specialise/Specialise.hs

    {-
    (c) The GRASP/AQUA Project, Glasgow University, 1993-1998

    \section[Specialise]{Stamping out overloading, and (optionally) polymorphism}
    -}

    {-# LANGUAGE CPP #-}
    module Specialise ( specProgram, specUnfolding ) where

    #include "HsVersions.h"

    import Id
    import TcType hiding( substTy, extendTvSubstList )
    import Type   hiding( substTy, extendTvSubstList )
    import Coercion( Coercion )
    import Module( Module )
    import CoreMonad
    import qualified CoreSubst
    import CoreUnfold
    import VarSet
    import VarEnv
    import CoreSyn
    import Rules
    import PprCore          ( pprParendExpr )
    import CoreUtils        ( exprIsTrivial, applyTypeToArgs )
    import CoreFVs          ( exprFreeVars, exprsFreeVars, idFreeVars )
    import UniqSupply
    import Name
    import MkId             ( voidArgId, voidPrimId )
    import Maybes           ( catMaybes, isJust )
    import BasicTypes
    import HscTypes
    import Bag
    import DynFlags
    import Util
    import Outputable
    import FastString
    import State

    #if __GLASGOW_HASKELL__ < 709
    import Control.Applicative (Applicative(..))
    #endif
    import Control.Monad
    import Data.Map (Map)
    import qualified Data.Map as Map
    import qualified FiniteMap as Map

    {-
    ************************************************************************
    *                                                                      *
    \subsection[notes-Specialise]{Implementation notes [SLPJ, Aug 18 1993]}
    *                                                                      *
    ************************************************************************

    These notes describe how we implement specialisation to eliminate
    overloading.

    The specialisation pass works on Core
    syntax, complete with all the explicit dictionary application,
    abstraction and construction as added by the type checker.  The
    existing type checker remains largely as it is.

    One important thought: the {\em types} passed to an overloaded
    function, and the {\em dictionaries} passed are mutually redundant.
    If the same function is applied to the same type(s) then it is sure to
    be applied to the same dictionary(s)---or rather to the same {\em
    values}.  (The arguments might look different but they will evaluate
    to the same value.)

    Second important thought: we know that we can make progress by
    treating dictionary arguments as static and worth specialising on.  So
    we can do without binding-time analysis, and instead specialise on
    dictionary arguments and no others.

    The basic idea
    ~~~~~~~~~~~~~~
    Suppose we have

            let f = <f_rhs>
            in <body>

    and suppose f is overloaded.

    STEP 1: CALL-INSTANCE COLLECTION

    We traverse <body>, accumulating all applications of f to types and
    dictionaries.

    (Might there be partial applications, to just some of its types and
    dictionaries?  In principle yes, but in practice the type checker only
    builds applications of f to all its types and dictionaries, so partial
    applications could only arise as a result of transformation, and even
    then I think it's unlikely.  In any case, we simply don't accumulate such
    partial applications.)

    STEP 2: EQUIVALENCES

    So now we have a collection of calls to f:
            f t1 t2 d1 d2
            f t3 t4 d3 d4
            ...
    Notice that f may take several type arguments.  To avoid ambiguity, we
    say that f is called at type t1/t2 and t3/t4.

    We take equivalence classes using equality of the *types* (ignoring
    the dictionary args, which as mentioned previously are redundant).

    STEP 3: SPECIALISATION

    For each equivalence class, choose a representative (f t1 t2 d1 d2),
    and create a local instance of f, defined thus:

            f@t1/t2 = <f_rhs> t1 t2 d1 d2

    f_rhs presumably has some big lambdas and dictionary lambdas, so lots
    of simplification will now result.  However we don't actually *do* that
    simplification.  Rather, we leave it for the simplifier to do.  If we
    *did* do it, though, we'd get more call instances from the specialised
    RHS.  We can work out what they are by instantiating the call-instance
    set from f's RHS with the types t1, t2.

    Add this new id to f's IdInfo, to record that f has a specialised version.

    Before doing any of this, check that f's IdInfo doesn't already
    tell us about an existing instance of f at the required type/s.
    (This might happen if specialisation was applied more than once, or
    it might arise from user SPECIALIZE pragmas.)

    Recursion
    ~~~~~~~~~
    Wait a minute!  What if f is recursive?  Then we can't just plug in
    its right-hand side, can we?

    But it's ok.  The type checker *always* creates non-recursive definitions
    for overloaded recursive functions.  For example:

            f x = f (x+x)           -- Yes I know its silly

    becomes

            f a (d::Num a) = let p = +.sel a d
                             in
                             letrec fl (y::a) = fl (p y y)
                             in
                             fl

    We still have recusion for non-overloaded functions which we
    speciailise, but the recursive call should get specialised to the
    same recursive version.

    Polymorphism 1
    ~~~~~~~~~~~~~~

    All this is crystal clear when the function is applied to *constant
    types*; that is, types which have no type variables inside.  But what if
    it is applied to non-constant types?  Suppose we find a call of f at type
    t1/t2.  There are two possibilities:

    (a) The free type variables of t1, t2 are in scope at the definition point
    of f.  In this case there's no problem, we proceed just as before.  A common
    example is as follows.  Here's the Haskell:

            g y = let f x = x+x
                  in f y + f y

    After typechecking we have

            g a (d::Num a) (y::a) = let f b (d'::Num b) (x::b) = +.sel b d' x x
                                    in +.sel a d (f a d y) (f a d y)

    Notice that the call to f is at type type "a"; a non-constant type.
    Both calls to f are at the same type, so we can specialise to give:

            g a (d::Num a) (y::a) = let f@a (x::a) = +.sel a d x x
                                    in +.sel a d (f@a y) (f@a y)

    (b) The other case is when the type variables in the instance types
    are *not* in scope at the definition point of f.  The example we are
    working with above is a good case.  There are two instances of (+.sel a d),
    but "a" is not in scope at the definition of +.sel.  Can we do anything?
    Yes, we can "common them up", a sort of limited common sub-expression deal.
    This would give:

            g a (d::Num a) (y::a) = let +.sel@a = +.sel a d
                                        f@a (x::a) = +.sel@a x x
                                    in +.sel@a (f@a y) (f@a y)

    This can save work, and can't be spotted by the type checker, because
    the two instances of +.sel weren't originally at the same type.

    Further notes on (b)

    * There are quite a few variations here.  For example, the defn of
      +.sel could be floated ouside the \y, to attempt to gain laziness.
      It certainly mustn't be floated outside the \d because the d has to
      be in scope too.

    * We don't want to inline f_rhs in this case, because
    that will duplicate code.  Just commoning up the call is the point.

    * Nothing gets added to +.sel's IdInfo.

    * Don't bother unless the equivalence class has more than one item!

    Not clear whether this is all worth it.  It is of course OK to
    simply discard call-instances when passing a big lambda.

    Polymorphism 2 -- Overloading
    ~~~~~~~~~~~~~~
    Consider a function whose most general type is

            f :: forall a b. Ord a => [a] -> b -> b

    There is really no point in making a version of g at Int/Int and another
    at Int/Bool, because it's only instancing the type variable "a" which
    buys us any efficiency. Since g is completely polymorphic in b there
    ain't much point in making separate versions of g for the different
    b types.

    That suggests that we should identify which of g's type variables
    are constrained (like "a") and which are unconstrained (like "b").
    Then when taking equivalence classes in STEP 2, we ignore the type args
    corresponding to unconstrained type variable.  In STEP 3 we make
    polymorphic versions.  Thus:

            f@t1/ = /\b -> <f_rhs> t1 b d1 d2

    We do this.

    Dictionary floating
    ~~~~~~~~~~~~~~~~~~~
    Consider this

            f a (d::Num a) = let g = ...
                             in
                             ...(let d1::Ord a = Num.Ord.sel a d in g a d1)...

    Here, g is only called at one type, but the dictionary isn't in scope at the
    definition point for g.  Usually the type checker would build a
    definition for d1 which enclosed g, but the transformation system
    might have moved d1's defn inward.  Solution: float dictionary bindings
    outwards along with call instances.

    Consider

            f x = let g p q = p==q
                      h r s = (r+s, g r s)
                  in
                  h x x

    Before specialisation, leaving out type abstractions we have

            f df x = let g :: Eq a => a -> a -> Bool
                         g dg p q = == dg p q
                         h :: Num a => a -> a -> (a, Bool)
                         h dh r s = let deq = eqFromNum dh
                                    in (+ dh r s, g deq r s)
                  in
                  h df x x

    After specialising h we get a specialised version of h, like this:

                        h' r s = let deq = eqFromNum df
                                 in (+ df r s, g deq r s)

    But we can't naively make an instance for g from this, because deq is not in scope
    at the defn of g.  Instead, we have to float out the (new) defn of deq
    to widen its scope.  Notice that this floating can't be done in advance -- it only
    shows up when specialisation is done.

    User SPECIALIZE pragmas
    ~~~~~~~~~~~~~~~~~~~~~~~
    Specialisation pragmas can be digested by the type checker, and implemented
    by adding extra definitions along with that of f, in the same way as before

            f@t1/t2 = <f_rhs> t1 t2 d1 d2

    Indeed the pragmas *have* to be dealt with by the type checker, because
    only it knows how to build the dictionaries d1 and d2!  For example

            g :: Ord a => [a] -> [a]
            {-# SPECIALIZE f :: [Tree Int] -> [Tree Int] #-}

    Here, the specialised version of g is an application of g's rhs to the
    Ord dictionary for (Tree Int), which only the type checker can conjure
    up.  There might not even *be* one, if (Tree Int) is not an instance of
    Ord!  (All the other specialision has suitable dictionaries to hand
    from actual calls.)

    Problem.  The type checker doesn't have to hand a convenient <f_rhs>, because
    it is buried in a complex (as-yet-un-desugared) binding group.
    Maybe we should say

            f@t1/t2 = f* t1 t2 d1 d2

    where f* is the Id f with an IdInfo which says "inline me regardless!".
    Indeed all the specialisation could be done in this way.
    That in turn means that the simplifier has to be prepared to inline absolutely
    any in-scope let-bound thing.

    Again, the pragma should permit polymorphism in unconstrained variables:

            h :: Ord a => [a] -> b -> b
            {-# SPECIALIZE h :: [Int] -> b -> b #-}

    We *insist* that all overloaded type variables are specialised to ground types,
    (and hence there can be no context inside a SPECIALIZE pragma).
    We *permit* unconstrained type variables to be specialised to
            - a ground type
            - or left as a polymorphic type variable
    but nothing in between.  So

            {-# SPECIALIZE h :: [Int] -> [c] -> [c] #-}

    is *illegal*.  (It can be handled, but it adds complication, and gains the
    programmer nothing.)

