GHC/Core/Opt/CprAnal.hs

    {-# LANGUAGE CPP #-}

    -- | Constructed Product Result analysis. Identifies functions that surely
    -- return heap-allocated records on every code path, so that we can eliminate
    -- said heap allocation by performing a worker/wrapper split.
    --
    -- See https://www.microsoft.com/en-us/research/publication/constructed-product-result-analysis-haskell/.
    -- CPR analysis should happen after strictness analysis.
    -- See Note [Phase ordering].
    module GHC.Core.Opt.CprAnal ( cprAnalProgram ) where

    #include "HsVersions.h"

    import GHC.Prelude

    import GHC.Driver.Session
    import GHC.Types.Demand
    import GHC.Types.Cpr
    import GHC.Core
    import GHC.Core.Seq
    import GHC.Utils.Outputable
    import GHC.Types.Var.Env
    import GHC.Types.Basic
    import GHC.Types.Id
    import GHC.Types.Id.Info
    import GHC.Core.DataCon
    import GHC.Core.Multiplicity
    import GHC.Core.Utils   ( exprIsHNF, dumpIdInfoOfProgram )
    import GHC.Core.Type
    import GHC.Core.FamInstEnv
    import GHC.Core.Opt.WorkWrap.Utils
    import GHC.Utils.Misc
    import GHC.Utils.Panic
    import GHC.Utils.Logger  ( Logger, dumpIfSet_dyn, DumpFormat (..) )
    import GHC.Data.Graph.UnVar -- for UnVarSet
    import GHC.Data.Maybe   ( isNothing )

    import Control.Monad ( guard )
    import Data.List ( mapAccumL )

    import GHC.Driver.Ppr
    _ = pprTrace -- Tired of commenting out the import all the time

    {- Note [Constructed Product Result]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The goal of Constructed Product Result analysis is to identify functions that
    surely return heap-allocated records on every code path, so that we can
    eliminate said heap allocation by performing a worker/wrapper split.

    @swap@ below is such a function:

      swap (a, b) = (b, a)

    A @case@ on an application of @swap@, like
    @case swap (10, 42) of (a, b) -> a + b@ could cancel away
    (by case-of-known-constructor) if we "inlined" @swap@ and simplified. We then
    say that @swap@ has the CPR property.

    We can't inline recursive functions, but similar reasoning applies there:

      f x n = case n of
        0 -> (x, 0)
        _ -> f (x+1) (n-1)

    Inductively, @case f 1 2 of (a, b) -> a + b@ could cancel away the constructed
    product with the case. So @f@, too, has the CPR property. But we can't really
    "inline" @f@, because it's recursive. Also, non-recursive functions like @swap@
    might be too big to inline (or even marked NOINLINE). We still want to exploit
    the CPR property, and that is exactly what the worker/wrapper transformation
    can do for us:

      $wf x n = case n of
        0 -> case (x, 0) of -> (a, b) -> (# a, b #)
        _ -> case f (x+1) (n-1) of (a, b) -> (# a, b #)
      f x n = case $wf x n of (# a, b #) -> (a, b)

    where $wf readily simplifies (by case-of-known-constructor and inlining @f@) to:

      $wf x n = case n of
        0 -> (# x, 0 #)
        _ -> $wf (x+1) (n-1)

    Now, a call site like @case f 1 2 of (a, b) -> a + b@ can inline @f@ and
    eliminate the heap-allocated pair constructor.

    Note [Phase ordering]
    ~~~~~~~~~~~~~~~~~~~~~
    We need to perform strictness analysis before CPR analysis, because that might
    unbox some arguments, in turn leading to more constructed products.
    Ideally, we would want the following pipeline:

    1. Strictness
    2. worker/wrapper (for strictness)
    3. CPR
    4. worker/wrapper (for CPR)

    Currently, we omit 2. and anticipate the results of worker/wrapper.
    See Note [CPR for binders that will be unboxed]
    and Note [Optimistic field binder CPR].
    An additional w/w pass would simplify things, but probably add slight overhead.
    So currently we have

