specialise/SpecConstr.hs

    {-
    ToDo [Oct 2013]
    ~~~~~~~~~~~~~~~
    1. Nuke ForceSpecConstr for good (it is subsumed by GHC.Types.SPEC in ghc-prim)
    2. Nuke NoSpecConstr

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

    \section[SpecConstr]{Specialise over constructors}
    -}

    {-# LANGUAGE CPP #-}

    module SpecConstr(
            specConstrProgram,
            SpecConstrAnnotation(..)
        ) where

    #include "HsVersions.h"

    import CoreSyn
    import CoreSubst
    import CoreUtils
    import CoreUnfold       ( couldBeSmallEnoughToInline )
    import CoreFVs          ( exprsFreeVarsList )
    import CoreMonad
    import Literal          ( litIsLifted )
    import HscTypes         ( ModGuts(..) )
    import WwLib            ( isWorkerSmallEnough, mkWorkerArgs )
    import DataCon
    import Coercion         hiding( substCo )
    import Rules
    import Type             hiding ( substTy )
    import TyCon            ( tyConName )
    import Id
    import PprCore          ( pprParendExpr )
    import MkCore           ( mkImpossibleExpr )
    import Var
    import VarEnv
    import VarSet
    import Name
    import BasicTypes
    import DynFlags         ( DynFlags(..), GeneralFlag( Opt_SpecConstrKeen )
                            , gopt, hasPprDebug )
    import Maybes           ( orElse, catMaybes, isJust, isNothing )
    import Demand
    import GHC.Serialized   ( deserializeWithData )
    import Util
    import Pair
    import UniqSupply
    import Outputable
    import FastString
    import UniqFM
    import MonadUtils
    import Control.Monad    ( zipWithM )
    import Data.List
    import PrelNames        ( specTyConName )
    import Module
    import TyCon ( TyCon )
    import GHC.Exts( SpecConstrAnnotation(..) )
    import Data.Ord( comparing )

    {-
    -----------------------------------------------------
                            Game plan
    -----------------------------------------------------

    Consider
            drop n []     = []
            drop 0 xs     = []
            drop n (x:xs) = drop (n-1) xs

    After the first time round, we could pass n unboxed.  This happens in
    numerical code too.  Here's what it looks like in Core:

            drop n xs = case xs of
                          []     -> []
                          (y:ys) -> case n of
                                      I# n# -> case n# of
                                                 0 -> []
                                                 _ -> drop (I# (n# -# 1#)) xs

    Notice that the recursive call has an explicit constructor as argument.
    Noticing this, we can make a specialised version of drop

            RULE: drop (I# n#) xs ==> drop' n# xs

            drop' n# xs = let n = I# n# in ...orig RHS...

    Now the simplifier will apply the specialisation in the rhs of drop', giving

            drop' n# xs = case xs of
                          []     -> []
                          (y:ys) -> case n# of
                                      0 -> []
                                      _ -> drop' (n# -# 1#) xs

    Much better!

    We'd also like to catch cases where a parameter is carried along unchanged,
    but evaluated each time round the loop:

            f i n = if i>0 || i>n then i else f (i*2) n

    Here f isn't strict in n, but we'd like to avoid evaluating it each iteration.
    In Core, by the time we've w/wd (f is strict in i) we get

            f i# n = case i# ># 0 of
                       False -> I# i#
                       True  -> case n of { I# n# ->
                                case i# ># n# of
                                    False -> I# i#
                                    True  -> f (i# *# 2#) n

    At the call to f, we see that the argument, n is known to be (I# n#),
    and n is evaluated elsewhere in the body of f, so we can play the same
    trick as above.

    Note [Reboxing]
    ~~~~~~~~~~~~~~~
    We must be careful not to allocate the same constructor twice.  Consider
            f p = (...(case p of (a,b) -> e)...p...,
                   ...let t = (r,s) in ...t...(f t)...)
    At the recursive call to f, we can see that t is a pair.  But we do NOT want
    to make a specialised copy:
            f' a b = let p = (a,b) in (..., ...)
    because now t is allocated by the caller, then r and s are passed to the
    recursive call, which allocates the (r,s) pair again.

    This happens if
      (a) the argument p is used in other than a case-scrutinisation way.
      (b) the argument to the call is not a 'fresh' tuple; you have to
            look into its unfolding to see that it's a tuple

    Hence the "OR" part of Note [Good arguments] below.

    ALTERNATIVE 2: pass both boxed and unboxed versions.  This no longer saves
    allocation, but does perhaps save evals. In the RULE we'd have
    something like

      f (I# x#) = f' (I# x#) x#

    If at the call site the (I# x) was an unfolding, then we'd have to
    rely on CSE to eliminate the duplicate allocation.... This alternative
    doesn't look attractive enough to pursue.

    ALTERNATIVE 3: ignore the reboxing problem.  The trouble is that
    the conservative reboxing story prevents many useful functions from being
    specialised.  Example:
            foo :: Maybe Int -> Int -> Int
            foo   (Just m) 0 = 0
            foo x@(Just m) n = foo x (n-m)
    Here the use of 'x' will clearly not require boxing in the specialised function.

    The strictness analyser has the same problem, in fact.  Example:
            f p@(a,b) = ...
    If we pass just 'a' and 'b' to the worker, it might need to rebox the
    pair to create (a,b).  A more sophisticated analysis might figure out
    precisely the cases in which this could happen, but the strictness
    analyser does no such analysis; it just passes 'a' and 'b', and hopes
    for the best.

    So my current choice is to make SpecConstr similarly aggressive, and
    ignore the bad potential of reboxing.

    Note [Good arguments]
    ~~~~~~~~~~~~~~~~~~~~~
    So we look for

    * A self-recursive function.  Ignore mutual recursion for now,
      because it's less common, and the code is simpler for self-recursion.

    * EITHER

       a) At a recursive call, one or more parameters is an explicit
          constructor application
            AND
          That same parameter is scrutinised by a case somewhere in
          the RHS of the function

      OR

        b) At a recursive call, one or more parameters has an unfolding
           that is an explicit constructor application
            AND
          That same parameter is scrutinised by a case somewhere in
          the RHS of the function
            AND
          Those are the only uses of the parameter (see Note [Reboxing])

    What to abstract over
    ~~~~~~~~~~~~~~~~~~~~~
    There's a bit of a complication with type arguments.  If the call
    site looks like

            f p = ...f ((:) [a] x xs)...

    then our specialised function look like

            f_spec x xs = let p = (:) [a] x xs in ....as before....

    This only makes sense if either
      a) the type variable 'a' is in scope at the top of f, or
      b) the type variable 'a' is an argument to f (and hence fs)

    Actually, (a) may hold for value arguments too, in which case
    we may not want to pass them.  Suppose 'x' is in scope at f's
    defn, but xs is not.  Then we'd like

            f_spec xs = let p = (:) [a] x xs in ....as before....

    Similarly (b) may hold too.  If x is already an argument at the
    call, no need to pass it again.

    Finally, if 'a' is not in scope at the call site, we could abstract
    it as we do the term variables:

            f_spec a x xs = let p = (:) [a] x xs in ...as before...

    So the grand plan is:

            * abstract the call site to a constructor-only pattern
              e.g.  C x (D (f p) (g q))  ==>  C s1 (D s2 s3)

            * Find the free variables of the abstracted pattern

            * Pass these variables, less any that are in scope at
              the fn defn.  But see Note [Shadowing] below.

    NOTICE that we only abstract over variables that are not in scope,
    so we're in no danger of shadowing variables used in "higher up"
    in f_spec's RHS.

    Note [Shadowing]
    ~~~~~~~~~~~~~~~~
    In this pass we gather up usage information that may mention variables
    that are bound between the usage site and the definition site; or (more
    seriously) may be bound to something different at the definition site.
    For example:

            f x = letrec g y v = let x = ...
                                 in ...(g (a,b) x)...

    Since 'x' is in scope at the call site, we may make a rewrite rule that
    looks like
            RULE forall a,b. g (a,b) x = ...
    But this rule will never match, because it's really a different 'x' at
    the call site -- and that difference will be manifest by the time the
    simplifier gets to it.  [A worry: the simplifier doesn't *guarantee*
    no-shadowing, so perhaps it may not be distinct?]

    Anyway, the rule isn't actually wrong, it's just not useful.  One possibility
    is to run deShadowBinds before running SpecConstr, but instead we run the
    simplifier.  That gives the simplest possible program for SpecConstr to
    chew on; and it virtually guarantees no shadowing.

    Note [Specialising for constant parameters]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    This one is about specialising on a *constant* (but not necessarily
    constructor) argument

        foo :: Int -> (Int -> Int) -> Int
        foo 0 f = 0
        foo m f = foo (f m) (+1)

    It produces

        lvl_rmV :: GHC.Base.Int -> GHC.Base.Int
        lvl_rmV =
          \ (ds_dlk :: GHC.Base.Int) ->
            case ds_dlk of wild_alH { GHC.Base.I# x_alG ->
            GHC.Base.I# (GHC.Prim.+# x_alG 1)

        T.$wfoo :: GHC.Prim.Int# -> (GHC.Base.Int -> GHC.Base.Int) ->
        GHC.Prim.Int#
        T.$wfoo =
          \ (ww_sme :: GHC.Prim.Int#) (w_smg :: GHC.Base.Int -> GHC.Base.Int) ->
            case ww_sme of ds_Xlw {
              __DEFAULT ->
            case w_smg (GHC.Base.I# ds_Xlw) of w1_Xmo { GHC.Base.I# ww1_Xmz ->
            T.$wfoo ww1_Xmz lvl_rmV
            };
              0 -> 0
            }

    The recursive call has lvl_rmV as its argument, so we could create a specialised copy
    with that argument baked in; that is, not passed at all.   Now it can perhaps be inlined.

    When is this worth it?  Call the constant 'lvl'
    - If 'lvl' has an unfolding that is a constructor, see if the corresponding
      parameter is scrutinised anywhere in the body.

    - If 'lvl' has an unfolding that is a inlinable function, see if the corresponding
      parameter is applied (...to enough arguments...?)

      Also do this is if the function has RULES?

    Also

    Note [Specialising for lambda parameters]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        foo :: Int -> (Int -> Int) -> Int
        foo 0 f = 0
        foo m f = foo (f m) (\n -> n-m)

    This is subtly different from the previous one in that we get an
    explicit lambda as the argument:

        T.$wfoo :: GHC.Prim.Int# -> (GHC.Base.Int -> GHC.Base.Int) ->
        GHC.Prim.Int#
        T.$wfoo =
          \ (ww_sm8 :: GHC.Prim.Int#) (w_sma :: GHC.Base.Int -> GHC.Base.Int) ->
            case ww_sm8 of ds_Xlr {
              __DEFAULT ->
            case w_sma (GHC.Base.I# ds_Xlr) of w1_Xmf { GHC.Base.I# ww1_Xmq ->
            T.$wfoo
              ww1_Xmq
              (\ (n_ad3 :: GHC.Base.Int) ->
                 case n_ad3 of wild_alB { GHC.Base.I# x_alA ->
                 GHC.Base.I# (GHC.Prim.-# x_alA ds_Xlr)
                 })
            };
              0 -> 0
            }

    I wonder if SpecConstr couldn't be extended to handle this? After all,
    lambda is a sort of constructor for functions and perhaps it already
    has most of the necessary machinery?

    Furthermore, there's an immediate win, because you don't need to allocate the lambda
    at the call site; and if perchance it's called in the recursive call, then you
    may avoid allocating it altogether.  Just like for constructors.

    Looks cool, but probably rare...but it might be easy to implement.

