictness analysis, we'll get
       Rec { {-# INLINABLE $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-loop breaker. 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.

    @occAnalUnfolding@ 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 this
    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.

    ************************************************************************
    *                                                                      *
                       Making nodes
    *                                                                      *
    ************************************************************************
    -}

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

    noImpRuleEdges :: ImpRuleEdges
    noImpRuleEdges = emptyVarEnv

    type LetrecNode = Node Unique Details  -- Node comes from Digraph
                                           -- The Unique key is gotten from the Id
    data Details
      = ND { nd_bndr :: Id          -- Binder
           , nd_rhs  :: CoreExpr    -- RHS, already occ-analysed
           , nd_rhs_bndrs :: [CoreBndr] -- Outer lambdas of RHS
                                        -- INVARIANT: (nd_rhs_bndrs nd, _) ==
                                        --              collectBinders (nd_rhs nd)

           , 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_nodes
                                    -- See Note [Weak loop breakers]

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

           , nd_score :: NodeScore
      }

    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)
                 ])

    -- The NodeScore is compared lexicographically;
    --      e.g. lower rank wins regardless of size
    type NodeScore = ( Int     -- Rank: lower => more likely to be picked as loop breaker
                     , Int     -- Size of rhs: higher => more likely to be picked as LB
                               -- Maxes out at maxExprSize; we just use it to prioritise
                               -- small functions
                     , Bool )  -- Was it a loop breaker before?
                               -- True => more likely to be picked
                               -- Note [Loop breakers, node scoring, and stability]

    rank :: NodeScore -> Int
    rank (r, _, _) = r

    makeNode :: OccEnv -> ImpRuleEdges -> VarSet
             -> (Var, CoreExpr) -> LetrecNode
    -- See Note [Recursive bindings: the grand plan]
    makeNode env imp_rule_edges bndr_set (bndr, rhs)
      = (details, varUnique bndr, nonDetKeysUniqSet node_fvs)
        -- It's OK to use nonDetKeysUniqSet here as stronglyConnCompFromEdgedVerticesR
        -- is still deterministic with edges in nondeterministic order as
        -- explained in Note [Deterministic SCC] in Digraph.
      where
        details = ND { nd_bndr            = bndr
                     , nd_rhs             = rhs'
                     , nd_rhs_bndrs       = bndrs'
                     , nd_uds             = rhs_usage3
                     , nd_inl             = inl_fvs
                     , nd_weak            = node_fvs `minusVarSet` inl_fvs
                     , nd_active_rule_fvs = active_rule_fvs
                     , nd_score           = pprPanic "makeNodeDetails" (ppr bndr) }

        -- Constructing the edges for the main Rec computation
        -- See Note [Forming Rec groups]
        (bndrs, body) = collectBinders rhs
        (rhs_usage1, bndrs', body') = occAnalRecRhs env bndrs body
        rhs' = mkLams bndrs' body'
        rhs_usage2 = rhs_usage1 +++ all_rule_uds
                       -- Note [Rules are extra RHSs]
                       -- Note [Rule dependency info]
        rhs_usage3 = case mb_unf_uds of
                       Just unf_uds -> rhs_usage2 +++ unf_uds
                       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_w_uds :: [(CoreRule, UsageDetails, UsageDetails)]
        rules_w_uds = occAnalRules env (Just (length bndrs)) Recursive bndr

        rules_w_rhs_fvs :: [(Activation, VarSet)]    -- Find the RHS fvs
        rules_w_rhs_fvs = maybe id (\ids -> ((AlwaysActive, ids):))
                                   (lookupVarEnv imp_rule_edges bndr)
          -- See Note [Preventing loops due to imported functions rules]
                          [ (ru_act rule, udFreeVars bndr_set rhs_uds)
                          | (rule, _, rhs_uds) <- rules_w_uds ]
        all_rule_uds = combineUsageDetailsList $
                         concatMap (\(_, l, r) -> [l, r]) rules_w_uds
        active_rule_fvs = unionVarSets [fvs | (a,fvs) <- rules_w_rhs_fvs
                                            , is_active a]

        -- Finding the usage details of the INLINE pragma (if any)
        mb_unf_uds = occAnalUnfolding env Recursive bndr

        -- Find the "nd_inl" free vars; for the loop-breaker phase
        inl_fvs = case mb_unf_uds of
                    Nothing -> udFreeVars bndr_set rhs_usage1 -- No INLINE, use RHS
                    Just unf_uds -> udFreeVars bndr_set unf_uds
                          -- 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

