{-
(c) The University of Glasgow 2006
(c) The GRASP/AQUA Project, Glasgow University, 2000


FunDeps - functional dependencies

It's better to read it as: "if we know these, then we're going to know these"
-}

{-# LANGUAGE CPP #-}

module FunDeps (
        FunDepEqn(..), pprEquation,
        improveFromInstEnv, improveFromAnother,
        checkInstCoverage, checkFunDeps,
        pprFundeps
    ) where

#include "HsVersions.h"

import GhcPrelude

import Name
import Var
import Class
import Type
import TcType( transSuperClasses )
import CoAxiom( TypeEqn )
import Unify
import FamInst( injTyVarsOfTypes )
import InstEnv
import VarSet
import VarEnv
import Outputable
import ErrUtils( Validity(..), allValid )
import SrcLoc
import Util

import Pair             ( Pair(..) )
import Data.List        ( nubBy )
import Data.Maybe
import Data.Foldable    ( fold )

{-
************************************************************************
*                                                                      *
\subsection{Generate equations from functional dependencies}
*                                                                      *
************************************************************************


Each functional dependency with one variable in the RHS is responsible
for generating a single equality. For instance:
     class C a b | a -> b
The constraints ([Wanted] C Int Bool) and [Wanted] C Int alpha
will generate the following FunDepEqn
     FDEqn { fd_qtvs = []
           , fd_eqs  = [Pair Bool alpha]
           , fd_pred1 = C Int Bool
           , fd_pred2 = C Int alpha
           , fd_loc = ... }
However notice that a functional dependency may have more than one variable
in the RHS which will create more than one pair of types in fd_eqs. Example:
     class C a b c | a -> b c
     [Wanted] C Int alpha alpha
     [Wanted] C Int Bool beta
Will generate:
     FDEqn { fd_qtvs = []
           , fd_eqs  = [Pair Bool alpha, Pair alpha beta]
           , fd_pred1 = C Int Bool
           , fd_pred2 = C Int alpha
           , fd_loc = ... }

INVARIANT: Corresponding types aren't already equal
That is, there exists at least one non-identity equality in FDEqs.

Assume:
       class C a b c | a -> b c
       instance C Int x x
And:   [Wanted] C Int Bool alpha
We will /match/ the LHS of fundep equations, producing a matching substitution
and create equations for the RHS sides. In our last example we'd have generated:
      ({x}, [fd1,fd2])
where
       fd1 = FDEq 1 Bool x
       fd2 = FDEq 2 alpha x
To ``execute'' the equation, make fresh type variable for each tyvar in the set,
instantiate the two types with these fresh variables, and then unify or generate
a new constraint. In the above example we would generate a new unification
variable 'beta' for x and produce the following constraints:
     [Wanted] (Bool ~ beta)
     [Wanted] (alpha ~ beta)

Notice the subtle difference between the above class declaration and:
       class C a b c | a -> b, a -> c
where we would generate:
      ({x},[fd1]),({x},[fd2])
This means that the template variable would be instantiated to different
unification variables when producing the FD constraints.

Finally, the position parameters will help us rewrite the wanted constraint ``on the spot''
-}

data FunDepEqn loc
  = FDEqn { FunDepEqn loc -> [TyVar]
fd_qtvs :: [TyVar]   -- Instantiate these type and kind vars
                                 --   to fresh unification vars,
                                 -- Non-empty only for FunDepEqns arising from instance decls

          , FunDepEqn loc -> [TypeEqn]
fd_eqs   :: [TypeEqn]  -- Make these pairs of types equal
          , FunDepEqn loc -> PredType
fd_pred1 :: PredType   -- The FunDepEqn arose from
          , FunDepEqn loc -> PredType
fd_pred2 :: PredType   --  combining these two constraints
          , FunDepEqn loc -> loc
fd_loc   :: loc  }

{-
Given a bunch of predicates that must hold, such as

        C Int t1, C Int t2, C Bool t3, ?x::t4, ?x::t5

improve figures out what extra equations must hold.
For example, if we have

        class C a b | a->b where ...

then improve will return

        [(t1,t2), (t4,t5)]

NOTA BENE:

  * improve does not iterate.  It's possible that when we make
    t1=t2, for example, that will in turn trigger a new equation.
    This would happen if we also had
        C t1 t7, C t2 t8
    If t1=t2, we also get t7=t8.

    improve does *not* do this extra step.  It relies on the caller
    doing so.

