DmdAnal: Implement Boxity Analysis (#19871)

This patch fixes some abundant reboxing of `DynFlags` in
`GHC.HsToCore.Match.Literal.warnAboutOverflowedLit` (which was the topic
of #19407) by introducing a Boxity analysis to GHC, done as part of demand
analysis. This allows to accurately capture ad-hoc unboxing decisions previously
made in worker/wrapper in demand analysis now, where the boxity info can
propagate through demand signatures.

See the new `Note [Boxity analysis]`. The actual fix for #19407 is described in
`Note [No lazy, Unboxed demand in demand signature]`, but
`Note [Finalising boxity for demand signature]` is probably a better entry-point.

To support the fix for #19407, I had to change (what was)
`Note [Add demands for strict constructors]` a bit
(now `Note [Unboxing evaluated arguments]`). In particular, we now take care of
it in `finaliseBoxity` (which is only called from demand analaysis) instead of
`wantToUnboxArg`.

I also had to resurrect `Note [Product demands for function body]` and rename
it to `Note [Unboxed demand on function bodies returning small products]` to
avoid huge regressions in `join004` and `join007`, thereby fixing #4267 again.
See the updated Note for details.

A nice side-effect is that the worker/wrapper transformation no longer needs to
look at strictness info and other bits such as `InsideInlineableFun` flags
(needed for `Note [Do not unbox class dictionaries]`) at all. It simply collects
boxity info from argument demands and interprets them with a severely simplified
`wantToUnboxArg`. All the smartness is in `finaliseBoxity`, which could be moved
to DmdAnal completely, if it wasn't for the call to `dubiousDataConInstArgTys`
which would be awkward to export.

I spent some time figuring out the reason for why `T16197` failed prior to my
amendments to `Note [Unboxing evaluated arguments]`. After having it figured
out, I minimised it a bit and added `T16197b`, which simply compares computed
strictness signatures and thus should be far simpler to eyeball.

The 12% ghc/alloc regression in T11545 is because of the additional `Boxity`
field in `Poly` and `Prod` that results in more allocation during `lubSubDmd`
and `plusSubDmd`. I made sure in the ticky profiles that the number of calls
to those functions stayed the same. We can bear such an increase here, as we
recently improved it by -68% (in b760c1f).
T18698* regress slightly because there is more unboxing of dictionaries
happening and that causes Lint (mostly) to allocate more.

Fixes #19871, #19407, #4267, #16859, #18907 and #13331.

Metric Increase:
    T11545
    T18698a
    T18698b

Metric Decrease:
    T12425
    T16577
    T18223
    T18282
    T4267
    T9961

13 files changed, 977 insertions, 525 deletions

diff --git a/compiler/GHC/Builtin/PrimOps.hs b/compiler/GHC/Builtin/PrimOps.hs
index 40f5e65605..164d1e2ea7 100644
--- a/compiler/GHC/Builtin/PrimOps.hs
+++ b/compiler/GHC/Builtin/PrimOps.hs
@@ -38,7 +38,7 @@ import GHC.Builtin.Names ( gHC_PRIMOPWRAPPERS )
 import GHC.Core.TyCon    ( TyCon, isPrimTyCon, PrimRep(..) )
 import GHC.Core.Type
 import GHC.Types.RepType ( tyConPrimRep1 )
-import GHC.Types.Basic   ( Arity, Boxity(..) )
+import GHC.Types.Basic   ( Arity )
 import GHC.Types.Fixity  ( Fixity(..), FixityDirection(..) )
 import GHC.Types.SrcLoc  ( wiredInSrcSpan )
 import GHC.Types.ForeignCall ( CLabelString )
diff --git a/compiler/GHC/Core/Make.hs b/compiler/GHC/Core/Make.hs
index b43344a92c..3387523e20 100644
--- a/compiler/GHC/Core/Make.hs
+++ b/compiler/GHC/Core/Make.hs
@@ -65,7 +65,6 @@ import GHC.Types.Demand
 import GHC.Types.Name      hiding ( varName )
 import GHC.Types.Literal
 import GHC.Types.Unique.Supply
-import GHC.Types.Basic
 
 import GHC.Core
 import GHC.Core.Utils ( exprType, needsCaseBinding, mkSingleAltCase, bindNonRec )
diff --git a/compiler/GHC/Core/Opt/CprAnal.hs b/compiler/GHC/Core/Opt/CprAnal.hs
index d3f6a248ce..65468cd037 100644
--- a/compiler/GHC/Core/Opt/CprAnal.hs
+++ b/compiler/GHC/Core/Opt/CprAnal.hs
@@ -21,14 +21,13 @@ import GHC.Types.Id.Info
 import GHC.Types.Demand
 import GHC.Types.Cpr
 
-import GHC.Core.DataCon
 import GHC.Core.FamInstEnv
-import GHC.Core.Multiplicity
-import GHC.Core.Opt.WorkWrap.Utils
+import GHC.Core.DataCon
 import GHC.Core.Type
 import GHC.Core.Utils
 import GHC.Core
 import GHC.Core.Seq
+import GHC.Core.Opt.WorkWrap.Utils
 
 import GHC.Data.Graph.UnVar -- for UnVarSet
 
@@ -639,30 +638,23 @@ nonVirgin env = env { ae_virgin = False }
 -- See Note [CPR for binders that will be unboxed].
 extendSigEnvForArg :: AnalEnv -> Id -> AnalEnv
 extendSigEnvForArg env id
-  = extendSigEnv env id (CprSig (argCprType env (idType id) (idDemandInfo id)))
+  = extendSigEnv env id (CprSig (argCprType (idDemandInfo id)))
 
 -- | Produces a 'CprType' according to how a strict argument will be unboxed.
 -- Examples:
 --
---   * A head-strict demand @1L@ on @Int@ would translate to @1@
---   * A product demand @1P(1L,L)@ on @(Int, Bool)@ would translate to @1(1,)@
---   * A product demand @1P(1L,L)@ on @(a , Bool)@ would translate to @1(,)@,
---     because the unboxing strategy would not unbox the @a@.
-argCprType :: AnalEnv -> Type -> Demand -> CprType
-argCprType env arg_ty dmd = CprType 0 (go arg_ty dmd)
+--   * A head-strict demand @1!L@ would translate to @1@
+--   * A product demand @1!P(1!L,L)@ would translate to @1(1,)@
+--   * A product demand @1!P(1L,L)@ would translate to @1(,)@,
+--     because the first field will not be unboxed.
+argCprType :: Demand -> CprType
+argCprType dmd = CprType 0 (go dmd)
   where
-    go ty dmd
-      | Unbox (DataConPatContext { dcpc_dc = dc, dcpc_tc_args = tc_args }) ds
-          <- wantToUnboxArg (ae_fam_envs env) MaybeArgOfInlineableFun ty dmd
-      -- No existentials; see Note [Which types are unboxed?])
-      -- Otherwise we'd need to call dataConRepInstPat here and thread a
-      -- UniqSupply. So argCprType is a bit less aggressive than it could
-      -- be, for the sake of coding convenience.
-      , null (dataConExTyCoVars dc)
-      , let arg_tys = map scaledThing (dataConInstArgTys dc tc_args)
-      = ConCpr (dataConTag dc) (zipWith go arg_tys ds)
-      | otherwise
-      = topCpr
+    go (n :* sd)
+      | isAbs n               = topCpr
+      | Prod Unboxed ds <- sd = ConCpr fIRST_TAG (strictMap go ds)
+      | Poly Unboxed _  <- sd = ConCpr fIRST_TAG []
+      | otherwise             = topCpr
 
 {- Note [Safe abortion in the fixed-point iteration]
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
diff --git a/compiler/GHC/Core/Opt/DmdAnal.hs b/compiler/GHC/Core/Opt/DmdAnal.hs
index 5f209701a9..fa4bed48f0 100644
--- a/compiler/GHC/Core/Opt/DmdAnal.hs
+++ b/compiler/GHC/Core/Opt/DmdAnal.hs
@@ -32,7 +32,8 @@ import GHC.Core.Utils
 import GHC.Core.TyCon
 import GHC.Core.Type
 import GHC.Core.FVs      ( rulesRhsFreeIds, bndrRuleAndUnfoldingIds )
-import GHC.Core.Coercion ( Coercion, coVarsOfCo )
+import GHC.Core.Coercion ( Coercion )
+import GHC.Core.TyCo.FVs ( coVarsOfCos )
 import GHC.Core.FamInstEnv
 import GHC.Core.Opt.Arity ( typeArity )
 import GHC.Utils.Misc
@@ -55,8 +56,9 @@ _ = pprTrace -- Tired of commenting out the import all the time
 -}
 
 -- | Options for the demand analysis
-newtype DmdAnalOpts = DmdAnalOpts
-   { dmd_strict_dicts :: Bool -- ^ Use strict dictionaries
+data DmdAnalOpts = DmdAnalOpts
+   { dmd_strict_dicts :: !Bool -- ^ Use strict dictionaries
+   , dmd_unbox_width  :: !Int  -- ^ Use strict dictionaries
    }
 
 -- This is a strict alternative to (,)
@@ -276,8 +278,10 @@ dmdAnalBindLetUp top_lvl env id rhs anal_body = WithDmdType final_ty (R (NonRec
   where
     WithDmdType body_ty body'   = anal_body env
     WithDmdType body_ty' id_dmd = findBndrDmd env body_ty id
-    !id'                = setBindIdDemandInfo top_lvl id id_dmd
-    (rhs_ty, rhs')     = dmdAnalStar env (dmdTransformThunkDmd rhs id_dmd) rhs
+    -- See Note [Finalising boxity for demand signature] in "GHC.Core.Opt.WorkWrap.Utils"
+    id_dmd'            = finaliseBoxity (ae_fam_envs env) NotInsideInlineableFun (idType id) id_dmd
+    !id'               = setBindIdDemandInfo top_lvl id id_dmd'
+    (rhs_ty, rhs')     = dmdAnalStar env (dmdTransformThunkDmd rhs id_dmd') rhs
 
     -- See Note [Absence analysis for stable unfoldings and RULES]
     rule_fvs           = bndrRuleAndUnfoldingIds id
@@ -425,21 +429,24 @@ dmdAnal' env dmd (Case scrut case_bndr ty [Alt alt bndrs rhs])
   | is_single_data_alt alt
   = let
         WithDmdType rhs_ty rhs'           = dmdAnal env dmd rhs
-        WithDmdType alt_ty1 dmds          = findBndrsDmds env rhs_ty bndrs
+        WithDmdType alt_ty1 fld_dmds      = findBndrsDmds env rhs_ty bndrs
         WithDmdType alt_ty2 case_bndr_dmd = findBndrDmd env alt_ty1 case_bndr
+        !case_bndr'                       = setIdDemandInfo case_bndr case_bndr_dmd
         -- Evaluation cardinality on the case binder is irrelevant and a no-op.
         -- What matters is its nested sub-demand!
+        -- NB: If case_bndr_dmd is absDmd, boxity will say Unboxed, which is
+        -- what we want, because then `seq` will put a `seqDmd` on its scrut.
         (_ :* case_bndr_sd) = case_bndr_dmd
         -- Compute demand on the scrutinee
         -- FORCE the result, otherwise thunks will end up retaining the
         -- whole DmdEnv
         !(!bndrs', !scrut_sd)
           | DataAlt _ <- alt
-          , id_dmds <- addCaseBndrDmd case_bndr_sd dmds
-          -- See Note [Demand on scrutinee of a product case]
-          = let !new_info = setBndrsDemandInfo bndrs id_dmds
-                !new_prod = mkProd id_dmds
-            in (new_info, new_prod)
+          -- See Note [Demand on the scrutinee of a product case]
+          -- See Note [Demand on case-alternative binders]
+          , (!scrut_sd, fld_dmds') <- addCaseBndrDmd case_bndr_sd fld_dmds
+          , let !bndrs' = setBndrsDemandInfo bndrs fld_dmds'
+          = (bndrs', scrut_sd)
           | otherwise
           -- __DEFAULT and literal alts. Simply add demands and discard the
           -- evaluation cardinality, as we evaluate the scrutinee exactly once.
@@ -454,7 +461,6 @@ dmdAnal' env dmd (Case scrut case_bndr ty [Alt alt bndrs rhs])
 
         WithDmdType scrut_ty scrut' = dmdAnal env scrut_sd scrut
         res_ty             = alt_ty3 `plusDmdType` toPlusDmdArg scrut_ty
-        !case_bndr'        = setIdDemandInfo case_bndr case_bndr_dmd
     in
 --    pprTrace "dmdAnal:Case1" (vcat [ text "scrut" <+> ppr scrut
 --                                   , text "dmd" <+> ppr dmd
@@ -482,8 +488,9 @@ dmdAnal' env dmd (Case scrut case_bndr ty alts)
             WithDmdType rest_ty as' = combineAltDmds as
           in WithDmdType (lubDmdType cur_ty rest_ty) (a':as')
 
-        WithDmdType scrut_ty scrut'   = dmdAnal env topSubDmd scrut
-        WithDmdType alt_ty1 case_bndr' = annotateBndr env alt_ty case_bndr
+        WithDmdType alt_ty1 case_bndr_dmd = findBndrDmd env alt_ty case_bndr
+        !case_bndr'                       = setIdDemandInfo case_bndr case_bndr_dmd
+        WithDmdType scrut_ty scrut'       = dmdAnal env topSubDmd scrut
                                -- NB: Base case is botDmdType, for empty case alternatives
                                --     This is a unit for lubDmdType, and the right result
                                --     when there really are no alternatives
@@ -549,12 +556,30 @@ dmdAnalSumAlt env dmd case_bndr (Alt con bndrs rhs)
   | WithDmdType rhs_ty rhs' <- dmdAnal env dmd rhs
   , WithDmdType alt_ty dmds <- findBndrsDmds env rhs_ty bndrs
   , let (_ :* case_bndr_sd) = findIdDemand alt_ty case_bndr
-        -- See Note [Demand on scrutinee of a product case]
-        id_dmds              = addCaseBndrDmd case_bndr_sd dmds
+        -- See Note [Demand on case-alternative binders]
+        -- we can't use the scrut_sd, because it says 'Prod' and we'll use
+        -- topSubDmd anyway for scrutinees of sum types.
+        (!_scrut_sd, dmds') = addCaseBndrDmd case_bndr_sd dmds
         -- Do not put a thunk into the Alt
-        !new_ids  = setBndrsDemandInfo bndrs id_dmds
+        !new_ids            = setBndrsDemandInfo bndrs dmds'
   = WithDmdType alt_ty (Alt con new_ids rhs')
 
+-- Precondition: The SubDemand is not a Call
+-- See Note [Demand on the scrutinee of a product case]
+-- and Note [Demand on case-alternative binders]
+addCaseBndrDmd :: SubDemand -- On the case binder
+               -> [Demand]  -- On the fields of the constructor
+               -> (SubDemand, [Demand])
+                            -- SubDemand on the case binder incl. field demands
+                            -- and final demands for the components of the constructor
+addCaseBndrDmd case_sd fld_dmds
+  | Just (_, ds) <- viewProd (length fld_dmds) scrut_sd
+  = (scrut_sd, ds)
+  | otherwise
+  = pprPanic "was a call demand" (ppr case_sd $$ ppr fld_dmds) -- See the Precondition
+  where
+    scrut_sd = case_sd `plusSubDmd` mkProd Unboxed fld_dmds
+
 {-
 Note [Analysing with absent demand]
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -674,6 +699,51 @@ worker, so the worker will rebuild
      x = (a, absent-error)
 and that'll crash.
 