    SPECIALISING INSTANCE DECLARATIONS
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider

            instance Foo a => Foo [a] where
                    ...
            {-# SPECIALIZE instance Foo [Int] #-}

    The original instance decl creates a dictionary-function
    definition:

            dfun.Foo.List :: forall a. Foo a -> Foo [a]

    The SPECIALIZE pragma just makes a specialised copy, just as for
    ordinary function definitions:

            dfun.Foo.List@Int :: Foo [Int]
            dfun.Foo.List@Int = dfun.Foo.List Int dFooInt

    The information about what instance of the dfun exist gets added to
    the dfun's IdInfo in the same way as a user-defined function too.

    Automatic instance decl specialisation?
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Can instance decls be specialised automatically?  It's tricky.
    We could collect call-instance information for each dfun, but
    then when we specialised their bodies we'd get new call-instances
    for ordinary functions; and when we specialised their bodies, we might get
    new call-instances of the dfuns, and so on.  This all arises because of
    the unrestricted mutual recursion between instance decls and value decls.

    Still, there's no actual problem; it just means that we may not do all
    the specialisation we could theoretically do.

    Furthermore, instance decls are usually exported and used non-locally,
    so we'll want to compile enough to get those specialisations done.

    Lastly, there's no such thing as a local instance decl, so we can
    survive solely by spitting out *usage* information, and then reading that
    back in as a pragma when next compiling the file.  So for now,
    we only specialise instance decls in response to pragmas.

    SPITTING OUT USAGE INFORMATION
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    To spit out usage information we need to traverse the code collecting
    call-instance information for all imported (non-prelude?) functions
    and data types. Then we equivalence-class it and spit it out.

    This is done at the top-level when all the call instances which escape
    must be for imported functions and data types.

    *** Not currently done ***

    Partial specialisation by pragmas
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    What about partial specialisation:

            k :: (Ord a, Eq b) => [a] -> b -> b -> [a]
            {-# SPECIALIZE k :: Eq b => [Int] -> b -> b -> [a] #-}

    or even

            {-# SPECIALIZE k :: Eq b => [Int] -> [b] -> [b] -> [a] #-}

    Seems quite reasonable.  Similar things could be done with instance decls:

            instance (Foo a, Foo b) => Foo (a,b) where
                    ...
            {-# SPECIALIZE instance Foo a => Foo (a,Int) #-}
            {-# SPECIALIZE instance Foo b => Foo (Int,b) #-}

    Ho hum.  Things are complex enough without this.  I pass.

    Requirements for the simplifer
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The simplifier has to be able to take advantage of the specialisation.

    * When the simplifier finds an application of a polymorphic f, it looks in
    f's IdInfo in case there is a suitable instance to call instead.  This converts

            f t1 t2 d1 d2   ===>   f_t1_t2

    Note that the dictionaries get eaten up too!

    * Dictionary selection operations on constant dictionaries must be
      short-circuited:

            +.sel Int d     ===>  +Int

    The obvious way to do this is in the same way as other specialised
    calls: +.sel has inside it some IdInfo which tells that if it's applied
    to the type Int then it should eat a dictionary and transform to +Int.

    In short, dictionary selectors need IdInfo inside them for constant
    methods.

    * Exactly the same applies if a superclass dictionary is being
      extracted:

            Eq.sel Int d   ===>   dEqInt

    * Something similar applies to dictionary construction too.  Suppose
    dfun.Eq.List is the function taking a dictionary for (Eq a) to
    one for (Eq [a]).  Then we want

            dfun.Eq.List Int d      ===> dEq.List_Int

    Where does the Eq [Int] dictionary come from?  It is built in
    response to a SPECIALIZE pragma on the Eq [a] instance decl.

    In short, dfun Ids need IdInfo with a specialisation for each
    constant instance of their instance declaration.

    All this uses a single mechanism: the SpecEnv inside an Id

    What does the specialisation IdInfo look like?
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    The SpecEnv of an Id maps a list of types (the template) to an expression

            [Type]  |->  Expr

    For example, if f has this SpecInfo:

            [Int, a]  ->  \d:Ord Int. f' a

    it means that we can replace the call

            f Int t  ===>  (\d. f' t)

    This chucks one dictionary away and proceeds with the
    specialised version of f, namely f'.

    What can't be done this way?
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    There is no way, post-typechecker, to get a dictionary for (say)
    Eq a from a dictionary for Eq [a].  So if we find

            ==.sel [t] d

    we can't transform to

            eqList (==.sel t d')

    where
            eqList :: (a->a->Bool) -> [a] -> [a] -> Bool

    Of course, we currently have no way to automatically derive
    eqList, nor to connect it to the Eq [a] instance decl, but you
    can imagine that it might somehow be possible.  Taking advantage
    of this is permanently ruled out.

    Still, this is no great hardship, because we intend to eliminate
    overloading altogether anyway!

    A note about non-tyvar dictionaries
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Some Ids have types like

            forall a,b,c. Eq a -> Ord [a] -> tau

    This seems curious at first, because we usually only have dictionary
    args whose types are of the form (C a) where a is a type variable.
    But this doesn't hold for the functions arising from instance decls,
    which sometimes get arguments with types of form (C (T a)) for some
    type constructor T.

    Should we specialise wrt this compound-type dictionary?  We used to say
    "no", saying:
            "This is a heuristic judgement, as indeed is the fact that we
            specialise wrt only dictionaries.  We choose *not* to specialise
            wrt compound dictionaries because at the moment the only place
            they show up is in instance decls, where they are simply plugged
            into a returned dictionary.  So nothing is gained by specialising
            wrt them."

    But it is simpler and more uniform to specialise wrt these dicts too;
    and in future GHC is likely to support full fledged type signatures
    like
            f :: Eq [(a,b)] => ...

    ************************************************************************
    *                                                                      *
    \subsubsection{The new specialiser}
    *                                                                      *
    ************************************************************************

    Our basic game plan is this.  For let(rec) bound function
            f :: (C a, D c) => (a,b,c,d) -> Bool

    * Find any specialised calls of f, (f ts ds), where
      ts are the type arguments t1 .. t4, and
      ds are the dictionary arguments d1 .. d2.

    * Add a new definition for f1 (say):

            f1 = /\ b d -> (..body of f..) t1 b t3 d d1 d2

      Note that we abstract over the unconstrained type arguments.

    * Add the mapping

            [t1,b,t3,d]  |->  \d1 d2 -> f1 b d

      to the specialisations of f.  This will be used by the
      simplifier to replace calls
                    (f t1 t2 t3 t4) da db
      by
                    (\d1 d1 -> f1 t2 t4) da db

      All the stuff about how many dictionaries to discard, and what types
      to apply the specialised function to, are handled by the fact that the
      SpecEnv contains a template for the result of the specialisation.

    We don't build *partial* specialisations for f.  For example:

      f :: Eq a => a -> a -> Bool
      {-# SPECIALISE f :: (Eq b, Eq c) => (b,c) -> (b,c) -> Bool #-}

    Here, little is gained by making a specialised copy of f.
    There's a distinct danger that the specialised version would
    first build a dictionary for (Eq b, Eq c), and then select the (==)
    method from it!  Even if it didn't, not a great deal is saved.

    We do, however, generate polymorphic, but not overloaded, specialisations:

      f :: Eq a => [a] -> b -> b -> b
      ... SPECIALISE f :: [Int] -> b -> b -> b ...

    Hence, the invariant is this:

            *** no specialised version is overloaded ***

    ************************************************************************
    *                                                                      *
    \subsubsection{The exported function}
    *                                                                      *
    ************************************************************************
    -}

    specProgram :: ModGuts -> CoreM ModGuts
    specProgram guts@(ModGuts { mg_module = this_mod
                              , mg_rules = local_rules
                              , mg_binds = binds })
      = do { dflags <- getDynFlags

                 -- Specialise the bindings of this module
           ; (binds', uds) <- runSpecM dflags (go binds)

                 -- Specialise imported functions
           ; hpt_rules <- getRuleBase
           ; let rule_base = extendRuleBaseList hpt_rules local_rules
           ; (new_rules, spec_binds) <- specImports dflags this_mod emptyVarSet rule_base uds

           ; let final_binds | null spec_binds = binds'
                             | otherwise       = Rec (flattenBinds spec_binds) : binds'
                       -- Note [Glom the bindings if imported functions are specialised]

           ; return (guts { mg_binds = final_binds
                          , mg_rules = new_rules ++ local_rules }) }
      where
            -- We need to start with a Subst that knows all the things
            -- that are in scope, so that the substitution engine doesn't
            -- accidentally re-use a unique that's already in use
            -- Easiest thing is to do it all at once, as if all the top-level
            -- decls were mutually recursive
        top_subst = SE { se_subst = CoreSubst.mkEmptySubst $ mkInScopeSet $ mkVarSet $
                                    bindersOfBinds binds
                       , se_interesting = emptyVarSet }

        go []           = return ([], emptyUDs)
        go (bind:binds) = do (binds', uds) <- go binds
                             (bind', uds') <- specBind top_subst bind uds
                             return (bind' ++ binds', uds')

    specImports :: DynFlags
                -> Module
                -> VarSet           -- Don't specialise these ones
                                    -- See Note [Avoiding recursive specialisation]
                -> RuleBase         -- Rules from this module and the home package
                                    -- (but not external packages, which can change)
                -> UsageDetails     -- Calls for imported things, and floating bindings
                -> CoreM ( [CoreRule]   -- New rules
                         , [CoreBind] ) -- Specialised bindings and floating bindings
    specImports dflags this_mod done rule_base uds
      = do { let import_calls = varEnvElts (ud_calls uds)
           ; (rules, spec_binds) <- go rule_base import_calls
           ; return (rules, wrapDictBinds (ud_binds uds) spec_binds) }
      where
        go _ [] = return ([], [])
        go rb (CIS fn calls_for_fn : other_calls)
          = do { (rules1, spec_binds1) <- specImport dflags this_mod done rb fn $
                                          Map.toList calls_for_fn
               ; (rules2, spec_binds2) <- go (extendRuleBaseList rb rules1) other_calls
               ; return (rules1 ++ rules2, spec_binds1 ++ spec_binds2) }

    specImport :: DynFlags
               -> Module
               -> VarSet                -- Don't specialise these
                                        -- See Note [Avoiding recursive specialisation]
               -> RuleBase              -- Rules from this module
               -> Id -> [CallInfo]      -- Imported function and calls for it
               -> CoreM ( [CoreRule]    -- New rules
                        , [CoreBind] )  -- Specialised bindings
    specImport dflags this_mod done rb fn calls_for_fn
      | fn `elemVarSet` done
      = return ([], [])     -- No warning.  This actually happens all the time
                            -- when specialising a recursive function, because
                            -- the RHS of the specialised function contains a recursive
                            -- call to the original function

      | null calls_for_fn   -- We filtered out all the calls in deleteCallsMentioning
      = return ([], [])

      | wantSpecImport dflags unfolding
      , Just rhs <- maybeUnfoldingTemplate unfolding
      = do {     -- Get rules from the external package state
                 -- We keep doing this in case we "page-fault in"
                 -- more rules as we go along
           ; hsc_env <- getHscEnv
           ; eps <- liftIO $ hscEPS hsc_env
           ; let full_rb = unionRuleBase rb (eps_rule_base eps)
                 rules_for_fn = getRules full_rb fn

