typecheck/TcDerivInfer.hs

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

    Functions for inferring (and simplifying) the context for derived instances.
    -}

    {-# LANGUAGE CPP #-}
    {-# LANGUAGE MultiWayIf #-}

    module TcDerivInfer (inferConstraints, simplifyInstanceContexts) where

    #include "HsVersions.h"

    import GhcPrelude

    import Bag
    import BasicTypes
    import Class
    import DataCon
    import ErrUtils
    import Inst
    import Outputable
    import Pair
    import PrelNames
    import TcDerivUtils
    import TcEnv
    import TcGenDeriv
    import TcGenFunctor
    import TcGenGenerics
    import TcMType
    import TcRnMonad
    import TcOrigin
    import Constraint
    import Predicate
    import TcType
    import TyCon
    import TyCoPpr (pprTyVars)
    import Type
    import TcSimplify
    import TcValidity (validDerivPred)
    import TcUnify (buildImplicationFor, checkConstraints)
    import TysWiredIn (typeToTypeKind)
    import Unify (tcUnifyTy)
    import Util
    import Var
    import VarSet

    import Control.Monad
    import Control.Monad.Trans.Class  (lift)
    import Control.Monad.Trans.Reader (ask)
    import Data.List                  (sortBy)
    import Data.Maybe

    ----------------------

    inferConstraints :: DerivSpecMechanism
                     -> DerivM ([ThetaOrigin], [TyVar], [TcType])
    -- inferConstraints figures out the constraints needed for the
    -- instance declaration generated by a 'deriving' clause on a
    -- data type declaration. It also returns the new in-scope type
    -- variables and instance types, in case they were changed due to
    -- the presence of functor-like constraints.
    -- See Note [Inferring the instance context]

    -- e.g. inferConstraints
    --        C Int (T [a])    -- Class and inst_tys
    --        :RTList a        -- Rep tycon and its arg tys
    -- where T [a] ~R :RTList a
    --
    -- Generate a sufficiently large set of constraints that typechecking the
    -- generated method definitions should succeed.   This set will be simplified
    -- before being used in the instance declaration
    inferConstraints mechanism
      = do { DerivEnv { denv_tvs      = tvs
                      , denv_cls      = main_cls
                      , denv_inst_tys = inst_tys } <- ask
           ; wildcard <- isStandaloneWildcardDeriv
           ; let infer_constraints :: DerivM ([ThetaOrigin], [TyVar], [TcType])
                 infer_constraints =
                   case mechanism of
                     DerivSpecStock{dsm_stock_dit = dit}
                       -> inferConstraintsStock dit
                     DerivSpecAnyClass
                       -> infer_constraints_simple inferConstraintsAnyclass
                     DerivSpecNewtype { dsm_newtype_dit =
                                          DerivInstTys{dit_cls_tys = cls_tys}
                                      , dsm_newtype_rep_ty = rep_ty }
                       -> infer_constraints_simple $
                          inferConstraintsCoerceBased cls_tys rep_ty
                     DerivSpecVia { dsm_via_cls_tys = cls_tys
                                  , dsm_via_ty = via_ty }
                       -> infer_constraints_simple $
                          inferConstraintsCoerceBased cls_tys via_ty

                 -- Most deriving strategies do not need to do anything special to
                 -- the type variables and arguments to the class in the derived
                 -- instance, so they can pass through unchanged. The exception to
                 -- this rule is stock deriving. See
                 -- Note [Inferring the instance context].
                 infer_constraints_simple
                   :: DerivM [ThetaOrigin]
                   -> DerivM ([ThetaOrigin], [TyVar], [TcType])
                 infer_constraints_simple infer_thetas = do
                   thetas <- infer_thetas
                   pure (thetas, tvs, inst_tys)

                 -- Constraints arising from superclasses
                 -- See Note [Superclasses of derived instance]
                 cls_tvs  = classTyVars main_cls
                 sc_constraints = ASSERT2( equalLength cls_tvs inst_tys
                                         , ppr main_cls <+> ppr inst_tys )
                                  [ mkThetaOrigin (mkDerivOrigin wildcard)
                                                  TypeLevel [] [] [] $
                                    substTheta cls_subst (classSCTheta main_cls) ]
                 cls_subst = ASSERT( equalLength cls_tvs inst_tys )
                             zipTvSubst cls_tvs inst_tys

           ; (inferred_constraints, tvs', inst_tys') <- infer_constraints
           ; lift $ traceTc "inferConstraints" $ vcat
                  [ ppr main_cls <+> ppr inst_tys'
                  , ppr inferred_constraints
                  ]
           ; return ( sc_constraints ++ inferred_constraints
                    , tvs', inst_tys' ) }

    -- | Like 'inferConstraints', but used only in the case of the @stock@ deriving
    -- strategy. The constraints are inferred by inspecting the fields of each data
    -- constructor. In this example:
    --
    -- > data Foo = MkFoo Int Char deriving Show
    --
    -- We would infer the following constraints ('ThetaOrigin's):
    --
    -- > (Show Int, Show Char)
    --
    -- Note that this function also returns the type variables ('TyVar's) and
    -- class arguments ('TcType's) for the resulting instance. This is because
    -- when deriving 'Functor'-like classes, we must sometimes perform kind
    -- substitutions to ensure the resulting instance is well kinded, which may
    -- affect the type variables and class arguments. In this example:
    --
    -- > newtype Compose (f :: k -> Type) (g :: Type -> k) (a :: Type) =
    -- >   Compose (f (g a)) deriving stock Functor
    --
    -- We must unify @k@ with @Type@ in order for the resulting 'Functor' instance
    -- to be well kinded, so we return @[]@/@[Type, f, g]@ for the
    -- 'TyVar's/'TcType's, /not/ @[k]@/@[k, f, g]@.
    -- See Note [Inferring the instance context].
    inferConstraintsStock :: DerivInstTys
                          -> DerivM ([ThetaOrigin], [TyVar], [TcType])
    inferConstraintsStock (DerivInstTys { dit_cls_tys     = cls_tys
                                        , dit_tc          = tc
                                        , dit_tc_args     = tc_args
                                        , dit_rep_tc      = rep_tc
                                        , dit_rep_tc_args = rep_tc_args })
      = do DerivEnv { denv_tvs      = tvs
                    , denv_cls      = main_cls
                    , denv_inst_tys = inst_tys } <- ask
           wildcard <- isStandaloneWildcardDeriv