    1. Strictness
    2. CPR
    3. worker/wrapper (for strictness and CPR)
    -}

    --
    -- * Analysing programs
    --

    cprAnalProgram :: Logger -> DynFlags -> FamInstEnvs -> CoreProgram -> IO CoreProgram
    cprAnalProgram logger dflags fam_envs binds = do
      let env            = emptyAnalEnv fam_envs
      let binds_plus_cpr = snd $ mapAccumL cprAnalTopBind env binds
      dumpIfSet_dyn logger dflags Opt_D_dump_cpr_signatures "Cpr signatures" FormatText $
        dumpIdInfoOfProgram (ppr . cprInfo) binds_plus_cpr
      -- See Note [Stamp out space leaks in demand analysis] in GHC.Core.Opt.DmdAnal
      seqBinds binds_plus_cpr `seq` return binds_plus_cpr

    -- Analyse a (group of) top-level binding(s)
    cprAnalTopBind :: AnalEnv
                   -> CoreBind
                   -> (AnalEnv, CoreBind)
    cprAnalTopBind env (NonRec id rhs)
      = (env', NonRec id' rhs')
      where
        (id', rhs', env') = cprAnalBind TopLevel env id rhs

    cprAnalTopBind env (Rec pairs)
      = (env', Rec pairs')
      where
        (env', pairs') = cprFix TopLevel env pairs

    --
    -- * Analysing expressions
    --

    -- | The abstract semantic function ⟦_⟧ : Expr -> Env -> A from
    -- "Constructed Product Result Analysis for Haskell"
    cprAnal, cprAnal'
      :: AnalEnv
      -> CoreExpr            -- ^ expression to be denoted by a 'CprType'
      -> (CprType, CoreExpr) -- ^ the updated expression and its 'CprType'

    cprAnal env e = -- pprTraceWith "cprAnal" (\res -> ppr (fst (res)) $$ ppr e) $
                      cprAnal' env e

    cprAnal' _ (Lit lit)     = (topCprType, Lit lit)
    cprAnal' _ (Type ty)     = (topCprType, Type ty)      -- Doesn't happen, in fact
    cprAnal' _ (Coercion co) = (topCprType, Coercion co)

    cprAnal' env (Var var)   = (cprTransform env var, Var var)

    cprAnal' env (Cast e co)
      = (cpr_ty, Cast e' co)
      where
        (cpr_ty, e') = cprAnal env e

    cprAnal' env (Tick t e)
      = (cpr_ty, Tick t e')
      where
        (cpr_ty, e') = cprAnal env e

    cprAnal' env (App fun (Type ty))
      = (fun_ty, App fun' (Type ty))
      where
        (fun_ty, fun') = cprAnal env fun

    cprAnal' env (App fun arg)
      = (res_ty, App fun' arg')
      where
        (fun_ty, fun') = cprAnal env fun
        -- In contrast to DmdAnal, there is no useful (non-nested) CPR info to be
        -- had by looking into the CprType of arg.
        (_, arg')      = cprAnal env arg
        res_ty         = applyCprTy fun_ty

    cprAnal' env (Lam var body)
      | isTyVar var
      , (body_ty, body') <- cprAnal env body
      = (body_ty, Lam var body')
      | otherwise
      = (lam_ty, Lam var body')
      where
        -- See Note [CPR for binders that will be unboxed]
        env'             = extendSigEnvForArg env var
        (body_ty, body') = cprAnal env' body
        lam_ty           = abstractCprTy body_ty

    cprAnal' env (Case scrut case_bndr ty alts)
      = (res_ty, Case scrut' case_bndr ty alts')
      where
        (scrut_ty, scrut') = cprAnal env scrut
        env'               = extendSigEnv env case_bndr (CprSig scrut_ty)
        (alt_tys, alts')   = mapAndUnzip (cprAnalAlt env' scrut_ty) alts
        res_ty             = foldl' lubCprType botCprType alt_tys

    cprAnal' env (Let (NonRec id rhs) body)
      = (body_ty, Let (NonRec id' rhs') body')
      where
        (id', rhs', env') = cprAnalBind NotTopLevel env id rhs
        (body_ty, body')  = cprAnal env' body

    cprAnal' env (Let (Rec pairs) body)
      = body_ty `seq` (body_ty, Let (Rec pairs') body')
      where
        (env', pairs')   = cprFix NotTopLevel env pairs
        (body_ty, body') = cprAnal env' body