+Note [Demand on case-alternative binders]
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+The demand on a binder in a case alternative comes
+  (a) From the demand on the binder itself
+  (b) From the demand on the case binder
+Forgetting (b) led directly to #10148.
+
+Example. Source code:
+  f x@(p,_) = if p then foo x else True
+
+  foo (p,True) = True
+  foo (p,q)    = foo (q,p)
+
+After strictness analysis, forgetting (b):
+  f = \ (x_an1 [Dmd=1P(1L,ML)] :: (Bool, Bool)) ->
+      case x_an1
+      of wild_X7 [Dmd=MP(ML,ML)]
+      { (p_an2 [Dmd=1L], ds_dnz [Dmd=A]) ->
+      case p_an2 of _ {
+        False -> GHC.Types.True;
+        True -> foo wild_X7 }
+
+Note that ds_dnz is syntactically dead, but the expression bound to it is
+reachable through the case binder wild_X7. Now watch what happens if we inline
+foo's wrapper:
+  f = \ (x_an1 [Dmd=1P(1L,ML)] :: (Bool, Bool)) ->
+      case x_an1
+      of _ [Dmd=MP(ML,ML)]
+      { (p_an2 [Dmd=1L], ds_dnz [Dmd=A]) ->
+      case p_an2 of _ {
+        False -> GHC.Types.True;
+        True -> $wfoo_soq GHC.Types.True ds_dnz }
+
+Look at that! ds_dnz has come back to life in the call to $wfoo_soq! A second
+run of demand analysis would no longer infer ds_dnz to be absent.
+But unlike occurrence analysis, which infers properties of the *syntactic*
+shape of the program, the results of demand analysis describe expressions
+*semantically* and are supposed to be mostly stable across Simplification.
+That's why we should better account for (b).
+In #10148, we ended up emitting a single-entry thunk instead of an updateable
+thunk for a let binder that was an an absent case-alt binder during DmdAnal.
+
+This is needed even for non-product types, in case the case-binder
+is used but the components of the case alternative are not.
+
 Note [Aggregated demand for cardinality]
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 FIXME: This Note should be named [LetUp vs. LetDown] and probably predates
@@ -725,43 +795,42 @@ strict in |y|.
 ************************************************************************
 -}
 
-dmdTransform :: AnalEnv         -- ^ The strictness environment
-             -> Id              -- ^ The function
-             -> SubDemand       -- ^ The demand on the function
-             -> DmdType         -- ^ The demand type of the function in this context
-                                -- Returned DmdEnv includes the demand on
-                                -- this function plus demand on its free variables
-
+dmdTransform :: AnalEnv   -- ^ The analysis environment
+             -> Id        -- ^ The variable
+             -> SubDemand -- ^ The evaluation context of the var
+             -> DmdType   -- ^ The demand type unleashed by the variable in this
+                          -- context. The returned DmdEnv includes the demand on
+                          -- this function plus demand on its free variables
 -- See Note [What are demand signatures?] in "GHC.Types.Demand"
-dmdTransform env var dmd
+dmdTransform env var sd
   -- Data constructors
   | isDataConWorkId var
-  = dmdTransformDataConSig (idArity var) dmd
+  = dmdTransformDataConSig (idArity var) sd
   -- Dictionary component selectors
   -- Used to be controlled by a flag.
   -- See #18429 for some perf measurements.
   | Just _ <- isClassOpId_maybe var
-  = -- pprTrace "dmdTransform:DictSel" (ppr var $$ ppr dmd) $
-    dmdTransformDictSelSig (idDmdSig var) dmd
+  = -- pprTrace "dmdTransform:DictSel" (ppr var $$ ppr (idDmdSig var) $$ ppr sd) $
+    dmdTransformDictSelSig (idDmdSig var) sd
   -- Imported functions
   | isGlobalId var
-  , let res = dmdTransformSig (idDmdSig var) dmd
-  = -- pprTrace "dmdTransform:import" (vcat [ppr var, ppr (idDmdSig var), ppr dmd, ppr res])
+  , let res = dmdTransformSig (idDmdSig var) sd
+  = -- pprTrace "dmdTransform:import" (vcat [ppr var, ppr (idDmdSig var), ppr sd, ppr res])
     res
   -- Top-level or local let-bound thing for which we use LetDown ('useLetUp').
   -- In that case, we have a strictness signature to unleash in our AnalEnv.
   | Just (sig, top_lvl) <- lookupSigEnv env var
-  , let fn_ty = dmdTransformSig sig dmd
-  = -- pprTrace "dmdTransform:LetDown" (vcat [ppr var, ppr sig, ppr dmd, ppr fn_ty]) $
+  , let fn_ty = dmdTransformSig sig sd
+  = -- pprTrace "dmdTransform:LetDown" (vcat [ppr var, ppr sig, ppr sd, ppr fn_ty]) $
     case top_lvl of
-      NotTopLevel -> addVarDmd fn_ty var (C_11 :* dmd)
+      NotTopLevel -> addVarDmd fn_ty var (C_11 :* sd)
       TopLevel
         | isInterestingTopLevelFn var
         -- Top-level things will be used multiple times or not at
         -- all anyway, hence the multDmd below: It means we don't
         -- have to track whether @var@ is used strictly or at most
         -- once, because ultimately it never will.
-        -> addVarDmd fn_ty var (C_0N `multDmd` (C_11 :* dmd)) -- discard strictness
+        -> addVarDmd fn_ty var (C_0N `multDmd` (C_11 :* sd)) -- discard strictness
         | otherwise
         -> fn_ty -- don't bother tracking; just annotate with 'topDmd' later
   -- Everything else:
@@ -769,8 +838,8 @@ dmdTransform env var dmd
   --   * Lambda binders
   --   * Case and constructor field binders
   | otherwise
-  = -- pprTrace "dmdTransform:other" (vcat [ppr var, ppr sig, ppr dmd, ppr res]) $
-    unitDmdType (unitVarEnv var (C_11 :* dmd))
+  = -- pprTrace "dmdTransform:other" (vcat [ppr var, ppr boxity, ppr sd]) $
+    unitDmdType (unitVarEnv var (C_11 :* sd))
 
 {- *********************************************************************
 *                                                                      *
@@ -802,15 +871,21 @@ dmdAnalRhsSig top_lvl rec_flag env let_dmd id rhs
   where
     rhs_arity = idArity id
     -- See Note [Demand signatures are computed for a threshold demand based on idArity]
-    rhs_dmd -- See Note [Demand analysis for join points]
-            -- See Note [Invariants on join points] invariant 2b, in GHC.Core
-            --     rhs_arity matches the join arity of the join point
-            | isJoinId id
-            = mkCalledOnceDmds rhs_arity let_dmd
-            | otherwise
-            = mkCalledOnceDmds rhs_arity topSubDmd
-
-    WithDmdType rhs_dmd_ty rhs' = dmdAnal env rhs_dmd rhs
+
+    rhs_dmd = mkCalledOnceDmds rhs_arity body_dmd
+
+    body_dmd
+      | isJoinId id
+      -- See Note [Demand analysis for join points]
+      -- See Note [Invariants on join points] invariant 2b, in GHC.Core
+      --     rhs_arity matches the join arity of the join point
+      = let_dmd
+      | otherwise
+      -- See Note [Unboxed demand on function bodies returning small products]
+      = unboxedWhenSmall (ae_opts env) (unboxableResultWidth env id) topSubDmd
+
+    -- See Note [Do not unbox class dictionaries]
+    WithDmdType rhs_dmd_ty rhs' = dmdAnal (adjustInlFun id env) rhs_dmd rhs
     DmdType rhs_fv rhs_dmds rhs_div = rhs_dmd_ty
 
     sig = mkDmdSigForArity rhs_arity (DmdType sig_fv rhs_dmds rhs_div)
@@ -829,6 +904,7 @@ dmdAnalRhsSig top_lvl rec_flag env let_dmd id rhs
     --        might turn into used-many even if the signature was stable and
     --        we'd have to do an additional iteration. reuseEnv makes sure that
     --        we never get used-once info for FVs of recursive functions.
+    --        See #14816 where we try to get rid of reuseEnv.
     rhs_fv1 = case rec_flag of
                 Recursive    -> reuseEnv rhs_fv
                 NonRecursive -> rhs_fv
@@ -839,6 +915,26 @@ dmdAnalRhsSig top_lvl rec_flag env let_dmd id rhs
     -- See Note [Lazy and unleashable free variables]
     !(!lazy_fv, !sig_fv) = partitionVarEnv isWeakDmd rhs_fv2
 
+unboxableResultWidth :: AnalEnv -> Id -> Maybe Arity
+unboxableResultWidth env id
+  | (pis,ret_ty) <- splitPiTys (idType id)
+  , count (not . isNamedBinder) pis == idArity id
+  , Just (tc, _tc_args, _co) <- normSplitTyConApp_maybe (ae_fam_envs env) ret_ty
+  , Just dc <- tyConSingleAlgDataCon_maybe tc
+  , null (dataConExTyCoVars dc) -- Can't unbox results with existentials
+  = Just (dataConRepArity dc)
+  | otherwise
+  = Nothing
+
+unboxedWhenSmall :: DmdAnalOpts -> Maybe Arity -> SubDemand -> SubDemand
+-- See Note [Unboxed demand on function bodies returning small products]
+unboxedWhenSmall opts mb_n sd
+  | Just n <- mb_n
+  , n <= dmd_unbox_width opts
+  = unboxSubDemand sd
+  | otherwise
+  = sd
+
 -- | If given the (local, non-recursive) let-bound 'Id', 'useLetUp' determines
 -- whether we should process the binding up (body before rhs) or down (rhs
 -- before body).
@@ -1056,34 +1152,6 @@ Now f's optimised RHS will be \x.a, but if we change g to (error "..")
 (since it is apparently Absent) and then inline (\x. fst g) we get
 disaster.  But regardless, #18638 was a more complicated version of
 this, that actually happened in practice.
-
-Historical Note [Product demands for function body]
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-In 2013 I spotted this example, in shootout/binary_trees:
-
-    Main.check' = \ b z ds. case z of z' { I# ip ->
-                                case ds_d13s of
-                                  Main.Nil -> z'
-                                  Main.Node s14k s14l s14m ->
-                                    Main.check' (not b)
-                                      (Main.check' b
-                                         (case b {
-                                            False -> I# (-# s14h s14k);
-                                            True  -> I# (+# s14h s14k)
-                                          })
-                                         s14l)
-                                     s14m   }   }   }
-
-Here we *really* want to unbox z, even though it appears to be used boxed in
-the Nil case.  Partly the Nil case is not a hot path.  But more specifically,
-the whole function gets the CPR property if we do.
-
-That motivated using a demand of C1(C1(C1(P(L,L)))) for the RHS, where
-(solely because the result was a product) we used a product demand
-(albeit with lazy components) for the body. But that gives very silly
-behaviour -- see #17932.   Happily it turns out now to be entirely
-unnecessary: we get good results with C1(C1(C1(L))).   So I simply
-deleted the special case.
 -}
 
 {- *********************************************************************
@@ -1159,7 +1227,6 @@ dmdFix top_lvl env let_dmd orig_pairs
 