    mkLoopBreakerNodes :: TopLevelFlag
                       -> VarSet
                       -> UsageDetails   -- for BODY of let
                       -> [Details]
                       -> (UsageDetails, -- adjusted
                           [LetrecNode])
    -- Does four things
    --   a) tag each binder with its occurrence info
    --   b) add a NodeScore to each node
    --   c) make a Node with the right dependency edges for
    --      the loop-breaker SCC analysis
    --   d) adjust each RHS's usage details according to
    --      the binder's (new) shotness and join-point-hood
    mkLoopBreakerNodes lvl bndr_set body_uds details_s
      = (final_uds, zipWith mk_lb_node details_s bndrs')
      where
        (final_uds, bndrs') = tagRecBinders lvl body_uds
                                [ (nd_bndr nd, nd_uds nd, nd_rhs_bndrs nd)
                                | nd <- details_s ]
        mk_lb_node nd@(ND { nd_bndr = bndr, nd_rhs = rhs, nd_inl = inl_fvs }) bndr'
          = (nd', varUnique bndr, nonDetKeysUniqSet lb_deps)
                  -- It's OK to use nonDetKeysUniqSet here as
                  -- stronglyConnCompFromEdgedVerticesR is still deterministic with edges
                  -- in nondeterministic order as explained in
                  -- Note [Deterministic SCC] in Digraph.
          where
            nd'     = nd { nd_bndr = bndr', nd_score = score }
            score   = nodeScore bndr bndr' rhs lb_deps
            lb_deps = 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 } <- details_s
            , let trimmed_rule_fvs = rule_fvs `intersectVarSet` bndr_set
            , not (isEmptyVarSet trimmed_rule_fvs) ]

    ------------------------------------------
    nodeScore :: Id        -- Binder has old occ-info (just for loop-breaker-ness)
              -> Id        -- Binder with new occ-info
              -> CoreExpr  -- RHS
              -> VarSet    -- Loop-breaker dependencies
              -> NodeScore
    nodeScore old_bndr new_bndr bind_rhs lb_deps
      | not (isId old_bndr)     -- A type or cercion variable is never a loop breaker
      = (100, 0, False)

      | old_bndr `elemVarSet` lb_deps  -- Self-recursive things are great loop breakers
      = (0, 0, True)                   -- See Note [Self-recursion and loop breakers]

      | exprIsTrivial rhs
      = mk_score 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

      | DFunUnfolding { df_args = args } <- id_unfolding
        -- Never choose a DFun as a loop breaker
        -- Note [DFuns should not be loop breakers]
      = (9, length args, is_lb)

        -- Data structures are more important than INLINE pragmas
        -- so that dictionary/method recursion unravels

      | CoreUnfolding { uf_guidance = UnfWhen {} } <- id_unfolding
      = mk_score 6

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

      | isStableUnfolding id_unfolding
      , can_unfold
      = mk_score 3

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

      | can_unfold  -- The Id has some kind of unfolding
      = mk_score 1

      | otherwise
      = (0, 0, is_lb)

      where
        mk_score :: Int -> NodeScore
        mk_score rank = (rank, rhs_size, is_lb)

        is_lb    = isStrongLoopBreaker (idOccInfo old_bndr)
        rhs      = case id_unfolding of
                     CoreUnfolding { uf_src = src, uf_tmpl = unf_rhs }
                        | isStableSource src
                        -> unf_rhs
                     _  -> bind_rhs
           -- 'bind_rhs' is irrelevant for inlining things with a stable unfolding
        rhs_size = case id_unfolding of
                     CoreUnfolding { uf_guidance = guidance }
                        | UnfIfGoodArgs { ug_size = size } <- guidance
                        -> size
                     _  -> cheapExprSize rhs

        can_unfold   = canUnfold id_unfolding
        id_unfolding = realIdUnfolding old_bndr
           -- realIdUnfolding: Ignore loop-breaker-ness here because
           -- that is what we are setting!

            -- Checking for a constructor application
            -- Cheap and cheerful; the simplifier 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

    maxExprSize :: Int
    maxExprSize = 20  -- Rather arbitrary

    cheapExprSize :: CoreExpr -> Int
    -- Maxes out at maxExprSize
    cheapExprSize e
      = go 0 e
      where
        go n e | n >= maxExprSize = n
               | otherwise        = go1 n e

        go1 n (Var {})        = n+1
        go1 n (Lit {})        = n+1
        go1 n (Type {})       = n
        go1 n (Coercion {})   = n
        go1 n (Tick _ e)      = go1 n e
        go1 n (Cast e _)      = go1 n e
        go1 n (App f a)       = go (go1 n f) a
        go1 n (Lam b e)
          | isTyVar b         = go1 n e
          | otherwise         = go (n+1) e
        go1 n (Let b e)       = gos (go1 n e) (rhssOfBind b)
        go1 n (Case e _ _ as) = gos (go1 n e) (rhssOfAlts as)

        gos n [] = n
        gos n (e:es) | n >= maxExprSize = n
                     | otherwise        = gos (go1 n e) es

    betterLB :: NodeScore -> NodeScore -> Bool
    -- If  n1 `betterLB` n2  then choose n1 as the loop breaker
    betterLB (rank1, size1, lb1) (rank2, size2, _)
      | rank1 < rank2 = True
      | rank1 > rank2 = False
      | size1 < size2 = False   -- Make the bigger n2 into the loop breaker
      | size1 > size2 = True
      | lb1           = True    -- Tie-break: if n1 was a loop breaker before, choose it
      | otherwise     = False   -- See Note [Loop breakers, node scoring, and stability]

    {- Note [Self-recursion and loop breakers]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    If we have
       rec { f = ...f...g...
           ; g = .....f...   }
    then 'f' has to be a loop breaker anyway, so we may as well choose it
    right away, so that g can inline freely.

