Linear types (#15981)

This is the first step towards implementation of the linear types proposal
(https://github.com/ghc-proposals/ghc-proposals/pull/111).

It features

* A language extension -XLinearTypes
* Syntax for linear functions in the surface language
* Linearity checking in Core Lint, enabled with -dlinear-core-lint
* Core-to-core passes are mostly compatible with linearity
* Fields in a data type can be linear or unrestricted; linear fields
  have multiplicity-polymorphic constructors.
  If -XLinearTypes is disabled, the GADT syntax defaults to linear fields

The following items are not yet supported:

* a # m -> b syntax (only prefix FUN is supported for now)
* Full multiplicity inference (multiplicities are really only checked)
* Decent linearity error messages
* Linear let, where, and case expressions in the surface language
  (each of these currently introduce the unrestricted variant)
* Multiplicity-parametric fields
* Syntax for annotating lambda-bound or let-bound with a multiplicity
* Syntax for non-linear/multiple-field-multiplicity records
* Linear projections for records with a single linear field
* Linear pattern synonyms
* Multiplicity coercions (test LinearPolyType)

A high-level description can be found at
https://ghc.haskell.org/trac/ghc/wiki/LinearTypes/Implementation
Following the link above you will find a description of the changes made to Core.
This commit has been authored by

* Richard Eisenberg
* Krzysztof Gogolewski
* Matthew Pickering
* Arnaud Spiwack

With contributions from:

* Mark Barbone
* Alexander Vershilov

Updates haddock submodule.

10 files changed, 199 insertions, 129 deletions

diff --git a/compiler/GHC/Iface/Env.hs b/compiler/GHC/Iface/Env.hs
index 088bce8d77..09679d0542 100644
--- a/compiler/GHC/Iface/Env.hs
+++ b/compiler/GHC/Iface/Env.hs
@@ -251,7 +251,7 @@ lookupIfaceTyVar (occ, _)
         ; return (lookupFsEnv (if_tv_env lcl) occ) }
 
 lookupIfaceVar :: IfaceBndr -> IfL (Maybe TyCoVar)
-lookupIfaceVar (IfaceIdBndr (occ, _))
+lookupIfaceVar (IfaceIdBndr (_, occ, _))
   = do  { lcl <- getLclEnv
         ; return (lookupFsEnv (if_id_env lcl) occ) }
 lookupIfaceVar (IfaceTvBndr (occ, _))
diff --git a/compiler/GHC/Iface/Ext/Ast.hs b/compiler/GHC/Iface/Ext/Ast.hs
index 24a3aa7c5b..968acbb3c2 100644
--- a/compiler/GHC/Iface/Ext/Ast.hs
+++ b/compiler/GHC/Iface/Ext/Ast.hs
@@ -31,15 +31,17 @@ import GHC.Types.Basic
 import GHC.Data.BooleanFormula
 import GHC.Core.Class             ( FunDep, className, classSCSelIds )
 import GHC.Core.Utils             ( exprType )
-import GHC.Core.ConLike           ( conLikeName )
+import GHC.Core.ConLike           ( conLikeName, ConLike(RealDataCon) )
 import GHC.Core.TyCon             ( TyCon, tyConClass_maybe )
 import GHC.Core.FVs
+import GHC.Core.DataCon           ( dataConNonlinearType )
 import GHC.HsToCore               ( deSugarExpr )
 import GHC.Types.FieldLabel
 import GHC.Hs
 import GHC.Driver.Types
 import GHC.Unit.Module            ( ModuleName, ml_hs_file )
 import GHC.Utils.Monad            ( concatMapM, liftIO )
+import GHC.Types.Id               ( isDataConId_maybe )
 import GHC.Types.Name             ( Name, nameSrcSpan, setNameLoc, nameUnique )
 import GHC.Types.Name.Env         ( NameEnv, emptyNameEnv, extendNameEnv, lookupNameEnv )
 import GHC.Types.SrcLoc
@@ -606,11 +608,14 @@ instance ToHie (Context (Located Var)) where
           let name = case lookupNameEnv m (varName name') of
                 Just var -> var
                 Nothing-> name'
+              ty = case isDataConId_maybe name' of
+                      Nothing -> varType name'
+                      Just dc -> dataConNonlinearType dc
           pure
             [Node
               (mkSourcedNodeInfo org $ NodeInfo S.empty [] $
                 M.singleton (Right $ varName name)
-                            (IdentifierDetails (Just $ varType name')
+                            (IdentifierDetails (Just ty)
                                                (S.singleton context)))
               span
               []]
@@ -646,7 +651,7 @@ evVarsOfTermList (EvTypeable _ ev)  =
   case ev of
     EvTypeableTyCon _ e   -> concatMap evVarsOfTermList e
     EvTypeableTyApp e1 e2 -> concatMap evVarsOfTermList [e1,e2]
-    EvTypeableTrFun e1 e2 -> concatMap evVarsOfTermList [e1,e2]
+    EvTypeableTrFun e1 e2 e3 -> concatMap evVarsOfTermList [e1,e2,e3]
     EvTypeableTyLit e     -> evVarsOfTermList e
 evVarsOfTermList (EvFun{}) = []
 
@@ -718,6 +723,8 @@ instance HiePass p => HasType (LHsExpr (GhcPass p)) where
               HsLit _ l -> Just (hsLitType l)
               HsOverLit _ o -> Just (overLitType o)
 
+              HsConLikeOut _ (RealDataCon con) -> Just (dataConNonlinearType con)
+
               HsLam     _ (MG { mg_ext = groupTy }) -> Just (matchGroupType groupTy)
               HsLamCase _ (MG { mg_ext = groupTy }) -> Just (matchGroupType groupTy)
               HsCase _  _ (MG { mg_ext = groupTy }) -> Just (mg_res_ty groupTy)
@@ -1514,6 +1521,9 @@ instance ToHie (Located (DerivStrategy GhcRn)) where
 instance ToHie (Located OverlapMode) where
   toHie (L span _) = locOnly span
 
+instance ToHie a => ToHie (HsScaled GhcRn a) where
+  toHie (HsScaled w t) = concatM [toHie (arrowToHsType w), toHie t]
+
 instance ToHie (LConDecl GhcRn) where
   toHie (L span decl) = concatM $ makeNode decl span : case decl of
       ConDeclGADT { con_names = names, con_qvars = exp_vars, con_g_ext = imp_vars
@@ -1543,9 +1553,11 @@ instance ToHie (LConDecl GhcRn) where
           rhsScope = combineScopes ctxScope argsScope
           ctxScope = maybe NoScope mkLScope ctx
           argsScope = condecl_scope dets
-    where condecl_scope args = case args of
-            PrefixCon xs -> foldr combineScopes NoScope $ map mkLScope xs
-            InfixCon a b -> combineScopes (mkLScope a) (mkLScope b)
+    where condecl_scope :: HsConDeclDetails p -> Scope
+          condecl_scope args = case args of
+            PrefixCon xs -> foldr combineScopes NoScope $ map (mkLScope . hsScaledThing) xs
+            InfixCon a b -> combineScopes (mkLScope (hsScaledThing a))
+                                          (mkLScope (hsScaledThing b))
             RecCon x -> mkLScope x
 
