{-# LANGUAGE DeriveFunctor       #-}
{-# LANGUAGE GADTs               #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TupleSections       #-}

{-# OPTIONS_GHC -Wno-incomplete-record-updates #-}
-- (c) The University of Glasgow 2006
--
-- FamInstEnv: Type checked family instance declarations

module GHC.Core.FamInstEnv (
        FamInst(..), FamFlavor(..), famInstAxiom, famInstTyCon, famInstRHS,
        famInstsRepTyCons, famInstRepTyCon_maybe, dataFamInstRepTyCon,
        pprFamInst, pprFamInsts,
        mkImportedFamInst,

        FamInstEnvs, FamInstEnv, emptyFamInstEnv, emptyFamInstEnvs,
        unionFamInstEnv, extendFamInstEnv, extendFamInstEnvList,
        famInstEnvElts, famInstEnvSize, familyInstances, familyNameInstances,

        -- * CoAxioms
        mkCoAxBranch, mkBranchedCoAxiom, mkUnbranchedCoAxiom, mkSingleCoAxiom,
        mkNewTypeCoAxiom,

        FamInstMatch(..),
        lookupFamInstEnv, lookupFamInstEnvConflicts, lookupFamInstEnvByTyCon,

        isDominatedBy, apartnessCheck,

        -- Injectivity
        InjectivityCheckResult(..),
        lookupFamInstEnvInjectivityConflicts, injectiveBranches,

        -- Normalisation
        topNormaliseType, topNormaliseType_maybe,
        normaliseType, normaliseTcApp,
        topReduceTyFamApp_maybe, reduceTyFamApp_maybe
    ) where

import GHC.Prelude

import GHC.Core.Unify
import GHC.Core.Type as Type
import GHC.Core.TyCo.Rep
import GHC.Core.TyCon
import GHC.Core.Coercion
import GHC.Core.Coercion.Axiom
import GHC.Core.Reduction
import GHC.Core.RoughMap
import GHC.Types.Var.Set
import GHC.Types.Var.Env
import GHC.Types.Name
import GHC.Data.Maybe
import GHC.Types.Var
import GHC.Types.SrcLoc
import Control.Monad
import Data.List( mapAccumL )
import Data.Array( Array, assocs )

import GHC.Utils.Misc
import GHC.Utils.Outputable
import GHC.Utils.Panic
import GHC.Utils.Panic.Plain
import GHC.Data.Bag

{-
************************************************************************
*                                                                      *
          Type checked family instance heads
*                                                                      *
************************************************************************

Note [FamInsts and CoAxioms]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
* CoAxioms and FamInsts are just like
  DFunIds  and ClsInsts

* A CoAxiom is a System-FC thing: it can relate any two types

* A FamInst is a Haskell source-language thing, corresponding
  to a type/data family instance declaration.
    - The FamInst contains a CoAxiom, which is the evidence
      for the instance

    - The LHS of the CoAxiom is always of form F ty1 .. tyn
      where F is a type family
-}

data FamInst  -- See Note [FamInsts and CoAxioms]
  = FamInst { FamInst -> CoAxiom Unbranched
fi_axiom  :: CoAxiom Unbranched -- The new coercion axiom
                                              -- introduced by this family
                                              -- instance
                 -- INVARIANT: apart from freshening (see below)
                 --    fi_tvs = cab_tvs of the (single) axiom branch
                 --    fi_cvs = cab_cvs ...ditto...
                 --    fi_tys = cab_lhs ...ditto...
                 --    fi_rhs = cab_rhs ...ditto...

            , FamInst -> FamFlavor
fi_flavor :: FamFlavor

            -- Everything below here is a redundant,
            -- cached version of the two things above
            -- except that the TyVars are freshened
            , FamInst -> Name
fi_fam   :: Name          -- Family name

                -- Used for "rough matching"; same idea as for class instances
                -- See Note [Rough matching in class and family instances]
                -- in GHC.Core.Unify
            , FamInst -> [RoughMatchTc]
fi_tcs   :: [RoughMatchTc]  -- Top of type args
                -- INVARIANT: fi_tcs = roughMatchTcs fi_tys

            -- Used for "proper matching"; ditto
            , FamInst -> [TyVar]
fi_tvs :: [TyVar]      -- Template tyvars for full match
            , FamInst -> [TyVar]
fi_cvs :: [CoVar]      -- Template covars for full match
                 -- Like ClsInsts, these variables are always fresh
                 -- See Note [Template tyvars are fresh] in GHC.Core.InstEnv

            , FamInst -> [Type]
fi_tys    :: [Type]       --   The LHS type patterns
            -- May be eta-reduced; see Note [Eta reduction for data families]
            -- in GHC.Core.Coercion.Axiom

            , FamInst -> Type
fi_rhs :: Type         --   the RHS, with its freshened vars
            }

data FamFlavor
  = SynFamilyInst         -- A synonym family
  | DataFamilyInst TyCon  -- A data family, with its representation TyCon

{-
Note [Arity of data families]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Data family instances might legitimately be over- or under-saturated.

Under-saturation has two potential causes:
 U1) Eta reduction. See Note [Eta reduction for data families] in
     GHC.Core.Coercion.Axiom.
 U2) When the user has specified a return kind instead of written out patterns.
     Example:

       data family Sing (a :: k)
       data instance Sing :: Bool -> Type

     The data family tycon Sing has an arity of 2, the k and the a. But
     the data instance has only one pattern, Bool (standing in for k).
     This instance is equivalent to `data instance Sing (a :: Bool)`, but
     without the last pattern, we have an under-saturated data family instance.
     On its own, this example is not compelling enough to add support for
     under-saturation, but U1 makes this feature more compelling.

Over-saturation is also possible:
  O1) If the data family's return kind is a type variable (see also #12369),
      an instance might legitimately have more arguments than the family.
      Example:

        data family Fix :: (Type -> k) -> k
        data instance Fix f = MkFix1 (f (Fix f))
        data instance Fix f x = MkFix2 (f (Fix f x) x)

      In the first instance here, the k in the data family kind is chosen to
      be Type. In the second, it's (Type -> Type).

      However, we require that any over-saturation is eta-reducible. That is,
      we require that any extra patterns be bare unrepeated type variables;
      see Note [Eta reduction for data families] in GHC.Core.Coercion.Axiom.
      Accordingly, the FamInst is never over-saturated.

Why can we allow such flexibility for data families but not for type families?
Because data families can be decomposed -- that is, they are generative and
injective. A Type family is neither and so always must be applied to all its
arguments.
-}

-- Obtain the axiom of a family instance
famInstAxiom :: FamInst -> CoAxiom Unbranched
famInstAxiom :: FamInst -> CoAxiom Unbranched
famInstAxiom = FamInst -> CoAxiom Unbranched
fi_axiom

-- Split the left-hand side of the FamInst
famInstSplitLHS :: FamInst -> (TyCon, [Type])
famInstSplitLHS :: FamInst -> (TyCon, [Type])
famInstSplitLHS (FamInst { fi_axiom :: FamInst -> CoAxiom Unbranched
fi_axiom = CoAxiom Unbranched
axiom, fi_tys :: FamInst -> [Type]
fi_tys = [Type]
lhs })
  = (forall (br :: BranchFlag). CoAxiom br -> TyCon
coAxiomTyCon CoAxiom Unbranched
axiom, [Type]
lhs)

-- Get the RHS of the FamInst
famInstRHS :: FamInst -> Type
famInstRHS :: FamInst -> Type
famInstRHS = FamInst -> Type
fi_rhs

-- Get the family TyCon of the FamInst
famInstTyCon :: FamInst -> TyCon
famInstTyCon :: FamInst -> TyCon
famInstTyCon = forall (br :: BranchFlag). CoAxiom br -> TyCon
coAxiomTyCon forall b c a. (b -> c) -> (a -> b) -> a -> c
. FamInst -> CoAxiom Unbranched
famInstAxiom

-- Return the representation TyCons introduced by data family instances, if any
famInstsRepTyCons :: [FamInst] -> [TyCon]
famInstsRepTyCons :: [FamInst] -> [TyCon]
famInstsRepTyCons [FamInst]
fis = [TyCon
tc | FamInst { fi_flavor :: FamInst -> FamFlavor
fi_flavor = DataFamilyInst TyCon
tc } <- [FamInst]
fis]

-- Extracts the TyCon for this *data* (or newtype) instance
famInstRepTyCon_maybe :: FamInst -> Maybe TyCon
famInstRepTyCon_maybe :: FamInst -> Maybe TyCon
famInstRepTyCon_maybe FamInst
fi
  = case FamInst -> FamFlavor
fi_flavor FamInst
fi of
       DataFamilyInst TyCon
tycon -> forall a. a -> Maybe a
Just TyCon
tycon
       FamFlavor
SynFamilyInst        -> forall a. Maybe a
Nothing

dataFamInstRepTyCon :: FamInst -> TyCon
dataFamInstRepTyCon :: FamInst -> TyCon
dataFamInstRepTyCon FamInst
fi
  = case FamInst -> FamFlavor
fi_flavor FamInst
fi of
       DataFamilyInst TyCon
tycon -> TyCon
tycon
       FamFlavor
SynFamilyInst        -> forall a. HasCallStack => String -> SDoc -> a
pprPanic String
"dataFamInstRepTyCon" (forall a. Outputable a => a -> SDoc
ppr FamInst
fi)

{-
************************************************************************
*                                                                      *
        Pretty printing
*                                                                      *
************************************************************************
-}

instance NamedThing FamInst where
   getName :: FamInst -> Name
getName = forall (br :: BranchFlag). CoAxiom br -> Name
coAxiomName forall b c a. (b -> c) -> (a -> b) -> a -> c
. FamInst -> CoAxiom Unbranched
fi_axiom

instance Outputable FamInst where
   ppr :: FamInst -> SDoc
ppr = FamInst -> SDoc
pprFamInst

pprFamInst :: FamInst -> SDoc
-- Prints the FamInst as a family instance declaration
-- NB: This function, FamInstEnv.pprFamInst, is used only for internal,
--     debug printing. See GHC.Types.TyThing.Ppr.pprFamInst for printing for the user
pprFamInst :: FamInst -> SDoc
pprFamInst (FamInst { fi_flavor :: FamInst -> FamFlavor
fi_flavor = FamFlavor
flavor, fi_axiom :: FamInst -> CoAxiom Unbranched
fi_axiom = CoAxiom Unbranched
ax
                    , fi_tvs :: FamInst -> [TyVar]
fi_tvs = [TyVar]
tvs, fi_tys :: FamInst -> [Type]
fi_tys = [Type]
tys, fi_rhs :: FamInst -> Type
fi_rhs = Type
rhs })
  = SDoc -> BranchIndex -> SDoc -> SDoc
hang (SDoc
ppr_tc_sort SDoc -> SDoc -> SDoc
<+> String -> SDoc
text String
"instance"
             SDoc -> SDoc -> SDoc
<+> TyCon -> CoAxBranch -> SDoc
pprCoAxBranchUser (forall (br :: BranchFlag). CoAxiom br -> TyCon
coAxiomTyCon CoAxiom Unbranched
ax) (CoAxiom Unbranched -> CoAxBranch
coAxiomSingleBranch CoAxiom Unbranched
ax))
       BranchIndex
2 (SDoc -> SDoc
whenPprDebug SDoc
debug_stuff)
  where
    ppr_tc_sort :: SDoc
ppr_tc_sort = case FamFlavor
flavor of
                     FamFlavor
SynFamilyInst             -> String -> SDoc
text String
"type"
                     DataFamilyInst TyCon
tycon
                       | TyCon -> Bool
isDataTyCon     TyCon
tycon -> String -> SDoc
text String
"data"
                       | TyCon -> Bool
isNewTyCon      TyCon
tycon -> String -> SDoc
text String
"newtype"
                       | TyCon -> Bool
isAbstractTyCon TyCon
tycon -> String -> SDoc
text String
"data"
                       | Bool
otherwise             -> String -> SDoc
text String
"WEIRD" SDoc -> SDoc -> SDoc
<+> forall a. Outputable a => a -> SDoc
ppr TyCon
tycon

    debug_stuff :: SDoc
debug_stuff = [SDoc] -> SDoc
vcat [ String -> SDoc
text String
"Coercion axiom:" SDoc -> SDoc -> SDoc
<+> forall a. Outputable a => a -> SDoc
ppr CoAxiom Unbranched
ax
                       , String -> SDoc
text String
"Tvs:" SDoc -> SDoc -> SDoc
<+> forall a. Outputable a => a -> SDoc
ppr [TyVar]
tvs
                       , String -> SDoc
text String
"LHS:" SDoc -> SDoc -> SDoc
<+> forall a. Outputable a => a -> SDoc
ppr [Type]
tys
                       , String -> SDoc
text String
"RHS:" SDoc -> SDoc -> SDoc
<+> forall a. Outputable a => a -> SDoc
ppr Type
rhs ]

pprFamInsts :: [FamInst] -> SDoc
pprFamInsts :: [FamInst] -> SDoc
pprFamInsts [FamInst]
finsts = [SDoc] -> SDoc
vcat (forall a b. (a -> b) -> [a] -> [b]
map FamInst -> SDoc
pprFamInst [FamInst]
finsts)