           ; (rules1, spec_pairs, uds) <- runSpecM dflags $
                  specCalls (Just this_mod) emptySpecEnv rules_for_fn calls_for_fn fn rhs
           ; let spec_binds1 = [NonRec b r | (b,r) <- spec_pairs]
                 -- After the rules kick in we may get recursion, but
                 -- we rely on a global GlomBinds to sort that out later
                 -- See Note [Glom the bindings if imported functions are specialised]

                  -- Now specialise any cascaded calls
           ; (rules2, spec_binds2) <- -- pprTrace "specImport" (ppr fn $$ ppr uds $$ ppr rhs) $
                                      specImports dflags this_mod (extendVarSet done fn)
                                                         (extendRuleBaseList rb rules1)
                                                         uds

           ; return (rules2 ++ rules1, spec_binds2 ++ spec_binds1) }

      | otherwise
      = WARN( True, hang (ptext (sLit "specImport discarding:") <+> ppr fn <+> dcolon <+> ppr (idType fn))
                       2 (  (text "want:" <+> ppr (wantSpecImport dflags unfolding))
                         $$ (text "stable:" <+> ppr (isStableUnfolding unfolding))
                         $$ (text "calls:" <+> vcat (map (pprCallInfo fn) calls_for_fn)) ) )
        return ([], [])
      where
        unfolding = realIdUnfolding fn   -- We want to see the unfolding even for loop breakers

    wantSpecImport :: DynFlags -> Unfolding -> Bool
    -- See Note [Specialise imported INLINABLE things]
    wantSpecImport dflags unf
     = case unf of
         NoUnfolding      -> False
         OtherCon {}      -> False
         DFunUnfolding {} -> True
         CoreUnfolding { uf_src = src, uf_guidance = _guidance }
           | gopt Opt_SpecialiseAggressively dflags -> True
           | isStableSource src -> True
                   -- Specialise even INLINE things; it hasn't inlined yet,
                   -- so perhaps it never will.  Moreover it may have calls
                   -- inside it that we want to specialise
           | otherwise -> False    -- Stable, not INLINE, hence INLINEABLE

    {-
    Note [Specialise imported INLINABLE things]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    What imported functions do we specialise?  The basic set is
     * DFuns and things with INLINABLE pragmas.
    but with -fspecialise-aggressively we add
     * Anything with an unfolding template

    Trac #8874 has a good example of why we want to auto-specialise DFuns.

    We have the -fspecialise-aggressively flag (usually off), because we
    risk lots of orphan modules from over-vigorous specialisation.
    However it's not a big deal: anything non-recursive with an
    unfolding-template will probably have been inlined already.

    Note [Glom the bindings if imported functions are specialised]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Suppose we have an imported, *recursive*, INLINABLE function
       f :: Eq a => a -> a
       f = /\a \d x. ...(f a d)...
    In the module being compiled we have
       g x = f (x::Int)
    Now we'll make a specialised function
       f_spec :: Int -> Int
       f_spec = \x -> ...(f Int dInt)...
       {-# RULE  f Int _ = f_spec #-}
       g = \x. f Int dInt x
    Note that f_spec doesn't look recursive
    After rewriting with the RULE, we get
       f_spec = \x -> ...(f_spec)...
    BUT since f_spec was non-recursive before it'll *stay* non-recursive.
    The occurrence analyser never turns a NonRec into a Rec.  So we must
    make sure that f_spec is recursive.  Easiest thing is to make all
    the specialisations for imported bindings recursive.

    Note [Avoiding recursive specialisation]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    When we specialise 'f' we may find new overloaded calls to 'g', 'h' in
    'f's RHS.  So we want to specialise g,h.  But we don't want to
    specialise f any more!  It's possible that f's RHS might have a
    recursive yet-more-specialised call, so we'd diverge in that case.
    And if the call is to the same type, one specialisation is enough.
    Avoiding this recursive specialisation loop is the reason for the
    'done' VarSet passed to specImports and specImport.

    ************************************************************************
    *                                                                      *
    \subsubsection{@specExpr@: the main function}
    *                                                                      *
    ************************************************************************
    -}

    data SpecEnv
      = SE { se_subst :: CoreSubst.Subst
                 -- We carry a substitution down:
                 -- a) we must clone any binding that might float outwards,
                 --    to avoid name clashes
                 -- b) we carry a type substitution to use when analysing
                 --    the RHS of specialised bindings (no type-let!)

           , se_interesting :: VarSet
                 -- Dict Ids that we know something about
                 -- and hence may be worth specialising against
                 -- See Note [Interesting dictionary arguments]
         }

    emptySpecEnv :: SpecEnv
    emptySpecEnv = SE { se_subst = CoreSubst.emptySubst, se_interesting = emptyVarSet}

    specVar :: SpecEnv -> Id -> CoreExpr
    specVar env v = CoreSubst.lookupIdSubst (text "specVar") (se_subst env) v

    specExpr :: SpecEnv -> CoreExpr -> SpecM (CoreExpr, UsageDetails)

    ---------------- First the easy cases --------------------
    specExpr env (Type ty)     = return (Type     (substTy env ty), emptyUDs)
    specExpr env (Coercion co) = return (Coercion (substCo env co), emptyUDs)
    specExpr env (Var v)       = return (specVar env v, emptyUDs)
    specExpr _   (Lit lit)     = return (Lit lit,       emptyUDs)
    specExpr env (Cast e co)
      = do { (e', uds) <- specExpr env e
           ; return ((Cast e' (substCo env co)), uds) }
    specExpr env (Tick tickish body)
      = do { (body', uds) <- specExpr env body
           ; return (Tick (specTickish env tickish) body', uds) }

    ---------------- Applications might generate a call instance --------------------
    specExpr env expr@(App {})
      = go expr []
      where
        go (App fun arg) args = do (arg', uds_arg) <- specExpr env arg
                                   (fun', uds_app) <- go fun (arg':args)
                                   return (App fun' arg', uds_arg `plusUDs` uds_app)

        go (Var f)       args = case specVar env f of
                                    Var f' -> return (Var f', mkCallUDs env f' args)
                                    e'     -> return (e', emptyUDs) -- I don't expect this!
        go other         _    = specExpr env other

    ---------------- Lambda/case require dumping of usage details --------------------
    specExpr env e@(Lam _ _) = do
        (body', uds) <- specExpr env' body
        let (free_uds, dumped_dbs) = dumpUDs bndrs' uds
        return (mkLams bndrs' (wrapDictBindsE dumped_dbs body'), free_uds)
      where
        (bndrs, body) = collectBinders e
        (env', bndrs') = substBndrs env bndrs
            -- More efficient to collect a group of binders together all at once
            -- and we don't want to split a lambda group with dumped bindings

    specExpr env (Case scrut case_bndr ty alts)
      = do { (scrut', scrut_uds) <- specExpr env scrut
           ; (scrut'', case_bndr', alts', alts_uds)
                 <- specCase env scrut' case_bndr alts
           ; return (Case scrut'' case_bndr' (substTy env ty) alts'
                    , scrut_uds `plusUDs` alts_uds) }

    ---------------- Finally, let is the interesting case --------------------
    specExpr env (Let bind body)
      = do { -- Clone binders
             (rhs_env, body_env, bind') <- cloneBindSM env bind

             -- Deal with the body
           ; (body', body_uds) <- specExpr body_env body

            -- Deal with the bindings
          ; (binds', uds) <- specBind rhs_env bind' body_uds

            -- All done
          ; return (foldr Let body' binds', uds) }

    specTickish :: SpecEnv -> Tickish Id -> Tickish Id
    specTickish env (Breakpoint ix ids)
      = Breakpoint ix [ id' | id <- ids, Var id' <- [specVar env id]]
      -- drop vars from the list if they have a non-variable substitution.
      -- should never happen, but it's harmless to drop them anyway.
    specTickish _ other_tickish = other_tickish

    specCase :: SpecEnv
             -> CoreExpr            -- Scrutinee, already done
             -> Id -> [CoreAlt]
             -> SpecM ( CoreExpr    -- New scrutinee
                      , Id
                      , [CoreAlt]
                      , UsageDetails)
    specCase env scrut' case_bndr [(con, args, rhs)]
      | isDictId case_bndr           -- See Note [Floating dictionaries out of cases]
      , interestingDict env scrut'
      , not (isDeadBinder case_bndr && null sc_args')
      = do { (case_bndr_flt : sc_args_flt) <- mapM clone_me (case_bndr' : sc_args')

           ; let sc_rhss = [ Case (Var case_bndr_flt) case_bndr' (idType sc_arg')
                                  [(con, args', Var sc_arg')]
                           | sc_arg' <- sc_args' ]

                 -- Extend the substitution for RHS to map the *original* binders
                 -- to their floated verions.
                 mb_sc_flts :: [Maybe DictId]
                 mb_sc_flts = map (lookupVarEnv clone_env) args'
                 clone_env  = zipVarEnv sc_args' sc_args_flt
                 subst_prs  = (case_bndr, Var case_bndr_flt)
                            : [ (arg, Var sc_flt)
                              | (arg, Just sc_flt) <- args `zip` mb_sc_flts ]
                 env_rhs' = env_rhs { se_subst = CoreSubst.extendIdSubstList (se_subst env_rhs) subst_prs
                                    , se_interesting = se_interesting env_rhs `extendVarSetList`
                                                       (case_bndr_flt : sc_args_flt) }

           ; (rhs', rhs_uds)   <- specExpr env_rhs' rhs
           ; let scrut_bind    = mkDB (NonRec case_bndr_flt scrut')
                 case_bndr_set = unitVarSet case_bndr_flt
                 sc_binds      = [(NonRec sc_arg_flt sc_rhs, case_bndr_set)
                                 | (sc_arg_flt, sc_rhs) <- sc_args_flt `zip` sc_rhss ]
                 flt_binds     = scrut_bind : sc_binds
                 (free_uds, dumped_dbs) = dumpUDs (case_bndr':args') rhs_uds
                 all_uds = flt_binds `addDictBinds` free_uds
                 alt'    = (con, args', wrapDictBindsE dumped_dbs rhs')
           ; return (Var case_bndr_flt, case_bndr', [alt'], all_uds) }
      where
        (env_rhs, (case_bndr':args')) = substBndrs env (case_bndr:args)
        sc_args' = filter is_flt_sc_arg args'

        clone_me bndr = do { uniq <- getUniqueM
                           ; return (mkUserLocal occ uniq ty loc) }
           where
             name = idName bndr
             ty   = idType bndr
             occ  = nameOccName name
             loc  = getSrcSpan name

        arg_set = mkVarSet args'
        is_flt_sc_arg var =  isId var
                          && not (isDeadBinder var)
                          && isDictTy var_ty
                          && not (tyVarsOfType var_ty `intersectsVarSet` arg_set)
           where
             var_ty = idType var

    specCase env scrut case_bndr alts
      = do { (alts', uds_alts) <- mapAndCombineSM spec_alt alts
           ; return (scrut, case_bndr', alts', uds_alts) }
      where
        (env_alt, case_bndr') = substBndr env case_bndr
        spec_alt (con, args, rhs) = do
              (rhs', uds) <- specExpr env_rhs rhs
              let (free_uds, dumped_dbs) = dumpUDs (case_bndr' : args') uds
              return ((con, args', wrapDictBindsE dumped_dbs rhs'), free_uds)
            where
              (env_rhs, args') = substBndrs env_alt args

    {-
    Note [Floating dictionaries out of cases]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider
       g = \d. case d of { MkD sc ... -> ...(f sc)... }
    Naively we can't float d2's binding out of the case expression,
    because 'sc' is bound by the case, and that in turn means we can't
    specialise f, which seems a pity.

