    {-
    (c) The University of Glasgow 2006
    (c) The GRASP/AQUA Project, Glasgow University, 1992-1999

    Analysis functions over data types.  Specficially, detecting recursive types.

    This stuff is only used for source-code decls; it's recorded in interface
    files for imported data types.
    -}

    {-# LANGUAGE CPP #-}

    module TcTyDecls(
            calcRecFlags, RecTyInfo(..),
            calcSynCycles, calcClassCycles,
            RoleAnnots, extractRoleAnnots, emptyRoleAnnots, lookupRoleAnnots
        ) where

    #include "HsVersions.h"

    import TypeRep
    import HsSyn
    import Class
    import Type
    import Kind
    import HscTypes
    import TyCon
    import DataCon
    import Var
    import Name
    import NameEnv
    import VarEnv
    import VarSet
    import NameSet
    import Coercion ( ltRole )
    import Avail
    import Digraph
    import BasicTypes
    import SrcLoc
    import Outputable
    import UniqSet
    import Util
    import Maybes
    import Data.List

    #if __GLASGOW_HASKELL__ < 709
    import Control.Applicative (Applicative(..))
    #endif

    import Control.Monad

    {-
    ************************************************************************
    *                                                                      *
            Cycles in class and type synonym declarations
    *                                                                      *
    ************************************************************************

    Checking for class-decl loops is easy, because we don't allow class decls
    in interface files.

    We allow type synonyms in hi-boot files, but we *trust* hi-boot files,
    so we don't check for loops that involve them.  So we only look for synonym
    loops in the module being compiled.

    We check for type synonym and class cycles on the *source* code.
    Main reasons:

      a) Otherwise we'd need a special function to extract type-synonym tycons
         from a type, whereas we already have the free vars pinned on the decl

      b) If we checked for type synonym loops after building the TyCon, we
            can't do a hoistForAllTys on the type synonym rhs, (else we fall into
            a black hole) which seems unclean.  Apart from anything else, it'd mean
            that a type-synonym rhs could have for-alls to the right of an arrow,
            which means adding new cases to the validity checker

            Indeed, in general, checking for cycles beforehand means we need to
            be less careful about black holes through synonym cycles.

    The main disadvantage is that a cycle that goes via a type synonym in an
    .hi-boot file can lead the compiler into a loop, because it assumes that cycles
    only occur entirely within the source code of the module being compiled.
    But hi-boot files are trusted anyway, so this isn't much worse than (say)
    a kind error.

    [  NOTE ----------------------------------------------
    If we reverse this decision, this comment came from tcTyDecl1, and should
     go back there
            -- dsHsType, not tcHsKindedType, to avoid a loop.  tcHsKindedType does hoisting,
            -- which requires looking through synonyms... and therefore goes into a loop
            -- on (erroneously) recursive synonyms.
            -- Solution: do not hoist synonyms, because they'll be hoisted soon enough
            --           when they are substituted

    We'd also need to add back in this definition

    synonymTyConsOfType :: Type -> [TyCon]
    -- Does not look through type synonyms at all
    -- Return a list of synonym tycons
    synonymTyConsOfType ty
      = nameEnvElts (go ty)
      where
         go :: Type -> NameEnv TyCon  -- The NameEnv does duplicate elim
         go (TyVarTy v)               = emptyNameEnv
         go (TyConApp tc tys)         = go_tc tc tys
         go (AppTy a b)               = go a `plusNameEnv` go b
         go (FunTy a b)               = go a `plusNameEnv` go b
         go (ForAllTy _ ty)           = go ty

         go_tc tc tys | isTypeSynonymTyCon tc = extendNameEnv (go_s tys)
                                                              (tyConName tc) tc
                      | otherwise             = go_s tys
         go_s tys = foldr (plusNameEnv . go) emptyNameEnv tys
    ---------------------------------------- END NOTE ]
    -}

    mkSynEdges :: [LTyClDecl Name] -> [(LTyClDecl Name, Name, [Name])]
    mkSynEdges syn_decls = [ (ldecl, name, nameSetElems fvs)
                           | ldecl@(L _ (SynDecl { tcdLName = L _ name
                                                 , tcdFVs = fvs })) <- syn_decls ]

    calcSynCycles :: [LTyClDecl Name] -> [SCC (LTyClDecl Name)]
    calcSynCycles = stronglyConnCompFromEdgedVertices . mkSynEdges

    {-
    Note [Superclass cycle check]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We can't allow cycles via superclasses because it would result in the
    type checker looping when it canonicalises a class constraint (superclasses
    are added during canonicalisation).  More precisely, given a constraint
        C ty1 .. tyn
    we want to instantiate all of C's superclasses, transitively, and
    that set must be finite.  So if
         class (D b, E b a) => C a b
    then when we encounter the constraint
         C ty1 ty2
    we'll instantiate the superclasses
         (D ty2, E ty2 ty1)
    and then *their* superclasses, and so on.  This set must be finite!