    cprAnalAlt
      :: AnalEnv
      -> CprType -- ^ CPR type of the scrutinee
      -> Alt Var -- ^ current alternative
      -> (CprType, Alt Var)
    cprAnalAlt env scrut_ty (Alt con bndrs rhs)
      = (rhs_ty, Alt con bndrs rhs')
      where
        env_alt
          | DataAlt dc <- con
          , let ids = filter isId bndrs
          , CprType arity cpr <- scrut_ty
          , ASSERT( arity == 0 ) True
          = case unpackConFieldsCpr dc cpr of
              AllFieldsSame field_cpr
                | let sig = mkCprSig 0 field_cpr
                -> extendSigEnvAllSame env ids sig
              ForeachField field_cprs
                | let sigs = zipWith (mkCprSig . idArity) ids field_cprs
                -> extendSigEnvList env (zipEqual "cprAnalAlt" ids sigs)
          | otherwise
          = env
        (rhs_ty, rhs') = cprAnal env_alt rhs

    --
    -- * CPR transformer
    --

    cprTransform :: AnalEnv         -- ^ The analysis environment
                 -> Id              -- ^ The function
                 -> CprType         -- ^ The demand type of the function
    cprTransform env id
      = -- pprTrace "cprTransform" (vcat [ppr id, ppr sig])
        sig
      where
        sig
          -- Top-level binding, local let-binding or case binder
          | Just sig <- lookupSigEnv env id
          = getCprSig sig
          -- See Note [CPR for data structures]
          | Just rhs <- cprDataStructureUnfolding_maybe id
          = fst $ cprAnal env rhs
          -- Imported function or data con worker
          | isGlobalId id
          = getCprSig (idCprInfo id)
          | otherwise
          = topCprType

    --
    -- * Bindings
    --

    -- Recursive bindings
    cprFix :: TopLevelFlag
           -> AnalEnv                    -- Does not include bindings for this binding
           -> [(Id,CoreExpr)]
           -> (AnalEnv, [(Id,CoreExpr)]) -- Binders annotated with CPR info
    cprFix top_lvl orig_env orig_pairs
      = loop 1 init_env init_pairs
      where
        init_sig id rhs
          -- See Note [CPR for data structures]
          | isDataStructure id rhs = topCprSig
          | otherwise              = mkCprSig 0 botCpr
        -- See Note [Initialising strictness] in GHC.Core.Opt.DmdAnal
        orig_virgin = ae_virgin orig_env
        init_pairs | orig_virgin  = [(setIdCprInfo id (init_sig id rhs), rhs) | (id, rhs) <- orig_pairs ]
                   | otherwise    = orig_pairs
        init_env = extendSigEnvFromIds orig_env (map fst init_pairs)

        -- The fixed-point varies the idCprInfo field of the binders and and their
        -- entries in the AnalEnv, and terminates if that annotation does not change
        -- any more.
        loop :: Int -> AnalEnv -> [(Id,CoreExpr)] -> (AnalEnv, [(Id,CoreExpr)])
        loop n env pairs
          | found_fixpoint = (reset_env', pairs')
          | otherwise      = loop (n+1) env' pairs'
          where
            -- In all but the first iteration, delete the virgin flag
            -- See Note [Initialising strictness] in GHC.Core.Opt.DmdAnal
            (env', pairs') = step (applyWhen (n/=1) nonVirgin env) pairs
            -- Make sure we reset the virgin flag to what it was when we are stable
            reset_env'     = env'{ ae_virgin = orig_virgin }
            found_fixpoint = map (idCprInfo . fst) pairs' == map (idCprInfo . fst) pairs

        step :: AnalEnv -> [(Id, CoreExpr)] -> (AnalEnv, [(Id, CoreExpr)])
        step env pairs = mapAccumL go env pairs
          where
            go env (id, rhs) = (env', (id', rhs'))
              where
                (id', rhs', env') = cprAnalBind top_lvl env id rhs

