% % (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. \begin{code}

    module OccurAnal (
            occurAnalysePgm, occurAnalyseExpr
        ) where

    #include "HsVersions.h"

    import CoreSyn
    import CoreFVs
    import Type		( tyVarsOfType )
    import CoreUtils        ( exprIsTrivial, isDefaultAlt, mkCoerceI, isExpandableApp )
    import Coercion		( CoercionI(..), mkSymCoI )
    import Id
    import NameEnv
    import NameSet
    import Name		( Name, localiseName )
    import BasicTypes
    import VarSet
    import VarEnv
    import Var              ( varUnique )
    import Maybes           ( orElse )
    import Digraph          ( SCC(..), stronglyConnCompFromEdgedVerticesR )
    import PrelNames        ( buildIdKey, foldrIdKey, runSTRepIdKey, augmentIdKey )
    import Unique
    import UniqFM
    import Util             ( mapAndUnzip, filterOut )
    import Bag
    import Outputable
    import FastString
    import Data.List

\end{code} %************************************************************************ %* * \subsection[OccurAnal-main]{Counting occurrences: main function} %* * %************************************************************************ Here's the externally-callable interface: \begin{code}

    occurAnalysePgm :: Maybe (Activation -> Bool) -> [CoreRule]
                    -> [CoreBind] -> [CoreBind]
    occurAnalysePgm active_rule imp_rules binds
      = snd (go (initOccEnv active_rule imp_rules) binds)
      where
        initial_uds = addIdOccs emptyDetails (rulesFreeVars imp_rules)
        -- The RULES keep things alive!

        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 env bind bs_usage

    occurAnalyseExpr :: CoreExpr -> CoreExpr
            -- Do occurrence analysis, and discard occurence info returned
    occurAnalyseExpr expr
      = snd (occAnal (initOccEnv all_active_rules []) expr)
      where
        -- To be conservative, we say that all inlines and rules are active
        all_active_rules = Just (\_ -> True)

\end{code} %************************************************************************ %* * \subsection[OccurAnal-main]{Counting occurrences: main function} %* * %************************************************************************ Bindings ~~~~~~~~ \begin{code}

    occAnalBind :: OccEnv 		-- The incoming OccEnv
    	    -> OccEnv		-- Same, but trimmed by (binderOf bind)
                -> CoreBind
                -> UsageDetails             -- Usage details of scope
                -> (UsageDetails,           -- Of the whole let(rec)
                    [CoreBind])

    occAnalBind env _ (NonRec binder rhs) body_usage
      | isTyCoVar 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_usage3, [NonRec tagged_binder rhs'])
      where
        (body_usage', tagged_binder) = tagBinder body_usage binder
        (rhs_usage1, rhs')           = occAnalRhs env (idOccInfo 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]

\end{code} Note [Dead code] ~~~~~~~~~~~~~~~~ Dropping dead code for recursive bindings is done in a very simple way: the entire set of bindings is dropped if none of its binders are mentioned in its body; otherwise none are. This seems to miss an obvious improvement. letrec f = ...g... g = ...f... in ...g... ===> letrec f = ...g... g = ...(...g...)... in ...g... Now 'f' is unused! But it's OK! Dependency analysis will sort this out into a letrec for 'g' and a 'let' for 'f', and then 'f' will get dropped. It isn't easy to do a perfect job in one blow. Consider letrec f = ...g... g = ...h... h = ...k... k = ...m... m = ...m... in ...m... Note [Loop breaking and RULES] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Loop breaking is surprisingly subtle. First read the section 4 of "Secrets of the GHC inliner". This describes our basic plan. However things are made quite a bit more complicated by RULES. Remember * 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 [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 Example [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] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We avoid infinite inlinings by choosing loop breakers, and ensuring that a loop breaker cuts each loop. But what is a "loop"? 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. 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 (b) h is mentioned in f's RHS, and g appears in the RHS of a RULE of h or a transitive sequence of rules starting with h 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 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 is_active argument to idRhsRuleVars, and 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! We "solve" this by making g a "weak" or "rules-only" loop breaker, with OccInfo = IAmLoopBreaker True. 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. * 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 = 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 dependency is respected * 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, so it should be treated *exactly* like an extra 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 #-} Example [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. \begin{code}

    occAnalBind _ env (Rec pairs) body_usage
      = foldr (occAnalRec env) (body_usage, []) sccs
    	-- For a recursive group, we
    	--	* occ-analyse all the RHSs
    	--	* compute strongly-connected components
    	--	* feed those components to occAnalRec
      where
        -------------Dependency analysis ------------------------------
        bndr_set = mkVarSet (map fst pairs)

