    {-# LANGUAGE ViewPatterns #-}
    {-# LANGUAGE BinaryLiterals #-}
    {-# LANGUAGE PatternSynonyms #-}

    {-
    (c) The University of Glasgow 2006
    (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
    -}

    -- | A language to express the evaluation context of an expression as a
    -- 'Demand' and track how an expression evaluates free variables and arguments
    -- in turn as a 'DmdType'.
    --
    -- Lays out the abstract domain for "GHC.Core.Opt.DmdAnal".
    module GHC.Types.Demand (
        -- * Demands
        Boxity(..),
        Card(C_00, C_01, C_0N, C_10, C_11, C_1N), CardNonAbs, CardNonOnce,
        Demand(AbsDmd, BotDmd, (:*)),
        SubDemand(Prod, Poly), mkProd, viewProd,
        -- ** Algebra
        absDmd, topDmd, botDmd, seqDmd, topSubDmd,
        -- *** Least upper bound
        lubCard, lubDmd, lubSubDmd,
        -- *** Greatest lower bound
        glbCard,
        -- *** Plus
        plusCard, plusDmd, plusSubDmd,
        -- *** Multiply
        multCard, multDmd, multSubDmd,
        -- ** Predicates on @Card@inalities and @Demand@s
        isAbs, isAtMostOnce, isStrict,
        isAbsDmd, isAtMostOnceDmd, isStrUsedDmd, isStrictDmd,
        isTopDmd, isWeakDmd, onlyBoxedArguments,
        -- ** Special demands
        evalDmd,
        -- *** Demands used in PrimOp signatures
        lazyApply1Dmd, lazyApply2Dmd, strictOnceApply1Dmd, strictManyApply1Dmd,
        -- ** Other @Demand@ operations
        oneifyCard, oneifyDmd, strictifyDmd, strictifyDictDmd, lazifyDmd,
        peelCallDmd, peelManyCalls, mkCalledOnceDmd, mkCalledOnceDmds,
        mkWorkerDemand, subDemandIfEvaluated,
        -- ** Extracting one-shot information
        callCards, argOneShots, argsOneShots, saturatedByOneShots,
        -- ** Manipulating Boxity of a Demand
        unboxDeeplyDmd,

        -- * Divergence
        Divergence(..), topDiv, botDiv, exnDiv, lubDivergence, isDeadEndDiv,

        -- * Demand environments
        DmdEnv(..), addVarDmdEnv, mkTermDmdEnv, nopDmdEnv, plusDmdEnv, plusDmdEnvs,
        reuseEnv,

        -- * Demand types
        DmdType(..), dmdTypeDepth,
        -- ** Algebra
        nopDmdType, botDmdType,
        lubDmdType, plusDmdType, multDmdType, discardArgDmds,
        -- ** Other operations
        peelFV, findIdDemand, addDemand, splitDmdTy, deferAfterPreciseException,

        -- * Demand signatures
        DmdSig(..), mkDmdSigForArity, mkClosedDmdSig, mkVanillaDmdSig,
        splitDmdSig, dmdSigDmdEnv, hasDemandEnvSig,
        nopSig, botSig, isNopSig, isBottomingSig, isDeadEndSig, isDeadEndAppSig,
        trimBoxityDmdSig, transferArgBoxityDmdSig,

        -- ** Handling arity adjustments
        prependArgsDmdSig, etaConvertDmdSig,

        -- * Demand transformers from demand signatures
        DmdTransformer, dmdTransformSig, dmdTransformDataConSig, dmdTransformDictSelSig,

        -- * Trim to a type shape
        TypeShape(..), trimToType, trimBoxity,

        -- * @seq@ing stuff
        seqDemand, seqDemandList, seqDmdType, seqDmdSig,

        -- * Zapping usage information
        zapUsageDemand, zapDmdEnvSig, zapUsedOnceDemand, zapUsedOnceSig
      ) where

    import GHC.Prelude

    import GHC.Types.Var
    import GHC.Types.Var.Env
    import GHC.Types.Unique.FM
    import GHC.Types.Basic
    import GHC.Data.Maybe   ( orElse )

    import GHC.Core.Type    ( Type, isTerminatingType )
    import GHC.Core.DataCon ( splitDataProductType_maybe, StrictnessMark, isMarkedStrict )
    import GHC.Core.Multiplicity    ( scaledThing )

    import GHC.Utils.Binary
    import GHC.Utils.Misc
    import GHC.Utils.Outputable
    import GHC.Utils.Panic

    import Data.Coerce (coerce)
    import Data.Function

    {-
    ************************************************************************
    *                                                                      *
               Boxity: Whether the box of something is used
    *                                                                      *
    ************************************************************************
    -}

    {- Note [Strictness and Unboxing]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    If an argument is used strictly by the function body, we may use use
    call-by-value instead of call-by-need for that argument. What's more, we may
    unbox an argument that is used strictly, discarding the box at the call site.
    This can reduce allocations of the program drastically if the box really isn't
    needed in the function body. Here's an example:
    ```
    even :: Int -> Bool
    even (I# 0) = True
    even (I# 1) = False
    even (I# n) = even (I# (n -# 2))
    ```
    All three code paths of 'even' are (a) strict in the argument, and (b)
    immediately discard the boxed 'Int'. Now if we have a call site like
    `even (I# 42)`, then it would be terrible to allocate the 'I#' box for the
    argument only to tear it apart immediately in the body of 'even'! Hence,
    worker/wrapper will allocate a wrapper for 'even' that not only uses
    call-by-value for the argument (e.g., `case I# 42 of b { $weven b }`), but also
    *unboxes* the argument, resulting in
    ```
    even :: Int -> Bool
    even (I# n) = $weven n
    $weven :: Int# -> Bool
    $weven 0 = True
    $weven 1 = False
    $weven n = $weven (n -# 2)
    ```
    And now the box in `even (I# 42)` will cancel away after inlining the wrapper.

    As far as the permission to unbox is concerned, *evaluatedness* of the argument
    is the important trait. Unboxing implies eager evaluation of an argument and
    we don't want to change the termination properties of the function. One way
    to ensure that is to unbox strict arguments only, but strictness is only a
    sufficient condition for evaluatedness.
    See Note [Unboxing evaluated arguments] in "GHC.Core.Opt.DmdAnal", where
    we manage to unbox *strict fields* of unboxed arguments that the function is not
    actually strict in, simply by realising that those fields have to be evaluated.

    Note [Boxity analysis]
    ~~~~~~~~~~~~~~~~~~~~~~
    Alas, we don't want to unbox *every* strict argument
    (as Note [Strictness and Unboxing] might suggest).
    Here's an example (from T19871):
    ```
    data Huge = H Bool Bool ... Bool
    ann :: Huge -> (Bool, Huge)
    ann h@(Huge True _ ... _) = (False, h)
    ann h                     = (True,  h)
    ```
    Unboxing 'h' yields
    ```
    $wann :: Bool -> Bool -> ... -> Bool -> (Bool, Huge)
    $wann True b2 ... bn = (False, Huge True b2 ... bn)
    $wann b1   b2 ... bn = (True,  Huge b1   b2 ... bn)
    ```
    The pair constructor really needs its fields boxed. But '$wann' doesn't get
    passed 'h' anymore, only its components! Ergo it has to reallocate the 'Huge'
    box, in a process called "reboxing". After w/w, call sites like
    `case ... of Just h -> ann h` pay for the allocation of the additional box.
    In earlier versions of GHC we simply accepted that reboxing would sometimes
    happen, but we found some cases where it made a big difference: #19407, for
    example.

    We therefore perform a simple syntactic boxity analysis that piggy-backs on
    demand analysis in order to determine whether the box of a strict argument is
    always discarded in the function body, in which case we can pass it unboxed
    without risking regressions such as in 'ann' above. But as soon as one use needs
    the box, we want Boxed to win over any Unboxed uses.

    The demand signature (cf. Note [Demand notation]) will say whether it uses
    its arguments boxed or unboxed. Indeed it does so for every sub-component of
    the argument demand. Here's an example:
    ```
    f :: (Int, Int) -> Bool
    f (a, b) = even (a + b) -- demand signature: <1!P(1!L,1!L)>
    ```
    The '!' indicates places where we want to unbox, the lack thereof indicates the
    box is used by the function. Boxity flags are part of the 'Poly' and 'Prod'
    'SubDemand's, see Note [Why Boxity in SubDemand and not in Demand?].
    The given demand signature says "Unbox the pair and then nestedly unbox its
    two fields". By contrast, the demand signature of 'ann' above would look like
    <1P(1L,L,...,L)>, lacking any '!'.

    A demand signature like <1P(1!L)> -- Boxed outside but Unboxed in the field --
    doesn't make a lot of sense, as we can never unbox the field without unboxing
    the containing record. See Note [Finalising boxity for demand signatures] in
    "GHC.Core.Opt.DmdAnal" for how we avoid to spread this and other kinds of
    misinformed boxities.

    Due to various practical reasons, Boxity Analysis is not conservative at times.
    Here are reasons for too much optimism:

     * Note [Function body boxity and call sites] is an observation about when it is
       beneficial to unbox a parameter that is returned from a function.
       Note [Unboxed demand on function bodies returning small products] derives
       a heuristic from the former Note, pretending that all call sites of a
       function need returned small products Unboxed.
     * Note [Boxity for bottoming functions] in DmdAnal makes all bottoming
       functions unbox their arguments, incurring reboxing in code paths that will
       diverge anyway. In turn we get more unboxing in hot code paths.

    Boxity analysis fixes a number of issues: #19871, #19407, #4267, #16859, #18907, #13331

    Note [Function body boxity and call sites]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider (from T5949)
    ```
    f n p = case n of
      0 -> p :: (a, b)
      _ -> f (n-1) p
    -- Worker/wrapper split if we decide to unbox:
    $wf n x y = case n of
      0 -> (# x, y #)
      _ -> $wf (n-1) x y
    f n (x,y) = case $wf n x y of (# r, s #) -> (r,s)
    ```
    When is it better to /not/ to unbox 'p'? That depends on the callers of 'f'!
    If all call sites

     1. Wouldn't need to allocate fresh boxes for 'p', and
     2. Needed the result pair of 'f' boxed

    Only then we'd see an increase in allocation resulting from unboxing. But as
    soon as only one of (1) or (2) holds, it really doesn't matter if 'f' unboxes
    'p' (and its result, it's important that CPR follows suit). For example
    ```
    res = ... case f m (field t) of (r1,r2) -> ...  -- (1) holds
    arg = ... [ f m (x,y) ] ...                     -- (2) holds
    ```
    Because one of the boxes in the call site can cancel away:
    ```
    res = ... case field1 t of (x1,x2) ->
              case field2 t of (y1,y2) ->
              case $wf x1 x2 y1 y2 of (#r1,r2#) -> ...
    arg = ... [ case $wf x1 x2 y1 y2 of (#r1,r2#) -> (r1,r2) ] ...
    ```
    And when call sites neither have arg boxes (1) nor need the result boxed (2),
    then hesitating to unbox means /more/ allocation in the call site because of the
    need for fresh argument boxes.

    Summary: If call sites that satisfy both (1) and (2) occur more often than call
    sites that satisfy neither condition, then it's best /not/ to unbox 'p'.

    Note [Unboxed demand on function bodies returning small products]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Note [Boxity analysis] achieves its biggest wins when we avoid reboxing huge
    records. But when we return small products from a function, we often get faster
    programs by pretending that the caller unboxes the result. Long version:

    Observation: Big record arguments (e.g., DynFlags) tend to be modified much less
                 frequently than small records (e.g., Int).
    Result:      Big records tend to be passed around boxed (unmodified) much more
                 frequently than small records.
    Consequence:  The larger the record, the more likely conditions (1) and (2) from
                 Note [Function body boxity and call sites] are met, in which case
                 unboxing returned parameters leads to reboxing.

    So we put an Unboxed demand on function bodies returning small products and a
    Boxed demand on the others. What is regarded a small product is controlled by
    the -fdmd-unbox-width flag.

    This also manages to unbox functions like
    ```
    sum z      []          = z
    sum (I# n) ((I# x):xs) = sum (I# (n +# x)) xs
    ```
    where we can unbox 'z' on the grounds that it's but a small box anyway. That in
    turn means that the I# allocation in the recursive call site can cancel away and
    we get a non-allocating loop, nice and tight.
    Note that this is the typical case in "Observation" above: A small box is
    unboxed, modified, the result reboxed for the recursive call.

    Originally, this came up in binary-trees' check' function and #4267 which
    (similarly) features a strict fold over a tree. We'd also regress in join004 and
    join007 if we didn't assume an optimistic Unboxed demand on the function body.
    T17932 features a (non-recursive) function that returns a large record, e.g.,
    ```
    flags (Options f x) = <huge> `seq` f
    ```
    and here we won't unbox 'f' because it has 5 fields (which is larger than the
    default -fdmd-unbox-width threshold).

    Why not focus on putting Unboxed demands on *all recursive* function?
    Then we'd unbox
    ```
    flags 0 (Options f x) = <huge> `seq` f
    flags n o             = flags (n-1) o
    ```
    and that seems hardly useful.
    (NB: Similar to 'f' from Note [Preserving Boxity of results is rarely a win],
    but there we only had 2 fields.)

    What about the Boxity of *fields* of a small, returned box? Consider
    ```
    sumIO :: Int -> Int -> IO Int
    sumIO 0 !z = return z     -- What DmdAnal sees: sumIO 0 z s = z `seq` (# s, z #)
    sumIO n !z = sumIO (n-1) (z+n)
    ```
    We really want 'z' to unbox here. Yet its use in the returned unboxed pair
    is fundamentally a Boxed one! CPR would manage to unbox it, but DmdAnal runs
    before that. There is an Unboxed use in the recursive call to 'go' though.
    But 'IO Int' returns a small product, and 'Int' is a small product itself.
    So we'll put the RHS of 'sumIO' under sub-demand '!P(L,L!P(L))', indicating that
    *if* we evaluate 'z', we don't need the box later on. And indeed the bang will
    evaluate `z`, so we conclude with a total demand of `1!P(L)` on `z` and unbox
    it.

    Unlike for recursive functions, where we can often speed up the loop by
    unboxing at the cost of a bit of reboxing in the base case, the wins for
    non-recursive functions quickly turn into losses when unboxing too deeply.
    That happens in T11545, T18109 and T18174. Therefore, we deeply unbox recursive
    function bodies but only shallowly unbox non-recursive function bodies (governed
    by the max_depth variable).

    The implementation is in 'GHC.Core.Opt.DmdAnal.unboxWhenSmall'. It is quite
    vital, guarding for regressions in test cases like #2387, #3586, #16040, #5075
    and #19871.

    Note that this is fundamentally working around a phase problem, namely that the
    results of boxity analysis depend on CPR analysis (and vice versa, of course).

    Note [unboxedWins]
    ~~~~~~~~~~~~~~~~~~
    We used to use '_unboxedWins' below in 'lubBoxity', which was too optimistic.

    While it worked around some shortcomings of the phase separation between Boxity
    analysis and CPR analysis, it was a gross hack which caused regressions itself
    that needed all kinds of fixes and workarounds. Examples (from #21119):

      * As #20767 says, L and B were no longer top and bottom of our lattice
      * In #20746 we unboxed huge Handle types that were never needed boxed in the
        first place. See Note [deferAfterPreciseException].
      * It also caused unboxing of huge records where we better shouldn't, for
        example in T19871.absent.
      * It became impossible to work with when implementing !7599, mostly due to the
        chaos that results from #20767.

    Conclusion: We should use 'boxedWins' in 'lubBoxity', #21119.
    Fortunately, we could come up with a number of better mechanisms to make up for
    the sometimes huge regressions that would have otherwise incured:

    1. A beefed up Note [Unboxed demand on function bodies returning small products]
       that works recursively fixes most regressions. It's a bit unsound, but
       pretty well-behaved.
    2. We saw bottoming functions spoil boxity in some less severe cases and
       countered that with Note [Boxity for bottoming functions].

    -}

    boxedWins :: Boxity -> Boxity -> Boxity
    boxedWins :: Boxity -> Boxity -> Boxity
    boxedWins Boxity
    Unboxed Boxity
    Unboxed = Boxity
    Unboxed
    boxedWins Boxity
    _       !Boxity
    _      = Boxity
    Boxed

    _unboxedWins :: Boxity -> Boxity -> Boxity
    -- See Note [unboxedWins]
    _unboxedWins :: Boxity -> Boxity -> Boxity
    _unboxedWins Boxity
    Boxed Boxity
    Boxed = Boxity
    Boxed
    _unboxedWins Boxity
    _     !Boxity
    _    = Boxity
    Unboxed

    lubBoxity :: Boxity -> Boxity -> Boxity
    -- See Note [Boxity analysis] for the lattice.
    lubBoxity :: Boxity -> Boxity -> Boxity
    lubBoxity = Boxity -> Boxity -> Boxity
    boxedWins

    {-
    ************************************************************************
    *                                                                      *
               Card: Combining Strictness and Usage
    *                                                                      *
    ************************************************************************
    -}

    {- Note [Evaluation cardinalities]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The demand analyser uses an (abstraction of) /evaluation cardinality/ of type
    Card, to specify how many times a term is evaluated. A Card C_lu
    represents an /interval/ of possible cardinalities [l..u], meaning

    * Evaluated /at least/ 'l' times (strictness).
      Hence 'l' is either 0 (lazy)
                       or 1 (strict)

    * Evaluated /at most/ 'u' times (usage).
      Hence 'u' is either 0 (not used at all),
                       or 1 (used at most once)
                       or n (no information)

    Intervals describe sets, so the underlying lattice is the powerset lattice.

    Usually l<=u, but we also have C_10, the interval [1,0], the empty interval,
    denoting the empty set.   This is the bottom element of the lattice.

    See Note [Demand notation] for the notation we use for each of the constructors.

    Note [Bit vector representation for Card]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    While the 6 inhabitants of Card admit an efficient representation as an
    enumeration, implementing operations such as lubCard, plusCard and multCard
    leads to unreasonably bloated code. This was the old defn for lubCard, for
    example:

      -- Handle C_10 (bot)
      lubCard C_10 n    = n    -- bot
      lubCard n    C_10 = n    -- bot
      -- Handle C_0N (top)
      lubCard C_0N _    = C_0N -- top
      lubCard _    C_0N = C_0N -- top
      -- Handle C_11
      lubCard C_00 C_11 = C_01 -- {0} ∪ {1} = {0,1}
      lubCard C_11 C_00 = C_01 -- {0} ∪ {1} = {0,1}
      lubCard C_11 n    = n    -- {1} is a subset of all other intervals
      lubCard n    C_11 = n    -- {1} is a subset of all other intervals
      -- Handle C_1N
      lubCard C_1N C_1N = C_1N -- reflexivity
      lubCard _    C_1N = C_0N -- {0} ∪ {1,n} = top
      lubCard C_1N _    = C_0N -- {0} ∪ {1,n} = top
      -- Handle C_01
      lubCard C_01 _    = C_01 -- {0} ∪ {0,1} = {0,1}
      lubCard _    C_01 = C_01 -- {0} ∪ {0,1} = {0,1}
      -- Handle C_00
      lubCard C_00 C_00 = C_00 -- reflexivity

    There's a much more compact way to encode these operations if Card is
    represented not as distinctly denoted intervals, but as the subset of the set
    of all cardinalities {0,1,n} instead. We represent such a subset as a bit vector
    of length 3 (which fits in an Int). That's actually pretty common for such
    powerset lattices.
    There's one bit per denoted cardinality that is set iff that cardinality is part
    of the denoted set, with n being the most significand bit (index 2) and 0 being
    represented by the least significand bit (index 0).

    How does that help? Well, for one, lubCard just becomes

      lubCard (Card a) (Card b) = Card (a .|. b)

    The other operations, 'plusCard' and 'multCard', become significantly more
    tricky, but immensely more compact. It's all straight-line code with a few bit
    twiddling instructions now!

    Note [Algebraic specification for plusCard and multCard]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The representation change in Note [Bit vector representation for Card] admits
    very dense definitions of 'plusCard' and 'multCard' in terms of bit twiddling,
    but the connection to the algebraic operations they implement is lost.
    It's helpful to have a written specification of what 'plusCard' and 'multCard'
    here that says what they should compute.

      * plusCard: a@[l1,u1] + b@[l2,u2] = r@[l1+l2,u1+u2].
          - In terms of sets, 0 ∈ r iff 0 ∈ a and 0 ∈ b.
            Examples: set in C_00 + C_00, C_01 + C_0N, but not in C_10 + C_00
          - In terms of sets, 1 ∈ r iff 1 ∈ a or 1 ∈ b.
            Examples: set in C_01 + C_00, C_0N + C_0N, but not in C_10 + C_00
          - In terms of sets, n ∈ r iff n ∈ a or n ∈ b, or (1 ∈ a and 1 ∈ b),
            so not unlike add with carry.
            Examples: set in C_01 + C_01, C_01 + C_0N, but not in C_10 + C_01
          - Handy special cases:
              o 'plusCard C_10' bumps up the strictness of its argument, just like
                'lubCard C_00' lazifies it, without touching upper bounds.
                See also 'strictifyCard'
              o Similarly, 'plusCard C_0N' discards usage information
                (incl. absence) but leaves strictness alone.

      * multCard: a@[l1,u1] * b@[l2,u2] = r@[l1*l2,u1*u2].
          - In terms of sets, 0 ∈ r iff 0 ∈ a or 0 ∈ b.
            Examples: set in C_00 * C_10, C_01 * C_1N, but not in C_10 * C_1N
          - In terms of sets, 1 ∈ r iff 1 ∈ a and 1 ∈ b.
            Examples: set in C_01 * C_01, C_01 * C_1N, but not in C_11 * C_10
          - In terms of sets, n ∈ r iff 1 ∈ r and (n ∈ a or n ∈ b).
            Examples: set in C_1N * C_01, C_1N * C_0N, but not in C_10 * C_1N
          - Handy special cases:
              o 'multCard C_1N c' is the same as 'plusCard c c' and
                drops used-once info. But unlike 'plusCard C_0N', it leaves absence
                and strictness.
              o 'multCard C_01' drops strictness info, like 'lubCard C_00'.
              o 'multCard C_0N' does both; it discards all strictness and used-once
                info and retains only absence info.
    -}

    -- | Describes an interval of /evaluation cardinalities/.
    -- See Note [Evaluation cardinalities]
    -- See Note [Bit vector representation for Card]
    newtype Card = Card Int
      deriving Card -> Card -> Bool
    (Card -> Card -> Bool) -> (Card -> Card -> Bool) -> Eq Card
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    $c== :: Card -> Card -> Bool
    == :: Card -> Card -> Bool
    $c/= :: Card -> Card -> Bool
    /= :: Card -> Card -> Bool
    Eq

    -- | A subtype of 'Card' for which the upper bound is never 0 (no 'C_00' or
    -- 'C_10'). The only four inhabitants are 'C_01', 'C_0N', 'C_11', 'C_1N'.
    -- Membership can be tested with 'isCardNonAbs'.
    -- See 'D' and 'Call' for use sites and explanation.
    type CardNonAbs = Card

    -- | A subtype of 'Card' for which the upper bound is never 1 (no 'C_01' or
    -- 'C_11'). The only four inhabitants are 'C_00', 'C_0N', 'C_10', 'C_1N'.
    -- Membership can be tested with 'isCardNonOnce'.
    -- See 'Poly' for use sites and explanation.
    type CardNonOnce = Card

    -- | Absent, {0}. Pretty-printed as A.
    pattern C_00 :: Card
    pattern $mC_00 :: forall {r}. Card -> ((# #) -> r) -> ((# #) -> r) -> r
    $bC_00 :: Card
    C_00 = Card 0b001
    -- | Bottom, {}. Pretty-printed as A.
    pattern C_10 :: Card
    pattern $mC_10 :: forall {r}. Card -> ((# #) -> r) -> ((# #) -> r) -> r
    $bC_10 :: Card
    C_10 = Card 0b000
    -- | Strict and used once, {1}. Pretty-printed as 1.
    pattern C_11 :: Card
    pattern $mC_11 :: forall {r}. Card -> ((# #) -> r) -> ((# #) -> r) -> r
    $bC_11 :: Card
    C_11 = Card 0b010
    -- | Used at most once, {0,1}. Pretty-printed as M.
    pattern C_01 :: Card
    pattern $mC_01 :: forall {r}. Card -> ((# #) -> r) -> ((# #) -> r) -> r
    $bC_01 :: Card
    C_01 = Card 0b011
    -- | Strict and used (possibly) many times, {1,n}. Pretty-printed as S.
    pattern C_1N :: Card
    pattern $mC_1N :: forall {r}. Card -> ((# #) -> r) -> ((# #) -> r) -> r
    $bC_1N :: Card
    C_1N = Card 0b110
    -- | Every possible cardinality; the top element, {0,1,n}. Pretty-printed as L.
    pattern C_0N :: Card
    pattern $mC_0N :: forall {r}. Card -> ((# #) -> r) -> ((# #) -> r) -> r
    $bC_0N :: Card
    C_0N = Card 0b111

    {-# COMPLETE C_00, C_01, C_0N, C_10, C_11, C_1N :: Card #-}

    _botCard, topCard :: Card
    _botCard :: Card
    _botCard = Card
    C_10
    topCard :: Card
    topCard = Card
    C_0N

    -- | True <=> lower bound is 1.
    isStrict :: Card -> Bool
    -- See Note [Bit vector representation for Card]
    isStrict :: Card -> Bool
    isStrict (Card Int
    c) = Int
    c Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    0b001 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    0 -- simply check 0 bit is not set

    -- | True <=> upper bound is 0.
    isAbs :: Card -> Bool
    -- See Note [Bit vector representation for Card]
    isAbs :: Card -> Bool
    isAbs (Card Int
    c) = Int
    c Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    0b110 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    0 -- simply check 1 and n bit are not set

    -- | True <=> upper bound is 1.
    isAtMostOnce :: Card -> Bool
    -- See Note [Bit vector representation for Card]
    isAtMostOnce :: Card -> Bool
    isAtMostOnce (Card Int
    c) = Int
    c Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    0b100 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    0 -- simply check n bit is not set

    -- | Is this a 'CardNonAbs'?
    isCardNonAbs :: Card -> Bool
    isCardNonAbs :: Card -> Bool
    isCardNonAbs = Bool -> Bool
    not (Bool -> Bool) -> (Card -> Bool) -> Card -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Card -> Bool
    isAbs

    -- | Is this a 'CardNonOnce'?
    isCardNonOnce :: Card -> Bool
    isCardNonOnce :: Card -> Bool
    isCardNonOnce Card
    n = Card -> Bool
    isAbs Card
    n Bool -> Bool -> Bool
    || Bool -> Bool
    not (Card -> Bool
    isAtMostOnce Card
    n)

    -- | Intersect with [0,1].
    oneifyCard :: Card -> Card
    oneifyCard :: Card -> Card
    oneifyCard = Card -> Card -> Card
    glbCard Card
    C_01

    -- | Intersect with [1,n]. The same as @'plusCard' 'C_10'@.
    strictifyCard :: Card -> Card
    strictifyCard :: Card -> Card
    strictifyCard = Card -> Card -> Card
    glbCard Card
    C_1N

    -- | Denotes '∪' on 'Card'.
    lubCard :: Card -> Card -> Card
    -- See Note [Bit vector representation for Card]
    lubCard :: Card -> Card -> Card
    lubCard (Card Int
    a) (Card Int
    b) = Int -> Card
    Card (Int
    a Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. Int
    b) -- main point of the bit-vector encoding!