    -- | Process the RHS of the binding for a sensible arity, add the CPR signature
    -- to the Id, and augment the environment with the signature as well.
    cprAnalBind
      :: TopLevelFlag
      -> AnalEnv
      -> Id
      -> CoreExpr
      -> (Id, CoreExpr, AnalEnv)
    cprAnalBind top_lvl env id rhs
      -- See Note [CPR for data structures]
      | isDataStructure id rhs
      = (id,  rhs,  env) -- Data structure => no code => need to analyse rhs
      | otherwise
      = (id', rhs', env')
      where
        (rhs_ty, rhs')  = cprAnal env rhs
        -- possibly trim thunk CPR info
        rhs_ty'
          -- See Note [CPR for thunks]
          | stays_thunk = trimCprTy rhs_ty
          -- See Note [CPR for sum types]
          | returns_sum = trimCprTy rhs_ty
          | otherwise   = rhs_ty
        -- See Note [Arity trimming for CPR signatures]
        sig  = mkCprSigForArity (idArity id) rhs_ty'
        id'  = setIdCprInfo id sig
        env' = extendSigEnv env id sig

        -- See Note [CPR for thunks]
        stays_thunk = is_thunk && not_strict
        is_thunk    = not (exprIsHNF rhs) && not (isJoinId id)
        not_strict  = not (isStrUsedDmd (idDemandInfo id))
        -- See Note [CPR for sum types]
        (_, ret_ty) = splitPiTys (idType id)
        not_a_prod  = isNothing (splitArgType_maybe (ae_fam_envs env) ret_ty)
        returns_sum = not (isTopLevel top_lvl) && not_a_prod

    isDataStructure :: Id -> CoreExpr -> Bool
    -- See Note [CPR for data structures]
    isDataStructure id rhs =
      idArity id == 0 && exprIsHNF rhs

    -- | Returns an expandable unfolding
    -- (See Note [exprIsExpandable] in "GHC.Core.Utils") that has
    -- So effectively is a constructor application.
    cprDataStructureUnfolding_maybe :: Id -> Maybe CoreExpr
    cprDataStructureUnfolding_maybe id = do
      -- There are only FinalPhase Simplifier runs after CPR analysis
      guard (activeInFinalPhase (idInlineActivation id))
      unf <- expandUnfolding_maybe (idUnfolding id)
      guard (isDataStructure id unf)
      return unf

    {- Note [Arity trimming for CPR signatures]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Although it doesn't affect correctness of the analysis per se, we have to trim
    CPR signatures to idArity. Here's what might happen if we don't:

      f x = if expensive
              then \y. Box y
              else \z. Box z
      g a b = f a b

    The two lambdas will have a CPR type of @1m@ (so construct a product after
    applied to one argument). Thus, @f@ will have a CPR signature of @2m@
    (constructs a product after applied to two arguments).
    But WW will never eta-expand @f@! In this case that would amount to possibly
    duplicating @expensive@ work.

    (Side note: Even if @f@'s 'idArity' happened to be 2, it would not do so, see
    Note [Don't eta expand in w/w].)

    So @f@ will not be worker/wrappered. But @g@ also inherited its CPR signature
    from @f@'s, so it *will* be WW'd:

      f x = if expensive
              then \y. Box y
              else \z. Box z
      $wg a b = case f a b of Box x -> x
      g a b = Box ($wg a b)

    And the case in @g@ can never cancel away, thus we introduced extra reboxing.
    Hence we always trim the CPR signature of a binding to idArity.
    -}

    data AnalEnv
      = AE
      { ae_sigs   :: SigEnv
      -- ^ Current approximation of signatures for local ids
      , ae_virgin :: Bool
      -- ^ True only on every first iteration in a fixed-point
      -- iteration. See Note [Initialising strictness] in "GHC.Core.Opt.DmdAnal"
      , ae_fam_envs :: FamInstEnvs
      -- ^ Needed when expanding type families and synonyms of product types.
      }

    instance Outputable AnalEnv where
      ppr (AE { ae_sigs = env, ae_virgin = virgin })
        = text "AE" <+> braces (vcat
             [ text "ae_virgin =" <+> ppr virgin
             , text "ae_sigs =" <+> ppr env ])