 instance ToHie (Located [LConDeclField GhcRn]) where
@@ -1657,8 +1669,9 @@ instance ToHie (TScoped (LHsType GhcRn)) where
         [ toHie ty
         , toHie $ TS (ResolvedScopes []) ki
         ]
-      HsFunTy _ a b ->
-        [ toHie a
+      HsFunTy _ w a b ->
+        [ toHie (arrowToHsType w)
+        , toHie a
         , toHie b
         ]
       HsListTy _ a ->
diff --git a/compiler/GHC/Iface/Ext/Types.hs b/compiler/GHC/Iface/Ext/Types.hs
index 3419e441a7..ce6b564b13 100644
--- a/compiler/GHC/Iface/Ext/Types.hs
+++ b/compiler/GHC/Iface/Ext/Types.hs
@@ -141,7 +141,7 @@ data HieType a
   | HAppTy a (HieArgs a)
   | HTyConApp IfaceTyCon (HieArgs a)
   | HForAllTy ((Name, a),ArgFlag) a
-  | HFunTy  a a
+  | HFunTy a a a
   | HQualTy a a           -- ^ type with constraint: @t1 => t2@ (see 'IfaceDFunTy')
   | HLitTy IfaceTyLit
   | HCastTy a
@@ -169,8 +169,9 @@ instance Binary (HieType TypeIndex) where
     putByte bh 3
     put_ bh bndr
     put_ bh a
-  put_ bh (HFunTy a b) = do
+  put_ bh (HFunTy w a b) = do
     putByte bh 4
+    put_ bh w
     put_ bh a
     put_ bh b
   put_ bh (HQualTy a b) = do
@@ -192,7 +193,7 @@ instance Binary (HieType TypeIndex) where
       1 -> HAppTy <$> get bh <*> get bh
       2 -> HTyConApp <$> get bh <*> get bh
       3 -> HForAllTy <$> get bh <*> get bh
-      4 -> HFunTy <$> get bh <*> get bh
+      4 -> HFunTy <$> get bh <*> get bh <*> get bh
       5 -> HQualTy <$> get bh <*> get bh
       6 -> HLitTy <$> get bh
       7 -> HCastTy <$> get bh
diff --git a/compiler/GHC/Iface/Ext/Utils.hs b/compiler/GHC/Iface/Ext/Utils.hs
index b0a6f84404..102f6db656 100644
--- a/compiler/GHC/Iface/Ext/Utils.hs
+++ b/compiler/GHC/Iface/Ext/Utils.hs
@@ -12,6 +12,7 @@ import GHC.Core.Map
 import GHC.Driver.Session    ( DynFlags )
 import GHC.Data.FastString   ( FastString, mkFastString )
 import GHC.Iface.Type
+import GHC.Core.Multiplicity
 import GHC.Types.Name hiding (varName)
 import GHC.Types.Name.Set
 import GHC.Utils.Outputable hiding ( (<>) )
@@ -156,8 +157,8 @@ hieTypeToIface = foldType go
     go (HLitTy l) = IfaceLitTy l
     go (HForAllTy ((n,k),af) t) = let b = (occNameFS $ getOccName n, k)
                                   in IfaceForAllTy (Bndr (IfaceTvBndr b) af) t
-    go (HFunTy a b)     = IfaceFunTy VisArg   a    b
-    go (HQualTy pred b) = IfaceFunTy InvisArg pred b
+    go (HFunTy w a b)   = IfaceFunTy VisArg   w       a    b
+    go (HQualTy pred b) = IfaceFunTy InvisArg many_ty pred b
     go (HCastTy a) = a
     go HCoercionTy = IfaceTyVar "<coercion type>"
     go (HTyConApp a xs) = IfaceTyConApp a (hieToIfaceArgs xs)
@@ -233,12 +234,13 @@ getTypeIndex t
       k <- getTypeIndex (varType v)
       i <- getTypeIndex t
       return $ HForAllTy ((varName v,k),a) i
-    go (FunTy { ft_af = af, ft_arg = a, ft_res = b }) = do
+    go (FunTy { ft_af = af, ft_mult = w, ft_arg = a, ft_res = b }) = do
       ai <- getTypeIndex a
       bi <- getTypeIndex b
+      wi <- getTypeIndex w
       return $ case af of
-                 InvisArg -> HQualTy ai bi
-                 VisArg   -> HFunTy ai bi
+                 InvisArg -> case w of Many -> HQualTy ai bi; _ -> error "Unexpected non-unrestricted predicate"
+                 VisArg   -> HFunTy wi ai bi
     go (LitTy a) = return $ HLitTy $ toIfaceTyLit a
     go (CastTy t _) = do
       i <- getTypeIndex t
diff --git a/compiler/GHC/Iface/Load.hs b/compiler/GHC/Iface/Load.hs
index 37ad1db8fe..53560ca732 100644
--- a/compiler/GHC/Iface/Load.hs
+++ b/compiler/GHC/Iface/Load.hs
@@ -54,7 +54,6 @@ import GHC.Builtin.Names
 import GHC.Builtin.Utils
 import GHC.Builtin.PrimOps    ( allThePrimOps, primOpFixity, primOpOcc )
 import GHC.Types.Id.Make      ( seqId )
-import GHC.Builtin.Types.Prim ( funTyConName )
 import GHC.Core.Rules
 import GHC.Core.TyCon
 import GHC.Types.Annotations
@@ -1060,7 +1059,6 @@ ghcPrimIface
     -- The fixities listed here for @`seq`@ or @->@ should match
     -- those in primops.txt.pp (from which Haddock docs are generated).
     fixities = (getOccName seqId, Fixity NoSourceText 0 InfixR)
-             : (occName funTyConName, funTyFixity)  -- trac #10145
              : mapMaybe mkFixity allThePrimOps
     mkFixity op = (,) (primOpOcc op) <$> primOpFixity op
 
diff --git a/compiler/GHC/Iface/Make.hs b/compiler/GHC/Iface/Make.hs
index b93d46e2d0..53385600ae 100644
--- a/compiler/GHC/Iface/Make.hs
+++ b/compiler/GHC/Iface/Make.hs
@@ -38,6 +38,7 @@ import GHC.Core.Coercion.Axiom
 import GHC.Core.ConLike
 import GHC.Core.DataCon
 import GHC.Core.Type
+import GHC.Core.Multiplicity
 import GHC.StgToCmm.Types (CgInfos (..))
 import GHC.Tc.Utils.TcType
 import GHC.Core.InstEnv
@@ -223,7 +224,7 @@ mkIface_ hsc_env
   = do
     let semantic_mod = canonicalizeHomeModule (hsc_dflags hsc_env) (moduleName this_mod)
         entities = typeEnvElts type_env
-        decls  = [ tyThingToIfaceDecl entity
+        decls  = [ tyThingToIfaceDecl (hsc_dflags hsc_env) entity
                  | entity <- entities,
                    let name = getName entity,
                    not (isImplicitTyThing entity),
@@ -384,12 +385,12 @@ Names too: see Note [Binders in Template Haskell] in "GHC.ThToHs", and
 ************************************************************************
 -}
 