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

        rec_edges :: [Node Details]
        rec_edges = {-# SCC "occAnalBind.assoc" #-}  map make_node pairs

        make_node (bndr, rhs)
            = (details, varUnique bndr, keysUFM out_edges)
    	where
              details = ND { nd_bndr = bndr, nd_rhs = rhs'
                           , nd_uds = rhs_usage3, nd_inl = inl_fvs}

              (rhs_usage1, rhs') = occAnalRhs env NoOccInfo rhs
              rhs_usage2 = addIdOccs rhs_usage1 rule_fvs -- Note [Rules are extra RHSs]
              rhs_usage3 = addIdOccs rhs_usage2 unf_fvs
              unf        = realIdUnfolding bndr     -- Ignore any current loop-breaker flag
              unf_fvs    = stableUnfoldingVars unf
              rule_fvs   = idRuleVars bndr          -- See Note [Rule dependency info]

              inl_fvs   = rhs_fvs `unionVarSet` unf_fvs
              rhs_fvs   = intersectUFM_C (\b _ -> b) bndr_set rhs_usage1
              out_edges = intersectUFM_C (\b _ -> b) bndr_set rhs_usage3
            -- (a -> b) means a mentions b
            -- Given the usage details (a UFM that gives occ info for each free var of
            -- the RHS) we can get the list of free vars -- or rather their Int keys --
            -- by just extracting the keys from the finite map.  Grimy, but fast.
            -- Previously we had this:
            --      [ bndr | bndr <- bndrs,
            --               maybeToBool (lookupVarEnv rhs_usage bndr)]
            -- which has n**2 cost, and this meant that edges_from alone
            -- consumed 10% of total runtime!

    -----------------------------
    occAnalRec :: OccEnv -> 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_usage}, _, _))
                 (body_usage, binds)
      | not (bndr `usedIn` body_usage)
      = (body_usage, binds)

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

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

      | otherwise	-- At this point we always build a single Rec
      = (final_usage, Rec pairs : binds)

      where
        bndrs    = [b | (ND { nd_bndr = b }, _, _) <- nodes]
        bndr_set = mkVarSet bndrs
        non_boring bndr = isId bndr &&
                          (isStableUnfolding (realIdUnfolding bndr) || idHasRules bndr)

    	----------------------------
    	-- Tag the binders with their occurrence info
        total_usage = foldl add_usage body_usage nodes
        add_usage usage_so_far (ND { nd_uds = rhs_usage }, _, _) = usage_so_far +++ rhs_usage
        (final_usage, tagged_nodes) = mapAccumL tag_node total_usage nodes

        tag_node :: UsageDetails -> Node Details -> (UsageDetails, Node Details)
    	-- (a) Tag the binders in the details with occ info
    	-- (b) Mark the binder with "weak loop-breaker" OccInfo
    	--	saying "no preInlineUnconditionally" if it is used
    	-- 	in any rule (lhs or rhs) of the recursive group
    	--      See Note [Weak loop breakers]
        tag_node usage (details@ND { nd_bndr = bndr }, k, ks)
          = (usage `delVarEnv` bndr, (details { nd_bndr = bndr2 }, k, ks))
          where
    	bndr2 | bndr `elemVarSet` all_rule_fvs = makeLoopBreaker True bndr1
    	      | otherwise  		       = bndr1
    	bndr1 = setBinderOcc usage bndr
        all_rule_fvs = bndr_set `intersectVarSet` foldr (unionVarSet . idRuleVars)
    						    emptyVarSet bndrs

    	----------------------------
    	-- Now reconstruct the cycle
        pairs | any non_boring bndrs
              = foldr (reOrderRec 0) [] $
                stronglyConnCompFromEdgedVerticesR loop_breaker_edges
              | otherwise
              = reOrderCycle 0 tagged_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, new_ks)
    	where
              new_ks = keysUFM (fst (extendFvs rule_fv_env inl_fvs))

        ------------------------------------
        rule_fv_env :: IdEnv IdSet  -- Variables from this group mentioned in RHS of rules
                                    -- Domain is *subset* of bound vars (others have no rule fvs)
        rule_fv_env = transClosureFV init_rule_fvs
        init_rule_fvs
          | Just is_active <- occ_rule_act env  -- See Note [Finding rule RHS free vars]
          = [ (b, rule_fvs)
            | b <- bndrs
    	, isId b
            , let rule_fvs = idRuleRhsVars is_active b
                             `intersectVarSet` bndr_set
            , not (isEmptyVarSet rule_fvs)]
          | otherwise
          = []

\end{code} @reOrderRec@ 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. ============== [June 98: I don't understand the following paragraphs, and I've changed the a=b case again so that it isn't a special case any more.] Here's a case that bit me: letrec a = b b = \x. BIG in ...a...a...a.... Re-ordering doesn't change the order of bindings, but there was no loop-breaker. My solution was to make a=b bindings record b as Many, rather like INLINE bindings. Perhaps something cleverer would suffice. =============== \begin{code}