    So we invert the case, by floating out a binding
    for 'sc_flt' thus:
        sc_flt = case d of { MkD sc ... -> sc }
    Now we can float the call instance for 'f'.  Indeed this is just
    what'll happen if 'sc' was originally bound with a let binding,
    but case is more efficient, and necessary with equalities. So it's
    good to work with both.

    You might think that this won't make any difference, because the
    call instance will only get nuked by the \d.  BUT if 'g' itself is
    specialised, then transitively we should be able to specialise f.

    In general, given
       case e of cb { MkD sc ... -> ...(f sc)... }
    we transform to
       let cb_flt = e
           sc_flt = case cb_flt of { MkD sc ... -> sc }
       in
       case cb_flt of bg { MkD sc ... -> ....(f sc_flt)... }

    The "_flt" things are the floated binds; we use the current substitution
    to substitute sc -> sc_flt in the RHS

    ************************************************************************
    *                                                                      *
                         Dealing with a binding
    *                                                                      *
    ************************************************************************
    -}

    specBind :: SpecEnv                     -- Use this for RHSs
             -> CoreBind
             -> UsageDetails                -- Info on how the scope of the binding
             -> SpecM ([CoreBind],          -- New bindings
                       UsageDetails)        -- And info to pass upstream

    -- Returned UsageDetails:
    --    No calls for binders of this bind
    specBind rhs_env (NonRec fn rhs) body_uds
      = do { (rhs', rhs_uds) <- specExpr rhs_env rhs
           ; (fn', spec_defns, body_uds1) <- specDefn rhs_env body_uds fn rhs

           ; let pairs = spec_defns ++ [(fn', rhs')]
                            -- fn' mentions the spec_defns in its rules,
                            -- so put the latter first

                 combined_uds = body_uds1 `plusUDs` rhs_uds
                    -- This way round a call in rhs_uds of a function f
                    -- at type T will override a call of f at T in body_uds1; and
                    -- that is good because it'll tend to keep "earlier" calls
                    -- See Note [Specialisation of dictionary functions]

                 (free_uds, dump_dbs, float_all) = dumpBindUDs [fn] combined_uds
                    -- See Note [From non-recursive to recursive]

                 final_binds :: [DictBind]
                 final_binds
                   | isEmptyBag dump_dbs = [mkDB $ NonRec b r | (b,r) <- pairs]
                   | otherwise = [flattenDictBinds dump_dbs pairs]

             ; if float_all then
                 -- Rather than discard the calls mentioning the bound variables
                 -- we float this binding along with the others
                  return ([], free_uds `snocDictBinds` final_binds)
               else
                 -- No call in final_uds mentions bound variables,
                 -- so we can just leave the binding here
                  return (map fst final_binds, free_uds) }

    specBind rhs_env (Rec pairs) body_uds
           -- Note [Specialising a recursive group]
      = do { let (bndrs,rhss) = unzip pairs
           ; (rhss', rhs_uds) <- mapAndCombineSM (specExpr rhs_env) rhss
           ; let scope_uds = body_uds `plusUDs` rhs_uds
                           -- Includes binds and calls arising from rhss

           ; (bndrs1, spec_defns1, uds1) <- specDefns rhs_env scope_uds pairs

           ; (bndrs3, spec_defns3, uds3)
                 <- if null spec_defns1  -- Common case: no specialisation
                    then return (bndrs1, [], uds1)
                    else do {            -- Specialisation occurred; do it again
                              (bndrs2, spec_defns2, uds2)
                                  <- specDefns rhs_env uds1 (bndrs1 `zip` rhss)
                            ; return (bndrs2, spec_defns2 ++ spec_defns1, uds2) }

           ; let (final_uds, dumped_dbs, float_all) = dumpBindUDs bndrs uds3
                 bind = flattenDictBinds dumped_dbs
                                         (spec_defns3 ++ zip bndrs3 rhss')

           ; if float_all then
                  return ([], final_uds `snocDictBind` bind)
               else
                  return ([fst bind], final_uds) }

    ---------------------------
    specDefns :: SpecEnv
              -> UsageDetails               -- Info on how it is used in its scope
              -> [(Id,CoreExpr)]            -- The things being bound and their un-processed RHS
              -> SpecM ([Id],               -- Original Ids with RULES added
                        [(Id,CoreExpr)],    -- Extra, specialised bindings
                        UsageDetails)       -- Stuff to fling upwards from the specialised versions

    -- Specialise a list of bindings (the contents of a Rec), but flowing usages
    -- upwards binding by binding.  Example: { f = ...g ...; g = ...f .... }
    -- Then if the input CallDetails has a specialised call for 'g', whose specialisation
    -- in turn generates a specialised call for 'f', we catch that in this one sweep.
    -- But not vice versa (it's a fixpoint problem).

    specDefns _env uds []
      = return ([], [], uds)
    specDefns env uds ((bndr,rhs):pairs)
      = do { (bndrs1, spec_defns1, uds1) <- specDefns env uds pairs
           ; (bndr1, spec_defns2, uds2)  <- specDefn env uds1 bndr rhs
           ; return (bndr1 : bndrs1, spec_defns1 ++ spec_defns2, uds2) }

    ---------------------------
    specDefn :: SpecEnv
             -> UsageDetails                -- Info on how it is used in its scope
             -> Id -> CoreExpr              -- The thing being bound and its un-processed RHS
             -> SpecM (Id,                  -- Original Id with added RULES
                       [(Id,CoreExpr)],     -- Extra, specialised bindings
                       UsageDetails)        -- Stuff to fling upwards from the specialised versions

    specDefn env body_uds fn rhs
      = do { let (body_uds_without_me, calls_for_me) = callsForMe fn body_uds
                 rules_for_me = idCoreRules fn
           ; (rules, spec_defns, spec_uds) <- specCalls Nothing env rules_for_me
                                                        calls_for_me fn rhs
           ; return ( fn `addIdSpecialisations` rules
                    , spec_defns
                    , body_uds_without_me `plusUDs` spec_uds) }
                    -- It's important that the `plusUDs` is this way
                    -- round, because body_uds_without_me may bind
                    -- dictionaries that are used in calls_for_me passed
                    -- to specDefn.  So the dictionary bindings in
                    -- spec_uds may mention dictionaries bound in
                    -- body_uds_without_me

    ---------------------------
    specCalls :: Maybe Module      -- Just this_mod  =>  specialising imported fn
                                   -- Nothing        =>  specialising local fn
              -> SpecEnv
              -> [CoreRule]                 -- Existing RULES for the fn
              -> [CallInfo]
              -> Id -> CoreExpr
              -> SpecM ([CoreRule],         -- New RULES for the fn
                        [(Id,CoreExpr)],    -- Extra, specialised bindings
                        UsageDetails)       -- New usage details from the specialised RHSs

    -- This function checks existing rules, and does not create
    -- duplicate ones. So the caller does not need to do this filtering.
    -- See 'already_covered'

    specCalls mb_mod env rules_for_me calls_for_me fn rhs
            -- The first case is the interesting one
      |  rhs_tyvars `lengthIs`     n_tyvars -- Rhs of fn's defn has right number of big lambdas
      && rhs_ids    `lengthAtLeast` n_dicts -- and enough dict args
      && notNull calls_for_me               -- And there are some calls to specialise
      && not (isNeverActive (idInlineActivation fn))
            -- Don't specialise NOINLINE things
            -- See Note [Auto-specialisation and RULES]

    --   && not (certainlyWillInline (idUnfolding fn))      -- And it's not small
    --      See Note [Inline specialisation] for why we do not
    --      switch off specialisation for inline functions

      = -- pprTrace "specDefn: some" (ppr fn $$ ppr calls_for_me $$ ppr rules_for_me) $
        do { stuff <- mapM spec_call calls_for_me
           ; let (spec_defns, spec_uds, spec_rules) = unzip3 (catMaybes stuff)
           ; return (spec_rules, spec_defns, plusUDList spec_uds) }

      | otherwise   -- No calls or RHS doesn't fit our preconceptions
      = WARN( not (exprIsTrivial rhs) && notNull calls_for_me,
              ptext (sLit "Missed specialisation opportunity for")
                                     <+> ppr fn $$ _trace_doc )
              -- Note [Specialisation shape]
        -- pprTrace "specDefn: none" (ppr fn <+> ppr calls_for_me) $
        return ([], [], emptyUDs)
      where
        _trace_doc = sep [ ppr rhs_tyvars, ppr n_tyvars
                         , ppr rhs_ids, ppr n_dicts
                         , ppr (idInlineActivation fn) ]

        fn_type            = idType fn
        fn_arity           = idArity fn
        fn_unf             = realIdUnfolding fn     -- Ignore loop-breaker-ness here
        (tyvars, theta, _) = tcSplitSigmaTy fn_type
        n_tyvars           = length tyvars
        n_dicts            = length theta
        inl_prag           = idInlinePragma fn
        inl_act            = inlinePragmaActivation inl_prag
        is_local           = isLocalId fn

            -- Figure out whether the function has an INLINE pragma
            -- See Note [Inline specialisations]

        (rhs_tyvars, rhs_ids, rhs_body) = collectTyAndValBinders rhs

        rhs_dict_ids = take n_dicts rhs_ids
        body         = mkLams (drop n_dicts rhs_ids) rhs_body
                    -- Glue back on the non-dict lambdas

        already_covered :: DynFlags -> [CoreExpr] -> Bool
        already_covered dflags args      -- Note [Specialisations already covered]
           = isJust (lookupRule dflags
                                (CoreSubst.substInScope (se_subst env), realIdUnfolding)
                                (const True)
                                fn args rules_for_me)

        mk_ty_args :: [Maybe Type] -> [TyVar] -> [CoreExpr]
        mk_ty_args [] poly_tvs
          = ASSERT( null poly_tvs ) []
        mk_ty_args (Nothing : call_ts) (poly_tv : poly_tvs)
          = Type (mkTyVarTy poly_tv) : mk_ty_args call_ts poly_tvs
        mk_ty_args (Just ty : call_ts) poly_tvs
          = Type ty : mk_ty_args call_ts poly_tvs
        mk_ty_args (Nothing : _) [] = panic "mk_ty_args"