 {- Note [Safe abortion in the fixed-point iteration]
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
 Fixed-point iteration may fail to terminate. But we cannot simply give up and
 return the environment and code unchanged! We still need to do one additional
 round, for two reasons:
@@ -1231,8 +1298,11 @@ unitDmdType :: DmdEnv -> DmdType
 unitDmdType dmd_env = DmdType dmd_env [] topDiv
 
 coercionDmdEnv :: Coercion -> DmdEnv
-coercionDmdEnv co = mapVarEnv (const topDmd) (getUniqSet $ coVarsOfCo co)
-                    -- The VarSet from coVarsOfCo is really a VarEnv Var
+coercionDmdEnv co = coercionsDmdEnv [co]
+
+coercionsDmdEnv :: [Coercion] -> DmdEnv
+coercionsDmdEnv cos = mapVarEnv (const topDmd) (getUniqSet $ coVarsOfCos cos)
+                      -- The VarSet from coVarsOfCos is really a VarEnv Var
 
 addVarDmd :: DmdType -> Var -> Demand -> DmdType
 addVarDmd (DmdType fv ds res) var dmd
@@ -1283,18 +1353,6 @@ setBndrsDemandInfo (b:bs) (d:ds) =
 setBndrsDemandInfo [] ds = assert (null ds) []
 setBndrsDemandInfo bs _  = pprPanic "setBndrsDemandInfo" (ppr bs)
 
-annotateBndr :: AnalEnv -> DmdType -> Var -> WithDmdType Var
--- The returned env has the var deleted
--- The returned var is annotated with demand info
--- according to the result demand of the provided demand type
--- No effect on the argument demands
-annotateBndr env dmd_ty var
-  | isId var  = WithDmdType dmd_ty' new_id
-  | otherwise = WithDmdType dmd_ty  var
-  where
-    new_id = setIdDemandInfo var dmd
-    WithDmdType dmd_ty' dmd = findBndrDmd env dmd_ty var
-
 annotateLamIdBndr :: AnalEnv
                   -> DmdType    -- Demand type of body
                   -> Id         -- Lambda binder
@@ -1308,8 +1366,11 @@ annotateLamIdBndr env dmd_ty id
     -- pprTrace "annLamBndr" (vcat [ppr id, ppr dmd_ty, ppr final_ty]) $
     WithDmdType main_ty new_id
   where
-    new_id  = setIdDemandInfo id dmd
-    main_ty = addDemand dmd dmd_ty'
+    -- See Note [Finalising boxity for demand signature] in "GHC.Core.Opt.WorkWrap.Utils"
+    -- and Note [Do not unbox class dictionaries]
+    dmd'    = finaliseBoxity (ae_fam_envs env) (ae_inl_fun env) (idType id) dmd
+    new_id  = setIdDemandInfo id dmd'
+    main_ty = addDemand dmd' dmd_ty'
     WithDmdType dmd_ty' dmd = findBndrDmd env dmd_ty id
 
 {- Note [NOINLINE and strictness]
@@ -1389,11 +1450,14 @@ demand put on them (topDmd), and add that to the "lazy_fv" returned by "dmdFix".
 
 
 data AnalEnv = AE
-   { ae_strict_dicts :: !Bool -- ^ Enable strict dict
-   , ae_sigs         :: !SigEnv
-   , ae_virgin       :: !Bool -- ^ True on first iteration only
-                              -- See Note [Initialising strictness]
-   , ae_fam_envs     :: !FamInstEnvs
+   { ae_opts      :: !DmdAnalOpts -- ^ Analysis options
+   , ae_sigs      :: !SigEnv
+   , ae_virgin    :: !Bool -- ^ True on first iteration only
+                           -- See Note [Initialising strictness]
+   , ae_fam_envs  :: !FamInstEnvs
+   , ae_inl_fun   :: !InsideInlineableFun
+                           -- ^ Whether we analyse the body of an inlineable fun.
+                           -- See Note [Do not unbox class dictionaries].
    }
 
         -- We use the se_env to tell us whether to
@@ -1408,16 +1472,16 @@ type SigEnv = VarEnv (DmdSig, TopLevelFlag)
 instance Outputable AnalEnv where
   ppr env = text "AE" <+> braces (vcat
          [ text "ae_virgin =" <+> ppr (ae_virgin env)
-         , text "ae_strict_dicts =" <+> ppr (ae_strict_dicts env)
          , text "ae_sigs =" <+> ppr (ae_sigs env)
          ])
 
 emptyAnalEnv :: DmdAnalOpts -> FamInstEnvs -> AnalEnv
 emptyAnalEnv opts fam_envs
-    = AE { ae_strict_dicts = dmd_strict_dicts opts
+    = AE { ae_opts         = opts
          , ae_sigs         = emptySigEnv
          , ae_virgin       = True
          , ae_fam_envs     = fam_envs
+         , ae_inl_fun      = NotInsideInlineableFun
          }
 
 emptySigEnv :: SigEnv
@@ -1445,6 +1509,13 @@ lookupSigEnv env id = lookupVarEnv (ae_sigs env) id
 nonVirgin :: AnalEnv -> AnalEnv
 nonVirgin env = env { ae_virgin = False }
 
+-- | Sets 'ae_inl_fun' according to whether the given 'Id' has an inlineable
+-- unfolding. See Note [Do not unbox class dictionaries].
+adjustInlFun :: Id -> AnalEnv -> AnalEnv
+adjustInlFun id env
+  | isStableUnfolding (realIdUnfolding id) = env { ae_inl_fun = InsideInlineableFun }
+  | otherwise                              = env { ae_inl_fun = NotInsideInlineableFun }
+
 findBndrsDmds :: AnalEnv -> DmdType -> [Var] -> WithDmdType [Demand]
 -- Return the demands on the Ids in the [Var]
 findBndrsDmds env dmd_ty bndrs
@@ -1472,9 +1543,9 @@ findBndrDmd env dmd_ty id
 
     strictify dmd
       -- See Note [Making dictionaries strict]
-      | ae_strict_dicts env
+      | dmd_strict_dicts (ae_opts env)
              -- We never want to strictify a recursive let. At the moment
-             -- annotateBndr is only call for non-recursive lets; if that
+             -- findBndrDmd is never called for recursive lets; if that
              -- changes, we need a RecFlag parameter and another guard here.
       = strictifyDictDmd id_ty dmd
       | otherwise
@@ -1522,7 +1593,7 @@ to inline one applied to a function. Sometimes this makes just enough
 of a difference to stop a function from inlining. This is documented in
 #18421.
 
-It's somewhat similar to Note [Do not unpack class dictionaries] although
+It's somewhat similar to Note [Do not unbox class dictionaries] although
 here our problem is with the inliner, not the specializer.
 
 Note [Initialising strictness]
diff --git a/compiler/GHC/Core/Opt/Pipeline.hs b/compiler/GHC/Core/Opt/Pipeline.hs
index 18ac910d15..ee79e28b60 100644
--- a/compiler/GHC/Core/Opt/Pipeline.hs
+++ b/compiler/GHC/Core/Opt/Pipeline.hs
@@ -1067,6 +1067,7 @@ dmdAnal :: Logger -> DynFlags -> FamInstEnvs -> [CoreRule] -> CoreProgram -> IO
 dmdAnal logger dflags fam_envs rules binds = do
   let !opts = DmdAnalOpts
                { dmd_strict_dicts = gopt Opt_DictsStrict dflags
+               , dmd_unbox_width  = dmdUnboxWidth dflags
                }
       binds_plus_dmds = dmdAnalProgram opts fam_envs rules binds
   Logger.putDumpFileMaybe logger Opt_D_dump_str_signatures "Strictness signatures" FormatText $
diff --git a/compiler/GHC/Core/Opt/SpecConstr.hs b/compiler/GHC/Core/Opt/SpecConstr.hs
index 718c840c96..966e86a344 100644
--- a/compiler/GHC/Core/Opt/SpecConstr.hs
+++ b/compiler/GHC/Core/Opt/SpecConstr.hs
@@ -1806,7 +1806,7 @@ calcSpecInfo fn (CP { cp_qvars = qvars, cp_args = pats }) extra_bndrs
     go_one env d          (Var v) = extendVarEnv_C plusDmd env v d
     go_one env (_n :* cd) e -- NB: _n does not have to be strict
       | (Var _, args) <- collectArgs e
-      , Just ds <- viewProd (length args) cd
+      , Just (_b, ds) <- viewProd (length args) cd -- TODO: We may want to look at boxity _b, though...
       = go env ds args
     go_one env _  _ = env
 
diff --git a/compiler/GHC/Core/Opt/WorkWrap.hs b/compiler/GHC/Core/Opt/WorkWrap.hs
index 976dcd5fe5..9becea0c18 100644
--- a/compiler/GHC/Core/Opt/WorkWrap.hs
+++ b/compiler/GHC/Core/Opt/WorkWrap.hs
@@ -734,8 +734,6 @@ splitFun ww_opts fn_id rhs
     uf_opts = so_uf_opts (wo_simple_opts ww_opts)
     fn_info = idInfo fn_id
     (arg_vars, body) = collectBinders rhs
-            -- collectBinders was not enough for GHC.Event.IntTable.insertWith
-            -- last time I checked, where manifest lambdas were wrapped in casts
 
     (wrap_dmds, div) = splitDmdSig (dmdSigInfo fn_info)
 
@@ -978,8 +976,7 @@ splitThunk :: WwOpts -> RecFlag -> Var -> Expr Var -> UniqSM [(Var, Expr Var)]
 splitThunk ww_opts is_rec x rhs
   = assert (not (isJoinId x)) $
     do { let x' = localiseId x -- See comment above
-       ; (useful,_, wrap_fn, fn_arg)
-           <- mkWWstr_one ww_opts NotArgOfInlineableFun x'
+       ; (useful,_, wrap_fn, fn_arg) <- mkWWstr_one ww_opts x'
        ; let res = [ (x, Let (NonRec x' rhs) (wrap_fn fn_arg)) ]
        ; if useful then assertPpr (isNonRec is_rec) (ppr x) -- The thunk must be non-recursive
                    return res
diff --git a/compiler/GHC/Core/Opt/WorkWrap/Utils.hs b/compiler/GHC/Core/Opt/WorkWrap/Utils.hs
index 38c103d866..c2287916db 100644
--- a/compiler/GHC/Core/Opt/WorkWrap/Utils.hs
+++ b/compiler/GHC/Core/Opt/WorkWrap/Utils.hs
@@ -10,8 +10,9 @@ A library for the ``worker\/wrapper'' back-end to the strictness analyser
 module GHC.Core.Opt.WorkWrap.Utils
    ( WwOpts(..), initWwOpts, mkWwBodies, mkWWstr, mkWWstr_one, mkWorkerArgs
    , DataConPatContext(..)
-   , UnboxingDecision(..), ArgOfInlineableFun(..), wantToUnboxArg
-   , findTypeShape, mkAbsentFiller, IsRecDataConResult(..), isRecDataCon
+   , UnboxingDecision(..), InsideInlineableFun(..), wantToUnboxArg
+   , findTypeShape, IsRecDataConResult(..), isRecDataCon, finaliseBoxity
+   , mkAbsentFiller
    , isWorkerSmallEnough
    )
 where
@@ -229,7 +230,7 @@ mkWwBodies opts fun_id arg_vars res_ty demands res_cpr
               res_ty' = GHC.Core.Subst.substTy subst res_ty
 
         ; (useful1, work_args, wrap_fn_str, fn_args)
-             <- mkWWstr opts inlineable_flag cloned_arg_vars
+             <- mkWWstr opts cloned_arg_vars
 
         -- Do CPR w/w.  See Note [Always do CPR w/w]
         ; (useful2, wrap_fn_cpr, work_fn_cpr, cpr_res_ty)
@@ -265,9 +266,6 @@ mkWwBodies opts fun_id arg_vars res_ty demands res_cpr
       = info `setOccInfo`       noOccInfo
 
     mb_join_arity = isJoinId_maybe fun_id
-    inlineable_flag -- See Note [Do not unpack class dictionaries]
-      | isStableUnfolding (realIdUnfolding fun_id) = MaybeArgOfInlineableFun
-      | otherwise                                  = NotArgOfInlineableFun
 
     -- Note [Do not split void functions]
     only_one_void_argument
@@ -562,59 +560,30 @@ data UnboxingDecision s
   -- The @[s]@ carries the bits of information with which we can continue
   -- unboxing, e.g. @s@ will be 'Demand' or 'Cpr'.
 