    -- | Denotes '∩' on 'Card'.
    glbCard :: Card -> Card -> Card
    -- See Note [Bit vector representation for Card]
    glbCard :: Card -> Card -> Card
    glbCard (Card Int
    a) (Card Int
    b) = Int -> Card
    Card (Int
    a Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    b)

    -- | Denotes '+' on lower and upper bounds of 'Card'.
    plusCard :: Card -> Card -> Card
    -- See Note [Algebraic specification for plusCard and multCard]
    plusCard :: Card -> Card -> Card
    plusCard (Card Int
    a) (Card Int
    b)
      = Int -> Card
    Card (Int
    bit0 Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. Int
    bit1 Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. Int
    bitN)
      where
        bit0 :: Int
    bit0 =  (Int
    a Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    b)                         Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    0b001
        bit1 :: Int
    bit1 =  (Int
    a Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. Int
    b)                         Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    0b010
        bitN :: Int
    bitN = ((Int
    a Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. Int
    b) Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. Int -> Int -> Int
    forall a. Bits a => a -> Int -> a
    shiftL (Int
    a Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    b) Int
    1) Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    0b100

    -- | Denotes '*' on lower and upper bounds of 'Card'.
    multCard :: Card -> Card -> Card
    -- See Note [Algebraic specification for plusCard and multCard]
    multCard :: Card -> Card -> Card
    multCard (Card Int
    a) (Card Int
    b)
      = Int -> Card
    Card (Int
    bit0 Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. Int
    bit1 Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. Int
    bitN)
      where
        bit0 :: Int
    bit0 = (Int
    a Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. Int
    b)                   Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    0b001
        bit1 :: Int
    bit1 = (Int
    a Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    b)                   Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    0b010
        bitN :: Int
    bitN = (Int
    a Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. Int
    b) Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int -> Int -> Int
    forall a. Bits a => a -> Int -> a
    shiftL Int
    bit1 Int
    1 Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    0b100

    {-
    ************************************************************************
    *                                                                      *
               Demand: Evaluation contexts
    *                                                                      *
    ************************************************************************
    -}

    -- | A demand describes
    --
    --   * How many times a variable is evaluated, via a 'Card'inality, and
    --   * How deep its value was evaluated in turn, via a 'SubDemand'.
    --
    -- Examples (using Note [Demand notation]):
    --
    --   * 'seq' puts demand @1A@ on its first argument: It evaluates the argument
    --     strictly (@1@), but not any deeper (@A@).
    --   * 'fst' puts demand @1P(1L,A)@ on its argument: It evaluates the argument
    --     pair strictly and the first component strictly, but no nested info
    --     beyond that (@L@). Its second argument is not used at all.
    --   * '$' puts demand @1C(1,L)@ on its first argument: It calls (@C@) the
    --     argument function with one argument, exactly once (@1@). No info
    --     on how the result of that call is evaluated (@L@).
    --   * 'maybe' puts demand @MC(M,L)@ on its second argument: It evaluates
    --     the argument function at most once ((M)aybe) and calls it once when
    --     it is evaluated.
    --   * @fst p + fst p@ puts demand @SP(SL,A)@ on @p@: It's @1P(1L,A)@
    --     multiplied by two, so we get @S@ (used at least once, possibly multiple
    --     times).
    --
    -- This data type is quite similar to @'Scaled' 'SubDemand'@, but it's scaled
    -- by 'Card', which is an /interval/ on 'Multiplicity', the upper bound of
    -- which could be used to infer uniqueness types. Also we treat 'AbsDmd' and
    -- 'BotDmd' specially, as the concept of a 'SubDemand' doesn't apply when there
    -- isn't any evaluation at all. If you don't care, simply use '(:*)'.
    data Demand
      = BotDmd
      -- ^ A bottoming demand, produced by a diverging function ('C_10'), hence there is no
      -- 'SubDemand' that describes how it was evaluated.

      | AbsDmd
      -- ^ An absent demand: Evaluated exactly 0 times ('C_00'), hence there is no
      -- 'SubDemand' that describes how it was evaluated.

      | D !CardNonAbs !SubDemand
      -- ^ Don't use this internal data constructor; use '(:*)' instead.
      -- Since BotDmd deals with 'C_10' and AbsDmd deals with 'C_00', the
      -- cardinality component is CardNonAbs
      deriving Demand -> Demand -> Bool
    (Demand -> Demand -> Bool)
    -> (Demand -> Demand -> Bool) -> Eq Demand
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    $c== :: Demand -> Demand -> Bool
    == :: Demand -> Demand -> Bool
    $c/= :: Demand -> Demand -> Bool
    /= :: Demand -> Demand -> Bool
    Eq

    -- | Only meant to be used in the pattern synonym below!
    viewDmdPair :: Demand -> (Card, SubDemand)
    viewDmdPair :: Demand -> (Card, SubDemand)
    viewDmdPair Demand
    BotDmd   = (Card
    C_10, SubDemand
    botSubDmd)
    viewDmdPair Demand
    AbsDmd   = (Card
    C_00, SubDemand
    botSubDmd)
    viewDmdPair (D Card
    n SubDemand
    sd) = (Card
    n, SubDemand
    sd)

    -- | @c :* sd@ is a demand that says \"evaluated @c@ times, and any trace in
    -- which it is evaluated will evaluate at least as deep as @sd@\".
    --
    -- Matching on this pattern synonym is a complete match.
    -- If the matched demand was 'AbsDmd', it will match as @C_00 :* seqSubDmd@.
    -- If the matched demand was 'BotDmd', it will match as @C_10 :* botSubDmd@.
    -- The builder of this pattern synonym simply /discards/ the 'SubDemand' if the
    -- 'Card' was absent and returns 'AbsDmd' or 'BotDmd' instead. It will assert
    -- that the discarded sub-demand was 'seqSubDmd' and 'botSubDmd', respectively.
    --
    -- Call sites should consider whether they really want to look at the
    -- 'SubDemand' of an absent demand and match on 'AbsDmd' and/or 'BotDmd'
    -- otherwise. Really, any other 'SubDemand' would be allowed and
    -- might work better, depending on context.
    pattern (:*) :: HasDebugCallStack => Card -> SubDemand -> Demand
    pattern n $m:* :: forall {r}.
    HasDebugCallStack =>
    Demand -> (Card -> SubDemand -> r) -> ((# #) -> r) -> r
    $b:* :: HasDebugCallStack => Card -> SubDemand -> Demand
    :* sd <- (viewDmdPair -> (n, sd)) where
      Card
    C_10 :* SubDemand
    sd = Demand
    BotDmd Demand -> (Demand -> Demand) -> Demand
    forall a b. a -> (a -> b) -> b
    & Bool -> SDoc -> Demand -> Demand
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (SubDemand
    sd SubDemand -> SubDemand -> Bool
    forall a. Eq a => a -> a -> Bool
    == SubDemand
    botSubDmd) (String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "B /=" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> SubDemand -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr SubDemand
    sd)
      Card
    C_00 :* SubDemand
    sd = Demand
    AbsDmd Demand -> (Demand -> Demand) -> Demand
    forall a b. a -> (a -> b) -> b
    & Bool -> SDoc -> Demand -> Demand
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (SubDemand
    sd SubDemand -> SubDemand -> Bool
    forall a. Eq a => a -> a -> Bool
    == SubDemand
    botSubDmd) (String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "A /=" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> SubDemand -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr SubDemand
    sd)
      Card
    n    :* SubDemand
    sd = Card -> SubDemand -> Demand
    D Card
    n SubDemand
    sd Demand -> (Demand -> Demand) -> Demand
    forall a b. a -> (a -> b) -> b
    & Bool -> SDoc -> Demand -> Demand
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (Card -> Bool
    isCardNonAbs Card
    n)  (Card -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Card
    n SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ SubDemand -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr SubDemand
    sd)
    {-# COMPLETE (:*) #-}

    -- | A sub-demand describes an /evaluation context/ (in the sense of an
    -- operational semantics), e.g. how deep the denoted thing is going to be
    -- evaluated. See 'Demand' for examples.
    --
    -- See Note [SubDemand denotes at least one evaluation] for a more detailed
    -- description of what a sub-demand means.
    --
    -- See Note [Demand notation] for the extensively used short-hand notation.
    -- See also Note [Why Boxity in SubDemand and not in Demand?].
    data SubDemand
      = Poly !Boxity !CardNonOnce
      -- ^ Polymorphic demand, the denoted thing is evaluated arbitrarily deep,
      -- with the specified cardinality at every level. The 'Boxity' applies only
      -- to the outer evaluation context as well as all inner evaluation context.
      -- See Note [Boxity in Poly] for why we want it to carry 'Boxity'.
      -- Expands to 'Call' via 'viewCall' and to 'Prod' via 'viewProd'.
      --
      -- @Poly b n@ is semantically equivalent to @Prod b [n :* Poly b n, ...]
      -- or @Call n (Poly Boxed n)@. 'viewCall' and 'viewProd' do these rewrites.
      --
      -- In Note [Demand notation]: @L  === P(L,L,...)@  and @L  === C(L)@,
      --                            @B  === P(B,B,...)@  and @B  === C(B)@,
      --                            @!A === !P(A,A,...)@ and @!A === C(A)@,
      --                            and so on.
      --
      -- We'll only see 'Poly' with 'C_10' (B), 'C_00' (A), 'C_0N' (L) and sometimes
      -- 'C_1N' (S) through 'plusSubDmd', never 'C_01' (M) or 'C_11' (1) (grep the
      -- source code). Hence 'CardNonOnce', which is closed under 'lub' and 'plus'.
      --
      -- Why doesn't this constructor simply carry a 'Demand' instead of its fields?
      -- See Note [Call SubDemand vs. evaluation Demand].
      | Call !CardNonAbs !SubDemand
      -- ^ @Call n sd@ describes the evaluation context of @n@ function
      -- applications (with one argument), where the result of each call is
      -- evaluated according to @sd@.
      -- @sd@ describes program traces in which the denoted thing was called at all,
      -- see Note [SubDemand denotes at least one evaluation].
      -- That Note also explains why it doesn't make sense for @n@ to be absent,
      -- hence we forbid it with 'CardNonAbs'. Absent call demands can still be
      -- expressed with 'Poly'.
      -- Used only for values of function type. Use the smart constructor 'mkCall'
      -- whenever possible!
      | Prod !Boxity ![Demand]
      -- ^ @Prod b ds@ describes the evaluation context of a case scrutinisation
      -- on an expression of product type, where the product components are
      -- evaluated according to @ds@. The 'Boxity' @b@ says whether or not the box
      -- of the product was used.

    -- | We have to respect Poly rewrites through 'viewCall' and 'viewProd'.
    instance Eq SubDemand where
      SubDemand
    d1 == :: SubDemand -> SubDemand -> Bool
    == SubDemand
    d2 = case SubDemand
    d1 of
        Prod Boxity
    b1 [Demand]
    ds1
          | Just (Boxity
    b2, [Demand]
    ds2) <- Int -> SubDemand -> Maybe (Boxity, [Demand])
    viewProd ([Demand] -> Int
    forall a. [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [Demand]
    ds1) SubDemand
    d2 -> Boxity
    b1 Boxity -> Boxity -> Bool
    forall a. Eq a => a -> a -> Bool
    == Boxity
    b2 Bool -> Bool -> Bool
    && [Demand]
    ds1 [Demand] -> [Demand] -> Bool
    forall a. Eq a => a -> a -> Bool
    == [Demand]
    ds2
        Call Card
    n1 SubDemand
    sd1
          | Just (Card
    n2, SubDemand
    sd2) <- SubDemand -> Maybe (Card, SubDemand)
    viewCall SubDemand
    d2              -> Card
    n1 Card -> Card -> Bool
    forall a. Eq a => a -> a -> Bool
    == Card
    n2 Bool -> Bool -> Bool
    && SubDemand
    sd1 SubDemand -> SubDemand -> Bool
    forall a. Eq a => a -> a -> Bool
    == SubDemand
    sd2
        Poly Boxity
    b1 Card
    n1
          | Poly Boxity
    b2 Card
    n2 <- SubDemand
    d2                           -> Boxity
    b1 Boxity -> Boxity -> Bool
    forall a. Eq a => a -> a -> Bool
    == Boxity
    b2 Bool -> Bool -> Bool
    && Card
    n1 Card -> Card -> Bool
    forall a. Eq a => a -> a -> Bool
    == Card
    n2
        SubDemand
    _                                              -> Bool
    False

    topSubDmd, botSubDmd, seqSubDmd :: SubDemand
    topSubDmd :: SubDemand
    topSubDmd = Boxity -> Card -> SubDemand
    Poly   Boxity
    Boxed Card
    C_0N
    botSubDmd :: SubDemand
    botSubDmd = Boxity -> Card -> SubDemand
    Poly Boxity
    Unboxed Card
    C_10
    seqSubDmd :: SubDemand
    seqSubDmd = Boxity -> Card -> SubDemand
    Poly Boxity
    Unboxed Card
    C_00

    -- | The uniform field demand when viewing a 'Poly' as a 'Prod', as in
    -- 'viewProd'.
    polyFieldDmd :: Boxity -> CardNonOnce -> Demand
    polyFieldDmd :: Boxity -> Card -> Demand
    polyFieldDmd Boxity
    _     Card
    C_00 = Demand
    AbsDmd
    polyFieldDmd Boxity
    _     Card
    C_10 = Demand
    BotDmd
    polyFieldDmd Boxity
    Boxed Card
    C_0N = Demand
    topDmd
    polyFieldDmd Boxity
    b     Card
    n    = Card
    n HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* Boxity -> Card -> SubDemand
    Poly Boxity
    b Card
    n Demand -> (Demand -> Demand) -> Demand
    forall a b. a -> (a -> b) -> b
    & Bool -> SDoc -> Demand -> Demand
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (Card -> Bool
    isCardNonOnce Card
    n) (Card -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Card
    n)

    -- | A smart constructor for 'Prod', applying rewrite rules along the semantic
    -- equality @Prod b [n :* Poly Boxed n, ...] === Poly b n@, simplifying to
    -- 'Poly' 'SubDemand's when possible. Examples:
    --
    --   * Rewrites @P(L,L)@ (e.g., arguments @Boxed@, @[L,L]@) to @L@
    --   * Rewrites @!P(L!L,L!L)@ (e.g., arguments @Unboxed@, @[L!L,L!L]@) to @!L@
    --   * Does not rewrite @P(1L)@, @P(L!L)@, @!P(L)@ or @P(L,A)@
    --
    mkProd :: Boxity -> [Demand] -> SubDemand
    mkProd :: Boxity -> [Demand] -> SubDemand
    mkProd Boxity
    b [Demand]
    ds
      | (Demand -> Bool) -> [Demand] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all (Demand -> Demand -> Bool
    forall a. Eq a => a -> a -> Bool
    == Demand
    AbsDmd) [Demand]
    ds = Boxity -> Card -> SubDemand
    Poly Boxity
    b Card
    C_00
      | (Demand -> Bool) -> [Demand] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all (Demand -> Demand -> Bool
    forall a. Eq a => a -> a -> Bool
    == Demand
    BotDmd) [Demand]
    ds = Boxity -> Card -> SubDemand
    Poly Boxity
    b Card
    C_10
      | dmd :: Demand
    dmd@(Card
    n :* Poly Boxity
    b2 Card
    m):[Demand]
    _ <- [Demand]
    ds
      , Card
    n Card -> Card -> Bool
    forall a. Eq a => a -> a -> Bool
    == Card
    m           -- don't rewrite P(SL)  to S
      , Boxity
    b Boxity -> Boxity -> Bool
    forall a. Eq a => a -> a -> Bool
    == Boxity
    b2          -- don't rewrite P(S!S) to !S
      , (Demand -> Bool) -> [Demand] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all (Demand -> Demand -> Bool
    forall a. Eq a => a -> a -> Bool
    == Demand
    dmd) [Demand]
    ds  -- don't rewrite P(L,A) to L
      = Boxity -> Card -> SubDemand
    Poly Boxity
    b Card
    n
      | Bool
    otherwise          = Boxity -> [Demand] -> SubDemand
    Prod Boxity
    b [Demand]
    ds

    -- | @viewProd n sd@ interprets @sd@ as a 'Prod' of arity @n@, expanding 'Poly'
    -- demands as necessary.
    viewProd :: Arity -> SubDemand -> Maybe (Boxity, [Demand])
    -- It's quite important that this function is optimised well;
    -- it is used by lubSubDmd and plusSubDmd.
    viewProd :: Int -> SubDemand -> Maybe (Boxity, [Demand])
    viewProd Int
    n (Prod Boxity
    b [Demand]
    ds)
      | [Demand]
    ds [Demand] -> Int -> Bool
    forall a. [a] -> Int -> Bool
    `lengthIs` Int
    n = (Boxity, [Demand]) -> Maybe (Boxity, [Demand])
    forall a. a -> Maybe a
    Just (Boxity
    b, [Demand]
    ds)
    -- Note the strict application to replicate: This makes sure we don't allocate
    -- a thunk for it, inlines it and lets case-of-case fire at call sites.
    viewProd Int
    n (Poly Boxity
    b Card
    card)
      | let !ds :: [Demand]
    ds = Int -> Demand -> [Demand]
    forall a. Int -> a -> [a]
    replicate Int
    n (Demand -> [Demand]) -> Demand -> [Demand]
    forall a b. (a -> b) -> a -> b
    $! Boxity -> Card -> Demand
    polyFieldDmd Boxity
    b Card
    card
      = (Boxity, [Demand]) -> Maybe (Boxity, [Demand])
    forall a. a -> Maybe a
    Just (Boxity
    b, [Demand]
    ds)
    viewProd Int
    _ SubDemand
    _
      = Maybe (Boxity, [Demand])
    forall a. Maybe a
    Nothing
    {-# INLINE viewProd #-} -- we want to fuse away the replicate and the allocation
                            -- for Arity. Otherwise, #18304 bites us.

    -- | A smart constructor for 'Call', applying rewrite rules along the semantic
    -- equality @Call C_0N (Poly C_0N) === Poly C_0N@, simplifying to 'Poly' 'SubDemand's
    -- when possible.
    mkCall :: CardNonAbs -> SubDemand -> SubDemand
    --mkCall C_1N sd@(Poly Boxed C_1N) = sd -- NO! #21085 strikes. See Note [mkCall and plusSubDmd]
    mkCall :: Card -> SubDemand -> SubDemand
    mkCall Card
    C_0N sd :: SubDemand
    sd@(Poly Boxity
    Boxed Card
    C_0N) = SubDemand
    sd
    mkCall Card
    n    SubDemand
    sd                   = Bool -> SDoc -> SubDemand -> SubDemand
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (Card -> Bool
    isCardNonAbs Card
    n) (Card -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Card
    n SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ SubDemand -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr SubDemand
    sd) (SubDemand -> SubDemand) -> SubDemand -> SubDemand
    forall a b. (a -> b) -> a -> b
    $
                                       Card -> SubDemand -> SubDemand
    Call Card
    n SubDemand
    sd

    -- | @viewCall sd@ interprets @sd@ as a 'Call', expanding 'Poly' subdemands as
    -- necessary.
    viewCall :: SubDemand -> Maybe (Card, SubDemand)
    viewCall :: SubDemand -> Maybe (Card, SubDemand)
    viewCall (Call Card
    n SubDemand
    sd) = (Card, SubDemand) -> Maybe (Card, SubDemand)
    forall a. a -> Maybe a
    Just (Card
    n :: Card, SubDemand
    sd)
    viewCall (Poly Boxity
    _ Card
    n)
      | Card -> Bool
    isAbs Card
    n          = (Card, SubDemand) -> Maybe (Card, SubDemand)
    forall a. a -> Maybe a
    Just (Card
    n :: Card, SubDemand
    botSubDmd)
      | Bool
    otherwise        = (Card, SubDemand) -> Maybe (Card, SubDemand)
    forall a. a -> Maybe a
    Just (Card
    n :: Card, Boxity -> Card -> SubDemand
    Poly Boxity
    Boxed Card
    n)
    viewCall SubDemand
    _           = Maybe (Card, SubDemand)
    forall a. Maybe a
    Nothing

    topDmd, absDmd, botDmd, seqDmd :: Demand
    topDmd :: Demand
    topDmd = Card
    C_0N HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* SubDemand
    topSubDmd
    absDmd :: Demand
    absDmd = Demand
    AbsDmd
    botDmd :: Demand
    botDmd = Demand
    BotDmd
    seqDmd :: Demand
    seqDmd = Card
    C_11 HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* SubDemand
    seqSubDmd

    -- | Sets 'Boxity' to 'Unboxed' for non-'Call' sub-demands and recurses into 'Prod'.
    unboxDeeplySubDmd :: SubDemand -> SubDemand
    unboxDeeplySubDmd :: SubDemand -> SubDemand
    unboxDeeplySubDmd (Poly Boxity
    _ Card
    n)  = Boxity -> Card -> SubDemand
    Poly Boxity
    Unboxed Card
    n
    unboxDeeplySubDmd (Prod Boxity
    _ [Demand]
    ds) = Boxity -> [Demand] -> SubDemand
    mkProd Boxity
    Unboxed ((Demand -> Demand) -> [Demand] -> [Demand]
    forall a b. (a -> b) -> [a] -> [b]
    strictMap Demand -> Demand
    unboxDeeplyDmd [Demand]
    ds)
    unboxDeeplySubDmd call :: SubDemand
    call@Call{} = SubDemand
    call