  * The equations unify types that are not already equal.  So there
    is no effect iff the result of improve is empty
-}

instFD :: FunDep TyVar -> [TyVar] -> [Type] -> FunDep Type
-- (instFD fd tvs tys) returns fd instantiated with (tvs -> tys)
instFD :: FunDep TyVar -> [TyVar] -> [PredType] -> FunDep PredType
instFD (ls :: [TyVar]
ls,rs :: [TyVar]
rs) tvs :: [TyVar]
tvs tys :: [PredType]
tys
  = ((TyVar -> PredType) -> [TyVar] -> [PredType]
forall a b. (a -> b) -> [a] -> [b]
map TyVar -> PredType
lookup [TyVar]
ls, (TyVar -> PredType) -> [TyVar] -> [PredType]
forall a b. (a -> b) -> [a] -> [b]
map TyVar -> PredType
lookup [TyVar]
rs)
  where
    env :: VarEnv PredType
env       = [TyVar] -> [PredType] -> VarEnv PredType
forall a. [TyVar] -> [a] -> VarEnv a
zipVarEnv [TyVar]
tvs [PredType]
tys
    lookup :: TyVar -> PredType
lookup tv :: TyVar
tv = VarEnv PredType -> TyVar -> PredType
forall a. VarEnv a -> TyVar -> a
lookupVarEnv_NF VarEnv PredType
env TyVar
tv

zipAndComputeFDEqs :: (Type -> Type -> Bool) -- Discard this FDEq if true
                   -> [Type] -> [Type]
                   -> [TypeEqn]
-- Create a list of (Type,Type) pairs from two lists of types,
-- making sure that the types are not already equal
zipAndComputeFDEqs :: (PredType -> PredType -> Bool)
-> [PredType] -> [PredType] -> [TypeEqn]
zipAndComputeFDEqs discard :: PredType -> PredType -> Bool
discard (ty1 :: PredType
ty1:tys1 :: [PredType]
tys1) (ty2 :: PredType
ty2:tys2 :: [PredType]
tys2)
 | PredType -> PredType -> Bool
discard PredType
ty1 PredType
ty2 = (PredType -> PredType -> Bool)
-> [PredType] -> [PredType] -> [TypeEqn]
zipAndComputeFDEqs PredType -> PredType -> Bool
discard [PredType]
tys1 [PredType]
tys2
 | Bool
otherwise       = PredType -> PredType -> TypeEqn
forall a. a -> a -> Pair a
Pair PredType
ty1 PredType
ty2 TypeEqn -> [TypeEqn] -> [TypeEqn]
forall a. a -> [a] -> [a]
: (PredType -> PredType -> Bool)
-> [PredType] -> [PredType] -> [TypeEqn]
zipAndComputeFDEqs PredType -> PredType -> Bool
discard [PredType]
tys1 [PredType]
tys2
zipAndComputeFDEqs _ _ _ = []