-tyThingToIfaceDecl :: TyThing -> IfaceDecl
-tyThingToIfaceDecl (AnId id)      = idToIfaceDecl id
-tyThingToIfaceDecl (ATyCon tycon) = snd (tyConToIfaceDecl emptyTidyEnv tycon)
-tyThingToIfaceDecl (ACoAxiom ax)  = coAxiomToIfaceDecl ax
-tyThingToIfaceDecl (AConLike cl)  = case cl of
-    RealDataCon dc -> dataConToIfaceDecl dc -- for ppr purposes only
+tyThingToIfaceDecl :: DynFlags -> TyThing -> IfaceDecl
+tyThingToIfaceDecl _ (AnId id)      = idToIfaceDecl id
+tyThingToIfaceDecl _ (ATyCon tycon) = snd (tyConToIfaceDecl emptyTidyEnv tycon)
+tyThingToIfaceDecl _ (ACoAxiom ax)  = coAxiomToIfaceDecl ax
+tyThingToIfaceDecl dflags (AConLike cl)  = case cl of
+    RealDataCon dc -> dataConToIfaceDecl dflags dc -- for ppr purposes only
     PatSynCon ps   -> patSynToIfaceDecl ps
 
 --------------------------
@@ -405,10 +406,10 @@ idToIfaceDecl id
               ifIdInfo    = toIfaceIdInfo (idInfo id) }
 
 --------------------------
-dataConToIfaceDecl :: DataCon -> IfaceDecl
-dataConToIfaceDecl dataCon
+dataConToIfaceDecl :: DynFlags -> DataCon -> IfaceDecl
+dataConToIfaceDecl dflags dataCon
   = IfaceId { ifName      = getName dataCon,
-              ifType      = toIfaceType (dataConUserType dataCon),
+              ifType      = toIfaceType (dataConDisplayType dflags dataCon),
               ifIdDetails = IfVanillaId,
               ifIdInfo    = [] }
 
@@ -555,7 +556,9 @@ tyConToIfaceDecl env tycon
                     ifConUserTvBinders = map toIfaceForAllBndr user_bndrs',
                     ifConEqSpec  = map (to_eq_spec . eqSpecPair) eq_spec,
                     ifConCtxt    = tidyToIfaceContext con_env2 theta,
-                    ifConArgTys  = map (tidyToIfaceType con_env2) arg_tys,
+                    ifConArgTys  =
+                      map (\(Scaled w t) -> (tidyToIfaceType con_env2 w
+                                          , (tidyToIfaceType con_env2 t))) arg_tys,
                     ifConFields  = dataConFieldLabels data_con,
                     ifConStricts = map (toIfaceBang con_env2)
                                        (dataConImplBangs data_con),
diff --git a/compiler/GHC/Iface/Rename.hs b/compiler/GHC/Iface/Rename.hs
index 0c7603c79a..50c73e56a9 100644
--- a/compiler/GHC/Iface/Rename.hs
+++ b/compiler/GHC/Iface/Rename.hs
@@ -557,7 +557,7 @@ rnIfaceConDecl d = do
     let rnIfConEqSpec (n,t) = (,) n <$> rnIfaceType t
     con_eq_spec <- mapM rnIfConEqSpec (ifConEqSpec d)
     con_ctxt <- mapM rnIfaceType (ifConCtxt d)
-    con_arg_tys <- mapM rnIfaceType (ifConArgTys d)
+    con_arg_tys <- mapM rnIfaceScaledType (ifConArgTys d)
     con_fields <- mapM rnFieldLabel (ifConFields d)
     let rnIfaceBang (IfUnpackCo co) = IfUnpackCo <$> rnIfaceCo co
         rnIfaceBang bang = pure bang
@@ -644,7 +644,7 @@ rnIfaceBndrs :: Rename [IfaceBndr]
 rnIfaceBndrs = mapM rnIfaceBndr
 
 rnIfaceBndr :: Rename IfaceBndr
-rnIfaceBndr (IfaceIdBndr (fs, ty)) = IfaceIdBndr <$> ((,) fs <$> rnIfaceType ty)
+rnIfaceBndr (IfaceIdBndr (w, fs, ty)) = IfaceIdBndr <$> ((,,) w fs <$> rnIfaceType ty)
 rnIfaceBndr (IfaceTvBndr tv_bndr) = IfaceTvBndr <$> rnIfaceTvBndr tv_bndr
 
 rnIfaceTvBndr :: Rename IfaceTvBndr
@@ -676,8 +676,8 @@ rnIfaceCo :: Rename IfaceCoercion
 rnIfaceCo (IfaceReflCo ty) = IfaceReflCo <$> rnIfaceType ty
 rnIfaceCo (IfaceGReflCo role ty mco)
   = IfaceGReflCo role <$> rnIfaceType ty <*> rnIfaceMCo mco
-rnIfaceCo (IfaceFunCo role co1 co2)
-    = IfaceFunCo role <$> rnIfaceCo co1 <*> rnIfaceCo co2
+rnIfaceCo (IfaceFunCo role w co1 co2)
+    = IfaceFunCo role <$> rnIfaceCo w <*> rnIfaceCo co1 <*> rnIfaceCo co2
 rnIfaceCo (IfaceTyConAppCo role tc cos)
     = IfaceTyConAppCo role <$> rnIfaceTyCon tc <*> mapM rnIfaceCo cos
 rnIfaceCo (IfaceAppCo co1 co2)
@@ -722,8 +722,8 @@ rnIfaceType (IfaceTyVar   n)   = pure (IfaceTyVar n)
 rnIfaceType (IfaceAppTy t1 t2)
     = IfaceAppTy <$> rnIfaceType t1 <*> rnIfaceAppArgs t2
 rnIfaceType (IfaceLitTy l)         = return (IfaceLitTy l)
-rnIfaceType (IfaceFunTy af t1 t2)
-    = IfaceFunTy af <$> rnIfaceType t1 <*> rnIfaceType t2
+rnIfaceType (IfaceFunTy af w t1 t2)
+    = IfaceFunTy af <$> rnIfaceType w <*> rnIfaceType t1 <*> rnIfaceType t2
 rnIfaceType (IfaceTupleTy s i tks)
     = IfaceTupleTy s i <$> rnIfaceAppArgs tks
 rnIfaceType (IfaceTyConApp tc tks)
@@ -735,6 +735,9 @@ rnIfaceType (IfaceCoercionTy co)
 rnIfaceType (IfaceCastTy ty co)
     = IfaceCastTy <$> rnIfaceType ty <*> rnIfaceCo co
 
+rnIfaceScaledType :: Rename (IfaceMult, IfaceType)
+rnIfaceScaledType (m, t) = (,) <$> rnIfaceType m <*> rnIfaceType t
+
 rnIfaceForAllBndr :: Rename (VarBndr IfaceBndr flag)
 rnIfaceForAllBndr (Bndr tv vis) = Bndr <$> rnIfaceBndr tv <*> pure vis
 