    It is OK for superclasses to be type synonyms for other classes, so
    must "look through" type synonyms. Eg
         type X a = C [a]
         class X a => C a   -- No!  Recursive superclass!

    We want definitions such as:

      class C cls a where cls a => a -> a
      class C D a => D a where

    to be accepted, even though a naive acyclicity check would reject the
    program as having a cycle between D and its superclass.  Why? Because
    when we instantiate
         D ty1
    we get the superclas
         C D ty1
    and C has no superclasses, so we have terminated with a finite set.

    More precisely, the rule is this: the superclasses sup_C of a class C
    are rejected iff:

      C \elem expand(sup_C)

    Where expand is defined as follows:

    (1)  expand(a ty1 ... tyN) = expand(ty1) \union ... \union expand(tyN)

    (2)  expand(D ty1 ... tyN) = {D}
                                 \union sup_D[ty1/x1, ..., tyP/xP]
                                 \union expand(ty(P+1)) ... \union expand(tyN)
               where (D x1 ... xM) is a class, P = min(M,N)

    (3)  expand(T ty1 ... tyN) = expand(ty1) \union ... \union expand(tyN)
            where T is not a class

    Eqn (1) is conservative; when there's a type variable at the head,
    look in all the argument types.  Eqn (2) expands superclasses; the
    third component of the union is like Eqn (1).  Eqn (3) happens mainly
    when the context is a (constraint) tuple, such as (Eq a, Show a).

    Furthermore, expand always looks through type synonyms.
    -}

    calcClassCycles :: Class -> [[TyCon]]
    calcClassCycles cls
      = nubBy eqAsCycle $
        expandTheta (unitUniqSet cls) [classTyCon cls] (classSCTheta cls) []
      where
        -- The last TyCon in the cycle is always the same as the first
        eqAsCycle xs ys = any (xs ==) (cycles (tail ys))
        cycles xs = take n . map (take n) . tails . cycle $ xs
          where n = length xs

        -- No more superclasses to expand ==> no problems with cycles
        -- See Note [Superclass cycle check]
        expandTheta :: UniqSet Class -- Path of Classes to here in set form
                    -> [TyCon]       -- Path to here
                    -> ThetaType     -- Superclass work list
                    -> [[TyCon]]     -- Input error paths
                    -> [[TyCon]]     -- Final error paths
        expandTheta _    _    []           = id
        expandTheta seen path (pred:theta) = expandType seen path pred . expandTheta seen path theta

        expandType seen path (TyConApp tc tys)
          -- Expand unsaturated classes to their superclass theta if they are yet unseen.
          -- If they have already been seen then we have detected an error!
          | Just cls <- tyConClass_maybe tc
          , let (env, remainder) = papp (classTyVars cls) tys
                rest_tys = either (const []) id remainder
          = if cls `elementOfUniqSet` seen
             then (reverse (classTyCon cls:path):)
                  . flip (foldr (expandType seen path)) tys
             else expandTheta (addOneToUniqSet seen cls) (tc:path)
                              (substTys (mkTopTvSubst env) (classSCTheta cls))
                  . flip (foldr (expandType seen path)) rest_tys

          -- For synonyms, try to expand them: some arguments might be
          -- phantoms, after all. We can expand with impunity because at
          -- this point the type synonym cycle check has already happened.
          | Just (tvs, rhs) <- synTyConDefn_maybe tc
          , let (env, remainder) = papp tvs tys
                rest_tys = either (const []) id remainder
          = expandType seen (tc:path) (substTy (mkTopTvSubst env) rhs)
            . flip (foldr (expandType seen path)) rest_tys