        ----------------------------------------------------------
            -- Specialise to one particular call pattern
        spec_call :: CallInfo                         -- Call instance
                  -> SpecM (Maybe ((Id,CoreExpr),     -- Specialised definition
                                   UsageDetails,      -- Usage details from specialised body
                                   CoreRule))         -- Info for the Id's SpecEnv
        spec_call (CallKey call_ts, (call_ds, _))
          = ASSERT( call_ts `lengthIs` n_tyvars  && call_ds `lengthIs` n_dicts )

            -- Suppose f's defn is  f = /\ a b c -> \ d1 d2 -> rhs
            -- Supppose the call is for f [Just t1, Nothing, Just t3] [dx1, dx2]

            -- Construct the new binding
            --      f1 = SUBST[a->t1,c->t3, d1->d1', d2->d2'] (/\ b -> rhs)
            -- PLUS the usage-details
            --      { d1' = dx1; d2' = dx2 }
            -- where d1', d2' are cloned versions of d1,d2, with the type substitution
            -- applied.  These auxiliary bindings just avoid duplication of dx1, dx2
            --
            -- Note that the substitution is applied to the whole thing.
            -- This is convenient, but just slightly fragile.  Notably:
            --      * There had better be no name clashes in a/b/c
            do { let
                    -- poly_tyvars = [b] in the example above
                    -- spec_tyvars = [a,c]
                    -- ty_args     = [t1,b,t3]
                    spec_tv_binds = [(tv,ty) | (tv, Just ty) <- rhs_tyvars `zip` call_ts]
                    env1          = extendTvSubstList env spec_tv_binds
                    (rhs_env, poly_tyvars) = substBndrs env1
                                                [tv | (tv, Nothing) <- rhs_tyvars `zip` call_ts]

                 -- Clone rhs_dicts, including instantiating their types
               ; inst_dict_ids <- mapM (newDictBndr rhs_env) rhs_dict_ids
               ; let (rhs_env2, dx_binds, spec_dict_args)
                                = bindAuxiliaryDicts rhs_env rhs_dict_ids call_ds inst_dict_ids
                     ty_args    = mk_ty_args call_ts poly_tyvars
                     rule_args  = ty_args ++ map Var inst_dict_ids
                     rule_bndrs = poly_tyvars ++ inst_dict_ids

               ; dflags <- getDynFlags
               ; if already_covered dflags rule_args then
                    return Nothing
                 else do
               {    -- Figure out the type of the specialised function
                 let body_ty = applyTypeToArgs rhs fn_type rule_args
                     (lam_args, app_args)           -- Add a dummy argument if body_ty is unlifted
                       | isUnLiftedType body_ty     -- C.f. WwLib.mkWorkerArgs
                       = (poly_tyvars ++ [voidArgId], poly_tyvars ++ [voidPrimId])
                       | otherwise = (poly_tyvars, poly_tyvars)
                     spec_id_ty = mkPiTypes lam_args body_ty

               ; spec_f <- newSpecIdSM fn spec_id_ty
               ; (spec_rhs, rhs_uds) <- specExpr rhs_env2 (mkLams lam_args body)
               ; let
                    -- The rule to put in the function's specialisation is:
                    --      forall b, d1',d2'.  f t1 b t3 d1' d2' = f1 b
                    herald = case mb_mod of
                               Nothing        -- Specialising local fn
                                   -> ptext (sLit "SPEC")
                               Just this_mod  -- Specialising imoprted fn
                                   -> ptext (sLit "SPEC/") <> ppr this_mod

                    rule_name = mkFastString $ showSDocForUser dflags neverQualify $
                                herald <+> ppr fn <+> hsep (map ppr_call_key_ty call_ts)
                                -- This name ends up in interface files, so use showSDocForUser,
                                -- otherwise uniques end up there, making builds
                                -- less deterministic (See #4012 comment:61 ff)

                    spec_env_rule = mkRule True {- Auto generated -} is_local
                                      rule_name
                                      inl_act       -- Note [Auto-specialisation and RULES]
                                      (idName fn)
                                      rule_bndrs
                                      rule_args
                                      (mkVarApps (Var spec_f) app_args)

                    -- Add the { d1' = dx1; d2' = dx2 } usage stuff
                    final_uds = foldr consDictBind rhs_uds dx_binds

                    --------------------------------------
                    -- Add a suitable unfolding if the spec_inl_prag says so
                    -- See Note [Inline specialisations]
                    (spec_inl_prag, spec_unf)
                      | not is_local && isStrongLoopBreaker (idOccInfo fn)
                      = (neverInlinePragma, noUnfolding)
                            -- See Note [Specialising imported functions] in OccurAnal

                      | InlinePragma { inl_inline = Inlinable } <- inl_prag
                      = (inl_prag { inl_inline = EmptyInlineSpec }, noUnfolding)

                      | otherwise
                      = (inl_prag, specUnfolding dflags (se_subst env)
                                                 poly_tyvars (ty_args ++ spec_dict_args)
                                                 fn_unf)

                    --------------------------------------
                    -- Adding arity information just propagates it a bit faster
                    --      See Note [Arity decrease] in Simplify
                    -- Copy InlinePragma information from the parent Id.
                    -- So if f has INLINE[1] so does spec_f
                    spec_f_w_arity = spec_f `setIdArity`      max 0 (fn_arity - n_dicts)
                                            `setInlinePragma` spec_inl_prag
                                            `setIdUnfolding`  spec_unf

               ; return (Just ((spec_f_w_arity, spec_rhs), final_uds, spec_env_rule)) } }

    bindAuxiliaryDicts
            :: SpecEnv
            -> [DictId] -> [CoreExpr]   -- Original dict bndrs, and the witnessing expressions
            -> [DictId]                 -- A cloned dict-id for each dict arg
            -> (SpecEnv,                -- Substitute for all orig_dicts
                [DictBind],             -- Auxiliary dict bindings
                [CoreExpr])             -- Witnessing expressions (all trivial)
    -- Bind any dictionary arguments to fresh names, to preserve sharing
    bindAuxiliaryDicts env@(SE { se_subst = subst, se_interesting = interesting })
                       orig_dict_ids call_ds inst_dict_ids
      = (env', dx_binds, spec_dict_args)
      where
        (dx_binds, spec_dict_args) = go call_ds inst_dict_ids
        env' = env { se_subst = CoreSubst.extendIdSubstList subst (orig_dict_ids `zip` spec_dict_args)
                   , se_interesting = interesting `unionVarSet` interesting_dicts }

        interesting_dicts = mkVarSet [ dx_id | (NonRec dx_id dx, _) <- dx_binds
                                     , interestingDict env dx ]
                      -- See Note [Make the new dictionaries interesting]

        go :: [CoreExpr] -> [CoreBndr] -> ([DictBind], [CoreExpr])
        go [] _  = ([], [])
        go (dx:dxs) (dx_id:dx_ids)
          | exprIsTrivial dx = (dx_binds, dx:args)
          | otherwise        = (mkDB (NonRec dx_id dx) : dx_binds, Var dx_id : args)
          where
            (dx_binds, args) = go dxs dx_ids
                 -- In the first case extend the substitution but not bindings;
                 -- in the latter extend the bindings but not the substitution.
                 -- For the former, note that we bind the *original* dict in the substitution,
                 -- overriding any d->dx_id binding put there by substBndrs
        go _ _ = pprPanic "bindAuxiliaryDicts" (ppr orig_dict_ids $$ ppr call_ds $$ ppr inst_dict_ids)

    {-
    Note [Make the new dictionaries interesting]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Important!  We're going to substitute dx_id1 for d
    and we want it to look "interesting", else we won't gather *any*
    consequential calls. E.g.
        f d = ...g d....
    If we specialise f for a call (f (dfun dNumInt)), we'll get
    a consequent call (g d') with an auxiliary definition
        d' = df dNumInt
    We want that consequent call to look interesting

    Note [From non-recursive to recursive]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Even in the non-recursive case, if any dict-binds depend on 'fn' we might
    have built a recursive knot

          f a d x = <blah>
          MkUD { ud_binds = d7 = MkD ..f..
               , ud_calls = ...(f T d7)... }

    The we generate

          Rec { fs x = <blah>[T/a, d7/d]
                f a d x = <blah>
                   RULE f T _ = fs
                d7 = ...f... }

    Here the recursion is only through the RULE.

    Note [Specialisation of dictionary functions]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Here is a nasty example that bit us badly: see Trac #3591

         class Eq a => C a
         instance Eq [a] => C [a]

    ---------------
         dfun :: Eq [a] -> C [a]
         dfun a d = MkD a d (meth d)

         d4 :: Eq [T] = <blah>
         d2 ::  C [T] = dfun T d4
         d1 :: Eq [T] = $p1 d2
         d3 ::  C [T] = dfun T d1

    None of these definitions is recursive. What happened was that we
    generated a specialisation:

         RULE forall d. dfun T d = dT  :: C [T]
         dT = (MkD a d (meth d)) [T/a, d1/d]
            = MkD T d1 (meth d1)

    But now we use the RULE on the RHS of d2, to get

        d2 = dT = MkD d1 (meth d1)
        d1 = $p1 d2

    and now d1 is bottom!  The problem is that when specialising 'dfun' we
    should first dump "below" the binding all floated dictionary bindings
    that mention 'dfun' itself.  So d2 and d3 (and hence d1) must be
    placed below 'dfun', and thus unavailable to it when specialising
    'dfun'.  That in turn means that the call (dfun T d1) must be
    discarded.  On the other hand, the call (dfun T d4) is fine, assuming
    d4 doesn't mention dfun.

    But look at this:

      class C a where { foo,bar :: [a] -> [a] }

      instance C Int where
         foo x = r_bar x
         bar xs = reverse xs

      r_bar :: C a => [a] -> [a]
      r_bar xs = bar (xs ++ xs)

    That translates to:

        r_bar a (c::C a) (xs::[a]) = bar a d (xs ++ xs)

        Rec { $fCInt :: C Int = MkC foo_help reverse
              foo_help (xs::[Int]) = r_bar Int $fCInt xs }

    The call (r_bar $fCInt) mentions $fCInt,
                            which mentions foo_help,
                            which mentions r_bar
    But we DO want to specialise r_bar at Int:

        Rec { $fCInt :: C Int = MkC foo_help reverse
              foo_help (xs::[Int]) = r_bar Int $fCInt xs

              r_bar a (c::C a) (xs::[a]) = bar a d (xs ++ xs)
                RULE r_bar Int _ = r_bar_Int

              r_bar_Int xs = bar Int $fCInt (xs ++ xs)
               }

    Note that, because of its RULE, r_bar joins the recursive
    group.  (In this case it'll unravel a short moment later.)