    Note [SpecConstr for casts]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider
        data family T a :: *
        data instance T Int = T Int

        foo n = ...
           where
             go (T 0) = 0
             go (T n) = go (T (n-1))

    The recursive call ends up looking like
            go (T (I# ...) `cast` g)
    So we want to spot the constructor application inside the cast.
    That's why we have the Cast case in argToPat

    Note [Local recursive groups]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    For a *local* recursive group, we can see all the calls to the
    function, so we seed the specialisation loop from the calls in the
    body, not from the calls in the RHS.  Consider:

      bar m n = foo n (n,n) (n,n) (n,n) (n,n)
       where
         foo n p q r s
           | n == 0    = m
           | n > 3000  = case p of { (p1,p2) -> foo (n-1) (p2,p1) q r s }
           | n > 2000  = case q of { (q1,q2) -> foo (n-1) p (q2,q1) r s }
           | n > 1000  = case r of { (r1,r2) -> foo (n-1) p q (r2,r1) s }
           | otherwise = case s of { (s1,s2) -> foo (n-1) p q r (s2,s1) }

    If we start with the RHSs of 'foo', we get lots and lots of specialisations,
    most of which are not needed.  But if we start with the (single) call
    in the rhs of 'bar' we get exactly one fully-specialised copy, and all
    the recursive calls go to this fully-specialised copy. Indeed, the original
    function is later collected as dead code.  This is very important in
    specialising the loops arising from stream fusion, for example in NDP where
    we were getting literally hundreds of (mostly unused) specialisations of
    a local function.

    In a case like the above we end up never calling the original un-specialised
    function.  (Although we still leave its code around just in case.)

    However, if we find any boring calls in the body, including *unsaturated*
    ones, such as
          letrec foo x y = ....foo...
          in map foo xs
    then we will end up calling the un-specialised function, so then we *should*
    use the calls in the un-specialised RHS as seeds.  We call these
    "boring call patterns", and callsToPats reports if it finds any of these.

    Note [Seeding top-level recursive groups]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    This seeding is done in the binding for seed_calls in specRec.

    1. If all the bindings in a top-level recursive group are local (not
       exported), then all the calls are in the rest of the top-level
       bindings.  This means we can specialise with those call patterns
       ONLY, and NOT with the RHSs of the recursive group (exactly like
       Note [Local recursive groups])

    2. But if any of the bindings are exported, the function may be called
       with any old arguments, so (for lack of anything better) we specialise
       based on
         (a) the call patterns in the RHS
         (b) the call patterns in the rest of the top-level bindings
       NB: before Apr 15 we used (a) only, but Dimitrios had an example
           where (b) was crucial, so I added that.
           Adding (b) also improved nofib allocation results:
                      multiplier: 4%   better
                      minimax:    2.8% better

    Actually in case (2), instead of using the calls from the RHS, it
    would be better to specialise in the importing module.  We'd need to
    add an INLINABLE pragma to the function, and then it can be
    specialised in the importing scope, just as is done for type classes
    in Specialise.specImports. This remains to be done (#10346).

    Note [Top-level recursive groups]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    To get the call usage information from "the rest of the top level
    bindings" (c.f. Note [Seeding top-level recursive groups]), we work
    backwards through the top-level bindings so we see the usage before we
    get to the binding of the function.  Before we can collect the usage
    though, we go through all the bindings and add them to the
    environment. This is necessary because usage is only tracked for
    functions in the environment.  These two passes are called
       'go' and 'goEnv'
    in specConstrProgram.  (Looks a bit revolting to me.)

    Note [Do not specialise diverging functions]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Specialising a function that just diverges is a waste of code.
    Furthermore, it broke GHC (simpl014) thus:
       {-# STR Sb #-}
       f = \x. case x of (a,b) -> f x
    If we specialise f we get
       f = \x. case x of (a,b) -> fspec a b
    But fspec doesn't have decent strictness info.  As it happened,
    (f x) :: IO t, so the state hack applied and we eta expanded fspec,
    and hence f.  But now f's strictness is less than its arity, which
    breaks an invariant.

    Note [Forcing specialisation]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    With stream fusion and in other similar cases, we want to fully
    specialise some (but not necessarily all!) loops regardless of their
    size and the number of specialisations.

    We allow a library to do this, in one of two ways (one which is
    deprecated):

      1) Add a parameter of type GHC.Types.SPEC (from ghc-prim) to the loop body.

      2) (Deprecated) Annotate a type with ForceSpecConstr from GHC.Exts,
         and then add *that* type as a parameter to the loop body

    The reason #2 is deprecated is because it requires GHCi, which isn't
    available for things like a cross compiler using stage1.

    Here's a (simplified) example from the `vector` package. You may bring
    the special 'force specialization' type into scope by saying:

      import GHC.Types (SPEC(..))

    or by defining your own type (again, deprecated):

      data SPEC = SPEC | SPEC2
      {-# ANN type SPEC ForceSpecConstr #-}

    (Note this is the exact same definition of GHC.Types.SPEC, just
    without the annotation.)

    After that, you say:

      foldl :: (a -> b -> a) -> a -> Stream b -> a
      {-# INLINE foldl #-}
      foldl f z (Stream step s _) = foldl_loop SPEC z s
        where
          foldl_loop !sPEC z s = case step s of
                                  Yield x s' -> foldl_loop sPEC (f z x) s'
                                  Skip       -> foldl_loop sPEC z s'
                                  Done       -> z

    SpecConstr will spot the SPEC parameter and always fully specialise
    foldl_loop. Note that

      * We have to prevent the SPEC argument from being removed by
        w/w which is why (a) SPEC is a sum type, and (b) we have to seq on
        the SPEC argument.

      * And lastly, the SPEC argument is ultimately eliminated by
        SpecConstr itself so there is no runtime overhead.

    This is all quite ugly; we ought to come up with a better design.

    ForceSpecConstr arguments are spotted in scExpr' and scTopBinds which then set
    sc_force to True when calling specLoop. This flag does four things:

      * Ignore specConstrThreshold, to specialise functions of arbitrary size
            (see scTopBind)
      * Ignore specConstrCount, to make arbitrary numbers of specialisations
            (see specialise)
      * Specialise even for arguments that are not scrutinised in the loop
            (see argToPat; Trac #4488)
      * Only specialise on recursive types a finite number of times
            (see is_too_recursive; Trac #5550; Note [Limit recursive specialisation])

    The flag holds only for specialising a single binding group, and NOT
    for nested bindings.  (So really it should be passed around explicitly
    and not stored in ScEnv.)  Trac #14379 turned out to be caused by
       f SPEC x = let g1 x = ...
                  in ...
    We force-specialise f (becuase of the SPEC), but that generates a specialised
    copy of g1 (as well as the original).  Alas g1 has a nested binding g2; and
    in each copy of g1 we get an unspecialised and specialised copy of g2; and so
    on. Result, exponential.  So the force-spec flag now only applies to one
    level of bindings at a time.

    Mechanism for this one-level-only thing:

     - Switch it on at the call to specRec, in scExpr and scTopBinds
     - Switch it off when doing the RHSs;
       this can be done very conveneniently in decreaseSpecCount

    What alternatives did I consider?

    * Annotating the loop itself doesn't work because (a) it is local and
      (b) it will be w/w'ed and having w/w propagating annotations somehow
      doesn't seem like a good idea. The types of the loop arguments
      really seem to be the most persistent thing.

    * Annotating the types that make up the loop state doesn't work,
      either, because (a) it would prevent us from using types like Either
      or tuples here, (b) we don't want to restrict the set of types that
      can be used in Stream states and (c) some types are fixed by the
      user (e.g., the accumulator here) but we still want to specialise as
      much as possible.

    Alternatives to ForceSpecConstr
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Instead of giving the loop an extra argument of type SPEC, we
    also considered *wrapping* arguments in SPEC, thus
      data SPEC a = SPEC a | SPEC2

      loop = \arg -> case arg of
                         SPEC state ->
                            case state of (x,y) -> ... loop (SPEC (x',y')) ...
                            S2 -> error ...
    The idea is that a SPEC argument says "specialise this argument
    regardless of whether the function case-analyses it".  But this
    doesn't work well:
      * SPEC must still be a sum type, else the strictness analyser
        eliminates it
      * But that means that 'loop' won't be strict in its real payload
    This loss of strictness in turn screws up specialisation, because
    we may end up with calls like
       loop (SPEC (case z of (p,q) -> (q,p)))
    Without the SPEC, if 'loop' were strict, the case would move out
    and we'd see loop applied to a pair. But if 'loop' isn't strict
    this doesn't look like a specialisable call.

    Note [Limit recursive specialisation]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    It is possible for ForceSpecConstr to cause an infinite loop of specialisation.
    Because there is no limit on the number of specialisations, a recursive call with
    a recursive constructor as an argument (for example, list cons) will generate
    a specialisation for that constructor. If the resulting specialisation also
    contains a recursive call with the constructor, this could proceed indefinitely.

    For example, if ForceSpecConstr is on:
      loop :: [Int] -> [Int] -> [Int]
      loop z []         = z
      loop z (x:xs)     = loop (x:z) xs
    this example will create a specialisation for the pattern
      loop (a:b) c      = loop' a b c

      loop' a b []      = (a:b)
      loop' a b (x:xs)  = loop (x:(a:b)) xs
    and a new pattern is found:
      loop (a:(b:c)) d  = loop'' a b c d
    which can continue indefinitely.

    Roman's suggestion to fix this was to stop after a couple of times on recursive types,
    but still specialising on non-recursive types as much as possible.

    To implement this, we count the number of times we have gone round the
    "specialise recursively" loop ('go' in 'specRec').  Once have gone round
    more than N times (controlled by -fspec-constr-recursive=N) we check

      - If sc_force is off, and sc_count is (Just max) then we don't
        need to do anything: trim_pats will limit the number of specs

      - Otherwise check if any function has now got more than (sc_count env)
        specialisations.  If sc_count is "no limit" then we arbitrarily
        choose 10 as the limit (ugh).

    See Trac #5550.   Also Trac #13623, where this test had become over-agressive,
    and we lost a wonderful specialisation that we really wanted!

    Note [NoSpecConstr]
    ~~~~~~~~~~~~~~~~~~~
    The ignoreDataCon stuff allows you to say
        {-# ANN type T NoSpecConstr #-}
    to mean "don't specialise on arguments of this type".  It was added
    before we had ForceSpecConstr.  Lacking ForceSpecConstr we specialised
    regardless of size; and then we needed a way to turn that *off*.  Now
    that we have ForceSpecConstr, this NoSpecConstr is probably redundant.
    (Used only for PArray.)

    -----------------------------------------------------
                    Stuff not yet handled
    -----------------------------------------------------

    Here are notes arising from Roman's work that I don't want to lose.

    Example 1
    ~~~~~~~~~
        data T a = T !a

        foo :: Int -> T Int -> Int
        foo 0 t = 0
        foo x t | even x    = case t of { T n -> foo (x-n) t }
                | otherwise = foo (x-1) t

    SpecConstr does no specialisation, because the second recursive call
    looks like a boxed use of the argument.  A pity.