{-
Note [Lazy axiom match]
~~~~~~~~~~~~~~~~~~~~~~~
It is Vitally Important that mkImportedFamInst is *lazy* in its axiom
parameter. The axiom is loaded lazily, via a forkM, in GHC.IfaceToCore. Sometime
later, mkImportedFamInst is called using that axiom. However, the axiom
may itself depend on entities which are not yet loaded as of the time
of the mkImportedFamInst. Thus, if mkImportedFamInst eagerly looks at the
axiom, a dependency loop spontaneously appears and GHC hangs. The solution
is simply for mkImportedFamInst never, ever to look inside of the axiom
until everything else is good and ready to do so. We can assume that this
readiness has been achieved when some other code pulls on the axiom in the
FamInst. Thus, we pattern match on the axiom lazily (in the where clause,
not in the parameter list) and we assert the consistency of names there
also.
-}

-- Make a family instance representation from the information found in an
-- interface file.  In particular, we get the rough match info from the iface
-- (instead of computing it here).
mkImportedFamInst :: Name               -- Name of the family
                  -> [RoughMatchTc]     -- Rough match info
                  -> CoAxiom Unbranched -- Axiom introduced
                  -> FamInst            -- Resulting family instance
mkImportedFamInst :: Name -> [RoughMatchTc] -> CoAxiom Unbranched -> FamInst
mkImportedFamInst Name
fam [RoughMatchTc]
mb_tcs CoAxiom Unbranched
axiom
  = FamInst {
      fi_fam :: Name
fi_fam    = Name
fam,
      fi_tcs :: [RoughMatchTc]
fi_tcs    = [RoughMatchTc]
mb_tcs,
      fi_tvs :: [TyVar]
fi_tvs    = [TyVar]
tvs,
      fi_cvs :: [TyVar]
fi_cvs    = [TyVar]
cvs,
      fi_tys :: [Type]
fi_tys    = [Type]
tys,
      fi_rhs :: Type
fi_rhs    = Type
rhs,
      fi_axiom :: CoAxiom Unbranched
fi_axiom  = CoAxiom Unbranched
axiom,
      fi_flavor :: FamFlavor
fi_flavor = FamFlavor
flavor }
  where
     -- See Note [Lazy axiom match]
     ~(CoAxBranch { cab_lhs :: CoAxBranch -> [Type]
cab_lhs = [Type]
tys
                  , cab_tvs :: CoAxBranch -> [TyVar]
cab_tvs = [TyVar]
tvs
                  , cab_cvs :: CoAxBranch -> [TyVar]
cab_cvs = [TyVar]
cvs
                  , cab_rhs :: CoAxBranch -> Type
cab_rhs = Type
rhs }) = CoAxiom Unbranched -> CoAxBranch
coAxiomSingleBranch CoAxiom Unbranched
axiom

         -- Derive the flavor for an imported FamInst rather disgustingly
         -- Maybe we should store it in the IfaceFamInst?
     flavor :: FamFlavor
flavor = case HasDebugCallStack => Type -> Maybe (TyCon, [Type])
splitTyConApp_maybe Type
rhs of
                Just (TyCon
tc, [Type]
_)
                  | Just CoAxiom Unbranched
ax' <- TyCon -> Maybe (CoAxiom Unbranched)
tyConFamilyCoercion_maybe TyCon
tc
                  , CoAxiom Unbranched
ax' forall a. Eq a => a -> a -> Bool
== CoAxiom Unbranched
axiom
                  -> TyCon -> FamFlavor
DataFamilyInst TyCon
tc
                Maybe (TyCon, [Type])
_ -> FamFlavor
SynFamilyInst

{-
************************************************************************
*                                                                      *
                FamInstEnv
*                                                                      *
************************************************************************

Note [FamInstEnv]
~~~~~~~~~~~~~~~~~
A FamInstEnv is a RoughMap of instance heads. Specifically, the keys are formed
by the family name and the instance arguments. That is, an instance:

    type instance Fam (Maybe Int) a

would insert into the instance environment an instance with a key of the form

  [RM_KnownTc Fam, RM_KnownTc Maybe, RM_WildCard]

See Note [RoughMap] in GHC.Core.RoughMap.


The same FamInstEnv includes both 'data family' and 'type family' instances.
Type families are reduced during type inference, but not data families;
the user explains when to use a data family instance by using constructors
and pattern matching.

Nevertheless it is still useful to have data families in the FamInstEnv:

 - For finding overlaps and conflicts

 - For finding the representation type...see FamInstEnv.topNormaliseType
   and its call site in GHC.Core.Opt.Simplify

 - In standalone deriving instance Eq (T [Int]) we need to find the
   representation type for T [Int]

Note [Varying number of patterns for data family axioms]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
For data families, the number of patterns may vary between instances.
For example
   data family T a b
   data instance T Int a = T1 a | T2
   data instance T Bool [a] = T3 a

Then we get a data type for each instance, and an axiom:
   data TInt a = T1 a | T2
   data TBoolList a = T3 a

   axiom ax7   :: T Int ~ TInt   -- Eta-reduced
   axiom ax8 a :: T Bool [a] ~ TBoolList a

These two axioms for T, one with one pattern, one with two;
see Note [Eta reduction for data families] in GHC.Core.Coercion.Axiom

Note [FamInstEnv determinism]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We turn FamInstEnvs into a list in some places that don't directly affect
the ABI. That happens in family consistency checks and when producing output
for `:info`. Unfortunately that nondeterminism is nonlocal and it's hard
to tell what it affects without following a chain of functions. It's also
easy to accidentally make that nondeterminism affect the ABI. Furthermore
the envs should be relatively small, so it should be free to use deterministic
maps here. Testing with nofib and validate detected no difference between
UniqFM and UniqDFM.
See Note [Deterministic UniqFM].
-}

type FamInstEnvs = (FamInstEnv, FamInstEnv)
     -- External package inst-env, Home-package inst-env

data FamInstEnv
  = FamIE !Int -- The number of instances, used to choose the smaller environment
               -- when checking type family consistency of home modules.
          !(RoughMap FamInst)
     -- See Note [FamInstEnv]
     -- See Note [FamInstEnv determinism]


instance Outputable FamInstEnv where
  ppr :: FamInstEnv -> SDoc
ppr (FamIE BranchIndex
_ RoughMap FamInst
fs) = String -> SDoc
text String
"FamIE" SDoc -> SDoc -> SDoc
<+> [SDoc] -> SDoc
vcat (forall a b. (a -> b) -> [a] -> [b]
map forall a. Outputable a => a -> SDoc
ppr forall a b. (a -> b) -> a -> b
$ forall a. RoughMap a -> [a]
elemsRM RoughMap FamInst
fs)

famInstEnvSize :: FamInstEnv -> Int
famInstEnvSize :: FamInstEnv -> BranchIndex
famInstEnvSize (FamIE BranchIndex
sz RoughMap FamInst
_) = BranchIndex
sz

-- | Create a 'FamInstEnv' from 'Name' indices.
-- INVARIANTS:
--  * The fs_tvs are distinct in each FamInst
--      of a range value of the map (so we can safely unify them)

emptyFamInstEnvs :: (FamInstEnv, FamInstEnv)
emptyFamInstEnvs :: (FamInstEnv, FamInstEnv)
emptyFamInstEnvs = (FamInstEnv
emptyFamInstEnv, FamInstEnv
emptyFamInstEnv)

emptyFamInstEnv :: FamInstEnv
emptyFamInstEnv :: FamInstEnv
emptyFamInstEnv = BranchIndex -> RoughMap FamInst -> FamInstEnv
FamIE BranchIndex
0 forall a. RoughMap a
emptyRM

famInstEnvElts :: FamInstEnv -> [FamInst]
famInstEnvElts :: FamInstEnv -> [FamInst]
famInstEnvElts (FamIE BranchIndex
_ RoughMap FamInst
rm) = forall a. RoughMap a -> [a]
elemsRM RoughMap FamInst
rm
  -- See Note [FamInstEnv determinism]

  -- It's OK to use nonDetStrictFoldUDFM here since we're just computing the
  -- size.

familyInstances :: (FamInstEnv, FamInstEnv) -> TyCon -> [FamInst]
familyInstances :: (FamInstEnv, FamInstEnv) -> TyCon -> [FamInst]
familyInstances (FamInstEnv, FamInstEnv)
envs TyCon
tc
  = (FamInstEnv, FamInstEnv) -> Name -> [FamInst]
familyNameInstances (FamInstEnv, FamInstEnv)
envs (TyCon -> Name
tyConName TyCon
tc)

familyNameInstances :: (FamInstEnv, FamInstEnv) -> Name -> [FamInst]
familyNameInstances :: (FamInstEnv, FamInstEnv) -> Name -> [FamInst]
familyNameInstances (FamInstEnv
pkg_fie, FamInstEnv
home_fie) Name
fam
  = FamInstEnv -> [FamInst]
get FamInstEnv
home_fie forall a. [a] -> [a] -> [a]
++ FamInstEnv -> [FamInst]
get FamInstEnv
pkg_fie
  where
    get :: FamInstEnv -> [FamInst]
    get :: FamInstEnv -> [FamInst]
get (FamIE BranchIndex
_ RoughMap FamInst
env) = forall a. [RoughMatchLookupTc] -> RoughMap a -> [a]
lookupRM [Name -> RoughMatchLookupTc
RML_KnownTc Name
fam] RoughMap FamInst
env


-- | Makes no particular effort to detect conflicts.
unionFamInstEnv :: FamInstEnv -> FamInstEnv -> FamInstEnv
unionFamInstEnv :: FamInstEnv -> FamInstEnv -> FamInstEnv
unionFamInstEnv (FamIE BranchIndex
sa RoughMap FamInst
a) (FamIE BranchIndex
sb RoughMap FamInst
b) = BranchIndex -> RoughMap FamInst -> FamInstEnv
FamIE (BranchIndex
sa forall a. Num a => a -> a -> a
+ BranchIndex
sb) (RoughMap FamInst
a forall a. RoughMap a -> RoughMap a -> RoughMap a
`unionRM` RoughMap FamInst
b)

extendFamInstEnvList :: FamInstEnv -> [FamInst] -> FamInstEnv
extendFamInstEnvList :: FamInstEnv -> [FamInst] -> FamInstEnv
extendFamInstEnvList FamInstEnv
inst_env [FamInst]
fis = forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl' FamInstEnv -> FamInst -> FamInstEnv
extendFamInstEnv FamInstEnv
inst_env [FamInst]
fis

extendFamInstEnv :: FamInstEnv -> FamInst -> FamInstEnv
extendFamInstEnv :: FamInstEnv -> FamInst -> FamInstEnv
extendFamInstEnv (FamIE BranchIndex
s RoughMap FamInst
inst_env)
                 ins_item :: FamInst
ins_item@(FamInst {fi_fam :: FamInst -> Name
fi_fam = Name
cls_nm})
  = BranchIndex -> RoughMap FamInst -> FamInstEnv
FamIE (BranchIndex
sforall a. Num a => a -> a -> a
+BranchIndex
1) forall a b. (a -> b) -> a -> b
$ forall a. [RoughMatchTc] -> a -> RoughMap a -> RoughMap a
insertRM [RoughMatchTc]
rough_tmpl FamInst
ins_item RoughMap FamInst
inst_env
  where
    rough_tmpl :: [RoughMatchTc]
rough_tmpl = Name -> RoughMatchTc
RM_KnownTc Name
cls_nm forall a. a -> [a] -> [a]
: FamInst -> [RoughMatchTc]
fi_tcs FamInst
ins_item

{-
************************************************************************
*                                                                      *
                Compatibility
*                                                                      *
************************************************************************

Note [Apartness]
~~~~~~~~~~~~~~~~
In dealing with closed type families, we must be able to check that one type
will never reduce to another. This check is called /apartness/. The check
is always between a target (which may be an arbitrary type) and a pattern.
Here is how we do it:

apart(target, pattern) = not (unify(flatten(target), pattern))

where flatten (implemented in flattenTys, below) converts all type-family
applications into fresh variables. (See
Note [Flattening type-family applications when matching instances] in GHC.Core.Unify.)

Note [Compatibility]
~~~~~~~~~~~~~~~~~~~~
Two patterns are /compatible/ if either of the following conditions hold:
1) The patterns are apart.
2) The patterns unify with a substitution S, and their right hand sides
equal under that substitution.

For open type families, only compatible instances are allowed. For closed
type families, the story is slightly more complicated. Consider the following:

type family F a where
  F Int = Bool
  F a   = Int

g :: Show a => a -> F a
g x = length (show x)

Should that type-check? No. We need to allow for the possibility that 'a'
might be Int and therefore 'F a' should be Bool. We can simplify 'F a' to Int
only when we can be sure that 'a' is not Int.

To achieve this, after finding a possible match within the equations, we have to
go back to all previous equations and check that, under the
substitution induced by the match, other branches are surely apart. (See
Note [Apartness].) This is similar to what happens with class
instance selection, when we need to guarantee that there is only a match and
no unifiers. The exact algorithm is different here because the
potentially-overlapping group is closed.

As another example, consider this:

type family G x where
  G Int = Bool
  G a   = Double

type family H y
-- no instances

Now, we want to simplify (G (H Char)). We can't, because (H Char) might later
simplify to be Int. So, (G (H Char)) is stuck, for now.

While everything above is quite sound, it isn't as expressive as we'd like.
Consider this:

type family J a where
  J Int = Int
  J a   = a

Can we simplify (J b) to b? Sure we can. Yes, the first equation matches if
b is instantiated with Int, but the RHSs coincide there, so it's all OK.

So, the rule is this: when looking up a branch in a closed type family, we
find a branch that matches the target, but then we make sure that the target
is apart from every previous *incompatible* branch. We don't check the
branches that are compatible with the matching branch, because they are either
irrelevant (clause 1 of compatible) or benign (clause 2 of compatible).

Note [Compatibility of eta-reduced axioms]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In newtype instances of data families we eta-reduce the axioms,
See Note [Eta reduction for data families] in GHC.Core.Coercion.Axiom. This means that
we sometimes need to test compatibility of two axioms that were eta-reduced to
different degrees, e.g.:


data family D a b c
newtype instance D a Int c = DInt (Maybe a)
  -- D a Int ~ Maybe
  -- lhs = [a, Int]
newtype instance D Bool Int Char = DIntChar Float
  -- D Bool Int Char ~ Float
  -- lhs = [Bool, Int, Char]

These are obviously incompatible. We could detect this by saturating
(eta-expanding) the shorter LHS with fresh tyvars until the lists are of
equal length, but instead we can just remove the tail of the longer list, as
those types will simply unify with the freshly introduced tyvars.