--- | A specialised Bool for an argument to 'wantToUnboxArg'.
--- See Note [Do not unpack class dictionaries].
-data ArgOfInlineableFun
-  = NotArgOfInlineableFun   -- ^ Definitely not in an inlineable fun.
-  | MaybeArgOfInlineableFun -- ^ We might be in an inlineable fun, so we won't
-                            -- unbox dictionary args.
-  deriving Eq
-
--- | Unboxing strategy for strict arguments.
-wantToUnboxArg :: FamInstEnvs -> ArgOfInlineableFun -> Type -> Demand -> UnboxingDecision Demand
+-- | Unwraps the 'Boxity' decision encoded in the given 'SubDemand' and returns
+-- a 'DataConPatContext' as well the nested demands on fields of the 'DataCon'
+-- to unbox.
+wantToUnboxArg
+  :: FamInstEnvs
+  -> Type                -- ^ Type of the argument
+  -> Demand              -- ^ How the arg was used
+  -> UnboxingDecision Demand
 -- See Note [Which types are unboxed?]
-wantToUnboxArg fam_envs inlineable_flag ty dmd
-  | isAbsDmd dmd
+wantToUnboxArg fam_envs ty (n :* sd)
+  | isAbs n
   = DropAbsent
 
-  | isStrUsedDmd dmd
-  , Just (tc, tc_args, co) <- normSplitTyConApp_maybe fam_envs ty
+  | Just (tc, tc_args, co) <- normSplitTyConApp_maybe fam_envs ty
   , Just dc <- tyConSingleAlgDataCon_maybe tc
   , let arity = dataConRepArity dc
-  -- See Note [Unpacking arguments with product and polymorphic demands]
-  , Just cs <- split_prod_dmd_arity dmd arity
-  -- See Note [Do not unpack class dictionaries]
-  , inlineable_flag == NotArgOfInlineableFun || not (isClassPred ty)
-  -- See Note [mkWWstr and unsafeCoerce]
-  , cs `lengthIs` arity
-  -- See Note [Add demands for strict constructors]
-  , let cs' = addDataConStrictness dc cs
-  = Unbox (DataConPatContext dc tc_args co) cs'
+  , Just (Unboxed, ds) <- viewProd arity sd -- See Note [Boxity Analysis]
+  -- NB: No strictness or evaluatedness checks here. That is done by
+  -- 'finaliseBoxity'!
+  = Unbox (DataConPatContext dc tc_args co) ds
 
   | otherwise
   = StopUnboxing
 
-  where
-    split_prod_dmd_arity dmd arity
-      -- For seqDmd, it should behave like <S(AAAA)>, for some
-      -- suitable arity
-      | isSeqDmd dmd        = Just (replicate arity absDmd)
-      | _ :* Prod ds <- dmd = Just ds
-      | otherwise           = Nothing
-
-addDataConStrictness :: DataCon -> [Demand] -> [Demand]
--- See Note [Add demands for strict constructors]
-addDataConStrictness con ds
-  | Nothing <- dataConWrapId_maybe con
-  -- DataCon worker=wrapper. Implies no strict fields, so nothing to do
-  = ds
-addDataConStrictness con ds
-  = zipWithEqual "addDataConStrictness" add ds strs
-  where
-    strs = dataConRepStrictness con
-    add dmd str | isMarkedStrict str = strictifyDmd dmd
-                | otherwise          = dmd
-
 
 -- | Unboxing strategy for constructed results.
 wantToUnboxResult :: FamInstEnvs -> Type -> Cpr -> UnboxingDecision Cpr
@@ -688,35 +657,8 @@ Note that the data constructor /can/ have evidence arguments: equality
 constraints, type classes etc.  So it can be GADT.  These evidence
 arguments are simply value arguments, and should not get in the way.
 
-Note [Unpacking arguments with product and polymorphic demands]
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-The argument is unpacked in a case if it has a product type and has a
-strict *and* used demand put on it. I.e., arguments, with demands such
-as the following ones:
-
-   <S,U(U, L)>
-   <S(L,S),U>
-
-will be unpacked, but
-
-   <S,U> or <B,U>
-
-will not, because the pieces aren't used. This is quite important otherwise
-we end up unpacking massive tuples passed to the bottoming function. Example:
-
-        f :: ((Int,Int) -> String) -> (Int,Int) -> a
-        f g pr = error (g pr)
-
-        main = print (f fst (1, error "no"))
-
-Does 'main' print "error 1" or "error no"?  We don't really want 'f'
-to unbox its second argument.  This actually happened in GHC's onwn
-source code, in Packages.applyPackageFlag, which ended up un-boxing
-the enormous DynFlags tuple, and being strict in the
-as-yet-un-filled-in unitState files.
-
-Note [Do not unpack class dictionaries]
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+Note [Do not unbox class dictionaries]
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 If we have
    f :: Ord a => [a] -> Int -> a
    {-# INLINABLE f #-}
@@ -729,12 +671,19 @@ BUT if f is strict in the Ord dictionary, we might unpack it, to get
    fw :: (a->a->Bool) -> [a] -> Int# -> a
 and the type-class specialiser can't specialise that. An example is #6056.
 
-But in any other situation a dictionary is just an ordinary value,
-and can be unpacked.  So we track the INLINABLE pragma, and switch
-off the unpacking in mkWWstr_one (see the isClassPred test).
+But in any other situation, a dictionary is just an ordinary value,
+and can be unpacked.  So we track the INLINABLE pragma, and discard the boxity
+flag in finaliseBoxity (see the isClassPred test).
 
 Historical note: #14955 describes how I got this fix wrong the first time.
 
+Note that the simplicity of this fix implies that INLINE functions (such as
+wrapper functions after the WW run) will never say that they unbox class
+dictionaries. That's not ideal, but not worth losing sleep over, as INLINE
+functions will have been inlined by the time we run demand analysis so we'll
+see the unboxing around the worker in client modules. I got aware of the issue
+in T5075 by the change in boxity of loop between demand analysis runs.
+
 Note [mkWWstr and unsafeCoerce]
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 By using unsafeCoerce, it is possible to make the number of demands fail to
@@ -742,14 +691,14 @@ match the number of constructor arguments; this happened in #8037.
 If so, the worker/wrapper split doesn't work right and we get a Core Lint
 bug.  The fix here is simply to decline to do w/w if that happens.
 
-Note [Add demands for strict constructors]
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+Note [Unboxing evaluated arguments]
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 Consider this program (due to Roman):
 
     data X a = X !a
 
     foo :: X Int -> Int -> Int
-    foo (X a) n = go 0
+    foo x@(X a) n = go 0
      where
        go i | i < n     = a + go (i+1)
             | otherwise = 0
@@ -758,12 +707,12 @@ We want the worker for 'foo' too look like this:
 
     $wfoo :: Int# -> Int# -> Int#
 
-with the first argument unboxed, so that it is not eval'd each time
-around the 'go' loop (which would otherwise happen, since 'foo' is not
-strict in 'a').  It is sound for the wrapper to pass an unboxed arg
-because X is strict, so its argument must be evaluated.  And if we
-*don't* pass an unboxed argument, we can't even repair it by adding a
-`seq` thus:
+with the first argument unboxed, so that it is not eval'd each time around the
+'go' loop (which would otherwise happen, since 'foo' is not strict in 'a'). It
+is sound for the wrapper to pass an unboxed arg because X is strict
+(see Note [Strictness and Unboxing] in "GHC.Core.Opt.DmdAnal"), so its argument
+must be evaluated. And if we *don't* pass an unboxed argument, we can't even
+repair it by adding a `seq` thus:
 
     foo (X a) n = a `seq` go 0
 
@@ -771,34 +720,38 @@ because the seq is discarded (very early) since X is strict!
 
 So here's what we do
 
-* We leave the demand-analysis alone.  The demand on 'a' in the
-  definition of 'foo' is <L, U(U)>; the strictness info is Lazy
-  because foo's body may or may not evaluate 'a'; but the usage info
-  says that 'a' is unpacked and its content is used.
+* Since this has nothing to do with how 'foo' uses 'a', we leave demand analysis
+  alone, but account for the additional evaluatedness when annotating the binder
+  in 'annotateLamIdBndr' via 'finaliseBoxity', which will retain the Unboxed boxity
+  on 'a' in the definition of 'foo' in the demand 'L!P(L)'; meaning it's used
+  lazily but unboxed nonetheless. This seems to contradict
+  Note [No lazy, Unboxed demands in demand signature], but we know that 'a' is
+  evaluated and thus can be unboxed.
 
-* During worker/wrapper, if we unpack a strict constructor (as we do
-  for 'foo'), we use 'addDataConStrictness' to bump up the strictness on
-  the strict arguments of the data constructor.
+* When 'finaliseBoxity' decides to unbox a record, it will zip the field demands
+  together with the respective 'StrictnessMark'. In case of 'x', it will pair
+  up the lazy field demand 'L!P(L)' on 'a' with 'MarkedStrict' to account for
+  the strict field.
 
-* That in turn means that, if the usage info supports doing so
-  (i.e. splitProdDmd_maybe returns Just), we will unpack that argument
-  -- even though the original demand (e.g. on 'a') was lazy.
+* Said 'StrictnessMark' is passed to the recursive invocation of
+  'finaliseBoxity' when deciding whether to unbox 'a'. 'a' was used lazily, but
+  since it also says 'MarkedStrict', we'll retain the 'Unboxed' boxity on 'a'.
 
-* What does "bump up the strictness" mean?  Just add a head-strict
-  demand to the strictness!  Even for a demand like <L,A> we can
-  safely turn it into <S,A>; remember case (1) of
-  Note [Worker/wrapper for Strictness and Absence].
+* Worker/wrapper will consult 'wantToUnboxArg' for its unboxing decision. It will
+  /not/ look at the strictness bits of the demand, only at Boxity flags. As such,
+  it will happily unbox 'a' despite the lazy demand on it.
 
-The net effect is that the w/w transformation is more aggressive about
-unpacking the strict arguments of a data constructor, when that
-eagerness is supported by the usage info.
+The net effect is that boxity analysis and the w/w transformation are more
+aggressive about unboxing the strict arguments of a data constructor than when
+looking at strictness info exclusively. It is very much like (Nested) CPR, which
+needs its nested fields to be evaluated in order for it to unbox nestedly.
 
 There is the usual danger of reboxing, which as usual we ignore. But
 if X is monomorphic, and has an UNPACK pragma, then this optimisation
 is even more important.  We don't want the wrapper to rebox an unboxed
 argument, and pass an Int to $wfoo!
 
-This works in nested situations like
+This works in nested situations like T10482
 
     data family Bar a
     data instance Bar (a, b) = BarPair !(Bar a) !(Bar b)
@@ -863,6 +816,68 @@ applying the strictness demands to the final result of DmdAnal. The result is
 that we get the strict demand signature we wanted even if we can't float
 the case on `x` up through the case on `burble`.
 
+Note [No nested Unboxed inside Boxed in demand signature]
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+Consider
+```
+f p@(x,y)
+  | even (x+y) = []
+  | otherwise  = [p]
+```
+Demand analysis will infer that the function body puts a demand of `1P(1!L,1!L)`
+on 'p', e.g., Boxed on the outside but Unboxed on the inside. But worker/wrapper
+can't unbox the pair components without unboxing the pair! So we better say
+`1P(1L,1L)` in the demand signature in order not to spread wrong Boxity info.
+That happens in 'finaliseBoxity'.
+
+Note [No lazy, Unboxed demands in demand signature]
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+Consider T19407:
+
+  data Huge = Huge Bool () ... () -- think: DynFlags
+  data T = T { h :: Huge, n :: Int }
+  f t@(T h _) = g h t
+  g (H b _ ... _) t = if b then 1 else n t
+
+The body of `g` puts (approx.) demand `L!P(A,1)` on `t`. But we better
+not put that demand in `g`'s demand signature, because worker/wrapper will not
+in general unbox a lazy-and-unboxed demand like `L!P(..)`.
+(The exception are known-to-be-evaluated arguments like strict fields,
+see Note [Unboxing evaluated arguments].)
+
+The program above is an example where spreading misinformed boxity through the
+signature is particularly egregious. If we give `g` that signature, then `f`
+puts demand `S!P(1!P(1L,A,..),ML)` on `t`. Now we will unbox `t` in `f` it and
+we get
+
+  f (T (H b _ ... _) n) = $wf b n
+  $wf b n = $wg b (T (H b x ... x) n)
+  $wg = ...
+
+Massive reboxing in `$wf`! Solution: Trim boxity on lazy demands in
+'finaliseBoxity', modulo Note [Unboxing evaluated arguments].
+
+Note [Finalising boxity for demand signature]
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+The worker/wrapper pass must strictly adhere to the boxity decisions encoded
+in the demand signature, because that is the information that demand analysis
+propagates throughout the program. Failing to implement the strategy laid out
+in the signature can result in reboxing in unexpected places. Hence, we must
+completely anticipate unboxing decisions during demand analysis and reflect
+these decicions in demand annotations. That is the job of 'finaliseBoxity',
+which is defined here and called from demand analysis.
+
+Here is a list of different Notes it has to take care of:
+
+  * Note [No lazy, Unboxed demands in demand signature] such as `L!P(L)` in
+    general, but still allow Note [Unboxing evaluated arguments]
+  * Note [No nested Unboxed inside Boxed in demand signature] such as `1P(1!L)`
+  * Implement fixes for corner cases Note [Do not unbox class dictionaries]
+    and Note [mkWWstr and unsafeCoerce]
+
+Then, in worker/wrapper blindly trusts the boxity info in the demand signature
+and will not look at strictness info *at all*, in 'wantToUnboxArg'.
+
 Note [non-algebraic or open body type warning]
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 There are a few cases where the W/W transformation is told that something
@@ -894,7 +909,6 @@ way to express existential types in the worker's type signature.
 -}
 
 mkWWstr :: WwOpts
-        -> ArgOfInlineableFun            -- See Note [Do not unpack class dictionaries]
         -> [Var]                         -- Wrapper args; have their demand info on them
                                          --  *Includes type variables*
         -> UniqSM (Bool,                 -- Is this useful
@@ -905,10 +919,10 @@ mkWWstr :: WwOpts
                    [CoreExpr])           -- Reboxed args for the call to the
                                          -- original RHS. Corresponds one-to-one
                                          -- with the wrapper arg vars
-mkWWstr opts inlineable_flag args
+mkWWstr opts args
   = go args
   where
-    go_one arg = mkWWstr_one opts inlineable_flag arg
+    go_one arg = mkWWstr_one opts arg
 
     go []           = return (False, [], nop_fn, [])
     go (arg : args) = do { (useful1, args1, wrap_fn1, wrap_arg)  <- go_one arg
@@ -925,12 +939,9 @@ mkWWstr opts inlineable_flag args
 --   * wrap_arg assumes work_args are in scope, and builds a ConApp that
 --        reconstructs the RHS of wrap_var that we pass to the original RHS
 -- See Note [Worker/wrapper for Strictness and Absence]
-mkWWstr_one :: WwOpts
-            -> ArgOfInlineableFun -- See Note [Do not unpack class dictionaries]
-            -> Var
-            -> UniqSM (Bool, [Var], CoreExpr -> CoreExpr, CoreExpr)
-mkWWstr_one opts inlineable_flag arg =
-  case wantToUnboxArg fam_envs inlineable_flag arg_ty arg_dmd of
+mkWWstr_one :: WwOpts -> Var -> UniqSM (Bool, [Var], CoreExpr -> CoreExpr, CoreExpr)
+mkWWstr_one opts arg =
+  case wantToUnboxArg fam_envs arg_ty arg_dmd of
     _ | isTyVar arg -> do_nothing
 