        $wfoo_sFw :: GHC.Prim.Int# -> T.T GHC.Base.Int -> GHC.Prim.Int#
        $wfoo_sFw =
          \ (ww_sFo [Just L] :: GHC.Prim.Int#) (w_sFq [Just L] :: T.T GHC.Base.Int) ->
             case ww_sFo of ds_Xw6 [Just L] {
               __DEFAULT ->
                    case GHC.Prim.remInt# ds_Xw6 2 of wild1_aEF [Dead Just A] {
                      __DEFAULT -> $wfoo_sFw (GHC.Prim.-# ds_Xw6 1) w_sFq;
                      0 ->
                        case w_sFq of wild_Xy [Just L] { T.T n_ad5 [Just U(L)] ->
                        case n_ad5 of wild1_aET [Just A] { GHC.Base.I# y_aES [Just L] ->
                        $wfoo_sFw (GHC.Prim.-# ds_Xw6 y_aES) wild_Xy
                        } } };
               0 -> 0

    Example 2
    ~~~~~~~~~
        data a :*: b = !a :*: !b
        data T a = T !a

        foo :: (Int :*: T Int) -> Int
        foo (0 :*: t) = 0
        foo (x :*: t) | even x    = case t of { T n -> foo ((x-n) :*: t) }
                      | otherwise = foo ((x-1) :*: t)

    Very similar to the previous one, except that the parameters are now in
    a strict tuple. Before SpecConstr, we have

        $wfoo_sG3 :: GHC.Prim.Int# -> T.T GHC.Base.Int -> GHC.Prim.Int#
        $wfoo_sG3 =
          \ (ww_sFU [Just L] :: GHC.Prim.Int#) (ww_sFW [Just L] :: T.T
        GHC.Base.Int) ->
            case ww_sFU of ds_Xws [Just L] {
              __DEFAULT ->
            case GHC.Prim.remInt# ds_Xws 2 of wild1_aEZ [Dead Just A] {
              __DEFAULT ->
                case ww_sFW of tpl_B2 [Just L] { T.T a_sFo [Just A] ->
                $wfoo_sG3 (GHC.Prim.-# ds_Xws 1) tpl_B2             -- $wfoo1
                };
              0 ->
                case ww_sFW of wild_XB [Just A] { T.T n_ad7 [Just S(L)] ->
                case n_ad7 of wild1_aFd [Just L] { GHC.Base.I# y_aFc [Just L] ->
                $wfoo_sG3 (GHC.Prim.-# ds_Xws y_aFc) wild_XB        -- $wfoo2
                } } };
              0 -> 0 }

    We get two specialisations:
    "SC:$wfoo1" [0] __forall {a_sFB :: GHC.Base.Int sc_sGC :: GHC.Prim.Int#}
                      Foo.$wfoo sc_sGC (Foo.T @ GHC.Base.Int a_sFB)
                      = Foo.$s$wfoo1 a_sFB sc_sGC ;
    "SC:$wfoo2" [0] __forall {y_aFp :: GHC.Prim.Int# sc_sGC :: GHC.Prim.Int#}
                      Foo.$wfoo sc_sGC (Foo.T @ GHC.Base.Int (GHC.Base.I# y_aFp))
                      = Foo.$s$wfoo y_aFp sc_sGC ;

    But perhaps the first one isn't good.  After all, we know that tpl_B2 is
    a T (I# x) really, because T is strict and Int has one constructor.  (We can't
    unbox the strict fields, because T is polymorphic!)

    ************************************************************************
    *                                                                      *
    \subsection{Top level wrapper stuff}
    *                                                                      *
    ************************************************************************
    -}

    specConstrProgram :: ModGuts -> CoreM ModGuts
    specConstrProgram guts
      = do
          dflags <- getDynFlags
          us     <- getUniqueSupplyM
          annos  <- getFirstAnnotations deserializeWithData guts
          this_mod <- getModule
          let binds' = reverse $ fst $ initUs us $ do
                        -- Note [Top-level recursive groups]
                        (env, binds) <- goEnv (initScEnv dflags this_mod annos)
                                              (mg_binds guts)
                            -- binds is identical to (mg_binds guts), except that the
                            -- binders on the LHS have been replaced by extendBndr
                            --   (SPJ this seems like overkill; I don't think the binders
                            --    will change at all; and we don't substitute in the RHSs anyway!!)
                        go env nullUsage (reverse binds)

          return (guts { mg_binds = binds' })
      where
        -- See Note [Top-level recursive groups]
        goEnv env []            = return (env, [])
        goEnv env (bind:binds)  = do (env', bind')   <- scTopBindEnv env bind
                                     (env'', binds') <- goEnv env' binds
                                     return (env'', bind' : binds')

        -- Arg list of bindings is in reverse order
        go _   _   []           = return []
        go env usg (bind:binds) = do (usg', bind') <- scTopBind env usg bind
                                     binds' <- go env usg' binds
                                     return (bind' : binds')

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Environment: goes downwards}
    *                                                                      *
    ************************************************************************

    Note [Work-free values only in environment]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The sc_vals field keeps track of in-scope value bindings, so
    that if we come across (case x of Just y ->...) we can reduce the
    case from knowing that x is bound to a pair.

    But only *work-free* values are ok here. For example if the envt had
        x -> Just (expensive v)
    then we do NOT want to expand to
         let y = expensive v in ...
    because the x-binding still exists and we've now duplicated (expensive v).

    This seldom happens because let-bound constructor applications are
    ANF-ised, but it can happen as a result of on-the-fly transformations in
    SpecConstr itself.  Here is Trac #7865:

            let {
              a'_shr =
                case xs_af8 of _ {
                  [] -> acc_af6;
                  : ds_dgt [Dmd=<L,A>] ds_dgu [Dmd=<L,A>] ->
                    (expensive x_af7, x_af7
                } } in
            let {
              ds_sht =
                case a'_shr of _ { (p'_afd, q'_afe) ->
                TSpecConstr_DoubleInline.recursive
                  (GHC.Types.: @ GHC.Types.Int x_af7 wild_X6) (q'_afe, p'_afd)
                } } in

    When processed knowing that xs_af8 was bound to a cons, we simplify to
       a'_shr = (expensive x_af7, x_af7)
    and we do NOT want to inline that at the occurrence of a'_shr in ds_sht.
    (There are other occurrences of a'_shr.)  No no no.

    It would be possible to do some on-the-fly ANF-ising, so that a'_shr turned
    into a work-free value again, thus
       a1 = expensive x_af7
       a'_shr = (a1, x_af7)
    but that's more work, so until its shown to be important I'm going to
    leave it for now.

    Note [Making SpecConstr keener]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider this, in (perf/should_run/T9339)
       last (filter odd [1..1000])

    After optimisation, including SpecConstr, we get:
       f :: Int# -> Int -> Int
       f x y = case case remInt# x 2# of
                 __DEFAULT -> case x of
                                __DEFAULT -> f (+# wild_Xp 1#) (I# x)
                                1000000# -> ...
                 0# -> case x of
                         __DEFAULT -> f (+# wild_Xp 1#) y
                        1000000#   -> y

    Not good!  We build an (I# x) box every time around the loop.
    SpecConstr (as described in the paper) does not specialise f, despite
    the call (f ... (I# x)) because 'y' is not scrutinied in the body.
    But it is much better to specialise f for the case where the argument
    is of form (I# x); then we build the box only when returning y, which
    is on the cold path.

    Another example:

       f x = ...(g x)....

    Here 'x' is not scrutinised in f's body; but if we did specialise 'f'
    then the call (g x) might allow 'g' to be specialised in turn.

    So sc_keen controls whether or not we take account of whether argument is
    scrutinised in the body.  True <=> ignore that, and speicalise whenever
    the function is applied to a data constructor.
    -}

    data ScEnv = SCE { sc_dflags    :: DynFlags,
                       sc_module    :: !Module,
                       sc_size      :: Maybe Int,   -- Size threshold
                                                    -- Nothing => no limit

                       sc_count     :: Maybe Int,   -- Max # of specialisations for any one fn
                                                    -- Nothing => no limit
                                                    -- See Note [Avoiding exponential blowup]

                       sc_recursive :: Int,         -- Max # of specialisations over recursive type.
                                                    -- Stops ForceSpecConstr from diverging.

                       sc_keen     :: Bool,         -- Specialise on arguments that are known
                                                    -- constructors, even if they are not
                                                    -- scrutinised in the body.  See
                                                    -- Note [Making SpecConstr keener]

                       sc_force     :: Bool,        -- Force specialisation?
                                                    -- See Note [Forcing specialisation]

                       sc_subst     :: Subst,       -- Current substitution
                                                    -- Maps InIds to OutExprs

                       sc_how_bound :: HowBoundEnv,
                            -- Binds interesting non-top-level variables
                            -- Domain is OutVars (*after* applying the substitution)

                       sc_vals      :: ValueEnv,
                            -- Domain is OutIds (*after* applying the substitution)
                            -- Used even for top-level bindings (but not imported ones)
                            -- The range of the ValueEnv is *work-free* values
                            -- such as (\x. blah), or (Just v)
                            -- but NOT (Just (expensive v))
                            -- See Note [Work-free values only in environment]

                       sc_annotations :: UniqFM SpecConstrAnnotation
                 }

    ---------------------
    type HowBoundEnv = VarEnv HowBound      -- Domain is OutVars

    ---------------------
    type ValueEnv = IdEnv Value             -- Domain is OutIds
    data Value    = ConVal AltCon [CoreArg] -- _Saturated_ constructors
                                            --   The AltCon is never DEFAULT
                  | LambdaVal               -- Inlinable lambdas or PAPs

    instance Outputable Value where
       ppr (ConVal con args) = ppr con <+> interpp'SP args
       ppr LambdaVal         = text "<Lambda>"

    ---------------------
    initScEnv :: DynFlags -> Module -> UniqFM SpecConstrAnnotation -> ScEnv
    initScEnv dflags this_mod anns
      = SCE { sc_dflags      = dflags,
              sc_module      = this_mod,
              sc_size        = specConstrThreshold dflags,
              sc_count       = specConstrCount     dflags,
              sc_recursive   = specConstrRecursive dflags,
              sc_keen        = gopt Opt_SpecConstrKeen dflags,
              sc_force       = False,
              sc_subst       = emptySubst,
              sc_how_bound   = emptyVarEnv,
              sc_vals        = emptyVarEnv,
              sc_annotations = anns }

    data HowBound = RecFun  -- These are the recursive functions for which
                            -- we seek interesting call patterns

                  | RecArg  -- These are those functions' arguments, or their sub-components;
                            -- we gather occurrence information for these

    instance Outputable HowBound where
      ppr RecFun = text "RecFun"
      ppr RecArg = text "RecArg"

    scForce :: ScEnv -> Bool -> ScEnv
    scForce env b = env { sc_force = b }

    lookupHowBound :: ScEnv -> Id -> Maybe HowBound
    lookupHowBound env id = lookupVarEnv (sc_how_bound env) id

    scSubstId :: ScEnv -> Id -> CoreExpr
    scSubstId env v = lookupIdSubst (text "scSubstId") (sc_subst env) v

    scSubstTy :: ScEnv -> Type -> Type
    scSubstTy env ty = substTy (sc_subst env) ty

    scSubstCo :: ScEnv -> Coercion -> Coercion
    scSubstCo env co = substCo (sc_subst env) co

    zapScSubst :: ScEnv -> ScEnv
    zapScSubst env = env { sc_subst = zapSubstEnv (sc_subst env) }

    extendScInScope :: ScEnv -> [Var] -> ScEnv
            -- Bring the quantified variables into scope
    extendScInScope env qvars = env { sc_subst = extendInScopeList (sc_subst env) qvars }