By doing this, in case the LHS are unifiable, the yielded substitution won't
mention the tyvars that appear in the tail we dropped off, and we might try
to test equality RHSes of different kinds, but that's fine since this case
occurs only for data families, where the RHS is a unique tycon and the equality
fails anyway.
-}

-- See Note [Compatibility]
compatibleBranches :: CoAxBranch -> CoAxBranch -> Bool
compatibleBranches :: CoAxBranch -> CoAxBranch -> Bool
compatibleBranches (CoAxBranch { cab_lhs :: CoAxBranch -> [Type]
cab_lhs = [Type]
lhs1, cab_rhs :: CoAxBranch -> Type
cab_rhs = Type
rhs1 })
                   (CoAxBranch { cab_lhs :: CoAxBranch -> [Type]
cab_lhs = [Type]
lhs2, cab_rhs :: CoAxBranch -> Type
cab_rhs = Type
rhs2 })
  = let ([Type]
commonlhs1, [Type]
commonlhs2) = forall a b. [a] -> [b] -> ([a], [b])
zipAndUnzip [Type]
lhs1 [Type]
lhs2
             -- See Note [Compatibility of eta-reduced axioms]
    in case BindFun -> [Type] -> [Type] -> UnifyResult
tcUnifyTysFG BindFun
alwaysBindFun [Type]
commonlhs1 [Type]
commonlhs2 of
      UnifyResult
SurelyApart -> Bool
True
      Unifiable Subst
subst
        | Subst -> Type -> Type
Type.substTyAddInScope Subst
subst Type
rhs1 Type -> Type -> Bool
`eqType`
          Subst -> Type -> Type
Type.substTyAddInScope Subst
subst Type
rhs2
        -> Bool
True
      UnifyResult
_ -> Bool
False

-- | Result of testing two type family equations for injectiviy.
data InjectivityCheckResult
   = InjectivityAccepted
    -- ^ Either RHSs are distinct or unification of RHSs leads to unification of
    -- LHSs
   | InjectivityUnified CoAxBranch CoAxBranch
    -- ^ RHSs unify but LHSs don't unify under that substitution.  Relevant for
    -- closed type families where equation after unification might be
    -- overlapped (in which case it is OK if they don't unify).  Constructor
    -- stores axioms after unification.

-- | Check whether two type family axioms don't violate injectivity annotation.
injectiveBranches :: [Bool] -> CoAxBranch -> CoAxBranch
                  -> InjectivityCheckResult
injectiveBranches :: [Bool] -> CoAxBranch -> CoAxBranch -> InjectivityCheckResult
injectiveBranches [Bool]
injectivity
                  ax1 :: CoAxBranch
ax1@(CoAxBranch { cab_tvs :: CoAxBranch -> [TyVar]
cab_tvs = [TyVar]
tvs1, cab_lhs :: CoAxBranch -> [Type]
cab_lhs = [Type]
lhs1, cab_rhs :: CoAxBranch -> Type
cab_rhs = Type
rhs1 })
                  ax2 :: CoAxBranch
ax2@(CoAxBranch { cab_tvs :: CoAxBranch -> [TyVar]
cab_tvs = [TyVar]
tvs2, cab_lhs :: CoAxBranch -> [Type]
cab_lhs = [Type]
lhs2, cab_rhs :: CoAxBranch -> Type
cab_rhs = Type
rhs2 })
  -- See Note [Verifying injectivity annotation], case 1.
  = let getInjArgs :: [Type] -> [Type]
getInjArgs  = forall a. [Bool] -> [a] -> [a]
filterByList [Bool]
injectivity
        in_scope :: InScopeSet
in_scope    = [TyVar] -> InScopeSet
mkInScopeSetList ([TyVar]
tvs1 forall a. [a] -> [a] -> [a]
++ [TyVar]
tvs2)
    in case Bool -> InScopeSet -> Type -> Type -> Maybe Subst
tcUnifyTyWithTFs Bool
True InScopeSet
in_scope Type
rhs1 Type
rhs2 of -- True = two-way pre-unification
       Maybe Subst
Nothing -> InjectivityCheckResult
InjectivityAccepted
         -- RHS are different, so equations are injective.
         -- This is case 1A from Note [Verifying injectivity annotation]

       Just Subst
subst -- RHS unify under a substitution
          -- If LHSs are equal under the substitution used for RHSs then this pair
          -- of equations does not violate injectivity annotation. If LHSs are not
          -- equal under that substitution then this pair of equations violates
          -- injectivity annotation, but for closed type families it still might
          -- be the case that one LHS after substitution is unreachable.
          | [Type] -> [Type] -> Bool
eqTypes [Type]
lhs1Subst [Type]
lhs2Subst  -- check case 1B1 from Note.
          -> InjectivityCheckResult
InjectivityAccepted
          | Bool
otherwise
          -> CoAxBranch -> CoAxBranch -> InjectivityCheckResult
InjectivityUnified ( CoAxBranch
ax1 { cab_lhs :: [Type]
cab_lhs = HasDebugCallStack => Subst -> [Type] -> [Type]
Type.substTys Subst
subst [Type]
lhs1
                                      , cab_rhs :: Type
cab_rhs = HasDebugCallStack => Subst -> Type -> Type
Type.substTy  Subst
subst Type
rhs1 })
                                ( CoAxBranch
ax2 { cab_lhs :: [Type]
cab_lhs = HasDebugCallStack => Subst -> [Type] -> [Type]
Type.substTys Subst
subst [Type]
lhs2
                                      , cab_rhs :: Type
cab_rhs = HasDebugCallStack => Subst -> Type -> Type
Type.substTy  Subst
subst Type
rhs2 })
                  -- Payload of InjectivityUnified used only for check 1B2, only
                  -- for closed type families
        where
          lhs1Subst :: [Type]
lhs1Subst = HasDebugCallStack => Subst -> [Type] -> [Type]
Type.substTys Subst
subst ([Type] -> [Type]
getInjArgs [Type]
lhs1)
          lhs2Subst :: [Type]
lhs2Subst = HasDebugCallStack => Subst -> [Type] -> [Type]
Type.substTys Subst
subst ([Type] -> [Type]
getInjArgs [Type]
lhs2)

-- takes a CoAxiom with unknown branch incompatibilities and computes
-- the compatibilities
-- See Note [Storing compatibility] in GHC.Core.Coercion.Axiom
computeAxiomIncomps :: [CoAxBranch] -> [CoAxBranch]
computeAxiomIncomps :: [CoAxBranch] -> [CoAxBranch]
computeAxiomIncomps [CoAxBranch]
branches
  = forall a b. (a, b) -> b
snd (forall (t :: * -> *) s a b.
Traversable t =>
(s -> a -> (s, b)) -> s -> t a -> (s, t b)
mapAccumL [CoAxBranch] -> CoAxBranch -> ([CoAxBranch], CoAxBranch)
go [] [CoAxBranch]
branches)
  where
    go :: [CoAxBranch] -> CoAxBranch -> ([CoAxBranch], CoAxBranch)
    go :: [CoAxBranch] -> CoAxBranch -> ([CoAxBranch], CoAxBranch)
go [CoAxBranch]
prev_brs CoAxBranch
cur_br
       = (CoAxBranch
cur_br forall a. a -> [a] -> [a]
: [CoAxBranch]
prev_brs, CoAxBranch
new_br)
       where
         new_br :: CoAxBranch
new_br = CoAxBranch
cur_br { cab_incomps :: [CoAxBranch]
cab_incomps = [CoAxBranch] -> CoAxBranch -> [CoAxBranch]
mk_incomps [CoAxBranch]
prev_brs CoAxBranch
cur_br }

    mk_incomps :: [CoAxBranch] -> CoAxBranch -> [CoAxBranch]
    mk_incomps :: [CoAxBranch] -> CoAxBranch -> [CoAxBranch]
mk_incomps [CoAxBranch]
prev_brs CoAxBranch
cur_br
       = forall a. (a -> Bool) -> [a] -> [a]
filter (Bool -> Bool
not forall b c a. (b -> c) -> (a -> b) -> a -> c
. CoAxBranch -> CoAxBranch -> Bool
compatibleBranches CoAxBranch
cur_br) [CoAxBranch]
prev_brs

{-
************************************************************************
*                                                                      *
           Constructing axioms
    These functions are here because tidyType / tcUnifyTysFG
    are not available in GHC.Core.Coercion.Axiom

    Also computeAxiomIncomps is too sophisticated for CoAxiom
*                                                                      *
************************************************************************

Note [Tidy axioms when we build them]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Like types and classes, we build axioms fully quantified over all
their variables, and tidy them when we build them. For example,
we print out axioms and don't want to print stuff like
    F k k a b = ...
Instead we must tidy those kind variables.  See #7524.

We could instead tidy when we print, but that makes it harder to get
things like injectivity errors to come out right. Danger of
     Type family equation violates injectivity annotation.
     Kind variable ‘k’ cannot be inferred from the right-hand side.
     In the type family equation:
        PolyKindVars @[k1] @[k2] ('[] @k1) = '[] @k2

Note [Always number wildcard types in CoAxBranch]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the following example (from the DataFamilyInstanceLHS test case):

  data family Sing (a :: k)
  data instance Sing (_ :: MyKind) where
      SingA :: Sing A
      SingB :: Sing B

If we're not careful during tidying, then when this program is compiled with
-ddump-types, we'll get the following information:

  COERCION AXIOMS
    axiom DataFamilyInstanceLHS.D:R:SingMyKind_0 ::
      Sing _ = DataFamilyInstanceLHS.R:SingMyKind_ _

It's misleading to have a wildcard type appearing on the RHS like
that. To avoid this issue, when building a CoAxiom (which is what eventually
gets printed above), we tidy all the variables in an env that already contains
'_'. Thus, any variable named '_' will be renamed, giving us the nicer output
here:

  COERCION AXIOMS
    axiom DataFamilyInstanceLHS.D:R:SingMyKind_0 ::
      Sing _1 = DataFamilyInstanceLHS.R:SingMyKind_ _1

Which is at least legal syntax.

See also Note [CoAxBranch type variables] in GHC.Core.Coercion.Axiom; note that we
are tidying (changing OccNames only), not freshening, in accordance with
that Note.
-}

-- all axiom roles are Nominal, as this is only used with type families
mkCoAxBranch :: [TyVar] -- original, possibly stale, tyvars
             -> [TyVar] -- Extra eta tyvars
             -> [CoVar] -- possibly stale covars
             -> [Type]  -- LHS patterns
             -> Type    -- RHS
             -> [Role]
             -> SrcSpan
             -> CoAxBranch
mkCoAxBranch :: [TyVar]
-> [TyVar]
-> [TyVar]
-> [Type]
-> Type
-> [Role]
-> SrcSpan
-> CoAxBranch
mkCoAxBranch [TyVar]
tvs [TyVar]
eta_tvs [TyVar]
cvs [Type]
lhs Type
rhs [Role]
roles SrcSpan
loc
  = CoAxBranch { cab_tvs :: [TyVar]
cab_tvs     = [TyVar]
tvs'
               , cab_eta_tvs :: [TyVar]
cab_eta_tvs = [TyVar]
eta_tvs'
               , cab_cvs :: [TyVar]
cab_cvs     = [TyVar]
cvs'
               , cab_lhs :: [Type]
cab_lhs     = TidyEnv -> [Type] -> [Type]
tidyTypes TidyEnv
env [Type]
lhs
               , cab_roles :: [Role]
cab_roles   = [Role]
roles
               , cab_rhs :: Type
cab_rhs     = TidyEnv -> Type -> Type
tidyType TidyEnv
env Type
rhs
               , cab_loc :: SrcSpan
cab_loc     = SrcSpan
loc
               , cab_incomps :: [CoAxBranch]
cab_incomps = [CoAxBranch]
placeHolderIncomps }
  where
    (TidyEnv
env1, [TyVar]
tvs')     = TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
tidyVarBndrs TidyEnv
init_tidy_env [TyVar]
tvs
    (TidyEnv
env2, [TyVar]
eta_tvs') = TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
tidyVarBndrs TidyEnv
env1          [TyVar]
eta_tvs
    (TidyEnv
env,  [TyVar]
cvs')     = TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
tidyVarBndrs TidyEnv
env2          [TyVar]
cvs
    -- See Note [Tidy axioms when we build them]
    -- See also Note [CoAxBranch type variables] in GHC.Core.Coercion.Axiom

    init_occ_env :: TidyOccEnv
init_occ_env = [OccName] -> TidyOccEnv
initTidyOccEnv [String -> OccName
mkTyVarOcc String
"_"]
    init_tidy_env :: TidyEnv
init_tidy_env = TidyOccEnv -> TidyEnv
mkEmptyTidyEnv TidyOccEnv
init_occ_env
    -- See Note [Always number wildcard types in CoAxBranch]