    -- | Sets 'Boxity' to 'Unboxed' for the 'Demand', recursing into 'Prod's.
    -- Don't recurse into lazy arguments; see GHC.Core.Opt.DmdAnal
    --    Note [No lazy, Unboxed demands in demand signature]
    unboxDeeplyDmd :: Demand -> Demand
    unboxDeeplyDmd :: Demand -> Demand
    unboxDeeplyDmd Demand
    AbsDmd   = Demand
    AbsDmd
    unboxDeeplyDmd Demand
    BotDmd   = Demand
    BotDmd
    unboxDeeplyDmd dmd :: Demand
    dmd@(D Card
    n SubDemand
    sd) | Card -> Bool
    isStrict Card
    n = Card -> SubDemand -> Demand
    D Card
    n (SubDemand -> SubDemand
    unboxDeeplySubDmd SubDemand
    sd)
                                | Bool
    otherwise  = Demand
    dmd

    multDmd :: Card -> Demand -> Demand
    multDmd :: Card -> Demand -> Demand
    multDmd Card
    C_11 Demand
    dmd       = Demand
    dmd -- An optimisation
    -- The following four lines make sure that we rewrite to AbsDmd and BotDmd
    -- whenever the leading cardinality is absent (C_00 or C_10).
    -- Otherwise it may happen that the SubDemand is not 'botSubDmd', triggering
    -- the assertion in `:*`.
    -- Example: `multDmd B 1L = BA`, so with an inner `seqSubDmd`. Our lattice
    -- allows us to always rewrite this to proper BotDmd and we maintain the
    -- invariant that this is indeed the case.
    multDmd Card
    C_00 Demand
    _        = Demand
    AbsDmd
    multDmd Card
    _    Demand
    AbsDmd   = Demand
    AbsDmd
    multDmd Card
    C_10 (D Card
    n SubDemand
    _)  = if Card -> Bool
    isStrict Card
    n then Demand
    BotDmd else Demand
    AbsDmd
    multDmd Card
    n    Demand
    BotDmd   = if Card -> Bool
    isStrict Card
    n then Demand
    BotDmd else Demand
    AbsDmd
    -- See Note [SubDemand denotes at least one evaluation] for the strictifyCard
    multDmd Card
    n    (D Card
    m SubDemand
    sd) = Card -> Card -> Card
    multCard Card
    n Card
    m HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* Card -> SubDemand -> SubDemand
    multSubDmd (Card -> Card
    strictifyCard Card
    n) SubDemand
    sd

    multSubDmd :: Card -> SubDemand -> SubDemand
    multSubDmd :: Card -> SubDemand -> SubDemand
    multSubDmd Card
    C_11 SubDemand
    sd           = SubDemand
    sd -- An optimisation, for when sd is a deep Prod
    -- The following three equations don't have an impact on Demands, only on
    -- Boxity. They are needed so that we don't trigger the assertions in `:*`
    -- when called from `multDmd`.
    multSubDmd Card
    C_00 SubDemand
    _            = SubDemand
    seqSubDmd -- Otherwise `multSubDmd A L == A /= !A`
    multSubDmd Card
    C_10 (Poly Boxity
    _ Card
    n)   = if Card -> Bool
    isStrict Card
    n then SubDemand
    botSubDmd else SubDemand
    seqSubDmd -- Otherwise `multSubDmd B L == B /= !B`
    multSubDmd Card
    C_10 (Call Card
    n SubDemand
    _)   = if Card -> Bool
    isStrict Card
    n then SubDemand
    botSubDmd else SubDemand
    seqSubDmd -- Otherwise we'd call `mkCall` with absent cardinality
    multSubDmd Card
    n    (Poly Boxity
    b Card
    m)   = Boxity -> Card -> SubDemand
    Poly Boxity
    b (Card -> Card -> Card
    multCard Card
    n Card
    m)
    multSubDmd Card
    n    (Call Card
    n' SubDemand
    sd) = Card -> SubDemand -> SubDemand
    mkCall (Card -> Card -> Card
    multCard Card
    n Card
    n') SubDemand
    sd
    multSubDmd Card
    n    (Prod Boxity
    b [Demand]
    ds)  = Boxity -> [Demand] -> SubDemand
    mkProd Boxity
    b ((Demand -> Demand) -> [Demand] -> [Demand]
    forall a b. (a -> b) -> [a] -> [b]
    strictMap (Card -> Demand -> Demand
    multDmd Card
    n) [Demand]
    ds)

    lazifyIfStrict :: Card -> SubDemand -> SubDemand
    lazifyIfStrict :: Card -> SubDemand -> SubDemand
    lazifyIfStrict Card
    n SubDemand
    sd = Card -> SubDemand -> SubDemand
    multSubDmd (Card -> Card -> Card
    glbCard Card
    C_01 Card
    n) SubDemand
    sd

    -- | Denotes '∪' on 'Demand'.
    lubDmd :: Demand -> Demand -> Demand
    lubDmd :: Demand -> Demand -> Demand
    lubDmd Demand
    BotDmd      Demand
    dmd2        = Demand
    dmd2
    lubDmd Demand
    dmd1        Demand
    BotDmd      = Demand
    dmd1
    lubDmd (Card
    n1 :* SubDemand
    sd1) (Card
    n2 :* SubDemand
    sd2) = -- pprTraceWith "lubDmd" (\it -> ppr (n1:*sd1) $$ ppr (n2:*sd2) $$ ppr it) $
      Card -> Card -> Card
    lubCard Card
    n1 Card
    n2 HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* SubDemand -> SubDemand -> SubDemand
    lubSubDmd SubDemand
    sd1 SubDemand
    sd2

    lubSubDmd :: SubDemand -> SubDemand -> SubDemand
    -- Shortcuts for neutral and absorbing elements.
    -- Below we assume that Boxed always wins.
    lubSubDmd :: SubDemand -> SubDemand -> SubDemand
    lubSubDmd (Poly Boxity
    Unboxed Card
    C_10)  SubDemand
    sd                   = SubDemand
    sd
    lubSubDmd SubDemand
    sd                   (Poly Boxity
    Unboxed Card
    C_10)  = SubDemand
    sd
    lubSubDmd sd :: SubDemand
    sd@(Poly Boxity
    Boxed Card
    C_0N) SubDemand
    _                    = SubDemand
    sd
    lubSubDmd SubDemand
    _                    sd :: SubDemand
    sd@(Poly Boxity
    Boxed Card
    C_0N) = SubDemand
    sd
    -- Handle Prod
    lubSubDmd (Prod Boxity
    b1 [Demand]
    ds1) (Poly Boxity
    b2 Card
    n2)
      | let !d :: Demand
    d = Boxity -> Card -> Demand
    polyFieldDmd Boxity
    b2 Card
    n2
      = Boxity -> [Demand] -> SubDemand
    mkProd (Boxity -> Boxity -> Boxity
    lubBoxity Boxity
    b1 Boxity
    b2) ((Demand -> Demand) -> [Demand] -> [Demand]
    forall a b. (a -> b) -> [a] -> [b]
    strictMap (Demand -> Demand -> Demand
    lubDmd Demand
    d) [Demand]
    ds1)
    lubSubDmd (Prod Boxity
    b1 [Demand]
    ds1) (Prod Boxity
    b2 [Demand]
    ds2)
      | [Demand] -> [Demand] -> Bool
    forall a b. [a] -> [b] -> Bool
    equalLength [Demand]
    ds1 [Demand]
    ds2
      = Boxity -> [Demand] -> SubDemand
    mkProd (Boxity -> Boxity -> Boxity
    lubBoxity Boxity
    b1 Boxity
    b2) ((Demand -> Demand -> Demand) -> [Demand] -> [Demand] -> [Demand]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    strictZipWith Demand -> Demand -> Demand
    lubDmd [Demand]
    ds1 [Demand]
    ds2)
    -- Handle Call
    lubSubDmd (Call Card
    n1 SubDemand
    sd1) (SubDemand -> Maybe (Card, SubDemand)
    viewCall -> Just (Card
    n2, SubDemand
    sd2)) =
      Card -> SubDemand -> SubDemand
    mkCall (Card -> Card -> Card
    lubCard Card
    n1 Card
    n2) (SubDemand -> SubDemand -> SubDemand
    lubSubDmd SubDemand
    sd1 SubDemand
    sd2)
    -- Handle Poly
    lubSubDmd (Poly Boxity
    b1 Card
    n1) (Poly Boxity
    b2 Card
    n2) = Boxity -> Card -> SubDemand
    Poly (Boxity -> Boxity -> Boxity
    lubBoxity Boxity
    b1 Boxity
    b2) (Card -> Card -> Card
    lubCard Card
    n1 Card
    n2)
    -- Other Poly case by commutativity
    lubSubDmd sd1 :: SubDemand
    sd1@Poly{}   SubDemand
    sd2          = SubDemand -> SubDemand -> SubDemand
    lubSubDmd SubDemand
    sd2 SubDemand
    sd1
    -- Otherwise (Call `lub` Prod) return Top
    lubSubDmd SubDemand
    _            SubDemand
    _            = SubDemand
    topSubDmd

    -- | Denotes '+' on 'Demand'.
    plusDmd :: Demand -> Demand -> Demand
    plusDmd :: Demand -> Demand -> Demand
    plusDmd Demand
    AbsDmd      Demand
    dmd2        = Demand
    dmd2
    plusDmd Demand
    dmd1        Demand
    AbsDmd      = Demand
    dmd1
    plusDmd (Card
    n1 :* SubDemand
    sd1) (Card
    n2 :* SubDemand
    sd2) = -- pprTraceWith "plusDmd" (\it -> ppr (n1:*sd1) $$ ppr (n2:*sd2) $$ ppr it) $
      -- Why lazify? See Note [SubDemand denotes at least one evaluation]
      -- and also Note [Unrealised opportunity in plusDmd] which applies when both
      -- n1 and n2 are lazy already
      Card -> Card -> Card
    plusCard Card
    n1 Card
    n2 HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* SubDemand -> SubDemand -> SubDemand
    plusSubDmd (Card -> SubDemand -> SubDemand
    lazifyIfStrict Card
    n1 SubDemand
    sd1) (Card -> SubDemand -> SubDemand
    lazifyIfStrict Card
    n2 SubDemand
    sd2)

    plusSubDmd :: SubDemand -> SubDemand -> SubDemand
    -- Shortcuts for neutral and absorbing elements.
    -- Below we assume that Boxed always wins.
    plusSubDmd :: SubDemand -> SubDemand -> SubDemand
    plusSubDmd (Poly Boxity
    Unboxed Card
    C_00)  SubDemand
    sd                   = SubDemand
    sd
    plusSubDmd SubDemand
    sd                   (Poly Boxity
    Unboxed Card
    C_00)  = SubDemand
    sd
    plusSubDmd sd :: SubDemand
    sd@(Poly Boxity
    Boxed Card
    C_1N) SubDemand
    _                    = SubDemand
    sd
    plusSubDmd SubDemand
    _                    sd :: SubDemand
    sd@(Poly Boxity
    Boxed Card
    C_1N) = SubDemand
    sd
    -- Handle Prod
    plusSubDmd (Prod Boxity
    b1 [Demand]
    ds1) (Poly Boxity
    b2 Card
    n2)
      | let !d :: Demand
    d = Boxity -> Card -> Demand
    polyFieldDmd Boxity
    b2 Card
    n2
      = Boxity -> [Demand] -> SubDemand
    mkProd (Boxity -> Boxity -> Boxity
    lubBoxity Boxity
    b1 Boxity
    b2) ((Demand -> Demand) -> [Demand] -> [Demand]
    forall a b. (a -> b) -> [a] -> [b]
    strictMap (Demand -> Demand -> Demand
    plusDmd Demand
    d) [Demand]
    ds1)
    plusSubDmd (Prod Boxity
    b1 [Demand]
    ds1) (Prod Boxity
    b2 [Demand]
    ds2)
      | [Demand] -> [Demand] -> Bool
    forall a b. [a] -> [b] -> Bool
    equalLength [Demand]
    ds1 [Demand]
    ds2
      = Boxity -> [Demand] -> SubDemand
    mkProd (Boxity -> Boxity -> Boxity
    lubBoxity Boxity
    b1 Boxity
    b2) ((Demand -> Demand -> Demand) -> [Demand] -> [Demand] -> [Demand]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    strictZipWith Demand -> Demand -> Demand
    plusDmd [Demand]
    ds1 [Demand]
    ds2)
    -- Handle Call
    plusSubDmd (Call Card
    n1 SubDemand
    sd1) (SubDemand -> Maybe (Card, SubDemand)
    viewCall -> Just (Card
    n2, SubDemand
    sd2)) =
      Card -> SubDemand -> SubDemand
    mkCall (Card -> Card -> Card
    plusCard Card
    n1 Card
    n2) (SubDemand -> SubDemand -> SubDemand
    lubSubDmd SubDemand
    sd1 SubDemand
    sd2)
    -- Handle Poly
    plusSubDmd (Poly Boxity
    b1 Card
    n1) (Poly Boxity
    b2 Card
    n2) = Boxity -> Card -> SubDemand
    Poly (Boxity -> Boxity -> Boxity
    lubBoxity Boxity
    b1 Boxity
    b2) (Card -> Card -> Card
    plusCard Card
    n1 Card
    n2)
    -- Other Poly case by commutativity
    plusSubDmd sd1 :: SubDemand
    sd1@Poly{}   SubDemand
    sd2          = SubDemand -> SubDemand -> SubDemand
    plusSubDmd SubDemand
    sd2 SubDemand
    sd1
    -- Otherwise (Call `plus` Prod) return Top
    plusSubDmd SubDemand
    _            SubDemand
    _            = SubDemand
    topSubDmd

    -- | Used to suppress pretty-printing of an uninformative demand
    isTopDmd :: Demand -> Bool
    isTopDmd :: Demand -> Bool
    isTopDmd Demand
    dmd = Demand
    dmd Demand -> Demand -> Bool
    forall a. Eq a => a -> a -> Bool
    == Demand
    topDmd

    isAbsDmd :: Demand -> Bool
    isAbsDmd :: Demand -> Bool
    isAbsDmd (Card
    n :* SubDemand
    _) = Card -> Bool
    isAbs Card
    n

    -- | Contrast with isStrictUsedDmd. See Note [Strict demands]
    isStrictDmd :: Demand -> Bool
    isStrictDmd :: Demand -> Bool
    isStrictDmd (Card
    n :* SubDemand
    _) = Card -> Bool
    isStrict Card
    n

    -- | Not absent and used strictly. See Note [Strict demands]
    isStrUsedDmd :: Demand -> Bool
    isStrUsedDmd :: Demand -> Bool
    isStrUsedDmd (Card
    n :* SubDemand
    _) = Card -> Bool
    isStrict Card
    n Bool -> Bool -> Bool
    && Bool -> Bool
    not (Card -> Bool
    isAbs Card
    n)

    -- | Is the value used at most once?
    isAtMostOnceDmd :: Demand -> Bool
    isAtMostOnceDmd :: Demand -> Bool
    isAtMostOnceDmd (Card
    n :* SubDemand
    _) = Card -> Bool
    isAtMostOnce Card
    n

    -- | We try to avoid tracking weak free variable demands in strictness
    -- signatures for analysis performance reasons.
    -- See Note [Lazy and unleashable free variables] in "GHC.Core.Opt.DmdAnal".
    isWeakDmd :: Demand -> Bool
    isWeakDmd :: Demand -> Bool
    isWeakDmd dmd :: Demand
    dmd@(Card
    n :* SubDemand
    _) = Bool -> Bool
    not (Card -> Bool
    isStrict Card
    n) Bool -> Bool -> Bool
    && Demand -> Bool
    is_plus_idem_dmd Demand
    dmd
      where
        -- @is_plus_idem_* thing@ checks whether @thing `plus` thing = thing@,
        -- e.g. if @thing@ is idempotent wrt. to @plus@.
        -- is_plus_idem_card n = plusCard n n == n
        is_plus_idem_card :: Card -> Bool
    is_plus_idem_card = Card -> Bool
    isCardNonOnce
        -- is_plus_idem_dmd dmd = plusDmd dmd dmd == dmd
        is_plus_idem_dmd :: Demand -> Bool
    is_plus_idem_dmd Demand
    AbsDmd    = Bool
    True
        is_plus_idem_dmd Demand
    BotDmd    = Bool
    True
        is_plus_idem_dmd (Card
    n :* SubDemand
    sd) = Card -> Bool
    is_plus_idem_card Card
    n Bool -> Bool -> Bool
    && SubDemand -> Bool
    is_plus_idem_sub_dmd SubDemand
    sd
        -- is_plus_idem_sub_dmd sd = plusSubDmd sd sd == sd
        is_plus_idem_sub_dmd :: SubDemand -> Bool
    is_plus_idem_sub_dmd (Poly Boxity
    _ Card
    n)  = Bool -> Bool -> Bool
    forall a. HasCallStack => Bool -> a -> a
    assert (Card -> Bool
    isCardNonOnce Card
    n) Bool
    True
        is_plus_idem_sub_dmd (Prod Boxity
    _ [Demand]
    ds) = (Demand -> Bool) -> [Demand] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all Demand -> Bool
    is_plus_idem_dmd [Demand]
    ds
        is_plus_idem_sub_dmd (Call Card
    n SubDemand
    _)  = Card -> Bool
    is_plus_idem_card Card
    n

    evalDmd :: Demand
    evalDmd :: Demand
    evalDmd = Card
    C_1N HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* SubDemand
    topSubDmd

    -- | First argument of 'GHC.Exts.maskAsyncExceptions#': @1C(1,L)@.
    -- Called exactly once.
    strictOnceApply1Dmd :: Demand
    strictOnceApply1Dmd :: Demand
    strictOnceApply1Dmd = Card
    C_11 HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* Card -> SubDemand -> SubDemand
    mkCall Card
    C_11 SubDemand
    topSubDmd

    -- | First argument of 'GHC.Exts.atomically#': @SC(S,L)@.
    -- Called at least once, possibly many times.
    strictManyApply1Dmd :: Demand
    strictManyApply1Dmd :: Demand
    strictManyApply1Dmd = Card
    C_1N HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* Card -> SubDemand -> SubDemand
    mkCall Card
    C_1N SubDemand
    topSubDmd

    -- | First argument of catch#: @MC(1,L)@.
    -- Evaluates its arg lazily, but then applies it exactly once to one argument.
    lazyApply1Dmd :: Demand
    lazyApply1Dmd :: Demand
    lazyApply1Dmd = Card
    C_01 HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* Card -> SubDemand -> SubDemand
    mkCall Card
    C_11 SubDemand
    topSubDmd

    -- | Second argument of catch#: @MC(1,C(1,L))@.
    -- Evaluates its arg lazily, but then applies it exactly once to two arguments.
    lazyApply2Dmd :: Demand
    lazyApply2Dmd :: Demand
    lazyApply2Dmd = Card
    C_01 HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* Card -> SubDemand -> SubDemand
    mkCall Card
    C_11 (Card -> SubDemand -> SubDemand
    mkCall Card
    C_11 SubDemand
    topSubDmd)

    -- | Make a 'Demand' evaluated at-most-once.
    oneifyDmd :: Demand -> Demand
    oneifyDmd :: Demand -> Demand
    oneifyDmd Demand
    AbsDmd    = Demand
    AbsDmd
    oneifyDmd Demand
    BotDmd    = Demand
    BotDmd
    oneifyDmd (Card
    n :* SubDemand
    sd) = Card -> Card
    oneifyCard Card
    n HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* SubDemand
    sd

    -- | Make a 'Demand' evaluated at-least-once (e.g. strict).
    strictifyDmd :: Demand -> Demand
    strictifyDmd :: Demand -> Demand
    strictifyDmd = Demand -> Demand -> Demand
    plusDmd Demand
    seqDmd

    -- | If the argument is a guaranteed-terminating type
    --   (i.e. a non-newtype dictionary) give it strict demand.
    --   This is sound because terminating types can't be bottom:
    --         See GHC.Core Note [NON-BOTTOM-DICTS invariant]
    -- Also split the product type & demand and recur in order to similarly
    -- strictify the argument's contained used non-newtype superclass dictionaries.
    -- We use the demand as our recursive measure to guarantee termination.
    strictifyDictDmd :: Type -> Demand -> Demand
    strictifyDictDmd :: Type -> Demand -> Demand
    strictifyDictDmd Type
    ty (Card
    n :* Prod Boxity
    b [Demand]
    ds)
      | Bool -> Bool
    not (Card -> Bool
    isAbs Card
    n)
      , Just [Type]
    field_tys <- Type -> Maybe [Type]
    as_non_newtype_dict Type
    ty
      = Card
    C_1N HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* Boxity -> [Demand] -> SubDemand
    mkProd Boxity
    b ((Type -> Demand -> Demand) -> [Type] -> [Demand] -> [Demand]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    zipWith Type -> Demand -> Demand
    strictifyDictDmd [Type]
    field_tys [Demand]
    ds)
          -- main idea: ensure it's strict
      where
        -- Return a TyCon and a list of field types if the given
        -- type is a non-newtype dictionary type
        as_non_newtype_dict :: Type -> Maybe [Type]
    as_non_newtype_dict Type
    ty
          | HasDebugCallStack => Type -> Bool
    Type -> Bool
    isTerminatingType Type
    ty
          , Just (TyCon
    _tc, [Type]
    _arg_tys, DataCon
    _data_con, [Scaled Type]
    field_tys) <- Type -> Maybe (TyCon, [Type], DataCon, [Scaled Type])
    splitDataProductType_maybe Type
    ty
          = [Type] -> Maybe [Type]
    forall a. a -> Maybe a
    Just ((Scaled Type -> Type) -> [Scaled Type] -> [Type]
    forall a b. (a -> b) -> [a] -> [b]
    map Scaled Type -> Type
    forall a. Scaled a -> a
    scaledThing [Scaled Type]
    field_tys)
          | Bool
    otherwise
          = Maybe [Type]
    forall a. Maybe a
    Nothing
    strictifyDictDmd Type
    _  Demand
    dmd = Demand
    dmd

    -- | Make a 'Demand' lazy.
    lazifyDmd :: Demand -> Demand
    lazifyDmd :: Demand -> Demand
    lazifyDmd = Card -> Demand -> Demand
    multDmd Card
    C_01

    -- | Wraps the 'SubDemand' with a one-shot call demand: @d@ -> @C(1,d)@.
    mkCalledOnceDmd :: SubDemand -> SubDemand
    mkCalledOnceDmd :: SubDemand -> SubDemand
    mkCalledOnceDmd SubDemand
    sd = Card -> SubDemand -> SubDemand
    mkCall Card
    C_11 SubDemand
    sd

    -- | @mkCalledOnceDmds n d@ returns @C(1,C1...C(1,d))@ where there are @n@ @C1@'s.
    mkCalledOnceDmds :: Arity -> SubDemand -> SubDemand
    mkCalledOnceDmds :: Int -> SubDemand -> SubDemand
    mkCalledOnceDmds Int
    arity SubDemand
    sd = (SubDemand -> SubDemand) -> SubDemand -> [SubDemand]
    forall a. (a -> a) -> a -> [a]
    iterate SubDemand -> SubDemand
    mkCalledOnceDmd SubDemand
    sd [SubDemand] -> Int -> SubDemand
    forall a. HasCallStack => [a] -> Int -> a
    !! Int
    arity

    -- | Peels one call level from the sub-demand, and also returns how many
    -- times we entered the lambda body.
    peelCallDmd :: SubDemand -> (Card, SubDemand)
    peelCallDmd :: SubDemand -> (Card, SubDemand)
    peelCallDmd SubDemand
    sd = SubDemand -> Maybe (Card, SubDemand)
    viewCall SubDemand
    sd Maybe (Card, SubDemand) -> (Card, SubDemand) -> (Card, SubDemand)
    forall a. Maybe a -> a -> a
    `orElse` (Card
    topCard, SubDemand
    topSubDmd)

    -- Peels multiple nestings of 'Call' sub-demands and also returns
    -- whether it was unsaturated in the form of a 'Card'inality, denoting
    -- how many times the lambda body was entered.
    -- See Note [Demands from unsaturated function calls].
    peelManyCalls :: Arity -> SubDemand -> (Card, SubDemand)
    peelManyCalls :: Int -> SubDemand -> (Card, SubDemand)
    peelManyCalls Int
    k SubDemand
    sd = Int -> Card -> SubDemand -> (Card, SubDemand)
    forall {t}.
    (Eq t, Num t) =>
    t -> Card -> SubDemand -> (Card, SubDemand)
    go Int
    k Card
    C_11 SubDemand
    sd
      where
        go :: t -> Card -> SubDemand -> (Card, SubDemand)
    go t
    0 !Card
    n !SubDemand
    sd                        = (Card
    n, SubDemand
    sd)
        go t
    k !Card
    n (SubDemand -> Maybe (Card, SubDemand)
    viewCall -> Just (Card
    m, SubDemand
    sd)) = t -> Card -> SubDemand -> (Card, SubDemand)
    go (t
    kt -> t -> t
    forall a. Num a => a -> a -> a
    -t
    1) (Card
    n Card -> Card -> Card
    `multCard` Card
    m) SubDemand
    sd
        go t
    _ Card
    _  SubDemand
    _                          = (Card
    topCard, SubDemand
    topSubDmd)
    {-# INLINE peelManyCalls #-} -- so that the pair cancels away in a `fst _` context

    -- | Extract the 'SubDemand' of a 'Demand'.
    -- PRECONDITION: The SubDemand must be used in a context where the expression
    -- denoted by the Demand is under evaluation.
    subDemandIfEvaluated :: Demand -> SubDemand
    subDemandIfEvaluated :: Demand -> SubDemand
    subDemandIfEvaluated (Card
    _ :* SubDemand
    sd) = SubDemand
    sd