    Conclusion: we catch the nasty case using filter_dfuns in
    callsForMe. To be honest I'm not 100% certain that this is 100%
    right, but it works.  Sigh.

    Note [Specialising a recursive group]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider
        let rec { f x = ...g x'...
                ; g y = ...f y'.... }
        in f 'a'
    Here we specialise 'f' at Char; but that is very likely to lead to
    a specialisation of 'g' at Char.  We must do the latter, else the
    whole point of specialisation is lost.

    But we do not want to keep iterating to a fixpoint, because in the
    presence of polymorphic recursion we might generate an infinite number
    of specialisations.

    So we use the following heuristic:
      * Arrange the rec block in dependency order, so far as possible
        (the occurrence analyser already does this)

      * Specialise it much like a sequence of lets

      * Then go through the block a second time, feeding call-info from
        the RHSs back in the bottom, as it were

    In effect, the ordering maxmimises the effectiveness of each sweep,
    and we do just two sweeps.   This should catch almost every case of
    monomorphic recursion -- the exception could be a very knotted-up
    recursion with multiple cycles tied up together.

    This plan is implemented in the Rec case of specBindItself.

    Note [Specialisations already covered]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We obviously don't want to generate two specialisations for the same
    argument pattern.  There are two wrinkles

    1. We do the already-covered test in specDefn, not when we generate
    the CallInfo in mkCallUDs.  We used to test in the latter place, but
    we now iterate the specialiser somewhat, and the Id at the call site
    might therefore not have all the RULES that we can see in specDefn

    2. What about two specialisations where the second is an *instance*
    of the first?  If the more specific one shows up first, we'll generate
    specialisations for both.  If the *less* specific one shows up first,
    we *don't* currently generate a specialisation for the more specific
    one.  (See the call to lookupRule in already_covered.)  Reasons:
      (a) lookupRule doesn't say which matches are exact (bad reason)
      (b) if the earlier specialisation is user-provided, it's
          far from clear that we should auto-specialise further

    Note [Auto-specialisation and RULES]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider:
       g :: Num a => a -> a
       g = ...

       f :: (Int -> Int) -> Int
       f w = ...
       {-# RULE f g = 0 #-}

    Suppose that auto-specialisation makes a specialised version of
    g::Int->Int That version won't appear in the LHS of the RULE for f.
    So if the specialisation rule fires too early, the rule for f may
    never fire.

    It might be possible to add new rules, to "complete" the rewrite system.
    Thus when adding
            RULE forall d. g Int d = g_spec
    also add
            RULE f g_spec = 0

    But that's a bit complicated.  For now we ask the programmer's help,
    by *copying the INLINE activation pragma* to the auto-specialised
    rule.  So if g says {-# NOINLINE[2] g #-}, then the auto-spec rule
    will also not be active until phase 2.  And that's what programmers
    should jolly well do anyway, even aside from specialisation, to ensure
    that g doesn't inline too early.

    This in turn means that the RULE would never fire for a NOINLINE
    thing so not much point in generating a specialisation at all.

    Note [Specialisation shape]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We only specialise a function if it has visible top-level lambdas
    corresponding to its overloading.  E.g. if
            f :: forall a. Eq a => ....
    then its body must look like
            f = /\a. \d. ...

    Reason: when specialising the body for a call (f ty dexp), we want to
    substitute dexp for d, and pick up specialised calls in the body of f.

    This doesn't always work.  One example I came across was this:
            newtype Gen a = MkGen{ unGen :: Int -> a }

            choose :: Eq a => a -> Gen a
            choose n = MkGen (\r -> n)

            oneof = choose (1::Int)

    It's a silly exapmle, but we get
            choose = /\a. g `cast` co
    where choose doesn't have any dict arguments.  Thus far I have not
    tried to fix this (wait till there's a real example).

    Mind you, then 'choose' will be inlined (since RHS is trivial) so
    it doesn't matter.  This comes up with single-method classes

       class C a where { op :: a -> a }
       instance C a => C [a] where ....
    ==>
       $fCList :: C a => C [a]
       $fCList = $copList |> (...coercion>...)
       ....(uses of $fCList at particular types)...

    So we suppress the WARN if the rhs is trivial.

    Note [Inline specialisations]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Here is what we do with the InlinePragma of the original function
      * Activation/RuleMatchInfo: both transferred to the
                                  specialised function
      * InlineSpec:
           (a) An INLINE pragma is transferred
           (b) An INLINABLE pragma is *not* transferred

    Why (a): transfer INLINE pragmas? The point of INLINE was precisely to
    specialise the function at its call site, and arguably that's not so
    important for the specialised copies.  BUT *pragma-directed*
    specialisation now takes place in the typechecker/desugarer, with
    manually specified INLINEs.  The specialisation here is automatic.
    It'd be very odd if a function marked INLINE was specialised (because
    of some local use), and then forever after (including importing
    modules) the specialised version wasn't INLINEd.  After all, the
    programmer said INLINE!

    You might wonder why we specialise INLINE functions at all.  After
    all they should be inlined, right?  Two reasons:

     * Even INLINE functions are sometimes not inlined, when they aren't
       applied to interesting arguments.  But perhaps the type arguments
       alone are enough to specialise (even though the args are too boring
       to trigger inlining), and it's certainly better to call the
       specialised version.

     * The RHS of an INLINE function might call another overloaded function,
       and we'd like to generate a specialised version of that function too.
       This actually happens a lot. Consider
          replicateM_ :: (Monad m) => Int -> m a -> m ()
          {-# INLINABLE replicateM_ #-}
          replicateM_ d x ma = ...
       The strictness analyser may transform to
          replicateM_ :: (Monad m) => Int -> m a -> m ()
          {-# INLINE replicateM_ #-}
          replicateM_ d x ma = case x of I# x' -> $wreplicateM_ d x' ma

          $wreplicateM_ :: (Monad m) => Int# -> m a -> m ()
          {-# INLINABLE $wreplicateM_ #-}
          $wreplicateM_ = ...
       Now an importing module has a specialised call to replicateM_, say
       (replicateM_ dMonadIO).  We certainly want to specialise $wreplicateM_!
       This particular example had a huge effect on the call to replicateM_
       in nofib/shootout/n-body.

    Why (b): discard INLINEABLE pragmas? See Trac #4874 for persuasive examples.
    Suppose we have
        {-# INLINABLE f #-}
        f :: Ord a => [a] -> Int
        f xs = letrec f' = ...f'... in f'
    Then, when f is specialised and optimised we might get
        wgo :: [Int] -> Int#
        wgo = ...wgo...
        f_spec :: [Int] -> Int
        f_spec xs = case wgo xs of { r -> I# r }
    and we clearly want to inline f_spec at call sites.  But if we still
    have the big, un-optimised of f (albeit specialised) captured in an
    INLINABLE pragma for f_spec, we won't get that optimisation.

    So we simply drop INLINABLE pragmas when specialising. It's not really
    a complete solution; ignoring specalisation for now, INLINABLE functions
    don't get properly strictness analysed, for example. But it works well
    for examples involving specialisation, which is the dominant use of
    INLINABLE.  See Trac #4874.

    ************************************************************************
    *                                                                      *
    \subsubsection{UsageDetails and suchlike}
    *                                                                      *
    ************************************************************************
    -}

    data UsageDetails
      = MkUD {
            ud_binds :: !(Bag DictBind),
                            -- Floated dictionary bindings
                            -- The order is important;
                            -- in ds1 `union` ds2, bindings in ds2 can depend on those in ds1
                            -- (Remember, Bags preserve order in GHC.)

            ud_calls :: !CallDetails

            -- INVARIANT: suppose bs = bindersOf ud_binds
            -- Then 'calls' may *mention* 'bs',
            -- but there should be no calls *for* bs
        }

    instance Outputable UsageDetails where
      ppr (MkUD { ud_binds = dbs, ud_calls = calls })
            = ptext (sLit "MkUD") <+> braces (sep (punctuate comma
                    [ptext (sLit "binds") <+> equals <+> ppr dbs,
                     ptext (sLit "calls") <+> equals <+> ppr calls]))

    -- | A 'DictBind' is a binding along with a cached set containing its free
    -- variables (both type variables and dictionaries)
    type DictBind = (CoreBind, VarSet)

    type DictExpr = CoreExpr

    emptyUDs :: UsageDetails
    emptyUDs = MkUD { ud_binds = emptyBag, ud_calls = emptyVarEnv }

    ------------------------------------------------------------
    type CallDetails  = IdEnv CallInfoSet
    newtype CallKey   = CallKey [Maybe Type]                        -- Nothing => unconstrained type argument

    -- CallInfo uses a Map, thereby ensuring that
    -- we record only one call instance for any key
    --
    -- The list of types and dictionaries is guaranteed to
    -- match the type of f
    data CallInfoSet = CIS Id (Map CallKey ([DictExpr], VarSet))
                            -- Range is dict args and the vars of the whole
                            -- call (including tyvars)
                            -- [*not* include the main id itself, of course]

    type CallInfo = (CallKey, ([DictExpr], VarSet))

    instance Outputable CallInfoSet where
      ppr (CIS fn map) = hang (ptext (sLit "CIS") <+> ppr fn)
                            2 (ppr map)

    pprCallInfo :: Id -> CallInfo -> SDoc
    pprCallInfo fn (CallKey mb_tys, (dxs, _))
      = hang (ppr fn)
           2 (fsep (map ppr_call_key_ty mb_tys ++ map pprParendExpr dxs))

    ppr_call_key_ty :: Maybe Type -> SDoc
    ppr_call_key_ty Nothing   = char '_'
    ppr_call_key_ty (Just ty) = char '@' <+> pprParendType ty

    instance Outputable CallKey where
      ppr (CallKey ts) = ppr ts

    -- Type isn't an instance of Ord, so that we can control which
    -- instance we use.  That's tiresome here.  Oh well
    instance Eq CallKey where
      k1 == k2 = case k1 `compare` k2 of { EQ -> True; _ -> False }

    instance Ord CallKey where
      compare (CallKey k1) (CallKey k2) = cmpList cmp k1 k2
                    where
                      cmp Nothing   Nothing   = EQ
                      cmp Nothing   (Just _)  = LT
                      cmp (Just _)  Nothing   = GT
                      cmp (Just t1) (Just t2) = cmpType t1 t2

    unionCalls :: CallDetails -> CallDetails -> CallDetails
    unionCalls c1 c2 = plusVarEnv_C unionCallInfoSet c1 c2

    unionCallInfoSet :: CallInfoSet -> CallInfoSet -> CallInfoSet
    unionCallInfoSet (CIS f calls1) (CIS _ calls2) = CIS f (calls1 `Map.union` calls2)

    callDetailsFVs :: CallDetails -> VarSet
    callDetailsFVs calls = foldVarEnv (unionVarSet . callInfoFVs) emptyVarSet calls

    callInfoFVs :: CallInfoSet -> VarSet
    callInfoFVs (CIS _ call_info) = Map.foldRight (\(_,fv) vs -> unionVarSet fv vs) emptyVarSet call_info