-- all of the following code is here to avoid mutual dependencies with
-- Coercion
mkBranchedCoAxiom :: Name -> TyCon -> [CoAxBranch] -> CoAxiom Branched
mkBranchedCoAxiom :: Name -> TyCon -> [CoAxBranch] -> CoAxiom Branched
mkBranchedCoAxiom Name
ax_name TyCon
fam_tc [CoAxBranch]
branches
  = CoAxiom { co_ax_unique :: Unique
co_ax_unique   = Name -> Unique
nameUnique Name
ax_name
            , co_ax_name :: Name
co_ax_name     = Name
ax_name
            , co_ax_tc :: TyCon
co_ax_tc       = TyCon
fam_tc
            , co_ax_role :: Role
co_ax_role     = Role
Nominal
            , co_ax_implicit :: Bool
co_ax_implicit = Bool
False
            , co_ax_branches :: Branches Branched
co_ax_branches = [CoAxBranch] -> Branches Branched
manyBranches ([CoAxBranch] -> [CoAxBranch]
computeAxiomIncomps [CoAxBranch]
branches) }

mkUnbranchedCoAxiom :: Name -> TyCon -> CoAxBranch -> CoAxiom Unbranched
mkUnbranchedCoAxiom :: Name -> TyCon -> CoAxBranch -> CoAxiom Unbranched
mkUnbranchedCoAxiom Name
ax_name TyCon
fam_tc CoAxBranch
branch
  = CoAxiom { co_ax_unique :: Unique
co_ax_unique   = Name -> Unique
nameUnique Name
ax_name
            , co_ax_name :: Name
co_ax_name     = Name
ax_name
            , co_ax_tc :: TyCon
co_ax_tc       = TyCon
fam_tc
            , co_ax_role :: Role
co_ax_role     = Role
Nominal
            , co_ax_implicit :: Bool
co_ax_implicit = Bool
False
            , co_ax_branches :: Branches Unbranched
co_ax_branches = CoAxBranch -> Branches Unbranched
unbranched (CoAxBranch
branch { cab_incomps :: [CoAxBranch]
cab_incomps = [] }) }

mkSingleCoAxiom :: Role -> Name
                -> [TyVar] -> [TyVar] -> [CoVar]
                -> TyCon -> [Type] -> Type
                -> CoAxiom Unbranched
-- Make a single-branch CoAxiom, including making the branch itself
-- Used for both type family (Nominal) and data family (Representational)
-- axioms, hence passing in the Role
mkSingleCoAxiom :: Role
-> Name
-> [TyVar]
-> [TyVar]
-> [TyVar]
-> TyCon
-> [Type]
-> Type
-> CoAxiom Unbranched
mkSingleCoAxiom Role
role Name
ax_name [TyVar]
tvs [TyVar]
eta_tvs [TyVar]
cvs TyCon
fam_tc [Type]
lhs_tys Type
rhs_ty
  = CoAxiom { co_ax_unique :: Unique
co_ax_unique   = Name -> Unique
nameUnique Name
ax_name
            , co_ax_name :: Name
co_ax_name     = Name
ax_name
            , co_ax_tc :: TyCon
co_ax_tc       = TyCon
fam_tc
            , co_ax_role :: Role
co_ax_role     = Role
role
            , co_ax_implicit :: Bool
co_ax_implicit = Bool
False
            , co_ax_branches :: Branches Unbranched
co_ax_branches = CoAxBranch -> Branches Unbranched
unbranched (CoAxBranch
branch { cab_incomps :: [CoAxBranch]
cab_incomps = [] }) }
  where
    branch :: CoAxBranch
branch = [TyVar]
-> [TyVar]
-> [TyVar]
-> [Type]
-> Type
-> [Role]
-> SrcSpan
-> CoAxBranch
mkCoAxBranch [TyVar]
tvs [TyVar]
eta_tvs [TyVar]
cvs [Type]
lhs_tys Type
rhs_ty
                          (forall a b. (a -> b) -> [a] -> [b]
map (forall a b. a -> b -> a
const Role
Nominal) [TyVar]
tvs)
                          (forall a. NamedThing a => a -> SrcSpan
getSrcSpan Name
ax_name)

-- | Create a coercion constructor (axiom) suitable for the given
--   newtype 'TyCon'. The 'Name' should be that of a new coercion
--   'CoAxiom', the 'TyVar's the arguments expected by the @newtype@ and
--   the type the appropriate right hand side of the @newtype@, with
--   the free variables a subset of those 'TyVar's.
mkNewTypeCoAxiom :: Name -> TyCon -> [TyVar] -> [Role] -> Type -> CoAxiom Unbranched
mkNewTypeCoAxiom :: Name -> TyCon -> [TyVar] -> [Role] -> Type -> CoAxiom Unbranched
mkNewTypeCoAxiom Name
name TyCon
tycon [TyVar]
tvs [Role]
roles Type
rhs_ty
  = CoAxiom { co_ax_unique :: Unique
co_ax_unique   = Name -> Unique
nameUnique Name
name
            , co_ax_name :: Name
co_ax_name     = Name
name
            , co_ax_implicit :: Bool
co_ax_implicit = Bool
True  -- See Note [Implicit axioms] in GHC.Core.TyCon
            , co_ax_role :: Role
co_ax_role     = Role
Representational
            , co_ax_tc :: TyCon
co_ax_tc       = TyCon
tycon
            , co_ax_branches :: Branches Unbranched
co_ax_branches = CoAxBranch -> Branches Unbranched
unbranched (CoAxBranch
branch { cab_incomps :: [CoAxBranch]
cab_incomps = [] }) }
  where
    branch :: CoAxBranch
branch = [TyVar]
-> [TyVar]
-> [TyVar]
-> [Type]
-> Type
-> [Role]
-> SrcSpan
-> CoAxBranch
mkCoAxBranch [TyVar]
tvs [] [] ([TyVar] -> [Type]
mkTyVarTys [TyVar]
tvs) Type
rhs_ty
                          [Role]
roles (forall a. NamedThing a => a -> SrcSpan
getSrcSpan Name
name)

{-
************************************************************************
*                                                                      *
                Looking up a family instance
*                                                                      *
************************************************************************

@lookupFamInstEnv@ looks up in a @FamInstEnv@, using a one-way match.
Multiple matches are only possible in case of type families (not data
families), and then, it doesn't matter which match we choose (as the
instances are guaranteed confluent).

We return the matching family instances and the type instance at which it
matches.  For example, if we lookup 'T [Int]' and have a family instance

  data instance T [a] = ..

desugared to

  data :R42T a = ..
  coe :Co:R42T a :: T [a] ~ :R42T a

we return the matching instance '(FamInst{.., fi_tycon = :R42T}, Int)'.
-}

-- when matching a type family application, we get a FamInst,
-- and the list of types the axiom should be applied to
data FamInstMatch = FamInstMatch { FamInstMatch -> FamInst
fim_instance :: FamInst
                                 , FamInstMatch -> [Type]
fim_tys      :: [Type]
                                 , FamInstMatch -> [Coercion]
fim_cos      :: [Coercion]
                                 }
  -- See Note [Over-saturated matches]

instance Outputable FamInstMatch where
  ppr :: FamInstMatch -> SDoc
ppr (FamInstMatch { fim_instance :: FamInstMatch -> FamInst
fim_instance = FamInst
inst
                    , fim_tys :: FamInstMatch -> [Type]
fim_tys      = [Type]
tys
                    , fim_cos :: FamInstMatch -> [Coercion]
fim_cos      = [Coercion]
cos })
    = String -> SDoc
text String
"match with" SDoc -> SDoc -> SDoc
<+> SDoc -> SDoc
parens (forall a. Outputable a => a -> SDoc
ppr FamInst
inst) SDoc -> SDoc -> SDoc
<+> forall a. Outputable a => a -> SDoc
ppr [Type]
tys SDoc -> SDoc -> SDoc
<+> forall a. Outputable a => a -> SDoc
ppr [Coercion]
cos

lookupFamInstEnvByTyCon :: FamInstEnvs -> TyCon -> [FamInst]
lookupFamInstEnvByTyCon :: (FamInstEnv, FamInstEnv) -> TyCon -> [FamInst]
lookupFamInstEnvByTyCon (FamInstEnv
pkg_ie, FamInstEnv
home_ie) TyCon
fam_tc
  = FamInstEnv -> [FamInst]
get FamInstEnv
pkg_ie forall a. [a] -> [a] -> [a]
++ FamInstEnv -> [FamInst]
get FamInstEnv
home_ie
  where
    get :: FamInstEnv -> [FamInst]
get (FamIE BranchIndex
_ RoughMap FamInst
rm) = forall a. [RoughMatchLookupTc] -> RoughMap a -> [a]
lookupRM [Name -> RoughMatchLookupTc
RML_KnownTc (TyCon -> Name
tyConName TyCon
fam_tc)] RoughMap FamInst
rm

lookupFamInstEnv
    :: FamInstEnvs
    -> TyCon -> [Type]          -- What we are looking for
    -> [FamInstMatch]           -- Successful matches
-- Precondition: the tycon is saturated (or over-saturated)

lookupFamInstEnv :: (FamInstEnv, FamInstEnv) -> TyCon -> [Type] -> [FamInstMatch]
lookupFamInstEnv
   = forall a.
FamInstLookupMode a
-> (FamInstEnv, FamInstEnv) -> TyCon -> [Type] -> [a]
lookup_fam_inst_env FamInstLookupMode FamInstMatch
WantMatches

lookupFamInstEnvConflicts
    :: FamInstEnvs
    -> FamInst          -- Putative new instance
    -> [FamInst]   -- Conflicting matches (don't look at the fim_tys field)
-- E.g. when we are about to add
--    f : type instance F [a] = a->a
-- we do (lookupFamInstConflicts f [b])
-- to find conflicting matches
--
-- Precondition: the tycon is saturated (or over-saturated)

lookupFamInstEnvConflicts :: (FamInstEnv, FamInstEnv) -> FamInst -> [FamInst]
lookupFamInstEnvConflicts (FamInstEnv, FamInstEnv)
envs FamInst
fam_inst
  = forall a.
FamInstLookupMode a
-> (FamInstEnv, FamInstEnv) -> TyCon -> [Type] -> [a]
lookup_fam_inst_env (FamInst -> FamInstLookupMode FamInst
WantConflicts FamInst
fam_inst) (FamInstEnv, FamInstEnv)
envs TyCon
fam [Type]
tys
  where
    (TyCon
fam, [Type]
tys) = FamInst -> (TyCon, [Type])
famInstSplitLHS FamInst
fam_inst

--------------------------------------------------------------------------------
--                 Type family injectivity checking bits                      --
--------------------------------------------------------------------------------

{- Note [Verifying injectivity annotation]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Injectivity means that the RHS of a type family uniquely determines the LHS (see
Note [Type inference for type families with injectivity]).  The user informs us about
injectivity using an injectivity annotation and it is GHC's task to verify that
this annotation is correct w.r.t. type family equations. Whenever we see a new
equation of a type family we need to make sure that adding this equation to the
already known equations of a type family does not violate the injectivity annotation
supplied by the user (see Note [Injectivity annotation]).  Of course if the type
family has no injectivity annotation then no check is required.  But if a type
family has injectivity annotation we need to make sure that the following
conditions hold:

1. For each pair of *different* equations of a type family, one of the following
   conditions holds:

   A:  RHSs are different. (Check done in GHC.Core.FamInstEnv.injectiveBranches)

   B1: OPEN TYPE FAMILIES: If the RHSs can be unified under some substitution
       then it must be possible to unify the LHSs under the same substitution.
       Example:

          type family FunnyId a = r | r -> a
          type instance FunnyId Int = Int
          type instance FunnyId a = a

       RHSs of these two equations unify under [ a |-> Int ] substitution.
       Under this substitution LHSs are equal therefore these equations don't
       violate injectivity annotation. (Check done in GHC.Core.FamInstEnv.injectiveBranches)

   B2: CLOSED TYPE FAMILIES: If the RHSs can be unified under some
       substitution then either the LHSs unify under the same substitution or
       the LHS of the latter equation is overlapped by earlier equations.
       Example 1:

          type family SwapIntChar a = r | r -> a where
              SwapIntChar Int  = Char
              SwapIntChar Char = Int
              SwapIntChar a    = a

       Say we are checking the last two equations. RHSs unify under [ a |->
       Int ] substitution but LHSs don't. So we apply the substitution to LHS
       of last equation and check whether it is overlapped by any of previous
       equations. Since it is overlapped by the first equation we conclude
       that pair of last two equations does not violate injectivity
       annotation. (Check done in GHC.Tc.Validity.checkValidCoAxiom#gather_conflicts)

   A special case of B is when RHSs unify with an empty substitution ie. they
   are identical.

   If any of the above two conditions holds we conclude that the pair of
   equations does not violate injectivity annotation. But if we find a pair
   of equations where neither of the above holds we report that this pair
   violates injectivity annotation because for a given RHS we don't have a
   unique LHS. (Note that (B) actually implies (A).)

   Note that we only take into account these LHS patterns that were declared
   as injective.

2. If an RHS of a type family equation is a bare type variable then
   all LHS variables (including implicit kind variables) also have to be bare.
   In other words, this has to be a sole equation of that type family and it has
   to cover all possible patterns.  So for example this definition will be
   rejected:

      type family W1 a = r | r -> a
      type instance W1 [a] = a

   If it were accepted we could call `W1 [W1 Int]`, which would reduce to
   `W1 Int` and then by injectivity we could conclude that `[W1 Int] ~ Int`,
   which is bogus. Checked FamInst.bareTvInRHSViolated.

3. If the RHS of a type family equation is a type family application then the type
   family is rejected as not injective. This is checked by FamInst.isTFHeaded.

4. If a LHS type variable that is declared as injective is not mentioned in an
   injective position in the RHS then the type family is rejected as not
   injective.  "Injective position" means either an argument to a type
   constructor or argument to a type family on injective position.
   There are subtleties here. See Note [Coverage condition for injective type families]
   in GHC.Tc.Instance.Family.

Check (1) must be done for all family instances (transitively) imported. Other
checks (2-4) should be done just for locally written equations, as they are checks
involving just a single equation, not about interactions. Doing the other checks for
imported equations led to #17405, as the behavior of check (4) depends on
-XUndecidableInstances (see Note [Coverage condition for injective type families] in
FamInst), which may vary between modules.