    This is really just a cheap hack. Consider
       rec { f = ...g...
           ; g = ..f..h...
          ;  h = ...f....}
    Here f or g are better loop breakers than h; but we might accidentally
    choose h.  Finding the minimal set of loop breakers is hard.

    Note [Loop breakers, node scoring, and stability]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    To choose a loop breaker, we give a NodeScore to each node in the SCC,
    and pick the one with the best score (according to 'betterLB').

    We need to be jolly careful (Trac #12425, #12234) about the stability
    of this choice. Suppose we have

        let rec { f = ...g...g...
                ; g = ...f...f... }
        in
        case x of
          True  -> ...f..
          False -> ..f...

    In each iteration of the simplifier the occurrence analyser OccAnal
    chooses a loop breaker. Suppose in iteration 1 it choose g as the loop
    breaker. That means it is free to inline f.

    Suppose that GHC decides to inline f in the branches of the case, but
    (for some reason; eg it is not saturated) in the rhs of g. So we get

        let rec { f = ...g...g...
                ; g = ...f...f... }
        in
        case x of
          True  -> ...g...g.....
          False -> ..g..g....

    Now suppose that, for some reason, in the next iteration the occurrence
    analyser chooses f as the loop breaker, so it can freely inline g. And
    again for some reason the simplifier inlines g at its calls in the case
    branches, but not in the RHS of f. Then we get

        let rec { f = ...g...g...
                ; g = ...f...f... }
        in
        case x of
          True  -> ...(...f...f...)...(...f..f..).....
          False -> ..(...f...f...)...(..f..f...)....

    You can see where this is going! Each iteration of the simplifier
    doubles the number of calls to f or g. No wonder GHC is slow!

    (In the particular example in comment:3 of #12425, f and g are the two
    mutually recursive fmap instances for CondT and Result. They are both
    marked INLINE which, oddly, is why they don't inline in each other's
    RHS, because the call there is not saturated.)

    The root cause is that we flip-flop on our choice of loop breaker. I
    always thought it didn't matter, and indeed for any single iteration
    to terminate, it doesn't matter. But when we iterate, it matters a
    lot!!

    So The Plan is this:
       If there is a tie, choose the node that
       was a loop breaker last time round

    Hence the is_lb field of NodeScore

    ************************************************************************
    *                                                                      *
                       Right hand sides
    *                                                                      *
    ************************************************************************
    -}

    occAnalRhs :: OccEnv -> RecFlag -> Id -> [CoreBndr] -> CoreExpr
               -> (UsageDetails, [CoreBndr], CoreExpr)
                  -- Returned usage details covers only the RHS,
                  -- and *not* the RULE or INLINE template for the Id
    occAnalRhs env Recursive _ bndrs body
      = occAnalRecRhs env bndrs body
    occAnalRhs env NonRecursive id bndrs body
      = occAnalNonRecRhs env id bndrs body

    occAnalRecRhs :: OccEnv -> [CoreBndr] -> CoreExpr    -- Rhs lambdas, body
               -> (UsageDetails, [CoreBndr], CoreExpr)
                  -- Returned usage details covers only the RHS,
                  -- and *not* the RULE or INLINE template for the Id
    occAnalRecRhs env bndrs body = occAnalLamOrRhs (rhsCtxt env) bndrs body

    occAnalNonRecRhs :: OccEnv
                     -> Id -> [CoreBndr] -> CoreExpr    -- Binder; rhs lams, body
                         -- Binder is already tagged with occurrence info
                     -> (UsageDetails, [CoreBndr], CoreExpr)
                  -- Returned usage details covers only the RHS,
                  -- and *not* the RULE or INLINE template for the Id
    occAnalNonRecRhs env bndr bndrs body
      = occAnalLamOrRhs rhs_env bndrs body
      where
        -- See Note [Cascading inlines]
        env1 | certainly_inline = env
             | otherwise        = rhsCtxt env

        -- See Note [Sources of one-shot information]
        rhs_env = env1 { occ_one_shots = argOneShots dmd }

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

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

    occAnalUnfolding :: OccEnv
                     -> RecFlag
                     -> Id
                     -> Maybe UsageDetails
                          -- Just the analysis, not a new unfolding. The unfolding
                          -- got analysed when it was created and we don't need to
                          -- update it.
    occAnalUnfolding env rec_flag id
      = case realIdUnfolding id of -- ignore previous loop-breaker flag
          CoreUnfolding { uf_tmpl = rhs, uf_src = src }
            | not (isStableSource src)
            -> Nothing
            | otherwise
            -> Just $ markAllMany usage
            where
              (bndrs, body) = collectBinders rhs
              (usage, _, _) = occAnalRhs env rec_flag id bndrs body

          DFunUnfolding { df_bndrs = bndrs, df_args = args }
            -> Just $ zapDetails (delDetailsList usage bndrs)
            where
              usage = foldr (+++) emptyDetails (map (fst . occAnal env) args)