    -- See Note [Demand on the worker] in GHC.Core.Opt.WorkWrap
    mkWorkerDemand :: Int -> Demand
    mkWorkerDemand :: Int -> Demand
    mkWorkerDemand Int
    n = Card
    C_01 HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* Int -> SubDemand
    forall {t}. (Eq t, Num t) => t -> SubDemand
    go Int
    n
      where go :: t -> SubDemand
    go t
    0 = SubDemand
    topSubDmd
            go t
    n = Card -> SubDemand -> SubDemand
    mkCall Card
    C_01 (SubDemand -> SubDemand) -> SubDemand -> SubDemand
    forall a b. (a -> b) -> a -> b
    $ t -> SubDemand
    go (t
    nt -> t -> t
    forall a. Num a => a -> a -> a
    -t
    1)

    argsOneShots :: DmdSig -> Arity -> [[OneShotInfo]]
    -- ^ See Note [Computing one-shot info]
    argsOneShots :: DmdSig -> Int -> [[OneShotInfo]]
    argsOneShots (DmdSig (DmdType DmdEnv
    _ [Demand]
    arg_ds)) Int
    n_val_args
      | Bool
    unsaturated_call = []
      | Bool
    otherwise = [Demand] -> [[OneShotInfo]]
    go [Demand]
    arg_ds
      where
        unsaturated_call :: Bool
    unsaturated_call = [Demand]
    arg_ds [Demand] -> Int -> Bool
    forall a. [a] -> Int -> Bool
    `lengthExceeds` Int
    n_val_args

        go :: [Demand] -> [[OneShotInfo]]
    go []               = []
        go (Demand
    arg_d : [Demand]
    arg_ds) = Demand -> [OneShotInfo]
    argOneShots Demand
    arg_d [OneShotInfo] -> [[OneShotInfo]] -> [[OneShotInfo]]
    forall {a}. [a] -> [[a]] -> [[a]]
    `cons` [Demand] -> [[OneShotInfo]]
    go [Demand]
    arg_ds

        -- Avoid list tail like [ [], [], [] ]
        cons :: [a] -> [[a]] -> [[a]]
    cons [] [] = []
        cons [a]
    a  [[a]]
    as = [a]
    a[a] -> [[a]] -> [[a]]
    forall a. a -> [a] -> [a]
    :[[a]]
    as

    argOneShots :: Demand          -- ^ depending on saturation
                -> [OneShotInfo]
    -- ^ See Note [Computing one-shot info]
    argOneShots :: Demand -> [OneShotInfo]
    argOneShots Demand
    AbsDmd    = [] -- This defn conflicts with 'saturatedByOneShots',
    argOneShots Demand
    BotDmd    = [] -- according to which we should return
                               -- @repeat OneShotLam@ here...
    argOneShots (Card
    _ :* SubDemand
    sd) = (Card -> OneShotInfo) -> [Card] -> [OneShotInfo]
    forall a b. (a -> b) -> [a] -> [b]
    map Card -> OneShotInfo
    go (SubDemand -> [Card]
    callCards SubDemand
    sd)
      where
        go :: Card -> OneShotInfo
    go Card
    n | Card -> Bool
    isAtMostOnce Card
    n = OneShotInfo
    OneShotLam
             | Bool
    otherwise      = OneShotInfo
    NoOneShotInfo

    -- | See Note [Computing one-shot info]
    callCards :: SubDemand -> [Card]
    callCards :: SubDemand -> [Card]
    callCards (Call Card
    n SubDemand
    sd) = Card
    n Card -> [Card] -> [Card]
    forall a. a -> [a] -> [a]
    : SubDemand -> [Card]
    callCards SubDemand
    sd
    callCards (Poly Boxity
    _ Card
    _n) = [] -- n is never C_01 or C_11 so we may as well stop here
    callCards Prod{}      = []

    -- |
    -- @saturatedByOneShots n C(M,C(M,...)) = True@
    --   <=>
    -- There are at least n nested C(M,..) calls.
    -- See Note [Demand on the worker] in GHC.Core.Opt.WorkWrap
    saturatedByOneShots :: Int -> Demand -> Bool
    saturatedByOneShots :: Int -> Demand -> Bool
    saturatedByOneShots Int
    _ Demand
    AbsDmd    = Bool
    True
    saturatedByOneShots Int
    _ Demand
    BotDmd    = Bool
    True
    saturatedByOneShots Int
    n (Card
    _ :* SubDemand
    sd) = Card -> Bool
    isAtMostOnce (Card -> Bool) -> Card -> Bool
    forall a b. (a -> b) -> a -> b
    $ (Card, SubDemand) -> Card
    forall a b. (a, b) -> a
    fst ((Card, SubDemand) -> Card) -> (Card, SubDemand) -> Card
    forall a b. (a -> b) -> a -> b
    $ Int -> SubDemand -> (Card, SubDemand)
    peelManyCalls Int
    n SubDemand
    sd

    {- Note [Strict demands]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    'isStrUsedDmd' returns true only of demands that are
       both strict
       and  used

    In particular, it is False for <B> (i.e. strict and not used,
    cardinality C_10), which can and does arise in, say (#7319)
       f x = raise# <some exception>
    Then 'x' is not used, so f gets strictness <B> -> .
    Now the w/w generates
       fx = let x <B> = absentError "unused"
            in raise <some exception>
    At this point we really don't want to convert to
       fx = case absentError "unused" of x -> raise <some exception>
    Since the program is going to diverge, this swaps one error for another,
    but it's really a bad idea to *ever* evaluate an absent argument.
    In #7319 we get
       T7319.exe: Oops!  Entered absent arg w_s1Hd{v} [lid] [base:GHC.Base.String{tc 36u}]

    Note [SubDemand denotes at least one evaluation]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider a demand `n :* sd` on a binding `let x = e in <body>`.
    (Similarly, a call sub-demand `Cn(sd)` on a lambda `\_. e`).
    While `n` describes how *often* `x` had been evaluated in <body>,
    the sub-demand `sd` describes how *deep* `e` has been evaluated, under the
    following

      PREMISE: *for all program traces where `x` had been evaluated at all*

    That is, `sd` disregards all program traces where `x` had not been evaluated,
    because it can't describe the depth of an evaluation that never happened.
    NB: The Premise only makes a difference for lower bounds/strictness.
    Upper bounds/usage are unaffected by adding or leaving out evaluations that
    never happen.

    The Premise comes into play when we have lazy Demands. For example, if `x` was
    demanded with `LP(SL,A)`, so perhaps the full expression was
      let x = (e1, e2) in (x `seq` fun y `seq` case x of (a,b) -> a, True)
    then `x` will be evaluated lazily, but in any trace in which `x` is evaluated,
    the pair in its RHS will ultimately be evaluated deeply with sub-demand
    `P(SL,A)`. That means that `e1` is ultimately evaluated strictly, even though
    evaluation of the field does not directly follow the eval of `x` due to the
    intermittent call `fun y`.

    How does the additional strictness help? The long version is the list of
    examples at the end of this Note (as procured in #21081 and #18903).
    The short version is

      * We get to take advantage of call-by-value/let-to-case in more situations,
        as for e1 above. See example "More let-to-case" below.
      * Note [Eta reduction based on evaluation context] applies in more situations.
        See example "More eta reduction" below.
      * We get to unbox more results, see example "More CPR" below.

    It seems like we don't give up anything in return. Indeed that is the case:

      * If we dropped the Premise, then a lazy `n` in `nP(m..)` would always force
        `m` to be lazy, too. That is quite redundant! It seems wasteful not to use
        the lower bound of `m` for something more useful. So indeed we give up on
        nothing in return for some nice wins.
      * Even if `n` is absent (so the Premise does hold for no trace whatsoever),
        it's pretty easy to describe how `e` was evaluated. Answer: 'botSubDmd'.
        We use it when expanding 'Absent' and 'Bottom' demands in 'viewDmdPair' as
        well as when expanding absent 'Poly's to 'Call' sub-demands in 'viewCall'.

    Of course, we now have to maintain the Premise when we unpack and rebuild
    Demands. For strict demands, we know that the Premise indeed always holds for
    any program trace abstracted over, whereas we have to be careful for lazy
    demands.

    In particular, when doing `plusDmd` we have to *lazify* the nested SubDemand
    if the outer cardinality is lazy. E.g.,
      LP(SL) + SP(L) = (L+S)P((M*SL)+L) = SP(L+L) = SP(L)
    Multiplying with `M`/`C_01` is the "lazify" part here and is implemented in
    `lazifyIfStrict`. Example proving that point:
      d2 :: <LP(SL)><SP(A)>
      d2 x y = y `seq` (case x of (a,b) -> a, True)
      -- What is the demand on x in (d2 x x)? NOT SP(SL)!!

    We used to apply the same reasoning to Call SubDemands `Cn(sd)` in `plusSubDmd`,
    but that led to #21717, because different calls return different heap objects.
    See Note [Call SubDemand vs. evaluation Demand].

    There are a couple more examples that improve in T21081.
    Here is a selection of those examples demonstrating the usefulness of The
    Premise:

      * "More let-to-case" (from testcase T21081):
        ```hs
        f :: (Bool, Bool) -> (Bool, Bool)
        f pr = (case pr of (a,b) -> a /= b, True)
        g :: Int -> (Bool, Bool)
        g x = let y = let z = odd x in (z,z) in f y
        ```
        Although `f` is lazy in `pr`, we could case-bind `z` because it is always
        evaluated when `y` is evaluated. So we give `pr` demand `LP(SL,SL)`
        (most likely with better upper bounds/usage) and demand analysis then
        infers a strict demand for `z`.

      * "More eta reduction" (from testcase T21081):
        ```hs
        myfoldl :: (a -> b -> a) -> a -> [b] -> a
        myfoldl f z [] = z
        myfoldl f !z (x:xs) = myfoldl (\a b -> f a b) (f z x) xs
        ```
        Here, we can give `f` a demand of `LC(S,C(1,L))` (instead of the lazier
        `LC(L,C(1,L))`) which says "Whenever `f` is evaluated (lazily), it is also
        called with two arguments".
        And Note [Eta reduction based on evaluation context] means we can rewrite
        `\a b -> f a b` to `f` in the call site of `myfoldl`. Nice!

      * "More CPR" (from testcase T18903):
        ```hs
        h :: Int -> Int
        h m =
          let g :: Int -> (Int,Int)
              g 1 = (m, 0)
              g n = (2 * n, 2 `div` n)
              {-# NOINLINE g #-}
          in case m of
            1 -> 0
            2 -> snd (g m)
            _ -> uncurry (+) (g m)
        ```
        We want to give `g` the demand `MC(1,P(MP(L),1P(L)))`, so we see that in each
        call site of `g`, we are strict in the second component of the returned
        pair. That in turn means that Nested CPR can unbox the result of the
        division even though it might throw.

    Note [Unrealised opportunity in plusDmd]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Recall the lazification of SubDemands happening in `plusDmd` as described in
    Note [SubDemand denotes at least one evaluation].

    We *could* do better when both Demands are lazy already. Example
      (fun 1, fun 2)
    Both args put Demand SC(S,L) on `fun`. The lazy pair arg context lazifies
    this to LC(S,L), and it would be reasonable to report this Demand on `fun` for
    the entire pair expression; after all, `fun` is called whenever it is evaluated.
    But our definition of `plusDmd` will compute
      LC(S,L) + LC(S,L) = (L+L)(M*C(S,L) + M*C(S,L)) = L(C(L,L)) = L
    Which is clearly less precise.
    Doing better here could mean to `lub` when both demands are lazy, e.g.,
      LC(S,L) + LC(S,L) = (L+L)(C(S,L) ⊔ C(S,L)) = L(C(S,L))
    Indeed that's what we did at one point between 9.4 and 9.6 after !7599, but it
    means that we need a function `lubPlusSubDmd` that lubs on lower bounds but
    plus'es upper bounds, implying maintenance challenges and complicated
    explanations.

    Plus, NoFib says that this special case doesn't bring all that much
    (geom. mean +0.0% counted instructions), so we don't bother anymore.

    Note [Call SubDemand vs. evaluation Demand]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Although both evaluation Demands and Call SubDemands carry a (Card,SubDemand)
    pair, their interpretation is quite different. Example:

      f x = fst x * snd x
        -- f :: <SP(1L,1L)>, because 1P(1L,A)+1P(A,1L) = SP(1L,1L)
      g x = fst (x 1) * snd (x 2)
        -- g :: <SC(S,P(ML,ML))>, because 1C(1,P(1L,A))+1C(1,P(A,1L)) = SC(S,P(ML,ML))

    The point about this example is that both demands have P(A,1L)/P(1L,A) as
    sub-expressions, but when these sub-demands occur

      1. under an evaluation demand, we combine with `plusSubDmd`
      2. whereas under a Call sub-demand, we combine with `lubSubDmd`

    And thus (1) yields a stricter demand on the pair components than (2).

    In #21717 we saw that we really need lub in (2), because otherwise we make an
    unsound prediction in `g (\n -> if n == 1 then (1,1) else (bot,2))`; we'd say
    that the `bot` expression is always evaluated, when it clearly is not.
    Operationally, every call to `g` gives back a potentially distinct,
    heap-allocated pair with potentially different contents, and we must `lubSubDmd`
    over all such calls to approximate how any of those pairs might be used.

    That is in stark contrast to f's argument `x`: Operationally, every eval of
    `x` must yield the same pair and `f` evaluates both components of that pair.
    The theorem "every eval of `x` returns the same heap object" is a very strong
    MUST-alias property and we capitalise on that by using `plusSubDmd` in (1).

    And indeed we *must* use `plusSubDmd` in (1) for sound upper bounds in an
    analysis that assumes call-by-need (as opposed to the weaker call-by-name) for
    let bindings. Consider

      h x = fst x * fst x
        -- h :: <SP(SL,A)>

    And the expression `let a=1; p=(a,a)} in h p`. Here, *although* the RHS of `p`
    is only evaluated once under call-by-need, `a` is still evaluated twice.
    If we had used `lubSubDmd`, we'd see SP(1L,A) and the 1L unsoundly says "exactly
    once".

    If the analysis had assumed call-by-name, it would be sound to say "a is used
    once in p": p is used multiple times and hence so would a, as if p was a
    function. So using `plusSubDmd` does not only yield better strictness, it is
    also "holding up the other end of the bargain" of the call-by-need assumption
    for upper bounds.

    (To SG's knowledge, the distinction between call-by-name and call-by-need does
    not matter for strictness analysis/lower bounds, thus it would be sound to use
    `lubSubDmd` all the time there.)

    Note [mkCall and plusSubDmd]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We never rewrite a strict, non-absent Call sub-demand like C(S,S) to a
    polymorphic sub-demand like S, otherwise #21085 strikes. Consider the
    following inequality (would also for M and 1 instead of L and S, but we forbid
    such Polys):

      L+S = S = C(S,S) < C(S,L) = C(L,L)+C(S,S)

    Note that L=C(L,L). If we also had S=C(S,S), we'd be in trouble: Now
    `plusSubDmd` would no longer maintain the equality relation on sub-demands,
    much less monotonicity. Bad!

    Clearly, `n <= Cn(n)` is unproblematic, as is `n >= Cn(n)` for any `n`
    except 1 and S. But `C(S,S) >= S` would mean trouble, because then we'd get
    the problematic `C(S,S) = S`. We have just established that `S < C(S,S)`!
    As such, the rewrite C(S,S) to S is anti-monotone and we forbid it, first
    and foremost in `mkCall` (which is the only place that rewrites Cn(n) to n).

    Crisis and #21085 averted!

    Note [Computing one-shot info]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider a call
        f (\pqr. e1) (\xyz. e2) e3
    where f has usage signature
        <C(M,C(L,C(M,L)))><C(M,L)><L>
    Then argsOneShots returns a [[OneShotInfo]] of
        [[OneShot,NoOneShotInfo,OneShot],  [OneShot]]
    The occurrence analyser propagates this one-shot infor to the
    binders \pqr and \xyz;
    see Note [Sources of one-shot information] in GHC.Core.Opt.OccurAnal.

    Note [Boxity in Poly]
    ~~~~~~~~~~~~~~~~~~~~~
    To support Note [Boxity analysis], it makes sense that 'Prod' carries a
    'Boxity'. But why does 'Poly' have to carry a 'Boxity', too? Shouldn't all
    'Poly's be 'Boxed'? Couldn't we simply use 'Prod Unboxed' when we need to
    express an unboxing demand?

    'botSubDmd' (B) needs to be the bottom of the lattice, so it needs to be an
    Unboxed demand (and deeply, at that). Similarly, 'seqSubDmd' (A) is an Unboxed
    demand. So why not say that Polys with absent cardinalities have Unboxed boxity?
    That doesn't work, because we also need the boxed equivalents. Here's an example
    for A (function 'absent' in T19871):
    ```
    f _ True  = 1
    f a False = a `seq` 2
      -- demand on a: MA, the A is short for `Poly Boxed C_00`

    g a = a `seq` f a True
      -- demand on a: SA, which is `Poly Boxed C_00`

    h True  p       = g p -- SA on p (inherited from g)
    h False p@(x,y) = x+y -- S!P(1!L,1!L) on p
    ```
    If A is treated as Unboxed, we get reboxing in the call site to 'g'.
    So we obviously would need a Boxed variant of A. Rather than introducing a lot
    of special cases, we just carry the Boxity in 'Poly'. Plus, we could most likely
    find examples like the above for any other cardinality.

    Note [Why Boxity in SubDemand and not in Demand?]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In #19871, we started out by storing 'Boxity' in 'SubDemand', in the 'Prod'
    constructor only. But then we found that we weren't able to express the unboxing
    'seqSubDmd', because that one really is a `Poly C_00` sub-demand.
    We then tried to store the Boxity in 'Demand' instead, for these reasons:

      1. The whole boxity-of-seq business comes to a satisfying conclusion
      2. Putting Boxity in the SubDemand is weird to begin with, because it
         describes the box and not its fields, just as the evaluation cardinality
         of a Demand describes how often the box is used. It makes more sense that
         Card and Boxity travel together. Also the alternative would have been to
         store Boxity with Poly, which is even weirder and more redundant.

    But then we regressed in T7837 (grep #19871 for boring specifics), which needed
    to transfer an ambient unboxed *demand* on a dictionary selector to its argument
    dictionary, via a 'Call' sub-demand `C(1,sd)`, as
    Note [Demand transformer for a dictionary selector] explains. Annoyingly,
    the boxity info has to be stored in the *sub-demand* `sd`! There's no demand
    to store the boxity in. So we bit the bullet and now we store Boxity in
    'SubDemand', both in 'Prod' *and* 'Poly'. See also Note [Boxity in Poly].

    Note [Demand transformer for data constructors]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider the expression (x,y) with sub-demand P(SL,A).  What is the demand on
    x,y?  Obviously `x` is used strictly, and `y` not at all. So we want to
    decompose a product demand, and feed its components demands into the
    arguments.  That is the job of dmdTransformDataConSig.  More precisely,

     * it gets the demand on the data constructor itself;
       in the above example that is C(1,C(1,P(SL,A)))
     * it returns the demands on the arguments;
       in the above example that is [SL, A]

    Nasty wrinkle. Consider this code (#22475 has more realistic examples but
    assume this is what the demand analyser sees)

       data T = MkT !Int Bool
       get :: T -> Bool
       get (MkT _ b) = b

       foo = let v::Int = I# 7
                 t::T   = MkT v True
             in get t

    Now `v` is unused by `get`, /but/ we can't give `v` an Absent demand,
    else we'll drop the binding and replace it with an error thunk.
    Then the code generator (more specifically GHC.Stg.InferTags.Rewrite)
    will add an extra eval of MkT's argument to give
       foo = let v::Int = error "absent"
                 t::T   = case v of v' -> MkT v' True
             in get t

    Boo!  Because of this extra eval (added in STG-land), the truth is that `MkT`
    may (or may not) evaluate its arguments (as established in #21497). Hence the
    use of `bump` in dmdTransformDataConSig, which adds in a `C_01` eval. The
    `C_01` says "may or may not evaluate" which is absolutely faithful to what
    InferTags.Rewrite does.

    In particular it is very important /not/ to make that a `C_11` eval,
    see Note [Data-con worker strictness].
    -}

    {- *********************************************************************
    *                                                                      *
                     Divergence: Whether evaluation surely diverges
    *                                                                      *
    ********************************************************************* -}

    -- | 'Divergence' characterises whether something surely diverges.
    -- Models a subset lattice of the following exhaustive set of divergence
    -- results:
    --
    -- [n] nontermination (e.g. loops)
    -- [i] throws imprecise exception
    -- [p] throws precise exception
    -- [c] converges (reduces to WHNF).
    --
    -- The different lattice elements correspond to different subsets, indicated by
    -- juxtaposition of indicators (e.g. __nc__ definitely doesn't throw an
    -- exception, and may or may not reduce to WHNF).
    --
    -- @
    --             Dunno (nipc)
    --                  |
    --            ExnOrDiv (nip)
    --                  |
    --            Diverges (ni)
    -- @
    --
    -- As you can see, we don't distinguish __n__ and __i__.
    -- See Note [Precise exceptions and strictness analysis] for why __p__ is so
    -- special compared to __i__.
    data Divergence
      = Diverges -- ^ Definitely throws an imprecise exception or diverges.
      | ExnOrDiv -- ^ Definitely throws a *precise* exception, an imprecise
                 --   exception or diverges. Never converges, hence 'isDeadEndDiv'!
                 --   See scenario 1 in Note [Precise exceptions and strictness analysis].
      | Dunno    -- ^ Might diverge, throw any kind of exception or converge.
      deriving Divergence -> Divergence -> Bool
    (Divergence -> Divergence -> Bool)
    -> (Divergence -> Divergence -> Bool) -> Eq Divergence
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    $c== :: Divergence -> Divergence -> Bool
    == :: Divergence -> Divergence -> Bool
    $c/= :: Divergence -> Divergence -> Bool
    /= :: Divergence -> Divergence -> Bool
    Eq

    lubDivergence :: Divergence -> Divergence -> Divergence
    lubDivergence :: Divergence -> Divergence -> Divergence
    lubDivergence Divergence
    Diverges Divergence
    div      = Divergence
    div
    lubDivergence Divergence
    div      Divergence
    Diverges = Divergence
    div
    lubDivergence Divergence
    ExnOrDiv Divergence
    ExnOrDiv = Divergence
    ExnOrDiv
    lubDivergence Divergence
    _        Divergence
    _        = Divergence
    Dunno
    -- This needs to commute with defaultFvDmd, i.e.
    -- defaultFvDmd (r1 `lubDivergence` r2) = defaultFvDmd r1 `lubDmd` defaultFvDmd r2
    -- (See Note [Default demand on free variables and arguments] for why)

    -- | See Note [Asymmetry of plusDmdType], which concludes that 'plusDivergence'
    -- needs to be symmetric.
    -- Strictly speaking, we should have @plusDivergence Dunno Diverges = ExnOrDiv@.
    -- But that regresses in too many places (every infinite loop, basically) to be
    -- worth it and is only relevant in higher-order scenarios
    -- (e.g. Divergence of @f (throwIO blah)@).
    -- So 'plusDivergence' currently is 'glbDivergence', really.
    plusDivergence :: Divergence -> Divergence -> Divergence
    plusDivergence :: Divergence -> Divergence -> Divergence
    plusDivergence Divergence
    Dunno    Divergence
    Dunno    = Divergence
    Dunno
    plusDivergence Divergence
    Diverges Divergence
    _        = Divergence
    Diverges
    plusDivergence Divergence
    _        Divergence
    Diverges = Divergence
    Diverges
    plusDivergence Divergence
    _        Divergence
    _        = Divergence
    ExnOrDiv

    -- | In a non-strict scenario, we might not force the Divergence, in which case
    -- we might converge, hence Dunno.
    multDivergence :: Card -> Divergence -> Divergence
    multDivergence :: Card -> Divergence -> Divergence
    multDivergence Card
    n Divergence
    _ | Bool -> Bool
    not (Card -> Bool
    isStrict Card
    n) = Divergence
    Dunno
    multDivergence Card
    _ Divergence
    d                    = Divergence
    d

    topDiv, exnDiv, botDiv :: Divergence
    topDiv :: Divergence
    topDiv = Divergence
    Dunno
    exnDiv :: Divergence
    exnDiv = Divergence
    ExnOrDiv
    botDiv :: Divergence
    botDiv = Divergence
    Diverges

    -- | True if the 'Divergence' indicates that evaluation will not return.
    -- See Note [Dead ends].
    isDeadEndDiv :: Divergence -> Bool
    isDeadEndDiv :: Divergence -> Bool
    isDeadEndDiv Divergence
    Diverges = Bool
    True
    isDeadEndDiv Divergence
    ExnOrDiv = Bool
    True
    isDeadEndDiv Divergence
    Dunno    = Bool
    False

    -- See Notes [Default demand on free variables and arguments]
    -- and Scenario 1 in [Precise exceptions and strictness analysis]
    defaultFvDmd :: Divergence -> Demand
    defaultFvDmd :: Divergence -> Demand
    defaultFvDmd Divergence
    Dunno    = Demand
    absDmd
    defaultFvDmd Divergence
    ExnOrDiv = Demand
    absDmd -- This is the whole point of ExnOrDiv!
    defaultFvDmd Divergence
    Diverges = Demand
    botDmd -- Diverges

    defaultArgDmd :: Divergence -> Demand
    -- TopRes and BotRes are polymorphic, so that
    --      BotRes === (Bot -> BotRes) === ...
    --      TopRes === (Top -> TopRes) === ...
    -- This function makes that concrete
    -- Also see Note [Default demand on free variables and arguments]
    defaultArgDmd :: Divergence -> Demand
    defaultArgDmd Divergence
    Dunno    = Demand
    topDmd
    -- NB: not botDmd! We don't want to mask the precise exception by forcing the
    -- argument. But it is still absent.
    defaultArgDmd Divergence
    ExnOrDiv = Demand
    absDmd
    defaultArgDmd Divergence
    Diverges = Demand
    botDmd

    {- Note [Precise vs imprecise exceptions]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    An exception is considered to be /precise/ when it is thrown by the 'raiseIO#'
    primop. It follows that all other primops (such as 'raise#' or
    division-by-zero) throw /imprecise/ exceptions. Note that the actual type of
    the exception thrown doesn't have any impact!