    -- | An environment storing 'CprSig's for local Ids.
    -- Puts binders with 'topCprSig' in a space-saving 'IntSet'.
    -- See Note [Efficient Top sigs in SigEnv].
    data SigEnv
      = SE
      { se_tops :: !UnVarSet
      -- ^ All these Ids have 'topCprSig'. Like a 'VarSet', but more efficient.
      , se_sigs :: !(VarEnv CprSig)
      -- ^ Ids that have something other than 'topCprSig'.
      }

    instance Outputable SigEnv where
      ppr (SE { se_tops = tops, se_sigs = sigs })
        = text "SE" <+> braces (vcat
             [ text "se_tops =" <+> ppr tops
             , text "se_sigs =" <+> ppr sigs ])

    emptyAnalEnv :: FamInstEnvs -> AnalEnv
    emptyAnalEnv fam_envs
      = AE
      { ae_sigs = SE emptyUnVarSet emptyVarEnv
      , ae_virgin = True
      , ae_fam_envs = fam_envs
      }

    modifySigEnv :: (SigEnv -> SigEnv) -> AnalEnv -> AnalEnv
    modifySigEnv f env = env { ae_sigs = f (ae_sigs env) }

    lookupSigEnv :: AnalEnv -> Id -> Maybe CprSig
    -- See Note [Efficient Top sigs in SigEnv]
    lookupSigEnv AE{ae_sigs = SE tops sigs} id
      | id `elemUnVarSet` tops = Just topCprSig
      | otherwise              = lookupVarEnv sigs id

    extendSigEnv :: AnalEnv -> Id -> CprSig -> AnalEnv
    -- See Note [Efficient Top sigs in SigEnv]
    extendSigEnv env id sig
      | isTopCprSig sig
      = modifySigEnv (\se -> se{se_tops = extendUnVarSet id (se_tops se)}) env
      | otherwise
      = modifySigEnv (\se -> se{se_sigs = extendVarEnv (se_sigs se) id sig}) env

    -- | Extend an environment with the (Id, CPR sig) pairs
    extendSigEnvList :: AnalEnv -> [(Id, CprSig)] -> AnalEnv
    extendSigEnvList env ids_cprs
      = foldl' (\env (id, sig) -> extendSigEnv env id sig) env ids_cprs

    -- | Extend an environment with the CPR sigs attached to the ids
    extendSigEnvFromIds :: AnalEnv -> [Id] -> AnalEnv
    extendSigEnvFromIds env ids
      = foldl' (\env id -> extendSigEnv env id (idCprInfo id)) env ids

    -- | Extend an environment with the same CPR sig for all ids
    extendSigEnvAllSame :: AnalEnv -> [Id] -> CprSig -> AnalEnv
    extendSigEnvAllSame env ids sig
      = foldl' (\env id -> extendSigEnv env id sig) env ids

    nonVirgin :: AnalEnv -> AnalEnv
    nonVirgin env = env { ae_virgin = False }

    -- | A version of 'extendSigEnv' for a binder of which we don't see the RHS
    -- needed to compute a 'CprSig' (e.g. lambdas and DataAlt field binders).
    -- In this case, we can still look at their demand to attach CPR signatures
    -- anticipating the unboxing done by worker/wrapper.
    -- See Note [CPR for binders that will be unboxed].
    extendSigEnvForArg :: AnalEnv -> Id -> AnalEnv
    extendSigEnvForArg env id
      = extendSigEnv env id (CprSig (argCprType env (idType id) (idDemandInfo id)))

    -- | Produces a 'CprType' according to how a strict argument will be unboxed.
    -- Examples:
    --
    --   * A head-strict demand @1L@ on @Int@ would translate to @1@
    --   * A product demand @1P(1L,L)@ on @(Int, Bool)@ would translate to @1(1,)@
    --   * A product demand @1P(1L,L)@ on @(a , Bool)@ would translate to @1(,)@,
    --     because the unboxing strategy would not unbox the @a@.
    argCprType :: AnalEnv -> Type -> Demand -> CprType
    argCprType env arg_ty dmd = CprType 0 (go arg_ty dmd)
      where
        go ty dmd
          | Unbox (DataConPatContext { dcpc_dc = dc, dcpc_tc_args = tc_args }) ds
              <- wantToUnbox (ae_fam_envs env) no_inlineable_prag ty dmd
          -- No existentials; see Note [Which types are unboxed?])
          -- Otherwise we'd need to call dataConRepInstPat here and thread a
          -- UniqSupply. So argCprType is a bit less aggressive than it could
          -- be, for the sake of coding convenience.
          , null (dataConExTyCoVars dc)
          , let arg_tys = map scaledThing (dataConInstArgTys dc tc_args)
          = ConCpr (dataConTag dc) (zipWith go arg_tys ds)
          | otherwise
          = topCpr
        -- Rather than maintaining in AnalEnv whether we are in an INLINEABLE
        -- function, we just assume that we aren't. That flag is only relevant
        -- to Note [Do not unpack class dictionaries], the few unboxing
        -- opportunities on dicts it prohibits are probably irrelevant to CPR.
        no_inlineable_prag = False

    {- Note [Safe abortion in the fixed-point iteration]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Fixed-point iteration may fail to terminate. But we cannot simply give up and
    return the environment and code unchanged! We still need to do one additional
    round, to ensure that all expressions have been traversed at least once, and any
    unsound CPR annotations have been updated.