          _ -> Nothing

    occAnalRules :: OccEnv
                 -> Maybe JoinArity -- If the binder is (or MAY become) a join
                                    -- point, what its join arity is (or WOULD
                                    -- become). See Note [Rules and join points].
                 -> RecFlag
                 -> Id
                 -> [(CoreRule,      -- Each (non-built-in) rule
                      UsageDetails,  -- Usage details for LHS
                      UsageDetails)] -- Usage details for RHS
    occAnalRules env mb_expected_join_arity rec_flag id
      = [ (rule, lhs_uds, rhs_uds) | rule@Rule {} <- idCoreRules id
                                   , let (lhs_uds, rhs_uds) = occ_anal_rule rule ]
      where
        occ_anal_rule (Rule { ru_bndrs = bndrs, ru_args = args, ru_rhs = rhs })
          = (lhs_uds, final_rhs_uds)
          where
            lhs_uds = addManyOccsSet emptyDetails $
                        (exprsFreeVars args `delVarSetList` bndrs)
            (rhs_bndrs, rhs_body) = collectBinders rhs
            (rhs_uds, _, _) = occAnalRhs env rec_flag id rhs_bndrs rhs_body
                                -- Note [Rules are extra RHSs]
                                -- Note [Rule dependency info]
            final_rhs_uds = adjust_tail_info args $ markAllMany $
                              (rhs_uds `delDetailsList` bndrs)
        occ_anal_rule _
          = (emptyDetails, emptyDetails)

        adjust_tail_info args uds -- see Note [Rules and join points]
          = case mb_expected_join_arity of
              Just ar | args `lengthIs` ar -> uds
              _                            -> markAllNonTailCalled uds
    {-
    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 _)  = occAnalApp env (expr, [], [])
        -- At one stage, I gathered the idRuleVars for the variable 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)
      = (addManyOccsSet 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
      = (markAllNonTailCalled usage, Tick tickish body')

      | Breakpoint _ ids <- tickish
      = (usage_lam +++ foldr addManyOccs emptyDetails ids, 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 = markAllNonTailCalled (markAllInsideLam usage)
                      -- TODO There may be ways to make ticks and join points play
                      -- nicer together, but right now there are problems:
                      --   let j x = ... in tick<t> (j 1)
                      -- Making j a join point may cause the simplifier to drop t
                      -- (if the tick is put into the continuation). So we don't
                      -- count j 1 as a tail call.

    occAnal env (Cast expr co)
      = case occAnal env expr of { (usage, expr') ->
        let usage1 = zapDetailsIf (isRhsEnv env) usage
            usage2 = addManyOccsSet usage1 (coVarsOfCo co)
              -- See Note [Gather occurrences of coercion variables]
        in (markAllNonTailCalled 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') ->
        (markAllNonTailCalled 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 occAnalLamOrRhs env binders body of { (usage, tagged_binders, body') ->
        let
            expr'       = mkLams tagged_binders body'
            usage1      = markAllNonTailCalled usage
            one_shot_gp = all isOneShotBndr tagged_binders
            final_usage | one_shot_gp = usage1
                        | otherwise   = markAllInsideLam usage1
        in
        (final_usage, expr') }
      where
        (binders, body) = collectBinders expr

    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 = markAllNonTailCalled scrut_usage +++ alts_usage1
                            -- Alts can have tail calls, but the scrutinee can't
        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
          = (usage', setIdOccInfo bndr final_occ_info)
          where
            occ_info       = lookupDetails usage bndr
            usage'         = usage `delDetails` bndr
            final_occ_info = case occ_info of IAmDead -> IAmDead
                                              _       -> 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 0, 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 NotTopLevel
                         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
           | isRhsEnv env && is_exp = markAllNonTailCalled $
                                      markAllInsideLam args_uds
           | otherwise              = markAllNonTailCalled args_uds
           -- We mark the free vars of the argument of a constructor or PAP
           -- as "inside-lambda", if it is the RHS of a let(rec).
           -- This means that nothing gets inlined into a constructor or PAP
           -- argument position, which is what we want.  Typically those
           -- constructor arguments are just variables, or trivial expressions.
           -- We use inside-lam because it's like eta-expanding the PAP.
           --
           -- This is the *whole point* of the isRhsEnv predicate
           -- See Note [Arguments of let-bound constructors]

        n_val_args = valArgCount args
        n_args     = length args
        fun_uds    = mkOneOcc env fun (n_val_args > 0) n_args
        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) guaranteed_val_args
        guaranteed_val_args = n_val_args + length (takeWhile isOneShotInfo
                                                             (occ_one_shots env))
            -- See Note [Sources of one-shot information], bullet point A']

    occAnalApp env (fun, args, ticks)
      = (markAllNonTailCalled (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 []

    zapDetailsIf :: Bool              -- If this is true
                 -> UsageDetails      -- Then do zapDetails on this
                 -> UsageDetails
    zapDetailsIf True  uds = zapDetails uds
    zapDetailsIf False uds = uds

    {-
    Note [Sources of one-shot information]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The occurrence analyser obtains one-shot-lambda information from two sources:

    A:  Saturated applications:  eg   f e1 .. en

        In general, given a call (f e1 .. en) we can propagate one-shot info from
        f's strictness signature into e1 .. en, but /only/ if n is enough to
        saturate the strictness signature. A strictness signature like

              f :: C1(C1(L))LS

        means that *if f is applied to three arguments* then it will guarantee to
        call its first argument at most once, and to call the result of that at
        most once. But if f has fewer than three arguments, all bets are off; e.g.

              map (f (\x y. expensive) e2) xs

        Here the \x y abstraction may be called many times (once for each element of
        xs) so we should not mark x and y as one-shot. But if it was

              map (f (\x y. expensive) 3 2) xs

        then the first argument of f will be called at most once.