    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

           , nd_uds  :: UsageDetails  -- Usage from RHS,
                                      -- including RULES and InlineRule unfolding

           , nd_inl  :: IdSet       -- Other binders *from this Rec group* mentioned in
           }                        --   its InlineRule unfolding (if present)
                                    --   AND the  RHS
                                    -- but *excluding* any RULES
                                    -- This is the IdSet that may be used if the Id is inlined

    reOrderRec :: Int -> SCC (Node Details)
               -> [(Id,CoreExpr)] -> [(Id,CoreExpr)]
    -- Sorted into a plausible order.  Enough of the Ids have
    --      IAmALoopBreaker pragmas that there are no loops left.
    reOrderRec _ (AcyclicSCC (ND { nd_bndr = bndr, nd_rhs = rhs }, _, _))
                                       pairs = (bndr, rhs) : pairs
    reOrderRec depth (CyclicSCC cycle) pairs = reOrderCycle depth cycle pairs

    reOrderCycle :: Int -> [Node Details] -> [(Id,CoreExpr)] -> [(Id,CoreExpr)]
    reOrderCycle _ [] _
      = panic "reOrderCycle"
    reOrderCycle _ [(ND { nd_bndr = bndr, nd_rhs = rhs }, _, _)] pairs
      =    -- Common case of simple self-recursion
        (makeLoopBreaker False bndr, rhs) : pairs

    reOrderCycle depth (bind : binds) pairs
      =     -- Choose a loop breaker, mark it no-inline,
            -- do SCC analysis on the rest, and recursively sort them out
    --    pprTrace "reOrderCycle" (ppr [b | (ND { nd_bndr = b }, _, _) <- bind:binds]) $
        foldr (reOrderRec new_depth)
              ([ (makeLoopBreaker False bndr, rhs)
               | (ND { nd_bndr = bndr, nd_rhs = rhs }, _, _) <- chosen_binds] ++ pairs)
    	  (stronglyConnCompFromEdgedVerticesR unchosen)
      where
        (chosen_binds, unchosen) = choose_loop_breaker [bind] (score bind) [] binds

        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

            -- This loop looks for the bind with the lowest score
            -- to pick as the loop  breaker.  The rest accumulate in
        choose_loop_breaker loop_binds _loop_sc acc []
            = (loop_binds, 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_binds loop_sc acc (bind : binds)
            | sc < loop_sc  -- Lower score so pick this new one
            = choose_loop_breaker [bind] sc (loop_binds ++ acc) binds

    	| approximate_loop_breaker && sc == loop_sc
    	= choose_loop_breaker (bind : loop_binds) loop_sc acc binds

            | otherwise     -- Higher score so don't pick it
            = choose_loop_breaker loop_binds loop_sc (bind : acc) binds
            where
              sc = score bind

        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 inl_source <- isStableCoreUnfolding_maybe (idUnfolding bndr)
    	= case inl_source of
    	     InlineWrapper {} -> 10  -- Note [INLINE pragmas]
    	     _other	      ->  3  -- Data structures are more important than this
    	     		             -- so that dictionary/method recursion unravels
    		-- Note that this case hits all InlineRule things, so we
    		-- never look at 'rhs for InlineRule stuff. That's right, because
    		-- 'rhs' is irrelevant for inlining things with an InlineRule

            | 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 (Note _ e) = is_con_app e
        is_con_app _          = False

    makeLoopBreaker :: Bool -> Id -> Id
    -- Set the loop-breaker flag: see Note [Weak loop breakers]
    makeLoopBreaker weak bndr
      = ASSERT2( isId bndr, ppr bndr ) setIdOccInfo bndr (IAmALoopBreaker weak)

\end{code} 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 [INLINE 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. Usually this is just a question of optimisation. But a particularly bad case is wrappers generated by the demand analyser: if you make then into a loop breaker you may get an infinite inlining loop. For example: rec { $wfoo x = ....foo x.... {-loop brk-} foo x = ...$wfoo x... } The interface file sees the unfolding for $wfoo, and sees that foo is strict (and hence it gets an auto-generated wrapper). Result: an infinite inlining in the importing scope. So be a bit careful if you change this. A good example is Tree.repTree in nofib/spectral/minimax. If the repTree wrapper is chosen as the loop breaker then compiling Game.hs goes into an infinite loop. This happened when we gave is_con_app a lower score than inline candidates: Tree.repTree = __inline_me (/\a. \w w1 w2 -> case Tree.$wrepTree @ a w w1 w2 of { (# ww1, ww2 #) -> Branch @ a ww1 ww2 }) Tree.$wrepTree = /\a w w1 w2 -> (# w2_smP, map a (Tree a) (Tree.repTree a w1 w) (w w2) #) Here we do *not* want to choose 'repTree' as the loop breaker. 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 reOrderRec. [June 98, SLPJ] I've undone this change; I don't understand it. See notes with reOrderRec. \begin{code}