    Note [Efficient Top sigs in SigEnv]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    It's pretty common for binders in the SigEnv to have a 'topCprSig'.
    Wide records with 100 fields like in T9675 even will generate code where the
    majority of binders has Top signature. To save some allocations, we store
    those binders with a Top signature in a separate UnVarSet (which is an IntSet
    with a convenient Var-tailored API).

    Why store top signatures at all in the SigEnv? After all, when 'cprTransform'
    encounters a locally-bound Id without an entry in the SigEnv, it should behave
    as if that binder has a Top signature!
    Well, the problem is when case binders should have a Top signatures. They always
    have an unfolding and thus look to 'cprTransform' as if they bind a data
    structure, Note [CPR for data structures], and thus would always have the CPR
    property. So we need some mechanism to separate data structures from case
    binders with a Top signature, and the UnVarSet provides that in the least
    convoluted way I can think of.

    Note [CPR for binders that will be unboxed]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    If a lambda-bound variable will be unboxed by worker/wrapper (so it must be
    demanded strictly), then give it a CPR signature. Here's a concrete example
    ('f1' in test T10482a), assuming h is strict:

      f1 :: Int -> Int
      f1 x = case h x of
              A -> x
              B -> f1 (x-1)
              C -> x+1

    If we notice that 'x' is used strictly, we can give it the CPR
    property; and hence f1 gets the CPR property too.  It's sound (doesn't
    change strictness) to give it the CPR property because by the time 'x'
    is returned (case A above), it'll have been evaluated (by the wrapper
    of 'h' in the example).

    Moreover, if f itself is strict in x, then we'll pass x unboxed to
    f1, and so the boxed version *won't* be available; in that case it's
    very helpful to give 'x' the CPR property.

    This is all done in 'extendSigEnvForArg'.

    Note that

      * Whether or not something unboxes is decided by 'wantToUnbox', else we may
        get over-optimistic CPR results (e.g., from \(x :: a) -> x!).

      * If the demand unboxes deeply, we can give the binder a /nested/ CPR
        property, e.g.

          g :: (Int, Int) -> Int
          g p = case p of
            (x, y) | x < 0     -> 0
                   | otherwise -> x

        `x` should have the CPR property because it will be unboxed. We do so
        by giving `p` the Nested CPR property `1(1,)`, indicating that we not only
        have `p` available unboxed, but also its field `x`. Analysis of the Case
        will then transfer the CPR property to `x`.

        Before we were able to express Nested CPR, we used to guess which field
        binders should get the CPR property.
        See Historic Note [Optimistic field binder CPR].

      * See Note [CPR examples]

    Historic Note [Optimistic field binder CPR]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    This Note describes how we used to guess whether fields have the CPR property
    before we were able to express Nested CPR for arguments.

    Consider

      data T a = MkT a
      f :: T Int -> Int
      f x = ... (case x of
        MkT y -> y) ...

    And assume we know from strictness analysis that `f` is strict in `x` and its
    field `y` and we unbox both. Then we give `x` the CPR property according
    to Note [CPR for binders that will be unboxed]. But `x`'s sole field `y`
    likewise will be unboxed and it should also get the CPR property. We'd
    need a *nested* CPR property here for `x` to express that and unwrap one level
    when we analyse the Case to give the CPR property to `y`.