-- Improve a class constraint from another class constraint
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
improveFromAnother :: loc
                   -> PredType -- Template item (usually given, or inert)
                   -> PredType -- Workitem [that can be improved]
                   -> [FunDepEqn loc]
-- Post: FDEqs always oriented from the other to the workitem
--       Equations have empty quantified variables
improveFromAnother :: loc -> PredType -> PredType -> [FunDepEqn loc]
improveFromAnother loc :: loc
loc pred1 :: PredType
pred1 pred2 :: PredType
pred2
  | Just (cls1 :: Class
cls1, tys1 :: [PredType]
tys1) <- PredType -> Maybe (Class, [PredType])
getClassPredTys_maybe PredType
pred1
  , Just (cls2 :: Class
cls2, tys2 :: [PredType]
tys2) <- PredType -> Maybe (Class, [PredType])
getClassPredTys_maybe PredType
pred2
  , Class
cls1 Class -> Class -> Bool
forall a. Eq a => a -> a -> Bool
== Class
cls2
  = [ FDEqn :: forall loc.
[TyVar]
-> [TypeEqn] -> PredType -> PredType -> loc -> FunDepEqn loc
FDEqn { fd_qtvs :: [TyVar]
fd_qtvs = [], fd_eqs :: [TypeEqn]
fd_eqs = [TypeEqn]
eqs, fd_pred1 :: PredType
fd_pred1 = PredType
pred1, fd_pred2 :: PredType
fd_pred2 = PredType
pred2, fd_loc :: loc
fd_loc = loc
loc }
    | let (cls_tvs :: [TyVar]
cls_tvs, cls_fds :: [FunDep TyVar]
cls_fds) = Class -> ([TyVar], [FunDep TyVar])
classTvsFds Class
cls1
    , FunDep TyVar
fd <- [FunDep TyVar]
cls_fds
    , let (ltys1 :: [PredType]
ltys1, rs1 :: [PredType]
rs1) = FunDep TyVar -> [TyVar] -> [PredType] -> FunDep PredType
instFD FunDep TyVar
fd [TyVar]
cls_tvs [PredType]
tys1
          (ltys2 :: [PredType]
ltys2, rs2 :: [PredType]
rs2) = FunDep TyVar -> [TyVar] -> [PredType] -> FunDep PredType
instFD FunDep TyVar
fd [TyVar]
cls_tvs [PredType]
tys2
    , [PredType] -> [PredType] -> Bool
eqTypes [PredType]
ltys1 [PredType]
ltys2               -- The LHSs match
    , let eqs :: [TypeEqn]
eqs = (PredType -> PredType -> Bool)
-> [PredType] -> [PredType] -> [TypeEqn]
zipAndComputeFDEqs PredType -> PredType -> Bool
eqType [PredType]
rs1 [PredType]
rs2
    , Bool -> Bool
not ([TypeEqn] -> Bool
forall (t :: * -> *) a. Foldable t => t a -> Bool
null [TypeEqn]
eqs) ]

improveFromAnother _ _ _ = []


-- Improve a class constraint from instance declarations
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

instance Outputable (FunDepEqn a) where
  ppr :: FunDepEqn a -> SDoc
ppr = FunDepEqn a -> SDoc
forall a. FunDepEqn a -> SDoc
pprEquation

pprEquation :: FunDepEqn a -> SDoc
pprEquation :: FunDepEqn a -> SDoc
pprEquation (FDEqn { fd_qtvs :: forall loc. FunDepEqn loc -> [TyVar]
fd_qtvs = [TyVar]
qtvs, fd_eqs :: forall loc. FunDepEqn loc -> [TypeEqn]
fd_eqs = [TypeEqn]
pairs })
  = [SDoc] -> SDoc
vcat [String -> SDoc
text "forall" SDoc -> SDoc -> SDoc
<+> SDoc -> SDoc
braces ((TyVar -> SDoc) -> [TyVar] -> SDoc
forall a. (a -> SDoc) -> [a] -> SDoc
pprWithCommas TyVar -> SDoc
forall a. Outputable a => a -> SDoc
ppr [TyVar]
qtvs),
          Int -> SDoc -> SDoc
nest 2 ([SDoc] -> SDoc
vcat [ PredType -> SDoc
forall a. Outputable a => a -> SDoc
ppr PredType
t1 SDoc -> SDoc -> SDoc
<+> String -> SDoc
text "~" SDoc -> SDoc -> SDoc
<+> PredType -> SDoc
forall a. Outputable a => a -> SDoc
ppr PredType
t2
                       | Pair t1 :: PredType
t1 t2 :: PredType
t2 <- [TypeEqn]
pairs])]