           let inst_ty    = mkTyConApp tc tc_args
               tc_binders = tyConBinders rep_tc
               choose_level bndr
                 | isNamedTyConBinder bndr = KindLevel
                 | otherwise               = TypeLevel
               t_or_ks = map choose_level tc_binders ++ repeat TypeLevel
                  -- want to report *kind* errors when possible

                  -- Constraints arising from the arguments of each constructor
               con_arg_constraints
                 :: (CtOrigin -> TypeOrKind
                              -> Type
                              -> [([PredOrigin], Maybe TCvSubst)])
                 -> ([ThetaOrigin], [TyVar], [TcType])
               con_arg_constraints get_arg_constraints
                 = let (predss, mbSubsts) = unzip
                         [ preds_and_mbSubst
                         | data_con <- tyConDataCons rep_tc
                         , (arg_n, arg_t_or_k, arg_ty)
                             <- zip3 [1..] t_or_ks $
                                dataConInstOrigArgTys data_con all_rep_tc_args
                           -- No constraints for unlifted types
                           -- See Note [Deriving and unboxed types]
                         , not (isUnliftedType arg_ty)
                         , let orig = DerivOriginDC data_con arg_n wildcard
                         , preds_and_mbSubst
                             <- get_arg_constraints orig arg_t_or_k arg_ty
                         ]
                       preds = concat predss
                       -- If the constraints require a subtype to be of kind
                       -- (* -> *) (which is the case for functor-like
                       -- constraints), then we explicitly unify the subtype's
                       -- kinds with (* -> *).
                       -- See Note [Inferring the instance context]
                       subst        = foldl' composeTCvSubst
                                             emptyTCvSubst (catMaybes mbSubsts)
                       unmapped_tvs = filter (\v -> v `notElemTCvSubst` subst
                                                 && not (v `isInScope` subst)) tvs
                       (subst', _)  = substTyVarBndrs subst unmapped_tvs
                       preds'       = map (substPredOrigin subst') preds
                       inst_tys'    = substTys subst' inst_tys
                       tvs'         = tyCoVarsOfTypesWellScoped inst_tys'
                   in ([mkThetaOriginFromPreds preds'], tvs', inst_tys')

               is_generic  = main_cls `hasKey` genClassKey
               is_generic1 = main_cls `hasKey` gen1ClassKey
               -- is_functor_like: see Note [Inferring the instance context]
               is_functor_like = tcTypeKind inst_ty `tcEqKind` typeToTypeKind
                              || is_generic1

               get_gen1_constraints :: Class -> CtOrigin -> TypeOrKind -> Type
                                    -> [([PredOrigin], Maybe TCvSubst)]
               get_gen1_constraints functor_cls orig t_or_k ty
                  = mk_functor_like_constraints orig t_or_k functor_cls $
                    get_gen1_constrained_tys last_tv ty

               get_std_constrained_tys :: CtOrigin -> TypeOrKind -> Type
                                       -> [([PredOrigin], Maybe TCvSubst)]
               get_std_constrained_tys orig t_or_k ty
                   | is_functor_like
                   = mk_functor_like_constraints orig t_or_k main_cls $
                     deepSubtypesContaining last_tv ty
                   | otherwise
                   = [( [mk_cls_pred orig t_or_k main_cls ty]
                      , Nothing )]

               mk_functor_like_constraints :: CtOrigin -> TypeOrKind
                                           -> Class -> [Type]
                                           -> [([PredOrigin], Maybe TCvSubst)]
               -- 'cls' is usually main_cls (Functor or Traversable etc), but if
               -- main_cls = Generic1, then 'cls' can be Functor; see
               -- get_gen1_constraints
               --
               -- For each type, generate two constraints,
               -- [cls ty, kind(ty) ~ (*->*)], and a kind substitution that results
               -- from unifying  kind(ty) with * -> *. If the unification is
               -- successful, it will ensure that the resulting instance is well
               -- kinded. If not, the second constraint will result in an error
               -- message which points out the kind mismatch.
               -- See Note [Inferring the instance context]
               mk_functor_like_constraints orig t_or_k cls
                  = map $ \ty -> let ki = tcTypeKind ty in
                                 ( [ mk_cls_pred orig t_or_k cls ty
                                   , mkPredOrigin orig KindLevel
                                       (mkPrimEqPred ki typeToTypeKind) ]
                                 , tcUnifyTy ki typeToTypeKind
                                 )

               rep_tc_tvs      = tyConTyVars rep_tc
               last_tv         = last rep_tc_tvs
               -- When we first gather up the constraints to solve, most of them
               -- contain rep_tc_tvs, i.e., the type variables from the derived
               -- datatype's type constructor. We don't want these type variables
               -- to appear in the final instance declaration, so we must
               -- substitute each type variable with its counterpart in the derived
               -- instance. rep_tc_args lists each of these counterpart types in
               -- the same order as the type variables.
               all_rep_tc_args
                 = rep_tc_args ++ map mkTyVarTy
                                      (drop (length rep_tc_args) rep_tc_tvs)