    Lacking Nested CPR, we have to guess a bit, by looking for

      (A) Flat CPR on the scrutinee
      (B) A variable scrutinee. Otherwise surely it can't be a parameter.
      (C) Strict demand on the field binder `y` (or it binds a strict field)

    While (A) is a necessary condition to give a field the CPR property, there are
    ways in which (B) and (C) are too lax, leading to unsound analysis results and
    thus reboxing in the wrapper:

      (b) We could scrutinise some other variable than a parameter, like in

            g :: T Int -> Int
            g x = let z = foo x in -- assume `z` has CPR property
                  case z of MkT y -> y

          Lacking Nested CPR and multiple levels of unboxing, only the outer box
          of `z` will be available and a case on `y` won't actually cancel away.
          But it's simple, and nothing terrible happens if we get it wrong. e.g.
          #10694.

      (c) A strictly used field binder doesn't mean the function is strict in it.

            h :: T Int -> Int -> Int
            h !x 0 = 0
            h  x 0 = case x of MkT y -> y

          Here, `y` is used strictly, but the field of `x` certainly is not and
          consequently will not be available unboxed.
          Why not look at the demand of `x` instead to determine whether `y` is
          unboxed? Because the 'idDemandInfo' on `x` will not have been propagated
          to its occurrence in the scrutinee when CprAnal runs directly after
          DmdAnal.

    We used to give the case binder the CPR property unconditionally instead of
    deriving it from the case scrutinee.
    See Historical Note [Optimistic case binder CPR].

    Historical Note [Optimistic case binder CPR]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We used to give the case binder the CPR property unconditionally, which is too
    optimistic (#19232). Here are the details:

    Inside the alternative, the case binder always has the CPR property, meaning
    that a case on it will successfully cancel.
    Example:
      f True  x = case x of y { I# x' -> if x' ==# 3
                                         then y
                                         else I# 8 }
      f False x = I# 3
    By giving 'y' the CPR property, we ensure that 'f' does too, so we get
      f b x = case fw b x of { r -> I# r }
      fw True  x = case x of y { I# x' -> if x' ==# 3 then x' else 8 }
      fw False x = 3
    Of course there is the usual risk of re-boxing: we have 'x' available boxed
    and unboxed, but we return the unboxed version for the wrapper to box. If the
    wrapper doesn't cancel with its caller, we'll end up re-boxing something that
    we did have available in boxed form.

    Note [CPR for sum types]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    At the moment we do not do CPR for let-bindings that
       * non-top level
       * bind a sum type
    Reason: I found that in some benchmarks we were losing let-no-escapes,
    which messed it all up.  Example
       let j = \x. ....
       in case y of
            True  -> j False
            False -> j True
    If we w/w this we get
       let j' = \x. ....
       in case y of
            True  -> case j' False of { (# a #) -> Just a }
            False -> case j' True of { (# a #) -> Just a }
    Notice that j' is not a let-no-escape any more.

    However this means in turn that the *enclosing* function
    may be CPR'd (via the returned Justs).  But in the case of
    sums, there may be Nothing alternatives; and that messes
    up the sum-type CPR.

    Conclusion: only do this for products.  It's still not
    guaranteed OK for products, but sums definitely lose sometimes.

    Note [CPR for thunks]
    ~~~~~~~~~~~~~~~~~~~~~
    If the rhs is a thunk, we usually forget the CPR info, because
    it is presumably shared (else it would have been inlined, and
    so we'd lose sharing if w/w'd it into a function).  E.g.

            let r = case expensive of
                      (a,b) -> (b,a)
            in ...

    If we marked r as having the CPR property, then we'd w/w into

            let $wr = \() -> case expensive of
                                (a,b) -> (# b, a #)
                r = case $wr () of
                      (# b,a #) -> (b,a)
            in ...

    But now r is a thunk, which won't be inlined, so we are no further ahead.
    But consider

            f x = let r = case expensive of (a,b) -> (b,a)
                  in if foo r then r else (x,x)

    Does f have the CPR property?  Well, no.

    However, if the strictness analyser has figured out (in a previous
    iteration) that it's strict, then we DON'T need to forget the CPR info.
    Instead we can retain the CPR info and do the thunk-splitting transform
    (see WorkWrap.splitThunk).