improveFromInstEnv :: InstEnvs
                   -> (PredType -> SrcSpan -> loc)
                   -> PredType
                   -> [FunDepEqn loc] -- Needs to be a FunDepEqn because
                                      -- of quantified variables
-- Post: Equations oriented from the template (matching instance) to the workitem!
improveFromInstEnv :: InstEnvs
-> (PredType -> SrcSpan -> loc) -> PredType -> [FunDepEqn loc]
improveFromInstEnv inst_env :: InstEnvs
inst_env mk_loc :: PredType -> SrcSpan -> loc
mk_loc pred :: PredType
pred
  | Just (cls :: Class
cls, tys :: [PredType]
tys) <- ASSERT2( isClassPred pred, ppr pred )
                       PredType -> Maybe (Class, [PredType])
getClassPredTys_maybe PredType
pred
  , let (cls_tvs :: [TyVar]
cls_tvs, cls_fds :: [FunDep TyVar]
cls_fds) = Class -> ([TyVar], [FunDep TyVar])
classTvsFds Class
cls
        instances :: [ClsInst]
instances          = InstEnvs -> Class -> [ClsInst]
classInstances InstEnvs
inst_env Class
cls
        rough_tcs :: [Maybe Name]
rough_tcs          = [PredType] -> [Maybe Name]
roughMatchTcs [PredType]
tys
  = [ FDEqn :: forall loc.
[TyVar]
-> [TypeEqn] -> PredType -> PredType -> loc -> FunDepEqn loc
FDEqn { fd_qtvs :: [TyVar]
fd_qtvs = [TyVar]
meta_tvs, fd_eqs :: [TypeEqn]
fd_eqs = [TypeEqn]
eqs
            , fd_pred1 :: PredType
fd_pred1 = PredType
p_inst, fd_pred2 :: PredType
fd_pred2 = PredType
pred
            , fd_loc :: loc
fd_loc = PredType -> SrcSpan -> loc
mk_loc PredType
p_inst (TyVar -> SrcSpan
forall a. NamedThing a => a -> SrcSpan
getSrcSpan (ClsInst -> TyVar
is_dfun ClsInst
ispec)) }
    | FunDep TyVar
fd <- [FunDep TyVar]
cls_fds             -- Iterate through the fundeps first,
                                -- because there often are none!
    , let trimmed_tcs :: [Maybe Name]
trimmed_tcs = [TyVar] -> FunDep TyVar -> [Maybe Name] -> [Maybe Name]
trimRoughMatchTcs [TyVar]
cls_tvs FunDep TyVar
fd [Maybe Name]
rough_tcs
                -- Trim the rough_tcs based on the head of the fundep.
                -- Remember that instanceCantMatch treats both arguments
                -- symmetrically, so it's ok to trim the rough_tcs,
                -- rather than trimming each inst_tcs in turn
    , ClsInst
ispec <- [ClsInst]
instances
    , (meta_tvs :: [TyVar]
meta_tvs, eqs :: [TypeEqn]
eqs) <- [TyVar]
-> FunDep TyVar
-> ClsInst
-> [PredType]
-> [Maybe Name]
-> [([TyVar], [TypeEqn])]
improveClsFD [TyVar]
cls_tvs FunDep TyVar
fd ClsInst
ispec
                                      [PredType]
tys [Maybe Name]
trimmed_tcs -- NB: orientation
    , let p_inst :: PredType
p_inst = Class -> [PredType] -> PredType
mkClassPred Class
cls (ClsInst -> [PredType]
is_tys ClsInst
ispec)
    ]
improveFromInstEnv _ _ _ = []


improveClsFD :: [TyVar] -> FunDep TyVar    -- One functional dependency from the class
             -> ClsInst                    -- An instance template
             -> [Type] -> [Maybe Name]     -- Arguments of this (C tys) predicate
             -> [([TyCoVar], [TypeEqn])]   -- Empty or singleton

improveClsFD :: [TyVar]
-> FunDep TyVar
-> ClsInst
-> [PredType]
-> [Maybe Name]
-> [([TyVar], [TypeEqn])]
improveClsFD clas_tvs :: [TyVar]
clas_tvs fd :: FunDep TyVar
fd
             (ClsInst { is_tvs :: ClsInst -> [TyVar]
is_tvs = [TyVar]
qtvs, is_tys :: ClsInst -> [PredType]
is_tys = [PredType]
tys_inst, is_tcs :: ClsInst -> [Maybe Name]
is_tcs = [Maybe Name]
rough_tcs_inst })
             tys_actual :: [PredType]
tys_actual rough_tcs_actual :: [Maybe Name]
rough_tcs_actual

-- Compare instance      {a,b}    C sx sp sy sq
--         with wanted     [W] C tx tp ty tq
--         for fundep (x,y -> p,q)  from class  (C x p y q)
-- If (sx,sy) unifies with (tx,ty), take the subst S

-- 'qtvs' are the quantified type variables, the ones which can be instantiated
-- to make the types match.  For example, given
--      class C a b | a->b where ...
--      instance C (Maybe x) (Tree x) where ..
--
-- and a wanted constraint of form (C (Maybe t1) t2),
-- then we will call checkClsFD with
--
--      is_qtvs = {x}, is_tys = [Maybe x,  Tree x]
--                     tys_actual = [Maybe t1, t2]
--
-- We can instantiate x to t1, and then we want to force
--      (Tree x) [t1/x]  ~   t2

  | [Maybe Name] -> [Maybe Name] -> Bool
instanceCantMatch [Maybe Name]
rough_tcs_inst [Maybe Name]
rough_tcs_actual
  = []          -- Filter out ones that can't possibly match,