     DropAbsent
@@ -940,7 +951,7 @@ mkWWstr_one opts inlineable_flag arg =
          -- (that's what mkAbsentFiller does)
       -> return (True, [], nop_fn, absent_filler)
 
-    Unbox dcpc cs -> unbox_one_arg opts arg cs dcpc
+    Unbox dcpc ds -> unbox_one_arg opts arg ds dcpc
 
     _ -> do_nothing -- Other cases, like StopUnboxing
 
@@ -955,17 +966,17 @@ unbox_one_arg :: WwOpts
           -> [Demand]
           -> DataConPatContext
           -> UniqSM (Bool, [Var], CoreExpr -> CoreExpr, CoreExpr)
-unbox_one_arg opts arg_var cs
+unbox_one_arg opts arg_var ds
           DataConPatContext { dcpc_dc = dc, dcpc_tc_args = tc_args
                             , dcpc_co = co }
   = do { pat_bndrs_uniqs <- getUniquesM
        ; let ex_name_fss = map getOccFS $ dataConExTyCoVars dc
              (ex_tvs', arg_ids) =
                dataConRepFSInstPat (ex_name_fss ++ repeat ww_prefix) pat_bndrs_uniqs (idMult arg_var) dc tc_args
-             arg_ids' = zipWithEqual "unbox_one_arg" setIdDemandInfo arg_ids cs
+             arg_ids' = zipWithEqual "unbox_one_arg" setIdDemandInfo arg_ids ds
              unbox_fn = mkUnpackCase (Var arg_var) co (idMult arg_var)
                                      dc (ex_tvs' ++ arg_ids')
-       ; (_, worker_args, wrap_fn, wrap_args) <- mkWWstr opts NotArgOfInlineableFun (ex_tvs' ++ arg_ids')
+       ; (_, worker_args, wrap_fn, wrap_args) <- mkWWstr opts (ex_tvs' ++ arg_ids')
        ; let wrap_arg = mkConApp dc (map Type tc_args ++ wrap_args) `mkCast` mkSymCo co
        ; return (True, worker_args, unbox_fn . wrap_fn, wrap_arg) }
                           -- Don't pass the arg, rebox instead
@@ -1009,42 +1020,45 @@ mkAbsentFiller opts arg
 
 {- Note [Worker/wrapper for Strictness and Absence]
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-The worker/wrapper transformation, mkWWstr_one, takes into account
-several possibilities to decide if the function is worthy for
-splitting:
+The worker/wrapper transformation, mkWWstr_one, takes concrete action
+based on the 'UnboxingDescision' returned by 'wantToUnboxArg'.
+The latter takes into account several possibilities to decide if the
+function is worthy for splitting:
 
 1. If an argument is absent, it would be silly to pass it to
-   the worker.  Hence the isAbsDmd case.  This case must come
-   first because a demand like <S,A> or <B,A> is possible.
-   E.g. <B,A> comes from a function like
+   the worker.  Hence the DropAbsent case.  This case must come
+   first because the bottom demand B is also strict.
+   E.g. B comes from a function like
        f x = error "urk"
-   and <S,A> can come from Note [Add demands for strict constructors]
-
-2. If the argument is evaluated strictly, and we can split the
-   product demand (splitProdDmd_maybe), then unbox it and w/w its
-   pieces.  For example
-
-    f :: (Int, Int) -> Int
-    f p = (case p of (a,b) -> a) + 1
-  is split to
-    f :: (Int, Int) -> Int
-    f p = case p of (a,b) -> $wf a
-
-    $wf :: Int -> Int
-    $wf a = a + 1
-
-  and
-    g :: Bool -> (Int, Int) -> Int
-    g c p = case p of (a,b) ->
-               if c then a else b
-  is split to
-   g c p = case p of (a,b) -> $gw c a b
-   $gw c a b = if c then a else b
-
-2a But do /not/ split if the components are not used; that is, the
-   usage is just 'Used' rather than 'UProd'. In this case
-   splitProdDmd_maybe returns Nothing.  Otherwise we risk decomposing
-   a massive tuple which is barely used.  Example:
+   and the absent demand A can come from Note [Unboxing evaluated arguments]
+
+2. If the argument is evaluated strictly (or known to be eval'd),
+   we can take a view into the product demand ('viewProd'). In accordance
+   with Note [Boxity analysis], 'wantToUnboxArg' will say 'Unbox'.
+   'mkWWstr_one' then follows suit it and recurses into the fields of the
+   product demand. For example
+
+     f :: (Int, Int) -> Int
+     f p = (case p of (a,b) -> a) + 1
+   is split to
+     f :: (Int, Int) -> Int
+     f p = case p of (a,b) -> $wf a
+
+     $wf :: Int -> Int
+     $wf a = a + 1
+
+   and
+     g :: Bool -> (Int, Int) -> Int
+     g c p = case p of (a,b) ->
+                if c then a else b
+   is split to
+     g c p = case p of (a,b) -> $gw c a b
+     $gw c a b = if c then a else b
+
+2a But do /not/ split if Boxity Analysis said "Boxed".
+   In this case, 'wantToUnboxArg' returns 'StopUnboxing'.
+   Otherwise we risk decomposing and reboxing a massive
+   tuple which is barely used. Example:
 
         f :: ((Int,Int) -> String) -> (Int,Int) -> a
         f g pr = error (g pr)
@@ -1055,10 +1069,11 @@ splitting:
    Imagine that it had millions of fields. This actually happened
    in GHC itself where the tuple was DynFlags
 
-3. A plain 'seqDmd', which is head-strict with usage UHead, can't
-   be split by splitProdDmd_maybe.  But we want it to behave just
-   like U(AAAA) for suitable number of absent demands. So we have
-   a special case for it, with arity coming from the data constructor.
+3. In all other cases (e.g., lazy, used demand and not eval'd),
+   'finaliseBoxity' will have cleared the Boxity flag to 'Boxed'
+   (see Note [Finalising boxity for demand signature]) and
+   'wantToUnboxArg' returns 'StopUnboxing' so that 'mkWWstr_one'
+   stops unboxing.
 
 Note [Worker/wrapper for bottoming functions]
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -1162,7 +1177,7 @@ Needless to say, there are some wrinkles:
      Ideally, we'd just look at the 'StrictnessMark' of the DataCon's field, but
      it's quite nasty to thread the marks though 'mkWWstr' and 'mkWWstr_one'.
      So we rather look out for a necessary condition for strict fields:
-     Note [Add demands for strict constructors] makes it so that the demand on
+     Note [Unboxing evaluated arguments] makes it so that the demand on
      'zs' is absent and /strict/: It will get cardinality 'C_10', the empty
      interval, rather than 'C_00'. Hence the 'isStrictDmd' check: It guarantees
      we never fill in an error-thunk for an absent strict field.
@@ -1395,6 +1410,56 @@ isRecDataCon fam_envs fuel dc
             -> combineIRDCRs (map (\dc -> go_dc (subWithInf fuel 1) rec_tc' dc) dcs)
                 -- See Note [Detecting recursive data constructors], point (4)
 
+-- | A specialised Bool for an argument to 'finaliseBoxity'.
+-- See Note [Do not unbox class dictionaries].
+data InsideInlineableFun
+  = NotInsideInlineableFun -- ^ Not in an inlineable fun.
+  | InsideInlineableFun    -- ^ We are in an inlineable fun, so we won't
+                           -- unbox dictionary args.
+  deriving Eq
+
+-- | This function makes sure that the demand only says 'Unboxed' where
+-- worker/wrapper should actually unbox and trims any boxity beyond that.
+-- Called for every demand annotation during DmdAnal.
+--
+-- > data T a = T !a
+-- > f :: (T (Int,Int), Int) -> ()
+-- > f p = ... -- demand on p: 1!P(L!P(L!P(L), L!P(L)), L!P(L))
+--
+-- 'finaliseBoxity' will trim the demand on 'p' to 1!P(L!P(LP(L), LP(L)), LP(L)).
+-- This is done when annotating lambdas and thunk bindings.
+-- See Note [Finalising boxity for demand signature]
+finaliseBoxity
+  :: FamInstEnvs
+  -> InsideInlineableFun    -- ^ See the haddocks on 'InsideInlineableFun'
+  -> Type                   -- ^ Type of the argument
+  -> Demand                 -- ^ How the arg was used
+  -> Demand
+finaliseBoxity env in_inl_fun ty dmd = go NotMarkedStrict ty dmd
+  where
+    go mark ty dmd@(n :* _) =
+      case wantToUnboxArg env ty dmd of
+        DropAbsent -> dmd
+        Unbox DataConPatContext{dcpc_dc=dc, dcpc_tc_args=tc_args} ds
+          -- See Note [No lazy, Unboxed demands in demand signature]
+          -- See Note [Unboxing evaluated arguments]
+          | isStrict n || isMarkedStrict mark
+          -- See Note [Do not unbox class dictionaries]
+          , in_inl_fun == NotInsideInlineableFun || not (isClassPred ty)
+          -- See Note [mkWWstr and unsafeCoerce]
+          , ds `lengthIs` dataConRepArity dc
+          , let arg_tys = dubiousDataConInstArgTys dc tc_args
+          -> -- pprTrace "finaliseBoxity:Unbox" (ppr ty $$ ppr dmd $$ ppr ds) $
+             n :* (mkProd Unboxed $! zip_go_with_marks dc arg_tys ds)
+        -- See Note [No nested Unboxed inside Boxed in demand signature]
+        _ -> trimBoxity dmd
+
+    -- See Note [Unboxing evaluated arguments]
+    zip_go_with_marks dc arg_tys ds = case dataConWrapId_maybe dc of
+      Nothing -> strictZipWith  (go NotMarkedStrict)          arg_tys ds
+                    -- Shortcut when DataCon worker=wrapper
+      Just _  -> strictZipWith3 go  (dataConRepStrictness dc) arg_tys ds
+
 {-
 ************************************************************************
 *                                                                      *
diff --git a/compiler/GHC/Driver/Session.hs b/compiler/GHC/Driver/Session.hs
index aaedf4f2d7..478a0f7737 100644
--- a/compiler/GHC/Driver/Session.hs
+++ b/compiler/GHC/Driver/Session.hs
@@ -479,6 +479,9 @@ data DynFlags = DynFlags {
                                         --   a pattern against. A safe guard
                                         --   against exponential blow-up.
   simplTickFactor       :: Int,         -- ^ Multiplier for simplifier ticks
+  dmdUnboxWidth         :: !Int,        -- ^ Whether DmdAnal should optimistically put an
+                                        --   Unboxed demand on returned products with at most
+                                        --   this number of fields
   specConstrThreshold   :: Maybe Int,   -- ^ Threshold for SpecConstr
   specConstrCount       :: Maybe Int,   -- ^ Max number of specialisations for any one function
   specConstrRecursive   :: Int,         -- ^ Max number of specialisations for recursive types
@@ -1101,6 +1104,7 @@ defaultDynFlags mySettings llvmConfig =
         maxUncoveredPatterns    = 4,
         maxPmCheckModels        = 30,
         simplTickFactor         = 100,
+        dmdUnboxWidth           = 3,      -- Default: Assume an unboxed demand on function bodies returning a triple
         specConstrThreshold     = Just 2000,
         specConstrCount         = Just 3,
         specConstrRecursive     = 3,
@@ -2657,6 +2661,8 @@ dynamic_flags_deps = [
           ; return d })))
   , make_ord_flag defFlag "fsimpl-tick-factor"
       (intSuffix (\n d -> d { simplTickFactor = n }))
+  , make_ord_flag defFlag "fdmd-unbox-width"
+      (intSuffix (\n d -> d { dmdUnboxWidth = n }))
   , make_ord_flag defFlag "fspec-constr-threshold"
       (intSuffix (\n d -> d { specConstrThreshold = Just n }))
   , make_ord_flag defFlag "fno-spec-constr-threshold"
diff --git a/compiler/GHC/Types/Basic.hs b/compiler/GHC/Types/Basic.hs
index db4b8f9e23..342d9d3688 100644
--- a/compiler/GHC/Types/Basic.hs
+++ b/compiler/GHC/Types/Basic.hs
@@ -503,6 +503,12 @@ instance Outputable Boxity where
   ppr Boxed   = text "Boxed"
   ppr Unboxed = text "Unboxed"
 
+instance Binary Boxity where -- implemented via isBoxed-isomorphism to Bool
+  put_ bh = put_ bh . isBoxed
+  get bh  = do
+    b <- get bh
+    pure $ if b then Boxed else Unboxed
+
 {-
 ************************************************************************
 *                                                                      *
diff --git a/compiler/GHC/Types/Demand.hs b/compiler/GHC/Types/Demand.hs
index 96b5b21bf7..ed7ef25aa8 100644
--- a/compiler/GHC/Types/Demand.hs
+++ b/compiler/GHC/Types/Demand.hs
@@ -16,9 +16,10 @@
 -- 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), mkProd, viewProd,
+    SubDemand(Prod, Poly), mkProd, viewProd, unboxSubDemand,
     -- ** Algebra
     absDmd, topDmd, botDmd, seqDmd, topSubDmd,
     -- *** Least upper bound
@@ -30,7 +31,7 @@ module GHC.Types.Demand (
     -- ** Predicates on @Card@inalities and @Demand@s
     isAbs, isUsedOnce, isStrict,
     isAbsDmd, isUsedOnceDmd, isStrUsedDmd, isStrictDmd,
-    isTopDmd, isSeqDmd, isWeakDmd,
+    isTopDmd, isWeakDmd,
     -- ** Special demands
     evalDmd,
     -- *** Demands used in PrimOp signatures
@@ -38,7 +39,6 @@ module GHC.Types.Demand (
     -- ** Other @Demand@ operations
     oneifyCard, oneifyDmd, strictifyDmd, strictifyDictDmd, mkWorkerDemand,
     peelCallDmd, peelManyCalls, mkCalledOnceDmd, mkCalledOnceDmds,
-    addCaseBndrDmd,
     -- ** Extracting one-shot information
     argOneShots, argsOneShots, saturatedByOneShots,
 