            -- Extend the substitution
    extendScSubst :: ScEnv -> Var -> OutExpr -> ScEnv
    extendScSubst env var expr = env { sc_subst = extendSubst (sc_subst env) var expr }

    extendScSubstList :: ScEnv -> [(Var,OutExpr)] -> ScEnv
    extendScSubstList env prs = env { sc_subst = extendSubstList (sc_subst env) prs }

    extendHowBound :: ScEnv -> [Var] -> HowBound -> ScEnv
    extendHowBound env bndrs how_bound
      = env { sc_how_bound = extendVarEnvList (sc_how_bound env)
                                [(bndr,how_bound) | bndr <- bndrs] }

    extendBndrsWith :: HowBound -> ScEnv -> [Var] -> (ScEnv, [Var])
    extendBndrsWith how_bound env bndrs
      = (env { sc_subst = subst', sc_how_bound = hb_env' }, bndrs')
      where
        (subst', bndrs') = substBndrs (sc_subst env) bndrs
        hb_env' = sc_how_bound env `extendVarEnvList`
                        [(bndr,how_bound) | bndr <- bndrs']

    extendBndrWith :: HowBound -> ScEnv -> Var -> (ScEnv, Var)
    extendBndrWith how_bound env bndr
      = (env { sc_subst = subst', sc_how_bound = hb_env' }, bndr')
      where
        (subst', bndr') = substBndr (sc_subst env) bndr
        hb_env' = extendVarEnv (sc_how_bound env) bndr' how_bound

    extendRecBndrs :: ScEnv -> [Var] -> (ScEnv, [Var])
    extendRecBndrs env bndrs  = (env { sc_subst = subst' }, bndrs')
                          where
                            (subst', bndrs') = substRecBndrs (sc_subst env) bndrs

    extendBndr :: ScEnv -> Var -> (ScEnv, Var)
    extendBndr  env bndr  = (env { sc_subst = subst' }, bndr')
                          where
                            (subst', bndr') = substBndr (sc_subst env) bndr

    extendValEnv :: ScEnv -> Id -> Maybe Value -> ScEnv
    extendValEnv env _  Nothing   = env
    extendValEnv env id (Just cv)
     | valueIsWorkFree cv      -- Don't duplicate work!!  Trac #7865
     = env { sc_vals = extendVarEnv (sc_vals env) id cv }
    extendValEnv env _ _ = env

    extendCaseBndrs :: ScEnv -> OutExpr -> OutId -> AltCon -> [Var] -> (ScEnv, [Var])
    -- When we encounter
    --      case scrut of b
    --          C x y -> ...
    -- we want to bind b, to (C x y)
    -- NB1: Extends only the sc_vals part of the envt
    -- NB2: Kill the dead-ness info on the pattern binders x,y, since
    --      they are potentially made alive by the [b -> C x y] binding
    extendCaseBndrs env scrut case_bndr con alt_bndrs
       = (env2, alt_bndrs')
     where
       live_case_bndr = not (isDeadBinder case_bndr)
       env1 | Var v <- stripTicksTopE (const True) scrut
                             = extendValEnv env v cval
            | otherwise      = env  -- See Note [Add scrutinee to ValueEnv too]
       env2 | live_case_bndr = extendValEnv env1 case_bndr cval
            | otherwise      = env1

       alt_bndrs' | case scrut of { Var {} -> True; _ -> live_case_bndr }
                  = map zap alt_bndrs
                  | otherwise
                  = alt_bndrs

       cval = case con of
                    DEFAULT    -> Nothing
                    LitAlt {}  -> Just (ConVal con [])
                    DataAlt {} -> Just (ConVal con vanilla_args)
                          where
                            vanilla_args = map Type (tyConAppArgs (idType case_bndr)) ++
                                           varsToCoreExprs alt_bndrs

       zap v | isTyVar v = v                -- See NB2 above
             | otherwise = zapIdOccInfo v

    decreaseSpecCount :: ScEnv -> Int -> ScEnv
    -- See Note [Avoiding exponential blowup]
    decreaseSpecCount env n_specs
      = env { sc_force = False   -- See Note [Forcing specialisation]
            , sc_count = case sc_count env of
                           Nothing -> Nothing
                           Just n  -> Just (n `div` (n_specs + 1)) }
            -- The "+1" takes account of the original function;
            -- See Note [Avoiding exponential blowup]

    ---------------------------------------------------
    -- See Note [Forcing specialisation]
    ignoreType    :: ScEnv -> Type   -> Bool
    ignoreDataCon  :: ScEnv -> DataCon -> Bool
    forceSpecBndr :: ScEnv -> Var    -> Bool

    ignoreDataCon env dc = ignoreTyCon env (dataConTyCon dc)

    ignoreType env ty
      = case tyConAppTyCon_maybe ty of
          Just tycon -> ignoreTyCon env tycon
          _          -> False

    ignoreTyCon :: ScEnv -> TyCon -> Bool
    ignoreTyCon env tycon
      = lookupUFM (sc_annotations env) tycon == Just NoSpecConstr

    forceSpecBndr env var = forceSpecFunTy env . snd . splitForAllTys . varType $ var

    forceSpecFunTy :: ScEnv -> Type -> Bool
    forceSpecFunTy env = any (forceSpecArgTy env) . fst . splitFunTys

    forceSpecArgTy :: ScEnv -> Type -> Bool
    forceSpecArgTy env ty
      | Just ty' <- coreView ty = forceSpecArgTy env ty'

    forceSpecArgTy env ty
      | Just (tycon, tys) <- splitTyConApp_maybe ty
      , tycon /= funTyCon
          = tyConName tycon == specTyConName
            || lookupUFM (sc_annotations env) tycon == Just ForceSpecConstr
            || any (forceSpecArgTy env) tys

    forceSpecArgTy _ _ = False

    {-
    Note [Add scrutinee to ValueEnv too]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider this:
       case x of y
         (a,b) -> case b of c
                    I# v -> ...(f y)...
    By the time we get to the call (f y), the ValueEnv
    will have a binding for y, and for c
        y -> (a,b)
        c -> I# v
    BUT that's not enough!  Looking at the call (f y) we
    see that y is pair (a,b), but we also need to know what 'b' is.
    So in extendCaseBndrs we must *also* add the binding
       b -> I# v
    else we lose a useful specialisation for f.  This is necessary even
    though the simplifier has systematically replaced uses of 'x' with 'y'
    and 'b' with 'c' in the code.  The use of 'b' in the ValueEnv came
    from outside the case.  See Trac #4908 for the live example.

    Note [Avoiding exponential blowup]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The sc_count field of the ScEnv says how many times we are prepared to
    duplicate a single function.  But we must take care with recursive
    specialisations.  Consider

            let $j1 = let $j2 = let $j3 = ...
                                in
                                ...$j3...
                      in
                      ...$j2...
            in
            ...$j1...

    If we specialise $j1 then in each specialisation (as well as the original)
    we can specialise $j2, and similarly $j3.  Even if we make just *one*
    specialisation of each, because we also have the original we'll get 2^n
    copies of $j3, which is not good.

    So when recursively specialising we divide the sc_count by the number of
    copies we are making at this level, including the original.

    ************************************************************************
    *                                                                      *
    \subsection{Usage information: flows upwards}
    *                                                                      *
    ************************************************************************
    -}

    data ScUsage
       = SCU {
            scu_calls :: CallEnv,           -- Calls
                                            -- The functions are a subset of the
                                            --      RecFuns in the ScEnv

            scu_occs :: !(IdEnv ArgOcc)     -- Information on argument occurrences
         }                                  -- The domain is OutIds

    type CallEnv = IdEnv [Call]
    data Call = Call Id [CoreArg] ValueEnv
            -- The arguments of the call, together with the
            -- env giving the constructor bindings at the call site
            -- We keep the function mainly for debug output

    instance Outputable ScUsage where
      ppr (SCU { scu_calls = calls, scu_occs = occs })
        = text "SCU" <+> braces (sep [ ptext (sLit "calls =") <+> ppr calls
                                             , text "occs =" <+> ppr occs ])

    instance Outputable Call where
      ppr (Call fn args _) = ppr fn <+> fsep (map pprParendExpr args)

    nullUsage :: ScUsage
    nullUsage = SCU { scu_calls = emptyVarEnv, scu_occs = emptyVarEnv }

    combineCalls :: CallEnv -> CallEnv -> CallEnv
    combineCalls = plusVarEnv_C (++)
      where
    --    plus cs ds | length res > 1
    --               = pprTrace "combineCalls" (vcat [ text "cs:" <+> ppr cs
    --                                               , text "ds:" <+> ppr ds])
    --                 res
    --               | otherwise = res
    --       where
    --          res = cs ++ ds

    combineUsage :: ScUsage -> ScUsage -> ScUsage
    combineUsage u1 u2 = SCU { scu_calls = combineCalls (scu_calls u1) (scu_calls u2),
                               scu_occs  = plusVarEnv_C combineOcc (scu_occs u1) (scu_occs u2) }

    combineUsages :: [ScUsage] -> ScUsage
    combineUsages [] = nullUsage
    combineUsages us = foldr1 combineUsage us

    lookupOccs :: ScUsage -> [OutVar] -> (ScUsage, [ArgOcc])
    lookupOccs (SCU { scu_calls = sc_calls, scu_occs = sc_occs }) bndrs
      = (SCU {scu_calls = sc_calls, scu_occs = delVarEnvList sc_occs bndrs},
         [lookupVarEnv sc_occs b `orElse` NoOcc | b <- bndrs])

    data ArgOcc = NoOcc     -- Doesn't occur at all; or a type argument
                | UnkOcc    -- Used in some unknown way

                | ScrutOcc  -- See Note [ScrutOcc]
                     (DataConEnv [ArgOcc])   -- How the sub-components are used

    type DataConEnv a = UniqFM a     -- Keyed by DataCon

    {- Note  [ScrutOcc]
    ~~~~~~~~~~~~~~~~~~~
    An occurrence of ScrutOcc indicates that the thing, or a `cast` version of the thing,
    is *only* taken apart or applied.

      Functions, literal: ScrutOcc emptyUFM
      Data constructors:  ScrutOcc subs,

    where (subs :: UniqFM [ArgOcc]) gives usage of the *pattern-bound* components,
    The domain of the UniqFM is the Unique of the data constructor

    The [ArgOcc] is the occurrences of the *pattern-bound* components
    of the data structure.  E.g.
            data T a = forall b. MkT a b (b->a)
    A pattern binds b, x::a, y::b, z::b->a, but not 'a'!

    -}

    instance Outputable ArgOcc where
      ppr (ScrutOcc xs) = text "scrut-occ" <> ppr xs
      ppr UnkOcc        = text "unk-occ"
      ppr NoOcc         = text "no-occ"

    evalScrutOcc :: ArgOcc
    evalScrutOcc = ScrutOcc emptyUFM

    -- Experimentally, this vesion of combineOcc makes ScrutOcc "win", so
    -- that if the thing is scrutinised anywhere then we get to see that
    -- in the overall result, even if it's also used in a boxed way
    -- This might be too aggressive; see Note [Reboxing] Alternative 3
    combineOcc :: ArgOcc -> ArgOcc -> ArgOcc
    combineOcc NoOcc         occ           = occ
    combineOcc occ           NoOcc         = occ
    combineOcc (ScrutOcc xs) (ScrutOcc ys) = ScrutOcc (plusUFM_C combineOccs xs ys)
    combineOcc UnkOcc        (ScrutOcc ys) = ScrutOcc ys
    combineOcc (ScrutOcc xs) UnkOcc        = ScrutOcc xs
    combineOcc UnkOcc        UnkOcc        = UnkOcc

    combineOccs :: [ArgOcc] -> [ArgOcc] -> [ArgOcc]
    combineOccs xs ys = zipWithEqual "combineOccs" combineOcc xs ys

    setScrutOcc :: ScEnv -> ScUsage -> OutExpr -> ArgOcc -> ScUsage
    -- _Overwrite_ the occurrence info for the scrutinee, if the scrutinee
    -- is a variable, and an interesting variable
    setScrutOcc env usg (Cast e _) occ      = setScrutOcc env usg e occ
    setScrutOcc env usg (Tick _ e) occ      = setScrutOcc env usg e occ
    setScrutOcc env usg (Var v)    occ
      | Just RecArg <- lookupHowBound env v = usg { scu_occs = extendVarEnv (scu_occs usg) v occ }
      | otherwise                           = usg
    setScrutOcc _env usg _other _occ        -- Catch-all
      = usg