    occAnalRhs :: OccEnv
               -> OccInfo -> CoreExpr    -- Binder and rhs
                                    -- For non-recs the binder is alrady tagged
                                    -- with occurrence info
               -> (UsageDetails, CoreExpr)
                  -- Returned usage details covers only the RHS,
                  -- and *not* the RULE or INLINE template for the Id
    occAnalRhs env occ rhs
      = occAnal ctxt rhs
      where
        ctxt | certainly_inline = env
             | otherwise        = rhsCtxt env
            -- Note that we generally use an rhsCtxt.  This tells the occ anal n
            -- that it's looking at an RHS, which has an effect in occAnalApp
            --
            -- 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.
            -- Crude solution: use rhsCtxt for things that occur just once...

        certainly_inline = case occ of
                                OneOcc in_lam one_br _ -> not in_lam && one_br
                                _                      -> False

    addIdOccs :: UsageDetails -> VarSet -> UsageDetails
    addIdOccs usage id_set = foldVarSet add usage id_set
      where
        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.)

\end{code} Expressions ~~~~~~~~~~~ \begin{code}

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

    occAnal _   (Type t)  = (emptyDetails, Type t)
    occAnal env (Var v)   = (mkOneOcc env v False, Var v)
        -- 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.

\end{code} We regard variables that occur as constructor arguments as "dangerousToDup": \begin{verbatim} module A where f x = let y = expensive x in let z = (True,y) in (case z of {(p,q)->q}, case z of {(p,q)->q}) \end{verbatim} 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. \begin{code}

    occAnal _   expr@(Lit _) = (emptyDetails, expr)

\end{code} \begin{code}

    occAnal env (Note note@(SCC _) body)
      = case occAnal env body of { (usage, body') ->
        (mapVarEnv markInsideSCC usage, Note note body')
        }

    occAnal env (Note note body)
      = case occAnal env body of { (usage, body') ->
        (usage, Note note body')
        }

    occAnal env (Cast expr co)
      = case occAnal env expr of { (usage, expr') ->
          (markManyIf (isRhsEnv env) usage, 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.
        }

\end{code} \begin{code}

    occAnal env app@(App _ _)
      = occAnalApp env (collectArgs 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) | isTyCoVar x
      = case occAnal env body of { (body_usage, body') ->
        (body_usage, Lam x body')
        }

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

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

            --      URGH!  Sept 99: we don't seem to be able to use binders' here, because
            --      we get linear-typed things in the resulting program that we can't handle yet.
            --      (e.g. PrelShow)  TODO

            really_final_usage = if linear then
                                    final_usage
                                 else
                                    mapVarEnv markInsideLam final_usage
        in
        (really_final_usage,
         mkLams tagged_binders body') }
      where
        env_body        = vanillaCtxt (trimOccEnv env binders)
    		        -- Body is (no longer) an RhsContext
        (binders, body) = collectBinders expr
        binders'        = oneShotGroup env binders
        linear          = all is_one_shot binders'
        is_one_shot b   = isId b && isOneShotBndr b

    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  = foldr1 combineAltsUsageDetails alts_usage_s
            (alts_usage1, tagged_bndr) = tag_case_bndr alts_usage bndr
            total_usage = scrut_usage +++ alts_usage1
        in
        total_usage `seq` (total_usage, Case scrut' tagged_bndr ty alts') }}
      where
    	-- Note [Case binder usage]
    	-- ~~~~~~~~~~~~~~~~~~~~~~~~
            -- The case binder gets a usage of either "many" or "dead", never "one".
            -- Reason: we like to inline single occurrences, to eliminate a binding,
            -- but inlining a case binder *doesn't* eliminate a binding.
            -- We *don't* want to transform
            --      case x of w { (p,q) -> f w }
            -- into
            --      case x of w { (p,q) -> f (p,q) }
        tag_case_bndr usage bndr
          = case lookupVarEnv usage bndr of
              Nothing -> (usage,                  setIdOccInfo bndr IAmDead)
              Just _  -> (usage `delVarEnv` bndr, setIdOccInfo bndr NoOccInfo)

        alt_env      = mkAltEnv env scrut bndr
        occ_anal_alt = occAnalAlt alt_env bndr

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

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

    occAnalArgs :: OccEnv -> [CoreExpr] -> (UsageDetails, [CoreExpr])
    occAnalArgs env args
      = case mapAndUnzip (occAnal arg_env) args of  { (arg_uds_s, args') ->
        (foldr (+++) emptyDetails arg_uds_s, args')}
      where
        arg_env = vanillaCtxt env