  | Bool
otherwise
  = ASSERT2( equalLength tys_inst tys_actual &&
             equalLength tys_inst clas_tvs
            , ppr tys_inst <+> ppr tys_actual )

    case [PredType] -> [PredType] -> Maybe TCvSubst
tcMatchTyKis [PredType]
ltys1 [PredType]
ltys2 of
        Nothing  -> []
        Just subst :: TCvSubst
subst | Maybe TCvSubst -> Bool
forall a. Maybe a -> Bool
isJust (TCvSubst -> [PredType] -> [PredType] -> Maybe TCvSubst
tcMatchTyKisX TCvSubst
subst [PredType]
rtys1 [PredType]
rtys2)
                        -- Don't include any equations that already hold.
                        -- Reason: then we know if any actual improvement has happened,
                        --         in which case we need to iterate the solver
                        -- In making this check we must taking account of the fact that any
                        -- qtvs that aren't already instantiated can be instantiated to anything
                        -- at all
                        -- NB: We can't do this 'is-useful-equation' check element-wise
                        --     because of:
                        --           class C a b c | a -> b c
                        --           instance C Int x x
                        --           [Wanted] C Int alpha Int
                        -- We would get that  x -> alpha  (isJust) and x -> Int (isJust)
                        -- so we would produce no FDs, which is clearly wrong.
                  -> []

                  | [TypeEqn] -> Bool
forall (t :: * -> *) a. Foldable t => t a -> Bool
null [TypeEqn]
fdeqs
                  -> []

                  | Bool
otherwise
                  -> -- pprTrace "iproveClsFD" (vcat
                     --  [ text "is_tvs =" <+> ppr qtvs
                     --  , text "tys_inst =" <+> ppr tys_inst
                     --  , text "tys_actual =" <+> ppr tys_actual
                     --  , text "ltys1 =" <+> ppr ltys1
                     --  , text "ltys2 =" <+> ppr ltys2
                     --  , text "subst =" <+> ppr subst ]) $
                     [([TyVar]
meta_tvs, [TypeEqn]
fdeqs)]
                        -- We could avoid this substTy stuff by producing the eqn
                        -- (qtvs, ls1++rs1, ls2++rs2)
                        -- which will re-do the ls1/ls2 unification when the equation is
                        -- executed.  What we're doing instead is recording the partial
                        -- work of the ls1/ls2 unification leaving a smaller unification problem
                  where
                    rtys1' :: [PredType]
rtys1' = (PredType -> PredType) -> [PredType] -> [PredType]
forall a b. (a -> b) -> [a] -> [b]
map (TCvSubst -> PredType -> PredType
substTyUnchecked TCvSubst
subst) [PredType]
rtys1

                    fdeqs :: [TypeEqn]
fdeqs = (PredType -> PredType -> Bool)
-> [PredType] -> [PredType] -> [TypeEqn]
zipAndComputeFDEqs (\_ _ -> Bool
False) [PredType]
rtys1' [PredType]
rtys2
                        -- Don't discard anything!
                        -- We could discard equal types but it's an overkill to call
                        -- eqType again, since we know for sure that /at least one/
                        -- equation in there is useful)

                    meta_tvs :: [TyVar]
meta_tvs = [ TyVar -> PredType -> TyVar
setVarType TyVar
tv (TCvSubst -> PredType -> PredType
substTyUnchecked TCvSubst
subst (TyVar -> PredType
varType TyVar
tv))
                               | TyVar
tv <- [TyVar]
qtvs, TyVar
tv TyVar -> TCvSubst -> Bool
`notElemTCvSubst` TCvSubst
subst ]
                        -- meta_tvs are the quantified type variables
                        -- that have not been substituted out
                        --
                        -- Eg.  class C a b | a -> b
                        --      instance C Int [y]
                        -- Given constraint C Int z
                        -- we generate the equation
                        --      ({y}, [y], z)
                        --
                        -- But note (a) we get them from the dfun_id, so they are *in order*
                        --              because the kind variables may be mentioned in the
                        --              type variabes' kinds
                        --          (b) we must apply 'subst' to the kinds, in case we have
                        --              matched out a kind variable, but not a type variable
                        --              whose kind mentions that kind variable!
                        --          Trac #6015, #6068
  where
    (ltys1 :: [PredType]
ltys1, rtys1 :: [PredType]
rtys1) = FunDep TyVar -> [TyVar] -> [PredType] -> FunDep PredType
instFD FunDep TyVar
fd [TyVar]
clas_tvs [PredType]
tys_inst
    (ltys2 :: [PredType]
ltys2, rtys2 :: [PredType]
rtys2) = FunDep TyVar -> [TyVar] -> [PredType] -> FunDep PredType
instFD FunDep TyVar
fd [TyVar]
clas_tvs [PredType]
tys_actual