    {-
    ************************************************************************
    *                                                                      *
    \subsection{The main recursive function}
    *                                                                      *
    ************************************************************************

    The main recursive function gathers up usage information, and
    creates specialised versions of functions.
    -}

    scExpr, scExpr' :: ScEnv -> CoreExpr -> UniqSM (ScUsage, CoreExpr)
            -- The unique supply is needed when we invent
            -- a new name for the specialised function and its args

    scExpr env e = scExpr' env e

    scExpr' env (Var v)      = case scSubstId env v of
                                Var v' -> return (mkVarUsage env v' [], Var v')
                                e'     -> scExpr (zapScSubst env) e'

    scExpr' env (Type t)     = return (nullUsage, Type (scSubstTy env t))
    scExpr' env (Coercion c) = return (nullUsage, Coercion (scSubstCo env c))
    scExpr' _   e@(Lit {})   = return (nullUsage, e)
    scExpr' env (Tick t e)   = do (usg, e') <- scExpr env e
                                  return (usg, Tick t e')
    scExpr' env (Cast e co)  = do (usg, e') <- scExpr env e
                                  return (usg, mkCast e' (scSubstCo env co))
                                  -- Important to use mkCast here
                                  -- See Note [SpecConstr call patterns]
    scExpr' env e@(App _ _)  = scApp env (collectArgs e)
    scExpr' env (Lam b e)    = do let (env', b') = extendBndr env b
                                  (usg, e') <- scExpr env' e
                                  return (usg, Lam b' e')

    scExpr' env (Case scrut b ty alts)
      = do  { (scrut_usg, scrut') <- scExpr env scrut
            ; case isValue (sc_vals env) scrut' of
                    Just (ConVal con args) -> sc_con_app con args scrut'
                    _other                 -> sc_vanilla scrut_usg scrut'
            }
      where
        sc_con_app con args scrut'  -- Known constructor; simplify
         = do { let (_, bs, rhs) = findAlt con alts
                                      `orElse` (DEFAULT, [], mkImpossibleExpr ty)
                    alt_env'     = extendScSubstList env ((b,scrut') : bs `zip` trimConArgs con args)
              ; scExpr alt_env' rhs }

        sc_vanilla scrut_usg scrut' -- Normal case
         = do { let (alt_env,b') = extendBndrWith RecArg env b
                            -- Record RecArg for the components

              ; (alt_usgs, alt_occs, alts')
                    <- mapAndUnzip3M (sc_alt alt_env scrut' b') alts

              ; let scrut_occ  = foldr combineOcc NoOcc alt_occs
                    scrut_usg' = setScrutOcc env scrut_usg scrut' scrut_occ
                    -- The combined usage of the scrutinee is given
                    -- by scrut_occ, which is passed to scScrut, which
                    -- in turn treats a bare-variable scrutinee specially

              ; return (foldr combineUsage scrut_usg' alt_usgs,
                        Case scrut' b' (scSubstTy env ty) alts') }

        sc_alt env scrut' b' (con,bs,rhs)
         = do { let (env1, bs1) = extendBndrsWith RecArg env bs
                    (env2, bs2) = extendCaseBndrs env1 scrut' b' con bs1
              ; (usg, rhs') <- scExpr env2 rhs
              ; let (usg', b_occ:arg_occs) = lookupOccs usg (b':bs2)
                    scrut_occ = case con of
                                   DataAlt dc -> ScrutOcc (unitUFM dc arg_occs)
                                   _          -> ScrutOcc emptyUFM
              ; return (usg', b_occ `combineOcc` scrut_occ, (con, bs2, rhs')) }

    scExpr' env (Let (NonRec bndr rhs) body)
      | isTyVar bndr        -- Type-lets may be created by doBeta
      = scExpr' (extendScSubst env bndr rhs) body

      | otherwise
      = do  { let (body_env, bndr') = extendBndr env bndr
            ; rhs_info  <- scRecRhs env (bndr',rhs)

            ; let body_env2 = extendHowBound body_env [bndr'] RecFun
                               -- Note [Local let bindings]
                  rhs'      = ri_new_rhs rhs_info
                  body_env3 = extendValEnv body_env2 bndr' (isValue (sc_vals env) rhs')

            ; (body_usg, body') <- scExpr body_env3 body

              -- NB: For non-recursive bindings we inherit sc_force flag from
              -- the parent function (see Note [Forcing specialisation])
            ; (spec_usg, specs) <- specNonRec env body_usg rhs_info

            ; return (body_usg { scu_calls = scu_calls body_usg `delVarEnv` bndr' }
                        `combineUsage` spec_usg,  -- Note [spec_usg includes rhs_usg]
                      mkLets [NonRec b r | (b,r) <- ruleInfoBinds rhs_info specs] body')
            }

    -- A *local* recursive group: see Note [Local recursive groups]
    scExpr' env (Let (Rec prs) body)
      = do  { let (bndrs,rhss)      = unzip prs
                  (rhs_env1,bndrs') = extendRecBndrs env bndrs
                  rhs_env2          = extendHowBound rhs_env1 bndrs' RecFun
                  force_spec        = any (forceSpecBndr env) bndrs'
                    -- Note [Forcing specialisation]

            ; rhs_infos <- mapM (scRecRhs rhs_env2) (bndrs' `zip` rhss)
            ; (body_usg, body')     <- scExpr rhs_env2 body

            -- NB: start specLoop from body_usg
            ; (spec_usg, specs) <- specRec NotTopLevel (scForce rhs_env2 force_spec)
                                           body_usg rhs_infos
                    -- Do not unconditionally generate specialisations from rhs_usgs
                    -- Instead use them only if we find an unspecialised call
                    -- See Note [Local recursive groups]

            ; let all_usg = spec_usg `combineUsage` body_usg  -- Note [spec_usg includes rhs_usg]
                  bind'   = Rec (concat (zipWith ruleInfoBinds rhs_infos specs))

            ; return (all_usg { scu_calls = scu_calls all_usg `delVarEnvList` bndrs' },
                      Let bind' body') }

    {-
    Note [Local let bindings]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    It is not uncommon to find this

       let $j = \x. <blah> in ...$j True...$j True...

    Here $j is an arbitrary let-bound function, but it often comes up for
    join points.  We might like to specialise $j for its call patterns.
    Notice the difference from a letrec, where we look for call patterns
    in the *RHS* of the function.  Here we look for call patterns in the
    *body* of the let.

    At one point I predicated this on the RHS mentioning the outer
    recursive function, but that's not essential and might even be
    harmful.  I'm not sure.
    -}

    scApp :: ScEnv -> (InExpr, [InExpr]) -> UniqSM (ScUsage, CoreExpr)

    scApp env (Var fn, args)        -- Function is a variable
      = ASSERT( not (null args) )
        do  { args_w_usgs <- mapM (scExpr env) args
            ; let (arg_usgs, args') = unzip args_w_usgs
                  arg_usg = combineUsages arg_usgs
            ; case scSubstId env fn of
                fn'@(Lam {}) -> scExpr (zapScSubst env) (doBeta fn' args')
                            -- Do beta-reduction and try again

                Var fn' -> return (arg_usg `combineUsage` mkVarUsage env fn' args',
                                   mkApps (Var fn') args')

                other_fn' -> return (arg_usg, mkApps other_fn' args') }
                    -- NB: doing this ignores any usage info from the substituted
                    --     function, but I don't think that matters.  If it does
                    --     we can fix it.
      where
        doBeta :: OutExpr -> [OutExpr] -> OutExpr
        -- ToDo: adjust for System IF
        doBeta (Lam bndr body) (arg : args) = Let (NonRec bndr arg) (doBeta body args)
        doBeta fn              args         = mkApps fn args

    -- The function is almost always a variable, but not always.
    -- In particular, if this pass follows float-in,
    -- which it may, we can get
    --      (let f = ...f... in f) arg1 arg2
    scApp env (other_fn, args)
      = do  { (fn_usg,   fn')   <- scExpr env other_fn
            ; (arg_usgs, args') <- mapAndUnzipM (scExpr env) args
            ; return (combineUsages arg_usgs `combineUsage` fn_usg, mkApps fn' args') }

    ----------------------
    mkVarUsage :: ScEnv -> Id -> [CoreExpr] -> ScUsage
    mkVarUsage env fn args
      = case lookupHowBound env fn of
            Just RecFun -> SCU { scu_calls = unitVarEnv fn [Call fn args (sc_vals env)]
                               , scu_occs  = emptyVarEnv }
            Just RecArg -> SCU { scu_calls = emptyVarEnv
                               , scu_occs  = unitVarEnv fn arg_occ }
            Nothing     -> nullUsage
      where
        -- I rather think we could use UnkOcc all the time
        arg_occ | null args = UnkOcc
                | otherwise = evalScrutOcc

    ----------------------
    scTopBindEnv :: ScEnv -> CoreBind -> UniqSM (ScEnv, CoreBind)
    scTopBindEnv env (Rec prs)
      = do  { let (rhs_env1,bndrs') = extendRecBndrs env bndrs
                  rhs_env2          = extendHowBound rhs_env1 bndrs RecFun

                  prs'              = zip bndrs' rhss
            ; return (rhs_env2, Rec prs') }
      where
        (bndrs,rhss) = unzip prs

    scTopBindEnv env (NonRec bndr rhs)
      = do  { let (env1, bndr') = extendBndr env bndr
                  env2          = extendValEnv env1 bndr' (isValue (sc_vals env) rhs)
            ; return (env2, NonRec bndr' rhs) }

    ----------------------
    scTopBind :: ScEnv -> ScUsage -> CoreBind -> UniqSM (ScUsage, CoreBind)

    {-
    scTopBind _ usage _
      | pprTrace "scTopBind_usage" (ppr (scu_calls usage)) False
      = error "false"
    -}

    scTopBind env body_usage (Rec prs)
      | Just threshold <- sc_size env
      , not force_spec
      , not (all (couldBeSmallEnoughToInline (sc_dflags env) threshold) rhss)
                    -- No specialisation
      = -- pprTrace "scTopBind: nospec" (ppr bndrs) $
        do  { (rhs_usgs, rhss')   <- mapAndUnzipM (scExpr env) rhss
            ; return (body_usage `combineUsage` combineUsages rhs_usgs, Rec (bndrs `zip` rhss')) }

      | otherwise   -- Do specialisation
      = do  { rhs_infos <- mapM (scRecRhs env) prs

            ; (spec_usage, specs) <- specRec TopLevel (scForce env force_spec)
                                             body_usage rhs_infos

            ; return (body_usage `combineUsage` spec_usage,
                      Rec (concat (zipWith ruleInfoBinds rhs_infos specs))) }
      where
        (bndrs,rhss) = unzip prs
        force_spec   = any (forceSpecBndr env) bndrs
          -- Note [Forcing specialisation]

    scTopBind env usage (NonRec bndr rhs)   -- Oddly, we don't seem to specialise top-level non-rec functions
      = do  { (rhs_usg', rhs') <- scExpr env rhs
            ; return (usage `combineUsage` rhs_usg', NonRec bndr rhs') }

    ----------------------
    scRecRhs :: ScEnv -> (OutId, InExpr) -> UniqSM RhsInfo
    scRecRhs env (bndr,rhs)
      = do  { let (arg_bndrs,body)       = collectBinders rhs
                  (body_env, arg_bndrs') = extendBndrsWith RecArg env arg_bndrs
            ; (body_usg, body')         <- scExpr body_env body
            ; let (rhs_usg, arg_occs)    = lookupOccs body_usg arg_bndrs'
            ; return (RI { ri_rhs_usg = rhs_usg
                         , ri_fn = bndr, ri_new_rhs = mkLams arg_bndrs' body'
                         , ri_lam_bndrs = arg_bndrs, ri_lam_body = body
                         , ri_arg_occs = arg_occs }) }
                    -- The arg_occs says how the visible,
                    -- lambda-bound binders of the RHS are used
                    -- (including the TyVar binders)
                    -- Two pats are the same if they match both ways

