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

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

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

{-# LANGUAGE CPP, BangPatterns #-}

module OccurAnal (
        occurAnalysePgm, occurAnalyseExpr, occurAnalyseExpr_NoBinderSwap
    ) where

#include "HsVersions.h"

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

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

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

Here's the externally-callable interface:

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

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

    initial_uds = addIdOccs emptyDetails
                            (rulesFreeVars imp_rules `unionVarSet`
                             vectsFreeVars vects `unionVarSet`
    -- 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_rules_edges = foldr (plusVarEnv_C unionVarSet) emptyVarEnv
                            [ mapVarEnv (const maps_to) (exprFreeIds arg `delVarSetList` ru_bndrs imp_rule)
                            | imp_rule <- imp_rules
                            , let maps_to = exprFreeIds (ru_rhs imp_rule)
                                             `delVarSetList` ru_bndrs imp_rule
                            , arg <- ru_args imp_rule ]

    go :: OccEnv -> [CoreBind] -> (UsageDetails, [CoreBind])
    go _ []
        = (initial_uds, [])
    go env (bind:binds)
        = (final_usage, bind' ++ binds')
           (bs_usage, binds')   = go env binds
           (final_usage, bind') = occAnalBind env imp_rules_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)
    env = (initOccEnv all_active_rules) {occ_binder_swap = enable_binder_swap}
    -- To be conservative, we say that all inlines and rules are active
    all_active_rules = \_ -> True

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


occAnalBind :: OccEnv           -- The incoming OccEnv
            -> IdEnv IdSet      -- Mapping from FVs of imported RULE LHSs to RHS FVs
            -> CoreBind
            -> UsageDetails             -- Usage details of scope
            -> (UsageDetails,           -- Of the whole let(rec)

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

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

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

  | otherwise                   -- It's mentioned in the body
  = (body_usage' +++ rhs_usage4, [NonRec tagged_binder rhs'])
    (body_usage', tagged_binder) = tagBinder body_usage binder
    (rhs_usage1, rhs')           = occAnalNonRecRhs env tagged_binder rhs
    rhs_usage2 = addIdOccs rhs_usage1 (idUnfoldingVars binder)
    rhs_usage3 = addIdOccs rhs_usage2 (idRuleVars binder)
       -- See Note [Rules are extra RHSs] and Note [Rule dependency info]
    rhs_usage4 = maybe rhs_usage3 (addIdOccs rhs_usage3) $ lookupVarEnv imp_rules_edges binder
       -- See Note [Preventing loops due to imported functions rules]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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
        (a) g is mentioned in f's RHS `xor` f's INLINE rhs
            (see Note [Inline rules])
        (b) or h is mentioned in f's RHS, and
            g appears in the RHS of an active RULE of h
            or a transitive sequence of active rules starting with h

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

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

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

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

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

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

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

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

        Rec { f = f_rhs
              RULE f [] = g

              h = h_rhs
              g = h

    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

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

    We "solve" this by:

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

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

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

                                Inline  postInlineUnconditionally
        IAmLoopBreaker False    no      no
        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)

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]
  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

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

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

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

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

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

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

  - 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

type Binding = (Id,CoreExpr)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        | otherwise = 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    rec { plus = Clo plus1 ()

        ; plus1 _ n = Clo plus2 n

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

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

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

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

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

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

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

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

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

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

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

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

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

Annoyingly, we have to approximate SimplUtils.preInlineUnconditionally.
If we say "yes" when preInlineUnconditionally says "no" the simplifier iterates
        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.


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    alt_env = mkAltEnv env scrut bndr
    occ_anal_alt = occAnalAlt alt_env

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

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

occAnal env (Let bind body)
  = case occAnal env body                                of { (body_usage, body') ->
    case occAnalBind env emptyVarEnv 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]
    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')
    uds = fun_uds +++ final_args_uds

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

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

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

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

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

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

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

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

Note [Binders in case alternatives]
    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

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

occAnalAlt :: (OccEnv, Maybe (Id, CoreExpr))
           -> CoreAlt
           -> (UsageDetails, Alt IdWithOccInfo)
occAnalAlt (env, scrut_bind) (con, bndrs, rhs)
  = case occAnal env rhs of { (rhs_usage1, rhs1) ->
        (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
    (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 )
    captured = any (`usedIn` let_rhs_usg) bndrs
    -- The rhs of the let may include coercion variables
    -- if the scrutinee was a cast, so we must gather their
    -- usage. See Note [Gather occurrences of coercion variables]
    (let_rhs_usg, let_rhs') = occAnal env let_rhs
    (alt_usg', tagged_scrut_var) = tagBinder alt_usg scrut_var

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

*                                                                      *
*                                                                      *

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

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

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

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

instance Outputable OccEncl where
  ppr OccRhs     = ptext (sLit "occRhs")
  ppr OccVanilla = ptext (sLit "occVanilla")

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

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

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

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

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

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

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

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

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

    go ctxt (bndr:bndrs) rev_bndrs
      | isId bndr

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

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

transClosureFV :: UniqFM VarSet -> UniqFM VarSet
-- If (f,g), (g,h) are in the input, then (f,h) is in the output
--                                   as well as (f,g), (g,h)
transClosureFV env
  | no_change = env
  | otherwise = transClosureFV (listToUFM new_fv_list)
    (no_change, new_fv_list) = mapAccumL bump True (ufmToList env)
    bump no_change (b,fvs)
      | no_change_here = (no_change, (b,fvs))
      | otherwise      = (False,     (b,new_fvs))
        (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)
    extras :: VarSet    -- env(s)
    extras = foldUFM unionVarSet emptyVarSet $
             intersectUFM_C (\x _ -> x) env s

*                                                                      *
                    Binder swap
*                                                                      *

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

            data T = MkT !Int

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

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

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

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

    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 = mkLocalId (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!

*                                                                      *
*                                                                      *

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

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

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

combineAltsUsageDetails usage1 usage2
  = plusVarEnv_C orOccInfo usage1 usage2

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

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

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

type IdWithOccInfo = Id

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

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

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

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

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

*                                                                      *
\subsection{Operations over OccInfo}
*                                                                      *

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

  | id `elemVarEnv` occ_gbl_scrut env
  = unitVarEnv id NoOccInfo

  | otherwise
  = emptyDetails

markMany, markInsideLam :: OccInfo -> OccInfo

markMany _  = NoOccInfo

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

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

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

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

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