    GHC undertakes some effort not to apply an optimisation that would mask a
    /precise/ exception with some other source of nontermination, such as genuine
    divergence or an imprecise exception, so that the user can reliably
    intercept the precise exception with a catch handler before and after
    optimisations.

    See also the wiki page on precise exceptions:
    https://gitlab.haskell.org/ghc/ghc/wikis/exceptions/precise-exceptions
    Section 5 of "Tackling the awkward squad" talks about semantic concerns.
    Imprecise exceptions are actually more interesting than precise ones (which are
    fairly standard) from the perspective of semantics. See the paper "A Semantics
    for Imprecise Exceptions" for more details.

    Note [Dead ends]
    ~~~~~~~~~~~~~~~~
    We call an expression that either diverges or throws a precise or imprecise
    exception a "dead end". We used to call such an expression just "bottoming",
    but with the measures we take to preserve precise exception semantics
    (see Note [Precise exceptions and strictness analysis]), that is no longer
    accurate: 'exnDiv' is no longer the bottom of the Divergence lattice.

    Yet externally to demand analysis, we mostly care about being able to drop dead
    code etc., which is all due to the property that such an expression never
    returns, hence we consider throwing a precise exception to be a dead end.
    See also 'isDeadEndDiv'.

    Note [Precise exceptions and strictness analysis]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We have to take care to preserve precise exception semantics in strictness
    analysis (#17676). There are two scenarios that need careful treatment.

    The fixes were discussed at
    https://gitlab.haskell.org/ghc/ghc/wikis/fixing-precise-exceptions

    Recall that raiseIO# raises a *precise* exception, in contrast to raise# which
    raises an *imprecise* exception. See Note [Precise vs imprecise exceptions].

    Scenario 1: Precise exceptions in case alternatives
    ---------------------------------------------------
    Unlike raise# (which returns botDiv), we want raiseIO# to return exnDiv.
    Here's why. Consider this example from #13380 (similarly #17676):
      f x y | x>0       = raiseIO# Exc
            | y>0       = return 1
            | otherwise = return 2
    Is 'f' strict in 'y'? One might be tempted to say yes! But that plays fast and
    loose with the precise exception; after optimisation, (f 42 (error "boom"))
    turns from throwing the precise Exc to throwing the imprecise user error
    "boom". So, the defaultFvDmd of raiseIO# should be lazy (topDmd), which can be
    achieved by giving it divergence exnDiv.
    See Note [Default demand on free variables and arguments].

    Why don't we just give it topDiv instead of introducing exnDiv?
    Because then the simplifier will fail to discard raiseIO#'s continuation in
      case raiseIO# x s of { (# s', r #) -> <BIG> }
    which we'd like to optimise to
      case raiseIO# x s of {}
    Hence we came up with exnDiv. The default FV demand of exnDiv is lazy (and
    its default arg dmd is absent), but otherwise (in terms of 'isDeadEndDiv') it
    behaves exactly as botDiv, so that dead code elimination works as expected.
    This is tracked by T13380b.

    Scenario 2: Precise exceptions in case scrutinees
    -------------------------------------------------
    Consider (more complete examples in #148, #1592, testcase strun003)

      case foo x s of { (# s', r #) -> y }

    Is this strict in 'y'? Often not! If @foo x s@ might throw a precise exception
    (ultimately via raiseIO#), then we must not force 'y', which may fail to
    terminate or throw an imprecise exception, until we have performed @foo x s@.

    So we have to 'deferAfterPreciseException' (which 'lub's with 'exnDmdType' to
    model the exceptional control flow) when @foo x s@ may throw a precise
    exception. Motivated by T13380{d,e,f}.
    See Note [Which scrutinees may throw precise exceptions] in "GHC.Core.Opt.DmdAnal".

    We have to be careful not to discard dead-end Divergence from case
    alternatives, though (#18086):

      m = putStrLn "foo" >> error "bar"

    'm' should still have 'exnDiv', which is why it is not sufficient to lub with
    'nopDmdType' (which has 'topDiv') in 'deferAfterPreciseException'.

    Historical Note: This used to be called the "IO hack". But that term is rather
    a bad fit because
    1. It's easily confused with the "State hack", which also affects IO.
    2. Neither "IO" nor "hack" is a good description of what goes on here, which
       is deferring strictness results after possibly throwing a precise exception.
       The "hack" is probably not having to defer when we can prove that the
       expression may not throw a precise exception (increasing precision of the
       analysis), but that's just a favourable guess.

    Note [Exceptions and strictness]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We used to smart about catching exceptions, but we aren't anymore.
    See #14998 for the way it's resolved at the moment.

    Here's a historic breakdown:

    Apparently, exception handling prim-ops didn't use to have any special
    strictness signatures, thus defaulting to nopSig, which assumes they use their
    arguments lazily. Joachim was the first to realise that we could provide richer
    information. Thus, in 0558911f91c (Dec 13), he added signatures to
    primops.txt.pp indicating that functions like `catch#` and `catchRetry#` call
    their argument, which is useful information for usage analysis. Still with a
    'Lazy' strictness demand (i.e. 'lazyApply1Dmd'), though, and the world was fine.

    In 7c0fff4 (July 15), Simon argued that giving `catch#` et al. a
    'strictApply1Dmd' leads to substantial performance gains. That was at the cost
    of correctness, as #10712 proved. So, back to 'lazyApply1Dmd' in
    28638dfe79e (Dec 15).

    Motivated to reproduce the gains of 7c0fff4 without the breakage of #10712,
    Ben opened #11222. Simon made the demand analyser "understand catch" in
    9915b656 (Jan 16) by adding a new 'catchArgDmd', which basically said to call
    its argument strictly, but also swallow any thrown exceptions in
    'multDivergence'. This was realized by extending the 'Str' constructor of
    'ArgStr' with a 'ExnStr' field, indicating that it catches the exception, and
    adding a 'ThrowsExn' constructor to the 'Divergence' lattice as an element
    between 'Dunno' and 'Diverges'. Then along came #11555 and finally #13330,
    so we had to revert to 'lazyApply1Dmd' again in 701256df88c (Mar 17).

    This left the other variants like 'catchRetry#' having 'catchArgDmd', which is
    where #14998 picked up. Item 1 was concerned with measuring the impact of also
    making `catchRetry#` and `catchSTM#` have 'lazyApply1Dmd'. The result was that
    there was none. We removed the last usages of 'catchArgDmd' in 00b8ecb7
    (Apr 18). There was a lot of dead code resulting from that change, that we
    removed in ef6b283 (Jan 19): We got rid of 'ThrowsExn' and 'ExnStr' again and
    removed any code that was dealing with the peculiarities.

    Where did the speed-ups vanish to? In #14998, item 3 established that
    turning 'catch#' strict in its first argument didn't bring back any of the
    alleged performance benefits. Item 2 of that ticket finally found out that it
    was entirely due to 'catchException's new (since #11555) definition, which
    was simply

        catchException !io handler = catch io handler

    While 'catchException' is arguably the saner semantics for 'catch', it is an
    internal helper function in "GHC.IO". Its use in
    "GHC.IO.Handle.Internals.do_operation" made for the huge allocation differences:
    Remove the bang and you find the regressions we originally wanted to avoid with
    'catchArgDmd'. See also #exceptions_and_strictness# in "GHC.IO".

    So history keeps telling us that the only possibly correct strictness annotation
    for the first argument of 'catch#' is 'lazyApply1Dmd', because 'catch#' really
    is not strict in its argument: Just try this in GHCi

      :set -XScopedTypeVariables
      import Control.Exception
      catch undefined (\(_ :: SomeException) -> putStrLn "you'll see this")

    Any analysis that assumes otherwise will be broken in some way or another
    (beyond `-fno-pedantic-bottoms`).

    But then #13380 and #17676 suggest (in Mar 20) that we need to re-introduce a
    subtly different variant of `ThrowsExn` (which we call `ExnOrDiv` now) that is
    only used by `raiseIO#` in order to preserve precise exceptions by strictness
    analysis, while not impacting the ability to eliminate dead code.
    See Note [Precise exceptions and strictness analysis].

    Note [Default demand on free variables and arguments]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Free variables not mentioned in the environment of a 'DmdType'
    are demanded according to the demand type's Divergence:
      * In a Diverges (botDiv) context, that demand is botDmd
        (strict and absent).
      * In all other contexts, the demand is absDmd (lazy and absent).
    This is recorded in 'defaultFvDmd'.

    Similarly, we can eta-expand demand types to get demands on excess arguments
    not accounted for in the type, by consulting 'defaultArgDmd':
      * In a Diverges (botDiv) context, that demand is again botDmd.
      * In a ExnOrDiv (exnDiv) context, that demand is absDmd: We surely diverge
        before evaluating the excess argument, but don't want to eagerly evaluate
        it (cf. Note [Precise exceptions and strictness analysis]).
      * In a Dunno context (topDiv), the demand is topDmd, because
        it's perfectly possible to enter the additional lambda and evaluate it
        in unforeseen ways (so, not absent).

    Note [Bottom CPR iff Dead-Ending Divergence]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Both CPR analysis and Demand analysis handle recursive functions by doing
    fixed-point iteration. To find the *least* (e.g., most informative) fixed-point,
    iteration starts with the bottom element of the semantic domain. Diverging
    functions generally have the bottom element as their least fixed-point.

    One might think that CPR analysis and Demand analysis then agree in when a
    function gets a bottom denotation. E.g., whenever it has 'botCpr', it should
    also have 'botDiv'. But that is not the case, because strictness analysis has to
    be careful around precise exceptions, see Note [Precise vs imprecise exceptions].

    So Demand analysis gives some diverging functions 'exnDiv' (which is *not* the
    bottom element) when the CPR signature says 'botCpr', and that's OK. Here's an
    example (from #18086) where that is the case:

    ioTest :: IO ()
    ioTest = do
      putStrLn "hi"
      undefined

    However, one can loosely say that we give a function 'botCpr' whenever its
    'Divergence' is 'exnDiv' or 'botDiv', i.e., dead-ending. But that's just
    a consequence of fixed-point iteration, it's not important that they agree.

    ************************************************************************
    *                                                                      *
               Demand environments and types
    *                                                                      *
    ************************************************************************
    -}

    -- Subject to Note [Default demand on free variables and arguments]
    -- | Captures the result of an evaluation of an expression, by
    --
    --   * Listing how the free variables of that expression have been evaluated
    --     ('de_fvs')
    --   * Saying whether or not evaluation would surely diverge ('de_div')
    --
    -- See Note [Demand env Equality].
    data DmdEnv = DE { DmdEnv -> VarEnv Demand
    de_fvs :: !(VarEnv Demand), DmdEnv -> Divergence
    de_div :: !Divergence }

    instance Eq DmdEnv where
      DE VarEnv Demand
    fv1 Divergence
    div1 == :: DmdEnv -> DmdEnv -> Bool
    == DE VarEnv Demand
    fv2 Divergence
    div2
        = Divergence
    div1 Divergence -> Divergence -> Bool
    forall a. Eq a => a -> a -> Bool
    == Divergence
    div2 Bool -> Bool -> Bool
    && Divergence -> VarEnv Demand -> VarEnv Demand
    forall {k} {key :: k}.
    Divergence -> UniqFM key Demand -> UniqFM key Demand
    canonicalise Divergence
    div1 VarEnv Demand
    fv1 VarEnv Demand -> VarEnv Demand -> Bool
    forall a. Eq a => a -> a -> Bool
    == Divergence -> VarEnv Demand -> VarEnv Demand
    forall {k} {key :: k}.
    Divergence -> UniqFM key Demand -> UniqFM key Demand
    canonicalise Divergence
    div2 VarEnv Demand
    fv2
        where
          canonicalise :: Divergence -> UniqFM key Demand -> UniqFM key Demand
    canonicalise Divergence
    div UniqFM key Demand
    fv = (Demand -> Bool) -> UniqFM key Demand -> UniqFM key Demand
    forall {k} elt (key :: k).
    (elt -> Bool) -> UniqFM key elt -> UniqFM key elt
    filterUFM (Demand -> Demand -> Bool
    forall a. Eq a => a -> a -> Bool
    /= Divergence -> Demand
    defaultFvDmd Divergence
    div) UniqFM key Demand
    fv

    mkEmptyDmdEnv :: Divergence -> DmdEnv
    mkEmptyDmdEnv :: Divergence -> DmdEnv
    mkEmptyDmdEnv Divergence
    div = VarEnv Demand -> Divergence -> DmdEnv
    DE VarEnv Demand
    forall a. VarEnv a
    emptyVarEnv Divergence
    div

    -- | Build a potentially terminating 'DmdEnv' from a finite map that says what
    -- has been evaluated so far
    mkTermDmdEnv :: VarEnv Demand -> DmdEnv
    mkTermDmdEnv :: VarEnv Demand -> DmdEnv
    mkTermDmdEnv VarEnv Demand
    fvs = VarEnv Demand -> Divergence -> DmdEnv
    DE VarEnv Demand
    fvs Divergence
    topDiv

    nopDmdEnv :: DmdEnv
    nopDmdEnv :: DmdEnv
    nopDmdEnv = Divergence -> DmdEnv
    mkEmptyDmdEnv Divergence
    topDiv

    botDmdEnv :: DmdEnv
    botDmdEnv :: DmdEnv
    botDmdEnv = Divergence -> DmdEnv
    mkEmptyDmdEnv Divergence
    botDiv

    exnDmdEnv :: DmdEnv
    exnDmdEnv :: DmdEnv
    exnDmdEnv = Divergence -> DmdEnv
    mkEmptyDmdEnv Divergence
    exnDiv

    lubDmdEnv :: DmdEnv -> DmdEnv -> DmdEnv
    lubDmdEnv :: DmdEnv -> DmdEnv -> DmdEnv
    lubDmdEnv (DE VarEnv Demand
    fv1 Divergence
    d1) (DE VarEnv Demand
    fv2 Divergence
    d2) = VarEnv Demand -> Divergence -> DmdEnv
    DE VarEnv Demand
    lub_fv Divergence
    lub_div
      where
        -- See Note [Demand env Equality]
        lub_fv :: VarEnv Demand
    lub_fv  = (Demand -> Demand -> Demand)
    -> VarEnv Demand
    -> Demand
    -> VarEnv Demand
    -> Demand
    -> VarEnv Demand
    forall a.
    (a -> a -> a) -> VarEnv a -> a -> VarEnv a -> a -> VarEnv a
    plusVarEnv_CD Demand -> Demand -> Demand
    lubDmd VarEnv Demand
    fv1 (Divergence -> Demand
    defaultFvDmd Divergence
    d1) VarEnv Demand
    fv2 (Divergence -> Demand
    defaultFvDmd Divergence
    d2)
        lub_div :: Divergence
    lub_div = Divergence -> Divergence -> Divergence
    lubDivergence Divergence
    d1 Divergence
    d2

    addVarDmdEnv :: DmdEnv -> Id -> Demand -> DmdEnv
    addVarDmdEnv :: DmdEnv -> Id -> Demand -> DmdEnv
    addVarDmdEnv env :: DmdEnv
    env@(DE VarEnv Demand
    fvs Divergence
    div) Id
    id Demand
    dmd
      = VarEnv Demand -> Divergence -> DmdEnv
    DE (VarEnv Demand -> Id -> Demand -> VarEnv Demand
    forall a. VarEnv a -> Id -> a -> VarEnv a
    extendVarEnv VarEnv Demand
    fvs Id
    id (Demand
    dmd Demand -> Demand -> Demand
    `plusDmd` DmdEnv -> Id -> Demand
    lookupDmdEnv DmdEnv
    env Id
    id)) Divergence
    div

    plusDmdEnv :: DmdEnv -> DmdEnv -> DmdEnv
    plusDmdEnv :: DmdEnv -> DmdEnv -> DmdEnv
    plusDmdEnv (DE VarEnv Demand
    fv1 Divergence
    d1) (DE VarEnv Demand
    fv2 Divergence
    d2)
      -- In contrast to Note [Asymmetry of plusDmdType], this function is symmetric.
      | VarEnv Demand -> Bool
    forall a. VarEnv a -> Bool
    isEmptyVarEnv VarEnv Demand
    fv2, Divergence -> Demand
    defaultFvDmd Divergence
    d2 Demand -> Demand -> Bool
    forall a. Eq a => a -> a -> Bool
    == Demand
    absDmd
      = VarEnv Demand -> Divergence -> DmdEnv
    DE VarEnv Demand
    fv1 (Divergence
    d1 Divergence -> Divergence -> Divergence
    `plusDivergence` Divergence
    d2) -- a very common case that is much more efficient
      | VarEnv Demand -> Bool
    forall a. VarEnv a -> Bool
    isEmptyVarEnv VarEnv Demand
    fv1, Divergence -> Demand
    defaultFvDmd Divergence
    d1 Demand -> Demand -> Bool
    forall a. Eq a => a -> a -> Bool
    == Demand
    absDmd
      = VarEnv Demand -> Divergence -> DmdEnv
    DE VarEnv Demand
    fv2 (Divergence
    d1 Divergence -> Divergence -> Divergence
    `plusDivergence` Divergence
    d2) -- another very common case that is much more efficient
      | Bool
    otherwise
      = VarEnv Demand -> Divergence -> DmdEnv
    DE ((Demand -> Demand -> Demand)
    -> VarEnv Demand
    -> Demand
    -> VarEnv Demand
    -> Demand
    -> VarEnv Demand
    forall a.
    (a -> a -> a) -> VarEnv a -> a -> VarEnv a -> a -> VarEnv a
    plusVarEnv_CD Demand -> Demand -> Demand
    plusDmd VarEnv Demand
    fv1 (Divergence -> Demand
    defaultFvDmd Divergence
    d1) VarEnv Demand
    fv2 (Divergence -> Demand
    defaultFvDmd Divergence
    d2))
           (Divergence
    d1 Divergence -> Divergence -> Divergence
    `plusDivergence` Divergence
    d2)

    -- | 'DmdEnv' is a monoid via 'plusDmdEnv' and 'nopDmdEnv'; this is its 'msum'
    plusDmdEnvs :: [DmdEnv] -> DmdEnv
    plusDmdEnvs :: [DmdEnv] -> DmdEnv
    plusDmdEnvs []   = DmdEnv
    nopDmdEnv
    plusDmdEnvs [DmdEnv]
    pdas = (DmdEnv -> DmdEnv -> DmdEnv) -> [DmdEnv] -> DmdEnv
    forall a. HasCallStack => (a -> a -> a) -> [a] -> a
    foldl1' DmdEnv -> DmdEnv -> DmdEnv
    plusDmdEnv [DmdEnv]
    pdas

    multDmdEnv :: Card -> DmdEnv -> DmdEnv
    multDmdEnv :: Card -> DmdEnv -> DmdEnv
    multDmdEnv Card
    C_11 DmdEnv
    env          = DmdEnv
    env
    multDmdEnv Card
    C_00 DmdEnv
    _            = DmdEnv
    nopDmdEnv
    multDmdEnv Card
    n    (DE VarEnv Demand
    fvs Divergence
    div) = VarEnv Demand -> Divergence -> DmdEnv
    DE ((Demand -> Demand) -> VarEnv Demand -> VarEnv Demand
    forall a b. (a -> b) -> VarEnv a -> VarEnv b
    mapVarEnv (Card -> Demand -> Demand
    multDmd Card
    n) VarEnv Demand
    fvs) (Card -> Divergence -> Divergence
    multDivergence Card
    n Divergence
    div)

    reuseEnv :: DmdEnv -> DmdEnv
    reuseEnv :: DmdEnv -> DmdEnv
    reuseEnv = Card -> DmdEnv -> DmdEnv
    multDmdEnv Card
    C_1N

    lookupDmdEnv :: DmdEnv -> Id -> Demand
    -- See Note [Default demand on free variables and arguments]
    lookupDmdEnv :: DmdEnv -> Id -> Demand
    lookupDmdEnv (DE VarEnv Demand
    fv Divergence
    div) Id
    id = VarEnv Demand -> Id -> Maybe Demand
    forall a. VarEnv a -> Id -> Maybe a
    lookupVarEnv VarEnv Demand
    fv Id
    id Maybe Demand -> Demand -> Demand
    forall a. Maybe a -> a -> a
    `orElse` Divergence -> Demand
    defaultFvDmd Divergence
    div

    delDmdEnv :: DmdEnv -> Id -> DmdEnv
    delDmdEnv :: DmdEnv -> Id -> DmdEnv
    delDmdEnv (DE VarEnv Demand
    fv Divergence
    div) Id
    id = VarEnv Demand -> Divergence -> DmdEnv
    DE (VarEnv Demand
    fv VarEnv Demand -> Id -> VarEnv Demand
    forall a. VarEnv a -> Id -> VarEnv a
    `delVarEnv` Id
    id) Divergence
    div

    -- | Characterises how an expression
    --
    --    * Evaluates its free variables ('dt_env') including divergence info
    --    * Evaluates its arguments ('dt_args')
    --
    data DmdType
      = DmdType
      { DmdType -> DmdEnv
    dt_env  :: !DmdEnv     -- ^ Demands on free variables.
                               -- See Note [Demand type Divergence]
      , DmdType -> [Demand]
    dt_args :: ![Demand]   -- ^ Demand on arguments
      }

    -- | See Note [Demand env Equality].
    instance Eq DmdType where
      DmdType DmdEnv
    env1 [Demand]
    ds1 == :: DmdType -> DmdType -> Bool
    == DmdType DmdEnv
    env2 [Demand]
    ds2
        = [Demand]
    ds1 [Demand] -> [Demand] -> Bool
    forall a. Eq a => a -> a -> Bool
    == [Demand]
    ds2 -- cheap checks first
          Bool -> Bool -> Bool
    && DmdEnv
    env1 DmdEnv -> DmdEnv -> Bool
    forall a. Eq a => a -> a -> Bool
    == DmdEnv
    env2

    -- | Compute the least upper bound of two 'DmdType's elicited /by the same
    -- incoming demand/!
    lubDmdType :: DmdType -> DmdType -> DmdType
    lubDmdType :: DmdType -> DmdType -> DmdType
    lubDmdType DmdType
    d1 DmdType
    d2 = DmdEnv -> [Demand] -> DmdType
    DmdType DmdEnv
    lub_fv [Demand]
    lub_ds
      where
        n :: Int
    n = Int -> Int -> Int
    forall a. Ord a => a -> a -> a
    max (DmdType -> Int
    dmdTypeDepth DmdType
    d1) (DmdType -> Int
    dmdTypeDepth DmdType
    d2)
        (DmdType DmdEnv
    fv1 [Demand]
    ds1) = Int -> DmdType -> DmdType
    etaExpandDmdType Int
    n DmdType
    d1
        (DmdType DmdEnv
    fv2 [Demand]
    ds2) = Int -> DmdType -> DmdType
    etaExpandDmdType Int
    n DmdType
    d2
        lub_ds :: [Demand]
    lub_ds  = String
    -> (Demand -> Demand -> Demand) -> [Demand] -> [Demand] -> [Demand]
    forall a b c.
    HasDebugCallStack =>
    String -> (a -> b -> c) -> [a] -> [b] -> [c]
    zipWithEqual String
    "lubDmdType" Demand -> Demand -> Demand
    lubDmd [Demand]
    ds1 [Demand]
    ds2
        lub_fv :: DmdEnv
    lub_fv = DmdEnv -> DmdEnv -> DmdEnv
    lubDmdEnv DmdEnv
    fv1 DmdEnv
    fv2

    discardArgDmds :: DmdType -> DmdEnv
    discardArgDmds :: DmdType -> DmdEnv
    discardArgDmds (DmdType DmdEnv
    fv [Demand]
    _) = DmdEnv
    fv

    plusDmdType :: DmdType -> DmdEnv -> DmdType
    plusDmdType :: DmdType -> DmdEnv -> DmdType
    plusDmdType (DmdType DmdEnv
    fv [Demand]
    ds) DmdEnv
    fv'
      -- See Note [Asymmetry of plusDmdType]
      -- 'DmdEnv' forms a (monoidal) action on 'DmdType' via this operation.
      = DmdEnv -> [Demand] -> DmdType
    DmdType (DmdEnv -> DmdEnv -> DmdEnv
    plusDmdEnv DmdEnv
    fv DmdEnv
    fv') [Demand]
    ds

    botDmdType :: DmdType
    botDmdType :: DmdType
    botDmdType = DmdEnv -> [Demand] -> DmdType
    DmdType DmdEnv
    botDmdEnv []