          -- For non-class, non-synonyms, just check the arguments
          | otherwise
          = flip (foldr (expandType seen path)) tys

        expandType _    _    (TyVarTy {})     = id
        expandType _    _    (LitTy {})       = id
        expandType seen path (AppTy t1 t2)    = expandType seen path t1 . expandType seen path t2
        expandType seen path (FunTy t1 t2)    = expandType seen path t1 . expandType seen path t2
        expandType seen path (ForAllTy _tv t) = expandType seen path t

        papp :: [TyVar] -> [Type] -> ([(TyVar, Type)], Either [TyVar] [Type])
        papp []       tys      = ([], Right tys)
        papp tvs      []       = ([], Left tvs)
        papp (tv:tvs) (ty:tys) = ((tv, ty):env, remainder)
          where (env, remainder) = papp tvs tys

    {-
    ************************************************************************
    *                                                                      *
            Deciding which type constructors are recursive
    *                                                                      *
    ************************************************************************

    Identification of recursive TyCons
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The knot-tying parameters: @rec_details_list@ is an alist mapping @Name@s to
    @TyThing@s.

    Identifying a TyCon as recursive serves two purposes

    1.  Avoid infinite types.  Non-recursive newtypes are treated as
    "transparent", like type synonyms, after the type checker.  If we did
    this for all newtypes, we'd get infinite types.  So we figure out for
    each newtype whether it is "recursive", and add a coercion if so.  In
    effect, we are trying to "cut the loops" by identifying a loop-breaker.

    2.  Avoid infinite unboxing.  This has nothing to do with newtypes.
    Suppose we have
            data T = MkT Int T
            f (MkT x t) = f t
    Well, this function diverges, but we don't want the strictness analyser
    to diverge.  But the strictness analyser will diverge because it looks
    deeper and deeper into the structure of T.   (I believe there are
    examples where the function does something sane, and the strictness
    analyser still diverges, but I can't see one now.)

    Now, concerning (1), the FC2 branch currently adds a coercion for ALL
    newtypes.  I did this as an experiment, to try to expose cases in which
    the coercions got in the way of optimisations.  If it turns out that we
    can indeed always use a coercion, then we don't risk recursive types,
    and don't need to figure out what the loop breakers are.

    For newtype *families* though, we will always have a coercion, so they
    are always loop breakers!  So you can easily adjust the current
    algorithm by simply treating all newtype families as loop breakers (and
    indeed type families).  I think.

    For newtypes, we label some as "recursive" such that

        INVARIANT: there is no cycle of non-recursive newtypes

    In any loop, only one newtype need be marked as recursive; it is
    a "loop breaker".  Labelling more than necessary as recursive is OK,
    provided the invariant is maintained.

    A newtype M.T is defined to be "recursive" iff
            (a) it is declared in an hi-boot file (see RdrHsSyn.hsIfaceDecl)
            (b) it is declared in a source file, but that source file has a
                companion hi-boot file which declares the type
       or   (c) one can get from T's rhs to T via type
                synonyms, or non-recursive newtypes *in M*
                 e.g.  newtype T = MkT (T -> Int)

    (a) is conservative; declarations in hi-boot files are always
            made loop breakers. That's why in (b) we can restrict attention
            to tycons in M, because any loops through newtypes outside M
            will be broken by those newtypes
    (b) ensures that a newtype is not treated as a loop breaker in one place
    and later as a non-loop-breaker.  This matters in GHCi particularly, when
    a newtype T might be embedded in many types in the environment, and then
    T's source module is compiled.  We don't want T's recursiveness to change.

    The "recursive" flag for algebraic data types is irrelevant (never consulted)
    for types with more than one constructor.

    An algebraic data type M.T is "recursive" iff
            it has just one constructor, and
            (a) it is declared in an hi-boot file (see RdrHsSyn.hsIfaceDecl)
            (b) it is declared in a source file, but that source file has a
                companion hi-boot file which declares the type
     or     (c) one can get from its arg types to T via type synonyms,
                or by non-recursive newtypes or non-recursive product types in M
                 e.g.  data T = MkT (T -> Int) Bool
    Just like newtype in fact

    A type synonym is recursive if one can get from its
    right hand side back to it via type synonyms.  (This is
    reported as an error.)

    A class is recursive if one can get from its superclasses
    back to it.  (This is an error too.)