    This made a big difference to PrelBase.modInt, which had something like
            modInt = \ x -> let r = ... -> I# v in
                            ...body strict in r...
    r's RHS isn't a value yet; but modInt returns r in various branches, so
    if r doesn't have the CPR property then neither does modInt
    Another case I found in practice (in Complex.magnitude), looks like this:
                    let k = if ... then I# a else I# b
                    in ... body strict in k ....
    (For this example, it doesn't matter whether k is returned as part of
    the overall result; but it does matter that k's RHS has the CPR property.)
    Left to itself, the simplifier will make a join point thus:
                    let $j k = ...body strict in k...
                    if ... then $j (I# a) else $j (I# b)
    With thunk-splitting, we get instead
                    let $j x = let k = I#x in ...body strict in k...
                    in if ... then $j a else $j b
    This is much better; there's a good chance the I# won't get allocated.

    But what about botCpr? Consider
        lvl = error "boom"
        fac -1 = lvl
        fac 0 = 1
        fac n = n * fac (n-1)
    fac won't have the CPR property here when we trim every thunk! But the
    assumption is that error cases are rarely entered and we are diverging anyway,
    so WW doesn't hurt.

    Should we also trim CPR on DataCon application bindings?
    See Note [CPR for data structures]!

    Note [CPR for data structures]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Long static data structures (whether top-level or not) like

      xs = x1 : xs1
      xs1 = x2 : xs2
      xs2 = x3 : xs3

    should not get CPR signatures (#18154), because they

      * Never get WW'd, so their CPR signature should be irrelevant after analysis
        (in fact the signature might even be harmful for that reason)
      * Would need to be inlined/expanded to see their constructed product
      * Recording CPR on them blows up interface file sizes and is redundant with
        their unfolding. In case of Nested CPR, this blow-up can be quadratic!
        Reason: the CPR info for xs1 contains the CPR info for xs; the CPR info
        for xs2 contains that for xs1. And so on.

    Hence we don't analyse or annotate data structures in 'cprAnalBind'. To
    implement this, the isDataStructure guard is triggered for bindings that satisfy

      (1) idArity id == 0 (otherwise it's a function)
      (2) exprIsHNF rhs   (otherwise it's a thunk, Note [CPR for thunks] applies)

    But we can't just stop giving DataCon application bindings the CPR *property*,
    for example

      fac 0 = I# 1#
      fac n = n * fac (n-1)

    fac certainly has the CPR property and should be WW'd! But FloatOut will
    transform the first clause to

      lvl = I# 1#
      fac 0 = lvl

    If lvl doesn't have the CPR property, fac won't either. But lvl is a data
    structure, and hence (see above) will not have a CPR signature. So instead, when
    'cprAnal' meets a variable lacking a CPR signature to extrapolate into a CPR
    transformer, 'cprTransform' instead tries to get its unfolding (via
    'cprDataStructureUnfolding_maybe'), and analyses that instead.

    In practice, GHC generates a lot of (nested) TyCon and KindRep bindings, one
    for each data declaration. They should not have CPR signatures (blow up!).

    There is a perhaps surprising special case: KindRep bindings satisfy
    'isDataStructure' (so no CPR signature), but are marked NOINLINE at the same
    time (see the noinline wrinkle in Note [Grand plan for Typeable]). So there is
    no unfolding for 'cprDataStructureUnfolding_maybe' to look through and we'll
    return topCprType. And that is fine! We should refrain to look through NOINLINE
    data structures in general, as a constructed product could never be exposed
    after WW.

    It's also worth pointing out how ad-hoc this is: If we instead had

        f1 x = x:[]
        f2 x = x : f1 x
        f3 x = x : f2 x
        ...

    we still give every function an every deepening CPR signature. But it's very
    uncommon to find code like this, whereas the long static data structures from
    the beginning of this Note are very common because of GHC's strategy of ANF'ing
    data structure RHSs.

    Note [CPR examples]
    ~~~~~~~~~~~~~~~~~~~~
    Here are some examples (stranal/should_compile/T10482a) of the
    usefulness of Note [Optimistic field binder CPR].  The main
    point: all of these functions can have the CPR property.

        ------- f1 -----------
        -- x is used strictly by h, so it'll be available
        -- unboxed before it is returned in the True branch

        f1 :: Int -> Int
        f1 x = case h x x of
                True  -> x
                False -> f1 (x-1)

        ------- f3 -----------
        -- h is strict in x, so x will be unboxed before it
        -- is rerturned in the otherwise case.

        data T3 = MkT3 Int Int

        f1 :: T3 -> Int
        f1 (MkT3 x y) | h x y     = f3 (MkT3 x (y-1))
                      | otherwise = x
    -}