    -- | The demand type of doing nothing (lazy, absent, no Divergence
    -- information). Note that it is ''not'' the top of the lattice (which would be
    -- "may use everything"), so it is (no longer) called topDmdType.
    nopDmdType :: DmdType
    nopDmdType :: DmdType
    nopDmdType = DmdEnv -> [Demand] -> DmdType
    DmdType DmdEnv
    nopDmdEnv []

    -- | The demand type of an unspecified expression that is guaranteed to
    -- throw a (precise or imprecise) exception or diverge.
    exnDmdType :: DmdType
    exnDmdType :: DmdType
    exnDmdType = DmdEnv -> [Demand] -> DmdType
    DmdType DmdEnv
    exnDmdEnv []

    dmdTypeDepth :: DmdType -> Arity
    dmdTypeDepth :: DmdType -> Int
    dmdTypeDepth = [Demand] -> Int
    forall a. [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length ([Demand] -> Int) -> (DmdType -> [Demand]) -> DmdType -> Int
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . DmdType -> [Demand]
    dt_args

    -- | This makes sure we can use the demand type with n arguments after eta
    -- expansion, where n must not be lower than the demand types depth.
    -- It appends the argument list with the correct 'defaultArgDmd'.
    etaExpandDmdType :: Arity -> DmdType -> DmdType
    etaExpandDmdType :: Int -> DmdType -> DmdType
    etaExpandDmdType Int
    n d :: DmdType
    d@DmdType{dt_args :: DmdType -> [Demand]
    dt_args = [Demand]
    ds, dt_env :: DmdType -> DmdEnv
    dt_env = DmdEnv
    env}
      | Int
    n Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    depth = DmdType
    d
      | Int
    n Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    >  Int
    depth = DmdType
    d{dt_args = inc_ds}
      | Bool
    otherwise  = String -> SDoc -> DmdType
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "etaExpandDmdType: arity decrease" (Int -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Int
    n SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ DmdType -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr DmdType
    d)
      where depth :: Int
    depth = [Demand] -> Int
    forall a. [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [Demand]
    ds
            -- Arity increase:
            --  * Demands on FVs are still valid
            --  * Demands on args also valid, plus we can extend with defaultArgDmd
            --    as appropriate for the given Divergence
            --  * Divergence is still valid:
            --    - A dead end after 2 arguments stays a dead end after 3 arguments
            --    - The remaining case is Dunno, which is already topDiv
            inc_ds :: [Demand]
    inc_ds = Int -> [Demand] -> [Demand]
    forall a. Int -> [a] -> [a]
    take Int
    n ([Demand]
    ds [Demand] -> [Demand] -> [Demand]
    forall a. [a] -> [a] -> [a]
    ++ Demand -> [Demand]
    forall a. a -> [a]
    repeat (Divergence -> Demand
    defaultArgDmd (DmdEnv -> Divergence
    de_div DmdEnv
    env)))

    -- | A conservative approximation for a given 'DmdType' in case of an arity
    -- decrease. Currently, it's just nopDmdType.
    decreaseArityDmdType :: DmdType -> DmdType
    decreaseArityDmdType :: DmdType -> DmdType
    decreaseArityDmdType DmdType
    _ = DmdType
    nopDmdType

    splitDmdTy :: DmdType -> (Demand, DmdType)
    -- Split off one function argument
    -- We already have a suitable demand on all
    -- free vars, so no need to add more!
    splitDmdTy :: DmdType -> (Demand, DmdType)
    splitDmdTy ty :: DmdType
    ty@DmdType{dt_args :: DmdType -> [Demand]
    dt_args=Demand
    dmd:[Demand]
    args} = (Demand
    dmd, DmdType
    ty{dt_args=args})
    splitDmdTy ty :: DmdType
    ty@DmdType{dt_env :: DmdType -> DmdEnv
    dt_env=DmdEnv
    env}       = (Divergence -> Demand
    defaultArgDmd (DmdEnv -> Divergence
    de_div DmdEnv
    env), DmdType
    ty)

    multDmdType :: Card -> DmdType -> DmdType
    multDmdType :: Card -> DmdType -> DmdType
    multDmdType Card
    n (DmdType DmdEnv
    fv [Demand]
    args)
      = -- pprTrace "multDmdType" (ppr n $$ ppr fv $$ ppr (multDmdEnv n fv)) $
        DmdEnv -> [Demand] -> DmdType
    DmdType (Card -> DmdEnv -> DmdEnv
    multDmdEnv Card
    n DmdEnv
    fv)
                ((Demand -> Demand) -> [Demand] -> [Demand]
    forall a b. (a -> b) -> [a] -> [b]
    map (Card -> Demand -> Demand
    multDmd Card
    n) [Demand]
    args)

    peelFV :: DmdType -> Var -> (DmdType, Demand)
    peelFV :: DmdType -> Id -> (DmdType, Demand)
    peelFV (DmdType DmdEnv
    fv [Demand]
    ds) Id
    id = -- pprTrace "rfv" (ppr id <+> ppr dmd $$ ppr fv)
                                (DmdEnv -> [Demand] -> DmdType
    DmdType DmdEnv
    fv' [Demand]
    ds, Demand
    dmd)
      where
      -- Force these arguments so that old `Env` is not retained.
      !fv' :: DmdEnv
    fv' = DmdEnv
    fv DmdEnv -> Id -> DmdEnv
    `delDmdEnv` Id
    id
      !dmd :: Demand
    dmd = DmdEnv -> Id -> Demand
    lookupDmdEnv DmdEnv
    fv Id
    id

    addDemand :: Demand -> DmdType -> DmdType
    addDemand :: Demand -> DmdType -> DmdType
    addDemand Demand
    dmd (DmdType DmdEnv
    fv [Demand]
    ds) = DmdEnv -> [Demand] -> DmdType
    DmdType DmdEnv
    fv (Demand
    dmdDemand -> [Demand] -> [Demand]
    forall a. a -> [a] -> [a]
    :[Demand]
    ds)

    findIdDemand :: DmdType -> Var -> Demand
    findIdDemand :: DmdType -> Id -> Demand
    findIdDemand (DmdType DmdEnv
    fv [Demand]
    _) Id
    id = DmdEnv -> Id -> Demand
    lookupDmdEnv DmdEnv
    fv Id
    id

    -- | When e is evaluated after executing an IO action that may throw a precise
    -- exception, we act as if there is an additional control flow path that is
    -- taken if e throws a precise exception. The demand type of this control flow
    -- path
    --   * is lazy and absent ('topDmd') and boxed in all free variables and arguments
    --   * has 'exnDiv' 'Divergence' result
    -- See Note [Precise exceptions and strictness analysis]
    --
    -- So we can simply take a variant of 'nopDmdType', 'exnDmdType'.
    -- Why not 'nopDmdType'? Because then the result of 'e' can never be 'exnDiv'!
    -- That means failure to drop dead-ends, see #18086.
    deferAfterPreciseException :: DmdType -> DmdType
    deferAfterPreciseException :: DmdType -> DmdType
    deferAfterPreciseException = DmdType -> DmdType -> DmdType
    lubDmdType DmdType
    exnDmdType

    {- Note [deferAfterPreciseException]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The big picture is in Note [Precise exceptions and strictness analysis]
    The idea is that we want to treat
       case <I/O operation> of (# s', r #) -> rhs

    as if it was
       case <I/O operation> of
          Just (# s', r #) -> rhs
          Nothing          -> error

    That is, the I/O operation might throw an exception, so that 'rhs' never
    gets reached.  For example, we don't want to be strict in the strict free
    variables of 'rhs'.

    So we have the simple definition
      deferAfterPreciseException = lubDmdType (DmdType emptyDmdEnv [] exnDiv)

    Historically, when we had `lubBoxity = _unboxedWins` (see Note [unboxedWins]),
    we had a more complicated definition for deferAfterPreciseException to make sure
    it preserved boxity in its argument. That was needed for code like
       case <I/O operation> of
          (# s', r) -> f x

    which uses `x` *boxed*. If we `lub`bed it with `(DmdType emptyDmdEnv [] exnDiv)`
    we'd get an *unboxed* demand on `x` (because we let Unboxed win),
    which led to #20746.  Nowadays with `lubBoxity = boxedWins` we don't need
    the complicated definition.

    Note [Demand type Divergence]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In contrast to DmdSigs, DmdTypes are elicited under a specific incoming demand.
    This is described in detail in Note [Understanding DmdType and DmdSig].
    Here, we'll focus on what that means for a DmdType's Divergence in a higher-order
    scenario.

    Consider
      err x y = x `seq` y `seq` error (show x)
    this has a strictness signature of
      <1L><1L>b
    meaning that we don't know what happens when we call err in weaker contexts than
    C(1,C(1,L)), like @err `seq` ()@ (1A) and @err 1 `seq` ()@ (C(S,A)). We
    may not unleash the botDiv, hence assume topDiv. Of course, in
    @err 1 2 `seq` ()@ the incoming demand C(S,C(S,A)) is strong enough and we see
    that the expression diverges.

    Now consider a function
      f g = g 1 2
    with signature <C(1,C(1,L))>, and the expression
      f err `seq` ()
    now f puts a strictness demand of C(1,C(1,L)) onto its argument, which is unleashed
    on err via the App rule. In contrast to weaker head strictness, this demand is
    strong enough to unleash err's signature and hence we see that the whole
    expression diverges!

    Note [Demand env Equality]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    What is the difference between the Demand env {x->A} and {}?
    Answer: There is none! They have the exact same semantics, because any var that
    is not mentioned in 'de_fvs' implicitly has demand 'defaultFvDmd', based on
    the divergence of the demand env 'de_div'.
    Similarly, b{x->B, y->A} is the same as b{y->A}, because the default FV
    demand of BotDiv is B. But neither is equal to b{}, because y has demand B in
    the latter, not A as before.

    The Eq instance of DmdEnv must reflect that, otherwise we can get into monotonicity
    issues during fixed-point iteration ({x->A} /= {} /= {x->A} /= ...).
    It does so by filtering out any default FV demands prior to comparing 'de_fvs'.

    Note that 'lubDmdEnv' maintains this kind of equality by using 'plusVarEnv_CD',
    involving 'defaultFvDmd' for any entries present in one 'de_fvs' but not the
    other.

    Note [Asymmetry of plusDmdType]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    'plus' for DmdTypes is *asymmetrical*, because there can only one
    be one type contributing argument demands!  For example, given (e1 e2), we get
    a DmdType dt1 for e1, use its arg demand to analyse e2 giving dt2, and then do
    (dt1 `plusType` dt2). Similarly with
      case e of { p -> rhs }
    we get dt_scrut from the scrutinee and dt_rhs from the RHS, and then
    compute (dt_rhs `plusType` dt_scrut).

    We
     1. combine the information on the free variables,
     2. take the demand on arguments from the first argument
     3. combine the termination results, as in plusDivergence.

    Since we don't use argument demands of the second argument anyway, 'plus's
    second argument is just a 'PlusDmdType'.

    But note that the argument demand types are not guaranteed to be observed in
    left to right order. For example, analysis of a case expression will pass the
    demand type for the alts as the left argument and the type for the scrutinee as
    the right argument. Also, it is not at all clear if there is such an order;
    consider the LetUp case, where the RHS might be forced at any point while
    evaluating the let body.
    Therefore, it is crucial that 'plusDivergence' is symmetric!

    Note [Demands from unsaturated function calls]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider a demand transformer d1 -> d2 -> r for f.
    If a sufficiently detailed demand is fed into this transformer,
    e.g <C(1,C(1,L))> arising from "f x1 x2" in a strict, use-once context,
    then d1 and d2 is precisely the demand unleashed onto x1 and x2 (similar for
    the free variable environment) and furthermore the result information r is the
    one we want to use.

    An anonymous lambda is also an unsaturated function all (needs one argument,
    none given), so this applies to that case as well.

    But the demand fed into f might be less than C(1,C(1,L)). Then we have to
    'multDmdType' the announced demand type. Examples:
     * Not strict enough, e.g. C(1,C(1,L)):
       - We have to multiply all argument and free variable demands with C_01,
         zapping strictness.
       - We have to multiply divergence with C_01. If r says that f Diverges for sure,
         then this holds when the demand guarantees that two arguments are going to
         be passed. If the demand is lower, we may just as well converge.
         If we were tracking definite convergence, than that would still hold under
         a weaker demand than expected by the demand transformer.
     * Used more than once, e.g. C(S,C(1,L)):
       - Multiply with C_1N. Even if f puts a used-once demand on any of its argument
         or free variables, if we call f multiple times, we may evaluate this
         argument or free variable multiple times.

    In dmdTransformSig, we call peelManyCalls to find out the 'Card'inality with
    which we have to multiply and then call multDmdType with that.

    Similarly, dmdTransformDictSelSig and dmdAnal, when analyzing a Lambda, use
    peelCallDmd, which peels only one level, but also returns the demand put on the
    body of the function.
    -}

    {-
    ************************************************************************
    *                                                                      *
                         Demand signatures
    *                                                                      *
    ************************************************************************

    In a let-bound Id we record its demand signature.
    In principle, this demand signature is a demand transformer, mapping
    a demand on the Id into a DmdType, which gives
            a) the free vars of the Id's value
            b) the Id's arguments
            c) an indication of the result of applying
               the Id to its arguments

    However, in fact we store in the Id an extremely emasculated demand
    transformer, namely

                    a single DmdType
    (Nevertheless we dignify DmdSig as a distinct type.)

    This DmdType gives the demands unleashed by the Id when it is applied
    to as many arguments as are given in by the arg demands in the DmdType.
    Also see Note [Demand type Divergence] for the meaning of a Divergence in a
    strictness signature.

    If an Id is applied to less arguments than its arity, it means that
    the demand on the function at a call site is weaker than the vanilla
    call demand, used for signature inference. Therefore we place a top
    demand on all arguments. Otherwise, the demand is specified by Id's
    signature.

    For example, the demand transformer described by the demand signature
            DmdSig (DmdType {x -> <1L>} <A><1P(L,L)>)
    says that when the function is applied to two arguments, it
    unleashes demand 1L on the free var x, A on the first arg,
    and 1P(L,L) on the second.

    If this same function is applied to one arg, all we can say is that it
    uses x with 1L, and its arg with demand 1P(L,L).

    Note [Understanding DmdType and DmdSig]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Demand types are sound approximations of an expression's semantics relative to
    the incoming demand we put the expression under. Consider the following
    expression:

        \x y -> x `seq` (y, 2*x)

    Here is a table with demand types resulting from different incoming demands we
    put that expression under. Note the monotonicity; a stronger incoming demand
    yields a more precise demand type:

        incoming demand   |  demand type
        --------------------------------
        1A                  |  <L><L>{}
        C(1,C(1,L))           |  <1P(L)><L>{}
        C(1,C(1,1P(1P(L),A))) |  <1P(A)><A>{}

    Note that in the first example, the depth of the demand type was *higher* than
    the arity of the incoming call demand due to the anonymous lambda.
    The converse is also possible and happens when we unleash demand signatures.
    In @f x y@, the incoming call demand on f has arity 2. But if all we have is a
    demand signature with depth 1 for @f@ (which we can safely unleash, see below),
    the demand type of @f@ under a call demand of arity 2 has a *lower* depth of 1.

    So: Demand types are elicited by putting an expression under an incoming (call)
    demand, the arity of which can be lower or higher than the depth of the
    resulting demand type.
    In contrast, a demand signature summarises a function's semantics *without*
    immediately specifying the incoming demand it was produced under. Despite StrSig
    being a newtype wrapper around DmdType, it actually encodes two things:

      * The threshold (i.e., minimum arity) to unleash the signature
      * A demand type that is sound to unleash when the minimum arity requirement is
        met.

    Here comes the subtle part: The threshold is encoded in the wrapped demand
    type's depth! So in mkDmdSigForArity we make sure to trim the list of
    argument demands to the given threshold arity. Call sites will make sure that
    this corresponds to the arity of the call demand that elicited the wrapped
    demand type. See also Note [What are demand signatures?].
    -}

    -- | The depth of the wrapped 'DmdType' encodes the arity at which it is safe
    -- to unleash. Better construct this through 'mkDmdSigForArity'.
    -- See Note [Understanding DmdType and DmdSig]
    newtype DmdSig
      = DmdSig DmdType
      deriving DmdSig -> DmdSig -> Bool
    (DmdSig -> DmdSig -> Bool)
    -> (DmdSig -> DmdSig -> Bool) -> Eq DmdSig
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    $c== :: DmdSig -> DmdSig -> Bool
    == :: DmdSig -> DmdSig -> Bool
    $c/= :: DmdSig -> DmdSig -> Bool
    /= :: DmdSig -> DmdSig -> Bool
    Eq

    -- | Turns a 'DmdType' computed for the particular 'Arity' into a 'DmdSig'
    -- unleashable at that arity. See Note [Understanding DmdType and DmdSig].
    mkDmdSigForArity :: Arity -> DmdType -> DmdSig
    mkDmdSigForArity :: Int -> DmdType -> DmdSig
    mkDmdSigForArity Int
    arity dmd_ty :: DmdType
    dmd_ty@(DmdType DmdEnv
    fvs [Demand]
    args)
      | Int
    arity Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < DmdType -> Int
    dmdTypeDepth DmdType
    dmd_ty = DmdType -> DmdSig
    DmdSig (DmdType -> DmdSig) -> DmdType -> DmdSig
    forall a b. (a -> b) -> a -> b
    $ DmdEnv -> [Demand] -> DmdType
    DmdType DmdEnv
    fvs (Int -> [Demand] -> [Demand]
    forall a. Int -> [a] -> [a]
    take Int
    arity [Demand]
    args)
      | Bool
    otherwise                   = DmdType -> DmdSig
    DmdSig (Int -> DmdType -> DmdType
    etaExpandDmdType Int
    arity DmdType
    dmd_ty)

    mkClosedDmdSig :: [Demand] -> Divergence -> DmdSig
    mkClosedDmdSig :: [Demand] -> Divergence -> DmdSig
    mkClosedDmdSig [Demand]
    ds Divergence
    div = Int -> DmdType -> DmdSig
    mkDmdSigForArity ([Demand] -> Int
    forall a. [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [Demand]
    ds) (DmdEnv -> [Demand] -> DmdType
    DmdType (Divergence -> DmdEnv
    mkEmptyDmdEnv Divergence
    div) [Demand]
    ds)

    mkVanillaDmdSig :: Arity -> Divergence -> DmdSig
    mkVanillaDmdSig :: Int -> Divergence -> DmdSig
    mkVanillaDmdSig Int
    ar Divergence
    div = [Demand] -> Divergence -> DmdSig
    mkClosedDmdSig (Int -> Demand -> [Demand]
    forall a. Int -> a -> [a]
    replicate Int
    ar Demand
    topDmd) Divergence
    div

    splitDmdSig :: DmdSig -> ([Demand], Divergence)
    splitDmdSig :: DmdSig -> ([Demand], Divergence)
    splitDmdSig (DmdSig (DmdType DmdEnv
    env [Demand]
    dmds)) = ([Demand]
    dmds, DmdEnv -> Divergence
    de_div DmdEnv
    env)

    dmdSigDmdEnv :: DmdSig -> DmdEnv
    dmdSigDmdEnv :: DmdSig -> DmdEnv
    dmdSigDmdEnv (DmdSig (DmdType DmdEnv
    env [Demand]
    _)) = DmdEnv
    env

    hasDemandEnvSig :: DmdSig -> Bool
    hasDemandEnvSig :: DmdSig -> Bool
    hasDemandEnvSig = Bool -> Bool
    not (Bool -> Bool) -> (DmdSig -> Bool) -> DmdSig -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . VarEnv Demand -> Bool
    forall a. VarEnv a -> Bool
    isEmptyVarEnv (VarEnv Demand -> Bool)
    -> (DmdSig -> VarEnv Demand) -> DmdSig -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . DmdEnv -> VarEnv Demand
    de_fvs (DmdEnv -> VarEnv Demand)
    -> (DmdSig -> DmdEnv) -> DmdSig -> VarEnv Demand
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . DmdSig -> DmdEnv
    dmdSigDmdEnv

    botSig :: DmdSig
    botSig :: DmdSig
    botSig = DmdType -> DmdSig
    DmdSig DmdType
    botDmdType

    nopSig :: DmdSig
    nopSig :: DmdSig
    nopSig = DmdType -> DmdSig
    DmdSig DmdType
    nopDmdType

    isNopSig :: DmdSig -> Bool
    isNopSig :: DmdSig -> Bool
    isNopSig (DmdSig DmdType
    ty) = DmdType
    ty DmdType -> DmdType -> Bool
    forall a. Eq a => a -> a -> Bool
    == DmdType
    nopDmdType

    -- | True if the signature diverges or throws an exception in a saturated call.
    -- See Note [Dead ends].
    isDeadEndSig :: DmdSig -> Bool
    isDeadEndSig :: DmdSig -> Bool
    isDeadEndSig (DmdSig (DmdType DmdEnv
    env [Demand]
    _)) = Divergence -> Bool
    isDeadEndDiv (DmdEnv -> Divergence
    de_div DmdEnv
    env)

    -- | True if the signature diverges or throws an imprecise exception in a saturated call.
    -- NB: In constrast to 'isDeadEndSig' this returns False for 'exnDiv'.
    -- See Note [Dead ends]
    -- and Note [Precise vs imprecise exceptions].
    isBottomingSig :: DmdSig -> Bool
    isBottomingSig :: DmdSig -> Bool
    isBottomingSig (DmdSig (DmdType DmdEnv
    env [Demand]
    _)) = DmdEnv -> Divergence
    de_div DmdEnv
    env Divergence -> Divergence -> Bool
    forall a. Eq a => a -> a -> Bool
    == Divergence
    botDiv

    -- | True when the signature indicates all arguments are boxed
    onlyBoxedArguments :: DmdSig -> Bool
    onlyBoxedArguments :: DmdSig -> Bool
    onlyBoxedArguments (DmdSig (DmdType DmdEnv
    _ [Demand]
    dmds)) = (Demand -> Bool) -> [Demand] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all Demand -> Bool
    demandIsBoxed [Demand]
    dmds
     where
       demandIsBoxed :: Demand -> Bool
    demandIsBoxed Demand
    BotDmd    = Bool
    True
       demandIsBoxed Demand
    AbsDmd    = Bool
    True
       demandIsBoxed (Card
    _ :* SubDemand
    sd) = SubDemand -> Bool
    subDemandIsboxed SubDemand
    sd

       subDemandIsboxed :: SubDemand -> Bool
    subDemandIsboxed (Poly Boxity
    Unboxed Card
    _) = Bool
    False
       subDemandIsboxed (Poly Boxity
    _ Card
    _)       = Bool
    True
       subDemandIsboxed (Call Card
    _ SubDemand
    sd)      = SubDemand -> Bool
    subDemandIsboxed SubDemand
    sd
       subDemandIsboxed (Prod Boxity
    Unboxed [Demand]
    _) = Bool
    False
       subDemandIsboxed (Prod Boxity
    _ [Demand]
    ds)      = (Demand -> Bool) -> [Demand] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all Demand -> Bool
    demandIsBoxed [Demand]
    ds