@@ -71,7 +71,7 @@ module GHC.Types.Demand (
     DmdTransformer, dmdTransformSig, dmdTransformDataConSig, dmdTransformDictSelSig,
 
     -- * Trim to a type shape
-    TypeShape(..), trimToType,
+    TypeShape(..), trimToType, trimBoxity,
 
     -- * @seq@ing stuff
     seqDemand, seqDemandList, seqDmdType, seqDmdSig,
@@ -108,6 +108,260 @@ _ = pprTrace -- Tired of commenting out the import all the time
 {-
 ************************************************************************
 *                                                                      *
+           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 = $weven (n -# 2)
+```
+And now the box in `even (I# 42)` will cancel away after inlining the wrapper.
+
+As far as the permission to unbox is concerned, *evaluatedness* of the argument
+is the important trait. Unboxing implies eager evaluation of an argument and
+we don't want to change the termination properties of the function. One way
+to ensure that is to unbox strict arguments only, but strictness is only a
+sufficient condition for evaluatedness.
+See Note [Unboxing evaluated arguments] in "GHC.Core.Opt.WorkWrap.Utils", where
+we manage to unbox *strict fields* of unboxed arguments that the function is not
+actually strict in, simply by realising that those fields have to be evaluated.
+
+Note [Boxity analysis]
+~~~~~~~~~~~~~~~~~~~~~~
+Alas, we don't want to unbox *every* strict argument
+(as Note [Strictness and Unboxing] might suggest).
+Here's an example (from T19871):
+```
+data Huge = H Bool Bool ... Bool
+ann :: Huge -> (Bool, Huge)
+ann h@(Huge True _ ... _) = (False, h)
+ann h                     = (True,  h)
+```
+Unboxing 'h' yields
+```
+$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.
+(We don't adhere to that in 'lubBoxity', see Note [lubBoxity and plusBoxity].)
+
+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 signature] in
+"GHC.Core.Opt.WorkWrap.Utils" 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 [lubBoxity and plusBoxity] describes why we optimistically let Unboxed
+   win when combining different case alternatives.
+
+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.
+Consequnce:  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.)
+
+Note [lubBoxity and plusBoxity]
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+Should 'Boxed' win in 'lubBoxity' and 'plusBoxity'?
+The first intuition is Yes, because that would be the conservative choice:
+Responding 'Boxed' when there's the slightest chance we might need the box means
+we'll never need to rebox a value.
+
+For 'plusBoxity' the choice of 'boxedWins' is clear: When we need a value to be
+Boxed and Unboxed /in the same trace/, then we clearly need it to be Boxed.
+
+But if we chose 'boxedWins' for 'lubBoxity', we'd regress T3586. Smaller example
+```
+sumIO :: Int -> Int -> IO Int
+sumIO 0 !z = return 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.
+So we choose 'unboxedWins' for 'lubBoxity' to collect this win.
+
+Choosing 'unboxedWins' is not conservative. There clearly is ample room for
+examples that get worse by our choice. Here's a simple one (from T19871):
+```
+data Huge = H { f1 :: Bool, ... many fields ... }
+update :: Huge -> (Bool, Huge)
+update h@(Huge{f1=True}) = (False, h{f1=False})
+update h                 = (True,  h)
+```
+Here, we decide to unbox 'h' because it's used Unboxed in the first branch.
+
+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).
+-}
+
+boxedWins :: Boxity -> Boxity -> Boxity
+boxedWins Unboxed Unboxed = Unboxed
+boxedWins _       !_      = Boxed
+
+unboxedWins :: Boxity -> Boxity -> Boxity
+unboxedWins Boxed Boxed = Boxed
+unboxedWins _     !_    = Unboxed
+
+lubBoxity :: Boxity -> Boxity -> Boxity
+-- See Note [Boxity analysis] for the lattice.
+-- See Note [lubBoxity and plusBoxity].
+lubBoxity = unboxedWins
+
+plusBoxity :: Boxity -> Boxity -> Boxity
+-- See Note [lubBoxity and plusBoxity].
+plusBoxity = boxedWins
+
+{-
+************************************************************************
+*                                                                      *
            Card: Combining Strictness and Usage
 *                                                                      *
 ************************************************************************
@@ -406,20 +660,26 @@ pattern n :* sd <- (viewDmdPair -> (n, sd)) where
 --
 -- See Note [Call demands are relative]
 -- and Note [Demand notation].
+-- See also Note [Why Boxity in SubDemand and not in Demand?].
 data SubDemand
-  = Poly !CardNonOnce
+  = Poly !Boxity !CardNonOnce
   -- ^ Polymorphic demand, the denoted thing is evaluated arbitrarily deep,
-  -- with the specified cardinality at every level.
+  -- with the specified cardinality at every level. The 'Boxity' applies only
+  -- to the outer evaluation context; inner evaluation context can be regarded
+  -- as 'Boxed'. See Note [Boxity in Poly] for why we want it to carry 'Boxity'.
   -- Expands to 'Call' via 'viewCall' and to 'Prod' via 'viewProd'.
   --
-  -- @Poly n@ is semantically equivalent to @Prod [n :* Poly n, ...]@ or
-  -- @Call n (Poly n)@. 'mkCall' and 'mkProd' do these rewrites.
+  -- @Poly b n@ is semantically equivalent to @Prod b [n :* Poly Boxed n, ...]@
+  -- or @Call n (Poly Boxed n)@. 'viewCall' and 'viewProd' do these rewrites.
   --
-  -- In Note [Demand notation]: @L === P(L,L,...)@ and @L === CL(L)@,
-  --                            @B === P(B,B,...)@ and @B === CB(B)@, and so on.
+  -- In Note [Demand notation]: @L  === P(L,L,...)@  and @L  === CL(L)@,
+  --                            @B  === P(B,B,...)@  and @B  === CB(B)@,
+  --                            @!A === !P(A,A,...)@ and @!A === !CA(A)@,
+  --                            and so on.
   --
-  -- We only really use 'Poly' with 'C_10' (B), 'C_00' (A), 'C_0N' (L) and
-  -- sometimes 'C_1N' (S), hence 'CardNonOnce'.
+  -- 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'.
   | Call !CardNonAbs !SubDemand
   -- ^ @Call n sd@ describes the evaluation context of @n@ function
   -- applications, where every individual result is evaluated according to @sd@.
@@ -429,53 +689,68 @@ data SubDemand
   -- expressed with 'Poly'.
   -- Used only for values of function type. Use the smart constructor 'mkCall'
   -- whenever possible!
-  | Prod ![Demand]
-  -- ^ @Prod ds@ describes the evaluation context of a case scrutinisation
+  | 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@.
-  deriving Eq
+  -- 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
+  d1 == d2 = case d1 of
+    Prod b1 ds1
+      | Just (b2, ds2) <- viewProd (length ds1) d2 -> b1 == b2 && ds1 == ds2
+    Call n1 sd1
+      | Just (n2, sd2) <- viewCall d2              -> n1 == n2 && sd1 == sd2
+    Poly b1 n1
+      | Poly b2 n2 <- d2                           -> b1 == b2 && n1 == n2
+    _                                              -> False
 
-poly00, poly0N, poly1N, poly10 :: SubDemand
 topSubDmd, botSubDmd, seqSubDmd :: SubDemand
-poly00 = Poly C_00
-poly0N = Poly C_0N
-poly1N = Poly C_1N
-poly10 = Poly C_10
-topSubDmd = poly0N
-botSubDmd = poly10
-seqSubDmd = poly00
-
-polyDmd :: CardNonOnce -> Demand
-polyDmd C_00 = AbsDmd
-polyDmd C_10 = BotDmd
-polyDmd C_0N = C_0N :* poly0N
-polyDmd C_1N = C_1N :* poly1N
-polyDmd c    = pprPanic "non-once Card" (ppr c)
+topSubDmd = Poly   Boxed C_0N
+botSubDmd = Poly Unboxed C_10
+seqSubDmd = Poly Unboxed C_00
+
+-- | The uniform field demand when viewing a 'Poly' as a 'Prod', as in
+-- 'viewProd'.
+polyFieldDmd :: CardNonOnce -> Demand
+polyFieldDmd C_00 = AbsDmd
+polyFieldDmd C_10 = BotDmd
+polyFieldDmd C_0N = topDmd
+polyFieldDmd n    = C_1N :* Poly Boxed C_1N & assertPpr (isCardNonOnce n) (ppr n)
 
 -- | A smart constructor for 'Prod', applying rewrite rules along the semantic
--- equality @Prod [polyDmd n, ...] === polyDmd n@, simplifying to 'Poly'
--- 'SubDemand's when possible. Note that this degrades boxity information! E.g. a
--- polymorphic demand will never unbox.
-mkProd :: [Demand] -> SubDemand
-mkProd [] = seqSubDmd
--- We only want to simplify absent and bottom demands and unbox the others.
--- See also Note [L should win] and Note [Don't optimise LP(L,L,...) to L].
-mkProd ds
-  | all (== AbsDmd) ds = seqSubDmd
-  | all (== BotDmd) ds = botSubDmd
-  | otherwise          = Prod ds
+-- 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)@ (e.g., arguments @Unboxed@, @[L,L]@) to @!L@
+--   * Does not rewrite @P(1L)@, @P(L!L)@ or @P(L,A)@
+--
+mkProd :: Boxity -> [Demand] -> SubDemand
+mkProd b ds
+  | all (== AbsDmd) ds = Poly b C_00
+  | all (== BotDmd) ds = Poly b C_10
+  | dmd@(n :* Poly Boxed m):_ <- ds  -- don't rewrite P(L!L)
+  , n == m                           -- don't rewrite P(1L)
+  , all (== dmd) ds                  -- don't rewrite P(L,A)
+  = Poly b n
+  | otherwise          = Prod b ds
 
 -- | @viewProd n sd@ interprets @sd@ as a 'Prod' of arity @n@, expanding 'Poly'
 -- demands as necessary.
-viewProd :: Arity -> SubDemand -> Maybe [Demand]
+viewProd :: Arity -> SubDemand -> Maybe (Boxity, [Demand])
 -- It's quite important that this function is optimised well;
--- it is used by lubSubDmd and plusSubDmd. Note the strict
--- application to 'polyDmd':
-viewProd n (Prod ds)   | ds `lengthIs` n = Just ds
+-- it is used by lubSubDmd and plusSubDmd.
+viewProd n (Prod b ds)
+  | ds `lengthIs` n = Just (b, 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 n (Poly card)                   = Just $! (replicate n $! polyDmd card)
-viewProd _ _                             = Nothing
+viewProd n (Poly b card)
+  | let !ds = replicate n $! polyFieldDmd card
+  = Just (b, ds)
+viewProd _ _
+  = Nothing
 {-# INLINE viewProd #-} -- we want to fuse away the replicate and the allocation
                         -- for Arity. Otherwise, #18304 bites us.
 
@@ -483,38 +758,54 @@ viewProd _ _                             = Nothing
 -- equality @Call n (Poly n) === Poly n@, simplifying to 'Poly' 'SubDemand's
 -- when possible.
 mkCall :: CardNonAbs -> SubDemand -> SubDemand
-mkCall C_1N sd@(Poly C_1N) = sd
-mkCall C_0N sd@(Poly C_0N) = sd
-mkCall n    cd             = assertPpr (isCardNonAbs n) (ppr n $$ ppr cd) $
-                             Call n cd
+mkCall C_1N sd@(Poly Boxed C_1N) = sd
+mkCall C_0N sd@(Poly Boxed C_0N) = sd
+mkCall n    cd               = assertPpr (isCardNonAbs n) (ppr n $$ ppr cd) $
+                               Call n cd
+
+-- | @viewCall sd@ interprets @sd@ as a 'Call', expanding 'Poly' subdemands as
+-- necessary.
+viewCall :: SubDemand -> Maybe (Card, SubDemand)
+viewCall (Call n sd) = Just (n :: Card, sd)
+viewCall (Poly _ n)  = Just (n :: Card, Poly Boxed n)
+viewCall _           = Nothing
 
 topDmd, absDmd, botDmd, seqDmd :: Demand
-topDmd = polyDmd C_0N
+topDmd = C_0N :* topSubDmd
 absDmd = AbsDmd
 botDmd = BotDmd
 seqDmd = C_11 :* seqSubDmd
 