                   -- Stupid constraints
               stupid_constraints
                 = [ mkThetaOrigin deriv_origin TypeLevel [] [] [] $
                     substTheta tc_subst (tyConStupidTheta rep_tc) ]
               tc_subst = -- See the comment with all_rep_tc_args for an
                          -- explanation of this assertion
                          ASSERT( equalLength rep_tc_tvs all_rep_tc_args )
                          zipTvSubst rep_tc_tvs all_rep_tc_args

               -- Extra Data constraints
               -- The Data class (only) requires that for
               --    instance (...) => Data (T t1 t2)
               -- IF   t1:*, t2:*
               -- THEN (Data t1, Data t2) are among the (...) constraints
               -- Reason: when the IF holds, we generate a method
               --             dataCast2 f = gcast2 f
               --         and we need the Data constraints to typecheck the method
               extra_constraints = [mkThetaOriginFromPreds constrs]
                 where
                   constrs
                     | main_cls `hasKey` dataClassKey
                     , all (isLiftedTypeKind . tcTypeKind) rep_tc_args
                     = [ mk_cls_pred deriv_origin t_or_k main_cls ty
                       | (t_or_k, ty) <- zip t_or_ks rep_tc_args]
                     | otherwise
                     = []

               mk_cls_pred orig t_or_k cls ty
                    -- Don't forget to apply to cls_tys' too
                  = mkPredOrigin orig t_or_k (mkClassPred cls (cls_tys' ++ [ty]))
               cls_tys' | is_generic1 = []
                          -- In the awkward Generic1 case, cls_tys' should be
                          -- empty, since we are applying the class Functor.

                        | otherwise   = cls_tys

               deriv_origin = mkDerivOrigin wildcard

           if    -- Generic constraints are easy
              |  is_generic
               -> return ([], tvs, inst_tys)

                 -- Generic1 needs Functor
                 -- See Note [Getting base classes]
              |  is_generic1
               -> ASSERT( rep_tc_tvs `lengthExceeds` 0 )
                  -- Generic1 has a single kind variable
                  ASSERT( cls_tys `lengthIs` 1 )
                  do { functorClass <- lift $ tcLookupClass functorClassName
                     ; pure $ con_arg_constraints
                            $ get_gen1_constraints functorClass }

                 -- The others are a bit more complicated
              |  otherwise
               -> -- See the comment with all_rep_tc_args for an explanation of
                  -- this assertion
                  ASSERT2( equalLength rep_tc_tvs all_rep_tc_args
                         , ppr main_cls <+> ppr rep_tc
                           $$ ppr rep_tc_tvs $$ ppr all_rep_tc_args )
                    do { let (arg_constraints, tvs', inst_tys')
                               = con_arg_constraints get_std_constrained_tys
                       ; lift $ traceTc "inferConstraintsStock" $ vcat
                              [ ppr main_cls <+> ppr inst_tys'
                              , ppr arg_constraints
                              ]
                       ; return ( stupid_constraints ++ extra_constraints
                                                     ++ arg_constraints
                                , tvs', inst_tys') }

    -- | Like 'inferConstraints', but used only in the case of @DeriveAnyClass@,
    -- which gathers its constraints based on the type signatures of the class's
    -- methods instead of the types of the data constructor's field.
    --
    -- See Note [Gathering and simplifying constraints for DeriveAnyClass]
    -- for an explanation of how these constraints are used to determine the
    -- derived instance context.
    inferConstraintsAnyclass :: DerivM [ThetaOrigin]
    inferConstraintsAnyclass
      = do { DerivEnv { denv_cls      = cls
                      , denv_inst_tys = inst_tys } <- ask
           ; wildcard <- isStandaloneWildcardDeriv

           ; let gen_dms = [ (sel_id, dm_ty)
                           | (sel_id, Just (_, GenericDM dm_ty)) <- classOpItems cls ]

                 cls_tvs = classTyVars cls

                 do_one_meth :: (Id, Type) -> TcM ThetaOrigin
                   -- (Id,Type) are the selector Id and the generic default method type
                   -- NB: the latter is /not/ quantified over the class variables
                   -- See Note [Gathering and simplifying constraints for DeriveAnyClass]
                 do_one_meth (sel_id, gen_dm_ty)
                   = do { let (sel_tvs, _cls_pred, meth_ty)
                                       = tcSplitMethodTy (varType sel_id)
                              meth_ty' = substTyWith sel_tvs inst_tys meth_ty
                              (meth_tvs, meth_theta, meth_tau)
                                       = tcSplitNestedSigmaTys meth_ty'

                              gen_dm_ty' = substTyWith cls_tvs inst_tys gen_dm_ty
                              (dm_tvs, dm_theta, dm_tau)
                                         = tcSplitNestedSigmaTys gen_dm_ty'
                              tau_eq     = mkPrimEqPred meth_tau dm_tau
                        ; return (mkThetaOrigin (mkDerivOrigin wildcard) TypeLevel
                                    meth_tvs dm_tvs meth_theta (tau_eq:dm_theta)) }

           ; theta_origins <- lift $ mapM do_one_meth gen_dms
           ; return theta_origins }