    -- | Returns true if an application to n value args would diverge or throw an
    -- exception.
    --
    -- If a function having 'botDiv' is applied to a less number of arguments than
    -- its syntactic arity, we cannot say for sure that it is going to diverge.
    -- Hence this function conservatively returns False in that case.
    -- See Note [Dead ends].
    isDeadEndAppSig :: DmdSig -> Int -> Bool
    isDeadEndAppSig :: DmdSig -> Int -> Bool
    isDeadEndAppSig (DmdSig (DmdType DmdEnv
    env [Demand]
    ds)) Int
    n
      = Divergence -> Bool
    isDeadEndDiv (DmdEnv -> Divergence
    de_div DmdEnv
    env) Bool -> Bool -> Bool
    && Bool -> Bool
    not ([Demand] -> Int -> Bool
    forall a. [a] -> Int -> Bool
    lengthExceeds [Demand]
    ds Int
    n)

    trimBoxityDmdEnv :: DmdEnv -> DmdEnv
    trimBoxityDmdEnv :: DmdEnv -> DmdEnv
    trimBoxityDmdEnv (DE VarEnv Demand
    fvs Divergence
    div) = VarEnv Demand -> Divergence -> DmdEnv
    DE ((Demand -> Demand) -> VarEnv Demand -> VarEnv Demand
    forall a b. (a -> b) -> VarEnv a -> VarEnv b
    mapVarEnv Demand -> Demand
    trimBoxity VarEnv Demand
    fvs) Divergence
    div

    trimBoxityDmdType :: DmdType -> DmdType
    trimBoxityDmdType :: DmdType -> DmdType
    trimBoxityDmdType (DmdType DmdEnv
    env [Demand]
    ds) =
      DmdEnv -> [Demand] -> DmdType
    DmdType (DmdEnv -> DmdEnv
    trimBoxityDmdEnv DmdEnv
    env) ((Demand -> Demand) -> [Demand] -> [Demand]
    forall a b. (a -> b) -> [a] -> [b]
    map Demand -> Demand
    trimBoxity [Demand]
    ds)

    trimBoxityDmdSig :: DmdSig -> DmdSig
    trimBoxityDmdSig :: DmdSig -> DmdSig
    trimBoxityDmdSig = (DmdType -> DmdType) -> DmdSig -> DmdSig
    forall a b. Coercible a b => a -> b
    coerce DmdType -> DmdType
    trimBoxityDmdType

    -- | Transfers the boxity of the left arg to the demand structure of the right
    -- arg. This only makes sense if applied to new and old demands of the same
    -- value.
    transferBoxity :: Demand -> Demand -> Demand
    transferBoxity :: Demand -> Demand -> Demand
    transferBoxity Demand
    from Demand
    to = Demand -> Demand -> Demand
    go_dmd Demand
    from Demand
    to
      where
        go_dmd :: Demand -> Demand -> Demand
    go_dmd (Card
    from_n :* SubDemand
    from_sd) to_dmd :: Demand
    to_dmd@(Card
    to_n :* SubDemand
    to_sd)
          | Card -> Bool
    isAbs Card
    from_n Bool -> Bool -> Bool
    || Card -> Bool
    isAbs Card
    to_n = Demand
    to_dmd
          | Bool
    otherwise = case (SubDemand
    from_sd, SubDemand
    to_sd) of
              (Poly Boxity
    from_b Card
    _, Poly Boxity
    _ Card
    to_c) ->
                Card
    to_n HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* Boxity -> Card -> SubDemand
    Poly Boxity
    from_b Card
    to_c
              (SubDemand
    _, Prod Boxity
    _ [Demand]
    to_ds)
                | Just (Boxity
    from_b, [Demand]
    from_ds) <- Int -> SubDemand -> Maybe (Boxity, [Demand])
    viewProd ([Demand] -> Int
    forall a. [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [Demand]
    to_ds) SubDemand
    from_sd
                -> Card
    to_n HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* Boxity -> [Demand] -> SubDemand
    mkProd Boxity
    from_b ((Demand -> Demand -> Demand) -> [Demand] -> [Demand] -> [Demand]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    strictZipWith Demand -> Demand -> Demand
    go_dmd [Demand]
    from_ds [Demand]
    to_ds)
              (Prod Boxity
    from_b [Demand]
    from_ds, SubDemand
    _)
                | Just (Boxity
    _, [Demand]
    to_ds) <- Int -> SubDemand -> Maybe (Boxity, [Demand])
    viewProd ([Demand] -> Int
    forall a. [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [Demand]
    from_ds) SubDemand
    to_sd
                -> Card
    to_n HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* Boxity -> [Demand] -> SubDemand
    mkProd Boxity
    from_b ((Demand -> Demand -> Demand) -> [Demand] -> [Demand] -> [Demand]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    strictZipWith Demand -> Demand -> Demand
    go_dmd [Demand]
    from_ds [Demand]
    to_ds)
              (SubDemand, SubDemand)
    _ -> Demand -> Demand
    trimBoxity Demand
    to_dmd

    transferArgBoxityDmdType :: DmdType -> DmdType -> DmdType
    transferArgBoxityDmdType :: DmdType -> DmdType -> DmdType
    transferArgBoxityDmdType _from :: DmdType
    _from@(DmdType DmdEnv
    _ [Demand]
    from_ds) to :: DmdType
    to@(DmdType DmdEnv
    to_env [Demand]
    to_ds)
      | [Demand] -> [Demand] -> Bool
    forall a b. [a] -> [b] -> Bool
    equalLength [Demand]
    from_ds [Demand]
    to_ds
      = -- pprTraceWith "transfer" (\r -> ppr _from $$ ppr to $$ ppr r) $
        DmdEnv -> [Demand] -> DmdType
    DmdType DmdEnv
    to_env -- Only arg boxity! See Note [Don't change boxity without worker/wrapper]
                ((Demand -> Demand -> Demand) -> [Demand] -> [Demand] -> [Demand]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    zipWith Demand -> Demand -> Demand
    transferBoxity [Demand]
    from_ds [Demand]
    to_ds)
      | Bool
    otherwise
      = DmdType -> DmdType
    trimBoxityDmdType DmdType
    to

    transferArgBoxityDmdSig :: DmdSig -> DmdSig -> DmdSig
    transferArgBoxityDmdSig :: DmdSig -> DmdSig -> DmdSig
    transferArgBoxityDmdSig = (DmdType -> DmdType -> DmdType) -> DmdSig -> DmdSig -> DmdSig
    forall a b. Coercible a b => a -> b
    coerce DmdType -> DmdType -> DmdType
    transferArgBoxityDmdType

    prependArgsDmdSig :: Int -> DmdSig -> DmdSig
    -- ^ Add extra ('topDmd') arguments to a strictness signature.
    -- In contrast to 'etaConvertDmdSig', this /prepends/ additional argument
    -- demands. This is used by FloatOut.
    prependArgsDmdSig :: Int -> DmdSig -> DmdSig
    prependArgsDmdSig Int
    new_args sig :: DmdSig
    sig@(DmdSig dmd_ty :: DmdType
    dmd_ty@(DmdType DmdEnv
    env [Demand]
    dmds))
      | Int
    new_args Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    0        = DmdSig
    sig
      | DmdType
    dmd_ty DmdType -> DmdType -> Bool
    forall a. Eq a => a -> a -> Bool
    == DmdType
    nopDmdType = DmdSig
    sig
      | Bool
    otherwise            = DmdType -> DmdSig
    DmdSig (DmdEnv -> [Demand] -> DmdType
    DmdType DmdEnv
    env [Demand]
    dmds')
      where
        dmds' :: [Demand]
    dmds' = Bool -> SDoc -> [Demand] -> [Demand]
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (Int
    new_args Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    > Int
    0) (Int -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Int
    new_args) ([Demand] -> [Demand]) -> [Demand] -> [Demand]
    forall a b. (a -> b) -> a -> b
    $
                Int -> Demand -> [Demand]
    forall a. Int -> a -> [a]
    replicate Int
    new_args Demand
    topDmd [Demand] -> [Demand] -> [Demand]
    forall a. [a] -> [a] -> [a]
    ++ [Demand]
    dmds

    etaConvertDmdSig :: Arity -> DmdSig -> DmdSig
    -- ^ We are expanding (\x y. e) to (\x y z. e z) or reducing from the latter to
    -- the former (when the Simplifier identifies a new join points, for example).
    -- In contrast to 'prependArgsDmdSig', this /appends/ extra arg demands if
    -- necessary.
    -- This works by looking at the 'DmdType' (which was produced under a call
    -- demand for the old arity) and trying to transfer as many facts as we can to
    -- the call demand of new arity.
    -- An arity increase (resulting in a stronger incoming demand) can retain much
    -- of the info, while an arity decrease (a weakening of the incoming demand)
    -- must fall back to a conservative default.
    etaConvertDmdSig :: Int -> DmdSig -> DmdSig
    etaConvertDmdSig Int
    arity (DmdSig DmdType
    dmd_ty)
      | Int
    arity Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < DmdType -> Int
    dmdTypeDepth DmdType
    dmd_ty = DmdType -> DmdSig
    DmdSig (DmdType -> DmdSig) -> DmdType -> DmdSig
    forall a b. (a -> b) -> a -> b
    $ DmdType -> DmdType
    decreaseArityDmdType DmdType
    dmd_ty
      | Bool
    otherwise                   = DmdType -> DmdSig
    DmdSig (DmdType -> DmdSig) -> DmdType -> DmdSig
    forall a b. (a -> b) -> a -> b
    $ Int -> DmdType -> DmdType
    etaExpandDmdType Int
    arity DmdType
    dmd_ty

    {-
    ************************************************************************
    *                                                                      *
                         Demand transformers
    *                                                                      *
    ************************************************************************
    -}

    -- | A /demand transformer/ is a monotone function from an incoming evaluation
    -- context ('SubDemand') to a 'DmdType', describing how the denoted thing
    -- (i.e. expression, function) uses its arguments and free variables, and
    -- whether it diverges.
    --
    -- See Note [Understanding DmdType and DmdSig]
    -- and Note [What are demand signatures?].
    type DmdTransformer = SubDemand -> DmdType

    -- | Extrapolate a demand signature ('DmdSig') into a 'DmdTransformer'.
    --
    -- Given a function's 'DmdSig' and a 'SubDemand' for the evaluation context,
    -- return how the function evaluates its free variables and arguments.
    dmdTransformSig :: DmdSig -> DmdTransformer
    dmdTransformSig :: DmdSig -> DmdTransformer
    dmdTransformSig (DmdSig dmd_ty :: DmdType
    dmd_ty@(DmdType DmdEnv
    _ [Demand]
    arg_ds)) SubDemand
    sd
      = Card -> DmdType -> DmdType
    multDmdType ((Card, SubDemand) -> Card
    forall a b. (a, b) -> a
    fst ((Card, SubDemand) -> Card) -> (Card, SubDemand) -> Card
    forall a b. (a -> b) -> a -> b
    $ Int -> SubDemand -> (Card, SubDemand)
    peelManyCalls ([Demand] -> Int
    forall a. [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [Demand]
    arg_ds) SubDemand
    sd) DmdType
    dmd_ty
        -- see Note [Demands from unsaturated function calls]
        -- and Note [What are demand signatures?]

    -- | A special 'DmdTransformer' for data constructors that feeds product
    -- demands into the constructor arguments.
    dmdTransformDataConSig :: [StrictnessMark] -> DmdTransformer
    -- See Note [Demand transformer for data constructors]
    dmdTransformDataConSig :: [StrictnessMark] -> DmdTransformer
    dmdTransformDataConSig [StrictnessMark]
    str_marks SubDemand
    sd = case Int -> SubDemand -> Maybe (Boxity, [Demand])
    viewProd Int
    arity SubDemand
    body_sd of
      Just (Boxity
    _, [Demand]
    dmds) -> Card -> [Demand] -> DmdType
    mk_body_ty Card
    n [Demand]
    dmds
      Maybe (Boxity, [Demand])
    Nothing        -> DmdType
    nopDmdType
      where
        arity :: Int
    arity = [StrictnessMark] -> Int
    forall a. [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [StrictnessMark]
    str_marks
        (Card
    n, SubDemand
    body_sd) = Int -> SubDemand -> (Card, SubDemand)
    peelManyCalls Int
    arity SubDemand
    sd
        mk_body_ty :: Card -> [Demand] -> DmdType
    mk_body_ty Card
    n [Demand]
    dmds = DmdEnv -> [Demand] -> DmdType
    DmdType DmdEnv
    nopDmdEnv ((StrictnessMark -> Demand -> Demand)
    -> [StrictnessMark] -> [Demand] -> [Demand]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    zipWith (Card -> StrictnessMark -> Demand -> Demand
    bump Card
    n) [StrictnessMark]
    str_marks [Demand]
    dmds)
        bump :: Card -> StrictnessMark -> Demand -> Demand
    bump Card
    n StrictnessMark
    str Demand
    dmd | StrictnessMark -> Bool
    isMarkedStrict StrictnessMark
    str = Card -> Demand -> Demand
    multDmd Card
    n (Demand -> Demand -> Demand
    plusDmd Demand
    str_field_dmd Demand
    dmd)
                       | Bool
    otherwise          = Card -> Demand -> Demand
    multDmd Card
    n Demand
    dmd
        str_field_dmd :: Demand
    str_field_dmd = Card
    C_01 HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* SubDemand
    seqSubDmd -- Why not C_11? See Note [Data-con worker strictness]

    -- | A special 'DmdTransformer' for dictionary selectors that feeds the demand
    -- on the result into the indicated dictionary component (if saturated).
    -- See Note [Demand transformer for a dictionary selector].
    dmdTransformDictSelSig :: DmdSig -> DmdTransformer
    -- NB: This currently doesn't handle newtype dictionaries.
    -- It should simply apply call_sd directly to the dictionary, I suppose.
    dmdTransformDictSelSig :: DmdSig -> DmdTransformer
    dmdTransformDictSelSig (DmdSig (DmdType DmdEnv
    _ [Card
    _ :* SubDemand
    prod])) SubDemand
    call_sd
       | (Card
    n, SubDemand
    sd') <- SubDemand -> (Card, SubDemand)
    peelCallDmd SubDemand
    call_sd
       , Prod Boxity
    _ [Demand]
    sig_ds <- SubDemand
    prod
       = Card -> DmdType -> DmdType
    multDmdType Card
    n (DmdType -> DmdType) -> DmdType -> DmdType
    forall a b. (a -> b) -> a -> b
    $
         DmdEnv -> [Demand] -> DmdType
    DmdType DmdEnv
    nopDmdEnv [Card
    C_11 HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* Boxity -> [Demand] -> SubDemand
    mkProd Boxity
    Unboxed ((Demand -> Demand) -> [Demand] -> [Demand]
    forall a b. (a -> b) -> [a] -> [b]
    map (SubDemand -> Demand -> Demand
    enhance SubDemand
    sd') [Demand]
    sig_ds)]
       | Bool
    otherwise
       = DmdType
    nopDmdType -- See Note [Demand transformer for a dictionary selector]
      where
        enhance :: SubDemand -> Demand -> Demand
    enhance SubDemand
    _  Demand
    AbsDmd   = Demand
    AbsDmd
        enhance SubDemand
    _  Demand
    BotDmd   = Demand
    BotDmd
        enhance SubDemand
    sd Demand
    _dmd_var = Card
    C_11 HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* SubDemand
    sd  -- This is the one!
                                          -- C_11, because we multiply with n above
    dmdTransformDictSelSig DmdSig
    sig SubDemand
    sd = String -> SDoc -> DmdType
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "dmdTransformDictSelSig: no args" (DmdSig -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr DmdSig
    sig SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ SubDemand -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr SubDemand
    sd)

    {-
    Note [What are demand signatures?]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Demand analysis interprets expressions in the abstract domain of demand
    transformers. Given a (sub-)demand that denotes the evaluation context, the
    abstract transformer of an expression gives us back a demand type denoting
    how other things (like arguments and free vars) were used when the expression
    was evaluated. Here's an example:

      f x y =
        if x + expensive
          then \z -> z + y * ...
          else \z -> z * ...

    The abstract transformer (let's call it F_e) of the if expression (let's
    call it e) would transform an incoming (undersaturated!) head demand 1A into
    a demand type like {x-><1L>,y-><L>}<L>. In pictures:

         Demand ---F_e---> DmdType
         <1A>              {x-><1L>,y-><L>}<L>

    Let's assume that the demand transformers we compute for an expression are
    correct wrt. to some concrete semantics for Core. How do demand signatures fit
    in? They are strange beasts, given that they come with strict rules when to
    it's sound to unleash them.

    Fortunately, we can formalise the rules with Galois connections. Consider
    f's strictness signature, {}<1L><L>. It's a single-point approximation of
    the actual abstract transformer of f's RHS for arity 2. So, what happens is that
    we abstract *once more* from the abstract domain we already are in, replacing
    the incoming Demand by a simple lattice with two elements denoting incoming
    arity: A_2 = {<2, >=2} (where '<2' is the top element and >=2 the bottom
    element). Here's the diagram:

         A_2 -----f_f----> DmdType
          ^                   |
          | α               γ |
          |                   v
      SubDemand --F_f----> DmdType

    With
      α(C(1,C(1,_))) = >=2
      α(_)         =  <2
      γ(ty)        =  ty
    and F_f being the abstract transformer of f's RHS and f_f being the abstracted
    abstract transformer computable from our demand signature simply by

      f_f(>=2) = {}<1L><L>
      f_f(<2)  = multDmdType C_0N {}<1L><L>

    where multDmdType makes a proper top element out of the given demand type.

    In practice, the A_n domain is not just a simple Bool, but a Card, which is
    exactly the Card with which we have to multDmdType. The Card for arity n
    is computed by calling @peelManyCalls n@, which corresponds to α above.

    Note [Demand transformer for a dictionary selector]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Suppose we have a superclass selector 'sc_sel' and a class method
    selector 'op_sel', and a function that uses both, like this

    -- Strictness sig: 1P(1,A)
    sc_sel (x,y) = x

    -- Strictness sig: 1P(A,1)
    op_sel (p,q)= q

    f d v = op_sel (sc_sel d) v

    What do we learn about the demand on 'd'?  Alas, we see only the
    demand from 'sc_sel', namely '1P(1,A)'.  We /don't/ see that 'd' really has a nested
    demand '1P(1P(A,1C(1,1)),A)'.  On the other hand, if we inlined the two selectors
    we'd have

    f d x = case d of (x,_) ->
            case x of (_,q) ->
            q v

    If we analyse that, we'll get a richer, nested demand on 'd'.

    We want to behave /as if/ we'd inlined 'op_sel' and 'sc_sel'. We can do this
    easily by building a richer demand transformer for dictionary selectors than
    is expressible by a regular demand signature.
    And that is what 'dmdTransformDictSelSig' does: it transforms the demand on the
    result to a demand on the (single) argument.

    How does it do that?
    If we evaluate (op dict-expr) under demand 'd', then we can push the demand 'd'
    into the appropriate field of the dictionary. What *is* the appropriate field?
    We just look at the strictness signature of the class op, which will be
    something like: P(AAA1AAAAA). Then replace the '1' (or any other non-absent
    demand, really) by the demand 'd'. The '1' acts as if it was a demand variable,
    the whole signature really means `\d. P(AAAdAAAAA)` for any incoming
    demand 'd'.

    For single-method classes, which are represented by newtypes the signature
    of 'op' won't look like P(...), so matching on Prod will fail.
    That's fine: if we are doing strictness analysis we are also doing inlining,
    so we'll have inlined 'op' into a cast.  So we can bale out in a conservative
    way, returning nopDmdType. SG: Although we then probably want to apply the eval
    demand 'd' directly to 'op' rather than turning it into 'topSubDmd'...

    It is (just.. #8329) possible to be running strictness analysis *without*
    having inlined class ops from single-method classes.  Suppose you are using
    ghc --make; and the first module has a local -O0 flag.  So you may load a class
    without interface pragmas, ie (currently) without an unfolding for the class
    ops.   Now if a subsequent module in the --make sweep has a local -O flag
    you might do strictness analysis, but there is no inlining for the class op.
    This is weird, so I'm not worried about whether this optimises brilliantly; but
    it should not fall over.
    -}

    zapDmdEnv :: DmdEnv -> DmdEnv
    zapDmdEnv :: DmdEnv -> DmdEnv
    zapDmdEnv (DE VarEnv Demand
    _ Divergence
    div) = Divergence -> DmdEnv
    mkEmptyDmdEnv Divergence
    div

    -- | Remove the demand environment from the signature.
    zapDmdEnvSig :: DmdSig -> DmdSig
    zapDmdEnvSig :: DmdSig -> DmdSig
    zapDmdEnvSig (DmdSig (DmdType DmdEnv
    env [Demand]
    ds)) = DmdType -> DmdSig
    DmdSig (DmdEnv -> [Demand] -> DmdType
    DmdType (DmdEnv -> DmdEnv
    zapDmdEnv DmdEnv
    env) [Demand]
    ds)

    zapUsageDemand :: Demand -> Demand
    -- Remove the usage info, but not the strictness info, from the demand
    zapUsageDemand :: Demand -> Demand
    zapUsageDemand = KillFlags -> Demand -> Demand
    kill_usage (KillFlags -> Demand -> Demand) -> KillFlags -> Demand -> Demand
    forall a b. (a -> b) -> a -> b
    $ KillFlags
        { kf_abs :: Bool
    kf_abs         = Bool
    True
        , kf_used_once :: Bool
    kf_used_once   = Bool
    True
        , kf_called_once :: Bool
    kf_called_once = Bool
    True
        }

    -- | Remove all `C_01 :*` info (but not `CM` sub-demands) from the demand
    zapUsedOnceDemand :: Demand -> Demand
    zapUsedOnceDemand :: Demand -> Demand
    zapUsedOnceDemand = KillFlags -> Demand -> Demand
    kill_usage (KillFlags -> Demand -> Demand) -> KillFlags -> Demand -> Demand
    forall a b. (a -> b) -> a -> b
    $ KillFlags
        { kf_abs :: Bool
    kf_abs         = Bool
    False
        , kf_used_once :: Bool
    kf_used_once   = Bool
    True
        , kf_called_once :: Bool
    kf_called_once = Bool
    False
        }

    -- | Remove all `C_01 :*` info (but not `CM` sub-demands) from the strictness
    --   signature
    zapUsedOnceSig :: DmdSig -> DmdSig
    zapUsedOnceSig :: DmdSig -> DmdSig
    zapUsedOnceSig (DmdSig (DmdType DmdEnv
    env [Demand]
    ds))
        = DmdType -> DmdSig
    DmdSig (DmdEnv -> [Demand] -> DmdType
    DmdType DmdEnv
    env ((Demand -> Demand) -> [Demand] -> [Demand]
    forall a b. (a -> b) -> [a] -> [b]
    map Demand -> Demand
    zapUsedOnceDemand [Demand]
    ds))

    data KillFlags = KillFlags
        { KillFlags -> Bool
    kf_abs         :: Bool
        , KillFlags -> Bool
    kf_used_once   :: Bool
        , KillFlags -> Bool
    kf_called_once :: Bool
        }

    kill_usage_card :: KillFlags -> Card -> Card
    kill_usage_card :: KillFlags -> Card -> Card
    kill_usage_card KillFlags
    kfs Card
    C_00 | KillFlags -> Bool
    kf_abs KillFlags
    kfs       = Card
    C_0N
    kill_usage_card KillFlags
    kfs Card
    C_10 | KillFlags -> Bool
    kf_abs KillFlags
    kfs       = Card
    C_1N
    kill_usage_card KillFlags
    kfs Card
    C_01 | KillFlags -> Bool
    kf_used_once KillFlags
    kfs = Card
    C_0N
    kill_usage_card KillFlags
    kfs Card
    C_11 | KillFlags -> Bool
    kf_used_once KillFlags
    kfs = Card
    C_1N
    kill_usage_card KillFlags
    _   Card
    n                       = Card
    n

    kill_usage :: KillFlags -> Demand -> Demand
    kill_usage :: KillFlags -> Demand -> Demand
    kill_usage KillFlags
    _   Demand
    AbsDmd    = Demand
    AbsDmd
    kill_usage KillFlags
    _   Demand
    BotDmd    = Demand
    BotDmd
    kill_usage KillFlags
    kfs (Card
    n :* SubDemand
    sd) = KillFlags -> Card -> Card
    kill_usage_card KillFlags
    kfs Card
    n HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* KillFlags -> SubDemand -> SubDemand
    kill_usage_sd KillFlags
    kfs SubDemand
    sd

    kill_usage_sd :: KillFlags -> SubDemand -> SubDemand
    kill_usage_sd :: KillFlags -> SubDemand -> SubDemand
    kill_usage_sd KillFlags
    kfs (Call Card
    n SubDemand
    sd)
      | KillFlags -> Bool
    kf_called_once KillFlags
    kfs        = Card -> SubDemand -> SubDemand
    mkCall (Card -> Card -> Card
    lubCard Card
    C_1N Card
    n) (KillFlags -> SubDemand -> SubDemand
    kill_usage_sd KillFlags
    kfs SubDemand
    sd)
      | Bool
    otherwise                 = Card -> SubDemand -> SubDemand
    mkCall Card
    n                (KillFlags -> SubDemand -> SubDemand
    kill_usage_sd KillFlags
    kfs SubDemand
    sd)
    kill_usage_sd KillFlags
    kfs (Prod Boxity
    b [Demand]
    ds) = Boxity -> [Demand] -> SubDemand
    mkProd Boxity
    b ((Demand -> Demand) -> [Demand] -> [Demand]
    forall a b. (a -> b) -> [a] -> [b]
    map (KillFlags -> Demand -> Demand
    kill_usage KillFlags
    kfs) [Demand]
    ds)
    kill_usage_sd KillFlags
    _   SubDemand
    sd          = SubDemand
    sd