    Hi-boot types
    ~~~~~~~~~~~~~
    A data type read from an hi-boot file will have an AbstractTyCon as its AlgTyConRhs
    and will respond True to isAbstractTyCon. The idea is that we treat these as if one
    could get from these types to anywhere.  So when we see

            module Baz where
            import {-# SOURCE #-} Foo( T )
            newtype S = MkS T

    then we mark S as recursive, just in case. What that means is that if we see

            import Baz( S )
            newtype R = MkR S

    then we don't need to look inside S to compute R's recursiveness.  Since S is imported
    (not from an hi-boot file), one cannot get from R back to S except via an hi-boot file,
    and that means that some data type will be marked recursive along the way.  So R is
    unconditionly non-recursive (i.e. there'll be a loop breaker elsewhere if necessary)

    This in turn means that we grovel through fewer interface files when computing
    recursiveness, because we need only look at the type decls in the module being
    compiled, plus the outer structure of directly-mentioned types.
    -}

    data RecTyInfo = RTI { rti_promotable :: Bool
                         , rti_roles      :: Name -> [Role]
                         , rti_is_rec     :: Name -> RecFlag }

    calcRecFlags :: ModDetails -> Bool  -- hs-boot file?
                 -> RoleAnnots -> [TyThing] -> RecTyInfo
    -- The 'boot_names' are the things declared in M.hi-boot, if M is the current module.
    -- Any type constructors in boot_names are automatically considered loop breakers
    calcRecFlags boot_details is_boot mrole_env tyclss
      = RTI { rti_promotable = is_promotable
            , rti_roles      = roles
            , rti_is_rec     = is_rec }
      where
        rec_tycon_names = mkNameSet (map tyConName all_tycons)
        all_tycons = mapMaybe getTyCon tyclss
                       -- Recursion of newtypes/data types can happen via
                       -- the class TyCon, so tyclss includes the class tycons

        is_promotable = all (isPromotableTyCon rec_tycon_names) all_tycons

        roles = inferRoles is_boot mrole_env all_tycons

        ----------------- Recursion calculation ----------------
        is_rec n | n `elemNameSet` rec_names = Recursive
                 | otherwise                 = NonRecursive

        boot_name_set = availsToNameSet (md_exports boot_details)
        rec_names = boot_name_set     `unionNameSet`
                    nt_loop_breakers  `unionNameSet`
                    prod_loop_breakers

            -------------------------------------------------
            --                      NOTE
            -- These edge-construction loops rely on
            -- every loop going via tyclss, the types and classes
            -- in the module being compiled.  Stuff in interface
            -- files should be correctly marked.  If not (e.g. a
            -- type synonym in a hi-boot file) we can get an infinite
            -- loop.  We could program round this, but it'd make the code
            -- rather less nice, so I'm not going to do that yet.

        single_con_tycons = [ tc | tc <- all_tycons
                                 , not (tyConName tc `elemNameSet` boot_name_set)
                                     -- Remove the boot_name_set because they are
                                     -- going to be loop breakers regardless.
                                 , isSingleton (tyConDataCons tc) ]
            -- Both newtypes and data types, with exactly one data constructor

        (new_tycons, prod_tycons) = partition isNewTyCon single_con_tycons
            -- NB: we do *not* call isProductTyCon because that checks
            --     for vanilla-ness of data constructors; and that depends
            --     on empty existential type variables; and that is figured
            --     out by tcResultType; which uses tcMatchTy; which uses
            --     coreView; which calls coreExpandTyCon_maybe; which uses
            --     the recursiveness of the TyCon.  Result... a black hole.
            -- YUK YUK YUK

            --------------- Newtypes ----------------------
        nt_loop_breakers = mkNameSet (findLoopBreakers nt_edges)
        is_rec_nt tc = tyConName tc  `elemNameSet` nt_loop_breakers
            -- is_rec_nt is a locally-used helper function

        nt_edges = [(t, mk_nt_edges t) | t <- new_tycons]

        mk_nt_edges nt      -- Invariant: nt is a newtype
            = [ tc | tc <- nameEnvElts (tyConsOfType (new_tc_rhs nt))
                            -- tyConsOfType looks through synonyms
                   , tc `elem` new_tycons ]
               -- If not (tc `elem` new_tycons) we know that either it's a local *data* type,
               -- or it's imported.  Either way, it can't form part of a newtype cycle