    ----------------------
    ruleInfoBinds :: RhsInfo -> SpecInfo -> [(Id,CoreExpr)]
    ruleInfoBinds (RI { ri_fn = fn, ri_new_rhs = new_rhs })
                  (SI { si_specs = specs })
      = [(id,rhs) | OS { os_id = id, os_rhs = rhs } <- specs] ++
                  -- First the specialised bindings

        [(fn `addIdSpecialisations` rules, new_rhs)]
                  -- And now the original binding
      where
        rules = [r | OS { os_rule = r } <- specs]

    {-
    ************************************************************************
    *                                                                      *
                    The specialiser itself
    *                                                                      *
    ************************************************************************
    -}

    data RhsInfo
      = RI { ri_fn :: OutId                 -- The binder
           , ri_new_rhs :: OutExpr          -- The specialised RHS (in current envt)
           , ri_rhs_usg :: ScUsage          -- Usage info from specialising RHS

           , ri_lam_bndrs :: [InVar]       -- The *original* RHS (\xs.body)
           , ri_lam_body  :: InExpr        --   Note [Specialise original body]
           , ri_arg_occs  :: [ArgOcc]      -- Info on how the xs occur in body
        }

    data SpecInfo       -- Info about specialisations for a particular Id
      = SI { si_specs :: [OneSpec]          -- The specialisations we have generated

           , si_n_specs :: Int              -- Length of si_specs; used for numbering them

           , si_mb_unspec :: Maybe ScUsage  -- Just cs  => we have not yet used calls in the
           }                                --             from calls in the *original* RHS as
                                            --             seeds for new specialisations;
                                            --             if you decide to do so, here is the
                                            --             RHS usage (which has not yet been
                                            --             unleashed)
                                            -- Nothing => we have
                                            -- See Note [Local recursive groups]
                                            -- See Note [spec_usg includes rhs_usg]

            -- One specialisation: Rule plus definition
    data OneSpec =
      OS { os_pat  :: CallPat    -- Call pattern that generated this specialisation
         , os_rule :: CoreRule   -- Rule connecting original id with the specialisation
         , os_id   :: OutId      -- Spec id
         , os_rhs  :: OutExpr }  -- Spec rhs

    noSpecInfo :: SpecInfo
    noSpecInfo = SI { si_specs = [], si_n_specs = 0, si_mb_unspec = Nothing }

    ----------------------
    specNonRec :: ScEnv
               -> ScUsage         -- Body usage
               -> RhsInfo         -- Structure info usage info for un-specialised RHS
               -> UniqSM (ScUsage, SpecInfo)       -- Usage from RHSs (specialised and not)
                                                   --     plus details of specialisations

    specNonRec env body_usg rhs_info
      = specialise env (scu_calls body_usg) rhs_info
                   (noSpecInfo { si_mb_unspec = Just (ri_rhs_usg rhs_info) })

    ----------------------
    specRec :: TopLevelFlag -> ScEnv
            -> ScUsage                         -- Body usage
            -> [RhsInfo]                       -- Structure info and usage info for un-specialised RHSs
            -> UniqSM (ScUsage, [SpecInfo])    -- Usage from all RHSs (specialised and not)
                                               --     plus details of specialisations

    specRec top_lvl env body_usg rhs_infos
      = go 1 seed_calls nullUsage init_spec_infos
      where
        (seed_calls, init_spec_infos)    -- Note [Seeding top-level recursive groups]
           | isTopLevel top_lvl
           , any (isExportedId . ri_fn) rhs_infos   -- Seed from body and RHSs
           = (all_calls,     [noSpecInfo | _ <- rhs_infos])
           | otherwise                              -- Seed from body only
           = (calls_in_body, [noSpecInfo { si_mb_unspec = Just (ri_rhs_usg ri) }
                             | ri <- rhs_infos])

        calls_in_body = scu_calls body_usg
        calls_in_rhss = foldr (combineCalls . scu_calls . ri_rhs_usg) emptyVarEnv rhs_infos
        all_calls = calls_in_rhss `combineCalls` calls_in_body

        -- Loop, specialising, until you get no new specialisations
        go :: Int   -- Which iteration of the "until no new specialisations"
                    -- loop we are on; first iteration is 1
           -> CallEnv   -- Seed calls
                        -- Two accumulating parameters:
           -> ScUsage      -- Usage from earlier specialisations
           -> [SpecInfo]   -- Details of specialisations so far
           -> UniqSM (ScUsage, [SpecInfo])
        go n_iter seed_calls usg_so_far spec_infos
          | isEmptyVarEnv seed_calls
          = -- pprTrace "specRec1" (vcat [ ppr (map ri_fn rhs_infos)
            --                           , ppr seed_calls
            --                           , ppr body_usg ]) $
            return (usg_so_far, spec_infos)

          -- Limit recursive specialisation
          -- See Note [Limit recursive specialisation]
          | n_iter > sc_recursive env  -- Too many iterations of the 'go' loop
          , sc_force env || isNothing (sc_count env)
               -- If both of these are false, the sc_count
               -- threshold will prevent non-termination
          , any ((> the_limit) . si_n_specs) spec_infos
          = -- pprTrace "specRec2" (ppr (map (map os_pat . si_specs) spec_infos)) $
            return (usg_so_far, spec_infos)

          | otherwise
          = do  { specs_w_usg <- zipWithM (specialise env seed_calls) rhs_infos spec_infos
                ; let (extra_usg_s, new_spec_infos) = unzip specs_w_usg
                      extra_usg = combineUsages extra_usg_s
                      all_usg   = usg_so_far `combineUsage` extra_usg
                ; go (n_iter + 1) (scu_calls extra_usg) all_usg new_spec_infos }

        -- See Note [Limit recursive specialisation]
        the_limit = case sc_count env of
                      Nothing  -> 10    -- Ugh!
                      Just max -> max

    ----------------------
    specialise
       :: ScEnv
       -> CallEnv                     -- Info on newly-discovered calls to this function
       -> RhsInfo
       -> SpecInfo                    -- Original RHS plus patterns dealt with
       -> UniqSM (ScUsage, SpecInfo)  -- New specialised versions and their usage

    -- See Note [spec_usg includes rhs_usg]

    -- Note: this only generates *specialised* bindings
    -- The original binding is added by ruleInfoBinds
    --
    -- Note: the rhs here is the optimised version of the original rhs
    -- So when we make a specialised copy of the RHS, we're starting
    -- from an RHS whose nested functions have been optimised already.

    specialise env bind_calls (RI { ri_fn = fn, ri_lam_bndrs = arg_bndrs
                                  , ri_lam_body = body, ri_arg_occs = arg_occs })
                   spec_info@(SI { si_specs = specs, si_n_specs = spec_count
                                 , si_mb_unspec = mb_unspec })
      | isBottomingId fn      -- Note [Do not specialise diverging functions]
                              -- and do not generate specialisation seeds from its RHS
      = -- pprTrace "specialise bot" (ppr fn) $
        return (nullUsage, spec_info)

      | isNeverActive (idInlineActivation fn) -- See Note [Transfer activation]
        || null arg_bndrs                     -- Only specialise functions
      = -- pprTrace "specialise inactive" (ppr fn) $
        case mb_unspec of    -- Behave as if there was a single, boring call
          Just rhs_usg -> return (rhs_usg, spec_info { si_mb_unspec = Nothing })
                             -- See Note [spec_usg includes rhs_usg]
          Nothing      -> return (nullUsage, spec_info)

      | Just all_calls <- lookupVarEnv bind_calls fn
      = -- pprTrace "specialise entry {" (ppr fn <+> ppr all_calls) $
        do  { (boring_call, new_pats) <- callsToNewPats env fn spec_info arg_occs all_calls

            ; let n_pats = length new_pats
    --        ; if (not (null new_pats) || isJust mb_unspec) then
    --            pprTrace "specialise" (vcat [ ppr fn <+> text "with" <+> int n_pats <+> text "good patterns"
    --                                        , text "mb_unspec" <+> ppr (isJust mb_unspec)
    --                                        , text "arg_occs" <+> ppr arg_occs
    --                                        , text "good pats" <+> ppr new_pats])  $
    --               return ()
    --          else return ()

            ; let spec_env = decreaseSpecCount env n_pats
            ; (spec_usgs, new_specs) <- mapAndUnzipM (spec_one spec_env fn arg_bndrs body)
                                                     (new_pats `zip` [spec_count..])
                    -- See Note [Specialise original body]

            ; let spec_usg = combineUsages spec_usgs

                  -- If there were any boring calls among the seeds (= all_calls), then those
                  -- calls will call the un-specialised function.  So we should use the seeds
                  -- from the _unspecialised_ function's RHS, which are in mb_unspec, by returning
                  -- then in new_usg.
                  (new_usg, mb_unspec')
                      = case mb_unspec of
                          Just rhs_usg | boring_call -> (spec_usg `combineUsage` rhs_usg, Nothing)
                          _                          -> (spec_usg,                      mb_unspec)

    --        ; pprTrace "specialise return }"
    --             (vcat [ ppr fn
    --                   , text "boring_call:" <+> ppr boring_call
    --                   , text "new calls:" <+> ppr (scu_calls new_usg)]) $
    --          return ()

              ; return (new_usg, SI { si_specs = new_specs ++ specs
                                    , si_n_specs = spec_count + n_pats
                                    , si_mb_unspec = mb_unspec' }) }

      | otherwise  -- No new seeds, so return nullUsage
      = return (nullUsage, spec_info)

    ---------------------
    spec_one :: ScEnv
             -> OutId       -- Function
             -> [InVar]     -- Lambda-binders of RHS; should match patterns
             -> InExpr      -- Body of the original function
             -> (CallPat, Int)
             -> UniqSM (ScUsage, OneSpec)   -- Rule and binding

    -- spec_one creates a specialised copy of the function, together
    -- with a rule for using it.  I'm very proud of how short this
    -- function is, considering what it does :-).