diff --git a/compiler/GHC/Iface/Syntax.hs b/compiler/GHC/Iface/Syntax.hs
index 84e96f0706..2b0fcd2b76 100644
--- a/compiler/GHC/Iface/Syntax.hs
+++ b/compiler/GHC/Iface/Syntax.hs
@@ -69,7 +69,7 @@ import GHC.Data.BooleanFormula ( BooleanFormula, pprBooleanFormula, isTrue )
 import GHC.Types.Var( VarBndr(..), binderVar, tyVarSpecToBinders )
 import GHC.Core.TyCon ( Role (..), Injectivity(..), tyConBndrVisArgFlag )
 import GHC.Utils.Misc( dropList, filterByList, notNull, unzipWith, debugIsOn,
-                       seqList )
+                       seqList, zipWithEqual )
 import GHC.Core.DataCon (SrcStrictness(..), SrcUnpackedness(..))
 import GHC.Utils.Lexeme (isLexSym)
 import GHC.Builtin.Types ( constraintKindTyConName )
@@ -259,7 +259,7 @@ data IfaceConDecl
           -- See Note [DataCon user type variable binders] in GHC.Core.DataCon
         ifConEqSpec  :: IfaceEqSpec,        -- Equality constraints
         ifConCtxt    :: IfaceContext,       -- Non-stupid context
-        ifConArgTys  :: [IfaceType],        -- Arg types
+        ifConArgTys  :: [(IfaceMult, IfaceType)],-- Arg types
         ifConFields  :: [FieldLabel],  -- ...ditto... (field labels)
         ifConStricts :: [IfaceBang],
           -- Empty (meaning all lazy),
@@ -1026,7 +1026,7 @@ pprIfaceDecl _ (IfacePatSyn { ifName = name,
                              , ppWhen insert_empty_ctxt $ parens empty <+> darrow
                              , ex_msg
                              , pprIfaceContextArr prov_ctxt
-                             , pprIfaceType $ foldr (IfaceFunTy VisArg) pat_ty arg_tys ])
+                             , pprIfaceType $ foldr (IfaceFunTy VisArg many_ty) pat_ty arg_tys ])
       where
         univ_msg = pprUserIfaceForAll $ tyVarSpecToBinders univ_bndrs
         ex_msg   = pprUserIfaceForAll $ tyVarSpecToBinders ex_bndrs
@@ -1148,7 +1148,7 @@ pprIfaceConDecl ss gadt_style tycon tc_binders parent
 
     how_much = ss_how_much ss
     tys_w_strs :: [(IfaceBang, IfaceType)]
-    tys_w_strs = zip stricts arg_tys
+    tys_w_strs = zip stricts (map snd arg_tys)
     pp_prefix_con = pprPrefixIfDeclBndr how_much (occName name)
 
     -- If we're pretty-printing a H98-style declaration with existential
@@ -1165,11 +1165,17 @@ pprIfaceConDecl ss gadt_style tycon tc_binders parent
         -- because we don't have a Name for the tycon, only an OccName
     pp_tau | null fields
            = case pp_args ++ [pp_gadt_res_ty] of
-                (t:ts) -> fsep (t : map (arrow <+>) ts)
+                (t:ts) -> fsep (t : zipWithEqual "pprIfaceConDecl" (\(w,_) d -> ppr_arr w <+> d) arg_tys ts)
                 []     -> panic "pp_con_taus"
            | otherwise
            = sep [pp_field_args, arrow <+> pp_gadt_res_ty]
 
+    -- Constructors are linear by default, but we don't want to show
+    -- linear arrows when -XLinearTypes is disabled
+    ppr_arr w = sdocOption sdocLinearTypes (\linearTypes -> if linearTypes
+                                                            then ppr_fun_arrow w
+                                                            else arrow)
+
     ppr_bang IfNoBang = whenPprDebug $ char '_'
     ppr_bang IfStrict = char '!'
     ppr_bang IfUnpack = text "{-# UNPACK #-}"
@@ -1600,7 +1606,8 @@ freeNamesIfConDecl (IfCon { ifConExTCvs  = ex_tvs, ifConCtxt = ctxt
                           , ifConStricts = bangs })
   = fnList freeNamesIfBndr ex_tvs &&&
     freeNamesIfContext ctxt &&&
-    fnList freeNamesIfType arg_tys &&&
+    fnList freeNamesIfType (map fst arg_tys) &&& -- these are multiplicities, represented as types
+    fnList freeNamesIfType (map snd arg_tys) &&&
     mkNameSet (map flSelector flds) &&&
     fnList freeNamesIfType (map snd eq_spec) &&& -- equality constraints
     fnList freeNamesIfBang bangs
@@ -1624,7 +1631,7 @@ freeNamesIfType (IfaceTyConApp tc ts) = freeNamesIfTc tc &&& freeNamesIfAppArgs
 freeNamesIfType (IfaceTupleTy _ _ ts) = freeNamesIfAppArgs ts
 freeNamesIfType (IfaceLitTy _)        = emptyNameSet
 freeNamesIfType (IfaceForAllTy tv t)  = freeNamesIfVarBndr tv &&& freeNamesIfType t
-freeNamesIfType (IfaceFunTy _ s t)    = freeNamesIfType s &&& freeNamesIfType t
+freeNamesIfType (IfaceFunTy _ w s t)  = freeNamesIfType s &&& freeNamesIfType t &&& freeNamesIfType w
 freeNamesIfType (IfaceCastTy t c)     = freeNamesIfType t &&& freeNamesIfCoercion c
 freeNamesIfType (IfaceCoercionTy c)   = freeNamesIfCoercion c
 
@@ -1636,8 +1643,8 @@ freeNamesIfCoercion :: IfaceCoercion -> NameSet
 freeNamesIfCoercion (IfaceReflCo t) = freeNamesIfType t
 freeNamesIfCoercion (IfaceGReflCo _ t mco)
   = freeNamesIfType t &&& freeNamesIfMCoercion mco
-freeNamesIfCoercion (IfaceFunCo _ c1 c2)
-  = freeNamesIfCoercion c1 &&& freeNamesIfCoercion c2
+freeNamesIfCoercion (IfaceFunCo _ c_mult c1 c2)
+  = freeNamesIfCoercion c_mult &&& freeNamesIfCoercion c1 &&& freeNamesIfCoercion c2
 freeNamesIfCoercion (IfaceTyConAppCo _ tc cos)
   = freeNamesIfTc tc &&& fnList freeNamesIfCoercion cos
 freeNamesIfCoercion (IfaceAppCo c1 c2)
@@ -1699,7 +1706,7 @@ freeNamesIfTvBndr (_fs,k) = freeNamesIfKind k
     -- kinds can have Names inside, because of promotion
 
 freeNamesIfIdBndr :: IfaceIdBndr -> NameSet
-freeNamesIfIdBndr (_fs,k) = freeNamesIfKind k
+freeNamesIfIdBndr (_, _fs,k) = freeNamesIfKind k
 
 freeNamesIfIdInfo :: IfaceIdInfo -> NameSet
 freeNamesIfIdInfo = fnList freeNamesItem
diff --git a/compiler/GHC/Iface/Tidy.hs b/compiler/GHC/Iface/Tidy.hs
index efb72dc77d..5121c11681 100644
--- a/compiler/GHC/Iface/Tidy.hs
+++ b/compiler/GHC/Iface/Tidy.hs
@@ -217,7 +217,7 @@ globaliseAndTidyBootId :: Id -> Id
 --     * VanillaIdInfo (makes a conservative assumption about arity)
 --     * BootUnfolding (see Note [Inlining and hs-boot files] in GHC.CoreToIface)
 globaliseAndTidyBootId id
-  = globaliseId id `setIdType`      tidyTopType (idType id)
+  = updateIdTypeAndMult tidyTopType (globaliseId id)
                    `setIdUnfolding` BootUnfolding
 
 {-
diff --git a/compiler/GHC/Iface/Type.hs b/compiler/GHC/Iface/Type.hs
index 6ed05e3338..acd7b51330 100644
--- a/compiler/GHC/Iface/Type.hs
+++ b/compiler/GHC/Iface/Type.hs
@@ -26,6 +26,7 @@ module GHC.Iface.Type (
         IfaceType(..), IfacePredType, IfaceKind, IfaceCoercion(..),
         IfaceMCoercion(..),
         IfaceUnivCoProv(..),
+        IfaceMult,
         IfaceTyCon(..), IfaceTyConInfo(..), IfaceTyConSort(..),
         IfaceTyLit(..), IfaceAppArgs(..),
         IfaceContext, IfaceBndr(..), IfaceOneShot(..), IfaceLamBndr,
@@ -58,13 +59,16 @@ module GHC.Iface.Type (
         pprIfaceCoercion, pprParendIfaceCoercion,
         splitIfaceSigmaTy, pprIfaceTypeApp, pprUserIfaceForAll,
         pprIfaceCoTcApp, pprTyTcApp, pprIfacePrefixApp,
+        ppr_fun_arrow,
         isIfaceTauType,
 
         suppressIfaceInvisibles,
         stripIfaceInvisVars,
         stripInvisArgs,
 
-        mkIfaceTySubst, substIfaceTyVar, substIfaceAppArgs, inDomIfaceTySubst
+        mkIfaceTySubst, substIfaceTyVar, substIfaceAppArgs, inDomIfaceTySubst,
+
+        many_ty
     ) where
 
 #include "HsVersions.h"
@@ -73,8 +77,9 @@ import GHC.Prelude
 
 import {-# SOURCE #-} GHC.Builtin.Types
                                  ( coercibleTyCon, heqTyCon
-                                 , liftedRepDataConTyCon, tupleTyConName )
-import {-# SOURCE #-} GHC.Core.Type ( isRuntimeRepTy )
+                                 , liftedRepDataConTyCon, tupleTyConName
+                                 , manyDataConTyCon, oneDataConTyCon )
+import {-# SOURCE #-} GHC.Core.Type ( isRuntimeRepTy, isMultiplicityTy )
 
 import GHC.Core.TyCon hiding ( pprPromotionQuote )
 import GHC.Core.Coercion.Axiom
@@ -85,7 +90,6 @@ import GHC.Types.Basic
 import GHC.Utils.Binary
 import GHC.Utils.Outputable
 import GHC.Data.FastString
-import GHC.Data.FastString.Env
 import GHC.Utils.Misc
 
 import Data.Maybe( isJust )
@@ -109,21 +113,21 @@ data IfaceBndr          -- Local (non-top-level) binders
   = IfaceIdBndr {-# UNPACK #-} !IfaceIdBndr
   | IfaceTvBndr {-# UNPACK #-} !IfaceTvBndr
 
-type IfaceIdBndr  = (IfLclName, IfaceType)
+type IfaceIdBndr  = (IfaceType, IfLclName, IfaceType)
 type IfaceTvBndr  = (IfLclName, IfaceKind)
 
 ifaceTvBndrName :: IfaceTvBndr -> IfLclName
 ifaceTvBndrName (n,_) = n
 
 ifaceIdBndrName :: IfaceIdBndr -> IfLclName
-ifaceIdBndrName (n,_) = n
+ifaceIdBndrName (_,n,_) = n
 
 ifaceBndrName :: IfaceBndr -> IfLclName
 ifaceBndrName (IfaceTvBndr bndr) = ifaceTvBndrName bndr
 ifaceBndrName (IfaceIdBndr bndr) = ifaceIdBndrName bndr
 
 ifaceBndrType :: IfaceBndr -> IfaceType
-ifaceBndrType (IfaceIdBndr (_, t)) = t
+ifaceBndrType (IfaceIdBndr (_, _, t)) = t
 ifaceBndrType (IfaceTvBndr (_, t)) = t
 
 type IfaceLamBndr = (IfaceBndr, IfaceOneShot)
@@ -159,7 +163,7 @@ data IfaceType
                              -- See Note [Suppressing invisible arguments] for
                              -- an explanation of why the second field isn't
                              -- IfaceType, analogous to AppTy.
-  | IfaceFunTy     AnonArgFlag IfaceType IfaceType
+  | IfaceFunTy     AnonArgFlag IfaceMult IfaceType IfaceType
   | IfaceForAllTy  IfaceForAllBndr IfaceType
   | IfaceTyConApp  IfaceTyCon IfaceAppArgs  -- Not necessarily saturated
                                             -- Includes newtypes, synonyms, tuples
@@ -172,6 +176,8 @@ data IfaceType
        IfaceAppArgs               -- arity = length args
           -- For promoted data cons, the kind args are omitted
 
+type IfaceMult = IfaceType
+
 type IfacePredType = IfaceType
 type IfaceContext = [IfacePredType]
 
@@ -194,7 +200,7 @@ mkIfaceTyConKind :: [IfaceTyConBinder] -> IfaceKind -> IfaceKind
 mkIfaceTyConKind bndrs res_kind = foldr mk res_kind bndrs
   where
     mk :: IfaceTyConBinder -> IfaceKind -> IfaceKind
-    mk (Bndr tv (AnonTCB af))   k = IfaceFunTy af (ifaceBndrType tv) k
+    mk (Bndr tv (AnonTCB af))   k = IfaceFunTy af many_ty (ifaceBndrType tv) k
     mk (Bndr tv (NamedTCB vis)) k = IfaceForAllTy (Bndr tv vis) k
 
 ifaceForAllSpecToBndrs :: [IfaceForAllSpecBndr] -> [IfaceForAllBndr]
@@ -354,7 +360,7 @@ data IfaceMCoercion
 data IfaceCoercion
   = IfaceReflCo       IfaceType
   | IfaceGReflCo      Role IfaceType (IfaceMCoercion)
-  | IfaceFunCo        Role IfaceCoercion IfaceCoercion
+  | IfaceFunCo        Role IfaceCoercion IfaceCoercion IfaceCoercion
   | IfaceTyConAppCo   Role IfaceTyCon [IfaceCoercion]
   | IfaceAppCo        IfaceCoercion IfaceCoercion
   | IfaceForAllCo     IfaceBndr IfaceCoercion IfaceCoercion
@@ -438,7 +444,7 @@ splitIfaceSigmaTy ty
         = case split_foralls ty of { (bndrs, rho) -> (bndr:bndrs, rho) }
     split_foralls rho = ([], rho)
 
-    split_rho (IfaceFunTy InvisArg ty1 ty2)
+    split_rho (IfaceFunTy InvisArg _ ty1 ty2)
         = case split_rho ty2 of { (ps, tau) -> (ty1:ps, tau) }
     split_rho tau = ([], tau)
 
@@ -481,7 +487,7 @@ ifTypeIsVarFree ty = go ty
     go (IfaceTyVar {})         = False
     go (IfaceFreeTyVar {})     = False
     go (IfaceAppTy fun args)   = go fun && go_args args
-    go (IfaceFunTy _ arg res)  = go arg && go res
+    go (IfaceFunTy _ w arg res) = go w && go arg && go res
     go (IfaceForAllTy {})      = False
     go (IfaceTyConApp _ args)  = go_args args
     go (IfaceTupleTy _ _ args) = go_args args
@@ -516,7 +522,7 @@ substIfaceType env ty
     go (IfaceFreeTyVar tv)    = IfaceFreeTyVar tv
     go (IfaceTyVar tv)        = substIfaceTyVar env tv
     go (IfaceAppTy  t ts)     = IfaceAppTy  (go t) (substIfaceAppArgs env ts)
-    go (IfaceFunTy af t1 t2)  = IfaceFunTy af (go t1) (go t2)
+    go (IfaceFunTy af w t1 t2)  = IfaceFunTy af (go w) (go t1) (go t2)
     go ty@(IfaceLitTy {})     = ty
     go (IfaceTyConApp tc tys) = IfaceTyConApp tc (substIfaceAppArgs env tys)
     go (IfaceTupleTy s i tys) = IfaceTupleTy s i (substIfaceAppArgs env tys)
@@ -529,7 +535,7 @@ substIfaceType env ty
 
     go_co (IfaceReflCo ty)           = IfaceReflCo (go ty)
     go_co (IfaceGReflCo r ty mco)    = IfaceGReflCo r (go ty) (go_mco mco)
-    go_co (IfaceFunCo r c1 c2)       = IfaceFunCo r (go_co c1) (go_co c2)
+    go_co (IfaceFunCo r w c1 c2)     = IfaceFunCo r (go_co w) (go_co c1) (go_co c2)
     go_co (IfaceTyConAppCo r tc cos) = IfaceTyConAppCo r tc (go_cos cos)
     go_co (IfaceAppCo c1 c2)         = IfaceAppCo (go_co c1) (go_co c2)
     go_co (IfaceForAllCo {})         = pprPanic "substIfaceCoercion" (ppr ty)
@@ -729,7 +735,7 @@ pprIfacePrefixApp ctxt_prec pp_fun pp_tys
 
 isIfaceTauType :: IfaceType -> Bool
 isIfaceTauType (IfaceForAllTy _ _) = False
-isIfaceTauType (IfaceFunTy InvisArg _ _) = False
+isIfaceTauType (IfaceFunTy InvisArg _ _ _) = False
 isIfaceTauType _ = True
 
 -- ----------------------------- Printing binders ------------------------------------
@@ -747,7 +753,7 @@ pprIfaceLamBndr (b, IfaceNoOneShot) = ppr b
 pprIfaceLamBndr (b, IfaceOneShot)   = ppr b <> text "[OneShot]"
 
 pprIfaceIdBndr :: IfaceIdBndr -> SDoc
-pprIfaceIdBndr (name, ty) = parens (ppr name <+> dcolon <+> ppr ty)
+pprIfaceIdBndr (w, name, ty) = parens (ppr name <> brackets (ppr w) <+> dcolon <+> ppr ty)
 
 {- Note [Suppressing binder signatures]
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -844,17 +850,26 @@ pprIfaceType       = pprPrecIfaceType topPrec
 pprParendIfaceType = pprPrecIfaceType appPrec
 
 pprPrecIfaceType :: PprPrec -> IfaceType -> SDoc
--- We still need `eliminateRuntimeRep`, since the `pprPrecIfaceType` maybe
+-- We still need `hideNonStandardTypes`, since the `pprPrecIfaceType` may be
 -- called from other places, besides `:type` and `:info`.
-pprPrecIfaceType prec ty = eliminateRuntimeRep (ppr_ty prec) ty
+pprPrecIfaceType prec ty =
+  hideNonStandardTypes (ppr_ty prec) ty
+
+ppr_fun_arrow :: IfaceMult -> SDoc
+ppr_fun_arrow w
+  | (IfaceTyConApp tc _) <- w
+  , tc `ifaceTyConHasKey` (getUnique manyDataConTyCon) = arrow
+  | (IfaceTyConApp tc _) <- w
+  , tc `ifaceTyConHasKey` (getUnique oneDataConTyCon) = lollipop
+  | otherwise = mulArrow (pprIfaceType w)
 
 ppr_sigma :: PprPrec -> IfaceType -> SDoc
 ppr_sigma ctxt_prec ty
   = maybeParen ctxt_prec funPrec (pprIfaceSigmaType ShowForAllMust ty)
 
 ppr_ty :: PprPrec -> IfaceType -> SDoc
-ppr_ty ctxt_prec ty@(IfaceForAllTy {})        = ppr_sigma ctxt_prec ty
-ppr_ty ctxt_prec ty@(IfaceFunTy InvisArg _ _) = ppr_sigma ctxt_prec ty
+ppr_ty ctxt_prec ty@(IfaceForAllTy {})          = ppr_sigma ctxt_prec ty
+ppr_ty ctxt_prec ty@(IfaceFunTy InvisArg _ _ _) = ppr_sigma ctxt_prec ty
 
 ppr_ty _         (IfaceFreeTyVar tyvar) = ppr tyvar  -- This is the main reason for IfaceFreeTyVar!
 ppr_ty _         (IfaceTyVar tyvar)     = ppr tyvar  -- See Note [TcTyVars in IfaceType]
@@ -862,15 +877,15 @@ ppr_ty ctxt_prec (IfaceTyConApp tc tys) = pprTyTcApp ctxt_prec tc tys
 ppr_ty ctxt_prec (IfaceTupleTy i p tys) = pprTuple ctxt_prec i p tys
 ppr_ty _         (IfaceLitTy n)         = pprIfaceTyLit n
         -- Function types
-ppr_ty ctxt_prec (IfaceFunTy _ ty1 ty2)  -- Should be VisArg
+ppr_ty ctxt_prec (IfaceFunTy _ w ty1 ty2)  -- Should be VisArg
   = -- We don't want to lose synonyms, so we mustn't use splitFunTys here.
     maybeParen ctxt_prec funPrec $
-    sep [ppr_ty funPrec ty1, sep (ppr_fun_tail ty2)]
+    sep [ppr_ty funPrec ty1, sep (ppr_fun_tail w ty2)]
   where
-    ppr_fun_tail (IfaceFunTy VisArg ty1 ty2)
-      = (arrow <+> ppr_ty funPrec ty1) : ppr_fun_tail ty2
-    ppr_fun_tail other_ty
-      = [arrow <+> pprIfaceType other_ty]
+    ppr_fun_tail wthis (IfaceFunTy VisArg wnext ty1 ty2)
+      = (ppr_fun_arrow wthis <+> ppr_ty funPrec ty1) : ppr_fun_tail wnext ty2
+    ppr_fun_tail wthis other_ty
+      = [ppr_fun_arrow wthis <+> pprIfaceType other_ty]
 
 ppr_ty ctxt_prec (IfaceAppTy t ts)
   = if_print_coercions
@@ -928,9 +943,12 @@ syntactic overhead.
 
 For this reason it was decided that we would hide RuntimeRep variables
 for now (see #11549). We do this by defaulting all type variables of
-kind RuntimeRep to LiftedRep. This is done in a pass right before
-pretty-printing (defaultRuntimeRepVars, controlled by
--fprint-explicit-runtime-reps)
+kind RuntimeRep to LiftedRep.
+Likewise, we default all Multiplicity variables to Many.
+
+This is done in a pass right before pretty-printing
+(defaultNonStandardVars, controlled by
+-fprint-explicit-runtime-reps and -XLinearTypes)
 
 This applies to /quantified/ variables like 'w' above.  What about
 variables that are /free/ in the type being printed, which certainly
@@ -948,33 +966,36 @@ Conclusion: keep track of whether we we are in the kind of a
 binder; only if so, convert free RuntimeRep variables to LiftedRep.
 -}
 
--- | Default 'RuntimeRep' variables to 'LiftedRep'. e.g.
+-- | Default 'RuntimeRep' variables to 'LiftedRep', and 'Multiplicity'
+--   variables to 'Many'. For example:
 --
 -- @
 -- ($) :: forall (r :: GHC.Types.RuntimeRep) a (b :: TYPE r).
 --        (a -> b) -> a -> b
+-- Just :: forall (k :: Multiplicity) a. a # k -> Maybe a
 -- @
 --
 -- turns in to,
 --
 -- @ ($) :: forall a (b :: *). (a -> b) -> a -> b @
+-- @ Just :: forall a . a -> Maybe a @
 --
--- We do this to prevent RuntimeRep variables from incurring a significant
--- syntactic overhead in otherwise simple type signatures (e.g. ($)). See
--- Note [Defaulting RuntimeRep variables] and #11549 for further discussion.
---
-defaultRuntimeRepVars :: IfaceType -> IfaceType
-defaultRuntimeRepVars ty = go False emptyFsEnv ty
+-- We do this to prevent RuntimeRep and Multiplicity variables from
+-- incurring a significant syntactic overhead in otherwise simple
+-- type signatures (e.g. ($)). See Note [Defaulting RuntimeRep variables]
+-- and #11549 for further discussion.
+defaultNonStandardVars :: Bool -> Bool -> IfaceType -> IfaceType
+defaultNonStandardVars do_runtimereps do_multiplicities ty = go False emptyFsEnv ty
   where
     go :: Bool              -- True <=> Inside the kind of a binder
-       -> FastStringEnv ()  -- Set of enclosing forall-ed RuntimeRep variables
-       -> IfaceType         --  (replace them with LiftedRep)
+       -> FastStringEnv IfaceType -- Set of enclosing forall-ed RuntimeRep/Multiplicity variables
+       -> IfaceType
        -> IfaceType
     go ink subs (IfaceForAllTy (Bndr (IfaceTvBndr (var, var_kind)) argf) ty)
-     | isRuntimeRep var_kind
-      , isInvisibleArgFlag argf -- Don't default *visible* quantification
+     | isInvisibleArgFlag argf  -- Don't default *visible* quantification
                                 -- or we get the mess in #13963
-      = let subs' = extendFsEnv subs var ()
+     , Just substituted_ty <- check_substitution var_kind
+      = let subs' = extendFsEnv subs var substituted_ty
             -- Record that we should replace it with LiftedRep,
             -- and recurse, discarding the forall
         in go ink subs' ty
@@ -982,16 +1003,16 @@ defaultRuntimeRepVars ty = go False emptyFsEnv ty
     go ink subs (IfaceForAllTy bndr ty)
       = IfaceForAllTy (go_ifacebndr subs bndr) (go ink subs ty)
 
-    go _ subs ty@(IfaceTyVar tv)
-      | tv `elemFsEnv` subs
-      = IfaceTyConApp liftedRep IA_Nil
-      | otherwise
-      = ty
+    go _ subs ty@(IfaceTyVar tv) = case lookupFsEnv subs tv of
+      Just s -> s
+      Nothing -> ty
 
     go in_kind _ ty@(IfaceFreeTyVar tv)
       -- See Note [Defaulting RuntimeRep variables], about free vars
-      | in_kind && GHC.Core.Type.isRuntimeRepTy (tyVarKind tv)
-      = IfaceTyConApp liftedRep IA_Nil
+      | in_kind && do_runtimereps && GHC.Core.Type.isRuntimeRepTy (tyVarKind tv)
+      = liftedRep_ty
+      | do_multiplicities && GHC.Core.Type.isMultiplicityTy (tyVarKind tv)
+      = many_ty
       | otherwise
       = ty
 
@@ -1001,8 +1022,8 @@ defaultRuntimeRepVars ty = go False emptyFsEnv ty
     go ink subs (IfaceTupleTy sort is_prom tc_args)
       = IfaceTupleTy sort is_prom (go_args ink subs tc_args)
 
-    go ink subs (IfaceFunTy af arg res)
-      = IfaceFunTy af (go ink subs arg) (go ink subs res)
+    go ink subs (IfaceFunTy af w arg res)
+      = IfaceFunTy af (go ink subs w) (go ink subs arg) (go ink subs res)
 
     go ink subs (IfaceAppTy t ts)
       = IfaceAppTy (go ink subs t) (go_args ink subs ts)
@@ -1013,33 +1034,45 @@ defaultRuntimeRepVars ty = go False emptyFsEnv ty
     go _ _ ty@(IfaceLitTy {}) = ty
     go _ _ ty@(IfaceCoercionTy {}) = ty
 
-    go_ifacebndr :: FastStringEnv () -> IfaceForAllBndr -> IfaceForAllBndr
-    go_ifacebndr subs (Bndr (IfaceIdBndr (n, t)) argf)
-      = Bndr (IfaceIdBndr (n, go True subs t)) argf
+    go_ifacebndr :: FastStringEnv IfaceType -> IfaceForAllBndr -> IfaceForAllBndr
+    go_ifacebndr subs (Bndr (IfaceIdBndr (w, n, t)) argf)
+      = Bndr (IfaceIdBndr (w, n, go True subs t)) argf
     go_ifacebndr subs (Bndr (IfaceTvBndr (n, t)) argf)
       = Bndr (IfaceTvBndr (n, go True subs t)) argf
 
-    go_args :: Bool -> FastStringEnv () -> IfaceAppArgs -> IfaceAppArgs
+    go_args :: Bool -> FastStringEnv IfaceType -> IfaceAppArgs -> IfaceAppArgs
     go_args _ _ IA_Nil = IA_Nil
     go_args ink subs (IA_Arg ty argf args)
       = IA_Arg (go ink subs ty) argf (go_args ink subs args)
 
-    liftedRep :: IfaceTyCon
-    liftedRep = IfaceTyCon dc_name (IfaceTyConInfo IsPromoted IfaceNormalTyCon)
-      where dc_name = getName liftedRepDataConTyCon
-
-    isRuntimeRep :: IfaceType -> Bool
-    isRuntimeRep (IfaceTyConApp tc _) =
-        tc `ifaceTyConHasKey` runtimeRepTyConKey
-    isRuntimeRep _ = False
-
-eliminateRuntimeRep :: (IfaceType -> SDoc) -> IfaceType -> SDoc
-eliminateRuntimeRep f ty
+    check_substitution :: IfaceType -> Maybe IfaceType
+    check_substitution (IfaceTyConApp tc _)
+        | do_runtimereps, tc `ifaceTyConHasKey` runtimeRepTyConKey = Just liftedRep_ty
+        | do_multiplicities, tc `ifaceTyConHasKey` multiplicityTyConKey = Just many_ty
+    check_substitution _ = Nothing
+
+liftedRep_ty :: IfaceType
+liftedRep_ty =
+    IfaceTyConApp (IfaceTyCon dc_name (IfaceTyConInfo IsPromoted IfaceNormalTyCon))
+                  IA_Nil
+  where dc_name = getName liftedRepDataConTyCon
+
+many_ty :: IfaceType
+many_ty =
+    IfaceTyConApp (IfaceTyCon dc_name (IfaceTyConInfo IsPromoted IfaceNormalTyCon))
+                  IA_Nil
+  where dc_name = getName manyDataConTyCon
+
+hideNonStandardTypes :: (IfaceType -> SDoc) -> IfaceType -> SDoc
+hideNonStandardTypes f ty
   = sdocOption sdocPrintExplicitRuntimeReps $ \printExplicitRuntimeReps ->
+    sdocOption sdocLinearTypes $ \linearTypes ->
     getPprStyle      $ \sty    ->
-    if userStyle sty && not printExplicitRuntimeReps
-      then f (defaultRuntimeRepVars ty)
-      else f ty
+    let do_runtimerep = not printExplicitRuntimeReps
+        do_multiplicity = not linearTypes
+    in if userStyle sty
+       then f (defaultNonStandardVars do_runtimerep do_multiplicity ty)
+       else f ty
 
 instance Outputable IfaceAppArgs where
   ppr tca = pprIfaceAppArgs tca
@@ -1148,7 +1181,7 @@ data ShowForAllFlag = ShowForAllMust | ShowForAllWhen
 
 pprIfaceSigmaType :: ShowForAllFlag -> IfaceType -> SDoc
 pprIfaceSigmaType show_forall ty
-  = eliminateRuntimeRep ppr_fn ty
+  = hideNonStandardTypes ppr_fn ty
   where
     ppr_fn iface_ty =
       let (tvs, theta, tau) = splitIfaceSigmaTy iface_ty
@@ -1339,6 +1372,11 @@ pprTyTcApp' ctxt_prec tc tys printExplicitKinds debug
   , rep `ifaceTyConHasKey` liftedRepDataConKey
   = ppr_kind_type ctxt_prec
 
+  | tc `ifaceTyConHasKey` funTyConKey
+  , IA_Arg (IfaceTyConApp rep IA_Nil) Required args <- tys
+  , rep `ifaceTyConHasKey` manyDataConKey
+  = pprIfacePrefixApp ctxt_prec (parens arrow) (map (ppr_ty appPrec) (appArgsIfaceTypes $ stripInvisArgs printExplicitKinds args))
+
   | otherwise
   = getPprDebug $ \dbg ->
     if | not dbg && tc `ifaceTyConHasKey` errorMessageTypeErrorFamKey
@@ -1550,14 +1588,15 @@ ppr_co _         (IfaceGReflCo r ty IfaceMRefl)
 ppr_co ctxt_prec (IfaceGReflCo r ty (IfaceMCo co))
   = ppr_special_co ctxt_prec
     (text "GRefl" <+> ppr r <+> pprParendIfaceType ty) [co]
-ppr_co ctxt_prec (IfaceFunCo r co1 co2)
+ppr_co ctxt_prec (IfaceFunCo r cow co1 co2)
   = maybeParen ctxt_prec funPrec $
-    sep (ppr_co funPrec co1 : ppr_fun_tail co2)
+    sep (ppr_co funPrec co1 : ppr_fun_tail cow co2)
   where
-    ppr_fun_tail (IfaceFunCo r co1 co2)
-      = (arrow <> ppr_role r <+> ppr_co funPrec co1) : ppr_fun_tail co2
-    ppr_fun_tail other_co
-      = [arrow <> ppr_role r <+> pprIfaceCoercion other_co]
+    ppr_fun_tail cow' (IfaceFunCo r cow co1 co2)
+      = (coercionArrow cow' <> ppr_role r <+> ppr_co funPrec co1) : ppr_fun_tail cow co2
+    ppr_fun_tail cow' other_co
+      = [coercionArrow cow' <> ppr_role r <+> pprIfaceCoercion other_co]
+    coercionArrow w = mulArrow (ppr_co topPrec w)
 
 ppr_co _         (IfaceTyConAppCo r tc cos)
   = parens (pprIfaceCoTcApp topPrec tc cos) <> ppr_role r
@@ -1572,7 +1611,7 @@ ppr_co ctxt_prec co@(IfaceForAllCo {})
 
     split_co (IfaceForAllCo (IfaceTvBndr (name, _)) kind_co co')
       = let (tvs, co'') = split_co co' in ((name,kind_co):tvs,co'')
-    split_co (IfaceForAllCo (IfaceIdBndr (name, _)) kind_co co')
+    split_co (IfaceForAllCo (IfaceIdBndr (_, name, _)) kind_co co')
       = let (tvs, co'') = split_co co' in ((name,kind_co):tvs,co'')
     split_co co' = ([], co')
 
@@ -1777,9 +1816,10 @@ instance Binary IfaceType where
             putByte bh 2
             put_ bh ae
             put_ bh af
-    put_ bh (IfaceFunTy af ag ah) = do
+    put_ bh (IfaceFunTy af aw ag ah) = do
             putByte bh 3
             put_ bh af
+            put_ bh aw
             put_ bh ag
             put_ bh ah
     put_ bh (IfaceTyConApp tc tys)
@@ -1805,9 +1845,10 @@ instance Binary IfaceType where
                       af <- get bh
                       return (IfaceAppTy ae af)
               3 -> do af <- get bh
+                      aw <- get bh
                       ag <- get bh
                       ah <- get bh
-                      return (IfaceFunTy af ag ah)
+                      return (IfaceFunTy af aw ag ah)
               5 -> do { tc <- get bh; tys <- get bh
                       ; return (IfaceTyConApp tc tys) }
               6 -> do { a <- get bh; b <- get bh
@@ -1844,9 +1885,10 @@ instance Binary IfaceCoercion where
           put_ bh a
           put_ bh b
           put_ bh c
-  put_ bh (IfaceFunCo a b c) = do
+  put_ bh (IfaceFunCo a w b c) = do
           putByte bh 3
           put_ bh a
+          put_ bh w
           put_ bh b
           put_ bh c
   put_ bh (IfaceTyConAppCo a b c) = do
@@ -1922,9 +1964,10 @@ instance Binary IfaceCoercion where
                    c <- get bh
                    return $ IfaceGReflCo a b c
            3 -> do a <- get bh
+                   w <- get bh
                    b <- get bh
                    c <- get bh
-                   return $ IfaceFunCo a b c
+                   return $ IfaceFunCo a w b c
            4 -> do a <- get bh
                    b <- get bh
                    c <- get bh
@@ -2008,7 +2051,7 @@ instance NFData IfaceType where
     IfaceTyVar f1 -> rnf f1
     IfaceLitTy f1 -> rnf f1
     IfaceAppTy f1 f2 -> rnf f1 `seq` rnf f2
-    IfaceFunTy f1 f2 f3 -> f1 `seq` rnf f2 `seq` rnf f3
+    IfaceFunTy f1 f2 f3 f4 -> f1 `seq` rnf f2 `seq` rnf f3 `seq` rnf f4
     IfaceForAllTy f1 f2 -> f1 `seq` rnf f2
     IfaceTyConApp f1 f2 -> rnf f1 `seq` rnf f2
     IfaceCastTy f1 f2 -> rnf f1 `seq` rnf f2
@@ -2024,7 +2067,7 @@ instance NFData IfaceCoercion where
   rnf = \case
     IfaceReflCo f1 -> rnf f1
     IfaceGReflCo f1 f2 f3 -> f1 `seq` rnf f2 `seq` rnf f3
-    IfaceFunCo f1 f2 f3 -> f1 `seq` rnf f2 `seq` rnf f3
+    IfaceFunCo f1 f2 f3 f4 -> f1 `seq` rnf f2 `seq` rnf f3 `seq` rnf f4
     IfaceTyConAppCo f1 f2 f3 -> f1 `seq` rnf f2 `seq` rnf f3
     IfaceAppCo f1 f2 -> rnf f1 `seq` rnf f2
     IfaceForAllCo f1 f2 f3 -> rnf f1 `seq` rnf f2 `seq` rnf f3