            --------------- Product types ----------------------
        prod_loop_breakers = mkNameSet (findLoopBreakers prod_edges)

        prod_edges = [(tc, mk_prod_edges tc) | tc <- prod_tycons]

        mk_prod_edges tc    -- Invariant: tc is a product tycon
            = concatMap (mk_prod_edges1 tc) (dataConOrigArgTys (head (tyConDataCons tc)))

        mk_prod_edges1 ptc ty = concatMap (mk_prod_edges2 ptc) (nameEnvElts (tyConsOfType ty))

        mk_prod_edges2 ptc tc
            | tc `elem` prod_tycons   = [tc]                -- Local product
            | tc `elem` new_tycons    = if is_rec_nt tc     -- Local newtype
                                        then []
                                        else mk_prod_edges1 ptc (new_tc_rhs tc)
                    -- At this point we know that either it's a local non-product data type,
                    -- or it's imported.  Either way, it can't form part of a cycle
            | otherwise = []

    new_tc_rhs :: TyCon -> Type
    new_tc_rhs tc = snd (newTyConRhs tc)    -- Ignore the type variables

    getTyCon :: TyThing -> Maybe TyCon
    getTyCon (ATyCon tc) = Just tc
    getTyCon _           = Nothing

    findLoopBreakers :: [(TyCon, [TyCon])] -> [Name]
    -- Finds a set of tycons that cut all loops
    findLoopBreakers deps
      = go [(tc,tc,ds) | (tc,ds) <- deps]
      where
        go edges = [ name
                   | CyclicSCC ((tc,_,_) : edges') <- stronglyConnCompFromEdgedVerticesR edges,
                     name <- tyConName tc : go edges']

    {-
    ************************************************************************
    *                                                                      *
                      Promotion calculation
    *                                                                      *
    ************************************************************************

    See Note [Checking whether a group is promotable]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We only want to promote a TyCon if all its data constructors
    are promotable; it'd be very odd to promote some but not others.

    But the data constructors may mention this or other TyCons.

    So we treat the recursive uses as all OK (ie promotable) and
    do one pass to check that each TyCon is promotable.

    Currently type synonyms are not promotable, though that
    could change.
    -}

    isPromotableTyCon :: NameSet -> TyCon -> Bool
    isPromotableTyCon rec_tycons tc
      =  isAlgTyCon tc    -- Only algebraic; not even synonyms
                         -- (we could reconsider the latter)
      && ok_kind (tyConKind tc)
      && case algTyConRhs tc of
           DataTyCon { data_cons = cs } -> all ok_con cs
           NewTyCon { data_con = c }    -> ok_con c
           AbstractTyCon {}             -> False
           DataFamilyTyCon {}           -> False

      where
        ok_kind kind = all isLiftedTypeKind args && isLiftedTypeKind res
                where  -- Checks for * -> ... -> * -> *
                  (args, res) = splitKindFunTys kind

        -- See Note [Promoted data constructors] in TyCon
        ok_con con = all (isLiftedTypeKind . tyVarKind) ex_tvs
                  && null eq_spec   -- No constraints
                  && null theta
                  && all (isPromotableType rec_tycons) orig_arg_tys
           where
             (_, ex_tvs, eq_spec, theta, orig_arg_tys, _) = dataConFullSig con

    isPromotableType :: NameSet -> Type -> Bool
    -- Must line up with DataCon.promoteType
    -- But the function lives here because we must treat the
    -- *recursive* tycons as promotable
    isPromotableType rec_tcs con_arg_ty
      = go con_arg_ty
      where
        go (TyConApp tc tys) =  tys `lengthIs` tyConArity tc
                             && (tyConName tc `elemNameSet` rec_tcs
                                 || isJust (promotableTyCon_maybe tc))
                             && all go tys
        go (FunTy arg res)   = go arg && go res
        go (TyVarTy {})      = True
        go _                 = False

    {-
    ************************************************************************
    *                                                                      *
            Role annotations
    *                                                                      *
    ************************************************************************
    -}

    type RoleAnnots = NameEnv (LRoleAnnotDecl Name)

    extractRoleAnnots :: TyClGroup Name -> RoleAnnots
    extractRoleAnnots (TyClGroup { group_roles = roles })
      = mkNameEnv [ (tycon, role_annot)
                  | role_annot@(L _ (RoleAnnotDecl (L _ tycon) _)) <- roles ]

    emptyRoleAnnots :: RoleAnnots
    emptyRoleAnnots = emptyNameEnv

    lookupRoleAnnots :: RoleAnnots -> Name -> Maybe (LRoleAnnotDecl Name)
    lookupRoleAnnots = lookupNameEnv