        The one-shot info, derived from f's strictness signature, is
        computed by 'argsOneShots', called in occAnalApp.

    A': Non-obviously saturated applications: eg    build (f (\x y -> expensive))
        where f is as above.

        In this case, f is only manifestly applied to one argument, so it does not
        look saturated. So by the previous point, we should not use its strictness
        signature to learn about the one-shotness of \x y. But in this case we can:
        build is fully applied, so we may use its strictness signature; and from
        that we learn that build calls its argument with two arguments *at most once*.

        So there is really only one call to f, and it will have three arguments. In
        that sense, f is saturated, and we may proceed as described above.

        Hence the computation of 'guaranteed_val_args' in occAnalApp, using
        '(occ_one_shots env)'.  See also Trac #13227, comment:9

    B:  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)

        This information must have come from a previous run of the demanand
        analyser.

    Previously, the demand analyser would *also* set the one-shot information, but
    that code was buggy (see #11770), so doing it only in on place, namely here, is
    saner.

    Note [OneShots]
    ~~~~~~~~~~~~~~~
    When analysing an expression, the occ_one_shots argument contains information
    about how the function is being used. The length of the list indicates
    how many arguments will eventually be passed to the analysed expression,
    and the OneShotInfo indicates whether this application is once or multiple times.

    Example:

     Context of f                occ_one_shots when analysing f

     f 1 2                       [OneShot, OneShot]
     map (f 1)                   [OneShot, NoOneShotInfo]
     build f                     [OneShot, OneShot]
     f 1 2 `seq` f 2 1           [NoOneShotInfo, OneShot]

    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).
    -}

    occAnalLamOrRhs :: OccEnv -> [CoreBndr] -> CoreExpr
                    -> (UsageDetails, [CoreBndr], CoreExpr)
    occAnalLamOrRhs env [] body
      = case occAnal env body of (body_usage, body') -> (body_usage, [], body')
          -- RHS of thunk or nullary join point
    occAnalLamOrRhs env (bndr:bndrs) body
      | isTyVar bndr
      = -- Important: Keep the environment so that we don't inline into an RHS like
        --   \(@ x) -> C @x (f @x)
        -- (see the beginning of Note [Cascading inlines]).
        case occAnalLamOrRhs env bndrs body of
          (body_usage, bndrs', body') -> (body_usage, bndr:bndrs', body')
    occAnalLamOrRhs env binders body
      = 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
        in
        (final_usage, tagged_binders, body') }
      where
        (env_body, binders') = oneShotGroup env binders

    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]) = tagLamBinders 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     -- See Note [OneShots]
               , 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 constructor 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"

    -- See note [OneShots]
    type OneShots = [OneShotInfo]

    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 (\c n -> 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@(one_shot : ctxt') (bndr : bndrs) rev_bndrs
          | isId bndr = go ctxt' bndrs (bndr': rev_bndrs)
          | otherwise = go ctxt  bndrs (bndr : rev_bndrs)
          where
            bndr' = updOneShotInfo bndr one_shot
                   -- Use updOneShotInfo, not setOneShotInfo, as pre-existing
                   -- one-shot info might be better than what we can infer, e.g.
                   -- due to explicit use of the magic 'oneShot' function.
                   -- See Note [The oneShot function]

    markJoinOneShots :: Maybe JoinArity -> [Var] -> [Var]
    -- Mark the lambdas of a non-recursive join point as one-shot.
    -- This is good to prevent gratuitous float-out etc
    markJoinOneShots mb_join_arity bndrs
      = case mb_join_arity of
          Nothing -> bndrs
          Just n  -> go n bndrs
     where
       go 0 bndrs  = bndrs
       go _ []     = WARN( True, ppr mb_join_arity <+> ppr bndrs ) []
       go n (b:bs) = b' : go (n-1) bs
         where
           b' | isId b    = setOneShotLambda b
              | otherwise = b

    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 (nonDetUFMToList env)
          -- It's OK to use nonDetUFMToList here because we'll forget the
          -- ordering by creating a new set with listToUFM
        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 = nonDetFoldUFM unionVarSet emptyVarSet $
          -- It's OK to use nonDetFoldUFM here because unionVarSet commutes
                 intersectUFM_C (\x _ -> x) env (getUniqSet 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}
    *                                                                      *
    ************************************************************************

    Note [UsageDetails and zapping]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    On many occasions, we must modify all gathered occurrence data at once. For
    instance, all occurrences underneath a (non-one-shot) lambda set the
    'occ_in_lam' flag to become 'True'. We could use 'mapVarEnv' to do this, but
    that takes O(n) time and we will do this often---in particular, there are many
    places where tail calls are not allowed, and each of these causes all variables
    to get marked with 'NoTailCallInfo'.

    Instead of relying on `mapVarEnv`, then, we carry three 'IdEnv's around along
    with the 'OccInfoEnv'. Each of these extra environments is a "zapped set"
    recording which variables have been zapped in some way. Zapping all occurrence
    info then simply means setting the corresponding zapped set to the whole
    'OccInfoEnv', a fast O(1) operation.
    -}

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

    type ZappedSet = OccInfoEnv -- Values are ignored

    data UsageDetails
      = UD { ud_env       :: !OccInfoEnv
           , ud_z_many    :: ZappedSet   -- apply 'markMany' to these
           , ud_z_in_lam  :: ZappedSet   -- apply 'markInsideLam' to these
           , ud_z_no_tail :: ZappedSet } -- apply 'markNonTailCalled' to these
      -- INVARIANT: All three zapped sets are subsets of the OccInfoEnv

    instance Outputable UsageDetails where
      ppr ud = ppr (ud_env (flattenUsageDetails ud))

    -------------------
    -- UsageDetails API

    (+++), combineAltsUsageDetails
            :: UsageDetails -> UsageDetails -> UsageDetails
    (+++) = combineUsageDetailsWith addOccInfo
    combineAltsUsageDetails = combineUsageDetailsWith orOccInfo

    combineUsageDetailsList :: [UsageDetails] -> UsageDetails
    combineUsageDetailsList = foldl (+++) emptyDetails

    mkOneOcc :: OccEnv -> Id -> InterestingCxt -> JoinArity -> UsageDetails
    mkOneOcc env id int_cxt arity
      | isLocalId id
      = singleton $ OneOcc { occ_in_lam  = False
                           , occ_one_br  = True
                           , occ_int_cxt = int_cxt
                           , occ_tail    = AlwaysTailCalled arity }
      | id `elemVarSet` occ_gbl_scrut env
      = singleton noOccInfo

      | otherwise
      = emptyDetails
      where
        singleton info = emptyDetails { ud_env = unitVarEnv id info }

    addOneOcc :: UsageDetails -> Id -> OccInfo -> UsageDetails
    addOneOcc ud id info
      = ud { ud_env = extendVarEnv_C plus_zapped (ud_env ud) id info }
          `alterZappedSets` (`delVarEnv` id)
      where
        plus_zapped old new = doZapping ud id old `addOccInfo` new

    addManyOccsSet :: UsageDetails -> VarSet -> UsageDetails
    addManyOccsSet usage id_set = nonDetFoldUniqSet addManyOccs usage id_set
      -- It's OK to use nonDetFoldUFM here because addManyOccs commutes

    -- Add several occurrences, assumed not to be tail calls
    addManyOccs :: Var -> UsageDetails -> UsageDetails
    addManyOccs 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.)

    delDetails :: UsageDetails -> Id -> UsageDetails
    delDetails ud bndr
      = ud `alterUsageDetails` (`delVarEnv` bndr)

    delDetailsList :: UsageDetails -> [Id] -> UsageDetails
    delDetailsList ud bndrs
      = ud `alterUsageDetails` (`delVarEnvList` bndrs)

    emptyDetails :: UsageDetails
    emptyDetails = UD { ud_env       = emptyVarEnv
                      , ud_z_many    = emptyVarEnv
                      , ud_z_in_lam  = emptyVarEnv
                      , ud_z_no_tail = emptyVarEnv }

    isEmptyDetails :: UsageDetails -> Bool
    isEmptyDetails = isEmptyVarEnv . ud_env

    markAllMany, markAllInsideLam, markAllNonTailCalled, zapDetails
      :: UsageDetails -> UsageDetails
    markAllMany          ud = ud { ud_z_many    = ud_env ud }
    markAllInsideLam     ud = ud { ud_z_in_lam  = ud_env ud }
    markAllNonTailCalled ud = ud { ud_z_no_tail = ud_env ud }

    zapDetails = markAllMany . markAllNonTailCalled -- effectively sets to noOccInfo

    lookupDetails :: UsageDetails -> Id -> OccInfo
    lookupDetails ud id
      = case lookupVarEnv (ud_env ud) id of
          Just occ -> doZapping ud id occ
          Nothing  -> IAmDead

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

    udFreeVars :: VarSet -> UsageDetails -> VarSet
    -- Find the subset of bndrs that are mentioned in uds
    udFreeVars bndrs ud = restrictUniqSetToUFM bndrs (ud_env ud)