+-- | Sets 'Boxity' to 'Unboxed' for non-'Call' sub-demands.
+unboxSubDemand :: SubDemand -> SubDemand
+unboxSubDemand (Poly _ n)  = Poly Unboxed n
+unboxSubDemand (Prod _ ds) = mkProd Unboxed ds
+unboxSubDemand sd@Call{}   = sd
+
 -- | Denotes '∪' on 'SubDemand'.
 lubSubDmd :: SubDemand -> SubDemand -> SubDemand
 -- Handle botSubDmd (just an optimisation, the general case would do the same)
-lubSubDmd (Poly C_10) d2          = d2
-lubSubDmd d1          (Poly C_10) = d1
+lubSubDmd (Poly Unboxed C_10) d2                  = d2
+lubSubDmd d1                  (Poly Unboxed C_10) = d1
 -- Handle Prod
-lubSubDmd (Prod ds1) (Poly n2)  = Prod $ strictMap (lubDmd (polyDmd n2)) ds1
-lubSubDmd (Prod ds1) (Prod ds2)
-  | equalLength ds1 ds2         = Prod $ strictZipWith lubDmd ds1 ds2
+lubSubDmd (Prod b1 ds1) (Poly b2 n2)
+  | let !d = polyFieldDmd n2
+  = mkProd (lubBoxity b1 b2) (strictMap (lubDmd d) ds1)
+lubSubDmd (Prod b1 ds1) (Prod b2 ds2)
+  | equalLength ds1 ds2
+  = mkProd (lubBoxity b1 b2) (strictZipWith lubDmd ds1 ds2)
 -- Handle Call
-lubSubDmd (Call n1 sd1) (Poly n2)
+lubSubDmd (Call n1 sd1) sd2@(Poly _ n2)
   -- See Note [Call demands are relative]
   | isAbs n2  = mkCall (lubCard n2 n1) sd1
-  | otherwise = mkCall (lubCard n2 n1) (lubSubDmd sd1 (Poly n2))
+  | otherwise = mkCall (lubCard n2 n1) (lubSubDmd sd1 sd2)
 lubSubDmd (Call n1 d1)  (Call n2 d2)
   | otherwise = mkCall (lubCard n1 n2) (lubSubDmd d1 d2)
 -- Handle Poly. Exploit reflexivity (so we'll match the Prod or Call cases again).
-lubSubDmd (Poly n1)  (Poly n2) = Poly (lubCard n1 n2)
-lubSubDmd sd1@Poly{} sd2       = lubSubDmd sd2 sd1
+lubSubDmd (Poly b1 n1)  (Poly b2 n2) = Poly (lubBoxity b1 b2) (lubCard n1 n2)
+lubSubDmd sd1@Poly{}    sd2          = lubSubDmd sd2 sd1
 -- Otherwise (Call `lub` Prod) return Top
-lubSubDmd _          _         = topSubDmd
+lubSubDmd _             _            = topSubDmd
 
 -- | Denotes '∪' on 'Demand'.
 lubDmd :: Demand -> Demand -> Demand
@@ -523,24 +814,27 @@ lubDmd (n1 :* sd1) (n2 :* sd2) = lubCard n1 n2 :* lubSubDmd sd1 sd2
 -- | Denotes '+' on 'SubDemand'.
 plusSubDmd :: SubDemand -> SubDemand -> SubDemand
 -- Handle seqSubDmd (just an optimisation, the general case would do the same)
-plusSubDmd (Poly C_00) d2          = d2
-plusSubDmd d1          (Poly C_00) = d1
+plusSubDmd (Poly Unboxed C_00) d2                  = d2
+plusSubDmd d1                  (Poly Unboxed C_00) = d1
 -- Handle Prod
-plusSubDmd (Prod ds1) (Poly n2)  = Prod $ strictMap (plusDmd (polyDmd n2)) ds1
-plusSubDmd (Prod ds1) (Prod ds2)
-  | equalLength ds1 ds2          = Prod $ strictZipWith plusDmd ds1 ds2
+plusSubDmd (Prod b1 ds1) (Poly b2 n2)
+  | let !d = polyFieldDmd n2
+  = mkProd (plusBoxity b1 b2) (strictMap (plusDmd d) ds1)
+plusSubDmd (Prod b1 ds1) (Prod b2 ds2)
+  | equalLength ds1 ds2
+  = mkProd (plusBoxity b1 b2) (strictZipWith plusDmd ds1 ds2)
 -- Handle Call
-plusSubDmd (Call n1 d1) (Poly n2)
+plusSubDmd (Call n1 sd1) sd2@(Poly _ n2)
   -- See Note [Call demands are relative]
-  | isAbs n2  = mkCall (plusCard n2 n1) d1
-  | otherwise = mkCall (plusCard n2 n1) (lubSubDmd d1 (Poly n2))
-plusSubDmd (Call n1 d1) (Call n2 d2)
-  | otherwise = mkCall (plusCard n1 n2) (lubSubDmd d1 d2)
--- Handle Poly. Exploit (so we'll match the Prod or Call cases again).
-plusSubDmd (Poly n1)  (Poly n2) = Poly (plusCard n1 n2)
-plusSubDmd sd1@Poly{} sd2       = plusSubDmd sd2 sd1
+  | isAbs n2  = mkCall (plusCard n2 n1) sd1
+  | otherwise = mkCall (plusCard n2 n1) (lubSubDmd sd1 sd2)
+plusSubDmd (Call n1 sd1) (Call n2 sd2)
+  | otherwise = mkCall (plusCard n1 n2) (lubSubDmd sd1 sd2)
+-- Handle Poly. Exploit reflexivity (so we'll match the Prod or Call cases again).
+plusSubDmd (Poly b1 n1) (Poly b2 n2) = Poly (plusBoxity b1 b2) (plusCard n1 n2)
+plusSubDmd sd1@Poly{}   sd2          = plusSubDmd sd2 sd1
 -- Otherwise (Call `lub` Prod) return Top
-plusSubDmd _         _         = topSubDmd
+plusSubDmd _            _            = topSubDmd
 
 -- | Denotes '+' on 'Demand'.
 plusDmd :: Demand -> Demand -> Demand
@@ -549,11 +843,11 @@ plusDmd (n1 :* sd1) (n2 :* sd2) = plusCard n1 n2 :* plusSubDmd sd1 sd2
 multSubDmd :: Card -> SubDemand -> SubDemand
 multSubDmd C_11 sd           = sd
 multSubDmd C_00 _            = seqSubDmd
-multSubDmd C_10 (Poly n)     = if isStrict n then botSubDmd else seqSubDmd
+multSubDmd C_10 (Poly _ n)   = if isStrict n then botSubDmd else seqSubDmd
 multSubDmd C_10 (Call n _)   = if isStrict n then botSubDmd else seqSubDmd
-multSubDmd n    (Poly m)     = Poly (multCard n m)
+multSubDmd n    (Poly b m)   = Poly b (multCard n m)
 multSubDmd n    (Call n' sd) = mkCall (multCard n n') sd -- See Note [Call demands are relative]
-multSubDmd n    (Prod ds)    = Prod (strictMap (multDmd n) ds)
+multSubDmd n    (Prod b ds)  = mkProd b (strictMap (multDmd n) ds)
 
 multDmd :: Card -> Demand -> Demand
 -- The first two lines compute the same result as the last line, but won't
@@ -578,11 +872,6 @@ isStrictDmd (n :* _) = isStrict n
 isStrUsedDmd :: Demand -> Bool
 isStrUsedDmd (n :* _) = isStrict n && not (isAbs n)
 
-isSeqDmd :: Demand -> Bool
-isSeqDmd (C_11 :* sd) = sd == seqSubDmd
-isSeqDmd (C_1N :* sd) = sd == seqSubDmd
-isSeqDmd _            = False
-
 -- | Is the value used at most once?
 isUsedOnceDmd :: Demand -> Bool
 isUsedOnceDmd (n :* _) = isUsedOnce n
@@ -602,9 +891,9 @@ isWeakDmd dmd@(n :* _) = not (isStrict n) && is_plus_idem_dmd dmd
     is_plus_idem_dmd BotDmd    = True
     is_plus_idem_dmd (n :* sd) = is_plus_idem_card n && is_plus_idem_sub_dmd sd
     -- is_plus_idem_sub_dmd sd = plusSubDmd sd sd == sd
-    is_plus_idem_sub_dmd (Poly n)   = assert (isCardNonOnce n) True
-    is_plus_idem_sub_dmd (Prod ds)  = all is_plus_idem_dmd ds
-    is_plus_idem_sub_dmd (Call n _) = is_plus_idem_card n -- See Note [Call demands are relative]
+    is_plus_idem_sub_dmd (Poly _ n)  = assert (isCardNonOnce n) True
+    is_plus_idem_sub_dmd (Prod _ ds) = all is_plus_idem_dmd ds
+    is_plus_idem_sub_dmd (Call n _)  = is_plus_idem_card n -- See Note [Call demands are relative]
 
 evalDmd :: Demand
 evalDmd = C_1N :* topSubDmd
@@ -637,7 +926,7 @@ oneifyDmd (n :* sd) = oneifyCard n :* sd
 
 -- | Make a 'Demand' evaluated at-least-once (e.g. strict).
 strictifyDmd :: Demand -> Demand
-strictifyDmd AbsDmd    = BotDmd
+strictifyDmd AbsDmd    = seqDmd
 strictifyDmd BotDmd    = BotDmd
 strictifyDmd (n :* sd) = plusCard C_10 n :* sd
 
@@ -646,17 +935,11 @@ strictifyDmd (n :* sd) = plusCard C_10 n :* sd
 -- 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 ty (n :* Prod ds)
+strictifyDictDmd ty (n :* Prod b ds)
   | not (isAbs n)
   , Just field_tys <- as_non_newtype_dict ty
-  = C_1N :* -- main idea: ensure it's strict
-      if all (not . isAbsDmd) ds
-        then topSubDmd -- abstract to strict w/ arbitrary component use,
-                         -- since this smells like reboxing; results in CBV
-                         -- boxed
-                         --
-                         -- TODO revisit this if we ever do boxity analysis
-        else Prod (zipWith strictifyDictDmd field_tys ds)
+  = C_1N :* mkProd b (zipWith strictifyDictDmd field_tys 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
@@ -678,13 +961,6 @@ mkCalledOnceDmd sd = mkCall C_11 sd
 mkCalledOnceDmds :: Arity -> SubDemand -> SubDemand
 mkCalledOnceDmds arity sd = iterate mkCalledOnceDmd sd !! arity
 
--- | @viewCall sd@ interprets @sd@ as a 'Call', expanding 'TopSubDmd' and
--- 'SeqSubDmd' as necessary.
-viewCall :: SubDemand -> Maybe (Card, SubDemand)
-viewCall (Call n sd) = Just (n :: Card, sd)
-viewCall (Poly n)    = Just (n :: Card, Poly n)
-viewCall _           = Nothing
-
 -- | Peels one call level from the sub-demand, and also returns how many
 -- times we entered the lambda body.
 peelCallDmd :: SubDemand -> (Card, SubDemand)
@@ -706,15 +982,6 @@ mkWorkerDemand n = C_01 :* go n
   where go 0 = topSubDmd
         go n = Call C_01 $ go (n-1)
 
--- | Precondition: The SubDemand is not a Call
-addCaseBndrDmd :: SubDemand -- On the case binder
-               -> [Demand]  -- On the components of the constructor
-               -> [Demand]  -- Final demands for the components of the constructor
-addCaseBndrDmd sd alt_dmds
-  -- See Note [Demand on case-alternative binders]
-  | Prod ds <- plusSubDmd sd (Prod alt_dmds) = ds
-  | otherwise                                = alt_dmds
-
 argsOneShots :: DmdSig -> Arity -> [[OneShotInfo]]
 -- ^ See Note [Computing one-shot info]
 argsOneShots (DmdSig (DmdType _ arg_ds _)) n_val_args
@@ -810,77 +1077,6 @@ is hurt and we can assume that the nested demand is 'botSubDmd'. That ensures
 that @g@ above actually gets the @1P(L)@ demand on its second pair component,
 rather than the lazy @MP(L)@ if we 'lub'bed with an absent demand.
 
-Note [Demand on case-alternative binders]
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-The demand on a binder in a case alternative comes
-  (a) From the demand on the binder itself
-  (b) From the demand on the case binder
-Forgetting (b) led directly to #10148.
-
-Example. Source code:
-  f x@(p,_) = if p then foo x else True
-
-  foo (p,True) = True
-  foo (p,q)    = foo (q,p)
-
-After strictness analysis:
-  f = \ (x_an1 [Dmd=1P(1L,ML)] :: (Bool, Bool)) ->
-      case x_an1
-      of wild_X7 [Dmd=MP(ML,ML)]
-      { (p_an2 [Dmd=1L], ds_dnz [Dmd=A]) ->
-      case p_an2 of _ {
-        False -> GHC.Types.True;
-        True -> foo wild_X7 }
-
-It's true that ds_dnz is *itself* absent, but the use of wild_X7 means
-that it is very much alive and demanded.  See #10148 for how the
-consequences play out.
-
-This is needed even for non-product types, in case the case-binder
-is used but the components of the case alternative are not.
-
-Note [Don't optimise LP(L,L,...) to L]
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-These two SubDemands:
-   LP(L,L) (@Prod [topDmd, topDmd]@)   and   L (@topSubDmd@)
-are semantically equivalent, but we do not turn the former into
-the latter, for a regrettable-subtle reason.  Consider
-  f p1@(x,y) = (y,x)
-  g h p2@(_,_) = h p
-We want to unbox @p1@ of @f@, but not @p2@ of @g@, because @g@ only uses
-@p2@ boxed and we'd have to rebox. So we give @p1@ demand LP(L,L) and @p2@
-demand @L@ to inform 'GHC.Core.Opt.WorkWrap.Utils.wantToUnboxArg', which will
-say "unbox" for @p1@ and "don't unbox" for @p2@.
-
-So the solution is: don't aggressively collapse @Prod [topDmd, topDmd]@ to
-@topSubDmd@; instead leave it as-is. In effect we are using the UseDmd to do a
-little bit of boxity analysis.  Not very nice.
-
-Note [L should win]
-~~~~~~~~~~~~~~~~~~~
-Both in 'lubSubDmd' and 'plusSubDmd' we want @L `plusSubDmd` LP(..))@ to be @L@.
-Why?  Because U carries the implication the whole thing is used, box and all,
-so we don't want to w/w it, cf. Note [Don't optimise LP(L,L,...) to L].
-If we use it both boxed and unboxed, then we are definitely using the box,
-and so we are quite likely to pay a reboxing cost. So we make U win here.
-TODO: Investigate why since 2013, we don't.
-
-Example is in the Buffer argument of GHC.IO.Handle.Internals.writeCharBuffer
-
-Baseline: (A) Not making Used win (LP(..) wins)
-Compare with: (B) making Used win for lub and both
-
-            Min          -0.3%     -5.6%    -10.7%    -11.0%    -33.3%
-            Max          +0.3%    +45.6%    +11.5%    +11.5%     +6.9%
- Geometric Mean          -0.0%     +0.5%     +0.3%     +0.2%     -0.8%
-
-Baseline: (B) Making L win for both lub and both
-Compare with: (C) making L win for plus, but LP(..) win for lub
-
-            Min          -0.1%     -0.3%     -7.9%     -8.0%     -6.5%
-            Max          +0.1%     +1.0%    +21.0%    +21.0%     +0.5%
- Geometric Mean          +0.0%     +0.0%     -0.0%     -0.1%     -0.1%
-
 Note [Computing one-shot info]
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 Consider a call
@@ -892,6 +1088,57 @@ Then argsOneShots returns a [[OneShotInfo]] of
 The occurrence analyser propagates this one-shot infor to the
 binders \pqr and \xyz;
 see Note [Use 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. 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
+```
+(Caveat: Since Unboxed wins in lubBoxity, we'll unbox here anyway.)
+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 `C1(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].
 -}
 