See also Note [Injective type families] in GHC.Core.TyCon
-}


-- | Check whether an open type family equation can be added to already existing
-- instance environment without causing conflicts with supplied injectivity
-- annotations.  Returns list of conflicting axioms (type instance
-- declarations).
lookupFamInstEnvInjectivityConflicts
    :: [Bool]         -- injectivity annotation for this type family instance
                      -- INVARIANT: list contains at least one True value
    ->  FamInstEnvs   -- all type instances seen so far
    ->  FamInst       -- new type instance that we're checking
    -> [CoAxBranch]   -- conflicting instance declarations
lookupFamInstEnvInjectivityConflicts :: [Bool] -> (FamInstEnv, FamInstEnv) -> FamInst -> [CoAxBranch]
lookupFamInstEnvInjectivityConflicts [Bool]
injList (FamInstEnv, FamInstEnv)
fam_inst_envs
                             fam_inst :: FamInst
fam_inst@(FamInst { fi_axiom :: FamInst -> CoAxiom Unbranched
fi_axiom = CoAxiom Unbranched
new_axiom })
  | Bool -> Bool
not forall a b. (a -> b) -> a -> b
$ TyCon -> Bool
isOpenFamilyTyCon TyCon
fam
  = []

  | Bool
otherwise
  -- See Note [Verifying injectivity annotation]. This function implements
  -- check (1.B1) for open type families described there.
  = forall a b. (a -> b) -> [a] -> [b]
map (CoAxiom Unbranched -> CoAxBranch
coAxiomSingleBranch forall b c a. (b -> c) -> (a -> b) -> a -> c
. FamInst -> CoAxiom Unbranched
fi_axiom) forall a b. (a -> b) -> a -> b
$
    forall a. (a -> Bool) -> [a] -> [a]
filter FamInst -> Bool
isInjConflict forall a b. (a -> b) -> a -> b
$
    (FamInstEnv, FamInstEnv) -> TyCon -> [FamInst]
familyInstances (FamInstEnv, FamInstEnv)
fam_inst_envs TyCon
fam
    where
      fam :: TyCon
fam        = FamInst -> TyCon
famInstTyCon FamInst
fam_inst
      new_branch :: CoAxBranch
new_branch = CoAxiom Unbranched -> CoAxBranch
coAxiomSingleBranch CoAxiom Unbranched
new_axiom

      -- filtering function used by `lookup_inj_fam_conflicts` to check whether
      -- a pair of equations conflicts with the injectivity annotation.
      isInjConflict :: FamInst -> Bool
isInjConflict (FamInst { fi_axiom :: FamInst -> CoAxiom Unbranched
fi_axiom = CoAxiom Unbranched
old_axiom })
          | InjectivityCheckResult
InjectivityAccepted <-
            [Bool] -> CoAxBranch -> CoAxBranch -> InjectivityCheckResult
injectiveBranches [Bool]
injList (CoAxiom Unbranched -> CoAxBranch
coAxiomSingleBranch CoAxiom Unbranched
old_axiom) CoAxBranch
new_branch
          = Bool
False -- no conflict
          | Bool
otherwise = Bool
True


--------------------------------------------------------------------------------
--                    Type family overlap checking bits                       --
--------------------------------------------------------------------------------

{-
Note [Family instance overlap conflicts]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
- In the case of data family instances, any overlap is fundamentally a
  conflict (as these instances imply injective type mappings).

- In the case of type family instances, overlap is admitted as long as
  the right-hand sides of the overlapping rules coincide under the
  overlap substitution.  eg
       type instance F a Int = a
       type instance F Int b = b
  These two overlap on (F Int Int) but then both RHSs are Int,
  so all is well. We require that they are syntactically equal;
  anything else would be difficult to test for at this stage.
-}

------------------------------------------------------------
-- Might be a one-way match or a unifier
data FamInstLookupMode a where
  -- The FamInst we are trying to find conflicts against
  WantConflicts :: FamInst -> FamInstLookupMode FamInst
  WantMatches  :: FamInstLookupMode FamInstMatch

lookup_fam_inst_env'          -- The worker, local to this module
    :: forall a . FamInstLookupMode a
    -> FamInstEnv
    -> TyCon -> [Type]        -- What we are looking for
    -> [a]
lookup_fam_inst_env' :: forall a.
FamInstLookupMode a -> FamInstEnv -> TyCon -> [Type] -> [a]
lookup_fam_inst_env' FamInstLookupMode a
lookup_mode (FamIE BranchIndex
_ RoughMap FamInst
ie) TyCon
fam [Type]
match_tys
  | TyCon -> Bool
isOpenFamilyTyCon TyCon
fam
  , let xs :: [FamInst]
xs = (Bag FamInst, [FamInst]) -> [FamInst]
rm_fun (forall a. [RoughMatchLookupTc] -> RoughMap a -> (Bag a, [a])
lookupRM' [RoughMatchLookupTc]
rough_tmpl RoughMap FamInst
ie)   -- The common case
    -- Avoid doing any of the allocation below if there are no instances to look at.
  , Bool -> Bool
not forall a b. (a -> b) -> a -> b
$ forall (t :: * -> *) a. Foldable t => t a -> Bool
null [FamInst]
xs
  = forall (f :: * -> *) a b.
Foldable f =>
(a -> Maybe b) -> f a -> [b]
mapMaybe' FamInst -> Maybe a
check_fun [FamInst]
xs
  | Bool
otherwise = []
  where
    rough_tmpl :: [RoughMatchLookupTc]
    rough_tmpl :: [RoughMatchLookupTc]
rough_tmpl = Name -> RoughMatchLookupTc
RML_KnownTc (TyCon -> Name
tyConName TyCon
fam) forall a. a -> [a] -> [a]
: forall a b. (a -> b) -> [a] -> [b]
map Type -> RoughMatchLookupTc
typeToRoughMatchLookupTc [Type]
match_tys

    rm_fun :: (Bag FamInst, [FamInst]) -> [FamInst]
    ((Bag FamInst, [FamInst]) -> [FamInst]
rm_fun, FamInst -> Maybe a
check_fun) = case FamInstLookupMode a
lookup_mode of
                            WantConflicts FamInst
fam_inst -> (forall a b. (a, b) -> b
snd, FamInst -> FamInst -> Maybe FamInst
unify_fun FamInst
fam_inst)
                            FamInstLookupMode a
WantMatches -> (forall a. Bag a -> [a]
bagToList forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (a, b) -> a
fst, FamInst -> Maybe FamInstMatch
match_fun)

    -- Function used for finding unifiers
    unify_fun :: FamInst -> FamInst -> Maybe FamInst
unify_fun FamInst
orig_fam_inst item :: FamInst
item@(FamInst { fi_axiom :: FamInst -> CoAxiom Unbranched
fi_axiom = CoAxiom Unbranched
old_axiom, fi_tys :: FamInst -> [Type]
fi_tys = [Type]
tpl_tys, fi_tvs :: FamInst -> [TyVar]
fi_tvs = [TyVar]
tpl_tvs })

       = forall a. HasCallStack => Bool -> SDoc -> a -> a
assertPpr ([Type] -> TyCoVarSet
tyCoVarsOfTypes [Type]
tys TyCoVarSet -> TyCoVarSet -> Bool
`disjointVarSet` [TyVar] -> TyCoVarSet
mkVarSet [TyVar]
tpl_tvs)
                   ((forall a. Outputable a => a -> SDoc
ppr TyCon
fam SDoc -> SDoc -> SDoc
<+> forall a. Outputable a => a -> SDoc
ppr [Type]
tys) SDoc -> SDoc -> SDoc
$$
                    (forall a. Outputable a => a -> SDoc
ppr [TyVar]
tpl_tvs SDoc -> SDoc -> SDoc
<+> forall a. Outputable a => a -> SDoc
ppr [Type]
tpl_tys)) forall a b. (a -> b) -> a -> b
$
                -- Unification will break badly if the variables overlap
                -- They shouldn't because we allocate separate uniques for them
         if CoAxBranch -> CoAxBranch -> Bool
compatibleBranches (CoAxiom Unbranched -> CoAxBranch
coAxiomSingleBranch CoAxiom Unbranched
old_axiom) CoAxBranch
new_branch
           then forall a. Maybe a
Nothing
           else forall a. a -> Maybe a
Just FamInst
item
      -- See Note [Family instance overlap conflicts]
      where
        new_branch :: CoAxBranch
new_branch = CoAxiom Unbranched -> CoAxBranch
coAxiomSingleBranch (FamInst -> CoAxiom Unbranched
famInstAxiom FamInst
orig_fam_inst)
        (TyCon
fam, [Type]
tys) = FamInst -> (TyCon, [Type])
famInstSplitLHS FamInst
orig_fam_inst

    -- Function used for checking matches
    match_fun :: FamInst -> Maybe FamInstMatch
match_fun item :: FamInst
item@(FamInst { fi_tvs :: FamInst -> [TyVar]
fi_tvs = [TyVar]
tpl_tvs, fi_cvs :: FamInst -> [TyVar]
fi_cvs = [TyVar]
tpl_cvs
                            , fi_tys :: FamInst -> [Type]
fi_tys = [Type]
tpl_tys }) =  do
      Subst
subst <- [Type] -> [Type] -> Maybe Subst
tcMatchTys [Type]
tpl_tys [Type]
match_tys1
      forall (m :: * -> *) a. Monad m => a -> m a
return (FamInstMatch { fim_instance :: FamInst
fim_instance = FamInst
item
                             , fim_tys :: [Type]
fim_tys      = Subst -> [TyVar] -> [Type]
substTyVars Subst
subst [TyVar]
tpl_tvs forall a. [a] -> [a] -> [a]
`chkAppend` [Type]
match_tys2
                             , fim_cos :: [Coercion]
fim_cos      = forall a. HasCallStack => Bool -> a -> a
assert (forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (forall a. Maybe a -> Bool
isJust forall b c a. (b -> c) -> (a -> b) -> a -> c
. Subst -> TyVar -> Maybe Coercion
lookupCoVar Subst
subst) [TyVar]
tpl_cvs) forall a b. (a -> b) -> a -> b
$
                                               Subst -> [TyVar] -> [Coercion]
substCoVars Subst
subst [TyVar]
tpl_cvs
                             })
        where
          ([Type]
match_tys1, [Type]
match_tys2) = [Type] -> ([Type], [Type])
split_tys [Type]
tpl_tys

    -- Precondition: the tycon is saturated (or over-saturated)

    -- Deal with over-saturation
    -- See Note [Over-saturated matches]
    split_tys :: [Type] -> ([Type], [Type])
split_tys [Type]
tpl_tys
      | TyCon -> Bool
isTypeFamilyTyCon TyCon
fam
      = ([Type], [Type])
pre_rough_split_tys

      | Bool
otherwise
      = let ([Type]
match_tys1, [Type]
match_tys2) = forall b a. [b] -> [a] -> ([a], [a])
splitAtList [Type]
tpl_tys [Type]
match_tys
        in ([Type]
match_tys1, [Type]
match_tys2)

    ([Type]
pre_match_tys1, [Type]
pre_match_tys2) = forall a. BranchIndex -> [a] -> ([a], [a])
splitAt (TyCon -> BranchIndex
tyConArity TyCon
fam) [Type]
match_tys
    pre_rough_split_tys :: ([Type], [Type])
pre_rough_split_tys
      = ([Type]
pre_match_tys1, [Type]
pre_match_tys2)

lookup_fam_inst_env           -- The worker, local to this module
    :: FamInstLookupMode a
    -> FamInstEnvs
    -> TyCon -> [Type]        -- What we are looking for
    -> [a]         -- Successful matches

-- Precondition: the tycon is saturated (or over-saturated)

lookup_fam_inst_env :: forall a.
FamInstLookupMode a
-> (FamInstEnv, FamInstEnv) -> TyCon -> [Type] -> [a]
lookup_fam_inst_env FamInstLookupMode a
match_fun (FamInstEnv
pkg_ie, FamInstEnv
home_ie) TyCon
fam [Type]
tys
  =  forall a.
FamInstLookupMode a -> FamInstEnv -> TyCon -> [Type] -> [a]
lookup_fam_inst_env' FamInstLookupMode a
match_fun FamInstEnv
home_ie TyCon
fam [Type]
tys
  forall a. [a] -> [a] -> [a]
++ forall a.
FamInstLookupMode a -> FamInstEnv -> TyCon -> [Type] -> [a]
lookup_fam_inst_env' FamInstLookupMode a
match_fun FamInstEnv
pkg_ie  TyCon
fam [Type]
tys

{-
Note [Over-saturated matches]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
It's ok to look up an over-saturated type constructor.  E.g.
     type family F a :: * -> *
     type instance F (a,b) = Either (a->b)

The type instance gives rise to a newtype TyCon (at a higher kind
which you can't do in Haskell!):
     newtype FPair a b = FP (Either (a->b))

Then looking up (F (Int,Bool) Char) will return a FamInstMatch
     (FPair, [Int,Bool,Char])
The "extra" type argument [Char] just stays on the end.

We handle data families and type families separately here:

 * For type families, all instances of a type family must have the
   same arity, so we can precompute the split between the match_tys
   and the overflow tys. This is done in pre_rough_split_tys.

 * For data family instances, though, we need to re-split for each
   instance, because the breakdown might be different for each
   instance.  Why?  Because of eta reduction; see
   Note [Eta reduction for data families] in GHC.Core.Coercion.Axiom.
-}

-- checks if one LHS is dominated by a list of other branches
-- in other words, if an application would match the first LHS, it is guaranteed
-- to match at least one of the others. The RHSs are ignored.
-- This algorithm is conservative:
--   True -> the LHS is definitely covered by the others
--   False -> no information
-- It is currently (Oct 2012) used only for generating errors for
-- inaccessible branches. If these errors go unreported, no harm done.
-- This is defined here to avoid a dependency from CoAxiom to Unify
isDominatedBy :: CoAxBranch -> [CoAxBranch] -> Bool
isDominatedBy :: CoAxBranch -> [CoAxBranch] -> Bool
isDominatedBy CoAxBranch
branch [CoAxBranch]
branches
  = forall (t :: * -> *). Foldable t => t Bool -> Bool
or forall a b. (a -> b) -> a -> b
$ forall a b. (a -> b) -> [a] -> [b]
map CoAxBranch -> Bool
match [CoAxBranch]
branches
    where
      lhs :: [Type]
lhs = CoAxBranch -> [Type]
coAxBranchLHS CoAxBranch
branch
      match :: CoAxBranch -> Bool
match (CoAxBranch { cab_lhs :: CoAxBranch -> [Type]
cab_lhs = [Type]
tys })
        = forall a. Maybe a -> Bool
isJust forall a b. (a -> b) -> a -> b
$ [Type] -> [Type] -> Maybe Subst
tcMatchTys [Type]
tys [Type]
lhs

{-
************************************************************************
*                                                                      *
                Choosing an axiom application
*                                                                      *
************************************************************************

The lookupFamInstEnv function does a nice job for *open* type families,
but we also need to handle closed ones when normalising a type:
-}

reduceTyFamApp_maybe :: FamInstEnvs
                     -> Role              -- Desired role of result coercion
                     -> TyCon -> [Type]
                     -> Maybe Reduction
-- Attempt to do a *one-step* reduction of a type-family application
--    but *not* newtypes
-- Works on type-synonym families always; data-families only if
--     the role we seek is representational
-- It does *not* normalise the type arguments first, so this may not
--     go as far as you want. If you want normalised type arguments,
--     use topReduceTyFamApp_maybe
--
-- The TyCon can be oversaturated.
-- Works on both open and closed families
--
-- Always returns a *homogeneous* coercion -- type family reductions are always
-- homogeneous
reduceTyFamApp_maybe :: (FamInstEnv, FamInstEnv)
-> Role -> TyCon -> [Type] -> Maybe Reduction
reduceTyFamApp_maybe (FamInstEnv, FamInstEnv)
envs Role
role TyCon
tc [Type]
tys
  | Role
Phantom <- Role
role
  = forall a. Maybe a
Nothing

  | case Role
role of
      Role
Representational -> TyCon -> Bool
isOpenFamilyTyCon     TyCon
tc
      Role
_                -> TyCon -> Bool
isOpenTypeFamilyTyCon TyCon
tc
       -- If we seek a representational coercion
       -- (e.g. the call in topNormaliseType_maybe) then we can
       -- unwrap data families as well as type-synonym families;
       -- otherwise only type-synonym families
  , FamInstMatch { fim_instance :: FamInstMatch -> FamInst
fim_instance = FamInst { fi_axiom :: FamInst -> CoAxiom Unbranched
fi_axiom = CoAxiom Unbranched
ax }
                 , fim_tys :: FamInstMatch -> [Type]
fim_tys      = [Type]
inst_tys
                 , fim_cos :: FamInstMatch -> [Coercion]
fim_cos      = [Coercion]
inst_cos } : [FamInstMatch]
_ <- (FamInstEnv, FamInstEnv) -> TyCon -> [Type] -> [FamInstMatch]
lookupFamInstEnv (FamInstEnv, FamInstEnv)
envs TyCon
tc [Type]
tys
      -- NB: Allow multiple matches because of compatible overlap

  = let co :: Coercion
co = Role -> CoAxiom Unbranched -> [Type] -> [Coercion] -> Coercion
mkUnbranchedAxInstCo Role
role CoAxiom Unbranched
ax [Type]
inst_tys [Coercion]
inst_cos
    in forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$ Coercion -> Reduction
coercionRedn Coercion
co

  | Just CoAxiom Branched
ax <- TyCon -> Maybe (CoAxiom Branched)
isClosedSynFamilyTyConWithAxiom_maybe TyCon
tc
  , Just (BranchIndex
ind, [Type]
inst_tys, [Coercion]
inst_cos) <- CoAxiom Branched
-> [Type] -> Maybe (BranchIndex, [Type], [Coercion])
chooseBranch CoAxiom Branched
ax [Type]
tys
  = let co :: Coercion
co = forall (br :: BranchFlag).
Role
-> CoAxiom br -> BranchIndex -> [Type] -> [Coercion] -> Coercion
mkAxInstCo Role
role CoAxiom Branched
ax BranchIndex
ind [Type]
inst_tys [Coercion]
inst_cos
    in forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$ Coercion -> Reduction
coercionRedn Coercion
co

  | Just BuiltInSynFamily
ax           <- TyCon -> Maybe BuiltInSynFamily
isBuiltInSynFamTyCon_maybe TyCon
tc
  , Just (CoAxiomRule
coax,[Type]
ts,Type
ty) <- BuiltInSynFamily -> [Type] -> Maybe (CoAxiomRule, [Type], Type)
sfMatchFam BuiltInSynFamily
ax [Type]
tys
  , Role
role forall a. Eq a => a -> a -> Bool
== CoAxiomRule -> Role
coaxrRole CoAxiomRule
coax
  = let co :: Coercion
co = CoAxiomRule -> [Coercion] -> Coercion
mkAxiomRuleCo CoAxiomRule
coax (forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith Role -> Type -> Coercion
mkReflCo (CoAxiomRule -> [Role]
coaxrAsmpRoles CoAxiomRule
coax) [Type]
ts)
    in forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$ Coercion -> Type -> Reduction
mkReduction Coercion
co Type
ty

  | Bool
otherwise
  = forall a. Maybe a
Nothing

-- The axiom can be oversaturated. (Closed families only.)
chooseBranch :: CoAxiom Branched -> [Type]
             -> Maybe (BranchIndex, [Type], [Coercion])  -- found match, with args
chooseBranch :: CoAxiom Branched
-> [Type] -> Maybe (BranchIndex, [Type], [Coercion])
chooseBranch CoAxiom Branched
axiom [Type]
tys
  = do { let num_pats :: BranchIndex
num_pats = forall (br :: BranchFlag). CoAxiom br -> BranchIndex
coAxiomNumPats CoAxiom Branched
axiom
             ([Type]
target_tys, [Type]
extra_tys) = forall a. BranchIndex -> [a] -> ([a], [a])
splitAt BranchIndex
num_pats [Type]
tys
             branches :: Branches Branched
branches = forall (br :: BranchFlag). CoAxiom br -> Branches br
coAxiomBranches CoAxiom Branched
axiom
       ; (BranchIndex
ind, [Type]
inst_tys, [Coercion]
inst_cos)
           <- Array BranchIndex CoAxBranch
-> [Type] -> Maybe (BranchIndex, [Type], [Coercion])
findBranch (forall (br :: BranchFlag).
Branches br -> Array BranchIndex CoAxBranch
unMkBranches Branches Branched
branches) [Type]
target_tys
       ; forall (m :: * -> *) a. Monad m => a -> m a
return ( BranchIndex
ind, [Type]
inst_tys forall a. [a] -> [a] -> [a]
`chkAppend` [Type]
extra_tys, [Coercion]
inst_cos ) }

-- The axiom must *not* be oversaturated
findBranch :: Array BranchIndex CoAxBranch
           -> [Type]
           -> Maybe (BranchIndex, [Type], [Coercion])
    -- coercions relate requested types to returned axiom LHS at role N
findBranch :: Array BranchIndex CoAxBranch
-> [Type] -> Maybe (BranchIndex, [Type], [Coercion])
findBranch Array BranchIndex CoAxBranch
branches [Type]
target_tys
  = forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr (BranchIndex, CoAxBranch)
-> Maybe (BranchIndex, [Type], [Coercion])
-> Maybe (BranchIndex, [Type], [Coercion])
go forall a. Maybe a
Nothing (forall i e. Ix i => Array i e -> [(i, e)]
assocs Array BranchIndex CoAxBranch
branches)
  where
    go :: (BranchIndex, CoAxBranch)
       -> Maybe (BranchIndex, [Type], [Coercion])
       -> Maybe (BranchIndex, [Type], [Coercion])
    go :: (BranchIndex, CoAxBranch)
-> Maybe (BranchIndex, [Type], [Coercion])
-> Maybe (BranchIndex, [Type], [Coercion])
go (BranchIndex
index, CoAxBranch
branch) Maybe (BranchIndex, [Type], [Coercion])
other
      = let (CoAxBranch { cab_tvs :: CoAxBranch -> [TyVar]
cab_tvs = [TyVar]
tpl_tvs, cab_cvs :: CoAxBranch -> [TyVar]
cab_cvs = [TyVar]
tpl_cvs
                        , cab_lhs :: CoAxBranch -> [Type]
cab_lhs = [Type]
tpl_lhs
                        , cab_incomps :: CoAxBranch -> [CoAxBranch]
cab_incomps = [CoAxBranch]
incomps }) = CoAxBranch
branch
            in_scope :: InScopeSet
in_scope = TyCoVarSet -> InScopeSet
mkInScopeSet ([TyCoVarSet] -> TyCoVarSet
unionVarSets forall a b. (a -> b) -> a -> b
$
                            forall a b. (a -> b) -> [a] -> [b]
map ([Type] -> TyCoVarSet
tyCoVarsOfTypes forall b c a. (b -> c) -> (a -> b) -> a -> c
. CoAxBranch -> [Type]
coAxBranchLHS) [CoAxBranch]
incomps)
            -- See Note [Flattening type-family applications when matching instances]
            -- in GHC.Core.Unify
            flattened_target :: [Type]
flattened_target = InScopeSet -> [Type] -> [Type]
flattenTys InScopeSet
in_scope [Type]
target_tys
        in case [Type] -> [Type] -> Maybe Subst
tcMatchTys [Type]
tpl_lhs [Type]
target_tys of
        Just Subst
subst -- matching worked. now, check for apartness.
          |  [Type] -> CoAxBranch -> Bool
apartnessCheck [Type]
flattened_target CoAxBranch
branch
          -> -- matching worked & we're apart from all incompatible branches.
             -- success
             forall a. HasCallStack => Bool -> a -> a
assert (forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (forall a. Maybe a -> Bool
isJust forall b c a. (b -> c) -> (a -> b) -> a -> c
. Subst -> TyVar -> Maybe Coercion
lookupCoVar Subst
subst) [TyVar]
tpl_cvs) forall a b. (a -> b) -> a -> b
$
             forall a. a -> Maybe a
Just (BranchIndex
index, Subst -> [TyVar] -> [Type]
substTyVars Subst
subst [TyVar]
tpl_tvs, Subst -> [TyVar] -> [Coercion]
substCoVars Subst
subst [TyVar]
tpl_cvs)

        -- failure. keep looking
        Maybe Subst
_ -> Maybe (BranchIndex, [Type], [Coercion])
other

-- | Do an apartness check, as described in the "Closed Type Families" paper
-- (POPL '14). This should be used when determining if an equation
-- ('CoAxBranch') of a closed type family can be used to reduce a certain target
-- type family application.
apartnessCheck :: [Type]
  -- ^ /flattened/ target arguments. Make sure they're flattened! See
  -- Note [Flattening type-family applications when matching instances]
  -- in GHC.Core.Unify.
               -> CoAxBranch -- ^ the candidate equation we wish to use
                             -- Precondition: this matches the target
               -> Bool       -- ^ True <=> equation can fire
apartnessCheck :: [Type] -> CoAxBranch -> Bool
apartnessCheck [Type]
flattened_target (CoAxBranch { cab_incomps :: CoAxBranch -> [CoAxBranch]
cab_incomps = [CoAxBranch]
incomps })
  = forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (forall {a}. UnifyResultM a -> Bool
isSurelyApart
         forall b c a. (b -> c) -> (a -> b) -> a -> c
. BindFun -> [Type] -> [Type] -> UnifyResult
tcUnifyTysFG BindFun
alwaysBindFun [Type]
flattened_target
         forall b c a. (b -> c) -> (a -> b) -> a -> c
. CoAxBranch -> [Type]
coAxBranchLHS) [CoAxBranch]
incomps
  where
    isSurelyApart :: UnifyResultM a -> Bool
isSurelyApart UnifyResultM a
SurelyApart = Bool
True
    isSurelyApart UnifyResultM a
_           = Bool
False

{-
************************************************************************
*                                                                      *
                Looking up a family instance
*                                                                      *
************************************************************************

Note [Normalising types]
~~~~~~~~~~~~~~~~~~~~~~~~
The topNormaliseType function removes all occurrences of type families
and newtypes from the top-level structure of a type. normaliseTcApp does
the type family lookup and is fairly straightforward. normaliseType is
a little more involved.

The complication comes from the fact that a type family might be used in the
kind of a variable bound in a forall. We wish to remove this type family
application, but that means coming up with a fresh variable (with the new
kind). Thus, we need a substitution to be built up as we recur through the
type. However, an ordinary TCvSubst just won't do: when we hit a type variable
whose kind has changed during normalisation, we need both the new type
variable *and* the coercion. We could conjure up a new VarEnv with just this
property, but a usable substitution environment already exists:
LiftingContexts from the liftCoSubst family of functions, defined in GHC.Core.Coercion.
A LiftingContext maps a type variable to a coercion and a coercion variable to
a pair of coercions. Let's ignore coercion variables for now. Because the
coercion a type variable maps to contains the destination type (via
coercionKind), we don't need to store that destination type separately. Thus,
a LiftingContext has what we need: a map from type variables to (Coercion,
Type) pairs.

We also benefit because we can piggyback on the liftCoSubstVarBndr function to
deal with binders. However, I had to modify that function to work with this
application. Thus, we now have liftCoSubstVarBndrUsing, which takes
a function used to process the kind of the binder. We don't wish
to lift the kind, but instead normalise it. So, we pass in a callback function
that processes the kind of the binder.

After that brilliant explanation of all this, I'm sure you've forgotten the
dangling reference to coercion variables. What do we do with those? Nothing at
all. The point of normalising types is to remove type family applications, but
there's no sense in removing these from coercions. We would just get back a
new coercion witnessing the equality between the same types as the original
coercion. Because coercions are irrelevant anyway, there is no point in doing
this. So, whenever we encounter a coercion, we just say that it won't change.
That's what the CoercionTy case is doing within normalise_type.

Note [Normalisation and type synonyms]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We need to be a bit careful about normalising in the presence of type
synonyms (#13035).  Suppose S is a type synonym, and we have
   S t1 t2
If S is family-free (on its RHS) we can just normalise t1 and t2 and
reconstruct (S t1' t2').   Expanding S could not reveal any new redexes
because type families are saturated.

But if S has a type family on its RHS we expand /before/ normalising
the args t1, t2.  If we normalise t1, t2 first, we'll re-normalise them
after expansion, and that can lead to /exponential/ behaviour; see #13035.

Notice, though, that expanding first can in principle duplicate t1,t2,
which might contain redexes. I'm sure you could conjure up an exponential
case by that route too, but it hasn't happened in practice yet!
-}

topNormaliseType :: FamInstEnvs -> Type -> Type
topNormaliseType :: (FamInstEnv, FamInstEnv) -> Type -> Type
topNormaliseType (FamInstEnv, FamInstEnv)
env Type
ty
  = case (FamInstEnv, FamInstEnv) -> Type -> Maybe Reduction
topNormaliseType_maybe (FamInstEnv, FamInstEnv)
env Type
ty of
      Just Reduction
redn -> Reduction -> Type
reductionReducedType Reduction
redn
      Maybe Reduction
Nothing   -> Type
ty

topNormaliseType_maybe :: FamInstEnvs -> Type -> Maybe Reduction

-- ^ Get rid of *outermost* (or toplevel)
--      * type function redex
--      * data family redex
--      * newtypes
-- returning an appropriate Representational coercion.  Specifically, if
--   topNormaliseType_maybe env ty = Just (co, ty')
-- then
--   (a) co :: ty ~R ty'
--   (b) ty' is not a newtype, and is not a type-family or data-family redex
--
-- However, ty' can be something like (Maybe (F ty)), where
-- (F ty) is a redex.
--
-- Always operates homogeneously: the returned type has the same kind as the
-- original type, and the returned coercion is always homogeneous.
topNormaliseType_maybe :: (FamInstEnv, FamInstEnv) -> Type -> Maybe Reduction
topNormaliseType_maybe (FamInstEnv, FamInstEnv)
env Type
ty
  = do { ((Coercion
co, MCoercionN
mkind_co), Type
nty) <- forall ev.
NormaliseStepper ev -> (ev -> ev -> ev) -> Type -> Maybe (ev, Type)
topNormaliseTypeX NormaliseStepper (Coercion, MCoercionN)
stepper (Coercion, MCoercionN)
-> (Coercion, MCoercionN) -> (Coercion, MCoercionN)
combine Type
ty
       ; let hredn :: HetReduction
hredn = Reduction -> MCoercionN -> HetReduction
mkHetReduction (Coercion -> Type -> Reduction
mkReduction Coercion
co Type
nty) MCoercionN
mkind_co
       ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ Role -> HetReduction -> Reduction
homogeniseHetRedn Role
Representational HetReduction
hredn }
  where
    stepper :: NormaliseStepper (Coercion, MCoercionN)
stepper = NormaliseStepper (Coercion, MCoercionN)
unwrapNewTypeStepper' forall ev.
NormaliseStepper ev -> NormaliseStepper ev -> NormaliseStepper ev
`composeSteppers` NormaliseStepper (Coercion, MCoercionN)
tyFamStepper

    combine :: (Coercion, MCoercionN)
-> (Coercion, MCoercionN) -> (Coercion, MCoercionN)
combine (Coercion
c1, MCoercionN
mc1) (Coercion
c2, MCoercionN
mc2) = (Coercion
c1 Coercion -> Coercion -> Coercion
`mkTransCo` Coercion
c2, MCoercionN
mc1 MCoercionN -> MCoercionN -> MCoercionN
`mkTransMCo` MCoercionN
mc2)

    unwrapNewTypeStepper' :: NormaliseStepper (Coercion, MCoercionN)
    unwrapNewTypeStepper' :: NormaliseStepper (Coercion, MCoercionN)
unwrapNewTypeStepper' RecTcChecker
rec_nts TyCon
tc [Type]
tys
      = (, MCoercionN
MRefl) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NormaliseStepper Coercion
unwrapNewTypeStepper RecTcChecker
rec_nts TyCon
tc [Type]
tys

      -- second coercion below is the kind coercion relating the original type's kind
      -- to the normalised type's kind
    tyFamStepper :: NormaliseStepper (Coercion, MCoercionN)
    tyFamStepper :: NormaliseStepper (Coercion, MCoercionN)
tyFamStepper RecTcChecker
rec_nts TyCon
tc [Type]
tys  -- Try to step a type/data family
      = case (FamInstEnv, FamInstEnv) -> TyCon -> [Type] -> Maybe HetReduction
topReduceTyFamApp_maybe (FamInstEnv, FamInstEnv)
env TyCon
tc [Type]
tys of
          Just (HetReduction (Reduction Coercion
co Type
rhs) MCoercionN
res_co)
            -> forall ev. RecTcChecker -> Type -> ev -> NormaliseStepResult ev
NS_Step RecTcChecker
rec_nts Type
rhs (Coercion
co, MCoercionN
res_co)
          Maybe HetReduction
_ -> forall ev. NormaliseStepResult ev
NS_Done

---------------
-- | Try to simplify a type-family application, by *one* step
-- If topReduceTyFamApp_maybe env r F tys = Just (HetReduction (Reduction co rhs) res_co)
-- then    co     :: F tys ~R# rhs
--         res_co :: typeKind(F tys) ~ typeKind(rhs)
-- Type families and data families; always Representational role
topReduceTyFamApp_maybe :: FamInstEnvs -> TyCon -> [Type]
                        -> Maybe HetReduction
topReduceTyFamApp_maybe :: (FamInstEnv, FamInstEnv) -> TyCon -> [Type] -> Maybe HetReduction
topReduceTyFamApp_maybe (FamInstEnv, FamInstEnv)
envs TyCon
fam_tc [Type]
arg_tys
  | TyCon -> Bool
isFamilyTyCon TyCon
fam_tc   -- type families and data families
  , Just Reduction
redn <- (FamInstEnv, FamInstEnv)
-> Role -> TyCon -> [Type] -> Maybe Reduction
reduceTyFamApp_maybe (FamInstEnv, FamInstEnv)
envs Role
role TyCon
fam_tc [Type]
ntys
  = forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$
      Reduction -> MCoercionN -> HetReduction
mkHetReduction
        (HasDebugCallStack => Role -> TyCon -> [Coercion] -> Coercion
mkTyConAppCo Role
role TyCon
fam_tc [Coercion]
args_cos Coercion -> Reduction -> Reduction
`mkTransRedn` Reduction
redn)
        MCoercionN
res_co
  | Bool
otherwise
  = forall a. Maybe a
Nothing
  where
    role :: Role
role = Role
Representational
    ArgsReductions (Reductions [Coercion]
args_cos [Type]
ntys) MCoercionN
res_co
      = forall a.
(FamInstEnv, FamInstEnv) -> Role -> TyCoVarSet -> NormM a -> a
initNormM (FamInstEnv, FamInstEnv)
envs Role
role ([Type] -> TyCoVarSet
tyCoVarsOfTypes [Type]
arg_tys)
      forall a b. (a -> b) -> a -> b
$ TyCon -> [Type] -> NormM ArgsReductions
normalise_tc_args TyCon
fam_tc [Type]
arg_tys

---------------
normaliseType :: FamInstEnvs
              -> Role  -- desired role of coercion
              -> Type -> Reduction
normaliseType :: (FamInstEnv, FamInstEnv) -> Role -> Type -> Reduction
normaliseType (FamInstEnv, FamInstEnv)
env Role
role Type
ty
  = forall a.
(FamInstEnv, FamInstEnv) -> Role -> TyCoVarSet -> NormM a -> a
initNormM (FamInstEnv, FamInstEnv)
env Role
role (Type -> TyCoVarSet
tyCoVarsOfType Type
ty) forall a b. (a -> b) -> a -> b
$ Type -> NormM Reduction
normalise_type Type
ty

---------------
normaliseTcApp :: FamInstEnvs -> Role -> TyCon -> [Type] -> Reduction
-- See comments on normaliseType for the arguments of this function
normaliseTcApp :: (FamInstEnv, FamInstEnv) -> Role -> TyCon -> [Type] -> Reduction
normaliseTcApp (FamInstEnv, FamInstEnv)
env Role
role TyCon
tc [Type]
tys
  = forall a.
(FamInstEnv, FamInstEnv) -> Role -> TyCoVarSet -> NormM a -> a
initNormM (FamInstEnv, FamInstEnv)
env Role
role ([Type] -> TyCoVarSet
tyCoVarsOfTypes [Type]
tys) forall a b. (a -> b) -> a -> b
$
    TyCon -> [Type] -> NormM Reduction
normalise_tc_app TyCon
tc [Type]
tys

-------------------------------------------------------
--        Functions that work in the NormM monad
-------------------------------------------------------

-- See Note [Normalising types] about the LiftingContext
normalise_tc_app :: TyCon -> [Type] -> NormM Reduction
normalise_tc_app :: TyCon -> [Type] -> NormM Reduction
normalise_tc_app TyCon
tc [Type]
tys
  | ExpandsSyn [(TyVar, Type)]
tenv Type
rhs [Type]
tys' <- forall tyco. TyCon -> [tyco] -> ExpandSynResult tyco
expandSynTyCon_maybe TyCon
tc [Type]
tys
  , Bool -> Bool
not (TyCon -> Bool
isFamFreeTyCon TyCon
tc)  -- Expand and try again
  = -- A synonym with type families in the RHS
    -- Expand and try again
    -- See Note [Normalisation and type synonyms]
    Type -> NormM Reduction
normalise_type (Type -> [Type] -> Type
mkAppTys (HasDebugCallStack => Subst -> Type -> Type
substTy ([(TyVar, Type)] -> Subst
mkTvSubstPrs [(TyVar, Type)]
tenv) Type
rhs) [Type]
tys')

  | TyCon -> Bool
isFamilyTyCon TyCon
tc
  = -- A type-family application
    do { (FamInstEnv, FamInstEnv)
env <- NormM (FamInstEnv, FamInstEnv)
getEnv
       ; Role
role <- NormM Role
getRole
       ; ArgsReductions redns :: Reductions
redns@(Reductions [Coercion]
args_cos [Type]
ntys) MCoercionN
res_co <- TyCon -> [Type] -> NormM ArgsReductions
normalise_tc_args TyCon
tc [Type]
tys
       ; case (FamInstEnv, FamInstEnv)
-> Role -> TyCon -> [Type] -> Maybe Reduction
reduceTyFamApp_maybe (FamInstEnv, FamInstEnv)
env Role
role TyCon
tc [Type]
ntys of
           Just Reduction
redn1
             -> do { Reduction
redn2 <- Reduction -> NormM Reduction
normalise_reduction Reduction
redn1
                   ; let redn3 :: Reduction
redn3 = HasDebugCallStack => Role -> TyCon -> [Coercion] -> Coercion
mkTyConAppCo Role
role TyCon
tc [Coercion]
args_cos Coercion -> Reduction -> Reduction
`mkTransRedn` Reduction
redn2
                   ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ Role -> Reduction -> MCoercionN -> Reduction
assemble_result Role
role Reduction
redn3 MCoercionN
res_co }
           Maybe Reduction
_ -> -- No unique matching family instance exists;
                -- we do not do anything
                forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$
                  Role -> Reduction -> MCoercionN -> Reduction
assemble_result Role
role (Role -> TyCon -> Reductions -> Reduction
mkTyConAppRedn Role
role TyCon
tc Reductions
redns) MCoercionN
res_co }

  | Bool
otherwise
  = -- A synonym with no type families in the RHS; or data type etc
    -- Just normalise the arguments and rebuild
    do { ArgsReductions Reductions
redns MCoercionN
res_co <- TyCon -> [Type] -> NormM ArgsReductions
normalise_tc_args TyCon
tc [Type]
tys
       ; Role
role <- NormM Role
getRole
       ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$
            Role -> Reduction -> MCoercionN -> Reduction
assemble_result Role
role (Role -> TyCon -> Reductions -> Reduction
mkTyConAppRedn Role
role TyCon
tc Reductions
redns) MCoercionN
res_co }

  where
    assemble_result :: Role       -- r, ambient role in NormM monad
                    -> Reduction  -- orig_ty ~r nty, possibly heterogeneous (nty possibly of changed kind)
                    -> MCoercionN -- typeKind(orig_ty) ~N typeKind(nty)
                    -> Reduction  -- orig_ty ~r nty_casted
                                  -- where nty_casted has same kind as orig_ty
    assemble_result :: Role -> Reduction -> MCoercionN -> Reduction
assemble_result Role
r Reduction
redn MCoercionN
kind_co
      = Role -> Reduction -> MCoercionN -> Reduction
mkCoherenceRightMRedn Role
r Reduction
redn (MCoercionN -> MCoercionN
mkSymMCo MCoercionN
kind_co)

normalise_tc_args :: TyCon -> [Type] -> NormM ArgsReductions
normalise_tc_args :: TyCon -> [Type] -> NormM ArgsReductions
normalise_tc_args TyCon
tc [Type]
tys
  = do { Role
role <- NormM Role
getRole
       ; Type -> [Role] -> [Type] -> NormM ArgsReductions