    {-
      Example

         In-scope: a, x::a
         f = /\b \y::[(a,b)] -> ....f (b,c) ((:) (a,(b,c)) (x,v) (h w))...
              [c::*, v::(b,c) are presumably bound by the (...) part]
      ==>
         f_spec = /\ b c \ v::(b,c) hw::[(a,(b,c))] ->
                      (...entire body of f...) [b -> (b,c),
                                                y -> ((:) (a,(b,c)) (x,v) hw)]

         RULE:  forall b::* c::*,           -- Note, *not* forall a, x
                       v::(b,c),
                       hw::[(a,(b,c))] .

                f (b,c) ((:) (a,(b,c)) (x,v) hw) = f_spec b c v hw
    -}

    spec_one env fn arg_bndrs body (call_pat@(qvars, pats), rule_number)
      = do  { spec_uniq <- getUniqueM
            ; let spec_env   = extendScSubstList (extendScInScope env qvars)
                                                 (arg_bndrs `zip` pats)
                  fn_name    = idName fn
                  fn_loc     = nameSrcSpan fn_name
                  fn_occ     = nameOccName fn_name
                  spec_occ   = mkSpecOcc fn_occ
                  -- We use fn_occ rather than fn in the rule_name string
                  -- as we don't want the uniq to end up in the rule, and
                  -- hence in the ABI, as that can cause spurious ABI
                  -- changes (#4012).
                  rule_name  = mkFastString ("SC:" ++ occNameString fn_occ ++ show rule_number)
                  spec_name  = mkInternalName spec_uniq spec_occ fn_loc
    --      ; pprTrace "{spec_one" (ppr (sc_count env) <+> ppr fn
    --                              <+> ppr pats <+> text "-->" <+> ppr spec_name) $
    --        return ()

            -- Specialise the body
            ; (spec_usg, spec_body) <- scExpr spec_env body

    --      ; pprTrace "done spec_one}" (ppr fn) $
    --        return ()

                    -- And build the results
            ; let (spec_lam_args, spec_call_args) = mkWorkerArgs (sc_dflags env)
                                                                 qvars body_ty
                    -- Usual w/w hack to avoid generating
                    -- a spec_rhs of unlifted type and no args

                  spec_lam_args_str = handOutStrictnessInformation (fst (splitStrictSig spec_str)) spec_lam_args
                    -- Annotate the variables with the strictness information from
                    -- the function (see Note [Strictness information in worker binders])

                  spec_join_arity | isJoinId fn = Just (length spec_lam_args)
                                  | otherwise   = Nothing
                  spec_id    = mkLocalIdOrCoVar spec_name
                                                (mkLamTypes spec_lam_args body_ty)
                                 -- See Note [Transfer strictness]
                                 `setIdStrictness` spec_str
                                 `setIdArity` count isId spec_lam_args
                                 `asJoinId_maybe` spec_join_arity
                  spec_str   = calcSpecStrictness fn spec_lam_args pats

                    -- Conditionally use result of new worker-wrapper transform
                  spec_rhs   = mkLams spec_lam_args_str spec_body
                  body_ty    = exprType spec_body
                  rule_rhs   = mkVarApps (Var spec_id) spec_call_args
                  inline_act = idInlineActivation fn
                  this_mod   = sc_module spec_env
                  rule       = mkRule this_mod True {- Auto -} True {- Local -}
                                      rule_name inline_act fn_name qvars pats rule_rhs
                               -- See Note [Transfer activation]
            ; return (spec_usg, OS { os_pat = call_pat, os_rule = rule
                                   , os_id = spec_id
                                   , os_rhs = spec_rhs }) }

    -- See Note [Strictness information in worker binders]
    handOutStrictnessInformation :: [Demand] -> [Var] -> [Var]
    handOutStrictnessInformation = go
      where
        go _ [] = []
        go [] vs = vs
        go (d:dmds) (v:vs) | isId v = setIdDemandInfo v d : go dmds vs
        go dmds (v:vs) = v : go dmds vs

    calcSpecStrictness :: Id                     -- The original function
                       -> [Var] -> [CoreExpr]    -- Call pattern
                       -> StrictSig              -- Strictness of specialised thing
    -- See Note [Transfer strictness]
    calcSpecStrictness fn qvars pats
      = mkClosedStrictSig spec_dmds topRes
      where
        spec_dmds = [ lookupVarEnv dmd_env qv `orElse` topDmd | qv <- qvars, isId qv ]
        StrictSig (DmdType _ dmds _) = idStrictness fn

        dmd_env = go emptyVarEnv dmds pats

        go :: DmdEnv -> [Demand] -> [CoreExpr] -> DmdEnv
        go env ds (Type {} : pats)     = go env ds pats
        go env ds (Coercion {} : pats) = go env ds pats
        go env (d:ds) (pat : pats)     = go (go_one env d pat) ds pats
        go env _      _                = env

        go_one :: DmdEnv -> Demand -> CoreExpr -> DmdEnv
        go_one env d   (Var v) = extendVarEnv_C bothDmd env v d
        go_one env d e
               | Just ds <- splitProdDmd_maybe d  -- NB: d does not have to be strict
               , (Var _, args) <- collectArgs e = go env ds args
        go_one env _         _ = env

    {-
    Note [spec_usg includes rhs_usg]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In calls to 'specialise', the returned ScUsage must include the rhs_usg in
    the passed-in SpecInfo, unless there are no calls at all to the function.

    The caller can, indeed must, assume this.  He should not combine in rhs_usg
    himself, or he'll get rhs_usg twice -- and that can lead to an exponential
    blowup of duplicates in the CallEnv.  This is what gave rise to the massive
    performace loss in Trac #8852.

    Note [Specialise original body]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The RhsInfo for a binding keeps the *original* body of the binding.  We
    must specialise that, *not* the result of applying specExpr to the RHS
    (which is also kept in RhsInfo). Otherwise we end up specialising a
    specialised RHS, and that can lead directly to exponential behaviour.

    Note [Transfer activation]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
      This note is for SpecConstr, but exactly the same thing
      happens in the overloading specialiser; see
      Note [Auto-specialisation and RULES] in Specialise.

    In which phase should the specialise-constructor rules be active?
    Originally I made them always-active, but Manuel found that this
    defeated some clever user-written rules.  Then I made them active only
    in Phase 0; after all, currently, the specConstr transformation is
    only run after the simplifier has reached Phase 0, but that meant
    that specialisations didn't fire inside wrappers; see test
    simplCore/should_compile/spec-inline.

    So now I just use the inline-activation of the parent Id, as the
    activation for the specialiation RULE, just like the main specialiser;

    This in turn means there is no point in specialising NOINLINE things,
    so we test for that.

    Note [Transfer strictness]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    We must transfer strictness information from the original function to
    the specialised one.  Suppose, for example

      f has strictness     SS
            and a RULE     f (a:as) b = f_spec a as b

    Now we want f_spec to have strictness  LLS, otherwise we'll use call-by-need
    when calling f_spec instead of call-by-value.  And that can result in
    unbounded worsening in space (cf the classic foldl vs foldl')

    See Trac #3437 for a good example.

    The function calcSpecStrictness performs the calculation.

    Note [Strictness information in worker binders]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    After having calculated the strictness annotation for the worker (see Note
    [Transfer strictness] above), we also want to have this information attached to
    the worker’s arguments, for the benefit of later passes. The function
    handOutStrictnessInformation decomposes the strictness annotation calculated by
    calcSpecStrictness and attaches them to the variables.

    ************************************************************************
    *                                                                      *
    \subsection{Argument analysis}
    *                                                                      *
    ************************************************************************

    This code deals with analysing call-site arguments to see whether
    they are constructor applications.

    Note [Free type variables of the qvar types]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In a call (f @a x True), that we want to specialise, what variables should
    we quantify over.  Clearly over 'a' and 'x', but what about any type variables
    free in x's type?  In fact we don't need to worry about them because (f @a)
    can only be a well-typed application if its type is compatible with x, so any
    variables free in x's type must be free in (f @a), and hence either be gathered
    via 'a' itself, or be in scope at f's defn.  Hence we just take
      (exprsFreeVars pats).

    BUT phantom type synonyms can mess this reasoning up,
      eg   x::T b   with  type T b = Int
    So we apply expandTypeSynonyms to the bound Ids.
    See Trac # 5458.  Yuk.

    Note [SpecConstr call patterns]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    A "call patterns" that we collect is going to become the LHS of a RULE.
    It's important that it doesn't have
         e |> Refl
    or
        e |> g1 |> g2
    because both of these will be optimised by Simplify.simplRule. In the
    former case such optimisation benign, because the rule will match more
    terms; but in the latter we may lose a binding of 'g1' or 'g2', and
    end up with a rule LHS that doesn't bind the template variables
    (Trac #10602).

    The simplifier eliminates such things, but SpecConstr itself constructs
    new terms by substituting.  So the 'mkCast' in the Cast case of scExpr
    is very important!

    Note [Choosing patterns]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    If we get lots of patterns we may not want to make a specialisation
    for each of them (code bloat), so we choose as follows, implemented
    by trim_pats.

    * The flag -fspec-constr-count-N sets the sc_count field
      of the ScEnv to (Just n).  This limits the total number
      of specialisations for a given function to N.

    * -fno-spec-constr-count sets the sc_count field to Nothing,
      which switches of the limit.

    * The ghastly ForceSpecConstr trick also switches of the limit
      for a particular function

    * Otherwise we sort the patterns to choose the most general
      ones first; more general => more widely applicable.
    -}

    type CallPat = ([Var], [CoreExpr])      -- Quantified variables and arguments
                                            -- See Note [SpecConstr call patterns]

    callsToNewPats :: ScEnv -> Id
                   -> SpecInfo
                   -> [ArgOcc] -> [Call]
                   -> UniqSM (Bool, [CallPat])
            -- Result has no duplicate patterns,
            -- nor ones mentioned in done_pats
            -- Bool indicates that there was at least one boring pattern
    callsToNewPats env fn spec_info@(SI { si_specs = done_specs }) bndr_occs calls
      = do  { mb_pats <- mapM (callToPats env bndr_occs) calls

            ; let have_boring_call = any isNothing mb_pats

                  good_pats :: [CallPat]
                  good_pats = catMaybes mb_pats

                  -- Remove patterns we have already done
                  new_pats = filterOut is_done good_pats
                  is_done p = any (samePat p . os_pat) done_specs

                  -- Remove duplicates
                  non_dups = nubBy samePat new_pats

                  -- Remove ones that have too many worker variables
                  small_pats = filterOut too_big non_dups
                  too_big (vars,_) = not (isWorkerSmallEnough (sc_dflags env) vars)
                      -- We are about to construct w/w pair in 'spec_one'.
                      -- Omit specialisation leading to high arity workers.
                      -- See Note [Limit w/w arity] in WwLib

                    -- Discard specialisations if there are too many of them
                  trimmed_pats = trim_pats env fn spec_info small_pats

    --        ; pprTrace "callsToPats" (vcat [ text "calls:" <+> ppr calls
    --                                       , text "good_pats:" <+> ppr good_pats ]) $
    --          return ()

            ; return (have_boring_call, trimmed_pats) }

    trim_pats :: ScEnv -> Id -> SpecInfo -> [CallPat] -> [CallPat]
    -- See Note [Choosing patterns]
    trim_pats env fn (SI { si_n_specs = done_spec_count }) pats
      | sc_force env
        || isNothing mb_scc
        || n_remaining >= n_pats
      = pats          -- No need to trim

      | otherwise
      = emit_trace $  -- Need to trim, so keep the best ones
        take n_remaining sorted_pats

      where
        n_pats         = length pats
        spec_count'    = n_pats + done_spec_count
        n_remaining    = max_specs - done_spec_count
        mb_scc         = sc_count env
        Just max_specs = mb_scc

        sorted_pats = map fst $
                      sortBy (comparing snd) $
                      [(pat, pat_cons pat) | pat <- pats]
         -- Sort in order of increasing number of constructors
         -- (i.e. decreasing generality) and pick the initial
         -- segment of this list

        pat_cons :: CallPat -> Int
        -- How many data consturorst of literals are in
        -- the patten.  More data-cons => less general
        pat_cons (qs, ps) = foldr ((+) . n_cons) 0 ps
           where
              q_set = mkVarSet qs
              n_cons (Var v) | v `elemVarSet` q_set = 0
                             | otherwise            = 1
              n_cons (Cast e _)  = n_cons e
              n_cons (App e1 e2) = n_cons e1 + n_cons e2
              n_cons (Lit {})    = 1
              n_cons _           = 0

        emit_trace result
           | debugIsOn || hasPprDebug (sc_dflags env)
             -- Suppress this scary message for ordinary users!  Trac #5125
           = pprTrace "SpecConstr" msg result
           | otherwise
           = result
        msg = vcat [ sep [ text "Function" <+> quotes (ppr fn)
                         , nest 2 (text "has" <+>
                                   speakNOf spec_count' (text "call pattern") <> comma <+>
                                   text "but the limit is" <+> int max_specs) ]
                   , text "Use -fspec-constr-count=n to set the bound"
                   , text "Discarding:" <+> ppr (drop n_remaining sorted_pats) ]

    callToPats :: ScEnv -> [ArgOcc] -> Call -> UniqSM (Maybe CallPat)
            -- The [Var] is the variables to quantify over in the rule
            --      Type variables come first, since they may scope
            --      over the following term variables
            -- The [CoreExpr] are the argument patterns for the rule
    callToPats env bndr_occs (Call _ args con_env)
      | length args < length bndr_occs      -- Check saturated
      = return Nothing
      | otherwise
      = do  { let in_scope      = substInScope (sc_subst env)
            ; (interesting, pats) <- argsToPats env in_scope con_env args bndr_occs
            ; let pat_fvs       = exprsFreeVarsList pats
                    -- To get determinism we need the list of free variables in
                    -- deterministic order. Otherwise we end up creating
                    -- lambdas with different argument orders. See
                    -- determinism/simplCore/should_compile/spec-inline-determ.hs
                    -- for an example. For explanation of determinism
                    -- considerations See Note [Unique Determinism] in Unique.
                  in_scope_vars = getInScopeVars in_scope
                  qvars         = filterOut (`elemVarSet` in_scope_vars) pat_fvs
                    -- Quantify over variables that are not in scope
                    -- at the call site
                    -- See Note [Free type variables of the qvar types]
                    -- See Note [Shadowing] at the top