    ------------------------------------------------------------
    singleCall :: Id -> [Maybe Type] -> [DictExpr] -> UsageDetails
    singleCall id tys dicts
      = MkUD {ud_binds = emptyBag,
              ud_calls = unitVarEnv id $ CIS id $
                         Map.singleton (CallKey tys) (dicts, call_fvs) }
      where
        call_fvs = exprsFreeVars dicts `unionVarSet` tys_fvs
        tys_fvs  = tyVarsOfTypes (catMaybes tys)
            -- The type args (tys) are guaranteed to be part of the dictionary
            -- types, because they are just the constrained types,
            -- and the dictionary is therefore sure to be bound
            -- inside the binding for any type variables free in the type;
            -- hence it's safe to neglect tyvars free in tys when making
            -- the free-var set for this call
            -- BUT I don't trust this reasoning; play safe and include tys_fvs
            --
            -- We don't include the 'id' itself.

    mkCallUDs, mkCallUDs' :: SpecEnv -> Id -> [CoreExpr] -> UsageDetails
    mkCallUDs env f args
      = -- pprTrace "mkCallUDs" (vcat [ ppr f, ppr args, ppr res ])
        res
      where
        res = mkCallUDs' env f args

    mkCallUDs' env f args
      | not (want_calls_for f)  -- Imported from elsewhere
      || null theta             -- Not overloaded
      = emptyUDs

      |  not (all type_determines_value theta)
      || not (spec_tys `lengthIs` n_tyvars)
      || not ( dicts   `lengthIs` n_dicts)
      || not (any (interestingDict env) dicts)    -- Note [Interesting dictionary arguments]
      -- See also Note [Specialisations already covered]
      = -- pprTrace "mkCallUDs: discarding" _trace_doc
        emptyUDs    -- Not overloaded, or no specialisation wanted

      | otherwise
      = -- pprTrace "mkCallUDs: keeping" _trace_doc
        singleCall f spec_tys dicts
      where
        _trace_doc = vcat [ppr f, ppr args, ppr n_tyvars, ppr n_dicts
                          , ppr (map (interestingDict env) dicts)]
        (tyvars, theta, _) = tcSplitSigmaTy (idType f)
        constrained_tyvars = closeOverKinds (tyVarsOfTypes theta)
        n_tyvars           = length tyvars
        n_dicts            = length theta

        spec_tys = [mk_spec_ty tv ty | (tv, Type ty) <- tyvars `zip` args]
        dicts    = [dict_expr | (_, dict_expr) <- theta `zip` (drop n_tyvars args)]

        mk_spec_ty tyvar ty
            | tyvar `elemVarSet` constrained_tyvars = Just ty
            | otherwise                             = Nothing

        want_calls_for f = isLocalId f || isJust (maybeUnfoldingTemplate (realIdUnfolding f))
             -- For imported things, we gather call instances if
             -- there is an unfolding that we could in principle specialise
             -- We might still decide not to use it (consulting dflags)
             -- in specImports
             -- Use 'realIdUnfolding' to ignore the loop-breaker flag!

        type_determines_value pred    -- See Note [Type determines value]
            = case classifyPredType pred of
                ClassPred cls _ -> not (isIPClass cls)
                TuplePred ps    -> all type_determines_value ps
                EqPred {}       -> True
                IrredPred {}    -> True   -- Things like (D []) where D is a
                                          -- Constraint-ranged family; Trac #7785

    {-
    Note [Type determines value]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Only specialise if all overloading is on non-IP *class* params,
    because these are the ones whose *type* determines their *value*.  In
    parrticular, with implicit params, the type args *don't* say what the
    value of the implicit param is!  See Trac #7101

    However, consider
             type family D (v::*->*) :: Constraint
             type instance D [] = ()
             f :: D v => v Char -> Int
    If we see a call (f "foo"), we'll pass a "dictionary"
      () |> (g :: () ~ D [])
    and it's good to specialise f at this dictionary.

    So the question is: can an implicit parameter "hide inside" a
    type-family constraint like (D a).  Well, no.  We don't allow
            type instance D Maybe = ?x:Int
    Hence the IrredPred case in type_determines_value.
    See Trac #7785.

    Note [Interesting dictionary arguments]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider this
             \a.\d:Eq a.  let f = ... in ...(f d)...
    There really is not much point in specialising f wrt the dictionary d,
    because the code for the specialised f is not improved at all, because
    d is lambda-bound.  We simply get junk specialisations.

    What is "interesting"?  Just that it has *some* structure.  But what about
    variables?

     * A variable might be imported, in which case its unfolding
       will tell us whether it has useful structure

     * Local variables are cloned on the way down (to avoid clashes when
       we float dictionaries), and cloning drops the unfolding
       (cloneIdBndr).  Moreover, we make up some new bindings, and it's a
       nuisance to give them unfoldings.  So we keep track of the
       "interesting" dictionaries as a VarSet in SpecEnv.
       We have to take care to put any new interesting dictionary
       bindings in the set.

    We accidentally lost accurate tracking of local variables for a long
    time, because cloned variables don't have unfoldings. But makes a
    massive difference in a few cases, eg Trac #5113. For nofib as a
    whole it's only a small win: 2.2% improvement in allocation for ansi,
    1.2% for bspt, but mostly 0.0!  Average 0.1% increase in binary size.
    -}

    interestingDict :: SpecEnv -> CoreExpr -> Bool
    -- A dictionary argument is interesting if it has *some* structure
    interestingDict env (Var v) =  hasSomeUnfolding (idUnfolding v)
                                || isDataConWorkId v
                                || v `elemVarSet` se_interesting env
    interestingDict _ (Type _)                = False
    interestingDict _ (Coercion _)            = False
    interestingDict env (App fn (Type _))     = interestingDict env fn
    interestingDict env (App fn (Coercion _)) = interestingDict env fn
    interestingDict env (Tick _ a)            = interestingDict env a
    interestingDict env (Cast e _)            = interestingDict env e
    interestingDict _ _                       = True

    plusUDs :: UsageDetails -> UsageDetails -> UsageDetails
    plusUDs (MkUD {ud_binds = db1, ud_calls = calls1})
            (MkUD {ud_binds = db2, ud_calls = calls2})
      = MkUD { ud_binds = db1    `unionBags`   db2
             , ud_calls = calls1 `unionCalls`  calls2 }

    plusUDList :: [UsageDetails] -> UsageDetails
    plusUDList = foldr plusUDs emptyUDs

    -----------------------------
    _dictBindBndrs :: Bag DictBind -> [Id]
    _dictBindBndrs dbs = foldrBag ((++) . bindersOf . fst) [] dbs

    -- | Construct a 'DictBind' from a 'CoreBind'
    mkDB :: CoreBind -> DictBind
    mkDB bind = (bind, bind_fvs bind)

    -- | Identify the free variables of a 'CoreBind'
    bind_fvs :: CoreBind -> VarSet
    bind_fvs (NonRec bndr rhs) = pair_fvs (bndr,rhs)
    bind_fvs (Rec prs)         = foldl delVarSet rhs_fvs bndrs
                               where
                                 bndrs = map fst prs
                                 rhs_fvs = unionVarSets (map pair_fvs prs)

    pair_fvs :: (Id, CoreExpr) -> VarSet
    pair_fvs (bndr, rhs) = exprFreeVars rhs `unionVarSet` idFreeVars bndr
            -- Don't forget variables mentioned in the
            -- rules of the bndr.  C.f. OccAnal.addRuleUsage
            -- Also tyvars mentioned in its type; they may not appear in the RHS
            --      type T a = Int
            --      x :: T a = 3

    -- | Flatten a set of 'DictBind's and some other binding pairs into a single
    -- recursive binding, including some additional bindings.
    flattenDictBinds :: Bag DictBind -> [(Id,CoreExpr)] -> DictBind
    flattenDictBinds dbs pairs
      = (Rec bindings, fvs)
      where
        (bindings, fvs) = foldrBag add
                                   ([], emptyVarSet)
                                   (dbs `snocBag` mkDB (Rec pairs))
        add (NonRec b r, fvs') (pairs, fvs) =
          ((b,r) : pairs, fvs `unionVarSet` fvs')
        add (Rec prs1,   fvs') (pairs, fvs) =
          (prs1 ++ pairs, fvs `unionVarSet` fvs')

    snocDictBinds :: UsageDetails -> [DictBind] -> UsageDetails
    -- Add ud_binds to the tail end of the bindings in uds
    snocDictBinds uds dbs
      = uds { ud_binds = ud_binds uds `unionBags`
                         foldr consBag emptyBag dbs }

    consDictBind :: DictBind -> UsageDetails -> UsageDetails
    consDictBind bind uds = uds { ud_binds = bind `consBag` ud_binds uds }

    addDictBinds :: [DictBind] -> UsageDetails -> UsageDetails
    addDictBinds binds uds = uds { ud_binds = listToBag binds `unionBags` ud_binds uds }

    snocDictBind :: UsageDetails -> DictBind -> UsageDetails
    snocDictBind uds bind = uds { ud_binds = ud_binds uds `snocBag` bind }

    wrapDictBinds :: Bag DictBind -> [CoreBind] -> [CoreBind]
    wrapDictBinds dbs binds
      = foldrBag add binds dbs
      where
        add (bind,_) binds = bind : binds

    wrapDictBindsE :: Bag DictBind -> CoreExpr -> CoreExpr
    wrapDictBindsE dbs expr
      = foldrBag add expr dbs
      where
        add (bind,_) expr = Let bind expr