normalise_args (TyCon -> Type
tyConKind TyCon
tc) (Role -> TyCon -> [Role]
tyConRolesX Role
role TyCon
tc) [Type]
tys }

normalise_type :: Type -> NormM Reduction
-- Normalise the input type, by eliminating *all* type-function redexes
-- but *not* newtypes (which are visible to the programmer)
-- Returns with Refl if nothing happens
-- Does nothing to newtypes
-- The returned coercion *must* be *homogeneous*
-- See Note [Normalising types]
-- Try not to disturb type synonyms if possible

normalise_type :: Type -> NormM Reduction
normalise_type Type
ty
  = Type -> NormM Reduction
go Type
ty
  where
    go :: Type -> NormM Reduction
    go :: Type -> NormM Reduction
go (TyConApp TyCon
tc [Type]
tys) = TyCon -> [Type] -> NormM Reduction
normalise_tc_app TyCon
tc [Type]
tys
    go ty :: Type
ty@(LitTy {})
      = do { Role
r <- NormM Role
getRole
           ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ Role -> Type -> Reduction
mkReflRedn Role
r Type
ty }
    go (AppTy Type
ty1 Type
ty2) = Type -> [Type] -> NormM Reduction
go_app_tys Type
ty1 [Type
ty2]

    go (FunTy { ft_af :: Type -> AnonArgFlag
ft_af = AnonArgFlag
vis, ft_mult :: Type -> Type
ft_mult = Type
w, ft_arg :: Type -> Type
ft_arg = Type
ty1, ft_res :: Type -> Type
ft_res = Type
ty2 })
      = do { Reduction
arg_redn <- Type -> NormM Reduction
go Type
ty1
           ; Reduction
res_redn <- Type -> NormM Reduction
go Type
ty2
           ; Reduction
w_redn <- forall a. Role -> NormM a -> NormM a
withRole Role
Nominal forall a b. (a -> b) -> a -> b
$ Type -> NormM Reduction
go Type
w
           ; Role
r <- NormM Role
getRole
           ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ Role
-> AnonArgFlag -> Reduction -> Reduction -> Reduction -> Reduction
mkFunRedn Role
r AnonArgFlag
vis Reduction
w_redn Reduction
arg_redn Reduction
res_redn }
    go (ForAllTy (Bndr TyVar
tcvar ArgFlag
vis) Type
ty)
      = do { (LiftingContext
lc', TyVar
tv', Reduction
k_redn) <- TyVar -> NormM (LiftingContext, TyVar, Reduction)
normalise_var_bndr TyVar
tcvar
           ; Reduction
redn <- forall a. LiftingContext -> NormM a -> NormM a
withLC LiftingContext
lc' forall a b. (a -> b) -> a -> b
$ Type -> NormM Reduction
normalise_type Type
ty
           ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ ArgFlag -> TyVar -> Reduction -> Reduction -> Reduction
mkForAllRedn ArgFlag
vis TyVar
tv' Reduction
k_redn Reduction
redn }
    go (TyVarTy TyVar
tv)    = TyVar -> NormM Reduction
normalise_tyvar TyVar
tv
    go (CastTy Type
ty Coercion
co)
      = do { Reduction
redn <- Type -> NormM Reduction
go Type
ty
           ; LiftingContext
lc <- NormM LiftingContext
getLC
           ; let co' :: Coercion
co' = LiftingContext -> Coercion -> Coercion
substRightCo LiftingContext
lc Coercion
co
           ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ Role -> Type -> Coercion -> Reduction -> Coercion -> Reduction
mkCastRedn2 Role
Nominal Type
ty Coercion
co Reduction
redn Coercion
co'
             --       ^^^^^^^^^^^ uses castCoercionKind2
           }
    go (CoercionTy Coercion
co)
      = do { LiftingContext
lc <- NormM LiftingContext
getLC
           ; Role
r <- NormM Role
getRole
           ; let kco :: Coercion
kco = HasDebugCallStack => Role -> LiftingContext -> Type -> Coercion
liftCoSubst Role
Nominal LiftingContext
lc (Coercion -> Type
coercionType Coercion
co)
                 co' :: Coercion
co' = LiftingContext -> Coercion -> Coercion
substRightCo LiftingContext
lc Coercion
co
           ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ Role -> Coercion -> Coercion -> Coercion -> Reduction
mkProofIrrelRedn Role
r Coercion
kco Coercion
co Coercion
co' }

    go_app_tys :: Type   -- function
               -> [Type] -- args
               -> NormM Reduction
    -- cf. GHC.Tc.Solver.Rewrite.rewrite_app_ty_args
    go_app_tys :: Type -> [Type] -> NormM Reduction
go_app_tys (AppTy Type
ty1 Type
ty2) [Type]
tys = Type -> [Type] -> NormM Reduction
go_app_tys Type
ty1 (Type
ty2 forall a. a -> [a] -> [a]
: [Type]
tys)
    go_app_tys Type
fun_ty [Type]
arg_tys
      = do { fun_redn :: Reduction
fun_redn@(Reduction Coercion
fun_co Type
nfun) <- Type -> NormM Reduction
go Type
fun_ty
           ; case HasCallStack => Type -> Maybe (TyCon, [Type])
tcSplitTyConApp_maybe Type
nfun of
               Just (TyCon
tc, [Type]
xis) ->
                 do { Reduction
redn <- Type -> NormM Reduction
go (TyCon -> [Type] -> Type
mkTyConApp TyCon
tc ([Type]
xis forall a. [a] -> [a] -> [a]
++ [Type]
arg_tys))
                   -- rewrite_app_ty_args avoids redundantly processing the xis,
                   -- but that's a much more performance-sensitive function.
                   -- This type normalisation is not called in a loop.
                    ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$
                        Coercion -> [Coercion] -> Coercion
mkAppCos Coercion
fun_co (forall a b. (a -> b) -> [a] -> [b]
map Type -> Coercion
mkNomReflCo [Type]
arg_tys) Coercion -> Reduction -> Reduction
`mkTransRedn` Reduction
redn }
               Maybe (TyCon, [Type])
Nothing ->
                 do { ArgsReductions Reductions
redns MCoercionN
res_co
                        <- Type -> [Role] -> [Type] -> NormM ArgsReductions
normalise_args (HasDebugCallStack => Type -> Type
typeKind Type
nfun)
                                          (forall a. a -> [a]
repeat Role
Nominal)
                                          [Type]
arg_tys
                    ; Role
role <- NormM Role
getRole
                    ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$
                        Role -> Reduction -> MCoercionN -> Reduction
mkCoherenceRightMRedn Role
role
                          (Reduction -> Reductions -> Reduction
mkAppRedns Reduction
fun_redn Reductions
redns)
                          (MCoercionN -> MCoercionN
mkSymMCo MCoercionN
res_co) } }

normalise_args :: Kind    -- of the function
               -> [Role]  -- roles at which to normalise args
               -> [Type]  -- args
               -> NormM ArgsReductions
-- returns ArgsReductions (Reductions cos xis) res_co,
-- where each xi is the normalised version of the corresponding type,
-- each co is orig_arg ~ xi, and res_co :: kind(f orig_args) ~ kind(f xis).
-- NB: The xis might *not* have the same kinds as the input types,
-- but the resulting application *will* be well-kinded
-- cf. GHC.Tc.Solver.Rewrite.rewrite_args_slow
normalise_args :: Type -> [Role] -> [Type] -> NormM ArgsReductions
normalise_args Type
fun_ki [Role]
roles [Type]
args
  = do { [Reduction]
normed_args <- forall (m :: * -> *) a b c.
Applicative m =>
(a -> b -> m c) -> [a] -> [b] -> m [c]
zipWithM Role -> Type -> NormM Reduction
normalise1 [Role]
roles [Type]
args
       ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ HasDebugCallStack =>
[TyCoBinder]
-> Type -> TyCoVarSet -> [Role] -> [Reduction] -> ArgsReductions
simplifyArgsWorker [TyCoBinder]
ki_binders Type
inner_ki TyCoVarSet
fvs [Role]
roles [Reduction]
normed_args }
  where
    ([TyCoBinder]
ki_binders, Type
inner_ki) = Type -> ([TyCoBinder], Type)
splitPiTys Type
fun_ki
    fvs :: TyCoVarSet
fvs = [Type] -> TyCoVarSet
tyCoVarsOfTypes [Type]
args

    normalise1 :: Role -> Type -> NormM Reduction
normalise1 Role
role Type
ty
      = forall a. Role -> NormM a -> NormM a
withRole Role
role forall a b. (a -> b) -> a -> b
$ Type -> NormM Reduction
normalise_type Type
ty

normalise_tyvar :: TyVar -> NormM Reduction
normalise_tyvar :: TyVar -> NormM Reduction
normalise_tyvar TyVar
tv
  = forall a. HasCallStack => Bool -> a -> a
assert (TyVar -> Bool
isTyVar TyVar
tv) forall a b. (a -> b) -> a -> b
$
    do { LiftingContext
lc <- NormM LiftingContext
getLC
       ; Role
r  <- NormM Role
getRole
       ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ case LiftingContext -> Role -> TyVar -> Maybe Coercion
liftCoSubstTyVar LiftingContext
lc Role
r TyVar
tv of
           Just Coercion
co -> Coercion -> Reduction
coercionRedn Coercion
co
           Maybe Coercion
Nothing -> Role -> Type -> Reduction
mkReflRedn Role
r (TyVar -> Type
mkTyVarTy TyVar
tv) }

normalise_reduction :: Reduction -> NormM Reduction
normalise_reduction :: Reduction -> NormM Reduction
normalise_reduction (Reduction Coercion
co Type
ty)
  = do { Reduction
redn' <- Type -> NormM Reduction
normalise_type Type
ty
       ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ Coercion
co Coercion -> Reduction -> Reduction
`mkTransRedn` Reduction
redn' }

normalise_var_bndr :: TyCoVar -> NormM (LiftingContext, TyCoVar, Reduction)
normalise_var_bndr :: TyVar -> NormM (LiftingContext, TyVar, Reduction)
normalise_var_bndr TyVar
tcvar
  -- works for both tvar and covar
  = do { LiftingContext
lc1 <- NormM LiftingContext
getLC
       ; (FamInstEnv, FamInstEnv)
env <- NormM (FamInstEnv, FamInstEnv)
getEnv
       ; let callback :: LiftingContext -> Type -> Reduction
callback LiftingContext
lc Type
ki = forall a.
NormM a -> (FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a
runNormM (Type -> NormM Reduction
normalise_type Type
ki) (FamInstEnv, FamInstEnv)
env LiftingContext
lc Role
Nominal
       ; forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ forall r.
(r -> Coercion)
-> (LiftingContext -> Type -> r)
-> LiftingContext
-> TyVar
-> (LiftingContext, TyVar, r)
liftCoSubstVarBndrUsing Reduction -> Coercion
reductionCoercion LiftingContext -> Type -> Reduction
callback LiftingContext
lc1 TyVar
tcvar }

-- | a monad for the normalisation functions, reading 'FamInstEnvs',
-- a 'LiftingContext', and a 'Role'.
newtype NormM a = NormM { forall a.
NormM a -> (FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a
runNormM ::
                            FamInstEnvs -> LiftingContext -> Role -> a }
    deriving (forall a b. a -> NormM b -> NormM a
forall a b. (a -> b) -> NormM a -> NormM b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
-> (forall a b. a -> f b -> f a) -> Functor f
<$ :: forall a b. a -> NormM b -> NormM a
$c<$ :: forall a b. a -> NormM b -> NormM a
fmap :: forall a b. (a -> b) -> NormM a -> NormM b
$cfmap :: forall a b. (a -> b) -> NormM a -> NormM b
Functor)

initNormM :: FamInstEnvs -> Role
          -> TyCoVarSet   -- the in-scope variables
          -> NormM a -> a
initNormM :: forall a.
(FamInstEnv, FamInstEnv) -> Role -> TyCoVarSet -> NormM a -> a
initNormM (FamInstEnv, FamInstEnv)
env Role
role TyCoVarSet
vars (NormM (FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a
thing_inside)
  = (FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a
thing_inside (FamInstEnv, FamInstEnv)
env LiftingContext
lc Role
role
  where
    in_scope :: InScopeSet
in_scope = TyCoVarSet -> InScopeSet
mkInScopeSet TyCoVarSet
vars
    lc :: LiftingContext
lc       = InScopeSet -> LiftingContext
emptyLiftingContext InScopeSet
in_scope

getRole :: NormM Role
getRole :: NormM Role
getRole = forall a.
((FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a)
-> NormM a
NormM (\ (FamInstEnv, FamInstEnv)
_ LiftingContext
_ Role
r -> Role
r)

getLC :: NormM LiftingContext
getLC :: NormM LiftingContext
getLC = forall a.
((FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a)
-> NormM a
NormM (\ (FamInstEnv, FamInstEnv)
_ LiftingContext
lc Role
_ -> LiftingContext
lc)

getEnv :: NormM FamInstEnvs
getEnv :: NormM (FamInstEnv, FamInstEnv)
getEnv = forall a.
((FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a)
-> NormM a
NormM (\ (FamInstEnv, FamInstEnv)
env LiftingContext
_ Role
_ -> (FamInstEnv, FamInstEnv)
env)

withRole :: Role -> NormM a -> NormM a
withRole :: forall a. Role -> NormM a -> NormM a
withRole Role
r NormM a
thing = forall a.
((FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a)
-> NormM a
NormM forall a b. (a -> b) -> a -> b
$ \ (FamInstEnv, FamInstEnv)
envs LiftingContext
lc Role
_old_r -> forall a.
NormM a -> (FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a
runNormM NormM a
thing (FamInstEnv, FamInstEnv)
envs LiftingContext
lc Role
r

withLC :: LiftingContext -> NormM a -> NormM a
withLC :: forall a. LiftingContext -> NormM a -> NormM a
withLC LiftingContext
lc NormM a
thing = forall a.
((FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a)
-> NormM a
NormM forall a b. (a -> b) -> a -> b
$ \ (FamInstEnv, FamInstEnv)
envs LiftingContext
_old_lc Role
r -> forall a.
NormM a -> (FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a
runNormM NormM a
thing (FamInstEnv, FamInstEnv)
envs LiftingContext
lc Role
r

instance Monad NormM where
  NormM a
ma >>= :: forall a b. NormM a -> (a -> NormM b) -> NormM b
>>= a -> NormM b
fmb = forall a.
((FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a)
-> NormM a
NormM forall a b. (a -> b) -> a -> b
$ \(FamInstEnv, FamInstEnv)
env LiftingContext
lc Role
r ->
               let a :: a
a = forall a.
NormM a -> (FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a
runNormM NormM a
ma (FamInstEnv, FamInstEnv)
env LiftingContext
lc Role
r in
               forall a.
NormM a -> (FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a
runNormM (a -> NormM b
fmb a
a) (FamInstEnv, FamInstEnv)
env LiftingContext
lc Role
r

instance Applicative NormM where
  pure :: forall a. a -> NormM a
pure a
x = forall a.
((FamInstEnv, FamInstEnv) -> LiftingContext -> Role -> a)
-> NormM a
NormM forall a b. (a -> b) -> a -> b
$ \ (FamInstEnv, FamInstEnv)
_ LiftingContext
_ Role
_ -> a
x
  <*> :: forall a b. NormM (a -> b) -> NormM a -> NormM b
(<*>)  = forall (m :: * -> *) a b. Monad m => m (a -> b) -> m a -> m b
ap