{-
%************************************************************************
%*                                                                      *
        The Coverage condition for instance declarations
*                                                                      *
************************************************************************

Note [Coverage condition]
~~~~~~~~~~~~~~~~~~~~~~~~~
Example
      class C a b | a -> b
      instance theta => C t1 t2

For the coverage condition, we check
   (normal)    fv(t2) `subset` fv(t1)
   (liberal)   fv(t2) `subset` oclose(fv(t1), theta)

The liberal version  ensures the self-consistency of the instance, but
it does not guarantee termination. Example:

   class Mul a b c | a b -> c where
        (.*.) :: a -> b -> c

   instance Mul Int Int Int where (.*.) = (*)
   instance Mul Int Float Float where x .*. y = fromIntegral x * y
   instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v

In the third instance, it's not the case that fv([c]) `subset` fv(a,[b]).
But it is the case that fv([c]) `subset` oclose( theta, fv(a,[b]) )

But it is a mistake to accept the instance because then this defn:
        f = \ b x y -> if b then x .*. [y] else y
makes instance inference go into a loop, because it requires the constraint
        Mul a [b] b
-}

checkInstCoverage :: Bool   -- Be liberal
                  -> Class -> [PredType] -> [Type]
                  -> Validity
-- "be_liberal" flag says whether to use "liberal" coverage of
--              See Note [Coverage Condition] below
--
-- Return values
--    Nothing  => no problems
--    Just msg => coverage problem described by msg

checkInstCoverage :: Bool -> Class -> [PredType] -> [PredType] -> Validity
checkInstCoverage be_liberal :: Bool
be_liberal clas :: Class
clas theta :: [PredType]
theta inst_taus :: [PredType]
inst_taus
  = [Validity] -> Validity
allValid ((FunDep TyVar -> Validity) -> [FunDep TyVar] -> [Validity]
forall a b. (a -> b) -> [a] -> [b]
map FunDep TyVar -> Validity
fundep_ok [FunDep TyVar]
fds)
  where
    (tyvars :: [TyVar]
tyvars, fds :: [FunDep TyVar]
fds) = Class -> ([TyVar], [FunDep TyVar])
classTvsFds Class
clas
    fundep_ok :: FunDep TyVar -> Validity
fundep_ok fd :: FunDep TyVar
fd
       | Pair Bool -> Bool
forall (t :: * -> *). Foldable t => t Bool -> Bool
and (VarSet -> Bool
isEmptyVarSet (VarSet -> Bool) -> Pair VarSet -> Pair Bool
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Pair VarSet
undetermined_tvs) = Validity
IsValid
       | Bool
otherwise                                = SDoc -> Validity
NotValid SDoc
msg
       where
         (ls :: [PredType]
ls,rs :: [PredType]
rs) = FunDep TyVar -> [TyVar] -> [PredType] -> FunDep PredType
instFD FunDep TyVar
fd [TyVar]
tyvars [PredType]
inst_taus
         ls_tvs :: VarSet
ls_tvs = [PredType] -> VarSet
tyCoVarsOfTypes [PredType]
ls
         rs_tvs :: Pair VarSet
rs_tvs = [PredType] -> Pair VarSet
splitVisVarsOfTypes [PredType]
rs

         undetermined_tvs :: Pair VarSet
undetermined_tvs | Bool
be_liberal = Pair VarSet
liberal_undet_tvs
                          | Bool
otherwise  = Pair VarSet
conserv_undet_tvs

         closed_ls_tvs :: VarSet
closed_ls_tvs = [PredType] -> VarSet -> VarSet
oclose [PredType]
theta VarSet
ls_tvs
         liberal_undet_tvs :: Pair VarSet
liberal_undet_tvs = (VarSet -> VarSet -> VarSet
`minusVarSet` VarSet
closed_ls_tvs) (VarSet -> VarSet) -> Pair VarSet -> Pair VarSet