                  (ktvs, ids)   = partition isTyVar qvars
                  qvars'        = toposortTyVars ktvs ++ map sanitise ids
                    -- Order into kind variables, type variables, term variables
                    -- The kind of a type variable may mention a kind variable
                    -- and the type of a term variable may mention a type variable

                  sanitise id   = id `setIdType` expandTypeSynonyms (idType id)
                    -- See Note [Free type variables of the qvar types]

            ; -- pprTrace "callToPats"  (ppr args $$ ppr bndr_occs) $
              if interesting
              then return (Just (qvars', pats))
              else return Nothing }

        -- argToPat takes an actual argument, and returns an abstracted
        -- version, consisting of just the "constructor skeleton" of the
        -- argument, with non-constructor sub-expression replaced by new
        -- placeholder variables.  For example:
        --    C a (D (f x) (g y))  ==>  C p1 (D p2 p3)

    argToPat :: ScEnv
             -> InScopeSet                  -- What's in scope at the fn defn site
             -> ValueEnv                    -- ValueEnv at the call site
             -> CoreArg                     -- A call arg (or component thereof)
             -> ArgOcc
             -> UniqSM (Bool, CoreArg)

    -- Returns (interesting, pat),
    -- where pat is the pattern derived from the argument
    --            interesting=True if the pattern is non-trivial (not a variable or type)
    -- E.g.         x:xs         --> (True, x:xs)
    --              f xs         --> (False, w)        where w is a fresh wildcard
    --              (f xs, 'c')  --> (True, (w, 'c'))  where w is a fresh wildcard
    --              \x. x+y      --> (True, \x. x+y)
    --              lvl7         --> (True, lvl7)      if lvl7 is bound
    --                                                 somewhere further out

    argToPat _env _in_scope _val_env arg@(Type {}) _arg_occ
      = return (False, arg)

    argToPat env in_scope val_env (Tick _ arg) arg_occ
      = argToPat env in_scope val_env arg arg_occ
            -- Note [Notes in call patterns]
            -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            -- Ignore Notes.  In particular, we want to ignore any InlineMe notes
            -- Perhaps we should not ignore profiling notes, but I'm going to
            -- ride roughshod over them all for now.
            --- See Note [Notes in RULE matching] in Rules

    argToPat env in_scope val_env (Let _ arg) arg_occ
      = argToPat env in_scope val_env arg arg_occ
            -- See Note [Matching lets] in Rule.hs
            -- Look through let expressions
            -- e.g.         f (let v = rhs in (v,w))
            -- Here we can specialise for f (v,w)
            -- because the rule-matcher will look through the let.

    {- Disabled; see Note [Matching cases] in Rule.hs
    argToPat env in_scope val_env (Case scrut _ _ [(_, _, rhs)]) arg_occ
      | exprOkForSpeculation scrut  -- See Note [Matching cases] in Rule.hhs
      = argToPat env in_scope val_env rhs arg_occ
    -}

    argToPat env in_scope val_env (Cast arg co) arg_occ
      | not (ignoreType env ty2)
      = do  { (interesting, arg') <- argToPat env in_scope val_env arg arg_occ
            ; if not interesting then
                    wildCardPat ty2
              else do
            { -- Make a wild-card pattern for the coercion
              uniq <- getUniqueM
            ; let co_name = mkSysTvName uniq (fsLit "sg")
                  co_var  = mkCoVar co_name (mkCoercionType Representational ty1 ty2)
            ; return (interesting, Cast arg' (mkCoVarCo co_var)) } }
      where
        Pair ty1 ty2 = coercionKind co

    {-      Disabling lambda specialisation for now
            It's fragile, and the spec_loop can be infinite
    argToPat in_scope val_env arg arg_occ
      | is_value_lam arg
      = return (True, arg)
      where
        is_value_lam (Lam v e)         -- Spot a value lambda, even if
            | isId v       = True      -- it is inside a type lambda
            | otherwise    = is_value_lam e
        is_value_lam other = False
    -}

      -- Check for a constructor application
      -- NB: this *precedes* the Var case, so that we catch nullary constrs
    argToPat env in_scope val_env arg arg_occ
      | Just (ConVal (DataAlt dc) args) <- isValue val_env arg
      , not (ignoreDataCon env dc)        -- See Note [NoSpecConstr]
      , Just arg_occs <- mb_scrut dc
      = do  { let (ty_args, rest_args) = splitAtList (dataConUnivTyVars dc) args
            ; (_, args') <- argsToPats env in_scope val_env rest_args arg_occs
            ; return (True,
                      mkConApp dc (ty_args ++ args')) }
      where
        mb_scrut dc = case arg_occ of
                        ScrutOcc bs | Just occs <- lookupUFM bs dc
                                    -> Just (occs)  -- See Note [Reboxing]
                        _other      | sc_force env || sc_keen env
                                    -> Just (repeat UnkOcc)
                                    | otherwise
                                    -> Nothing

      -- Check if the argument is a variable that
      --    (a) is used in an interesting way in the function body
      --    (b) we know what its value is
      -- In that case it counts as "interesting"
    argToPat env in_scope val_env (Var v) arg_occ
      | sc_force env || case arg_occ of { UnkOcc -> False; _other -> True }, -- (a)
        is_value,                                                            -- (b)
           -- Ignoring sc_keen here to avoid gratuitously incurring Note [Reboxing]
           -- So sc_keen focused just on f (I# x), where we have freshly-allocated
           -- box that we can eliminate in the caller
        not (ignoreType env (varType v))
      = return (True, Var v)
      where
        is_value
            | isLocalId v = v `elemInScopeSet` in_scope
                            && isJust (lookupVarEnv val_env v)
                    -- Local variables have values in val_env
            | otherwise   = isValueUnfolding (idUnfolding v)
                    -- Imports have unfoldings

    --      I'm really not sure what this comment means
    --      And by not wild-carding we tend to get forall'd
    --      variables that are in scope, which in turn can
    --      expose the weakness in let-matching
    --      See Note [Matching lets] in Rules

      -- Check for a variable bound inside the function.
      -- Don't make a wild-card, because we may usefully share
      --    e.g.  f a = let x = ... in f (x,x)
      -- NB: this case follows the lambda and con-app cases!!
    -- argToPat _in_scope _val_env (Var v) _arg_occ
    --   = return (False, Var v)
            -- SLPJ : disabling this to avoid proliferation of versions
            -- also works badly when thinking about seeding the loop
            -- from the body of the let
            --       f x y = letrec g z = ... in g (x,y)
            -- We don't want to specialise for that *particular* x,y

      -- The default case: make a wild-card
      -- We use this for coercions too
    argToPat _env _in_scope _val_env arg _arg_occ
      = wildCardPat (exprType arg)

    wildCardPat :: Type -> UniqSM (Bool, CoreArg)
    wildCardPat ty
      = do { uniq <- getUniqueM
           ; let id = mkSysLocalOrCoVar (fsLit "sc") uniq ty
           ; return (False, varToCoreExpr id) }

    argsToPats :: ScEnv -> InScopeSet -> ValueEnv
               -> [CoreArg] -> [ArgOcc]  -- Should be same length
               -> UniqSM (Bool, [CoreArg])
    argsToPats env in_scope val_env args occs
      = do { stuff <- zipWithM (argToPat env in_scope val_env) args occs
           ; let (interesting_s, args') = unzip stuff
           ; return (or interesting_s, args') }

    isValue :: ValueEnv -> CoreExpr -> Maybe Value
    isValue _env (Lit lit)
      | litIsLifted lit = Nothing
      | otherwise       = Just (ConVal (LitAlt lit) [])

    isValue env (Var v)
      | Just cval <- lookupVarEnv env v
      = Just cval  -- You might think we could look in the idUnfolding here
                   -- but that doesn't take account of which branch of a
                   -- case we are in, which is the whole point

      | not (isLocalId v) && isCheapUnfolding unf
      = isValue env (unfoldingTemplate unf)
      where
        unf = idUnfolding v
            -- However we do want to consult the unfolding
            -- as well, for let-bound constructors!

    isValue env (Lam b e)
      | isTyVar b = case isValue env e of
                      Just _  -> Just LambdaVal
                      Nothing -> Nothing
      | otherwise = Just LambdaVal

    isValue env (Tick t e)
      | not (tickishIsCode t)
      = isValue env e

    isValue _env expr       -- Maybe it's a constructor application
      | (Var fun, args, _) <- collectArgsTicks (not . tickishIsCode) expr
      = case isDataConWorkId_maybe fun of

            Just con | args `lengthAtLeast` dataConRepArity con
                    -- Check saturated; might be > because the
                    --                  arity excludes type args
                    -> Just (ConVal (DataAlt con) args)

            _other | valArgCount args < idArity fun
                    -- Under-applied function
                   -> Just LambdaVal        -- Partial application

            _other -> Nothing

    isValue _env _expr = Nothing

    valueIsWorkFree :: Value -> Bool
    valueIsWorkFree LambdaVal       = True
    valueIsWorkFree (ConVal _ args) = all exprIsWorkFree args

    samePat :: CallPat -> CallPat -> Bool
    samePat (vs1, as1) (vs2, as2)
      = all2 same as1 as2
      where
        same (Var v1) (Var v2)
            | v1 `elem` vs1 = v2 `elem` vs2
            | v2 `elem` vs2 = False
            | otherwise     = v1 == v2

        same (Lit l1)    (Lit l2)    = l1==l2
        same (App f1 a1) (App f2 a2) = same f1 f2 && same a1 a2

        same (Type {}) (Type {}) = True     -- Note [Ignore type differences]
        same (Coercion {}) (Coercion {}) = True
        same (Tick _ e1) e2 = same e1 e2  -- Ignore casts and notes
        same (Cast e1 _) e2 = same e1 e2
        same e1 (Tick _ e2) = same e1 e2
        same e1 (Cast e2 _) = same e1 e2

        same e1 e2 = WARN( bad e1 || bad e2, ppr e1 $$ ppr e2)
                     False  -- Let, lambda, case should not occur
        bad (Case {}) = True
        bad (Let {})  = True
        bad (Lam {})  = True
        bad _other    = False

    {-
    Note [Ignore type differences]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We do not want to generate specialisations where the call patterns
    differ only in their type arguments!  Not only is it utterly useless,
    but it also means that (with polymorphic recursion) we can generate
    an infinite number of specialisations. Example is Data.Sequence.adjustTree,
    I think.
    -}