    -------------------
    -- Auxiliary functions for UsageDetails implementation

    combineUsageDetailsWith :: (OccInfo -> OccInfo -> OccInfo)
                            -> UsageDetails -> UsageDetails -> UsageDetails
    combineUsageDetailsWith plus_occ_info ud1 ud2
      | isEmptyDetails ud1 = ud2
      | isEmptyDetails ud2 = ud1
      | otherwise
      = UD { ud_env       = plusVarEnv_C plus_occ_info (ud_env ud1) (ud_env ud2)
           , ud_z_many    = plusVarEnv (ud_z_many    ud1) (ud_z_many    ud2)
           , ud_z_in_lam  = plusVarEnv (ud_z_in_lam  ud1) (ud_z_in_lam  ud2)
           , ud_z_no_tail = plusVarEnv (ud_z_no_tail ud1) (ud_z_no_tail ud2) }

    doZapping :: UsageDetails -> Var -> OccInfo -> OccInfo
    doZapping ud var occ
      = doZappingByUnique ud (varUnique var) occ

    doZappingByUnique :: UsageDetails -> Unique -> OccInfo -> OccInfo
    doZappingByUnique ud uniq
      = (if | in_subset ud_z_many    -> markMany
            | in_subset ud_z_in_lam  -> markInsideLam
            | otherwise              -> id) .
        (if | in_subset ud_z_no_tail -> markNonTailCalled
            | otherwise              -> id)
      where
        in_subset field = uniq `elemVarEnvByKey` field ud

    alterZappedSets :: UsageDetails -> (ZappedSet -> ZappedSet) -> UsageDetails
    alterZappedSets ud f
      = ud { ud_z_many    = f (ud_z_many    ud)
           , ud_z_in_lam  = f (ud_z_in_lam  ud)
           , ud_z_no_tail = f (ud_z_no_tail ud) }

    alterUsageDetails :: UsageDetails -> (OccInfoEnv -> OccInfoEnv) -> UsageDetails
    alterUsageDetails ud f
      = ud { ud_env = f (ud_env ud) }
          `alterZappedSets` f

    flattenUsageDetails :: UsageDetails -> UsageDetails
    flattenUsageDetails ud
      = ud { ud_env = mapUFM_Directly (doZappingByUnique ud) (ud_env ud) }
          `alterZappedSets` const emptyVarEnv

    -------------------
    -- See Note [Adjusting right-hand sides]
    adjustRhsUsage :: Maybe JoinArity -> RecFlag
                   -> [CoreBndr] -- Outer lambdas, AFTER occ anal
                   -> UsageDetails -> UsageDetails
    adjustRhsUsage mb_join_arity rec_flag bndrs usage
      = maybe_mark_lam (maybe_drop_tails usage)
      where
        maybe_mark_lam ud   | one_shot   = ud
                            | otherwise  = markAllInsideLam ud
        maybe_drop_tails ud | exact_join = ud
                            | otherwise  = markAllNonTailCalled ud

        one_shot = case mb_join_arity of
                     Just join_arity
                       | isRec rec_flag -> False
                       | otherwise      -> all isOneShotBndr (drop join_arity bndrs)
                     Nothing            -> all isOneShotBndr bndrs

        exact_join = case mb_join_arity of
                       Just join_arity -> join_arity == length bndrs
                       _               -> False

    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, bndr')
          where
            occ    = lookupDetails usage bndr
            bndr'  = setBinderOcc (markNonTailCalled occ) bndr
                       -- Don't try to make an argument into a join point
            usage1 = usage `delDetails` bndr
            usage2 | isId bndr = addManyOccsSet usage1 (idUnfoldingVars bndr)
                                   -- This is effectively the RHS of a
                                   -- non-join-point binding, so it's okay to use
                                   -- addManyOccsSet, which assumes no tail calls
                   | otherwise = usage1

    tagNonRecBinder :: TopLevelFlag           -- At top level?
                    -> UsageDetails           -- Of scope
                    -> CoreBndr               -- Binder
                    -> (UsageDetails,         -- Details with binder removed
                        IdWithOccInfo)        -- Tagged binder

    tagNonRecBinder lvl usage binder
     = let
         occ     = lookupDetails usage binder
         will_be_join = decideJoinPointHood lvl usage [binder]
         occ'    | will_be_join = occ -- must already be marked AlwaysTailCalled
                 | otherwise    = markNonTailCalled occ
         binder' = setBinderOcc occ' binder
         usage'  = usage `delDetails` binder
       in
       usage' `seq` (usage', binder')

    tagRecBinders :: TopLevelFlag           -- At top level?
                  -> UsageDetails           -- Of body of let ONLY
                  -> [(CoreBndr,            -- Binder
                       UsageDetails,        -- RHS usage details
                       [CoreBndr])]         -- Lambdas in new RHS
                  -> (UsageDetails,         -- Adjusted details for whole scope,
                                            -- with binders removed
                      [IdWithOccInfo])      -- Tagged binders
    -- Substantially more complicated than non-recursive case. Need to adjust RHS
    -- details *before* tagging binders (because the tags depend on the RHSes).
    tagRecBinders lvl body_uds triples
     = let
         (bndrs, rhs_udss, _) = unzip3 triples

         -- 1. Determine join-point-hood of whole group, as determined by
         --    the *unadjusted* usage details
         unadj_uds     = body_uds +++ combineUsageDetailsList rhs_udss
         will_be_joins = decideJoinPointHood lvl unadj_uds bndrs