\end{code} Applications are dealt with specially because we want the "build hack" to work. \begin{code}

    occAnalApp :: OccEnv
               -> (Expr CoreBndr, [Arg CoreBndr])
               -> (UsageDetails, Expr CoreBndr)
    occAnalApp env (Var fun, args)
      = case args_stuff of { (args_uds, args') ->
        let
           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
        in
        (fun_uds +++ final_args_uds, mkApps (Var fun) args') }
      where
        fun_uniq = idUnique fun
        fun_uds  = mkOneOcc env fun (valArgCount args > 0)
        is_exp = isExpandableApp fun (valArgCount args)
        	   -- See Note [CONLIKE pragma] in BasicTypes
    	   -- The definition of is_exp should match that in
    	   -- Simplify.prepareRhs

                    -- Hack for build, fold, runST
        args_stuff  | fun_uniq == buildIdKey    = appSpecial env 2 [True,True]  args
                    | fun_uniq == augmentIdKey  = appSpecial env 2 [True,True]  args
                    | fun_uniq == foldrIdKey    = appSpecial env 3 [False,True] args
                    | fun_uniq == runSTRepIdKey = appSpecial env 2 [True]       args
                            -- (foldr k z xs) may call k many times, but it never
                            -- shares a partial application of k; hence [False,True]
                            -- This means we can optimise
                            --      foldr (\x -> let v = ...x... in \y -> ...v...) z xs
                            -- by floating in the v

                    | otherwise = occAnalArgs env args

    occAnalApp env (fun, args)
      = case occAnal (addAppCtxt env args) fun of   { (fun_uds, 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.

        case occAnalArgs env args of        { (args_uds, args') ->
        let
            final_uds = fun_uds +++ args_uds
        in
        (final_uds, mkApps fun' args') }}

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

    appSpecial :: OccEnv
               -> Int -> CtxtTy     -- Argument number, and context to use for it
               -> [CoreExpr]
               -> (UsageDetails, [CoreExpr])
    appSpecial env n ctxt args
      = go n args
      where
        arg_env = vanillaCtxt env

        go _ [] = (emptyDetails, [])        -- Too few args

        go 1 (arg:args)                     -- The magic arg
          = case occAnal (setCtxtTy arg_env ctxt) arg of    { (arg_uds, arg') ->
            case occAnalArgs env args of                    { (args_uds, args') ->
            (arg_uds +++ args_uds, arg':args') }}

        go n (arg:args)
          = case occAnal arg_env arg of     { (arg_uds, arg') ->
            case go (n-1) args of           { (args_uds, args') ->
            (arg_uds +++ args_uds, arg':args') }}

\end{code} 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). \begin{code}

    occAnalAlt :: OccEnv
               -> CoreBndr
               -> CoreAlt
               -> (UsageDetails, Alt IdWithOccInfo)
    occAnalAlt env case_bndr (con, bndrs, rhs)
      = let
            env' = trimOccEnv env bndrs
        in
        case occAnal env' rhs of { (rhs_usage1, rhs1) ->
        let
    	proxies = getProxies env' case_bndr
    	(rhs_usage2, rhs2) = foldrBag wrapProxy (rhs_usage1, rhs1) proxies
            (alt_usg, tagged_bndrs) = tagLamBinders rhs_usage2 bndrs
            bndrs' = tagged_bndrs      -- See Note [Binders in case alternatives]
        in
        (alt_usg, (con, bndrs', rhs2)) }

    wrapProxy :: ProxyBind -> (UsageDetails, CoreExpr) -> (UsageDetails, CoreExpr)
    wrapProxy (bndr, rhs_var, co) (body_usg, body)
      | not (bndr `usedIn` body_usg)
      = (body_usg, body)
      | otherwise
      = (body_usg' +++ rhs_usg, Let (NonRec tagged_bndr rhs) body)
      where
        (body_usg', tagged_bndr) = tagBinder body_usg bndr
        rhs_usg = unitVarEnv rhs_var NoOccInfo	-- We don't need exact info
        rhs = mkCoerceI co (Var rhs_var)

\end{code} %************************************************************************ %* * OccEnv %* * %************************************************************************ \begin{code}

    data OccEnv
      = OccEnv { occ_encl  	  :: !OccEncl      -- Enclosing context information
        	   , occ_ctxt  	  :: !CtxtTy       -- Tells about linearity
    	   , occ_proxy 	  :: ProxyEnv
               , occ_rule_fvs :: ImpRuleUsage
               , occ_rule_act :: Maybe (Activation -> Bool)	-- Nothing => Rules are inactive
                 -- See Note [Finding rule RHS free vars]
        }