 {- *********************************************************************
@@ -1289,6 +1536,9 @@ plusDmdType (DmdType fv1 ds1 r1) (fv2, t2)
     -- See Note [Asymmetry of 'plus*']
     -- 'plus' takes the argument/result info from its *first* arg,
     -- using its second arg just for its free-var info.
+  | isEmptyVarEnv fv2, defaultFvDmd t2 == absDmd
+  = DmdType fv1 ds1 (r1 `plusDivergence` t2) -- a very common case that is much more efficient
+  | otherwise
   = DmdType (plusVarEnv_CD plusDmd fv1 (defaultFvDmd r1) fv2 (defaultFvDmd t2))
             ds1
             (r1 `plusDivergence` t2)
@@ -1566,10 +1816,10 @@ newtype DmdSig
   deriving Eq
 
 -- | Turns a 'DmdType' computed for the particular 'Arity' into a 'DmdSig'
--- unleashable at that arity. See Note [Understanding DmdType and DmdSig]
+-- unleashable at that arity. See Note [Understanding DmdType and DmdSig].
 mkDmdSigForArity :: Arity -> DmdType -> DmdSig
 mkDmdSigForArity arity dmd_ty@(DmdType fvs args div)
-  | arity < dmdTypeDepth dmd_ty = DmdSig (DmdType fvs (take arity args) div)
+  | arity < dmdTypeDepth dmd_ty = DmdSig $ DmdType fvs (take arity args) div
   | otherwise                   = DmdSig (etaExpandDmdType arity dmd_ty)
 
 mkClosedDmdSig :: [Demand] -> Divergence -> DmdSig
@@ -1671,26 +1921,28 @@ dmdTransformDataConSig arity sd = case go arity sd of
   Just dmds -> DmdType emptyDmdEnv dmds topDiv
   Nothing   -> nopDmdType -- Not saturated
   where
-    go 0 sd             = viewProd arity sd
+    go 0 sd             = snd <$> viewProd arity sd
     go n (Call C_11 sd) = go (n-1) sd  -- strict calls only!
     go _ _              = Nothing
 
 -- | 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 and it's unclear how
--- it could without additional parameters.
-dmdTransformDictSelSig (DmdSig (DmdType _ [(_ :* sig_sd)] _)) call_sd
+-- NB: This currently doesn't handle newtype dictionaries.
+-- It should simply apply call_sd directly to the dictionary, I suppose.
+dmdTransformDictSelSig (DmdSig (DmdType _ [_ :* prod] _)) call_sd
    | (n, sd') <- peelCallDmd call_sd
-   , Prod sig_ds  <- sig_sd
+   , Prod _ sig_ds <- prod
    = multDmdType n $
-     DmdType emptyDmdEnv [C_11 :* Prod (map (enhance sd') sig_ds)] topDiv
+     DmdType emptyDmdEnv [C_11 :* mkProd Unboxed (map (enhance sd') sig_ds)] topDiv
    | otherwise
    = nopDmdType -- See Note [Demand transformer for a dictionary selector]
   where
-    enhance sd old | isAbsDmd old = old
-                   | otherwise    = C_11 :* sd  -- This is the one!
-
+    enhance _  AbsDmd   = AbsDmd
+    enhance _  BotDmd   = BotDmd
+    enhance sd _dmd_var = C_11 :* sd  -- This is the one!
+                                      -- C_11, because we multiply with n above
 dmdTransformDictSelSig sig sd = pprPanic "dmdTransformDictSelSig: no args" (ppr sig $$ ppr sd)
 
 {-
@@ -1751,16 +2003,49 @@ 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,1C1(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' by the demand 'd'.
+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.
+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
@@ -1818,10 +2103,10 @@ kill_usage kfs (n :* sd) = kill_usage_card kfs n :* kill_usage_sd kfs sd
 
 kill_usage_sd :: KillFlags -> SubDemand -> SubDemand
 kill_usage_sd kfs (Call n sd)
-  | kf_called_once kfs      = mkCall (lubCard C_1N n) (kill_usage_sd kfs sd)
-  | otherwise               = mkCall n                       (kill_usage_sd kfs sd)
-kill_usage_sd kfs (Prod ds) = Prod (map (kill_usage kfs) ds)
-kill_usage_sd _   sd        = sd
+  | kf_called_once kfs        = mkCall (lubCard C_1N n) (kill_usage_sd kfs sd)
+  | otherwise                 = mkCall n                (kill_usage_sd kfs sd)
+kill_usage_sd kfs (Prod b ds) = mkProd b (map (kill_usage kfs) ds)
+kill_usage_sd _   sd          = sd
 
 {- *********************************************************************
 *                                                                      *
@@ -1843,12 +2128,22 @@ trimToType BotDmd    _  = BotDmd
 trimToType (n :* sd) ts
   = n :* go sd ts
   where
-    go (Prod ds)   (TsProd tss)
-      | equalLength ds tss    = Prod (zipWith trimToType ds tss)
+    go (Prod b ds) (TsProd tss)
+      | equalLength ds tss    = mkProd b (zipWith trimToType ds tss)
     go (Call n sd) (TsFun ts) = mkCall n (go sd ts)
     go sd@Poly{}   _          = sd
     go _           _          = topSubDmd
 
+-- | Drop all boxity
+trimBoxity :: Demand -> Demand
+trimBoxity AbsDmd    = AbsDmd
+trimBoxity BotDmd    = BotDmd
+trimBoxity (n :* sd) = n :* go sd
+  where
+    go (Poly _ n)  = Poly Boxed n
+    go (Prod _ ds) = mkProd Boxed (map trimBoxity ds)
+    go (Call n sd) = mkCall n $ go sd
+
 {-
 ************************************************************************
 *                                                                      *
@@ -1863,9 +2158,9 @@ seqDemand BotDmd    = ()
 seqDemand (_ :* sd) = seqSubDemand sd
 
 seqSubDemand :: SubDemand -> ()
-seqSubDemand (Prod ds)   = seqDemandList ds
+seqSubDemand (Prod _ ds) = seqDemandList ds
 seqSubDemand (Call _ sd) = seqSubDemand sd
-seqSubDemand (Poly _)    = ()
+seqSubDemand (Poly _ _)  = ()
 
 seqDemandList :: [Demand] -> ()
 seqDemandList = foldr (seq . seqDemand) ()
@@ -1905,19 +2200,21 @@ 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}
+  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",
-                                                  in code @polyDmd card@
+        |  card                     abbreviation: Same as "card card"
 
-  sd   ::= card                     @Poly card@
-        |  P(d,d,..)                @Prod [d1,d2,..]@
+  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',
@@ -1957,22 +2254,26 @@ instance Outputable Card where
 
 -- | See Note [Demand notation]
 instance Outputable Demand where
-  ppr AbsDmd              = char 'A'
-  ppr BotDmd              = char 'B'
-  ppr (C_0N :* Poly C_0N) = char 'L' -- Print LL as just L
-  ppr (C_1N :* Poly C_1N) = char 'S' -- Dito SS
-  ppr (n :* sd)           = ppr n <> ppr sd
+  ppr AbsDmd                    = char 'A'
+  ppr BotDmd                    = char 'B'
+  ppr (C_0N :* Poly Boxed C_0N) = char 'L' -- Print LL as just L
+  ppr (C_1N :* Poly Boxed C_1N) = char 'S' -- Dito SS
+  ppr (n :* sd)                 = ppr n <> ppr sd
 
 -- | See Note [Demand notation]
 instance Outputable SubDemand where
-  ppr (Poly sd)   = ppr sd
+  ppr (Poly b sd) = pp_boxity b <> ppr sd
   ppr (Call n sd) = char 'C' <> ppr n <> parens (ppr sd)
-  ppr (Prod ds)   = char 'P' <> parens (fields ds)
+  ppr (Prod b ds) = pp_boxity b <> char 'P' <> parens (fields ds)
     where
       fields []     = empty
       fields [x]    = ppr x
       fields (x:xs) = ppr x <> char ',' <> fields xs
 
+pp_boxity :: Boxity -> SDoc
+pp_boxity Unboxed = char '!'
+pp_boxity _       = empty
+
 instance Outputable Divergence where
   ppr Diverges = char 'b' -- for (b)ottom
   ppr ExnOrDiv = char 'x' -- for e(x)ception
@@ -2026,15 +2327,15 @@ instance Binary Demand where
     _    -> (n :*) <$> get bh
 
 instance Binary SubDemand where
-  put_ bh (Poly sd)   = putByte bh 0 *> put_ bh sd
+  put_ bh (Poly b sd) = putByte bh 0 *> put_ bh b *> put_ bh sd
   put_ bh (Call n sd) = putByte bh 1 *> put_ bh n *> put_ bh sd
-  put_ bh (Prod ds)   = putByte bh 2 *> put_ bh ds
+  put_ bh (Prod b ds) = putByte bh 2 *> put_ bh b *> put_ bh ds
   get bh = do
     h <- getByte bh
     case h of
-      0 -> Poly <$> get bh
+      0 -> Poly <$> get bh <*> get bh
       1 -> mkCall <$> get bh <*> get bh
-      2 -> Prod <$> get bh
+      2 -> Prod <$> get bh <*> get bh
       _ -> pprPanic "Binary:SubDemand" (ppr (fromIntegral h :: Int))
 
 instance Binary DmdSig where
diff --git a/compiler/GHC/Types/Id/Make.hs b/compiler/GHC/Types/Id/Make.hs
index e52c12ce71..9955a025ea 100644
--- a/compiler/GHC/Types/Id/Make.hs
+++ b/compiler/GHC/Types/Id/Make.hs
@@ -516,9 +516,12 @@ mkDictSelId name clas
 
     strict_sig = mkClosedDmdSig [arg_dmd] topDiv
     arg_dmd | new_tycon = evalDmd
-            | otherwise = C_1N :*
-                          Prod [ if name == sel_name then evalDmd else absDmd
-                               | sel_name <- sel_names ]
+            | otherwise = C_1N :* mkProd Unboxed dict_field_dmds
+            where
+              -- The evalDmd below is just a placeholder and will be replaced in
+              -- GHC.Types.Demand.dmdTransformDictSel
+              dict_field_dmds = [ if name == sel_name then evalDmd else absDmd
+                                | sel_name <- sel_names ]
 
 mkDictSelRhs :: Class
              -> Int         -- 0-indexed selector among (superclasses ++ methods)
diff --git a/compiler/GHC/Utils/Misc.hs b/compiler/GHC/Utils/Misc.hs
index 05e8365745..fbf52d1bdb 100644
--- a/compiler/GHC/Utils/Misc.hs
+++ b/compiler/GHC/Utils/Misc.hs
@@ -79,7 +79,7 @@ module GHC.Utils.Misc (
         transitiveClosure,
 
         -- * Strictness
-        seqList, strictMap, strictZipWith,
+        seqList, strictMap, strictZipWith, strictZipWith3,
 
         -- * Module names
         looksLikeModuleName,
@@ -991,8 +991,8 @@ seqList [] b = b
 seqList (x:xs) b = x `seq` seqList xs b
 
 strictMap :: (a -> b) -> [a] -> [b]
-strictMap _ [] = []
-strictMap f (x : xs) =
+strictMap _ []     = []
+strictMap f (x:xs) =
   let
     !x' = f x
     !xs' = strictMap f xs
@@ -1000,15 +1000,26 @@ strictMap f (x : xs) =
     x' : xs'
 
 strictZipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
-strictZipWith _ [] _ = []
-strictZipWith _ _ [] = []
-strictZipWith f (x : xs) (y: ys) =
+strictZipWith _ []     _      = []
+strictZipWith _ _      []     = []
+strictZipWith f (x:xs) (y:ys) =
   let
     !x' = f x y
     !xs' = strictZipWith f xs ys
   in
     x' : xs'
 
+strictZipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
+strictZipWith3 _ []     _      _      = []
+strictZipWith3 _ _      []     _      = []
+strictZipWith3 _ _      _      []     = []
+strictZipWith3 f (x:xs) (y:ys) (z:zs) =
+  let
+    !x' = f x y z
+    !xs' = strictZipWith3 f xs ys zs
+  in
+    x' : xs'
+
 
 -- Module names: