    {-# LANGUAGE DeriveDataTypeable #-}

    {-# OPTIONS_HADDOCK not-home #-}

    {-
    (c) The University of Glasgow 2006
    (c) The GRASP/AQUA Project, Glasgow University, 1998
    \section[GHC.Core.TyCo.Rep]{Type and Coercion - friends' interface}

    Note [The Type-related module hierarchy]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
      GHC.Core.Class
      GHC.Core.Coercion.Axiom
      GHC.Core.TyCon           imports GHC.Core.{Class, Coercion.Axiom}
      GHC.Core.TyCo.Rep        imports GHC.Core.{Class, Coercion.Axiom, TyCon}
      GHC.Core.TyCo.Ppr        imports GHC.Core.TyCo.Rep
      GHC.Core.TyCo.FVs        imports GHC.Core.TyCo.Rep
      GHC.Core.TyCo.Subst      imports GHC.Core.TyCo.{Rep, FVs, Ppr}
      GHC.Core.TyCo.Tidy       imports GHC.Core.TyCo.{Rep, FVs}
      GHC.Builtin.Types.Prim   imports GHC.Core.TyCo.Rep ( including mkTyConTy )
      GHC.Core.Coercion        imports GHC.Core.Type
    -}

    -- We expose the relevant stuff from this module via the Type module
    module GHC.Core.TyCo.Rep (

            -- * Types
            Type(..),

            TyLit(..),
            KindOrType, Kind,
            RuntimeRepType, LevityType,
            KnotTied,
            PredType, ThetaType, FRRType,     -- Synonyms
            ForAllTyFlag(..), FunTyFlag(..),

            -- * Coercions
            Coercion(..), CoSel(..), FunSel(..),
            UnivCoProvenance(..),
            CoercionHole(..), coHoleCoVar, setCoHoleCoVar, isHeteroKindCoHole,
            CoercionN, CoercionR, CoercionP, KindCoercion,
            MCoercion(..), MCoercionR, MCoercionN,

            -- * Functions over types
            mkNakedTyConTy, mkTyVarTy, mkTyVarTys,
            mkTyCoVarTy, mkTyCoVarTys,
            mkFunTy, mkNakedFunTy,
            mkVisFunTy, mkScaledFunTys,
            mkInvisFunTy, mkInvisFunTys,
            tcMkVisFunTy, tcMkInvisFunTy, tcMkScaledFunTy, tcMkScaledFunTys,
            mkForAllTy, mkForAllTys, mkInvisForAllTys,
            mkPiTy, mkPiTys,
            mkVisFunTyMany, mkVisFunTysMany,
            nonDetCmpTyLit, cmpTyLit,

            -- * Functions over coercions
            pickLR,

            -- ** Analyzing types
            TyCoFolder(..), foldTyCo, noView,

            -- * Sizes
            typeSize, typesSize, coercionSize,

            -- * Multiplicities
            Scaled(..), scaledMult, scaledThing, mapScaledType, Mult
        ) where

    import GHC.Prelude

    import {-# SOURCE #-} GHC.Core.TyCo.Ppr ( pprType, pprCo, pprTyLit )
    import {-# SOURCE #-} GHC.Builtin.Types
    import {-# SOURCE #-} GHC.Core.TyCo.FVs( tyCoVarsOfType ) -- Use in assertions
    import {-# SOURCE #-} GHC.Core.Type( chooseFunTyFlag, typeKind, typeTypeOrConstraint )

       -- Transitively pulls in a LOT of stuff, better to break the loop

    -- friends:
    import GHC.Types.Var
    import GHC.Types.Var.Set( elemVarSet )
    import GHC.Core.TyCon
    import GHC.Core.Coercion.Axiom

    -- others
    import GHC.Builtin.Names

    import GHC.Types.Basic ( LeftOrRight(..), pickLR )
    import GHC.Utils.Outputable
    import GHC.Data.FastString
    import GHC.Utils.Misc
    import GHC.Utils.Panic
    import GHC.Utils.Binary

    -- libraries
    import qualified Data.Data as Data hiding ( TyCon )
    import Data.IORef ( IORef )   -- for CoercionHole
    import Control.DeepSeq

    {- **********************************************************************
    *                                                                       *
                            Type
    *                                                                       *
    ********************************************************************** -}

    -- | The key representation of types within the compiler

    type KindOrType = Type -- See Note [Arguments to type constructors]

    -- | The key type representing kinds in the compiler.
    type Kind = Type

    -- | Type synonym used for types of kind RuntimeRep.
    type RuntimeRepType = Type

    -- | Type synonym used for types of kind Levity.
    type LevityType = Type

    -- A type with a syntactically fixed RuntimeRep, in the sense
    -- of Note [Fixed RuntimeRep] in GHC.Tc.Utils.Concrete.
    type FRRType = Type

    -- If you edit this type, you may need to update the GHC formalism
    -- See Note [GHC Formalism] in GHC.Core.Lint
    data Type
      -- See Note [Non-trivial definitional equality]
      = TyVarTy Var -- ^ Vanilla type or kind variable (*never* a coercion variable)

      | AppTy
            Type
            Type            -- ^ Type application to something other than a 'TyCon'. Parameters:
                            --
                            --  1) Function: must /not/ be a 'TyConApp' or 'CastTy',
                            --     must be another 'AppTy', or 'TyVarTy'
                            --     See Note [Respecting definitional equality] \(EQ1) about the
                            --     no 'CastTy' requirement
                            --
                            --  2) Argument type

      | TyConApp
            TyCon
            [KindOrType]    -- ^ Application of a 'TyCon', including newtypes /and/ synonyms.
                            -- Invariant: saturated applications of 'FunTyCon' must
                            -- use 'FunTy' and saturated synonyms must use their own
                            -- constructors. However, /unsaturated/ 'FunTyCon's
                            -- do appear as 'TyConApp's.
                            -- Parameters:
                            --
                            -- 1) Type constructor being applied to.
                            --
                            -- 2) Type arguments. Might not have enough type arguments
                            --    here to saturate the constructor.
                            --    Even type synonyms are not necessarily saturated;
                            --    for example unsaturated type synonyms
                            --    can appear as the right hand side of a type synonym.

      | ForAllTy  -- See Note [ForAllTy]
            {-# UNPACK #-} !ForAllTyBinder
            Type            -- ^ A Π type.
                 -- See Note [Why ForAllTy can quantify over a coercion variable]
                 -- INVARIANT: If the binder is a coercion variable, it must
                 --            be mentioned in the Type.
                 --            See Note [Unused coercion variable in ForAllTy]

      | FunTy      -- ^ FUN m t1 t2   Very common, so an important special case
                    -- See Note [Function types]
         { Type -> FunTyFlag
    ft_af   :: FunTyFlag    -- Is this (->/FUN) or (=>) or (==>)?
                                     -- This info is fully specified by the kinds in
                                     --      ft_arg and ft_res
                                     -- Note [FunTyFlag] in GHC.Types.Var

         , Type -> Type
    ft_mult :: Mult           -- Multiplicity; always Many for (=>) and (==>)
         , Type -> Type
    ft_arg  :: Type           -- Argument type
         , Type -> Type
    ft_res  :: Type }         -- Result type

      | LitTy TyLit     -- ^ Type literals are similar to type constructors.

      | CastTy
            Type
            KindCoercion  -- ^ A kind cast. The coercion is always nominal.
                          -- INVARIANT: The cast is never reflexive \(EQ2)
                          -- INVARIANT: The Type is not a CastTy (use TransCo instead) \(EQ3)
                          -- INVARIANT: The Type is not a ForAllTy over a tyvar \(EQ4)
                          -- See Note [Respecting definitional equality]

      | CoercionTy
            Coercion    -- ^ Injection of a Coercion into a type
                        -- This should only ever be used in the RHS of an AppTy,
                        -- in the list of a TyConApp, when applying a promoted
                        -- GADT data constructor

      deriving Typeable Type
    Typeable Type =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> Type -> c Type)
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        -> (forall r. r -> c r) -> Constr -> c Type)
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    instance Outputable Type where
      ppr :: Type -> SDoc
    ppr = Type -> SDoc
    pprType

    -- NOTE:  Other parts of the code assume that type literals do not contain
    -- types or type variables.
    data TyLit
      = NumTyLit Integer
      | StrTyLit FastString
      | CharTyLit Char
      deriving (TyLit -> TyLit -> Bool
    (TyLit -> TyLit -> Bool) -> (TyLit -> TyLit -> Bool) -> Eq TyLit
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    $c== :: TyLit -> TyLit -> Bool
    == :: TyLit -> TyLit -> Bool
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    /= :: TyLit -> TyLit -> Bool
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    -- Non-determinism arises due to uniqCompareFS
    nonDetCmpTyLit :: TyLit -> TyLit -> Ordering
    nonDetCmpTyLit :: TyLit -> TyLit -> Ordering
    nonDetCmpTyLit = (FastString -> NonDetFastString) -> TyLit -> TyLit -> Ordering
    forall r. Ord r => (FastString -> r) -> TyLit -> TyLit -> Ordering
    cmpTyLitWith FastString -> NonDetFastString
    NonDetFastString

    -- Slower than nonDetCmpTyLit but deterministic
    cmpTyLit :: TyLit -> TyLit -> Ordering
    cmpTyLit :: TyLit -> TyLit -> Ordering
    cmpTyLit = (FastString -> LexicalFastString) -> TyLit -> TyLit -> Ordering
    forall r. Ord r => (FastString -> r) -> TyLit -> TyLit -> Ordering
    cmpTyLitWith FastString -> LexicalFastString
    LexicalFastString

    {-# INLINE cmpTyLitWith #-}
    cmpTyLitWith :: Ord r => (FastString -> r) -> TyLit -> TyLit -> Ordering
    cmpTyLitWith :: forall r. Ord r => (FastString -> r) -> TyLit -> TyLit -> Ordering
    cmpTyLitWith FastString -> r
    _ (NumTyLit  Integer
    x) (NumTyLit  Integer
    y) = Integer -> Integer -> Ordering
    forall a. Ord a => a -> a -> Ordering
    compare Integer
    x Integer
    y
    cmpTyLitWith FastString -> r
    w (StrTyLit  FastString
    x) (StrTyLit  FastString
    y) = r -> r -> Ordering
    forall a. Ord a => a -> a -> Ordering
    compare (FastString -> r
    w FastString
    x) (FastString -> r
    w FastString
    y)
    cmpTyLitWith FastString -> r
    _ (CharTyLit Char
    x) (CharTyLit Char
    y) = Char -> Char -> Ordering
    forall a. Ord a => a -> a -> Ordering
    compare Char
    x Char
    y
    cmpTyLitWith FastString -> r
    _ TyLit
    a TyLit
    b = Int -> Int -> Ordering
    forall a. Ord a => a -> a -> Ordering
    compare (TyLit -> Int
    tag TyLit
    a) (TyLit -> Int
    tag TyLit
    b)
      where
        tag :: TyLit -> Int
        tag :: TyLit -> Int
    tag NumTyLit{}  = Int
    0
        tag StrTyLit{}  = Int
    1
        tag CharTyLit{} = Int
    2

    instance Outputable TyLit where
       ppr :: TyLit -> SDoc
    ppr = TyLit -> SDoc
    pprTyLit

    {- Note [Function types]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    FunTy is the constructor for a function type.  Here are the details:

    * The primitive function type constructor FUN has kind
         FUN :: forall (m :: Multiplicity) ->
                forall {r1 :: RuntimeRep} {r2 :: RuntimeRep}.
                TYPE r1 ->
                TYPE r2 ->
                Type
      mkTyConApp ensures that we convert a saturated application
        TyConApp FUN [m,r1,r2,t1,t2] into FunTy FTF_T_T m t1 t2
      dropping the 'r1' and 'r2' arguments; they are easily recovered
      from 't1' and 't2'. The FunTyFlag is always FTF_T_T, because
      we build constraint arrows (=>) with e.g. mkPhiTy and friends,
      never `mkTyConApp funTyCon args`.

    * For the time being its RuntimeRep quantifiers are left
      inferred. This is to allow for it to evolve.

    * Because the RuntimeRep args came first historically (that is,
      the arrow type constructor gained these arguments before gaining
      the Multiplicity argument), we wanted to be able to say
        type (->) = FUN Many
      which we do in library module GHC.Types. This means that the
      Multiplicity argument must precede the RuntimeRep arguments --
      and it means changing the name of the primitive constructor from
      (->) to FUN.

    * The multiplicity argument is dependent, because Typeable does not
      support a type such as `Multiplicity -> forall {r1 r2 :: RuntimeRep}. ...`.
      There is a plan to change the argument order and make the
      multiplicity argument nondependent in #20164.

    * Re the ft_af field: see Note [FunTyFlag] in GHC.Types.Var
      See Note [Types for coercions, predicates, and evidence]
      This visibility info makes no difference in Core; it matters
      only when we regard the type as a Haskell source type.

    Note [Types for coercions, predicates, and evidence]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We treat differently:

      (a) Predicate types
            Test: isPredTy
            Binders: DictIds
            Kind: Constraint
            Examples: (Eq a), and (a ~ b)

      (b) Coercion types are primitive, unboxed equalities
            Test: isCoVarTy
            Binders: CoVars (can appear in coercions)
            Kind: TYPE (TupleRep [])
            Examples: (t1 ~# t2) or (t1 ~R# t2)

      (c) Evidence types is the type of evidence manipulated by
          the type constraint solver.
            Test: isEvVarType
            Binders: EvVars
            Kind: Constraint or TYPE (TupleRep [])
            Examples: all coercion types and predicate types

    Coercion types and predicate types are mutually exclusive,
    but evidence types are a superset of both.

    When treated as a user type,

      - Predicates (of kind Constraint) are invisible and are
        implicitly instantiated

      - Coercion types, and non-pred evidence types (i.e. not
        of kind Constraint), are just regular old types, are
        visible, and are not implicitly instantiated.

    In a FunTy { ft_af = af } and af = FTF_C_T or FTF_C_C, the argument
    type is always a Predicate type.

    Note [Weird typing rule for ForAllTy]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Here are the typing rules for ForAllTy:

    tyvar : Type
    inner : TYPE r
    tyvar does not occur in r
    ------------------------------------
    ForAllTy (Bndr tyvar vis) inner : TYPE r

    inner : TYPE r
    ------------------------------------
    ForAllTy (Bndr covar vis) inner : Type

    Note that the kind of the result depends on whether the binder is a
    tyvar or a covar. The kind of a forall-over-tyvar is the same as
    the kind of the inner type. This is because quantification over types
    is erased before runtime. By contrast, the kind of a forall-over-covar
    is always Type, because a forall-over-covar is compiled into a function
    taking a 0-bit-wide erased coercion argument.

    Because the tyvar form above includes r in its result, we must
    be careful not to let any variables escape -- thus the last premise
    of the rule above.

    Note [Arguments to type constructors]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Because of kind polymorphism, in addition to type application we now
    have kind instantiation. We reuse the same notations to do so.

    For example:

      Just (* -> *) Maybe
      Right * Nat Zero

    are represented by:

      TyConApp (PromotedDataCon Just) [* -> *, Maybe]
      TyConApp (PromotedDataCon Right) [*, Nat, (PromotedDataCon Zero)]

    Important note: Nat is used as a *kind* and not as a type. This can be
    confusing, since type-level Nat and kind-level Nat are identical. We
    use the kind of (PromotedDataCon Right) to know if its arguments are
    kinds or types.

    This kind instantiation only happens in TyConApp currently.

    Note [Non-trivial definitional equality]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Is ((IO |> co1) Int |> co2) equal to (IO Int)?
    Assume
       co1 :: (Type->Type) ~ (Type->Wombat)
       co2 :: Wombat ~ Type
    Well, yes.  The casts are just getting in the way.
    See also Note [Respecting definitional equality].

    So we do this:

    (EQTYPE)
      The `eqType` function, which defines Core's type equality relation,
      - /ignores/ casts, and
      - /ignores/ coercion arguments
      - /provided/ two types have the same kind

    This allows us to be a little sloppier in keeping track of coercions, which is a
    good thing. It also means that eqType does not depend on eqCoercion, which is
    also a good thing.

    Why is this sensible? That is, why is something different than α-equivalence
    appropriate for the implementation of eqType?

    Anything smaller than ~ and homogeneous is an appropriate definition for
    equality. The type safety of FC depends only on ~. Let's say η : τ ~ σ. Any
    expression of type τ can be transmuted to one of type σ at any point by
    casting. The same is true of expressions of type σ. So in some sense, τ and σ
    are interchangeable.

    But let's be more precise. If we examine the typing rules of FC (say, those in
    https://richarde.dev/papers/2015/equalities/equalities.pdf)
    there are several places where the same metavariable is used in two different
    premises to a rule. (For example, see Ty_App.) There is an implicit equality
    check here. What definition of equality should we use? By convention, we use
    α-equivalence. Take any rule with one (or more) of these implicit equality
    checks. Then there is an admissible rule that uses ~ instead of the implicit
    check, adding in casts as appropriate.

    The only problem here is that ~ is heterogeneous. To make the kinds work out
    in the admissible rule that uses ~, it is necessary to homogenize the
    coercions. That is, if we have η : (τ : κ1) ~ (σ : κ2), then we don't use η;
    we use η |> kind η, which is homogeneous.

    The effect of this all is that eqType, the implementation of the implicit
    equality check, can use any homogeneous relation that is smaller than ~, as
    those rules must also be admissible.

    A more drawn out argument around all of this is presented in Section 7.2 of
    Richard E's thesis (http://richarde.dev/papers/2016/thesis/eisenberg-thesis.pdf).

    What would go wrong if we insisted on the casts matching? See the beginning of
    Section 8 in the unpublished paper above. Theoretically, nothing at all goes
    wrong. But in practical terms, getting the coercions right proved to be
    nightmarish. And types would explode: during kind-checking, we often produce
    reflexive kind coercions. When we try to cast by these, mkCastTy just discards
    them. But if we used an eqType that distinguished between Int and Int |> <*>,
    then we couldn't discard -- the output of kind-checking would be enormous,
    and we would need enormous casts with lots of CoherenceCo's to straighten
    them out.

    Would anything go wrong if eqType looked through type families? No, not at
    all. But that makes eqType rather hard to implement.

    Thus, the guideline for eqType is that it should be the largest
    easy-to-implement relation that is still smaller than ~ and homogeneous. The
    precise choice of relation is somewhat incidental, as long as the smart
    constructors and destructors in Type respect whatever relation is chosen.

    Another helpful principle with eqType is this:

     (EQ) If (t1 `eqType` t2) then I can replace t1 by t2 anywhere.

    This principle also tells us that eqType must relate only types with the
    same kinds.

    Interestingly, it must be the case that the free variables of t1 and t2
    might be different, even if t1 `eqType` t2. A simple example of this is
    if we have both cv1 :: k1 ~ k2 and cv2 :: k1 ~ k2 in the environment.
    Then t1 = t |> cv1 and t2 = t |> cv2 are eqType; yet cv1 is in the free
    vars of t1 and cv2 is in the free vars of t2. Unless we choose to implement
    eqType to be just α-equivalence, this wrinkle around free variables
    remains.

    Yet not all is lost: we can say that any two equal types share the same
    *relevant* free variables. Here, a relevant variable is a shallow
    free variable (see Note [Shallow and deep free variables] in GHC.Core.TyCo.FVs)
    that does not appear within a coercion. Note that type variables can
    appear within coercions (in, say, a Refl node), but that coercion variables
    cannot appear outside a coercion. We do not (yet) have a function to
    extract relevant free variables, but it would not be hard to write if
    the need arises.

    Note [Respecting definitional equality]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Note [Non-trivial definitional equality] introduces the property (EQ).
    How is this upheld?

    Any function that pattern matches on all the constructors will have to
    consider the possibility of CastTy. Presumably, those functions will handle
    CastTy appropriately and we'll be OK.

    More dangerous are the splitXXX functions. Let's focus on splitTyConApp.
    We don't want it to fail on (T a b c |> co). Happily, if we have
      (T a b c |> co) `eqType` (T d e f)
    then co must be reflexive. Why? eqType checks that the kinds are equal, as
    well as checking that (a `eqType` d), (b `eqType` e), and (c `eqType` f).
    By the kind check, we know that (T a b c |> co) and (T d e f) have the same
    kind. So the only way that co could be non-reflexive is for (T a b c) to have
    a different kind than (T d e f). But because T's kind is closed (all tycon kinds
    are closed), the only way for this to happen is that one of the arguments has
    to differ, leading to a contradiction. Thus, co is reflexive.

    Accordingly, by eliminating reflexive casts, splitTyConApp need not worry
    about outermost casts to uphold (EQ). Eliminating reflexive casts is done
    in mkCastTy. This is (EQ2) below.

    Unfortunately, that's not the end of the story. Consider comparing
      (T a b c)      =?       (T a b |> (co -> <Type>)) (c |> co)
    These two types have the same kind (Type), but the left type is a TyConApp
    while the right type is not. To handle this case, we say that the right-hand
    type is ill-formed, requiring an AppTy never to have a casted TyConApp
    on its left. It is easy enough to pull around the coercions to maintain
    this invariant, as done in Type.mkAppTy. In the example above, trying to
    form the right-hand type will instead yield (T a b (c |> co |> sym co) |> <Type>).
    Both the casts there are reflexive and will be dropped. Huzzah.

    This idea of pulling coercions to the right works for splitAppTy as well.

    However, there is one hiccup: it's possible that a coercion doesn't relate two
    Pi-types. For example, if we have @type family Fun a b where Fun a b = a -> b@,
    then we might have (T :: Fun Type Type) and (T |> axFun) Int. That axFun can't
    be pulled to the right. But we don't need to pull it: (T |> axFun) Int is not
    `eqType` to any proper TyConApp -- thus, leaving it where it is doesn't violate
    our (EQ) property.

    In order to detect reflexive casts reliably, we must make sure not
    to have nested casts: we update (t |> co1 |> co2) to (t |> (co1 `TransCo` co2)).
    This is (EQ3) below.

    One other troublesome case is ForAllTy. See Note [Weird typing rule for ForAllTy].
    The kind of the body is the same as the kind of the ForAllTy. Accordingly,

      ForAllTy tv (ty |> co)     and     (ForAllTy tv ty) |> co

    are `eqType`. But only the first can be split by splitForAllTy. So we forbid
    the second form, instead pushing the coercion inside to get the first form.
    This is done in mkCastTy.

    In sum, in order to uphold (EQ), we need the following invariants:

      (EQ1) No decomposable CastTy to the left of an AppTy,
            where a "decomposable cast" is one that relates
            either a FunTy to a FunTy, or a ForAllTy to a ForAllTy.
      (EQ2) No reflexive casts in CastTy.
      (EQ3) No nested CastTys.
      (EQ4) No CastTy over (ForAllTy (Bndr tyvar vis) body).
            See Note [Weird typing rule for ForAllTy]

    These invariants are all documented above, in the declaration for Type.

    Note [Equality on FunTys]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    A (FunTy vis mult arg res) is just an abbreviation for a
      TyConApp funTyCon [mult, arg_rep, res_rep, arg, res]
    where
      arg :: TYPE arg_rep
      res :: TYPE res_rep
    Note that the vis field of a FunTy appears nowhere in the
    equivalent TyConApp. In Core, this is OK, because we no longer
    care about the visibility of the argument in a FunTy
    (the vis distinguishes between arg -> res and arg => res).
    In the type-checker, we are careful not to decompose FunTys
    with an invisible argument. See also Note [Decomposing fat arrow c=>t]
    in GHC.Core.Type.

    In order to compare FunTys while respecting how they could
    expand into TyConApps, we must check
    the kinds of the arg and the res.

    Note [ForAllTy]
    ~~~~~~~~~~~~~~~
    A (ForAllTy (Bndr tcv vis) ty) can quantify over a TyVar or, less commonly, a CoVar.
    See Note [Why ForAllTy can quantify over a coercion variable] for why we need the latter.

    (FT1) Invariant: See Note [Weird typing rule for ForAllTy]

    (FT2) Invariant: in (ForAllTy (Bndr tcv vis) ty),
          if tcv is a CoVar, then vis = coreTyLamForAllTyFlag.
       Visibility is not important for coercion abstractions,
       because they are not user-visible.

    (FT3) Invariant: see Note [Unused coercion variable in ForAllTy]

    Note [Why ForAllTy can quantify over a coercion variable]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The ForAllTyBinder in a ForAllTy can be (most often) a TyVar or (rarely)
    a CoVar. We support quantifying over a CoVar here in order to support
    a homogeneous (~#) relation (someday -- not yet implemented). Here is
    the example:

      type (:~~:) :: forall k1 k2. k1 -> k2 -> Type
      data a :~~: b where
        HRefl :: a :~~: a

    Assuming homogeneous equality (that is, with
      (~#) :: forall k. k -> k -> TYPE (TupleRep '[])
    ) after rejigging to make equalities explicit, we get a constructor that
    looks like

      HRefl :: forall k1 k2 (a :: k1) (b :: k2).
               forall (cv :: k1 ~# k2). (a |> cv) ~# b
            => (:~~:) k1 k2 a b

    Note that we must cast `a` by a cv bound in the same type in order to
    make this work out.

    See also https://gitlab.haskell.org/ghc/ghc/-/wikis/dependent-haskell/phase2
    which gives a general road map that covers this space.  Having this feature in
    Core does *not* mean we have it in source Haskell.  See #15710 about that.

    Note [Unused coercion variable in ForAllTy]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Suppose we have
      \(co:t1 ~# t2). e

    What type should we give to the above expression?
      (1) forall (co:t1 ~# t2) -> t
      (2) (t1 ~# t2) -> t

    If co is used in t, (1) should be the right choice.
    if co is not used in t, we would like to have (1) and (2) equivalent.

    However, we want to keep eqType simple and don't want eqType (1) (2) to return
    True in any case.

    We decide to always construct (2) if co is not used in t.

    Thus in mkLamType, we check whether the variable is a coercion
    variable (of type (t1 ~# t2), and whether it is un-used in the
    body. If so, it returns a FunTy instead of a ForAllTy.

    There are cases we want to skip the check. For example, the check is
    unnecessary when it is known from the context that the input variable
    is a type variable.  In those cases, we use mkForAllTy.

    Note [Weird typing rule for ForAllTy]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Here is the (truncated) typing rule for the dependent ForAllTy:

      inner : TYPE r
      tyvar is not free in r
      ----------------------------------------
      ForAllTy (Bndr tyvar vis) inner : TYPE r

    Note that the kind of `inner` is the kind of the overall ForAllTy. This is
    necessary because every ForAllTy over a type variable is erased at runtime.
    Thus the runtime representation of a ForAllTy (as encoded, via TYPE rep, in
    the kind) must be the same as the representation of the body. We must check
    for skolem-escape, though. The skolem-escape would prevent a definition like

      undefined :: forall (r :: RuntimeRep) (a :: TYPE r). a

    because the type's kind (TYPE r) mentions the out-of-scope r. Luckily, the real
    type of undefined is

      undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a

    and that HasCallStack constraint neatly sidesteps the potential skolem-escape
    problem.

    If the bound variable is a coercion variable:

      inner : TYPE r
      covar is free in inner
      ------------------------------------
      ForAllTy (Bndr covar vis) inner : Type

    Here, the kind of the ForAllTy is just Type, because coercion abstractions
    are *not* erased. The "covar is free in inner" premise is solely to maintain
    the representation invariant documented in
    Note [Unused coercion variable in ForAllTy]. Though there is surface similarity
    between this free-var check and the one in the tyvar rule, these two restrictions
    are truly unrelated.

    -}

    -- | A type labeled 'KnotTied' might have knot-tied tycons in it. See
    -- Note [Type checking recursive type and class declarations] in
    -- "GHC.Tc.TyCl"
    type KnotTied ty = ty

    {- **********************************************************************
    *                                                                       *
                            PredType
    *                                                                       *
    ********************************************************************** -}

    -- | A type of the form @p@ of constraint kind represents a value whose type is
    -- the Haskell predicate @p@, where a predicate is what occurs before
    -- the @=>@ in a Haskell type.
    --
    -- We use 'PredType' as documentation to mark those types that we guarantee to
    -- have this kind.
    --
    -- It can be expanded into its representation, but:
    --
    -- * The type checker must treat it as opaque
    --
    -- * The rest of the compiler treats it as transparent
    --
    -- Consider these examples:
    --
    -- > f :: (Eq a) => a -> Int
    -- > g :: (?x :: Int -> Int) => a -> Int
    -- > h :: (r\l) => {r} => {l::Int | r}
    --
    -- Here the @Eq a@ and @?x :: Int -> Int@ and @r\l@ are all called \"predicates\"
    type PredType = Type

    -- | A collection of 'PredType's
    type ThetaType = [PredType]

    {-
    (We don't support TREX records yet, but the setup is designed
    to expand to allow them.)

    A Haskell qualified type, such as that for f,g,h above, is
    represented using
            * a FunTy for the double arrow
            * with a type of kind Constraint as the function argument

    The predicate really does turn into a real extra argument to the
    function.  If the argument has type (p :: Constraint) then the predicate p is
    represented by evidence of type p.

    %************************************************************************
    %*                                                                      *
                Simple constructors
    %*                                                                      *
    %************************************************************************

    These functions are here so that they can be used by GHC.Builtin.Types.Prim,
    which in turn is imported by Type
    -}

    mkTyVarTy  :: TyVar   -> Type
    mkTyVarTy :: TyVar -> Type
    mkTyVarTy TyVar
    v = Bool -> SDoc -> Type -> Type
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (TyVar -> Bool
    isTyVar TyVar
    v) (TyVar -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr TyVar
    v SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> SDoc
    dcolon SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr (TyVar -> Type
    tyVarKind TyVar
    v)) (Type -> Type) -> Type -> Type
    forall a b. (a -> b) -> a -> b
    $
                  TyVar -> Type
    TyVarTy TyVar
    v

    mkTyVarTys :: [TyVar] -> [Type]
    mkTyVarTys :: [TyVar] -> [Type]
    mkTyVarTys = (TyVar -> Type) -> [TyVar] -> [Type]
    forall a b. (a -> b) -> [a] -> [b]
    map TyVar -> Type
    mkTyVarTy -- a common use of mkTyVarTy

    mkTyCoVarTy :: TyCoVar -> Type
    mkTyCoVarTy :: TyVar -> Type
    mkTyCoVarTy TyVar
    v
      | TyVar -> Bool
    isTyVar TyVar
    v
      = TyVar -> Type
    TyVarTy TyVar
    v
      | Bool
    otherwise
      = KindCoercion -> Type
    CoercionTy (TyVar -> KindCoercion
    CoVarCo TyVar
    v)

    mkTyCoVarTys :: [TyCoVar] -> [Type]
    mkTyCoVarTys :: [TyVar] -> [Type]
    mkTyCoVarTys = (TyVar -> Type) -> [TyVar] -> [Type]
    forall a b. (a -> b) -> [a] -> [b]
    map TyVar -> Type
    mkTyCoVarTy

    infixr 3 `mkFunTy`, `mkInvisFunTy`, `mkVisFunTyMany`

    mkNakedFunTy :: FunTyFlag -> Kind -> Kind -> Kind
    -- See Note [Naked FunTy] in GHC.Builtin.Types
    -- Always Many multiplicity; kinds have no linearity
    mkNakedFunTy :: FunTyFlag -> Type -> Type -> Type
    mkNakedFunTy FunTyFlag
    af Type
    arg Type
    res
     =  FunTy { ft_af :: FunTyFlag
    ft_af   = FunTyFlag
    af, ft_mult :: Type
    ft_mult = Type
    manyDataConTy
              , ft_arg :: Type
    ft_arg  = Type
    arg, ft_res :: Type
    ft_res  = Type
    res }

    mkFunTy :: HasDebugCallStack => FunTyFlag -> Mult -> Type -> Type -> Type
    mkFunTy :: HasDebugCallStack => FunTyFlag -> Type -> Type -> Type -> Type
    mkFunTy FunTyFlag
    af Type
    mult Type
    arg Type
    res
      = Bool -> SDoc -> Type -> Type
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (FunTyFlag
    af FunTyFlag -> FunTyFlag -> Bool
    forall a. Eq a => a -> a -> Bool
    == HasDebugCallStack => Type -> Type -> FunTyFlag
    Type -> Type -> FunTyFlag
    chooseFunTyFlag Type
    arg Type
    res) ([SDoc] -> SDoc
    forall doc. IsDoc doc => [doc] -> doc
    vcat
          [ String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "af" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> FunTyFlag -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr FunTyFlag
    af
          , String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "chooseAAF" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> FunTyFlag -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr (HasDebugCallStack => Type -> Type -> FunTyFlag
    Type -> Type -> FunTyFlag
    chooseFunTyFlag Type
    arg Type
    res)
          , String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "arg" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    arg SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> SDoc
    dcolon SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr (HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind Type
    arg)
          , String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "res" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    res SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> SDoc
    dcolon SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr (HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind Type
    res) ]) (Type -> Type) -> Type -> Type
    forall a b. (a -> b) -> a -> b
    $
        FunTy { ft_af :: FunTyFlag
    ft_af   = FunTyFlag
    af
              , ft_mult :: Type
    ft_mult = Type
    mult
              , ft_arg :: Type
    ft_arg  = Type
    arg
              , ft_res :: Type
    ft_res  = Type
    res }

    mkInvisFunTy :: HasDebugCallStack => Type -> Type -> Type
    mkInvisFunTy :: HasDebugCallStack => Type -> Type -> Type
    mkInvisFunTy Type
    arg Type
    res
      = HasDebugCallStack => FunTyFlag -> Type -> Type -> Type -> Type
    FunTyFlag -> Type -> Type -> Type -> Type
    mkFunTy (TypeOrConstraint -> FunTyFlag
    invisArg (HasDebugCallStack => Type -> TypeOrConstraint
    Type -> TypeOrConstraint
    typeTypeOrConstraint Type
    res)) Type
    manyDataConTy Type
    arg Type
    res

    mkInvisFunTys :: HasDebugCallStack => [Type] -> Type -> Type
    mkInvisFunTys :: HasDebugCallStack => [Type] -> Type -> Type
    mkInvisFunTys [Type]
    args Type
    res
      = (Type -> Type -> Type) -> Type -> [Type] -> Type
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr (HasDebugCallStack => FunTyFlag -> Type -> Type -> Type -> Type
    FunTyFlag -> Type -> Type -> Type -> Type
    mkFunTy FunTyFlag
    af Type
    manyDataConTy) Type
    res [Type]
    args
      where
        af :: FunTyFlag
    af = TypeOrConstraint -> FunTyFlag
    invisArg (HasDebugCallStack => Type -> TypeOrConstraint
    Type -> TypeOrConstraint
    typeTypeOrConstraint Type
    res)

    mkVisFunTy :: HasDebugCallStack => Mult -> Type -> Type -> Type
    -- Always TypeLike, user-specified multiplicity.
    mkVisFunTy :: HasDebugCallStack => Type -> Type -> Type -> Type
    mkVisFunTy = HasDebugCallStack => FunTyFlag -> Type -> Type -> Type -> Type
    FunTyFlag -> Type -> Type -> Type -> Type
    mkFunTy FunTyFlag
    visArgTypeLike

    -- | Make nested arrow types
    -- | Special, common, case: Arrow type with mult Many
    mkVisFunTyMany :: HasDebugCallStack => Type -> Type -> Type
    -- Always TypeLike, multiplicity Many
    mkVisFunTyMany :: HasDebugCallStack => Type -> Type -> Type
    mkVisFunTyMany = HasDebugCallStack => Type -> Type -> Type -> Type
    Type -> Type -> Type -> Type
    mkVisFunTy Type
    manyDataConTy

    mkVisFunTysMany :: [Type] -> Type -> Type
    -- Always TypeLike, multiplicity Many
    mkVisFunTysMany :: [Type] -> Type -> Type
    mkVisFunTysMany [Type]
    tys Type
    ty = (Type -> Type -> Type) -> Type -> [Type] -> Type
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr HasDebugCallStack => Type -> Type -> Type
    Type -> Type -> Type
    mkVisFunTyMany Type
    ty [Type]
    tys

    ---------------
    mkScaledFunTy :: HasDebugCallStack => FunTyFlag -> Scaled Type -> Type -> Type
    mkScaledFunTy :: HasDebugCallStack => FunTyFlag -> Scaled Type -> Type -> Type
    mkScaledFunTy FunTyFlag
    af (Scaled Type
    mult Type
    arg) Type
    res = HasDebugCallStack => FunTyFlag -> Type -> Type -> Type -> Type
    FunTyFlag -> Type -> Type -> Type -> Type
    mkFunTy FunTyFlag
    af Type
    mult Type
    arg Type
    res

    mkScaledFunTys :: HasDebugCallStack => [Scaled Type] -> Type -> Type
    -- All visible args
    -- Result type can be TypeLike or ConstraintLike
    -- Example of the latter: dataConWrapperType for the data con of a class
    mkScaledFunTys :: HasDebugCallStack => [Scaled Type] -> Type -> Type
    mkScaledFunTys [Scaled Type]
    tys Type
    ty = (Scaled Type -> Type -> Type) -> Type -> [Scaled Type] -> Type
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr (HasDebugCallStack => FunTyFlag -> Scaled Type -> Type -> Type
    FunTyFlag -> Scaled Type -> Type -> Type
    mkScaledFunTy FunTyFlag
    af) Type
    ty [Scaled Type]
    tys
      where
        af :: FunTyFlag
    af = TypeOrConstraint -> FunTyFlag
    visArg (HasDebugCallStack => Type -> TypeOrConstraint
    Type -> TypeOrConstraint
    typeTypeOrConstraint Type
    ty)

    ---------------
    -- | Like 'mkTyCoForAllTy', but does not check the occurrence of the binder
    -- See Note [Unused coercion variable in ForAllTy]
    mkForAllTy :: ForAllTyBinder -> Type -> Type
    mkForAllTy :: ForAllTyBinder -> Type -> Type
    mkForAllTy ForAllTyBinder
    bndr Type
    body
      = Bool -> SDoc -> Type -> Type
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (ForAllTyBinder -> Bool
    good_bndr ForAllTyBinder
    bndr) (ForAllTyBinder -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr ForAllTyBinder
    bndr SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    body) (Type -> Type) -> Type -> Type
    forall a b. (a -> b) -> a -> b
    $
        ForAllTyBinder -> Type -> Type
    ForAllTy ForAllTyBinder
    bndr Type
    body
      where
        -- Check ForAllTy invariants
        good_bndr :: ForAllTyBinder -> Bool
    good_bndr (Bndr TyVar
    cv ForAllTyFlag
    vis)
          | TyVar -> Bool
    isCoVar TyVar
    cv = ForAllTyFlag
    vis ForAllTyFlag -> ForAllTyFlag -> Bool
    forall a. Eq a => a -> a -> Bool
    == ForAllTyFlag
    coreTyLamForAllTyFlag
                         -- See (FT2) in Note [ForAllTy]
                      Bool -> Bool -> Bool
    && (TyVar
    cv TyVar -> VarSet -> Bool
    `elemVarSet` Type -> VarSet
    tyCoVarsOfType Type
    body)
                         -- See (FT3) in Note [ForAllTy]
          | Bool
    otherwise = Bool
    True

    -- | Wraps foralls over the type using the provided 'TyCoVar's from left to right
    mkForAllTys :: [ForAllTyBinder] -> Type -> Type
    mkForAllTys :: [ForAllTyBinder] -> Type -> Type
    mkForAllTys [ForAllTyBinder]
    tyvars Type
    ty = (ForAllTyBinder -> Type -> Type)
    -> Type -> [ForAllTyBinder] -> Type
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr ForAllTyBinder -> Type -> Type
    ForAllTy Type
    ty [ForAllTyBinder]
    tyvars

    -- | Wraps foralls over the type using the provided 'InvisTVBinder's from left to right
    mkInvisForAllTys :: [InvisTVBinder] -> Type -> Type
    mkInvisForAllTys :: [InvisTVBinder] -> Type -> Type
    mkInvisForAllTys [InvisTVBinder]
    tyvars = [ForAllTyBinder] -> Type -> Type
    mkForAllTys ([InvisTVBinder] -> [ForAllTyBinder]
    forall a. [VarBndr a Specificity] -> [VarBndr a ForAllTyFlag]
    tyVarSpecToBinders [InvisTVBinder]
    tyvars)

    mkPiTy :: HasDebugCallStack => PiTyBinder -> Type -> Type
    mkPiTy :: HasDebugCallStack => PiTyBinder -> Type -> Type
    mkPiTy (Anon Scaled Type
    ty1 FunTyFlag
    af) Type
    ty2  = HasDebugCallStack => FunTyFlag -> Scaled Type -> Type -> Type
    FunTyFlag -> Scaled Type -> Type -> Type
    mkScaledFunTy FunTyFlag
    af Scaled Type
    ty1 Type
    ty2
    mkPiTy (Named ForAllTyBinder
    bndr) Type
    ty    = ForAllTyBinder -> Type -> Type
    mkForAllTy ForAllTyBinder
    bndr Type
    ty

    mkPiTys :: HasDebugCallStack => [PiTyBinder] -> Type -> Type
    mkPiTys :: HasDebugCallStack => [PiTyBinder] -> Type -> Type
    mkPiTys [PiTyBinder]
    tbs Type
    ty = (PiTyBinder -> Type -> Type) -> Type -> [PiTyBinder] -> Type
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr HasDebugCallStack => PiTyBinder -> Type -> Type
    PiTyBinder -> Type -> Type
    mkPiTy Type
    ty [PiTyBinder]
    tbs

    -- | 'mkNakedTyConTy' creates a nullary 'TyConApp'. In general you
    -- should rather use 'GHC.Core.Type.mkTyConTy', which picks the shared
    -- nullary TyConApp from inside the TyCon (via tyConNullaryTy.  But
    -- we have to build the TyConApp tc [] in that TyCon field; that's
    -- what 'mkNakedTyConTy' is for.
    mkNakedTyConTy :: TyCon -> Type
    mkNakedTyConTy :: TyCon -> Type
    mkNakedTyConTy TyCon
    tycon = TyCon -> [Type] -> Type
    TyConApp TyCon
    tycon []

    tcMkVisFunTy :: Mult -> Type -> Type -> Type
    -- Always TypeLike result, user-specified multiplicity.
    -- Does not have the assert-checking in mkFunTy: used by the typechecker
    -- to avoid looking at the result kind, which may not be zonked
    tcMkVisFunTy :: Type -> Type -> Type -> Type
    tcMkVisFunTy Type
    mult Type
    arg Type
    res
      = FunTy { ft_af :: FunTyFlag
    ft_af = FunTyFlag
    visArgTypeLike, ft_mult :: Type
    ft_mult = Type
    mult
              , ft_arg :: Type
    ft_arg = Type
    arg, ft_res :: Type
    ft_res = Type
    res }

    tcMkInvisFunTy :: TypeOrConstraint -> Type -> Type -> Type
    -- Always invisible (constraint) argument, result specified by res_torc
    -- Does not have the assert-checking in mkFunTy: used by the typechecker
    -- to avoid looking at the result kind, which may not be zonked
    tcMkInvisFunTy :: TypeOrConstraint -> Type -> Type -> Type
    tcMkInvisFunTy TypeOrConstraint
    res_torc Type
    arg Type
    res
      = FunTy { ft_af :: FunTyFlag
    ft_af = TypeOrConstraint -> FunTyFlag
    invisArg TypeOrConstraint
    res_torc, ft_mult :: Type
    ft_mult = Type
    manyDataConTy
              , ft_arg :: Type
    ft_arg = Type
    arg, ft_res :: Type
    ft_res = Type
    res }

    tcMkScaledFunTys :: [Scaled Type] -> Type -> Type
    -- All visible args
    -- Result type must be TypeLike
    -- No mkFunTy assert checking; result kind may not be zonked
    tcMkScaledFunTys :: [Scaled Type] -> Type -> Type
    tcMkScaledFunTys [Scaled Type]
    tys Type
    ty = (Scaled Type -> Type -> Type) -> Type -> [Scaled Type] -> Type
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr Scaled Type -> Type -> Type
    tcMkScaledFunTy Type
    ty [Scaled Type]
    tys

    tcMkScaledFunTy :: Scaled Type -> Type -> Type
    tcMkScaledFunTy :: Scaled Type -> Type -> Type
    tcMkScaledFunTy (Scaled Type
    mult Type
    arg) Type
    res = Type -> Type -> Type -> Type
    tcMkVisFunTy Type
    mult Type
    arg Type
    res

    {-
    %************************************************************************
    %*                                                                      *
                Coercions
    %*                                                                      *
    %************************************************************************
    -}

    -- | A 'Coercion' is concrete evidence of the equality/convertibility
    -- of two types.

    -- If you edit this type, you may need to update the GHC formalism
    -- See Note [GHC Formalism] in GHC.Core.Lint
    data Coercion
      -- Each constructor has a "role signature", indicating the way roles are
      -- propagated through coercions.
      --    -  P, N, and R stand for coercions of the given role
      --    -  e stands for a coercion of a specific unknown role
      --           (think "role polymorphism")
      --    -  "e" stands for an explicit role parameter indicating role e.
      --    -   _ stands for a parameter that is not a Role or Coercion.

      -- These ones mirror the shape of types
      = -- Refl :: _ -> N
        -- A special case reflexivity for a very common case: Nominal reflexivity
        -- If you need Representational, use (GRefl Representational ty MRefl)
        --                               not (SubCo (Refl ty))
        Refl Type  -- See Note [Refl invariant]

      -- GRefl :: "e" -> _ -> Maybe N -> e
      -- See Note [Generalized reflexive coercion]
      | GRefl Role Type MCoercionN  -- See Note [Refl invariant]
              -- Use (Refl ty), not (GRefl Nominal ty MRefl)
              -- Use (GRefl Representational _ _), not (SubCo (GRefl Nominal _ _))

      -- These ones simply lift the correspondingly-named
      -- Type constructors into Coercions

      -- TyConAppCo :: "e" -> _ -> ?? -> e
      -- See Note [TyConAppCo roles]
      | TyConAppCo Role TyCon [Coercion]    -- lift TyConApp
                   -- The TyCon is never a synonym;
                   -- we expand synonyms eagerly
                   -- But it can be a type function
                   -- TyCon is never a saturated (->); use FunCo instead

      | AppCo Coercion CoercionN             -- lift AppTy
              -- AppCo :: e -> N -> e

      -- See Note [ForAllCo]
      | ForAllCo
          { KindCoercion -> TyVar
    fco_tcv  :: TyCoVar
          , KindCoercion -> ForAllTyFlag
    fco_visL :: !ForAllTyFlag -- Visibility of coercionLKind
          , KindCoercion -> ForAllTyFlag
    fco_visR :: !ForAllTyFlag -- Visibility of coercionRKind
                                      -- See (FC7) of Note [ForAllCo]
          , KindCoercion -> KindCoercion
    fco_kind :: KindCoercion
          , KindCoercion -> KindCoercion
    fco_body :: Coercion }
             -- ForAllCo :: _ -> N -> e -> e

      | FunCo  -- FunCo :: "e" -> N/P -> e -> e -> e
               -- See Note [FunCo] for fco_afl, fco_afr
            { KindCoercion -> Role
    fco_role         :: Role
            , KindCoercion -> FunTyFlag
    fco_afl          :: FunTyFlag   -- Arrow for coercionLKind
            , KindCoercion -> FunTyFlag
    fco_afr          :: FunTyFlag   -- Arrow for coercionRKind
            , KindCoercion -> KindCoercion
    fco_mult         :: CoercionN
            , KindCoercion -> KindCoercion
    fco_arg, KindCoercion -> KindCoercion
    fco_res :: Coercion }
           -- (if the role "e" is Phantom, the first coercion is, too)
           -- the first coercion is for the multiplicity

      -- These are special
      | CoVarCo CoVar      -- :: _ -> (N or R)
                           -- result role depends on the tycon of the variable's type

      | AxiomCo CoAxiomRule [Coercion]
         -- The coercion arguments always *precisely* saturate
         -- arity of (that branch of) the CoAxiom. If there are
         -- any left over, we use AppCo.
         -- See [Coercion axioms applied to coercions]
         -- The roles of the argument coercions are determined
         -- by the cab_roles field of the relevant branch of the CoAxiom

      | UnivCo  -- See Note [UnivCo]
                -- Of kind (lty ~role rty)
          { KindCoercion -> UnivCoProvenance
    uco_prov         :: UnivCoProvenance
          , KindCoercion -> Role
    uco_role         :: Role
          , KindCoercion -> Type
    uco_lty, KindCoercion -> Type
    uco_rty :: Type
          , KindCoercion -> [KindCoercion]
    uco_deps         :: [Coercion]  -- Coercions on which it depends
                   --   See Note [The importance of tracking UnivCo dependencies]
          }

      | SymCo Coercion             -- :: e -> e
      | TransCo Coercion Coercion  -- :: e -> e -> e

      | SelCo CoSel Coercion  -- See Note [SelCo]

      | LRCo   LeftOrRight CoercionN     -- Decomposes (t_left t_right)
        -- :: _ -> N -> N
      | InstCo Coercion CoercionN
        -- :: e -> N -> e
        -- See Note [InstCo roles]

      -- Extract a kind coercion from a (heterogeneous) type coercion
      -- NB: all kind coercions are Nominal
      | KindCo Coercion
         -- :: e -> N

      | SubCo CoercionN                  -- Turns a ~N into a ~R
        -- :: N -> R

      | HoleCo CoercionHole              -- ^ See Note [Coercion holes]
                                         -- Only present during typechecking
      deriving Typeable KindCoercion
    Typeable KindCoercion =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> KindCoercion -> c KindCoercion)
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c KindCoercion)
    -> (KindCoercion -> Constr)
    -> (KindCoercion -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c KindCoercion))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e))
        -> Maybe (c KindCoercion))
    -> ((forall b. Data b => b -> b) -> KindCoercion -> KindCoercion)
    -> (forall r r'.
        (r -> r' -> r)
        -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r)
    -> (forall r r'.
        (r' -> r -> r)
        -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r)
    -> (forall u. (forall d. Data d => d -> u) -> KindCoercion -> [u])
    -> (forall u.
        Int -> (forall d. Data d => d -> u) -> KindCoercion -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion)
    -> Data KindCoercion
    KindCoercion -> Constr
    KindCoercion -> DataType
    (forall b. Data b => b -> b) -> KindCoercion -> KindCoercion
    forall a.
    Typeable a =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> a -> c a)
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c a)
    -> (a -> Constr)
    -> (a -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c a))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
    -> ((forall b. Data b => b -> b) -> a -> a)
    -> (forall r r'.
        (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall r r'.
        (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall u. (forall d. Data d => d -> u) -> a -> [u])
    -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> Data a
    forall u. Int -> (forall d. Data d => d -> u) -> KindCoercion -> u
    forall u. (forall d. Data d => d -> u) -> KindCoercion -> [u]
    forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r
    forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r
    forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion
    forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion
    forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c KindCoercion
    forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> KindCoercion -> c KindCoercion
    forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c KindCoercion)
    forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c KindCoercion)
    $cgfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> KindCoercion -> c KindCoercion
    gfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> KindCoercion -> c KindCoercion
    $cgunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c KindCoercion
    gunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c KindCoercion
    $ctoConstr :: KindCoercion -> Constr
    toConstr :: KindCoercion -> Constr
    $cdataTypeOf :: KindCoercion -> DataType
    dataTypeOf :: KindCoercion -> DataType
    $cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c KindCoercion)
    dataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c KindCoercion)
    $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c KindCoercion)
    dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c KindCoercion)
    $cgmapT :: (forall b. Data b => b -> b) -> KindCoercion -> KindCoercion
    gmapT :: (forall b. Data b => b -> b) -> KindCoercion -> KindCoercion
    $cgmapQl :: forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r
    gmapQl :: forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r
    $cgmapQr :: forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r
    gmapQr :: forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r
    $cgmapQ :: forall u. (forall d. Data d => d -> u) -> KindCoercion -> [u]
    gmapQ :: forall u. (forall d. Data d => d -> u) -> KindCoercion -> [u]
    $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> KindCoercion -> u
    gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> KindCoercion -> u
    $cgmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion
    gmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion
    $cgmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion
    gmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion
    $cgmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion
    gmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion
    Data.Data

    data CoSel  -- See Note [SelCo]
      = SelTyCon Int Role  -- Decomposes (T co1 ... con); zero-indexed
                           -- Invariant: Given: SelCo (SelTyCon i r) co
                           --            we have r == tyConRole (coercionRole co) tc
                           --                and tc1 == tc2
                           --            where T tc1 _ = coercionLKind co
                           --                  T tc2 _ = coercionRKind co
                           -- See Note [SelCo]

      | SelFun FunSel      -- Decomposes (co1 -> co2)

      | SelForAll          -- Decomposes (forall a. co)

      deriving( CoSel -> CoSel -> Bool
    (CoSel -> CoSel -> Bool) -> (CoSel -> CoSel -> Bool) -> Eq CoSel
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    $c== :: CoSel -> CoSel -> Bool
    == :: CoSel -> CoSel -> Bool
    $c/= :: CoSel -> CoSel -> Bool
    /= :: CoSel -> CoSel -> Bool
    Eq, Typeable CoSel
    Typeable CoSel =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> CoSel -> c CoSel)
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c CoSel)
    -> (CoSel -> Constr)
    -> (CoSel -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c CoSel))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CoSel))
    -> ((forall b. Data b => b -> b) -> CoSel -> CoSel)
    -> (forall r r'.
        (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r)
    -> (forall r r'.
        (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r)
    -> (forall u. (forall d. Data d => d -> u) -> CoSel -> [u])
    -> (forall u. Int -> (forall d. Data d => d -> u) -> CoSel -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d) -> CoSel -> m CoSel)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> CoSel -> m CoSel)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> CoSel -> m CoSel)
    -> Data CoSel
    CoSel -> Constr
    CoSel -> DataType
    (forall b. Data b => b -> b) -> CoSel -> CoSel
    forall a.
    Typeable a =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> a -> c a)
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c a)
    -> (a -> Constr)
    -> (a -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c a))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
    -> ((forall b. Data b => b -> b) -> a -> a)
    -> (forall r r'.
        (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall r r'.
        (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall u. (forall d. Data d => d -> u) -> a -> [u])
    -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> Data a
    forall u. Int -> (forall d. Data d => d -> u) -> CoSel -> u
    forall u. (forall d. Data d => d -> u) -> CoSel -> [u]
    forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r
    forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r
    forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> CoSel -> m CoSel
    forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CoSel -> m CoSel
    forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c CoSel
    forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> CoSel -> c CoSel
    forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c CoSel)
    forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CoSel)
    $cgfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> CoSel -> c CoSel
    gfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> CoSel -> c CoSel
    $cgunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c CoSel
    gunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c CoSel
    $ctoConstr :: CoSel -> Constr
    toConstr :: CoSel -> Constr
    $cdataTypeOf :: CoSel -> DataType
    dataTypeOf :: CoSel -> DataType
    $cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c CoSel)
    dataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c CoSel)
    $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CoSel)
    dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CoSel)
    $cgmapT :: (forall b. Data b => b -> b) -> CoSel -> CoSel
    gmapT :: (forall b. Data b => b -> b) -> CoSel -> CoSel
    $cgmapQl :: forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r
    gmapQl :: forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r
    $cgmapQr :: forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r
    gmapQr :: forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r
    $cgmapQ :: forall u. (forall d. Data d => d -> u) -> CoSel -> [u]
    gmapQ :: forall u. (forall d. Data d => d -> u) -> CoSel -> [u]
    $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> CoSel -> u
    gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> CoSel -> u
    $cgmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> CoSel -> m CoSel
    gmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> CoSel -> m CoSel
    $cgmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CoSel -> m CoSel
    gmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CoSel -> m CoSel
    $cgmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CoSel -> m CoSel
    gmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CoSel -> m CoSel
    Data.Data, Eq CoSel
    Eq CoSel =>
    (CoSel -> CoSel -> Ordering)
    -> (CoSel -> CoSel -> Bool)
    -> (CoSel -> CoSel -> Bool)
    -> (CoSel -> CoSel -> Bool)
    -> (CoSel -> CoSel -> Bool)
    -> (CoSel -> CoSel -> CoSel)
    -> (CoSel -> CoSel -> CoSel)
    -> Ord CoSel
    CoSel -> CoSel -> Bool
    CoSel -> CoSel -> Ordering
    CoSel -> CoSel -> CoSel
    forall a.
    Eq a =>
    (a -> a -> Ordering)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> a)
    -> (a -> a -> a)
    -> Ord a
    $ccompare :: CoSel -> CoSel -> Ordering
    compare :: CoSel -> CoSel -> Ordering
    $c< :: CoSel -> CoSel -> Bool
    < :: CoSel -> CoSel -> Bool
    $c<= :: CoSel -> CoSel -> Bool
    <= :: CoSel -> CoSel -> Bool
    $c> :: CoSel -> CoSel -> Bool
    > :: CoSel -> CoSel -> Bool
    $c>= :: CoSel -> CoSel -> Bool
    >= :: CoSel -> CoSel -> Bool
    $cmax :: CoSel -> CoSel -> CoSel
    max :: CoSel -> CoSel -> CoSel
    $cmin :: CoSel -> CoSel -> CoSel
    min :: CoSel -> CoSel -> CoSel
    Ord )

    data FunSel  -- See Note [SelCo]
      = SelMult  -- Multiplicity
      | SelArg   -- Argument of function
      | SelRes   -- Result of function
      deriving( FunSel -> FunSel -> Bool
    (FunSel -> FunSel -> Bool)
    -> (FunSel -> FunSel -> Bool) -> Eq FunSel
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    $c== :: FunSel -> FunSel -> Bool
    == :: FunSel -> FunSel -> Bool
    $c/= :: FunSel -> FunSel -> Bool
    /= :: FunSel -> FunSel -> Bool
    Eq, Typeable FunSel
    Typeable FunSel =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> FunSel -> c FunSel)
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c FunSel)
    -> (FunSel -> Constr)
    -> (FunSel -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c FunSel))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c FunSel))
    -> ((forall b. Data b => b -> b) -> FunSel -> FunSel)
    -> (forall r r'.
        (r -> r' -> r)
        -> r -> (forall d. Data d => d -> r') -> FunSel -> r)
    -> (forall r r'.
        (r' -> r -> r)
        -> r -> (forall d. Data d => d -> r') -> FunSel -> r)
    -> (forall u. (forall d. Data d => d -> u) -> FunSel -> [u])
    -> (forall u. Int -> (forall d. Data d => d -> u) -> FunSel -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d) -> FunSel -> m FunSel)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> FunSel -> m FunSel)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> FunSel -> m FunSel)
    -> Data FunSel
    FunSel -> Constr
    FunSel -> DataType
    (forall b. Data b => b -> b) -> FunSel -> FunSel
    forall a.
    Typeable a =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> a -> c a)
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c a)
    -> (a -> Constr)
    -> (a -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c a))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
    -> ((forall b. Data b => b -> b) -> a -> a)
    -> (forall r r'.
        (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall r r'.
        (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall u. (forall d. Data d => d -> u) -> a -> [u])
    -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> Data a
    forall u. Int -> (forall d. Data d => d -> u) -> FunSel -> u
    forall u. (forall d. Data d => d -> u) -> FunSel -> [u]
    forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r
    forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r
    forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> FunSel -> m FunSel
    forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> FunSel -> m FunSel
    forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c FunSel
    forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> FunSel -> c FunSel
    forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c FunSel)
    forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c FunSel)
    $cgfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> FunSel -> c FunSel
    gfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> FunSel -> c FunSel
    $cgunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c FunSel
    gunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c FunSel
    $ctoConstr :: FunSel -> Constr
    toConstr :: FunSel -> Constr
    $cdataTypeOf :: FunSel -> DataType
    dataTypeOf :: FunSel -> DataType
    $cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c FunSel)
    dataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c FunSel)
    $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c FunSel)
    dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c FunSel)
    $cgmapT :: (forall b. Data b => b -> b) -> FunSel -> FunSel
    gmapT :: (forall b. Data b => b -> b) -> FunSel -> FunSel
    $cgmapQl :: forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r
    gmapQl :: forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r
    $cgmapQr :: forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r
    gmapQr :: forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r
    $cgmapQ :: forall u. (forall d. Data d => d -> u) -> FunSel -> [u]
    gmapQ :: forall u. (forall d. Data d => d -> u) -> FunSel -> [u]
    $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> FunSel -> u
    gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> FunSel -> u
    $cgmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> FunSel -> m FunSel
    gmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> FunSel -> m FunSel
    $cgmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> FunSel -> m FunSel
    gmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> FunSel -> m FunSel
    $cgmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> FunSel -> m FunSel
    gmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> FunSel -> m FunSel
    Data.Data, Eq FunSel
    Eq FunSel =>
    (FunSel -> FunSel -> Ordering)
    -> (FunSel -> FunSel -> Bool)
    -> (FunSel -> FunSel -> Bool)
    -> (FunSel -> FunSel -> Bool)
    -> (FunSel -> FunSel -> Bool)
    -> (FunSel -> FunSel -> FunSel)
    -> (FunSel -> FunSel -> FunSel)
    -> Ord FunSel
    FunSel -> FunSel -> Bool
    FunSel -> FunSel -> Ordering
    FunSel -> FunSel -> FunSel
    forall a.
    Eq a =>
    (a -> a -> Ordering)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> a)
    -> (a -> a -> a)
    -> Ord a
    $ccompare :: FunSel -> FunSel -> Ordering
    compare :: FunSel -> FunSel -> Ordering
    $c< :: FunSel -> FunSel -> Bool
    < :: FunSel -> FunSel -> Bool
    $c<= :: FunSel -> FunSel -> Bool
    <= :: FunSel -> FunSel -> Bool
    $c> :: FunSel -> FunSel -> Bool
    > :: FunSel -> FunSel -> Bool
    $c>= :: FunSel -> FunSel -> Bool
    >= :: FunSel -> FunSel -> Bool
    $cmax :: FunSel -> FunSel -> FunSel
    max :: FunSel -> FunSel -> FunSel
    $cmin :: FunSel -> FunSel -> FunSel
    min :: FunSel -> FunSel -> FunSel
    Ord )

    type CoercionN = Coercion       -- always nominal
    type CoercionR = Coercion       -- always representational
    type CoercionP = Coercion       -- always phantom
    type KindCoercion = CoercionN   -- always nominal

    instance Outputable Coercion where
      ppr :: KindCoercion -> SDoc
    ppr = KindCoercion -> SDoc
    pprCo

    instance Outputable CoSel where
      ppr :: CoSel -> SDoc
    ppr (SelTyCon Int
    n Role
    r) = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Tc" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    parens (Int -> SDoc
    forall doc. IsLine doc => Int -> doc
    int Int
    n SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> SDoc
    forall doc. IsLine doc => doc
    comma SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> Role -> SDoc
    pprOneCharRole Role
    r)
      ppr CoSel
    SelForAll      = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "All"
      ppr (SelFun FunSel
    fs)    = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Fun" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    parens (FunSel -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr FunSel
    fs)

    pprOneCharRole :: Role -> SDoc
    pprOneCharRole :: Role -> SDoc
    pprOneCharRole Role
    Nominal          = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'N'
    pprOneCharRole Role
    Representational = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'R'
    pprOneCharRole Role
    Phantom          = Char -> SDoc
    forall doc. IsLine doc => Char -> doc
    char Char
    'P'

    instance Outputable FunSel where
      ppr :: FunSel -> SDoc
    ppr FunSel
    SelMult = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "mult"
      ppr FunSel
    SelArg  = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "arg"
      ppr FunSel
    SelRes  = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "res"

    instance Binary CoSel where
       put_ :: WriteBinHandle -> CoSel -> IO ()
    put_ WriteBinHandle
    bh (SelTyCon Int
    n Role
    r)   = do { WriteBinHandle -> Word8 -> IO ()
    putByte WriteBinHandle
    bh Word8
    0; WriteBinHandle -> Int -> IO ()
    forall a. Binary a => WriteBinHandle -> a -> IO ()
    put_ WriteBinHandle
    bh Int
    n; WriteBinHandle -> Role -> IO ()
    forall a. Binary a => WriteBinHandle -> a -> IO ()
    put_ WriteBinHandle
    bh Role
    r }
       put_ WriteBinHandle
    bh CoSel
    SelForAll        = WriteBinHandle -> Word8 -> IO ()
    putByte WriteBinHandle
    bh Word8
    1
       put_ WriteBinHandle
    bh (SelFun FunSel
    SelMult) = WriteBinHandle -> Word8 -> IO ()
    putByte WriteBinHandle
    bh Word8
    2
       put_ WriteBinHandle
    bh (SelFun FunSel
    SelArg)  = WriteBinHandle -> Word8 -> IO ()
    putByte WriteBinHandle
    bh Word8
    3
       put_ WriteBinHandle
    bh (SelFun FunSel
    SelRes)  = WriteBinHandle -> Word8 -> IO ()
    putByte WriteBinHandle
    bh Word8
    4

       get :: ReadBinHandle -> IO CoSel
    get ReadBinHandle
    bh = do { h <- ReadBinHandle -> IO Word8
    getByte ReadBinHandle
    bh
                   ; case h of
                       Word8
    0 -> do { n <- ReadBinHandle -> IO Int
    forall a. Binary a => ReadBinHandle -> IO a
    get ReadBinHandle
    bh; r <- get bh; return (SelTyCon n r) }
                       Word8
    1 -> CoSel -> IO CoSel
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return CoSel
    SelForAll
                       Word8
    2 -> CoSel -> IO CoSel
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return (FunSel -> CoSel
    SelFun FunSel
    SelMult)
                       Word8
    3 -> CoSel -> IO CoSel
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return (FunSel -> CoSel
    SelFun FunSel
    SelArg)
                       Word8
    _ -> CoSel -> IO CoSel
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return (FunSel -> CoSel
    SelFun FunSel
    SelRes) }

    instance NFData CoSel where
      rnf :: CoSel -> ()
    rnf (SelTyCon Int
    n Role
    r) = Int
    n Int -> () -> ()
    forall a b. a -> b -> b
    `seq` Role
    r Role -> () -> ()
    forall a b. a -> b -> b
    `seq` ()
      rnf CoSel
    SelForAll      = ()
      rnf (SelFun FunSel
    fs)    = FunSel
    fs FunSel -> () -> ()
    forall a b. a -> b -> b
    `seq` ()

    -- | A semantically more meaningful type to represent what may or may not be a
    -- useful 'Coercion'.
    data MCoercion
      = MRefl
        -- A trivial Reflexivity coercion
      | MCo Coercion
        -- Other coercions
      deriving Typeable MCoercionN
    Typeable MCoercionN =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> MCoercionN -> c MCoercionN)
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c MCoercionN)
    -> (MCoercionN -> Constr)
    -> (MCoercionN -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c MCoercionN))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e))
        -> Maybe (c MCoercionN))
    -> ((forall b. Data b => b -> b) -> MCoercionN -> MCoercionN)
    -> (forall r r'.
        (r -> r' -> r)
        -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r)
    -> (forall r r'.
        (r' -> r -> r)
        -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r)
    -> (forall u. (forall d. Data d => d -> u) -> MCoercionN -> [u])
    -> (forall u.
        Int -> (forall d. Data d => d -> u) -> MCoercionN -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN)
    -> Data MCoercionN
    MCoercionN -> Constr
    MCoercionN -> DataType
    (forall b. Data b => b -> b) -> MCoercionN -> MCoercionN
    forall a.
    Typeable a =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> a -> c a)
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c a)
    -> (a -> Constr)
    -> (a -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c a))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
    -> ((forall b. Data b => b -> b) -> a -> a)
    -> (forall r r'.
        (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall r r'.
        (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall u. (forall d. Data d => d -> u) -> a -> [u])
    -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> Data a
    forall u. Int -> (forall d. Data d => d -> u) -> MCoercionN -> u
    forall u. (forall d. Data d => d -> u) -> MCoercionN -> [u]
    forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r
    forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r
    forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN
    forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN
    forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c MCoercionN
    forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> MCoercionN -> c MCoercionN
    forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c MCoercionN)
    forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MCoercionN)
    $cgfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> MCoercionN -> c MCoercionN
    gfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> MCoercionN -> c MCoercionN
    $cgunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c MCoercionN
    gunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c MCoercionN
    $ctoConstr :: MCoercionN -> Constr
    toConstr :: MCoercionN -> Constr
    $cdataTypeOf :: MCoercionN -> DataType
    dataTypeOf :: MCoercionN -> DataType
    $cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c MCoercionN)
    dataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c MCoercionN)
    $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MCoercionN)
    dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MCoercionN)
    $cgmapT :: (forall b. Data b => b -> b) -> MCoercionN -> MCoercionN
    gmapT :: (forall b. Data b => b -> b) -> MCoercionN -> MCoercionN
    $cgmapQl :: forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r
    gmapQl :: forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r
    $cgmapQr :: forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r
    gmapQr :: forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r
    $cgmapQ :: forall u. (forall d. Data d => d -> u) -> MCoercionN -> [u]
    gmapQ :: forall u. (forall d. Data d => d -> u) -> MCoercionN -> [u]
    $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> MCoercionN -> u
    gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> MCoercionN -> u
    $cgmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN
    gmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN
    $cgmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN
    gmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN
    $cgmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN
    gmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN
    Data.Data
    type MCoercionR = MCoercion
    type MCoercionN = MCoercion

    instance Outputable MCoercion where
      ppr :: MCoercionN -> SDoc
    ppr MCoercionN
    MRefl    = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "MRefl"
      ppr (MCo KindCoercion
    co) = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "MCo" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> KindCoercion -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr KindCoercion
    co

    {- Note [Refl invariant]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    Invariant 1: Refl lifting
            Refl (similar for GRefl r ty MRefl) is always lifted as far as possible.
        For example
            (Refl T) (Refl a) (Refl b) is normalised (by mkAppCo) to  (Refl (T a b)).

        You might think that a consequences is:
             Every identity coercion has Refl at the root

        But that's not quite true because of coercion variables.  Consider
             g         where g :: Int~Int
             Left h    where h :: Maybe Int ~ Maybe Int
        etc.  So the consequence is only true of coercions that
        have no coercion variables.

    Invariant 2: TyConAppCo
       An application of (Refl T) to some coercions, at least one of which is
       NOT the identity, is normalised to TyConAppCo.  (They may not be
       fully saturated however.)  TyConAppCo coercions (like all coercions
       other than Refl) are NEVER the identity.

    Note [Generalized reflexive coercion]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    GRefl is a generalized reflexive coercion (see #15192). It wraps a kind
    coercion, which might be reflexive (MRefl) or any coercion (MCo co). The typing
    rules for GRefl:

      ty : k1
      ------------------------------------
      GRefl r ty MRefl: ty ~r ty

      ty : k1       co :: k1 ~ k2
      ------------------------------------
      GRefl r ty (MCo co) : ty ~r ty |> co

    Consider we have

       g1 :: s ~r t
       s  :: k1
       g2 :: k1 ~ k2

    and we want to construct a coercions co which has type

       (s |> g2) ~r t

    We can define

       co = Sym (GRefl r s g2) ; g1

    It is easy to see that

       Refl == GRefl Nominal ty MRefl :: ty ~n ty

    A nominal reflexive coercion is quite common, so we keep the special form Refl to
    save allocation.

    Note [SelCo]
    ~~~~~~~~~~~~
    The Coercion form SelCo allows us to decompose a structural coercion, one
    between ForallTys, or TyConApps, or FunTys.

    There are three forms, split by the CoSel field inside the SelCo:
    SelTyCon, SelForAll, and SelFun.

    * SelTyCon:

          co : (T s1..sn) ~r0 (T t1..tn)
          T is a data type, not a newtype, nor an arrow type
          r = tyConRole tc r0 i
          i < n    (i is zero-indexed)
          ----------------------------------
          SelCo (SelTyCon i r) co : si ~r ti

      "Not a newtype": see Note [SelCo and newtypes]
      "Not an arrow type": see SelFun below

       See Note [SelCo Cached Roles]

    * SelForAll:
          co : forall (a:k1).t1 ~r0 forall (a:k2).t2
          ----------------------------------
          SelCo SelForAll co : k1 ~N k2

      NB: SelForAll always gives a Nominal coercion.

    * The SelFun form, for functions, has three sub-forms for the three
      components of the function type (multiplicity, argument, result).

          co : (s1 %{m1}-> t1) ~r0 (s2 %{m2}-> t2)
          r = funRole r0 SelMult
          ----------------------------------
          SelCo (SelFun SelMult) co : m1 ~r m2

          co : (s1 %{m1}-> t1) ~r0 (s2 %{m2}-> t2)
          r = funRole r0 SelArg
          ----------------------------------
          SelCo (SelFun SelArg) co : s1 ~r s2

          co : (s1 %{m1}-> t1) ~r0 (s2 %{m2}-> t2)
          r = funRole r0 SelRes
          ----------------------------------
          SelCo (SelFun SelRes) co : t1 ~r t2

    Note [FunCo]
    ~~~~~~~~~~~~
    Just as FunTy has a ft_af :: FunTyFlag field, FunCo (which connects
    two function types) has two FunTyFlag fields:
         funco_afl, funco_afr :: FunTyFlag
    In all cases, the FunTyFlag is recoverable from the kinds of the argument
    and result types/coercions; but experiments show that it's better to
    cache it.

    Why does FunCo need /two/ flags? If we have a single method class,
    implemented as a newtype
       class C a where { op :: [a] -> a }
    then we can have a coercion
       co :: C Int ~R ([Int]->Int)
    So now we can define
       FunCo co <Bool> : (C Int => Bool) ~R (([Int]->Int) -> Bool)
    Notice that the left and right arrows are different!  Hence two flags,
    one for coercionLKind and one for coercionRKind.

    Note [Coercion axioms applied to coercions]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The reason coercion axioms can be applied to coercions and not just
    types is to allow for better optimization.  There are some cases where
    we need to be able to "push transitivity inside" an axiom in order to
    expose further opportunities for optimization.

    For example, suppose we have

      C a : t[a] ~ F a
      g   : b ~ c

    and we want to optimize

      sym (C b) ; t[g] ; C c

    which has the kind

      F b ~ F c

    (stopping through t[b] and t[c] along the way).

    We'd like to optimize this to just F g -- but how?  The key is
    that we need to allow axioms to be instantiated by *coercions*,
    not just by types.  Then we can (in certain cases) push
    transitivity inside the axiom instantiations, and then react
    opposite-polarity instantiations of the same axiom.  In this
    case, e.g., we match t[g] against the LHS of (C c)'s kind, to
    obtain the substitution  a |-> g  (note this operation is sort
    of the dual of lifting!) and hence end up with

      C g : t[b] ~ F c

    which indeed has the same kind as  t[g] ; C c.

    Now we have

      sym (C b) ; C g

    which can be optimized to F g.

    Note [Required foralls in Core]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider the CoreExpr (Lam a e) where `a` is a TyVar, and (e::e_ty).
    It has type
       forall a. e_ty
    Note the Specified visibility of (forall a. e_ty); the Core type just isn't able
    to express more than one visiblity, and we pick `Specified`.  See `exprType` and
    `mkLamType` in GHC.Core.Utils, and `GHC.Type.Var.coreLamForAllTyFlag`.

    So how can we ever get a term of type (forall a -> e_ty)?  Answer: /only/ via a
    cast built with ForAllCo.  See `GHC.Tc.Types.Evidence.mkWpForAllCast`.  This does
    not seem very satisfying, but it does the job.

    An alternative would be to put a visibility flag into `Lam` (a huge change),
    or into a `TyVar` (a more plausible change), but we leave that for the future.

    See also Note [ForAllTy and type equality] in GHC.Core.TyCo.Compare.

    Note [ForAllCo]
    ~~~~~~~~~~~~~~~
    See also Note [ForAllTy and type equality] in GHC.Core.TyCo.Compare.

    Constructing coercions between forall-types can be a bit tricky,
    because the kinds of the bound tyvars can be different.

    The typing rule is:

      kind_co : k1 ~N k2
      tv1:k1 |- co : t1 ~r t2
      if r=N, then vis1=vis2
      ------------------------------------
      ForAllCo (tv1:k1) vis1 vis2 kind_co co
         : forall (tv1:k1) <vis1>. t1
                  ~r
           forall (tv1:k2) <vis2>. (t2[tv1 |-> (tv1:k2) |> sym kind_co])

    Several things to note here

    (FC1) First, the TyCoVar stored in a ForAllCo is really just a convenience: this
      field should be a Name, as its kind is redundant. Thinking of the field as a
      Name is helpful in understanding what a ForAllCo means.  The kind of TyCoVar
      always matches the left-hand kind of the coercion.

      * The idea is that kind_co gives the two kinds of the tyvar. See how, in the
        conclusion, tv1 is assigned kind k1 on the left but kind k2 on the right.

      * Of course, a type variable can't have different kinds at the same time.
        So, in `co` itself we use (tv1 : k1); hence the premise
              tv1:k1 |- co : t1 ~r t2

      * The last wrinkle is that we need to fix the kinds in the conclusion. In
        t2, tv1 is assumed to have kind k1, but it has kind k2 in the conclusion of
         the rule. So we do a kind-fixing substitution, replacing (tv1:k1) with
         (tv1:k2) |> sym kind_co. This substitution is slightly bizarre, because it
        mentions the same name with different kinds, but it *is* well-kinded, noting
         that `(tv1:k2) |> sym kind_co` has kind k1.

      We could instead store just a Name in the ForAllCo, and it might even be
      more efficient to do so. But we can't add Names to, e.g., VarSets, and
      there generally is just an impedance mismatch in a bunch of places. So we
      use tv1. When we need tv2, we can use setTyVarKind.

    (FC2) Note that the kind coercion must be Nominal; and that the role `r` of
      the final coercion is the same as that of the body coercion.

    (FC3) A ForAllCo allows casting between visibilities.  For example:
             ForAllCo a Required Specified (SubCo (Refl ty))
               : (forall a -> ty) ~R (forall a. ty)
      But you can only cast between visiblities at Representational role;
      Hence the premise
          if r=N, then vis1=vis2
      in the typing rule.  See also Note [ForAllTy and type equality] in
      GHC.Core.TyCo.Compare.

    (FC4) See Note [Required foralls in Core].

    (FC5) In a /type/, in (ForAllTy cv ty) where cv is a CoVar, we insist that
      `cv` must appear free in `ty`; see Note [Unused coercion variable in ForAllTy]
      in GHC.Core.TyCo.Rep for the motivation.  If it does not appear free,
      use FunTy.

      However we do /not/ impose the same restriction on ForAllCo in /coercions/.
      Instead, in coercionLKind and coercionRKind, we use mkTyCoForAllTy to perform
      the check and construct a FunTy when necessary.  Why?
        * For a coercion, all that matters is its kind, So ForAllCo vs FunCo does not
           make a difference.
        * Even if cv occurs in body_co, it is possible that cv does not occur in the kind
          of body_co. Therefore the check in coercionKind is inevitable.

    (FC6) Invariant: in a ForAllCo where fco_tcv is a coercion variable, `cv`,
      we insist that `cv` appears only in positions that are erased. In fact we use
      a conservative approximation of this: we require that
           (almostDevoidCoVarOfCo cv fco_body)
      holds.  This function checks that `cv` appers only within the type in a Refl
      node and under a GRefl node (including in the Coercion stored in a GRefl).
      It's possible other places are OK, too, but this is a safe approximation.

      Why all this fuss?  See Section 5.8.5.2 of Richard's thesis. The idea is that
      we cannot prove that the type system is consistent with unrestricted use of this
      cv; the consistency proof uses an untyped rewrite relation that works over types
      with all coercions and casts removed. So, we can allow the cv to appear only in
      positions that are erased.

      Sadly, with heterogeneous equality, this restriction might be able to be
      violated; Richard's thesis is unable to prove that it isn't. Specifically, the
      liftCoSubst function might create an invalid coercion. Because a violation of
      the restriction might lead to a program that "goes wrong", it is checked all
      the time, even in a production compiler and without -dcore-lint. We *have*
      proved that the problem does not occur with homogeneous equality, so this
      check can be dropped once ~# is made to be homogeneous.

    (FC7) Invariant: in a ForAllCo, if fco_tcv is a CoVar, then
             fco_visL = fco_visR = coreTyLamForAllTyFlag
      c.f. (FT2) in Note [ForAllTy]

    Note [Predicate coercions]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    Suppose we have
       g :: a~b
    How can we coerce between types
       ([c]~a) => [a] -> c
    and
       ([c]~b) => [b] -> c
    where the equality predicate *itself* differs?

    Answer: we simply treat (~) as an ordinary type constructor, so these
    types really look like

       ((~) [c] a) -> [a] -> c
       ((~) [c] b) -> [b] -> c

    So the coercion between the two is obviously

       ((~) [c] g) -> [g] -> c

    Another way to see this to say that we simply collapse predicates to
    their representation type (see Type.coreView and Type.predTypeRep).

    This collapse is done by mkPredCo; there is no PredCo constructor
    in Coercion.  This is important because we need Nth to work on
    predicates too:
        SelCo (SelTyCon 1) ((~) [c] g) = g
    See Simplify.simplCoercionF, which generates such selections.

    Note [Roles]
    ~~~~~~~~~~~~
    Roles are a solution to the GeneralizedNewtypeDeriving problem, articulated
    in #1496. The full story is in docs/core-spec/core-spec.pdf. Also, see
    https://gitlab.haskell.org/ghc/ghc/wikis/roles-implementation

    Here is one way to phrase the problem:

    Given:
    newtype Age = MkAge Int
    type family F x
    type instance F Age = Bool
    type instance F Int = Char

    This compiles down to:
    axAge :: Age ~ Int
    axF1 :: F Age ~ Bool
    axF2 :: F Int ~ Char

    Then, we can make:
    (sym (axF1) ; F axAge ; axF2) :: Bool ~ Char

    Yikes!

    The solution is _roles_, as articulated in "Generative Type Abstraction and
    Type-level Computation" (POPL 2010), available at
    http://www.seas.upenn.edu/~sweirich/papers/popl163af-weirich.pdf

    The specification for roles has evolved somewhat since that paper. For the
    current full details, see the documentation in docs/core-spec. Here are some
    highlights.

    We label every equality with a notion of type equivalence, of which there are
    three options: Nominal, Representational, and Phantom. A ground type is
    nominally equivalent only with itself. A newtype (which is considered a ground
    type in Haskell) is representationally equivalent to its representation.
    Anything is "phantomly" equivalent to anything else. We use "N", "R", and "P"
    to denote the equivalences.

    The axioms above would be:
    axAge :: Age ~R Int
    axF1 :: F Age ~N Bool
    axF2 :: F Age ~N Char

    Then, because transitivity applies only to coercions proving the same notion
    of equivalence, the above construction is impossible.

    However, there is still an escape hatch: we know that any two types that are
    nominally equivalent are representationally equivalent as well. This is what
    the form SubCo proves -- it "demotes" a nominal equivalence into a
    representational equivalence. So, it would seem the following is possible:

    sub (sym axF1) ; F axAge ; sub axF2 :: Bool ~R Char   -- WRONG

    What saves us here is that the arguments to a type function F, lifted into a
    coercion, *must* prove nominal equivalence. So, (F axAge) is ill-formed, and
    we are safe.

    Roles are attached to parameters to TyCons. When lifting a TyCon into a
    coercion (through TyConAppCo), we need to ensure that the arguments to the
    TyCon respect their roles. For example:

    data T a b = MkT a (F b)

    If we know that a1 ~R a2, then we know (T a1 b) ~R (T a2 b). But, if we know
    that b1 ~R b2, we know nothing about (T a b1) and (T a b2)! This is because
    the type function F branches on b's *name*, not representation. So, we say
    that 'a' has role Representational and 'b' has role Nominal. The third role,
    Phantom, is for parameters not used in the type's definition. Given the
    following definition

    data Q a = MkQ Int

    the Phantom role allows us to say that (Q Bool) ~R (Q Char), because we
    can construct the coercion Bool ~P Char (using UnivCo).

    See the paper cited above for more examples and information.

    Note [TyConAppCo roles]
    ~~~~~~~~~~~~~~~~~~~~~~~
    The TyConAppCo constructor has a role parameter, indicating the role at
    which the coercion proves equality. The choice of this parameter affects
    the required roles of the arguments of the TyConAppCo. To help explain
    it, assume the following definition:

      type instance F Int = Bool   -- Axiom axF : F Int ~N Bool
      newtype Age = MkAge Int      -- Axiom axAge : Age ~R Int
      data Foo a = MkFoo a         -- Role on Foo's parameter is Representational

    TyConAppCo Nominal Foo axF : Foo (F Int) ~N Foo Bool
      For (TyConAppCo Nominal) all arguments must have role Nominal. Why?
      So that Foo Age ~N Foo Int does *not* hold.

    TyConAppCo Representational Foo (SubCo axF) : Foo (F Int) ~R Foo Bool
    TyConAppCo Representational Foo axAge       : Foo Age     ~R Foo Int
      For (TyConAppCo Representational), all arguments must have the roles
      corresponding to the result of tyConRoles on the TyCon. This is the
      whole point of having roles on the TyCon to begin with. So, we can
      have Foo Age ~R Foo Int, if Foo's parameter has role R.

      If a Representational TyConAppCo is over-saturated (which is otherwise fine),
      the spill-over arguments must all be at Nominal. This corresponds to the
      behavior for AppCo.

    TyConAppCo Phantom Foo (UnivCo Phantom Int Bool) : Foo Int ~P Foo Bool
      All arguments must have role Phantom. This one isn't strictly
      necessary for soundness, but this choice removes ambiguity.

    The rules here dictate the roles of the parameters to mkTyConAppCo
    (should be checked by Lint).

    Note [SelCo and newtypes]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    Suppose we have

      newtype N a = MkN Int
      type role N representational

    This yields axiom

      NTCo:N :: forall a. N a ~R Int

    We can then build

      co :: forall a b. N a ~R N b
      co = NTCo:N a ; sym (NTCo:N b)

    for any `a` and `b`. Because of the role annotation on N, if we use
    SelCo, we'll get out a representational coercion. That is:

      SelCo (SelTyCon 0 r) co :: forall a b. a ~r b

    Yikes! Clearly, this is terrible. The solution is simple: forbid
    SelCo to be used on newtypes if the internal coercion is representational.
    See the SelCo equation for GHC.Core.Lint.lintCoercion.

    This is not just some corner case discovered by a segfault somewhere;
    it was discovered in the proof of soundness of roles and described
    in the "Safe Coercions" paper (ICFP '14).

    Note [SelCo Cached Roles]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    Why do we cache the role of SelCo in the SelCo constructor?
    Because computing role(Nth i co) involves figuring out that

      co :: T tys1 ~ T tys2

    using coercionKind, and finding (coercionRole co), and then looking
    at the tyConRoles of T. Avoiding bad asymptotic behaviour here means
    we have to compute the kind and role of a coercion simultaneously,
    which makes the code complicated and inefficient.

    This only happens for SelCo. Caching the role solves the problem, and
    allows coercionKind and coercionRole to be simple.

    See #11735

    Note [InstCo roles]
    ~~~~~~~~~~~~~~~~~~~
    Here is (essentially) the typing rule for InstCo:

    g :: (forall a. t1) ~r (forall a. t2)
    w :: s1 ~N s2
    ------------------------------- InstCo
    InstCo g w :: (t1 [a |-> s1]) ~r (t2 [a |-> s2])

    Note that the Coercion w *must* be nominal. This is necessary
    because the variable a might be used in a "nominal position"
    (that is, a place where role inference would require a nominal
    role) in t1 or t2. If we allowed w to be representational, we
    could get bogus equalities.

    A more nuanced treatment might be able to relax this condition
    somewhat, by checking if t1 and/or t2 use their bound variables
    in nominal ways. If not, having w be representational is OK.

    %************************************************************************
    %*                                                                      *
                    UnivCo
    %*                                                                      *
    %************************************************************************

    Note [UnivCo]
    ~~~~~~~~~~~~~
    A UnivCo is a coercion whose proof does not directly express its role
    and kind (indeed for some UnivCos, like PluginProv, there /is/ no proof).

    The different kinds of UnivCo are described by UnivCoProvenance.  Really each
    is entirely separate, but they all share the need to represent these fields:

      UnivCo
          { uco_prov         :: UnivCoProvenance
          , uco_role         :: Role
          , uco_lty, uco_rty :: Type
          , uco_deps         :: [Coercion]  -- Coercions on which it depends

    Here,
     * uco_role, uco_lty, uco_rty express the type of the coercion
     * uco_prov says where it came from
     * uco_deps specifies the coercions on which this proof (which is not
       explicity given) depends. See
       Note [The importance of tracking UnivCo dependencies]
    -}

    -- | For simplicity, we have just one UnivCo that represents a coercion from
    -- some type to some other type, with (in general) no restrictions on the
    -- type. The UnivCoProvenance specifies more exactly what the coercion really
    -- is and why a program should (or shouldn't!) trust the coercion.
    -- It is reasonable to consider each constructor of 'UnivCoProvenance'
    -- as a totally independent coercion form; their only commonality is
    -- that they don't tell you what types they coercion between. (That info
    -- is in the 'UnivCo' constructor of 'Coercion'.
    data UnivCoProvenance
      = PhantomProv    -- ^ See Note [Phantom coercions]. Only in Phantom
                       -- roled coercions

      | ProofIrrelProv -- ^ From the fact that any two coercions are
                       --   considered equivalent. See Note [ProofIrrelProv].
                       -- Can be used in Nominal or Representational coercions

      | PluginProv String
          -- ^ From a plugin, which asserts that this coercion is sound.
          --   The string and the variable set are for the use by the plugin.

      deriving (UnivCoProvenance -> UnivCoProvenance -> Bool
    (UnivCoProvenance -> UnivCoProvenance -> Bool)
    -> (UnivCoProvenance -> UnivCoProvenance -> Bool)
    -> Eq UnivCoProvenance
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    $c== :: UnivCoProvenance -> UnivCoProvenance -> Bool
    == :: UnivCoProvenance -> UnivCoProvenance -> Bool
    $c/= :: UnivCoProvenance -> UnivCoProvenance -> Bool
    /= :: UnivCoProvenance -> UnivCoProvenance -> Bool
    Eq, Eq UnivCoProvenance
    Eq UnivCoProvenance =>
    (UnivCoProvenance -> UnivCoProvenance -> Ordering)
    -> (UnivCoProvenance -> UnivCoProvenance -> Bool)
    -> (UnivCoProvenance -> UnivCoProvenance -> Bool)
    -> (UnivCoProvenance -> UnivCoProvenance -> Bool)
    -> (UnivCoProvenance -> UnivCoProvenance -> Bool)
    -> (UnivCoProvenance -> UnivCoProvenance -> UnivCoProvenance)
    -> (UnivCoProvenance -> UnivCoProvenance -> UnivCoProvenance)
    -> Ord UnivCoProvenance
    UnivCoProvenance -> UnivCoProvenance -> Bool
    UnivCoProvenance -> UnivCoProvenance -> Ordering
    UnivCoProvenance -> UnivCoProvenance -> UnivCoProvenance
    forall a.
    Eq a =>
    (a -> a -> Ordering)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> a)
    -> (a -> a -> a)
    -> Ord a
    $ccompare :: UnivCoProvenance -> UnivCoProvenance -> Ordering
    compare :: UnivCoProvenance -> UnivCoProvenance -> Ordering
    $c< :: UnivCoProvenance -> UnivCoProvenance -> Bool
    < :: UnivCoProvenance -> UnivCoProvenance -> Bool
    $c<= :: UnivCoProvenance -> UnivCoProvenance -> Bool
    <= :: UnivCoProvenance -> UnivCoProvenance -> Bool
    $c> :: UnivCoProvenance -> UnivCoProvenance -> Bool
    > :: UnivCoProvenance -> UnivCoProvenance -> Bool
    $c>= :: UnivCoProvenance -> UnivCoProvenance -> Bool
    >= :: UnivCoProvenance -> UnivCoProvenance -> Bool
    $cmax :: UnivCoProvenance -> UnivCoProvenance -> UnivCoProvenance
    max :: UnivCoProvenance -> UnivCoProvenance -> UnivCoProvenance
    $cmin :: UnivCoProvenance -> UnivCoProvenance -> UnivCoProvenance
    min :: UnivCoProvenance -> UnivCoProvenance -> UnivCoProvenance
    Ord, Typeable UnivCoProvenance
    Typeable UnivCoProvenance =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> UnivCoProvenance -> c UnivCoProvenance)
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c UnivCoProvenance)
    -> (UnivCoProvenance -> Constr)
    -> (UnivCoProvenance -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c UnivCoProvenance))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e))
        -> Maybe (c UnivCoProvenance))
    -> ((forall b. Data b => b -> b)
        -> UnivCoProvenance -> UnivCoProvenance)
    -> (forall r r'.
        (r -> r' -> r)
        -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r)
    -> (forall r r'.
        (r' -> r -> r)
        -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r)
    -> (forall u.
        (forall d. Data d => d -> u) -> UnivCoProvenance -> [u])
    -> (forall u.
        Int -> (forall d. Data d => d -> u) -> UnivCoProvenance -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d)
        -> UnivCoProvenance -> m UnivCoProvenance)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d)
        -> UnivCoProvenance -> m UnivCoProvenance)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d)
        -> UnivCoProvenance -> m UnivCoProvenance)
    -> Data UnivCoProvenance
    UnivCoProvenance -> Constr
    UnivCoProvenance -> DataType
    (forall b. Data b => b -> b)
    -> UnivCoProvenance -> UnivCoProvenance
    forall a.
    Typeable a =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> a -> c a)
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c a)
    -> (a -> Constr)
    -> (a -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c a))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
    -> ((forall b. Data b => b -> b) -> a -> a)
    -> (forall r r'.
        (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall r r'.
        (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall u. (forall d. Data d => d -> u) -> a -> [u])
    -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> Data a
    forall u.
    Int -> (forall d. Data d => d -> u) -> UnivCoProvenance -> u
    forall u. (forall d. Data d => d -> u) -> UnivCoProvenance -> [u]
    forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r
    forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r
    forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d)
    -> UnivCoProvenance -> m UnivCoProvenance
    forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d)
    -> UnivCoProvenance -> m UnivCoProvenance
    forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c UnivCoProvenance
    forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> UnivCoProvenance -> c UnivCoProvenance
    forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c UnivCoProvenance)
    forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c UnivCoProvenance)
    $cgfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> UnivCoProvenance -> c UnivCoProvenance
    gfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> UnivCoProvenance -> c UnivCoProvenance
    $cgunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c UnivCoProvenance
    gunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c UnivCoProvenance
    $ctoConstr :: UnivCoProvenance -> Constr
    toConstr :: UnivCoProvenance -> Constr
    $cdataTypeOf :: UnivCoProvenance -> DataType
    dataTypeOf :: UnivCoProvenance -> DataType
    $cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c UnivCoProvenance)
    dataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c UnivCoProvenance)
    $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c UnivCoProvenance)
    dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c UnivCoProvenance)
    $cgmapT :: (forall b. Data b => b -> b)
    -> UnivCoProvenance -> UnivCoProvenance
    gmapT :: (forall b. Data b => b -> b)
    -> UnivCoProvenance -> UnivCoProvenance
    $cgmapQl :: forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r
    gmapQl :: forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r
    $cgmapQr :: forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r
    gmapQr :: forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r
    $cgmapQ :: forall u. (forall d. Data d => d -> u) -> UnivCoProvenance -> [u]
    gmapQ :: forall u. (forall d. Data d => d -> u) -> UnivCoProvenance -> [u]
    $cgmapQi :: forall u.
    Int -> (forall d. Data d => d -> u) -> UnivCoProvenance -> u
    gmapQi :: forall u.
    Int -> (forall d. Data d => d -> u) -> UnivCoProvenance -> u
    $cgmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d)
    -> UnivCoProvenance -> m UnivCoProvenance
    gmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d)
    -> UnivCoProvenance -> m UnivCoProvenance
    $cgmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d)
    -> UnivCoProvenance -> m UnivCoProvenance
    gmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d)
    -> UnivCoProvenance -> m UnivCoProvenance
    $cgmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d)
    -> UnivCoProvenance -> m UnivCoProvenance
    gmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d)
    -> UnivCoProvenance -> m UnivCoProvenance
    Data.Data)
      -- Why Ord?  See Note [Ord instance of IfaceType] in GHC.Iface.Type

    instance Outputable UnivCoProvenance where
      ppr :: UnivCoProvenance -> SDoc
    ppr UnivCoProvenance
    PhantomProv      = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "(phantom)"
      ppr UnivCoProvenance
    ProofIrrelProv   = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "(proof irrel)"
      ppr (PluginProv String
    str) = SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    parens (String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "plugin" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    brackets (String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    str))

    instance NFData UnivCoProvenance where
      rnf :: UnivCoProvenance -> ()
    rnf UnivCoProvenance
    p = UnivCoProvenance
    p UnivCoProvenance -> () -> ()
    forall a b. a -> b -> b
    `seq` ()

    instance Binary UnivCoProvenance where
      put_ :: WriteBinHandle -> UnivCoProvenance -> IO ()
    put_ WriteBinHandle
    bh UnivCoProvenance
    PhantomProv    = WriteBinHandle -> Word8 -> IO ()
    putByte WriteBinHandle
    bh Word8
    1
      put_ WriteBinHandle
    bh UnivCoProvenance
    ProofIrrelProv = WriteBinHandle -> Word8 -> IO ()
    putByte WriteBinHandle
    bh Word8
    2
      put_ WriteBinHandle
    bh (PluginProv String
    a) = WriteBinHandle -> Word8 -> IO ()
    putByte WriteBinHandle
    bh Word8
    3 IO () -> IO () -> IO ()
    forall a b. IO a -> IO b -> IO b
    forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
    >> WriteBinHandle -> String -> IO ()
    forall a. Binary a => WriteBinHandle -> a -> IO ()
    put_ WriteBinHandle
    bh String
    a
      get :: ReadBinHandle -> IO UnivCoProvenance
    get ReadBinHandle
    bh = do
          tag <- ReadBinHandle -> IO Word8
    getByte ReadBinHandle
    bh
          case tag of
               Word8
    1 -> UnivCoProvenance -> IO UnivCoProvenance
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return UnivCoProvenance
    PhantomProv
               Word8
    2 -> UnivCoProvenance -> IO UnivCoProvenance
    forall a. a -> IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return UnivCoProvenance
    ProofIrrelProv
               Word8
    3 -> do a <- ReadBinHandle -> IO String
    forall a. Binary a => ReadBinHandle -> IO a
    get ReadBinHandle
    bh
                       return $ PluginProv a
               Word8
    _ -> String -> IO UnivCoProvenance
    forall a. HasCallStack => String -> a
    panic (String
    "get UnivCoProvenance " String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ Word8 -> String
    forall a. Show a => a -> String
    show Word8
    tag)

    {- Note [Phantom coercions]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider
         data T a = T1 | T2
    Then we have
         T s ~R T t
    for any old s,t. The witness for this is (TyConAppCo T Rep co),
    where (co :: s ~P t) is a phantom coercion built with PhantomProv.
    The role of the UnivCo is always Phantom.  The Coercion stored is the
    (nominal) kind coercion between the types
       kind(s) ~N kind (t)

    Note [ProofIrrelProv]
    ~~~~~~~~~~~~~~~~~~~~~
    A ProofIrrelProv is a coercion between coercions. For example:

      data G a where
        MkG :: G Bool

    In core, we get

      G :: * -> *
      MkG :: forall (a :: *). (a ~# Bool) -> G a

    Now, consider 'MkG -- that is, MkG used in a type -- and suppose we want
    a proof that ('MkG a1 co1) ~ ('MkG a2 co2). This will have to be

      TyConAppCo Nominal MkG [co3, co4]
      where
        co3 :: co1 ~ co2
        co4 :: a1 ~ a2

    Note that
      co1 :: a1 ~ Bool
      co2 :: a2 ~ Bool

    Here,
      co3 = UnivCo ProofIrrelProv Nominal (CoercionTy co1) (CoercionTy co2) [co5]
      where
        co5 :: (a1 ~# Bool) ~# (a2 ~# Bool)
        co5 = TyConAppCo Nominal (~#) [<Consraint#>, <Constraint#>, co4, <Bool>]

    Note [The importance of tracking UnivCo dependencies]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    It is vital that `UnivCo` (a coercion that lacks a proper proof)
    tracks the coercions on which it depends. To see why, consider this program:

        type S :: Nat -> Nat

        data T (a::Nat) where
          T1 :: T 0
          T2 :: ...

        f :: T a -> S (a+1) -> S 1
        f = /\a (x:T a) (y:a).
            case x of
              T1 (gco : a ~# 0) -> y |> wco

    For this to typecheck we need `wco :: S (a+1) ~# S 1`, given that `gco : a ~# 0`.
    To prove that we need to know that `a+1 = 1` if `a=0`, which a plugin might know.
    So it solves `wco` by providing a `UnivCo (PluginProv "my-plugin") (a+1) 1 [gco]`.

        But the `uco_deps` in `PluginProv` must mention `gco`!

    Why? Otherwise we might float the entire expression (y |> wco) out of the
    the case alternative for `T1` which brings `gco` into scope. If this
    happens then we aren't far from a segmentation fault or much worse.
    See #23923 for a real-world example of this happening.

    So it is /crucial/ for the `UnivCo` to mention, in `uco_deps`, the coercion
    variables used by the plugin to justify the `UnivCo` that it builds.  You
    should think of it like `TyConAppCo`: the `UnivCo` proof constructor is
    applied to a list of coercions, just as `TyConAppCo` is

    It's very convenient to record a full coercion, not just a set of free coercion
    variables, because during typechecking those coercions might contain coercion
    holes `HoleCo`, which get filled in later.
    -}

    {- **********************************************************************
    %*                                                                      *
                    Coercion holes
    %*                                                                      *
    %********************************************************************* -}

    -- | A coercion to be filled in by the type-checker. See Note [Coercion holes]
    data CoercionHole
      = CoercionHole { CoercionHole -> TyVar
    ch_co_var  :: CoVar
                           -- See Note [CoercionHoles and coercion free variables]

                     , CoercionHole -> IORef (Maybe KindCoercion)
    ch_ref :: IORef (Maybe Coercion)

                     , CoercionHole -> Bool
    ch_hetero_kind :: Bool
                           -- True <=> arises from a kind-level equality
                           -- See Note [Equalities with incompatible kinds]
                           --     in GHC.Tc.Solver.Equality, wrinkle (EIK2)
                     }

    coHoleCoVar :: CoercionHole -> CoVar
    coHoleCoVar :: CoercionHole -> TyVar
    coHoleCoVar = CoercionHole -> TyVar
    ch_co_var

    isHeteroKindCoHole :: CoercionHole -> Bool
    isHeteroKindCoHole :: CoercionHole -> Bool
    isHeteroKindCoHole = CoercionHole -> Bool
    ch_hetero_kind

    setCoHoleCoVar :: CoercionHole -> CoVar -> CoercionHole
    setCoHoleCoVar :: CoercionHole -> TyVar -> CoercionHole
    setCoHoleCoVar CoercionHole
    h TyVar
    cv = CoercionHole
    h { ch_co_var = cv }

    instance Data.Data CoercionHole where
      -- don't traverse?
      toConstr :: CoercionHole -> Constr
    toConstr CoercionHole
    _   = String -> Constr
    abstractConstr String
    "CoercionHole"
      gunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c CoercionHole
    gunfold forall b r. Data b => c (b -> r) -> c r
    _ forall r. r -> c r
    _  = String -> Constr -> c CoercionHole
    forall a. HasCallStack => String -> a
    error String
    "gunfold"
      dataTypeOf :: CoercionHole -> DataType
    dataTypeOf CoercionHole
    _ = String -> DataType
    mkNoRepType String
    "CoercionHole"

    instance Outputable CoercionHole where
      ppr :: CoercionHole -> SDoc
    ppr (CoercionHole { ch_co_var :: CoercionHole -> TyVar
    ch_co_var = TyVar
    cv, ch_hetero_kind :: CoercionHole -> Bool
    ch_hetero_kind = Bool
    hk })
        = SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    braces (TyVar -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr TyVar
    cv SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> Bool -> SDoc -> SDoc
    forall doc. IsOutput doc => Bool -> doc -> doc
    ppWhen Bool
    hk (String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "[hk]"))

    instance Uniquable CoercionHole where
      getUnique :: CoercionHole -> Unique
    getUnique (CoercionHole { ch_co_var :: CoercionHole -> TyVar
    ch_co_var = TyVar
    cv }) = TyVar -> Unique
    forall a. Uniquable a => a -> Unique
    getUnique TyVar
    cv

    {- Note [Coercion holes]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    During typechecking, constraint solving for type classes works by
      - Generate an evidence Id,  d7 :: Num a
      - Wrap it in a Wanted constraint, [W] d7 :: Num a
      - Use the evidence Id where the evidence is needed
      - Solve the constraint later
      - When solved, add an enclosing let-binding  let d7 = .... in ....
        which actually binds d7 to the (Num a) evidence

    For equality constraints we use a different strategy.  See Note [The
    equality types story] in GHC.Builtin.Types.Prim for background on equality constraints.
      - For /boxed/ equality constraints, (t1 ~N t2) and (t1 ~R t2), it's just
        like type classes above. (Indeed, boxed equality constraints *are* classes.)
      - But for /unboxed/ equality constraints (t1 ~R# t2) and (t1 ~N# t2)
        we use a different plan

    For unboxed equalities:
      - Generate a CoercionHole, a mutable variable just like a unification
        variable
      - Wrap the CoercionHole in a Wanted constraint; see GHC.Tc.Utils.TcEvDest
      - Use the CoercionHole in a Coercion, via HoleCo
      - Solve the constraint later
      - When solved, fill in the CoercionHole by side effect, instead of
        doing the let-binding thing

    The main reason for all this is that there may be no good place to let-bind
    the evidence for unboxed equalities:

      - We emit constraints for kind coercions, to be used to cast a
        type's kind. These coercions then must be used in types. Because
        they might appear in a top-level type, there is no place to bind
        these (unlifted) coercions in the usual way.

      - A coercion for (forall a. t1) ~ (forall a. t2) will look like
           forall a. (coercion for t1~t2)
        But the coercion for (t1~t2) may mention 'a', and we don't have
        let-bindings within coercions.  We could add them, but coercion
        holes are easier.

      - Moreover, nothing is lost from the lack of let-bindings. For
        dictionaries want to achieve sharing to avoid recomputing the
        dictionary.  But coercions are entirely erased, so there's little
        benefit to sharing. Indeed, even if we had a let-binding, we
        always inline types and coercions at every use site and drop the
        binding.

    Other notes about HoleCo:

     * INVARIANT: CoercionHole and HoleCo are used only during type checking,
       and should never appear in Core. Just like unification variables; a Type
       can contain a TcTyVar, but only during type checking. If, one day, we
       use type-level information to separate out forms that can appear during
       type-checking vs forms that can appear in core proper, holes in Core will
       be ruled out.

     * See Note [CoercionHoles and coercion free variables]

     * Coercion holes can be compared for equality like other coercions:
       by looking at the types coerced.

    Note [CoercionHoles and coercion free variables]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Why does a CoercionHole contain a CoVar, as well as reference to
    fill in?  Because we want to treat that CoVar as a free variable of
    the coercion.  See #14584, and Note [What prevents a
    constraint from floating] in GHC.Tc.Solver, item (4):

            forall k. [W] co1 :: t1 ~# t2 |> co2
                      [W] co2 :: k ~# *

    Here co2 is a CoercionHole. But we /must/ know that it is free in
    co1, because that's all that stops it floating outside the
    implication.
    -}

    {- *********************************************************************
    *                                                                      *
                    foldType  and   foldCoercion
    *                                                                      *
    ********************************************************************* -}

    {- Note [foldType]
    ~~~~~~~~~~~~~~~~~~
    foldType is a bit more powerful than perhaps it looks:

    * You can fold with an accumulating parameter, via
         TyCoFolder env (Endo a)
      Recall newtype Endo a = Endo (a->a)

    * You can fold monadically with a monad M, via
         TyCoFolder env (M a)
      provided you have
         instance ..  => Monoid (M a)

    Note [mapType vs foldType]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    We define foldType here, but mapType in module Type. Why?

    * foldType is used in GHC.Core.TyCo.FVs for finding free variables.
      It's a very simple function that analyses a type,
      but does not construct one.

    * mapType constructs new types, and so it needs to call
      the "smart constructors", mkAppTy, mkCastTy, and so on.
      These are sophisticated functions, and can't be defined
      here in GHC.Core.TyCo.Rep.

    Note [Specialising foldType]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We inline foldType at every call site (there are not many), so that it
    becomes specialised for the particular monoid *and* TyCoFolder at
    that site.  This is just for efficiency, but walking over types is
    done a *lot* in GHC, so worth optimising.

    We were worried that
        TyCoFolder env (Endo a)
    might not eta-expand.  Recall newtype Endo a = Endo (a->a).

    In particular, given
       fvs :: Type -> TyCoVarSet
       fvs ty = appEndo (foldType tcf emptyVarSet ty) emptyVarSet

       tcf :: TyCoFolder enf (Endo a)
       tcf = TyCoFolder { tcf_tyvar = do_tv, ... }
          where
            do_tvs is tv = Endo do_it
               where
                 do_it acc | tv `elemVarSet` is  = acc
                           | tv `elemVarSet` acc = acc
                           | otherwise = acc `extendVarSet` tv

    we want to end up with
       fvs ty = go emptyVarSet ty emptyVarSet
         where
           go env (TyVarTy tv) acc = acc `extendVarSet` tv
           ..etc..

    And indeed this happens.
      - Selections from 'tcf' are done at compile time
      - 'go' is nicely eta-expanded.

    We were also worried about
       deep_fvs :: Type -> TyCoVarSet
       deep_fvs ty = appEndo (foldType deep_tcf emptyVarSet ty) emptyVarSet

       deep_tcf :: TyCoFolder enf (Endo a)
       deep_tcf = TyCoFolder { tcf_tyvar = do_tv, ... }
          where
            do_tvs is tv = Endo do_it
               where
                 do_it acc | tv `elemVarSet` is  = acc
                           | tv `elemVarSet` acc = acc
                           | otherwise = deep_fvs (varType tv)
                                         `unionVarSet` acc
                                         `extendVarSet` tv

    Here deep_fvs and deep_tcf are mutually recursive, unlike fvs and tcf.
    But, amazingly, we get good code here too. GHC is careful not to mark
    TyCoFolder data constructor for deep_tcf as a loop breaker, so the
    record selections still cancel.  And eta expansion still happens too.

    Note [Use explicit recursion in foldTyCo]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In foldTyCo you'll see things like:
        go_tys _   []     = mempty
        go_tys env (t:ts) = go_ty env t `mappend` go_tys env ts
    where we use /explicit recursion/.  You might wonder about using foldl instead:
        go_tys env = foldl (\t acc -> go_ty env t `mappend` acc) mempty
    Or maybe foldl', or foldr.

    But don't do that for two reasons (see #24591)

    * We sometimes instantiate `a` to (Endo VarSet). Remembering
         newtype Endo a = Endo (a->a)
      after inlining `foldTyCo` bodily, the explicit recursion looks like
        go_tys _   []     = \acc -> acc
        go_tys env (t:ts) = \acc -> go_ty env t (go_tys env ts acc)
      The strictness analyser has no problem spotting that this function is
      strict in `acc`, provided `go_ty` is.

      But in the foldl form that is /much/ less obvious, and the strictness
      analyser fails utterly.  Result: lots and lots of thunks get built.  In
      !12037, Mikolaj found that GHC allocated /six times/ as much heap
      on test perf/compiler/T9198 as a result of this single problem!

    * Second, while I think that using `foldr` would be fine (simple experiments in
      #24591 suggest as much), it builds a local loop (with env free) and I'm not 100%
      confident it'll be lambda lifted in the end. It seems more direct just to write
      the code we want.

      On the other hand in `go_cvs` we might hope that the `foldr` will fuse with the
      `dVarSetElems` so I have used `foldr`.
    -}

    data TyCoFolder env a
      = TyCoFolder
          { forall env a. TyCoFolder env a -> Type -> Maybe Type
    tcf_view  :: Type -> Maybe Type   -- Optional "view" function
                                              -- E.g. expand synonyms
          , forall env a. TyCoFolder env a -> env -> TyVar -> a
    tcf_tyvar :: env -> TyVar -> a    -- Does not automatically recur
          , forall env a. TyCoFolder env a -> env -> TyVar -> a
    tcf_covar :: env -> CoVar -> a    -- into kinds of variables
          , forall env a. TyCoFolder env a -> env -> CoercionHole -> a
    tcf_hole  :: env -> CoercionHole -> a
              -- ^ What to do with coercion holes.
              -- See Note [Coercion holes] in "GHC.Core.TyCo.Rep".

          , forall env a.
    TyCoFolder env a -> env -> TyVar -> ForAllTyFlag -> env
    tcf_tycobinder :: env -> TyCoVar -> ForAllTyFlag -> env
              -- ^ The returned env is used in the extended scope
          }

    {-# INLINE foldTyCo  #-}  -- See Note [Specialising foldType]
    foldTyCo :: Monoid a => TyCoFolder env a -> env
             -> (Type -> a, [Type] -> a, Coercion -> a, [Coercion] -> a)
    foldTyCo :: forall a env.
    Monoid a =>
    TyCoFolder env a
    -> env
    -> (Type -> a, [Type] -> a, KindCoercion -> a, [KindCoercion] -> a)
    foldTyCo (TyCoFolder { tcf_view :: forall env a. TyCoFolder env a -> Type -> Maybe Type
    tcf_view       = Type -> Maybe Type
    view
                         , tcf_tyvar :: forall env a. TyCoFolder env a -> env -> TyVar -> a
    tcf_tyvar      = env -> TyVar -> a
    tyvar
                         , tcf_tycobinder :: forall env a.
    TyCoFolder env a -> env -> TyVar -> ForAllTyFlag -> env
    tcf_tycobinder = env -> TyVar -> ForAllTyFlag -> env
    tycobinder
                         , tcf_covar :: forall env a. TyCoFolder env a -> env -> TyVar -> a
    tcf_covar      = env -> TyVar -> a
    covar
                         , tcf_hole :: forall env a. TyCoFolder env a -> env -> CoercionHole -> a
    tcf_hole       = env -> CoercionHole -> a
    cohole }) env
    env
      = (env -> Type -> a
    go_ty env
    env, env -> [Type] -> a
    go_tys env
    env, env -> KindCoercion -> a
    go_co env
    env, env -> [KindCoercion] -> a
    go_cos env
    env)
      where
        go_ty :: env -> Type -> a
    go_ty env
    env Type
    ty | Just Type
    ty' <- Type -> Maybe Type
    view Type
    ty = env -> Type -> a
    go_ty env
    env Type
    ty'
        go_ty env
    env (TyVarTy TyVar
    tv)      = env -> TyVar -> a
    tyvar env
    env TyVar
    tv
        go_ty env
    env (AppTy Type
    t1 Type
    t2)     = env -> Type -> a
    go_ty env
    env Type
    t1 a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> Type -> a
    go_ty env
    env Type
    t2
        go_ty env
    _   (LitTy {})        = a
    forall a. Monoid a => a
    mempty
        go_ty env
    env (CastTy Type
    ty KindCoercion
    co)    = env -> Type -> a
    go_ty env
    env Type
    ty a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> KindCoercion -> a
    go_co env
    env KindCoercion
    co
        go_ty env
    env (CoercionTy KindCoercion
    co)   = env -> KindCoercion -> a
    go_co env
    env KindCoercion
    co
        go_ty env
    env (FunTy FunTyFlag
    _ Type
    w Type
    arg Type
    res) = env -> Type -> a
    go_ty env
    env Type
    w a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> Type -> a
    go_ty env
    env Type
    arg a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> Type -> a
    go_ty env
    env Type
    res
        go_ty env
    env (TyConApp TyCon
    _ [Type]
    tys)  = env -> [Type] -> a
    go_tys env
    env [Type]
    tys
        go_ty env
    env (ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    vis) Type
    inner)
          = let !env' :: env
    env' = env -> TyVar -> ForAllTyFlag -> env
    tycobinder env
    env TyVar
    tv ForAllTyFlag
    vis  -- Avoid building a thunk here
            in env -> Type -> a
    go_ty env
    env (TyVar -> Type
    varType TyVar
    tv) a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> Type -> a
    go_ty env
    env' Type
    inner

        -- See Note [Use explicit recursion in foldTyCo]
        go_tys :: env -> [Type] -> a
    go_tys env
    _   []     = a
    forall a. Monoid a => a
    mempty
        go_tys env
    env (Type
    t:[Type]
    ts) = env -> Type -> a
    go_ty env
    env Type
    t a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> [Type] -> a
    go_tys env
    env [Type]
    ts