    -----------------------------
    -- 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 CtxtTy = [Bool]
            -- []           No info
            --
            -- True:ctxt    Analysing a function-valued expression that will be
            --                      applied just once
            --
            -- False:ctxt   Analysing a function-valued expression that may
            --                      be applied many times; but when it is,
            --                      the CtxtTy inside applies

    initOccEnv :: Maybe (Activation -> Bool) -> [CoreRule]
               -> OccEnv
    initOccEnv active_rule imp_rules
      = OccEnv { occ_encl  = OccVanilla
    	   , occ_ctxt  = []
    	   , occ_proxy = PE emptyVarEnv emptyVarSet
               , occ_rule_fvs = findImpRuleUsage active_rule imp_rules
               , occ_rule_act = active_rule }

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

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

    setCtxtTy :: OccEnv -> CtxtTy -> OccEnv
    setCtxtTy env ctxt = env { occ_ctxt = ctxt }

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

    oneShotGroup :: OccEnv -> [CoreBndr] -> [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 (OccEnv { occ_ctxt = ctxt }) bndrs
      = go ctxt bndrs []
      where
        go _ [] rev_bndrs = reverse rev_bndrs

        go (lin_ctxt:ctxt) (bndr:bndrs) rev_bndrs
            | isId bndr = go ctxt bndrs (bndr':rev_bndrs)
            where
              bndr' | lin_ctxt  = setOneShotLambda bndr
                    | otherwise = bndr

        go ctxt (bndr:bndrs) rev_bndrs = go ctxt bndrs (bndr:rev_bndrs)

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

\end{code} %************************************************************************ %* * ImpRuleUsage %* * %************************************************************************ \begin{code}

    type ImpRuleUsage = NameEnv UsageDetails
      -- Maps an *imported* Id f to the UsageDetails for *local* Ids
      -- used on the RHS for a *local* rule for f.

\end{code} Note [ImpRuleUsage] ~~~~~~~~~~~~~~~~ Consider this, where A.g is an imported Id f x = A.g x {-# RULE "foo" forall x. A.g x = f x #-} Obviously there's a loop, but the danger is that the occurrence analyser will say that 'f' is not a loop breaker. Then the simplifier will optimise 'f' to f x = f x and then gaily inline 'f'. Result infinite loop. More realistically, these kind of rules are generated when specialising imported INLINABLE Ids. Solution: treat an occurrence of A.g as an occurrence of all the local Ids that occur on the RULE's RHS. This mapping from imported Id to local Ids is held in occ_rule_fvs. \begin{code}

    findImpRuleUsage :: Maybe (Activation -> Bool) -> [CoreRule] -> ImpRuleUsage
    -- Find the *local* Ids that can be reached transitively,
    -- via local rules, from each *imported* Id.
    -- Sigh: this function seems more complicated than it is really worth
    findImpRuleUsage Nothing _ = emptyNameEnv
    findImpRuleUsage (Just is_active) rules
      = mkNameEnv [ (f, mapUFM (\_ -> NoOccInfo) ls)
                  | f <- rule_names
                  , let ls = find_lcl_deps f
                  , not (isEmptyVarSet ls) ]
      where
        rule_names    = map ru_fn rules
        rule_name_set = mkNameSet rule_names

        imp_deps :: NameEnv VarSet
          -- (f,g) means imported Id 'g' appears in RHS of
          --       rule for imported Id 'f', *or* does so transitively
        imp_deps = foldr add_imp emptyNameEnv rules
        add_imp rule acc
          | is_active (ruleActivation rule)
          = extendNameEnv_C unionVarSet acc (ru_fn rule)
                            (exprSomeFreeVars keep_imp (ru_rhs rule))
          | otherwise = acc
        keep_imp v = isId v && (idName v `elemNameSet` rule_name_set)
        full_imp_deps = transClosureFV (ufmToList imp_deps)

        lcl_deps :: NameEnv VarSet
          -- (f, l) means localId 'l' appears immediately
          --        in the RHS of a rule for imported Id 'f'
          -- Remember, many rules might have the same ru_fn
          -- so we do need to fold
        lcl_deps = foldr add_lcl emptyNameEnv rules
        add_lcl rule acc = extendNameEnv_C unionVarSet acc (ru_fn rule)
                                           (exprFreeIds (ru_rhs rule))

        find_lcl_deps :: Name -> VarSet
        find_lcl_deps f
          = foldVarSet (unionVarSet . lookup_lcl . idName) (lookup_lcl f)
                       (lookupNameEnv full_imp_deps f `orElse` emptyVarSet)
        lookup_lcl :: Name -> VarSet
        lookup_lcl g = lookupNameEnv lcl_deps g `orElse` emptyVarSet

    -------------
    transClosureFV :: Uniquable a => [(a, VarSet)] -> UniqFM VarSet
    -- If (f,g), (g,h) are in the input, then (f,h) is in the output
    transClosureFV fv_list
      | no_change = env
      | otherwise = transClosureFV new_fv_list
      where
        env = listToUFM fv_list
        (no_change, new_fv_list) = mapAccumL bump True fv_list
        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, Bool)
    -- (extendFVs env s) returns
    --     (s `union` env(s), env(s) `subset` s)
    extendFvs env s
      = foldVarSet add (s, True) s
      where
        add v (vs, no_change_so_far)
            = case lookupUFM env v of
                Just fvs | not (fvs `subVarSet` s)
                         -> (vs `unionVarSet` fvs, False)
                _        -> (vs, no_change_so_far)