    {-
    ************************************************************************
    *                                                                      *
            Role inference
    *                                                                      *
    ************************************************************************

    Note [Role inference]
    ~~~~~~~~~~~~~~~~~~~~~
    The role inference algorithm datatype definitions to infer the roles on the
    parameters. Although these roles are stored in the tycons, we can perform this
    algorithm on the built tycons, as long as we don't peek at an as-yet-unknown
    roles field! Ah, the magic of laziness.

    First, we choose appropriate initial roles. For families and classes, roles
    (including initial roles) are N. For datatypes, we start with the role in the
    role annotation (if any), or otherwise use Phantom. This is done in
    initialRoleEnv1.

    The function irGroup then propagates role information until it reaches a
    fixpoint, preferring N over (R or P) and R over P. To aid in this, we have a
    monad RoleM, which is a combination reader and state monad. In its state are
    the current RoleEnv, which gets updated by role propagation, and an update
    bit, which we use to know whether or not we've reached the fixpoint. The
    environment of RoleM contains the tycon whose parameters we are inferring, and
    a VarEnv from parameters to their positions, so we can update the RoleEnv.
    Between tycons, this reader information is missing; it is added by
    addRoleInferenceInfo.

    There are two kinds of tycons to consider: algebraic ones (excluding classes)
    and type synonyms. (Remember, families don't participate -- all their parameters
    are N.) An algebraic tycon processes each of its datacons, in turn. Note that
    a datacon's universally quantified parameters might be different from the parent
    tycon's parameters, so we use the datacon's univ parameters in the mapping from
    vars to positions. Note also that we don't want to infer roles for existentials
    (they're all at N, too), so we put them in the set of local variables. As an
    optimisation, we skip any tycons whose roles are already all Nominal, as there
    nowhere else for them to go. For synonyms, we just analyse their right-hand sides.

    irType walks through a type, looking for uses of a variable of interest and
    propagating role information. Because anything used under a phantom position
    is at phantom and anything used under a nominal position is at nominal, the
    irType function can assume that anything it sees is at representational. (The
    other possibilities are pruned when they're encountered.)

    The rest of the code is just plumbing.

    How do we know that this algorithm is correct? It should meet the following
    specification:

    Let Z be a role context -- a mapping from variables to roles. The following
    rules define the property (Z |- t : r), where t is a type and r is a role:

    Z(a) = r'        r' <= r
    ------------------------- RCVar
    Z |- a : r

    ---------- RCConst
    Z |- T : r               -- T is a type constructor

    Z |- t1 : r
    Z |- t2 : N
    -------------- RCApp
    Z |- t1 t2 : r

    forall i<=n. (r_i is R or N) implies Z |- t_i : r_i
    roles(T) = r_1 .. r_n
    ---------------------------------------------------- RCDApp
    Z |- T t_1 .. t_n : R

    Z, a:N |- t : r
    ---------------------- RCAll
    Z |- forall a:k.t : r

    We also have the following rules:

    For all datacon_i in type T, where a_1 .. a_n are universally quantified
    and b_1 .. b_m are existentially quantified, and the arguments are t_1 .. t_p,
    then if forall j<=p, a_1 : r_1 .. a_n : r_n, b_1 : N .. b_m : N |- t_j : R,
    then roles(T) = r_1 .. r_n

    roles(->) = R, R
    roles(~#) = N, N

    With -dcore-lint on, the output of this algorithm is checked in checkValidRoles,
    called from checkValidTycon.