        -- See Note [Use explicit recursion in foldTyCo]
        go_cos :: env -> [KindCoercion] -> a
    go_cos env
    _   []     = a
    forall a. Monoid a => a
    mempty
        go_cos env
    env (KindCoercion
    c:[KindCoercion]
    cs) = env -> KindCoercion -> a
    go_co env
    env KindCoercion
    c a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> [KindCoercion] -> a
    go_cos env
    env [KindCoercion]
    cs

        go_co :: env -> KindCoercion -> a
    go_co env
    env (Refl Type
    ty)                = env -> Type -> a
    go_ty env
    env Type
    ty
        go_co env
    env (GRefl Role
    _ Type
    ty MCoercionN
    MRefl)       = env -> Type -> a
    go_ty env
    env Type
    ty
        go_co env
    env (GRefl Role
    _ Type
    ty (MCo KindCoercion
    co))    = env -> Type -> a
    go_ty env
    env Type
    ty a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> KindCoercion -> a
    go_co env
    env KindCoercion
    co
        go_co env
    env (TyConAppCo Role
    _ TyCon
    _ [KindCoercion]
    args)    = env -> [KindCoercion] -> a
    go_cos env
    env [KindCoercion]
    args
        go_co env
    env (AppCo KindCoercion
    c1 KindCoercion
    c2)            = env -> KindCoercion -> a
    go_co env
    env KindCoercion
    c1 a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> KindCoercion -> a
    go_co env
    env KindCoercion
    c2
        go_co env
    env (CoVarCo TyVar
    cv)             = env -> TyVar -> a
    covar env
    env TyVar
    cv
        go_co env
    env (AxiomCo CoAxiomRule
    _ [KindCoercion]
    cos)          = env -> [KindCoercion] -> a
    go_cos env
    env [KindCoercion]
    cos
        go_co env
    env (HoleCo CoercionHole
    hole)            = env -> CoercionHole -> a
    cohole env
    env CoercionHole
    hole
        go_co env
    env (UnivCo { uco_lty :: KindCoercion -> Type
    uco_lty = Type
    t1, uco_rty :: KindCoercion -> Type
    uco_rty = Type
    t2, uco_deps :: KindCoercion -> [KindCoercion]
    uco_deps = [KindCoercion]
    deps })
                                           = env -> Type -> a
    go_ty env
    env Type
    t1 a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> Type -> a
    go_ty env
    env Type
    t2
                                             a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> [KindCoercion] -> a
    go_cos env
    env [KindCoercion]
    deps
        go_co env
    env (SymCo KindCoercion
    co)               = env -> KindCoercion -> a
    go_co env
    env KindCoercion
    co
        go_co env
    env (TransCo KindCoercion
    c1 KindCoercion
    c2)          = env -> KindCoercion -> a
    go_co env
    env KindCoercion
    c1 a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> KindCoercion -> a
    go_co env
    env KindCoercion
    c2
        go_co env
    env (SelCo CoSel
    _ KindCoercion
    co)             = env -> KindCoercion -> a
    go_co env
    env KindCoercion
    co
        go_co env
    env (LRCo LeftOrRight
    _ KindCoercion
    co)              = env -> KindCoercion -> a
    go_co env
    env KindCoercion
    co
        go_co env
    env (InstCo KindCoercion
    co KindCoercion
    arg)          = env -> KindCoercion -> a
    go_co env
    env KindCoercion
    co a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> KindCoercion -> a
    go_co env
    env KindCoercion
    arg
        go_co env
    env (KindCo KindCoercion
    co)              = env -> KindCoercion -> a
    go_co env
    env KindCoercion
    co
        go_co env
    env (SubCo KindCoercion
    co)               = env -> KindCoercion -> a
    go_co env
    env KindCoercion
    co

        go_co env
    env (FunCo { fco_mult :: KindCoercion -> KindCoercion
    fco_mult = KindCoercion
    cw, fco_arg :: KindCoercion -> KindCoercion
    fco_arg = KindCoercion
    c1, fco_res :: KindCoercion -> KindCoercion
    fco_res = KindCoercion
    c2 })
           = env -> KindCoercion -> a
    go_co env
    env KindCoercion
    cw a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> KindCoercion -> a
    go_co env
    env KindCoercion
    c1 a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> KindCoercion -> a
    go_co env
    env KindCoercion
    c2

        go_co env
    env (ForAllCo TyVar
    tv ForAllTyFlag
    _vis1 ForAllTyFlag
    _vis2 KindCoercion
    kind_co KindCoercion
    co)
          = env -> KindCoercion -> a
    go_co env
    env KindCoercion
    kind_co a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> Type -> a
    go_ty env
    env (TyVar -> Type
    varType TyVar
    tv)
                              a -> a -> a
    forall a. Monoid a => a -> a -> a
    `mappend` env -> KindCoercion -> a
    go_co env
    env' KindCoercion
    co
          where
            env' :: env
    env' = env -> TyVar -> ForAllTyFlag -> env
    tycobinder env
    env TyVar
    tv ForAllTyFlag
    Inferred

    -- | A view function that looks through nothing.
    noView :: Type -> Maybe Type
    noView :: Type -> Maybe Type
    noView Type
    _ = Maybe Type
    forall a. Maybe a
    Nothing

    {- *********************************************************************
    *                                                                      *
                       typeSize, coercionSize
    *                                                                      *
    ********************************************************************* -}

    -- NB: We put typeSize/coercionSize here because they are mutually
    --     recursive, and have the CPR property.  If we have mutual
    --     recursion across a hi-boot file, we don't get the CPR property
    --     and these functions allocate a tremendous amount of rubbish.
    --     It's not critical (because typeSize is really only used in
    --     debug mode, but I tripped over an example (T5642) in which
    --     typeSize was one of the biggest single allocators in all of GHC.
    --     And it's easy to fix, so I did.

    -- NB: typeSize does not respect `eqType`, in that two types that
    --     are `eqType` may return different sizes. This is OK, because this
    --     function is used only in reporting, not decision-making.

    typeSize :: Type -> Int
    -- The size of the syntax tree of a type.  No special treatment
    -- for type synonyms or type families.
    typeSize :: Type -> Int
    typeSize (LitTy {})                 = Int
    1
    typeSize (TyVarTy {})               = Int
    1
    typeSize (AppTy Type
    t1 Type
    t2)              = Type -> Int
    typeSize Type
    t1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + Type -> Int
    typeSize Type
    t2
    typeSize (FunTy FunTyFlag
    _ Type
    _ Type
    t1 Type
    t2)          = Type -> Int
    typeSize Type
    t1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + Type -> Int
    typeSize Type
    t2
    typeSize (ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    _) Type
    t)   = Type -> Int
    typeSize (TyVar -> Type
    varType TyVar
    tv) Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + Type -> Int
    typeSize Type
    t
    typeSize (TyConApp TyCon
    _ [Type]
    ts)            = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + [Type] -> Int
    typesSize [Type]
    ts
    typeSize (CastTy Type
    ty KindCoercion
    co)             = Type -> Int
    typeSize Type
    ty Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    co
    typeSize (CoercionTy KindCoercion
    co)            = KindCoercion -> Int
    coercionSize KindCoercion
    co

    typesSize :: [Type] -> Int
    typesSize :: [Type] -> Int
    typesSize [Type]
    tys = (Type -> Int -> Int) -> Int -> [Type] -> Int
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr (Int -> Int -> Int
    forall a. Num a => a -> a -> a
    (+) (Int -> Int -> Int) -> (Type -> Int) -> Type -> Int -> Int
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Type -> Int
    typeSize) Int
    0 [Type]
    tys

    coercionSize :: Coercion -> Int
    coercionSize :: KindCoercion -> Int
    coercionSize (Refl Type
    ty)             = Type -> Int
    typeSize Type
    ty
    coercionSize (GRefl Role
    _ Type
    ty MCoercionN
    MRefl)    = Type -> Int
    typeSize Type
    ty
    coercionSize (GRefl Role
    _ Type
    ty (MCo KindCoercion
    co)) = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + Type -> Int
    typeSize Type
    ty Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    co
    coercionSize (TyConAppCo Role
    _ TyCon
    _ [KindCoercion]
    args) = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + [Int] -> Int
    forall a. Num a => [a] -> a
    forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
    sum ((KindCoercion -> Int) -> [KindCoercion] -> [Int]
    forall a b. (a -> b) -> [a] -> [b]
    map KindCoercion -> Int
    coercionSize [KindCoercion]
    args)
    coercionSize (AppCo KindCoercion
    co KindCoercion
    arg)        = KindCoercion -> Int
    coercionSize KindCoercion
    co Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    arg
    coercionSize (ForAllCo { fco_kind :: KindCoercion -> KindCoercion
    fco_kind = KindCoercion
    h, fco_body :: KindCoercion -> KindCoercion
    fco_body = KindCoercion
    co })
                                       = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    co Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    h
    coercionSize (FunCo Role
    _ FunTyFlag
    _ FunTyFlag
    _ KindCoercion
    w KindCoercion
    c1 KindCoercion
    c2) = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    c1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    c2
                                                             Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    w
    coercionSize (CoVarCo TyVar
    _)         = Int
    1
    coercionSize (HoleCo CoercionHole
    _)          = Int
    1
    coercionSize (AxiomCo CoAxiomRule
    _ [KindCoercion]
    cs)      = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + [Int] -> Int
    forall a. Num a => [a] -> a
    forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
    sum ((KindCoercion -> Int) -> [KindCoercion] -> [Int]
    forall a b. (a -> b) -> [a] -> [b]
    map KindCoercion -> Int
    coercionSize [KindCoercion]
    cs)
    coercionSize (UnivCo { uco_lty :: KindCoercion -> Type
    uco_lty = Type
    t1, uco_rty :: KindCoercion -> Type
    uco_rty = Type
    t2 })  = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + Type -> Int
    typeSize Type
    t1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + Type -> Int
    typeSize Type
    t2
    coercionSize (SymCo KindCoercion
    co)          = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    co
    coercionSize (TransCo KindCoercion
    co1 KindCoercion
    co2)   = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    co1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    co2
    coercionSize (SelCo CoSel
    _ KindCoercion
    co)        = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    co
    coercionSize (LRCo  LeftOrRight
    _ KindCoercion
    co)        = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    co
    coercionSize (InstCo KindCoercion
    co KindCoercion
    arg)     = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    co Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    arg
    coercionSize (KindCo KindCoercion
    co)         = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    co
    coercionSize (SubCo KindCoercion
    co)          = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + KindCoercion -> Int
    coercionSize KindCoercion
    co

    {-
    ************************************************************************
    *                                                                      *
                        Multiplicities
    *                                                                      *
    ************************************************************************

    These definitions are here to avoid module loops, and to keep
    GHC.Core.Multiplicity above this module.

    -}

    -- | A shorthand for data with an attached 'Mult' element (the multiplicity).
    data Scaled a = Scaled !Mult a
      deriving (Typeable (Scaled a)
    Typeable (Scaled a) =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> Scaled a -> c (Scaled a))
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c (Scaled a))
    -> (Scaled a -> Constr)
    -> (Scaled a -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c (Scaled a)))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e))
        -> Maybe (c (Scaled a)))
    -> ((forall b. Data b => b -> b) -> Scaled a -> Scaled a)
    -> (forall r r'.
        (r -> r' -> r)
        -> r -> (forall d. Data d => d -> r') -> Scaled a -> r)
    -> (forall r r'.
        (r' -> r -> r)
        -> r -> (forall d. Data d => d -> r') -> Scaled a -> r)
    -> (forall u. (forall d. Data d => d -> u) -> Scaled a -> [u])
    -> (forall u. Int -> (forall d. Data d => d -> u) -> Scaled a -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a))
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a))
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a))
    -> Data (Scaled a)
    Scaled a -> Constr
    Scaled a -> DataType
    (forall b. Data b => b -> b) -> Scaled a -> Scaled a
    forall a. Data a => Typeable (Scaled a)
    forall a. Data a => Scaled a -> Constr
    forall a. Data a => Scaled a -> DataType
    forall a.
    Data a =>
    (forall b. Data b => b -> b) -> Scaled a -> Scaled a
    forall a u.
    Data a =>
    Int -> (forall d. Data d => d -> u) -> Scaled a -> u
    forall a u.
    Data a =>
    (forall d. Data d => d -> u) -> Scaled a -> [u]
    forall a r r'.
    Data a =>
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> Scaled a -> r
    forall a r r'.
    Data a =>
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> Scaled a -> r
    forall a (m :: * -> *).
    (Data a, Monad m) =>
    (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a)
    forall a (m :: * -> *).
    (Data a, MonadPlus m) =>
    (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a)
    forall a (c :: * -> *).
    Data a =>
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c (Scaled a)
    forall a (c :: * -> *).
    Data a =>
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> Scaled a -> c (Scaled a)
    forall a (t :: * -> *) (c :: * -> *).
    (Data a, Typeable t) =>
    (forall d. Data d => c (t d)) -> Maybe (c (Scaled a))
    forall a (t :: * -> * -> *) (c :: * -> *).
    (Data a, Typeable t) =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a))
    forall a.
    Typeable a =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> a -> c a)
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c a)
    -> (a -> Constr)
    -> (a -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c a))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
    -> ((forall b. Data b => b -> b) -> a -> a)
    -> (forall r r'.
        (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall r r'.
        (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall u. (forall d. Data d => d -> u) -> a -> [u])
    -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> Data a
    forall u. Int -> (forall d. Data d => d -> u) -> Scaled a -> u
    forall u. (forall d. Data d => d -> u) -> Scaled a -> [u]
    forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> Scaled a -> r
    forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> Scaled a -> r
    forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a)
    forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a)
    forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c (Scaled a)
    forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> Scaled a -> c (Scaled a)
    forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c (Scaled a))
    forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a))
    $cgfoldl :: forall a (c :: * -> *).
    Data a =>
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> Scaled a -> c (Scaled a)
    gfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> Scaled a -> c (Scaled a)
    $cgunfold :: forall a (c :: * -> *).
    Data a =>
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c (Scaled a)
    gunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c (Scaled a)
    $ctoConstr :: forall a. Data a => Scaled a -> Constr
    toConstr :: Scaled a -> Constr
    $cdataTypeOf :: forall a. Data a => Scaled a -> DataType
    dataTypeOf :: Scaled a -> DataType
    $cdataCast1 :: forall a (t :: * -> *) (c :: * -> *).
    (Data a, Typeable t) =>
    (forall d. Data d => c (t d)) -> Maybe (c (Scaled a))
    dataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c (Scaled a))
    $cdataCast2 :: forall a (t :: * -> * -> *) (c :: * -> *).
    (Data a, Typeable t) =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a))
    dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a))
    $cgmapT :: forall a.
    Data a =>
    (forall b. Data b => b -> b) -> Scaled a -> Scaled a
    gmapT :: (forall b. Data b => b -> b) -> Scaled a -> Scaled a
    $cgmapQl :: forall a r r'.
    Data a =>
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> Scaled a -> r
    gmapQl :: forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> Scaled a -> r
    $cgmapQr :: forall a r r'.
    Data a =>
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> Scaled a -> r
    gmapQr :: forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> Scaled a -> r
    $cgmapQ :: forall a u.
    Data a =>
    (forall d. Data d => d -> u) -> Scaled a -> [u]
    gmapQ :: forall u. (forall d. Data d => d -> u) -> Scaled a -> [u]
    $cgmapQi :: forall a u.
    Data a =>
    Int -> (forall d. Data d => d -> u) -> Scaled a -> u
    gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Scaled a -> u
    $cgmapM :: forall a (m :: * -> *).
    (Data a, Monad m) =>
    (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a)
    gmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a)
    $cgmapMp :: forall a (m :: * -> *).
    (Data a, MonadPlus m) =>
    (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a)
    gmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a)
    $cgmapMo :: forall a (m :: * -> *).
    (Data a, MonadPlus m) =>
    (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a)
    gmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a)
    Data.Data)
      -- You might think that this would be a natural candidate for
      -- Functor, Traversable but Krzysztof says (!3674) "it was too easy
      -- to accidentally lift functions (substitutions, zonking etc.) from
      -- Type -> Type to Scaled Type -> Scaled Type, ignoring
      -- multiplicities and causing bugs".  So we don't.
      --
      -- Being strict in a is worse for performance, so we are only strict on the
      -- Mult part of scaled.

    instance (Outputable a) => Outputable (Scaled a) where
       ppr :: Scaled a -> SDoc
    ppr (Scaled Type
    _cnt a
    t) = a -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr a
    t
         -- Do not print the multiplicity here because it tends to be too verbose

    scaledMult :: Scaled a -> Mult
    scaledMult :: forall a. Scaled a -> Type
    scaledMult (Scaled Type
    m a
    _) = Type
    m

    scaledThing :: Scaled a -> a
    scaledThing :: forall a. Scaled a -> a
    scaledThing (Scaled Type
    _ a
    t) = a
    t

    -- | Apply a function to both the Mult and the Type in a 'Scaled Type'
    mapScaledType :: (Type -> Type) -> Scaled Type -> Scaled Type
    mapScaledType :: (Type -> Type) -> Scaled Type -> Scaled Type
    mapScaledType Type -> Type
    f (Scaled Type
    m Type
    t) = Type -> Type -> Scaled Type
    forall a. Type -> a -> Scaled a
    Scaled (Type -> Type
    f Type
    m) (Type -> Type
    f Type
    t)

    {- |
    Mult is a type alias for Type.

    Mult must contain Type because multiplicity variables are mere type variables
    (of kind Multiplicity) in Haskell. So the simplest implementation is to make
    Mult be Type.

    Multiplicities can be formed with:
    - One: GHC.Types.One (= oneDataCon)
    - Many: GHC.Types.Many (= manyDataCon)
    - Multiplication: GHC.Types.MultMul (= multMulTyCon)

    So that Mult feels a bit more structured, we provide pattern synonyms and smart
    constructors for these.
    -}
    type Mult = Type