\end{code} %************************************************************************ %* * ProxyEnv %* * %************************************************************************ \begin{code}

    data ProxyEnv
       = PE (IdEnv (Id, [(Id,CoercionI)])) VarSet
         	-- Main env, and its free variables (of both range and domain)

\end{code} Note [ProxyEnv] ~~~~~~~~~~~~~~~ The ProxyEnv keeps track of the connection between case binders and scrutinee. Specifically, if sc |-> (sc, [...(cb, co)...]) is a binding in the ProxyEnv, then cb = sc |> coi Typically we add such a binding when encountering the case expression case (sc |> coi) of cb { ... } Things to note: * The domain of the ProxyEnv is the variable (or casted variable) scrutinees of enclosing cases. This is additionally used to ensure we gather occurrence info even for GlobalId scrutinees; see Note [Binder swap for GlobalId scrutinee] * The ProxyEnv is just an optimisation; you can throw away any element without losing correctness. And we do so when pushing it inside a binding (see trimProxyEnv). * One scrutinee might map to many case binders: Eg case sc of cb1 { DEFAULT -> ....case sc of cb2 { ... } .. } INVARIANTS * If sc1 |-> (sc2, [...(cb, co)...]), then sc1==sc2 It's a UniqFM and we sometimes need the domain Id * Any particular case binder 'cb' occurs only once in entire range * No loops The Main Reason for having a ProxyEnv is so that when we encounter case e of cb { pi -> ri } we can find all the in-scope variables derivable from 'cb', and effectively add let-bindings for them (or at least for the ones *mentioned* in ri) thus: case e of cb { pi -> let { x = ..cb..; y = ...cb.. } in ri } In this way we'll replace occurrences of 'x', 'y' with 'cb', which implements the Binder-swap idea (see Note [Binder swap]) The function getProxies finds these bindings; then we add just the necessary ones, using wrapProxy. 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 one use for the (small) occ_proxy 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 [getProxies is subtle] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ The code for getProxies isn't all that obvious. Consider case v |> cov of x { DEFAULT -> case x |> cox1 of y { DEFAULT -> case x |> cox2 of z { DEFAULT -> r These will give us a ProxyEnv looking like: x |-> (x, [(y, cox1), (z, cox2)]) v |-> (v, [(x, cov)]) From this we want to extract the bindings x = z |> sym cox2 v = x |> sym cov y = x |> cox1 Notice that later bindings may mention earlier ones, and that we need to go "both ways". 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. \begin{code}

    extendProxyEnv :: ProxyEnv -> Id -> CoercionI -> Id -> ProxyEnv
    -- (extendPE x co y) typically arises from
    --		  case (x |> co) of y { ... }
    -- It extends the proxy env with the binding
    -- 	               y = x |> co
    extendProxyEnv pe scrut co case_bndr
      | scrut == case_bndr = PE env1 fvs1	-- If case_bndr shadows scrut,
      | otherwise          = PE env2 fvs2	--   don't extend
      where
        PE env1 fvs1 = trimProxyEnv pe [case_bndr]
        env2 = extendVarEnv_Acc add single env1 scrut1 (case_bndr,co)
        single cb_co = (scrut1, [cb_co])
        add cb_co (x, cb_cos) = (x, cb_co:cb_cos)
        fvs2 = fvs1 `unionVarSet`  freeVarsCoI co
    		`extendVarSet` case_bndr
    		`extendVarSet` scrut1

        scrut1 = mkLocalId (localiseName (idName scrut)) (idType scrut)
    	-- 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 INLILNE or NOINLINE pragmas!

    -----------
    type ProxyBind = (Id, Id, CoercionI)

    getProxies :: OccEnv -> Id -> Bag ProxyBind
    -- Return a bunch of bindings [...(xi,ei)...]
    -- such that  let { ...; xi=ei; ... } binds the xi using y alone
    -- See Note [getProxies is subtle]
    getProxies (OccEnv { occ_proxy = PE pe _ }) case_bndr
      = -- pprTrace "wrapProxies" (ppr case_bndr) $
        go_fwd case_bndr
      where
        fwd_pe :: IdEnv (Id, CoercionI)
        fwd_pe = foldVarEnv add1 emptyVarEnv pe
               where
                 add1 (x,ycos) env = foldr (add2 x) env ycos
                 add2 x (y,co) env = extendVarEnv env y (x,co)