    Note [Role-checking data constructor arguments]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider
      data T a where
        MkT :: Eq b => F a -> (a->a) -> T (G a)

    Then we want to check the roles at which 'a' is used
    in MkT's type.  We want to work on the user-written type,
    so we need to take into account
      * the arguments:   (F a) and (a->a)
      * the context:     C a b
      * the result type: (G a)   -- this is in the eq_spec
    -}

    type RoleEnv    = NameEnv [Role]        -- from tycon names to roles

    -- This, and any of the functions it calls, must *not* look at the roles
    -- field of a tycon we are inferring roles about!
    -- See Note [Role inference]
    inferRoles :: Bool -> RoleAnnots -> [TyCon] -> Name -> [Role]
    inferRoles is_boot annots tycons
      = let role_env  = initialRoleEnv is_boot annots tycons
            role_env' = irGroup role_env tycons in
        \name -> case lookupNameEnv role_env' name of
          Just roles -> roles
          Nothing    -> pprPanic "inferRoles" (ppr name)

    initialRoleEnv :: Bool -> RoleAnnots -> [TyCon] -> RoleEnv
    initialRoleEnv is_boot annots = extendNameEnvList emptyNameEnv .
                                    map (initialRoleEnv1 is_boot annots)

    initialRoleEnv1 :: Bool -> RoleAnnots -> TyCon -> (Name, [Role])
    initialRoleEnv1 is_boot annots_env tc
      | isFamilyTyCon tc      = (name, map (const Nominal) tyvars)
      | isAlgTyCon tc         = (name, default_roles)
      | isTypeSynonymTyCon tc = (name, default_roles)
      | otherwise             = pprPanic "initialRoleEnv1" (ppr tc)
      where name         = tyConName tc
            tyvars       = tyConTyVars tc
            (kvs, tvs)   = span isKindVar tyvars

              -- if the number of annotations in the role annotation decl
              -- is wrong, just ignore it. We check this in the validity check.
            role_annots
              = case lookupNameEnv annots_env name of
                  Just (L _ (RoleAnnotDecl _ annots))
                    | annots `equalLength` tvs -> map unLoc annots
                  _                            -> map (const Nothing) tvs
            default_roles = map (const Nominal) kvs ++
                            zipWith orElse role_annots (repeat default_role)

            default_role
              | isClassTyCon tc = Nominal
              | is_boot         = Representational
              | otherwise       = Phantom

    irGroup :: RoleEnv -> [TyCon] -> RoleEnv
    irGroup env tcs
      = let (env', update) = runRoleM env $ mapM_ irTyCon tcs in
        if update
        then irGroup env' tcs
        else env'

    irTyCon :: TyCon -> RoleM ()
    irTyCon tc
      | isAlgTyCon tc
      = do { old_roles <- lookupRoles tc
           ; unless (all (== Nominal) old_roles) $  -- also catches data families,
                                                    -- which don't want or need role inference
        do { whenIsJust (tyConClass_maybe tc) (irClass tc_name)
           ; addRoleInferenceInfo tc_name (tyConTyVars tc) $
             mapM_ (irType emptyVarSet) (tyConStupidTheta tc)  -- See #8958
           ; mapM_ (irDataCon tc_name) (visibleDataCons $ algTyConRhs tc) }}

      | Just ty <- synTyConRhs_maybe tc
      = addRoleInferenceInfo tc_name (tyConTyVars tc) $
        irType emptyVarSet ty

      | otherwise
      = return ()

      where
        tc_name = tyConName tc

    -- any type variable used in an associated type must be Nominal
    irClass :: Name -> Class -> RoleM ()
    irClass tc_name cls
      = addRoleInferenceInfo tc_name cls_tvs $
        mapM_ ir_at (classATs cls)
      where
        cls_tvs    = classTyVars cls
        cls_tv_set = mkVarSet cls_tvs

        ir_at at_tc
          = mapM_ (updateRole Nominal) (varSetElems nvars)
          where nvars = (mkVarSet $ tyConTyVars at_tc) `intersectVarSet` cls_tv_set

    -- See Note [Role inference]
    irDataCon :: Name -> DataCon -> RoleM ()
    irDataCon tc_name datacon
      = addRoleInferenceInfo tc_name univ_tvs $
        mapM_ (irType ex_var_set) (eqSpecPreds eq_spec ++ theta ++ arg_tys)
          -- See Note [Role-checking data constructor arguments]
      where
        (univ_tvs, ex_tvs, eq_spec, theta, arg_tys, _res_ty) = dataConFullSig datacon
        ex_var_set = mkVarSet ex_tvs