    {- *********************************************************************
    *                                                                      *
                   TypeShape and demand trimming
    *                                                                      *
    ********************************************************************* -}

    data TypeShape -- See Note [Trimming a demand to a type]
                   --     in GHC.Core.Opt.DmdAnal
      = TsFun TypeShape
      | TsProd [TypeShape]
      | TsUnk

    trimToType :: Demand -> TypeShape -> Demand
    -- See Note [Trimming a demand to a type] in GHC.Core.Opt.DmdAnal
    trimToType :: Demand -> TypeShape -> Demand
    trimToType Demand
    AbsDmd    TypeShape
    _  = Demand
    AbsDmd
    trimToType Demand
    BotDmd    TypeShape
    _  = Demand
    BotDmd
    trimToType (Card
    n :* SubDemand
    sd) TypeShape
    ts
      = Card
    n HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* SubDemand -> TypeShape -> SubDemand
    go SubDemand
    sd TypeShape
    ts
      where
        go :: SubDemand -> TypeShape -> SubDemand
    go (Prod Boxity
    b [Demand]
    ds) (TsProd [TypeShape]
    tss)
          | [Demand] -> [TypeShape] -> Bool
    forall a b. [a] -> [b] -> Bool
    equalLength [Demand]
    ds [TypeShape]
    tss    = Boxity -> [Demand] -> SubDemand
    mkProd Boxity
    b ((Demand -> TypeShape -> Demand)
    -> [Demand] -> [TypeShape] -> [Demand]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    zipWith Demand -> TypeShape -> Demand
    trimToType [Demand]
    ds [TypeShape]
    tss)
        go (Call Card
    n SubDemand
    sd) (TsFun TypeShape
    ts) = Card -> SubDemand -> SubDemand
    mkCall Card
    n (SubDemand -> TypeShape -> SubDemand
    go SubDemand
    sd TypeShape
    ts)
        go sd :: SubDemand
    sd@Poly{}   TypeShape
    _          = SubDemand
    sd
        go SubDemand
    _           TypeShape
    _          = SubDemand
    topSubDmd

    -- | Drop all boxity
    trimBoxity :: Demand -> Demand
    trimBoxity :: Demand -> Demand
    trimBoxity Demand
    AbsDmd    = Demand
    AbsDmd
    trimBoxity Demand
    BotDmd    = Demand
    BotDmd
    trimBoxity (Card
    n :* SubDemand
    sd) = Card
    n HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :* SubDemand -> SubDemand
    go SubDemand
    sd
      where
        go :: SubDemand -> SubDemand
    go (Poly Boxity
    _ Card
    n)  = Boxity -> Card -> SubDemand
    Poly Boxity
    Boxed Card
    n
        go (Prod Boxity
    _ [Demand]
    ds) = Boxity -> [Demand] -> SubDemand
    mkProd Boxity
    Boxed ((Demand -> Demand) -> [Demand] -> [Demand]
    forall a b. (a -> b) -> [a] -> [b]
    map Demand -> Demand
    trimBoxity [Demand]
    ds)
        go (Call Card
    n SubDemand
    sd) = Card -> SubDemand -> SubDemand
    mkCall Card
    n (SubDemand -> SubDemand) -> SubDemand -> SubDemand
    forall a b. (a -> b) -> a -> b
    $ SubDemand -> SubDemand
    go SubDemand
    sd

    {-
    ************************************************************************
    *                                                                      *
                         'seq'ing demands
    *                                                                      *
    ************************************************************************
    -}

    seqDemand :: Demand -> ()
    seqDemand :: Demand -> ()
    seqDemand Demand
    AbsDmd    = ()
    seqDemand Demand
    BotDmd    = ()
    seqDemand (Card
    _ :* SubDemand
    sd) = SubDemand -> ()
    seqSubDemand SubDemand
    sd

    seqSubDemand :: SubDemand -> ()
    seqSubDemand :: SubDemand -> ()
    seqSubDemand (Prod Boxity
    _ [Demand]
    ds) = [Demand] -> ()
    seqDemandList [Demand]
    ds
    seqSubDemand (Call Card
    _ SubDemand
    sd) = SubDemand -> ()
    seqSubDemand SubDemand
    sd
    seqSubDemand (Poly Boxity
    _ Card
    _)  = ()

    seqDemandList :: [Demand] -> ()
    seqDemandList :: [Demand] -> ()
    seqDemandList = (Demand -> () -> ()) -> () -> [Demand] -> ()
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr (() -> () -> ()
    forall a b. a -> b -> b
    seq (() -> () -> ()) -> (Demand -> ()) -> Demand -> () -> ()
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Demand -> ()
    seqDemand) ()

    seqDmdType :: DmdType -> ()
    seqDmdType :: DmdType -> ()
    seqDmdType (DmdType DmdEnv
    env [Demand]
    ds) =
      DmdEnv -> ()
    seqDmdEnv DmdEnv
    env () -> () -> ()
    forall a b. a -> b -> b
    `seq` [Demand] -> ()
    seqDemandList [Demand]
    ds () -> () -> ()
    forall a b. a -> b -> b
    `seq` ()

    seqDmdEnv :: DmdEnv -> ()
    seqDmdEnv :: DmdEnv -> ()
    seqDmdEnv (DE VarEnv Demand
    fvs Divergence
    _) = (Demand -> ()) -> VarEnv Demand -> ()
    forall {k} elt (key :: k). (elt -> ()) -> UniqFM key elt -> ()
    seqEltsUFM Demand -> ()
    seqDemand VarEnv Demand
    fvs

    seqDmdSig :: DmdSig -> ()
    seqDmdSig :: DmdSig -> ()
    seqDmdSig (DmdSig DmdType
    ty) = DmdType -> ()
    seqDmdType DmdType
    ty

    {-
    ************************************************************************
    *                                                                      *
                         Outputable and Binary instances
    *                                                                      *
    ************************************************************************
    -}

    -- Just for debugging purposes.
    instance Show Card where
      show :: Card -> String
    show Card
    C_00 = String
    "C_00"
      show Card
    C_01 = String
    "C_01"
      show Card
    C_0N = String
    "C_0N"
      show Card
    C_10 = String
    "C_10"
      show Card
    C_11 = String
    "C_11"
      show Card
    C_1N = String
    "C_1N"

    {- Note [Demand notation]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    This Note should be kept up to date with the documentation of `-fstrictness`
    in the user's guide.

    For pretty-printing demands, we use quite a compact notation with some
    abbreviations. Here's the BNF:

      card ::= B                        {}
            |  A                        {0}
            |  M                        {0,1}
            |  L                        {0,1,n}
            |  1                        {1}
            |  S                        {1,n}

      box  ::= !                        Unboxed
            |  <empty>                  Boxed

      d    ::= card sd                  The :* constructor, just juxtaposition
            |  card                     abbreviation: Same as "card card"

      sd   ::= box card                 @Poly box card@
            |  box P(d,d,..)            @Prod box [d1,d2,..]@
            |  Ccard(sd)                @Call card sd@

    So, L can denote a 'Card', polymorphic 'SubDemand' or polymorphic 'Demand',
    but it's always clear from context which "overload" is meant. It's like
    return-type inference of e.g. 'read'.

    Examples are in the haddock for 'Demand'.

    This is the syntax for demand signatures:

      div ::= <empty>      topDiv
           |  x            exnDiv
           |  b            botDiv

      sig ::= {x->dx,y->dy,z->dz...}<d1><d2><d3>...<dn>div
                      ^              ^   ^   ^      ^   ^
                      |              |   |   |      |   |
                      |              \---+---+------/   |
                      |                  |              |
                 demand on free        demand on      divergence
                   variables           arguments      information
               (omitted if empty)                     (omitted if
                                                    no information)

    -}

    -- | See Note [Demand notation]
    -- Current syntax was discussed in #19016.
    instance Outputable Card where
      ppr :: Card -> SDoc
    ppr Card
    C_00 = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'A' -- "Absent"
      ppr Card
    C_01 = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'M' -- "Maybe"
      ppr Card
    C_0N = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'L' -- "Lazy"
      ppr Card
    C_11 = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    '1' -- "exactly 1"
      ppr Card
    C_1N = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'S' -- "Strict"
      ppr Card
    C_10 = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'B' -- "Bottom"

    -- | See Note [Demand notation]
    instance Outputable Demand where
      ppr :: Demand -> SDoc
    ppr Demand
    AbsDmd                    = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'A'
      ppr Demand
    BotDmd                    = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'B'
      ppr (Card
    C_0N :* Poly Boxity
    Boxed Card
    C_0N) = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'L' -- Print LL as just L
      ppr (Card
    C_1N :* Poly Boxity
    Boxed Card
    C_1N) = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'S' -- Dito SS
      ppr (Card
    n :* SubDemand
    sd)                 = Card -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Card
    n SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> SubDemand -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr SubDemand
    sd

    -- | See Note [Demand notation]
    instance Outputable SubDemand where
      ppr :: SubDemand -> SDoc
    ppr (Poly Boxity
    b Card
    n)  = Boxity -> SDoc
    pp_boxity Boxity
    b SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> Card -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Card
    n
      ppr (Call Card
    n SubDemand
    sd) = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'C' SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    parens (Card -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Card
    n SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> SDoc
    forall doc. IsLine doc => doc
    comma SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> SubDemand -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr SubDemand
    sd)
      ppr (Prod Boxity
    b [Demand]
    ds) = Boxity -> SDoc
    pp_boxity Boxity
    b SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'P' SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    parens ([Demand] -> SDoc
    forall {a}. Outputable a => [a] -> SDoc
    fields [Demand]
    ds)
        where
          fields :: [a] -> SDoc
    fields []     = SDoc
    forall doc. IsOutput doc => doc
    empty
          fields [a
    x]    = a -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr a
    x
          fields (a
    x:[a]
    xs) = a -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr a
    x SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    ',' SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> [a] -> SDoc
    fields [a]
    xs

    pp_boxity :: Boxity -> SDoc
    pp_boxity :: Boxity -> SDoc
    pp_boxity Boxity
    Unboxed = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    '!'
    pp_boxity Boxity
    _       = SDoc
    forall doc. IsOutput doc => doc
    empty

    instance Outputable Divergence where
      ppr :: Divergence -> SDoc
    ppr Divergence
    Diverges = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'b' -- for (b)ottom
      ppr Divergence
    ExnOrDiv = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'x' -- for e(x)ception
      ppr Divergence
    Dunno    = SDoc
    forall doc. IsOutput doc => doc
    empty

    instance Outputable DmdEnv where
      ppr :: DmdEnv -> SDoc
    ppr (DE VarEnv Demand
    fvs Divergence
    div)
        = Divergence -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Divergence
    div SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> if [(Unique, Demand)] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [(Unique, Demand)]
    fv_elts then SDoc
    forall doc. IsOutput doc => doc
    empty
                     else SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    braces ([SDoc] -> SDoc
    forall doc. IsLine doc => [doc] -> doc
    fsep (((Unique, Demand) -> SDoc) -> [(Unique, Demand)] -> [SDoc]
    forall a b. (a -> b) -> [a] -> [b]
    map (Unique, Demand) -> SDoc
    forall {a} {a}. (Outputable a, Outputable a) => (a, a) -> SDoc
    pp_elt [(Unique, Demand)]
    fv_elts))
        where
          pp_elt :: (a, a) -> SDoc
    pp_elt (a
    uniq, a
    dmd) = a -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr a
    uniq SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "->" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> a -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr a
    dmd
          fv_elts :: [(Unique, Demand)]
    fv_elts = VarEnv Demand -> [(Unique, Demand)]
    forall {k} (key :: k) elt. UniqFM key elt -> [(Unique, elt)]
    nonDetUFMToList VarEnv Demand
    fvs
            -- It's OK to use nonDetUFMToList here because we only do it for
            -- pretty printing

    instance Outputable DmdType where
      ppr :: DmdType -> SDoc
    ppr (DmdType DmdEnv
    fv [Demand]
    ds)
        = [SDoc] -> SDoc
    forall doc. IsLine doc => [doc] -> doc
    hcat ((Demand -> SDoc) -> [Demand] -> [SDoc]
    forall a b. (a -> b) -> [a] -> [b]
    map (SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    angleBrackets (SDoc -> SDoc) -> (Demand -> SDoc) -> Demand -> SDoc
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Demand -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr) [Demand]
    ds) SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> DmdEnv -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr DmdEnv
    fv

    instance Outputable DmdSig where
       ppr :: DmdSig -> SDoc
    ppr (DmdSig DmdType
    ty) = DmdType -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr DmdType
    ty

    instance Outputable TypeShape where
      ppr :: TypeShape -> SDoc
    ppr TypeShape
    TsUnk        = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "TsUnk"
      ppr (TsFun TypeShape
    ts)   = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "TsFun" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    parens (TypeShape -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr TypeShape
    ts)
      ppr (TsProd [TypeShape]
    tss) = SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    parens ([SDoc] -> SDoc
    forall doc. IsLine doc => [doc] -> doc
    hsep ([SDoc] -> SDoc) -> [SDoc] -> SDoc
    forall a b. (a -> b) -> a -> b
    $ SDoc -> [SDoc] -> [SDoc]
    forall doc. IsLine doc => doc -> [doc] -> [doc]
    punctuate SDoc
    forall doc. IsLine doc => doc
    comma ([SDoc] -> [SDoc]) -> [SDoc] -> [SDoc]
    forall a b. (a -> b) -> a -> b
    $ (TypeShape -> SDoc) -> [TypeShape] -> [SDoc]
    forall a b. (a -> b) -> [a] -> [b]
    map TypeShape -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [TypeShape]
    tss)

    instance Binary Card where
      put_ :: BinHandle -> Card -> IO ()
    put_ BinHandle
    bh Card
    C_00 = BinHandle -> Word8 -> IO ()
    putByte BinHandle
    bh Word8
    0
      put_ BinHandle
    bh Card
    C_01 = BinHandle -> Word8 -> IO ()
    putByte BinHandle
    bh Word8
    1
      put_ BinHandle
    bh Card
    C_0N = BinHandle -> Word8 -> IO ()
    putByte BinHandle
    bh Word8
    2
      put_ BinHandle
    bh Card
    C_11 = BinHandle -> Word8 -> IO ()
    putByte BinHandle
    bh Word8
    3
      put_ BinHandle
    bh Card
    C_1N = BinHandle -> Word8 -> IO ()
    putByte BinHandle
    bh Word8
    4
      put_ BinHandle
    bh Card
    C_10 = BinHandle -> Word8 -> IO ()
    putByte BinHandle
    bh Word8
    5
      get :: BinHandle -> IO Card
    get BinHandle
    bh = do
        h <- BinHandle -> IO Word8
    getByte BinHandle
    bh
        case h of
          Word8
    0 -> Card -> IO Card
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return Card
    C_00
          Word8
    1 -> Card -> IO Card
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return Card
    C_01
          Word8
    2 -> Card -> IO Card
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return Card
    C_0N
          Word8
    3 -> Card -> IO Card
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return Card
    C_11
          Word8
    4 -> Card -> IO Card
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return Card
    C_1N
          Word8
    5 -> Card -> IO Card
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return Card
    C_10
          Word8
    _ -> String -> SDoc -> IO Card
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "Binary:Card" (Int -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr (Word8 -> Int
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral Word8
    h :: Int))

    instance Binary Demand where
      put_ :: BinHandle -> Demand -> IO ()
    put_ BinHandle
    bh (Card
    n :* SubDemand
    sd) = BinHandle -> Card -> IO ()
    forall a. Binary a => BinHandle -> a -> IO ()
    put_ BinHandle
    bh Card
    n IO () -> IO () -> IO ()
    forall a b. IO a -> IO b -> IO b
    forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
    *> case Card
    n of
        Card
    C_00 -> () -> IO ()
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return ()
        Card
    C_10 -> () -> IO ()
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return ()
        Card
    _    -> BinHandle -> SubDemand -> IO ()
    forall a. Binary a => BinHandle -> a -> IO ()
    put_ BinHandle
    bh SubDemand
    sd
      get :: BinHandle -> IO Demand
    get BinHandle
    bh = BinHandle -> IO Card
    forall a. Binary a => BinHandle -> IO a
    get BinHandle
    bh IO Card -> (Card -> IO Demand) -> IO Demand
    forall a b. IO a -> (a -> IO b) -> IO b
    forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
    >>= \Card
    n -> case Card
    n of
        Card
    C_00 -> Demand -> IO Demand
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return Demand
    AbsDmd
        Card
    C_10 -> Demand -> IO Demand
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return Demand
    BotDmd
        Card
    _    -> (Card
    n HasDebugCallStack => Card -> SubDemand -> Demand
    Card -> SubDemand -> Demand
    :*) (SubDemand -> Demand) -> IO SubDemand -> IO Demand
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> BinHandle -> IO SubDemand
    forall a. Binary a => BinHandle -> IO a
    get BinHandle
    bh

    instance Binary SubDemand where
      put_ :: BinHandle -> SubDemand -> IO ()
    put_ BinHandle
    bh (Poly Boxity
    b Card
    sd) = BinHandle -> Word8 -> IO ()
    putByte BinHandle
    bh Word8
    0 IO () -> IO () -> IO ()
    forall a b. IO a -> IO b -> IO b
    forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
    *> BinHandle -> Boxity -> IO ()
    forall a. Binary a => BinHandle -> a -> IO ()
    put_ BinHandle
    bh Boxity
    b IO () -> IO () -> IO ()
    forall a b. IO a -> IO b -> IO b
    forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
    *> BinHandle -> Card -> IO ()
    forall a. Binary a => BinHandle -> a -> IO ()
    put_ BinHandle
    bh Card
    sd
      put_ BinHandle
    bh (Call Card
    n SubDemand
    sd) = BinHandle -> Word8 -> IO ()
    putByte BinHandle
    bh Word8
    1 IO () -> IO () -> IO ()
    forall a b. IO a -> IO b -> IO b
    forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
    *> BinHandle -> Card -> IO ()
    forall a. Binary a => BinHandle -> a -> IO ()
    put_ BinHandle
    bh Card
    n IO () -> IO () -> IO ()
    forall a b. IO a -> IO b -> IO b
    forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
    *> BinHandle -> SubDemand -> IO ()
    forall a. Binary a => BinHandle -> a -> IO ()
    put_ BinHandle
    bh SubDemand
    sd
      put_ BinHandle
    bh (Prod Boxity
    b [Demand]
    ds) = BinHandle -> Word8 -> IO ()
    putByte BinHandle
    bh Word8
    2 IO () -> IO () -> IO ()
    forall a b. IO a -> IO b -> IO b
    forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
    *> BinHandle -> Boxity -> IO ()
    forall a. Binary a => BinHandle -> a -> IO ()
    put_ BinHandle
    bh Boxity
    b IO () -> IO () -> IO ()
    forall a b. IO a -> IO b -> IO b
    forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
    *> BinHandle -> [Demand] -> IO ()
    forall a. Binary a => BinHandle -> a -> IO ()
    put_ BinHandle
    bh [Demand]
    ds
      get :: BinHandle -> IO SubDemand
    get BinHandle
    bh = do
        h <- BinHandle -> IO Word8
    getByte BinHandle
    bh
        case h of
          Word8
    0 -> Boxity -> Card -> SubDemand
    Poly (Boxity -> Card -> SubDemand)
    -> IO Boxity -> IO (Card -> SubDemand)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> BinHandle -> IO Boxity
    forall a. Binary a => BinHandle -> IO a
    get BinHandle
    bh IO (Card -> SubDemand) -> IO Card -> IO SubDemand
    forall a b. IO (a -> b) -> IO a -> IO b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> BinHandle -> IO Card
    forall a. Binary a => BinHandle -> IO a
    get BinHandle
    bh
          Word8
    1 -> Card -> SubDemand -> SubDemand
    mkCall (Card -> SubDemand -> SubDemand)
    -> IO Card -> IO (SubDemand -> SubDemand)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> BinHandle -> IO Card
    forall a. Binary a => BinHandle -> IO a
    get BinHandle
    bh IO (SubDemand -> SubDemand) -> IO SubDemand -> IO SubDemand
    forall a b. IO (a -> b) -> IO a -> IO b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> BinHandle -> IO SubDemand
    forall a. Binary a => BinHandle -> IO a
    get BinHandle
    bh
          Word8
    2 -> Boxity -> [Demand] -> SubDemand
    Prod (Boxity -> [Demand] -> SubDemand)
    -> IO Boxity -> IO ([Demand] -> SubDemand)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> BinHandle -> IO Boxity
    forall a. Binary a => BinHandle -> IO a
    get BinHandle
    bh IO ([Demand] -> SubDemand) -> IO [Demand] -> IO SubDemand
    forall a b. IO (a -> b) -> IO a -> IO b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> BinHandle -> IO [Demand]
    forall a. Binary a => BinHandle -> IO a
    get BinHandle
    bh
          Word8
    _ -> String -> SDoc -> IO SubDemand
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "Binary:SubDemand" (Int -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr (Word8 -> Int
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral Word8
    h :: Int))

    instance Binary Divergence where
      put_ :: BinHandle -> Divergence -> IO ()
    put_ BinHandle
    bh Divergence
    Dunno    = BinHandle -> Word8 -> IO ()
    putByte BinHandle
    bh Word8
    0
      put_ BinHandle
    bh Divergence
    ExnOrDiv = BinHandle -> Word8 -> IO ()
    putByte BinHandle
    bh Word8
    1
      put_ BinHandle
    bh Divergence
    Diverges = BinHandle -> Word8 -> IO ()
    putByte BinHandle
    bh Word8
    2
      get :: BinHandle -> IO Divergence
    get BinHandle
    bh = do
        h <- BinHandle -> IO Word8
    getByte BinHandle
    bh
        case h of
          Word8
    0 -> Divergence -> IO Divergence
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return Divergence
    Dunno
          Word8
    1 -> Divergence -> IO Divergence
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return Divergence
    ExnOrDiv
          Word8
    2 -> Divergence -> IO Divergence
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return Divergence
    Diverges
          Word8
    _ -> String -> SDoc -> IO Divergence
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "Binary:Divergence" (Int -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr (Word8 -> Int
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral Word8
    h :: Int))

    instance Binary DmdEnv where
      -- Ignore VarEnv when spitting out the DmdType
      put_ :: BinHandle -> DmdEnv -> IO ()
    put_ BinHandle
    bh (DE VarEnv Demand
    _ Divergence
    d) = BinHandle -> Divergence -> IO ()
    forall a. Binary a => BinHandle -> a -> IO ()
    put_ BinHandle
    bh Divergence
    d
      get :: BinHandle -> IO DmdEnv
    get BinHandle
    bh = VarEnv Demand -> Divergence -> DmdEnv
    DE VarEnv Demand
    forall a. VarEnv a
    emptyVarEnv (Divergence -> DmdEnv) -> IO Divergence -> IO DmdEnv
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> BinHandle -> IO Divergence
    forall a. Binary a => BinHandle -> IO a
    get BinHandle
    bh

    instance Binary DmdType where
      put_ :: BinHandle -> DmdType -> IO ()
    put_ BinHandle
    bh (DmdType DmdEnv
    fv [Demand]
    ds) = BinHandle -> DmdEnv -> IO ()
    forall a. Binary a => BinHandle -> a -> IO ()
    put_ BinHandle
    bh DmdEnv
    fv IO () -> IO () -> IO ()
    forall a b. IO a -> IO b -> IO b
    forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
    *> BinHandle -> [Demand] -> IO ()
    forall a. Binary a => BinHandle -> a -> IO ()
    put_ BinHandle
    bh [Demand]
    ds
      get :: BinHandle -> IO DmdType
    get BinHandle
    bh = DmdEnv -> [Demand] -> DmdType
    DmdType (DmdEnv -> [Demand] -> DmdType)
    -> IO DmdEnv -> IO ([Demand] -> DmdType)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> BinHandle -> IO DmdEnv
    forall a. Binary a => BinHandle -> IO a
    get BinHandle
    bh IO ([Demand] -> DmdType) -> IO [Demand] -> IO DmdType
    forall a b. IO (a -> b) -> IO a -> IO b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> BinHandle -> IO [Demand]
    forall a. Binary a => BinHandle -> IO a
    get BinHandle
    bh

    instance Binary DmdSig where
      put_ :: BinHandle -> DmdSig -> IO ()
    put_ BinHandle
    bh (DmdSig DmdType
    aa) = BinHandle -> DmdType -> IO ()
    forall a. Binary a => BinHandle -> a -> IO ()
    put_ BinHandle
    bh DmdType
    aa
      get :: BinHandle -> IO DmdSig
    get BinHandle
    bh = DmdType -> DmdSig
    DmdSig (DmdType -> DmdSig) -> IO DmdType -> IO DmdSig
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> BinHandle -> IO DmdType
    forall a. Binary a => BinHandle -> IO a
    get BinHandle
    bh