    ----------------------
    dumpUDs :: [CoreBndr] -> UsageDetails -> (UsageDetails, Bag DictBind)
    -- Used at a lambda or case binder; just dump anything mentioning the binder
    dumpUDs bndrs uds@(MkUD { ud_binds = orig_dbs, ud_calls = orig_calls })
      | null bndrs = (uds, emptyBag)  -- Common in case alternatives
      | otherwise  = -- pprTrace "dumpUDs" (ppr bndrs $$ ppr free_uds $$ ppr dump_dbs) $
                     (free_uds, dump_dbs)
      where
        free_uds = MkUD { ud_binds = free_dbs, ud_calls = free_calls }
        bndr_set = mkVarSet bndrs
        (free_dbs, dump_dbs, dump_set) = splitDictBinds orig_dbs bndr_set
        free_calls = deleteCallsMentioning dump_set $   -- Drop calls mentioning bndr_set on the floor
                     deleteCallsFor bndrs orig_calls    -- Discard calls for bndr_set; there should be
                                                        -- no calls for any of the dicts in dump_dbs

    dumpBindUDs :: [CoreBndr] -> UsageDetails -> (UsageDetails, Bag DictBind, Bool)
    -- Used at a lambda or case binder; just dump anything mentioning the binder
    dumpBindUDs bndrs (MkUD { ud_binds = orig_dbs, ud_calls = orig_calls })
      = -- pprTrace "dumpBindUDs" (ppr bndrs $$ ppr free_uds $$ ppr dump_dbs) $
        (free_uds, dump_dbs, float_all)
      where
        free_uds = MkUD { ud_binds = free_dbs, ud_calls = free_calls }
        bndr_set = mkVarSet bndrs
        (free_dbs, dump_dbs, dump_set) = splitDictBinds orig_dbs bndr_set
        free_calls = deleteCallsFor bndrs orig_calls
        float_all = dump_set `intersectsVarSet` callDetailsFVs free_calls

    callsForMe :: Id -> UsageDetails -> (UsageDetails, [CallInfo])
    callsForMe fn (MkUD { ud_binds = orig_dbs, ud_calls = orig_calls })
      = -- pprTrace ("callsForMe")
        --          (vcat [ppr fn,
        --                 text "Orig dbs ="     <+> ppr (_dictBindBndrs orig_dbs),
        --                 text "Orig calls ="   <+> ppr orig_calls,
        --                 text "Dep set ="      <+> ppr dep_set,
        --                 text "Calls for me =" <+> ppr calls_for_me]) $
        (uds_without_me, calls_for_me)
      where
        uds_without_me = MkUD { ud_binds = orig_dbs, ud_calls = delVarEnv orig_calls fn }
        calls_for_me = case lookupVarEnv orig_calls fn of
                            Nothing -> []
                            Just (CIS _ calls) -> filter_dfuns (Map.toList calls)

        dep_set = foldlBag go (unitVarSet fn) orig_dbs
        go dep_set (db,fvs) | fvs `intersectsVarSet` dep_set
                            = extendVarSetList dep_set (bindersOf db)
                            | otherwise = dep_set

            -- Note [Specialisation of dictionary functions]
        filter_dfuns | isDFunId fn = filter ok_call
                     | otherwise   = \cs -> cs

        ok_call (_, (_,fvs)) = not (fvs `intersectsVarSet` dep_set)

    ----------------------
    splitDictBinds :: Bag DictBind -> IdSet -> (Bag DictBind, Bag DictBind, IdSet)
    -- Returns (free_dbs, dump_dbs, dump_set)
    splitDictBinds dbs bndr_set
       = foldlBag split_db (emptyBag, emptyBag, bndr_set) dbs
                    -- Important that it's foldl not foldr;
                    -- we're accumulating the set of dumped ids in dump_set
       where
        split_db (free_dbs, dump_dbs, dump_idset) db@(bind, fvs)
            | dump_idset `intersectsVarSet` fvs     -- Dump it
            = (free_dbs, dump_dbs `snocBag` db,
               extendVarSetList dump_idset (bindersOf bind))

            | otherwise     -- Don't dump it
            = (free_dbs `snocBag` db, dump_dbs, dump_idset)

    ----------------------
    deleteCallsMentioning :: VarSet -> CallDetails -> CallDetails
    -- Remove calls *mentioning* bs
    deleteCallsMentioning bs calls
      = mapVarEnv filter_calls calls
      where
        filter_calls :: CallInfoSet -> CallInfoSet
        filter_calls (CIS f calls) = CIS f (Map.filter keep_call calls)
        keep_call (_, fvs) = not (fvs `intersectsVarSet` bs)

    deleteCallsFor :: [Id] -> CallDetails -> CallDetails
    -- Remove calls *for* bs
    deleteCallsFor bs calls = delVarEnvList calls bs

    {-
    ************************************************************************
    *                                                                      *
    \subsubsection{Boring helper functions}
    *                                                                      *
    ************************************************************************
    -}

    newtype SpecM a = SpecM (State SpecState a)

    data SpecState = SpecState {
                         spec_uniq_supply :: UniqSupply,
                         spec_dflags :: DynFlags
                     }

    instance Functor SpecM where
        fmap = liftM

    instance Applicative SpecM where
        pure = return
        (<*>) = ap

    instance Monad SpecM where
        SpecM x >>= f = SpecM $ do y <- x
                                   case f y of
                                       SpecM z ->
                                           z
        return x = SpecM $ return x
        fail str = SpecM $ fail str

    instance MonadUnique SpecM where
        getUniqueSupplyM
            = SpecM $ do st <- get
                         let (us1, us2) = splitUniqSupply $ spec_uniq_supply st
                         put $ st { spec_uniq_supply = us2 }
                         return us1

        getUniqueM
            = SpecM $ do st <- get
                         let (u,us') = takeUniqFromSupply $ spec_uniq_supply st
                         put $ st { spec_uniq_supply = us' }
                         return u

    instance HasDynFlags SpecM where
        getDynFlags = SpecM $ liftM spec_dflags get

    runSpecM :: DynFlags -> SpecM a -> CoreM a
    runSpecM dflags (SpecM spec)
        = do us <- getUniqueSupplyM
             let initialState = SpecState {
                                    spec_uniq_supply = us,
                                    spec_dflags = dflags
                                }
             return $ evalState spec initialState

    mapAndCombineSM :: (a -> SpecM (b, UsageDetails)) -> [a] -> SpecM ([b], UsageDetails)
    mapAndCombineSM _ []     = return ([], emptyUDs)
    mapAndCombineSM f (x:xs) = do (y, uds1) <- f x
                                  (ys, uds2) <- mapAndCombineSM f xs
                                  return (y:ys, uds1 `plusUDs` uds2)

    extendTvSubstList :: SpecEnv -> [(TyVar,Type)] -> SpecEnv
    extendTvSubstList env tv_binds
      = env { se_subst = CoreSubst.extendTvSubstList (se_subst env) tv_binds }

    substTy :: SpecEnv -> Type -> Type
    substTy env ty = CoreSubst.substTy (se_subst env) ty

    substCo :: SpecEnv -> Coercion -> Coercion
    substCo env co = CoreSubst.substCo (se_subst env) co

    substBndr :: SpecEnv -> CoreBndr -> (SpecEnv, CoreBndr)
    substBndr env bs = case CoreSubst.substBndr (se_subst env) bs of
                          (subst', bs') -> (env { se_subst = subst' }, bs')

    substBndrs :: SpecEnv -> [CoreBndr] -> (SpecEnv, [CoreBndr])
    substBndrs env bs = case CoreSubst.substBndrs (se_subst env) bs of
                          (subst', bs') -> (env { se_subst = subst' }, bs')

    cloneBindSM :: SpecEnv -> CoreBind -> SpecM (SpecEnv, SpecEnv, CoreBind)
    -- Clone the binders of the bind; return new bind with the cloned binders
    -- Return the substitution to use for RHSs, and the one to use for the body
    cloneBindSM env@(SE { se_subst = subst, se_interesting = interesting }) (NonRec bndr rhs)
      = do { us <- getUniqueSupplyM
           ; let (subst', bndr') = CoreSubst.cloneIdBndr subst us bndr
                 interesting' | interestingDict env rhs
                              = interesting `extendVarSet` bndr'
                              | otherwise = interesting
           ; return (env, env { se_subst = subst', se_interesting = interesting' }
                    , NonRec bndr' rhs) }

    cloneBindSM env@(SE { se_subst = subst, se_interesting = interesting }) (Rec pairs)
      = do { us <- getUniqueSupplyM
           ; let (subst', bndrs') = CoreSubst.cloneRecIdBndrs subst us (map fst pairs)
                 env' = env { se_subst = subst'
                            , se_interesting = interesting `extendVarSetList`
                                               [ v | (v,r) <- pairs, interestingDict env r ] }
           ; return (env', env', Rec (bndrs' `zip` map snd pairs)) }

    newDictBndr :: SpecEnv -> CoreBndr -> SpecM CoreBndr
    -- Make up completely fresh binders for the dictionaries
    -- Their bindings are going to float outwards
    newDictBndr env b = do { uniq <- getUniqueM
                           ; let n   = idName b
                                 ty' = substTy env (idType b)
                           ; return (mkUserLocal (nameOccName n) uniq ty' (getSrcSpan n)) }

    newSpecIdSM :: Id -> Type -> SpecM Id
        -- Give the new Id a similar occurrence name to the old one
    newSpecIdSM old_id new_ty
      = do  { uniq <- getUniqueM
            ; let name    = idName old_id
                  new_occ = mkSpecOcc (nameOccName name)
                  new_id  = mkUserLocal new_occ uniq new_ty (getSrcSpan name)
            ; return new_id }

    {-
                    Old (but interesting) stuff about unboxed bindings
                    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    What should we do when a value is specialised to a *strict* unboxed value?

            map_*_* f (x:xs) = let h = f x
                                   t = map f xs
                               in h:t

    Could convert let to case:

            map_*_Int# f (x:xs) = case f x of h# ->
                                  let t = map f xs
                                  in h#:t

    This may be undesirable since it forces evaluation here, but the value
    may not be used in all branches of the body. In the general case this
    transformation is impossible since the mutual recursion in a letrec
    cannot be expressed as a case.

    There is also a problem with top-level unboxed values, since our
    implementation cannot handle unboxed values at the top level.

    Solution: Lift the binding of the unboxed value and extract it when it
    is used:

            map_*_Int# f (x:xs) = let h = case (f x) of h# -> _Lift h#
                                      t = map f xs
                                  in case h of
                                     _Lift h# -> h#:t

    Now give it to the simplifier and the _Lifting will be optimised away.

    The benfit is that we have given the specialised "unboxed" values a
    very simplep lifted semantics and then leave it up to the simplifier to
    optimise it --- knowing that the overheads will be removed in nearly
    all cases.

    In particular, the value will only be evaluted in the branches of the
    program which use it, rather than being forced at the point where the
    value is bound. For example:

            filtermap_*_* p f (x:xs)
              = let h = f x
                    t = ...
                in case p x of
                    True  -> h:t
                    False -> t
       ==>
            filtermap_*_Int# p f (x:xs)
              = let h = case (f x) of h# -> _Lift h#
                    t = ...
                in case p x of
                    True  -> case h of _Lift h#
                               -> h#:t
                    False -> t

    The binding for h can still be inlined in the one branch and the
    _Lifting eliminated.

    Question: When won't the _Lifting be eliminated?

    Answer: When they at the top-level (where it is necessary) or when
    inlining would duplicate work (or possibly code depending on
    options). However, the _Lifting will still be eliminated if the
    strictness analyser deems the lifted binding strict.
    -}