    irType :: VarSet -> Type -> RoleM ()
    irType = go
      where
        go lcls (TyVarTy tv) = unless (tv `elemVarSet` lcls) $
                               updateRole Representational tv
        go lcls (AppTy t1 t2) = go lcls t1 >> mark_nominal lcls t2
        go lcls (TyConApp tc tys)
          = do { roles <- lookupRolesX tc
               ; zipWithM_ (go_app lcls) roles tys }
        go lcls (FunTy t1 t2) = go lcls t1 >> go lcls t2
        go lcls (ForAllTy tv ty) = go (extendVarSet lcls tv) ty
        go _    (LitTy {}) = return ()

        go_app _ Phantom _ = return ()                 -- nothing to do here
        go_app lcls Nominal ty = mark_nominal lcls ty  -- all vars below here are N
        go_app lcls Representational ty = go lcls ty

        mark_nominal lcls ty = let nvars = tyVarsOfType ty `minusVarSet` lcls in
                               mapM_ (updateRole Nominal) (varSetElems nvars)

    -- like lookupRoles, but with Nominal tags at the end for oversaturated TyConApps
    lookupRolesX :: TyCon -> RoleM [Role]
    lookupRolesX tc
      = do { roles <- lookupRoles tc
           ; return $ roles ++ repeat Nominal }

    -- gets the roles either from the environment or the tycon
    lookupRoles :: TyCon -> RoleM [Role]
    lookupRoles tc
      = do { env <- getRoleEnv
           ; case lookupNameEnv env (tyConName tc) of
               Just roles -> return roles
               Nothing    -> return $ tyConRoles tc }

    -- tries to update a role; won't ever update a role "downwards"
    updateRole :: Role -> TyVar -> RoleM ()
    updateRole role tv
      = do { var_ns <- getVarNs
           ; case lookupVarEnv var_ns tv of
           { Nothing -> pprPanic "updateRole" (ppr tv)
           ; Just n  -> do
           { name <- getTyConName
           ; updateRoleEnv name n role }}}

    -- the state in the RoleM monad
    data RoleInferenceState = RIS { role_env  :: RoleEnv
                                  , update    :: Bool }

    -- the environment in the RoleM monad
    type VarPositions = VarEnv Int
    data RoleInferenceInfo = RII { var_ns :: VarPositions
                                 , name   :: Name }

    -- See [Role inference]
    newtype RoleM a = RM { unRM :: Maybe RoleInferenceInfo
                                -> RoleInferenceState
                                -> (a, RoleInferenceState) }

    instance Functor RoleM where
        fmap = liftM

    instance Applicative RoleM where
        pure = return
        (<*>) = ap

    instance Monad RoleM where
      return x = RM $ \_ state -> (x, state)
      a >>= f  = RM $ \m_info state -> let (a', state') = unRM a m_info state in
                                       unRM (f a') m_info state'

    runRoleM :: RoleEnv -> RoleM () -> (RoleEnv, Bool)
    runRoleM env thing = (env', update)
      where RIS { role_env = env', update = update } = snd $ unRM thing Nothing state
            state = RIS { role_env  = env, update    = False }

    addRoleInferenceInfo :: Name -> [TyVar] -> RoleM a -> RoleM a
    addRoleInferenceInfo name tvs thing
      = RM $ \_nothing state -> ASSERT( isNothing _nothing )
                                unRM thing (Just info) state
      where info = RII { var_ns = mkVarEnv (zip tvs [0..]), name = name }

    getRoleEnv :: RoleM RoleEnv
    getRoleEnv = RM $ \_ state@(RIS { role_env = env }) -> (env, state)

    getVarNs :: RoleM VarPositions
    getVarNs = RM $ \m_info state ->
                    case m_info of
                      Nothing -> panic "getVarNs"
                      Just (RII { var_ns = var_ns }) -> (var_ns, state)

    getTyConName :: RoleM Name
    getTyConName = RM $ \m_info state ->
                        case m_info of
                          Nothing -> panic "getTyConName"
                          Just (RII { name = name }) -> (name, state)

    updateRoleEnv :: Name -> Int -> Role -> RoleM ()
    updateRoleEnv name n role
      = RM $ \_ state@(RIS { role_env = role_env }) -> ((),
             case lookupNameEnv role_env name of
               Nothing -> pprPanic "updateRoleEnv" (ppr name)
               Just roles -> let (before, old_role : after) = splitAt n roles in
                             if role `ltRole` old_role
                             then let roles' = before ++ role : after
                                      role_env' = extendNameEnv role_env name roles' in
                                  RIS { role_env = role_env', update = True }
                             else state )