    -- Like 'inferConstraints', but used only for @GeneralizedNewtypeDeriving@ and
    -- @DerivingVia@. Since both strategies generate code involving 'coerce', the
    -- inferred constraints set up the scaffolding needed to typecheck those uses
    -- of 'coerce'. In this example:
    --
    -- > newtype Age = MkAge Int deriving newtype Num
    --
    -- We would infer the following constraints ('ThetaOrigin's):
    --
    -- > (Num Int, Coercible Age Int)
    inferConstraintsCoerceBased :: [Type] -> Type
                                -> DerivM [ThetaOrigin]
    inferConstraintsCoerceBased cls_tys rep_ty = do
      DerivEnv { denv_tvs      = tvs
               , denv_cls      = cls
               , denv_inst_tys = inst_tys } <- ask
      sa_wildcard <- isStandaloneWildcardDeriv
      let -- The following functions are polymorphic over the representation
          -- type, since we might either give it the underlying type of a
          -- newtype (for GeneralizedNewtypeDeriving) or a @via@ type
          -- (for DerivingVia).
          rep_tys ty  = cls_tys ++ [ty]
          rep_pred ty = mkClassPred cls (rep_tys ty)
          rep_pred_o ty = mkPredOrigin deriv_origin TypeLevel (rep_pred ty)
                  -- rep_pred is the representation dictionary, from where
                  -- we are going to get all the methods for the final
                  -- dictionary
          deriv_origin = mkDerivOrigin sa_wildcard

          -- Next we collect constraints for the class methods
          -- If there are no methods, we don't need any constraints
          -- Otherwise we need (C rep_ty), for the representation methods,
          -- and constraints to coerce each individual method
          meth_preds :: Type -> [PredOrigin]
          meth_preds ty
            | null meths = [] -- No methods => no constraints
                              -- (#12814)
            | otherwise = rep_pred_o ty : coercible_constraints ty
          meths = classMethods cls
          coercible_constraints ty
            = [ mkPredOrigin (DerivOriginCoerce meth t1 t2 sa_wildcard)
                             TypeLevel (mkReprPrimEqPred t1 t2)
              | meth <- meths
              , let (Pair t1 t2) = mkCoerceClassMethEqn cls tvs
                                           inst_tys ty meth ]

          all_thetas :: Type -> [ThetaOrigin]
          all_thetas ty = [mkThetaOriginFromPreds $ meth_preds ty]

      pure (all_thetas rep_ty)

    {- Note [Inferring the instance context]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    There are two sorts of 'deriving', as represented by the two constructors
    for DerivContext:

      * InferContext mb_wildcard: This can either be:
        - The deriving clause for a data type.
            (e.g, data T a = T1 a deriving( Eq ))
          In this case, mb_wildcard = Nothing.
        - A standalone declaration with an extra-constraints wildcard
            (e.g., deriving instance _ => Eq (Foo a))
          In this case, mb_wildcard = Just loc, where loc is the location
          of the extra-constraints wildcard.

        Here we must infer an instance context,
        and generate instance declaration
          instance Eq a => Eq (T a) where ...

      * SupplyContext theta: standalone deriving
          deriving instance Eq a => Eq (T a)
        Here we only need to fill in the bindings;
        the instance context (theta) is user-supplied

    For the InferContext case, we must figure out the
    instance context (inferConstraintsStock). Suppose we are inferring
    the instance context for
        C t1 .. tn (T s1 .. sm)
    There are two cases

      * (T s1 .. sm) :: *         (the normal case)
        Then we behave like Eq and guess (C t1 .. tn t)
        for each data constructor arg of type t.  More
        details below.

      * (T s1 .. sm) :: * -> *    (the functor-like case)
        Then we behave like Functor.

    In both cases we produce a bunch of un-simplified constraints
    and them simplify them in simplifyInstanceContexts; see
    Note [Simplifying the instance context].

    In the functor-like case, we may need to unify some kind variables with * in
    order for the generated instance to be well-kinded. An example from
    #10524:

      newtype Compose (f :: k2 -> *) (g :: k1 -> k2) (a :: k1)
        = Compose (f (g a)) deriving Functor

    Earlier in the deriving pipeline, GHC unifies the kind of Compose f g
    (k1 -> *) with the kind of Functor's argument (* -> *), so k1 := *. But this
    alone isn't enough, since k2 wasn't unified with *:

      instance (Functor (f :: k2 -> *), Functor (g :: * -> k2)) =>
        Functor (Compose f g) where ...

    The two Functor constraints are ill-kinded. To ensure this doesn't happen, we:

      1. Collect all of a datatype's subtypes which require functor-like
         constraints.
      2. For each subtype, create a substitution by unifying the subtype's kind
         with (* -> *).
      3. Compose all the substitutions into one, then apply that substitution to
         all of the in-scope type variables and the instance types.

    Note [Getting base classes]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Functor and Typeable are defined in package 'base', and that is not available
    when compiling 'ghc-prim'.  So we must be careful that 'deriving' for stuff in
    ghc-prim does not use Functor or Typeable implicitly via these lookups.

    Note [Deriving and unboxed types]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We have some special hacks to support things like
       data T = MkT Int# deriving ( Show )

    Specifically, we use TcGenDeriv.box to box the Int# into an Int
    (which we know how to show), and append a '#'. Parentheses are not required
    for unboxed values (`MkT -3#` is a valid expression).