         -- 2. Adjust usage details of each RHS, taking into account the
         --    join-point-hood decision
         rhs_udss' = map adjust triples
         adjust (bndr, rhs_uds, rhs_bndrs)
           = adjustRhsUsage mb_join_arity Recursive rhs_bndrs rhs_uds
           where
             -- Can't use willBeJoinId_maybe here because we haven't tagged the
             -- binder yet (the tag depends on these adjustments!)
             mb_join_arity
               | will_be_joins
               , let occ = lookupDetails unadj_uds bndr
               , AlwaysTailCalled arity <- tailCallInfo occ
               = Just arity
               | otherwise
               = ASSERT(not will_be_joins) -- Should be AlwaysTailCalled if we're
                                           -- making join points!
                 Nothing

         -- 3. Compute final usage details from adjusted RHS details
         adj_uds   = body_uds +++ combineUsageDetailsList rhs_udss'

         -- 4. Tag each binder with its adjusted details modulo the
         --    join-point-hood decision
         occs      = map (lookupDetails adj_uds) bndrs
         occs'     | will_be_joins = occs
                   | otherwise     = map markNonTailCalled occs
         bndrs'    = zipWith setBinderOcc occs' bndrs

         -- 5. Drop the binders from the adjusted details and return
         usage'    = adj_uds `delDetailsList` bndrs
       in
       (usage', bndrs')

    setBinderOcc :: OccInfo -> CoreBndr -> CoreBndr
    setBinderOcc occ_info bndr
      | isTyVar bndr      = bndr
      | isExportedId bndr = if isManyOccs (idOccInfo bndr)
                              then bndr
                              else 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

    -- | Decide whether some bindings should be made into join points or not.
    -- Returns `False` if they can't be join points. Note that it's an
    -- all-or-nothing decision, as if multiple binders are given, they're assumed to
    -- be mutually recursive.
    --
    -- See Note [Invariants for join points] in CoreSyn.
    decideJoinPointHood :: TopLevelFlag -> UsageDetails
                        -> [CoreBndr]
                        -> Bool
    decideJoinPointHood TopLevel _ _
      = False
    decideJoinPointHood NotTopLevel usage bndrs
      | isJoinId (head bndrs)
      = WARN(not all_ok, text "OccurAnal failed to rediscover join point(s):" <+>
                           ppr bndrs)
        all_ok
      | otherwise
      = all_ok
      where
        -- See Note [Invariants on join points]; invariants cited by number below.
        -- Invariant 2 is always satisfiable by the simplifier by eta expansion.
        all_ok = -- Invariant 3: Either all are join points or none are
                 all ok bndrs

        ok bndr
          | -- Invariant 1: Only tail calls, all same join arity
            AlwaysTailCalled arity <- tailCallInfo (lookupDetails usage bndr)
          , -- Invariant 1 as applied to LHSes of rules
            all (ok_rule arity) (idCoreRules bndr)
            -- Invariant 4: Satisfies polymorphism rule
          , isValidJoinPointType arity (idType bndr)
          = True
          | otherwise
          = False

        ok_rule _ BuiltinRule{} = False -- only possible with plugin shenanigans
        ok_rule join_arity (Rule { ru_args = args })
          = length args == join_arity
            -- Invariant 1 as applied to LHSes of rules

    willBeJoinId_maybe :: CoreBndr -> Maybe JoinArity
    willBeJoinId_maybe bndr
      | AlwaysTailCalled arity <- tailCallInfo (idOccInfo bndr)
      = Just arity
      | otherwise
      = isJoinId_maybe bndr

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

    markMany, markInsideLam, markNonTailCalled :: OccInfo -> OccInfo

    markMany IAmDead = IAmDead
    markMany occ     = ManyOccs { occ_tail = occ_tail occ }

    markInsideLam occ@(OneOcc {}) = occ { occ_in_lam = True }
    markInsideLam occ             = occ

    markNonTailCalled IAmDead = IAmDead
    markNonTailCalled occ     = occ { occ_tail = NoTailCallInfo }

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

    addOccInfo a1 a2  = ASSERT( not (isDeadOcc a1 || isDeadOcc a2) )
                        ManyOccs { occ_tail = tailCallInfo a1 `andTailCallInfo`
                                              tailCallInfo a2 }
                                    -- 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 { occ_in_lam = in_lam1, occ_int_cxt = int_cxt1
                      , occ_tail   = tail1 })
              (OneOcc { occ_in_lam = in_lam2, occ_int_cxt = int_cxt2
                      , occ_tail   = tail2 })
      = OneOcc { occ_in_lam  = in_lam1 || in_lam2
               , occ_one_br  = False -- False, because it occurs in both branches
               , occ_int_cxt = int_cxt1 && int_cxt2
               , occ_tail    = tail1 `andTailCallInfo` tail2 }
    orOccInfo a1 a2 = ASSERT( not (isDeadOcc a1 || isDeadOcc a2) )
                      ManyOccs { occ_tail = tailCallInfo a1 `andTailCallInfo`
                                            tailCallInfo a2 }

    andTailCallInfo :: TailCallInfo -> TailCallInfo -> TailCallInfo
    andTailCallInfo info@(AlwaysTailCalled arity1) (AlwaysTailCalled arity2)
      | arity1 == arity2 = info
    andTailCallInfo _ _  = NoTailCallInfo