        go_fwd :: Id -> Bag ProxyBind
    	-- Return bindings derivable from case_bndr
        go_fwd case_bndr = -- pprTrace "go_fwd" (vcat [ppr case_bndr, text "fwd_pe =" <+> ppr fwd_pe,
                           --                         text "pe =" <+> ppr pe]) $
                           go_fwd' case_bndr

        go_fwd' case_bndr
            | Just (scrut, co) <- lookupVarEnv fwd_pe case_bndr
            = unitBag (scrut,  case_bndr, mkSymCoI co)
    	  `unionBags` go_fwd scrut
              `unionBags` go_bwd scrut [pr | pr@(cb,_) <- lookup_bwd scrut
                                           , cb /= case_bndr]
            | otherwise
            = emptyBag

        lookup_bwd :: Id -> [(Id, CoercionI)]
    	-- Return case_bndrs that are connected to scrut
        lookup_bwd scrut = case lookupVarEnv pe scrut of
              		  Nothing          -> []
    	  		  Just (_, cb_cos) -> cb_cos

        go_bwd :: Id -> [(Id, CoercionI)] -> Bag ProxyBind
        go_bwd scrut cb_cos = foldr (unionBags . go_bwd1 scrut) emptyBag cb_cos

        go_bwd1 :: Id -> (Id, CoercionI) -> Bag ProxyBind
        go_bwd1 scrut (case_bndr, co)
           = -- pprTrace "go_bwd1" (ppr case_bndr) $
             unitBag (case_bndr, scrut, co)
    	 `unionBags` go_bwd case_bndr (lookup_bwd case_bndr)

    -----------
    mkAltEnv :: OccEnv -> CoreExpr -> Id -> OccEnv
    -- Does two things: a) makes the occ_ctxt = OccVanilla
    -- 	    	    b) extends the ProxyEnv if possible
    mkAltEnv env scrut cb
      = env { occ_encl  = OccVanilla, occ_proxy = pe' }
      where
        pe  = occ_proxy env
        pe' = case scrut of
                 Var v           -> extendProxyEnv pe v (IdCo (idType v)) cb
                 Cast (Var v) co -> extendProxyEnv pe v (ACo co)          cb
    	     _other          -> trimProxyEnv pe [cb]

    -----------
    trimOccEnv :: OccEnv -> [CoreBndr] -> OccEnv
    trimOccEnv env bndrs = env { occ_proxy = trimProxyEnv (occ_proxy env) bndrs }

    -----------
    trimProxyEnv :: ProxyEnv -> [CoreBndr] -> ProxyEnv
    -- We are about to push this ProxyEnv inside a binding for 'bndrs'
    -- So dump any ProxyEnv bindings which mention any of the bndrs
    trimProxyEnv (PE pe fvs) bndrs
      | not (bndr_set `intersectsVarSet` fvs)
      = PE pe fvs
      | otherwise
      = PE pe' (fvs `minusVarSet` bndr_set)
      where
        pe' = mapVarEnv trim pe
        bndr_set = mkVarSet bndrs
        trim (scrut, cb_cos) | scrut `elemVarSet` bndr_set = (scrut, [])
    			 | otherwise = (scrut, filterOut discard cb_cos)
        discard (cb,co) = bndr_set `intersectsVarSet`
                          extendVarSet (freeVarsCoI co) cb

    -----------
    freeVarsCoI :: CoercionI -> VarSet
    freeVarsCoI (IdCo t) = tyVarsOfType t
    freeVarsCoI (ACo co) = tyVarsOfType co

\end{code} %************************************************************************ %* * \subsection[OccurAnal-types]{OccEnv} %* * %************************************************************************ \begin{code}

    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 InlineRule
    -- unfoldings, used for join points
    tagLamBinders usage binders = usage' `seq` (usage', bndrs')
      where
        (usage', bndrs') = mapAccumR tag_lam usage binders
        tag_lam usage bndr = (usage2, setBinderOcc usage bndr)
          where
            usage1 = usage `delVarEnv` bndr
            usage2 | isId bndr = addIdOccs usage1 (idUnfoldingVars bndr)
                   | otherwise = usage1

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

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

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

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

\end{code} %************************************************************************ %* * \subsection{Operations over OccInfo} %* * %************************************************************************ \begin{code}

    mkOneOcc :: OccEnv -> Id -> InterestingCxt -> UsageDetails
    mkOneOcc env id int_cxt
      | isLocalId id = unitVarEnv id (OneOcc False True int_cxt)
      | PE env _ <- occ_proxy env
      , id `elemVarEnv` env = unitVarEnv id NoOccInfo
      | Just uds <- lookupNameEnv (occ_rule_fvs env) (idName id)
      = uds
      | otherwise           = emptyDetails

    markMany, markInsideLam, markInsideSCC :: OccInfo -> OccInfo

    markMany _  = NoOccInfo

    markInsideSCC occ = markMany occ

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

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

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

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

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

\end{code}