    Note [Superclasses of derived instance]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In general, a derived instance decl needs the superclasses of the derived
    class too.  So if we have
            data T a = ...deriving( Ord )
    then the initial context for Ord (T a) should include Eq (T a).  Often this is
    redundant; we'll also generate an Ord constraint for each constructor argument,
    and that will probably generate enough constraints to make the Eq (T a) constraint
    be satisfied too.  But not always; consider:

     data S a = S
     instance Eq (S a)
     instance Ord (S a)

     data T a = MkT (S a) deriving( Ord )
     instance Num a => Eq (T a)

    The derived instance for (Ord (T a)) must have a (Num a) constraint!
    Similarly consider:
            data T a = MkT deriving( Data )
    Here there *is* no argument field, but we must nevertheless generate
    a context for the Data instances:
            instance Typeable a => Data (T a) where ...

    ************************************************************************
    *                                                                      *
             Finding the fixed point of deriving equations
    *                                                                      *
    ************************************************************************

    Note [Simplifying the instance context]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider

            data T a b = C1 (Foo a) (Bar b)
                       | C2 Int (T b a)
                       | C3 (T a a)
                       deriving (Eq)

    We want to come up with an instance declaration of the form

            instance (Ping a, Pong b, ...) => Eq (T a b) where
                    x == y = ...

    It is pretty easy, albeit tedious, to fill in the code "...".  The
    trick is to figure out what the context for the instance decl is,
    namely Ping, Pong and friends.

    Let's call the context reqd for the T instance of class C at types
    (a,b, ...)  C (T a b).  Thus:

            Eq (T a b) = (Ping a, Pong b, ...)

    Now we can get a (recursive) equation from the data decl.  This part
    is done by inferConstraintsStock.

            Eq (T a b) = Eq (Foo a) u Eq (Bar b)    -- From C1
                       u Eq (T b a) u Eq Int        -- From C2
                       u Eq (T a a)                 -- From C3

    Foo and Bar may have explicit instances for Eq, in which case we can
    just substitute for them.  Alternatively, either or both may have
    their Eq instances given by deriving clauses, in which case they
    form part of the system of equations.

    Now all we need do is simplify and solve the equations, iterating to
    find the least fixpoint.  This is done by simplifyInstanceConstraints.
    Notice that the order of the arguments can
    switch around, as here in the recursive calls to T.

    Let's suppose Eq (Foo a) = Eq a, and Eq (Bar b) = Ping b.

    We start with:

            Eq (T a b) = {}         -- The empty set

    Next iteration:
            Eq (T a b) = Eq (Foo a) u Eq (Bar b)    -- From C1
                       u Eq (T b a) u Eq Int        -- From C2
                       u Eq (T a a)                 -- From C3

            After simplification:
                       = Eq a u Ping b u {} u {} u {}
                       = Eq a u Ping b

    Next iteration:

            Eq (T a b) = Eq (Foo a) u Eq (Bar b)    -- From C1
                       u Eq (T b a) u Eq Int        -- From C2
                       u Eq (T a a)                 -- From C3

            After simplification:
                       = Eq a u Ping b
                       u (Eq b u Ping a)
                       u (Eq a u Ping a)

                       = Eq a u Ping b u Eq b u Ping a

    The next iteration gives the same result, so this is the fixpoint.  We
    need to make a canonical form of the RHS to ensure convergence.  We do
    this by simplifying the RHS to a form in which

            - the classes constrain only tyvars
            - the list is sorted by tyvar (major key) and then class (minor key)
            - no duplicates, of course

    Note [Deterministic simplifyInstanceContexts]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Canonicalisation uses nonDetCmpType which is nondeterministic. Sorting
    with nonDetCmpType puts the returned lists in a nondeterministic order.
    If we were to return them, we'd get class constraints in
    nondeterministic order.

    Consider:

      data ADT a b = Z a b deriving Eq

    The generated code could be either:

      instance (Eq a, Eq b) => Eq (Z a b) where

    Or:

      instance (Eq b, Eq a) => Eq (Z a b) where

    To prevent the order from being nondeterministic we only
    canonicalize when comparing and return them in the same order as
    simplifyDeriv returned them.
    See also Note [nonDetCmpType nondeterminism]
    -}

    simplifyInstanceContexts :: [DerivSpec [ThetaOrigin]]
                             -> TcM [DerivSpec ThetaType]
    -- Used only for deriving clauses or standalone deriving with an
    -- extra-constraints wildcard (InferContext)
    -- See Note [Simplifying the instance context]

    simplifyInstanceContexts [] = return []

    simplifyInstanceContexts infer_specs
      = do  { traceTc "simplifyInstanceContexts" $ vcat (map pprDerivSpec infer_specs)
            ; iterate_deriv 1 initial_solutions }
      where
        ------------------------------------------------------------------
            -- The initial solutions for the equations claim that each
            -- instance has an empty context; this solution is certainly
            -- in canonical form.
        initial_solutions :: [ThetaType]
        initial_solutions = [ [] | _ <- infer_specs ]

        ------------------------------------------------------------------
            -- iterate_deriv calculates the next batch of solutions,
            -- compares it with the current one; finishes if they are the
            -- same, otherwise recurses with the new solutions.
            -- It fails if any iteration fails
        iterate_deriv :: Int -> [ThetaType] -> TcM [DerivSpec ThetaType]
        iterate_deriv n current_solns
          | n > 20  -- Looks as if we are in an infinite loop
                    -- This can happen if we have -XUndecidableInstances
                    -- (See TcSimplify.tcSimplifyDeriv.)
          = pprPanic "solveDerivEqns: probable loop"
                     (vcat (map pprDerivSpec infer_specs) $$ ppr current_solns)
          | otherwise
          = do {      -- Extend the inst info from the explicit instance decls
                      -- with the current set of solutions, and simplify each RHS
                 inst_specs <- zipWithM newDerivClsInst current_solns infer_specs
               ; new_solns <- checkNoErrs $
                              extendLocalInstEnv inst_specs $
                              mapM gen_soln infer_specs

               ; if (current_solns `eqSolution` new_solns) then
                    return [ spec { ds_theta = soln }
                           | (spec, soln) <- zip infer_specs current_solns ]
                 else
                    iterate_deriv (n+1) new_solns }

        eqSolution a b = eqListBy (eqListBy eqType) (canSolution a) (canSolution b)
           -- Canonicalise for comparison
           -- See Note [Deterministic simplifyInstanceContexts]
        canSolution = map (sortBy nonDetCmpType)
        ------------------------------------------------------------------
        gen_soln :: DerivSpec [ThetaOrigin] -> TcM ThetaType
        gen_soln (DS { ds_loc = loc, ds_tvs = tyvars
                     , ds_cls = clas, ds_tys = inst_tys, ds_theta = deriv_rhs })
          = setSrcSpan loc  $
            addErrCtxt (derivInstCtxt the_pred) $
            do { theta <- simplifyDeriv the_pred tyvars deriv_rhs
                    -- checkValidInstance tyvars theta clas inst_tys
                    -- Not necessary; see Note [Exotic derived instance contexts]

               ; traceTc "TcDeriv" (ppr deriv_rhs $$ ppr theta)
                    -- Claim: the result instance declaration is guaranteed valid
                    -- Hence no need to call:
                    --   checkValidInstance tyvars theta clas inst_tys
               ; return theta }
          where
            the_pred = mkClassPred clas inst_tys

    derivInstCtxt :: PredType -> MsgDoc
    derivInstCtxt pred
      = text "When deriving the instance for" <+> parens (ppr pred)

    {-
    ***********************************************************************************
    *                                                                                 *
    *            Simplify derived constraints
    *                                                                                 *
    ***********************************************************************************
    -}

    -- | Given @instance (wanted) => C inst_ty@, simplify 'wanted' as much
    -- as possible. Fail if not possible.
    simplifyDeriv :: PredType -- ^ @C inst_ty@, head of the instance we are
                              -- deriving.  Only used for SkolemInfo.
                  -> [TyVar]  -- ^ The tyvars bound by @inst_ty@.
                  -> [ThetaOrigin] -- ^ Given and wanted constraints
                  -> TcM ThetaType -- ^ Needed constraints (after simplification),
                                   -- i.e. @['PredType']@.
    simplifyDeriv pred tvs thetas
      = do { (skol_subst, tvs_skols) <- tcInstSkolTyVars tvs -- Skolemize
                    -- The constraint solving machinery
                    -- expects *TcTyVars* not TyVars.
                    -- We use *non-overlappable* (vanilla) skolems
                    -- See Note [Overlap and deriving]

           ; let skol_set  = mkVarSet tvs_skols
                 skol_info = DerivSkol pred
                 doc = text "deriving" <+> parens (ppr pred)

                 mk_given_ev :: PredType -> TcM EvVar
                 mk_given_ev given =
                   let given_pred = substTy skol_subst given
                   in newEvVar given_pred

                 emit_wanted_constraints :: [TyVar] -> [PredOrigin] -> TcM ()
                 emit_wanted_constraints metas_to_be preds
                   = do { -- We instantiate metas_to_be with fresh meta type
                          -- variables. Currently, these can only be type variables
                          -- quantified in generic default type signatures.
                          -- See Note [Gathering and simplifying constraints for
                          -- DeriveAnyClass]
                          (meta_subst, _meta_tvs) <- newMetaTyVars metas_to_be

                        -- Now make a constraint for each of the instantiated predicates
                        ; let wanted_subst = skol_subst `unionTCvSubst` meta_subst
                              mk_wanted_ct (PredOrigin wanted orig t_or_k)
                                = do { ev <- newWanted orig (Just t_or_k) $
                                             substTyUnchecked wanted_subst wanted
                                     ; return (mkNonCanonical ev) }
                        ; cts <- mapM mk_wanted_ct preds

                        -- And emit them into the monad
                        ; emitSimples (listToCts cts) }

                 -- Create the implications we need to solve. For stock and newtype
                 -- deriving, these implication constraints will be simple class
                 -- constraints like (C a, Ord b).
                 -- But with DeriveAnyClass, we make an implication constraint.
                 -- See Note [Gathering and simplifying constraints for DeriveAnyClass]
                 mk_wanteds :: ThetaOrigin -> TcM WantedConstraints
                 mk_wanteds (ThetaOrigin { to_anyclass_skols  = ac_skols
                                         , to_anyclass_metas  = ac_metas
                                         , to_anyclass_givens = ac_givens
                                         , to_wanted_origins  = preds })
                   = do { ac_given_evs <- mapM mk_given_ev ac_givens
                        ; (_, wanteds)
                            <- captureConstraints $
                               checkConstraints skol_info ac_skols ac_given_evs $
                                  -- The checkConstraints bumps the TcLevel, and
                                  -- wraps the wanted constraints in an implication,
                                  -- when (but only when) necessary
                               emit_wanted_constraints ac_metas preds
                        ; pure wanteds }

           -- See [STEP DAC BUILD]
           -- Generate the implication constraints, one for each method, to solve
           -- with the skolemized variables.  Start "one level down" because
           -- we are going to wrap the result in an implication with tvs_skols,
           -- in step [DAC RESIDUAL]
           ; (tc_lvl, wanteds) <- pushTcLevelM $
                                  mapM mk_wanteds thetas

           ; traceTc "simplifyDeriv inputs" $
             vcat [ pprTyVars tvs $$ ppr thetas $$ ppr wanteds, doc ]

           -- See [STEP DAC SOLVE]
           -- Simplify the constraints, starting at the same level at which
           -- they are generated (c.f. the call to runTcSWithEvBinds in
           -- simplifyInfer)
           ; solved_wanteds <- setTcLevel tc_lvl   $
                               runTcSDeriveds      $
                               solveWantedsAndDrop $
                               unionsWC wanteds

           -- It's not yet zonked!  Obviously zonk it before peering at it
           ; solved_wanteds <- zonkWC solved_wanteds

           -- See [STEP DAC HOIST]
           -- Split the resulting constraints into bad and good constraints,
           -- building an @unsolved :: WantedConstraints@ representing all
           -- the constraints we can't just shunt to the predicates.
           -- See Note [Exotic derived instance contexts]
           ; let residual_simple = approximateWC True solved_wanteds
                 (bad, good) = partitionBagWith get_good residual_simple

                 get_good :: Ct -> Either Ct PredType
                 get_good ct | validDerivPred skol_set p
                             , isWantedCt ct
                             = Right p
                              -- TODO: This is wrong
                              -- NB re 'isWantedCt': residual_wanted may contain
                              -- unsolved CtDerived and we stick them into the
                              -- bad set so that reportUnsolved may decide what
                              -- to do with them
                             | otherwise
                             = Left ct
                               where p = ctPred ct

           ; traceTc "simplifyDeriv outputs" $
             vcat [ ppr tvs_skols, ppr residual_simple, ppr good, ppr bad ]

           -- Return the good unsolved constraints (unskolemizing on the way out.)
           ; let min_theta = mkMinimalBySCs id (bagToList good)
                 -- An important property of mkMinimalBySCs (used above) is that in
                 -- addition to removing constraints that are made redundant by
                 -- superclass relationships, it also removes _duplicate_
                 -- constraints.
                 -- See Note [Gathering and simplifying constraints for
                 --           DeriveAnyClass]
                 subst_skol = zipTvSubst tvs_skols $ mkTyVarTys tvs
                              -- The reverse substitution (sigh)

           -- See [STEP DAC RESIDUAL]
           ; min_theta_vars <- mapM newEvVar min_theta
           ; (leftover_implic, _)
               <- buildImplicationFor tc_lvl skol_info tvs_skols
                                      min_theta_vars solved_wanteds
           -- This call to simplifyTop is purely for error reporting
           -- See Note [Error reporting for deriving clauses]
           -- See also Note [Exotic derived instance contexts], which are caught
           -- in this line of code.
           ; simplifyTopImplic leftover_implic

           ; return (substTheta subst_skol min_theta) }

    {-
    Note [Overlap and deriving]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider some overlapping instances:
      instance Show a => Show [a] where ..
      instance Show [Char] where ...

    Now a data type with deriving:
      data T a = MkT [a] deriving( Show )

    We want to get the derived instance
      instance Show [a] => Show (T a) where...
    and NOT
      instance Show a => Show (T a) where...
    so that the (Show (T Char)) instance does the Right Thing

    It's very like the situation when we're inferring the type
    of a function
       f x = show [x]
    and we want to infer
       f :: Show [a] => a -> String

    BOTTOM LINE: use vanilla, non-overlappable skolems when inferring
                 the context for the derived instance.
                 Hence tcInstSkolTyVars not tcInstSuperSkolTyVars

    Note [Gathering and simplifying constraints for DeriveAnyClass]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    DeriveAnyClass works quite differently from stock and newtype deriving in
    the way it gathers and simplifies constraints to be used in a derived
    instance's context. Stock and newtype deriving gather constraints by looking
    at the data constructors of the data type for which we are deriving an
    instance. But DeriveAnyClass doesn't need to know about a data type's
    definition at all!

    To see why, consider this example of DeriveAnyClass:

      class Foo a where
        bar :: forall b. Ix b => a -> b -> String
        default bar :: (Show a, Ix c) => a -> c -> String
        bar x y = show x ++ show (range (y,y))

        baz :: Eq a => a -> a -> Bool
        default baz :: (Ord a, Show a) => a -> a -> Bool
        baz x y = compare x y == EQ

    Because 'bar' and 'baz' have default signatures, this generates a top-level
    definition for these generic default methods

      $gdm_bar :: forall a. Foo a
               => forall c. (Show a, Ix c)
               => a -> c -> String
      $gdm_bar x y = show x ++ show (range (y,y))

    (and similarly for baz).  Now consider a 'deriving' clause
      data Maybe s = ... deriving Foo

    This derives an instance of the form:
      instance (CX) => Foo (Maybe s) where
        bar = $gdm_bar
        baz = $gdm_baz

    Now it is GHC's job to fill in a suitable instance context (CX).  If
    GHC were typechecking the binding
       bar = $gdm bar
    it would
       * skolemise the expected type of bar
       * instantiate the type of $gdm_bar with meta-type variables
       * build an implication constraint

    [STEP DAC BUILD]
    So that's what we do.  We build the constraint (call it C1)

       forall[2] b. Ix b => (Show (Maybe s), Ix cc,
                            Maybe s -> b -> String
                                ~ Maybe s -> cc -> String)

    Here:
    * The level of this forall constraint is forall[2], because we are later
      going to wrap it in a forall[1] in [STEP DAC RESIDUAL]

    * The 'b' comes from the quantified type variable in the expected type
      of bar (i.e., 'to_anyclass_skols' in 'ThetaOrigin'). The 'cc' is a unification
      variable that comes from instantiating the quantified type variable 'c' in
      $gdm_bar's type (i.e., 'to_anyclass_metas' in 'ThetaOrigin).

    * The (Ix b) constraint comes from the context of bar's type
      (i.e., 'to_wanted_givens' in 'ThetaOrigin'). The (Show (Maybe s)) and (Ix cc)
      constraints come from the context of $gdm_bar's type
      (i.e., 'to_anyclass_givens' in 'ThetaOrigin').

    * The equality constraint (Maybe s -> b -> String) ~ (Maybe s -> cc -> String)
      comes from marrying up the instantiated type of $gdm_bar with the specified
      type of bar. Notice that the type variables from the instance, 's' in this
      case, are global to this constraint.

    Note that it is vital that we instantiate the `c` in $gdm_bar's type with a new
    unification variable for each iteration of simplifyDeriv. If we re-use the same
    unification variable across multiple iterations, then bad things can happen,
    such as #14933.

    Similarly for 'baz', givng the constraint C2

       forall[2]. Eq (Maybe s) => (Ord a, Show a,
                                  Maybe s -> Maybe s -> Bool
                                    ~ Maybe s -> Maybe s -> Bool)

    In this case baz has no local quantification, so the implication
    constraint has no local skolems and there are no unification
    variables.

    [STEP DAC SOLVE]
    We can combine these two implication constraints into a single
    constraint (C1, C2), and simplify, unifying cc:=b, to get:

       forall[2] b. Ix b => Show a
       /\
       forall[2]. Eq (Maybe s) => (Ord a, Show a)

    [STEP DAC HOIST]
    Let's call that (C1', C2').  Now we need to hoist the unsolved
    constraints out of the implications to become our candidate for
    (CX). That is done by approximateWC, which will return:

      (Show a, Ord a, Show a)

    Now we can use mkMinimalBySCs to remove superclasses and duplicates, giving

      (Show a, Ord a)

    And that's what GHC uses for CX.

    [STEP DAC RESIDUAL]
    In this case we have solved all the leftover constraints, but what if
    we don't?  Simple!  We just form the final residual constraint

       forall[1] s. CX => (C1',C2')

    and simplify that. In simple cases it'll succeed easily, because CX
    literally contains the constraints in C1', C2', but if there is anything
    more complicated it will be reported in a civilised way.

    Note [Error reporting for deriving clauses]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    A suprisingly tricky aspect of deriving to get right is reporting sensible
    error messages. In particular, if simplifyDeriv reaches a constraint that it
    cannot solve, which might include:

    1. Insoluble constraints
    2. "Exotic" constraints (See Note [Exotic derived instance contexts])

    Then we report an error immediately in simplifyDeriv.

    Another possible choice is to punt and let another part of the typechecker
    (e.g., simplifyInstanceContexts) catch the errors. But this tends to lead
    to worse error messages, so we do it directly in simplifyDeriv.

    simplifyDeriv checks for errors in a clever way. If the deriving machinery
    infers the context (Foo a)--that is, if this instance is to be generated:

      instance Foo a => ...

    Then we form an implication of the form:

      forall a. Foo a => <residual_wanted_constraints>

    And pass it to the simplifier. If the context (Foo a) is enough to discharge
    all the constraints in <residual_wanted_constraints>, then everything is
    hunky-dory. But if <residual_wanted_constraints> contains, say, an insoluble
    constraint, then (Foo a) won't be able to solve it, causing GHC to error.

    Note [Exotic derived instance contexts]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In a 'derived' instance declaration, we *infer* the context.  It's a
    bit unclear what rules we should apply for this; the Haskell report is
    silent.  Obviously, constraints like (Eq a) are fine, but what about
            data T f a = MkT (f a) deriving( Eq )
    where we'd get an Eq (f a) constraint.  That's probably fine too.

    One could go further: consider
            data T a b c = MkT (Foo a b c) deriving( Eq )
            instance (C Int a, Eq b, Eq c) => Eq (Foo a b c)

    Notice that this instance (just) satisfies the Paterson termination
    conditions.  Then we *could* derive an instance decl like this:

            instance (C Int a, Eq b, Eq c) => Eq (T a b c)
    even though there is no instance for (C Int a), because there just
    *might* be an instance for, say, (C Int Bool) at a site where we
    need the equality instance for T's.

    However, this seems pretty exotic, and it's quite tricky to allow
    this, and yet give sensible error messages in the (much more common)
    case where we really want that instance decl for C.

    So for now we simply require that the derived instance context
    should have only type-variable constraints.

    Here is another example:
            data Fix f = In (f (Fix f)) deriving( Eq )
    Here, if we are prepared to allow -XUndecidableInstances we
    could derive the instance
            instance Eq (f (Fix f)) => Eq (Fix f)
    but this is so delicate that I don't think it should happen inside
    'deriving'. If you want this, write it yourself!

    NB: if you want to lift this condition, make sure you still meet the
    termination conditions!  If not, the deriving mechanism generates
    larger and larger constraints.  Example:
      data Succ a = S a
      data Seq a = Cons a (Seq (Succ a)) | Nil deriving Show

    Note the lack of a Show instance for Succ.  First we'll generate
      instance (Show (Succ a), Show a) => Show (Seq a)
    and then
      instance (Show (Succ (Succ a)), Show (Succ a), Show a) => Show (Seq a)
    and so on.  Instead we want to complain of no instance for (Show (Succ a)).

    The bottom line
    ~~~~~~~~~~~~~~~
    Allow constraints which consist only of type variables, with no repeats.
    -}