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Pair VarSet
rs_tvs
         conserv_undet_tvs :: Pair VarSet
conserv_undet_tvs = (VarSet -> VarSet -> VarSet
`minusVarSet` VarSet
ls_tvs)        (VarSet -> VarSet) -> Pair VarSet -> Pair VarSet
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Pair VarSet
rs_tvs

         undet_set :: VarSet
undet_set = Pair VarSet -> VarSet
forall (t :: * -> *) m. (Foldable t, Monoid m) => t m -> m
fold Pair VarSet
undetermined_tvs

         msg :: SDoc
msg = Bool -> SDoc -> SDoc
pprWithExplicitKindsWhen
                 (VarSet -> Bool
isEmptyVarSet (VarSet -> Bool) -> VarSet -> Bool
forall a b. (a -> b) -> a -> b
$ Pair VarSet -> VarSet
forall a. Pair a -> a
pSnd Pair VarSet
undetermined_tvs) (SDoc -> SDoc) -> SDoc -> SDoc
forall a b. (a -> b) -> a -> b
$
               [SDoc] -> SDoc
vcat [ -- text "ls_tvs" <+> ppr ls_tvs
                      -- , text "closed ls_tvs" <+> ppr (closeOverKinds ls_tvs)
                      -- , text "theta" <+> ppr theta
                      -- , text "oclose" <+> ppr (oclose theta (closeOverKinds ls_tvs))
                      -- , text "rs_tvs" <+> ppr rs_tvs
                      [SDoc] -> SDoc
sep [ String -> SDoc
text "The"
                            SDoc -> SDoc -> SDoc
<+> Bool -> SDoc -> SDoc
ppWhen Bool
be_liberal (String -> SDoc
text "liberal")
                            SDoc -> SDoc -> SDoc
<+> String -> SDoc
text "coverage condition fails in class"
                            SDoc -> SDoc -> SDoc
<+> SDoc -> SDoc
quotes (Class -> SDoc
forall a. Outputable a => a -> SDoc
ppr Class
clas)
                          , Int -> SDoc -> SDoc
nest 2 (SDoc -> SDoc) -> SDoc -> SDoc
forall a b. (a -> b) -> a -> b
$ String -> SDoc
text "for functional dependency:"
                            SDoc -> SDoc -> SDoc
<+> SDoc -> SDoc
quotes (FunDep TyVar -> SDoc
forall a. Outputable a => FunDep a -> SDoc
pprFunDep FunDep TyVar
fd) ]
                    , [SDoc] -> SDoc
sep [ String -> SDoc
text "Reason: lhs type"SDoc -> SDoc -> SDoc
<>[PredType] -> SDoc
forall a. [a] -> SDoc
plural [PredType]
ls SDoc -> SDoc -> SDoc
<+> [PredType] -> SDoc
forall a. Outputable a => [a] -> SDoc
pprQuotedList [PredType]
ls
                          , Int -> SDoc -> SDoc
nest 2 (SDoc -> SDoc) -> SDoc -> SDoc
forall a b. (a -> b) -> a -> b
$
                            (if [PredType] -> Bool
forall a. [a] -> Bool
isSingleton [PredType]
ls
                             then String -> SDoc
text "does not"
                             else String -> SDoc
text "do not jointly")
                            SDoc -> SDoc -> SDoc
<+> String -> SDoc
text "determine rhs type"SDoc -> SDoc -> SDoc
<>[PredType] -> SDoc
forall a. [a] -> SDoc
plural [PredType]
rs
                            SDoc -> SDoc -> SDoc
<+> [PredType] -> SDoc
forall a. Outputable a => [a] -> SDoc
pprQuotedList [PredType]
rs ]
                    , String -> SDoc
text "Un-determined variable" SDoc -> SDoc -> SDoc
<> VarSet -> SDoc
pluralVarSet VarSet
undet_set SDoc -> SDoc -> SDoc
<> SDoc
colon
                            SDoc -> SDoc -> SDoc
<+> VarSet -> ([TyVar] -> SDoc) -> SDoc
pprVarSet VarSet
undet_set ((TyVar -> SDoc) -> [TyVar] -> SDoc
forall a. (a -> SDoc) -> [a] -> SDoc
pprWithCommas TyVar -> SDoc
forall a. Outputable a => a -> SDoc
ppr)
                    , Bool -> SDoc -> SDoc
ppWhen (Bool -> Bool
not Bool
be_liberal Bool -> Bool -> Bool
&&
                              Pair Bool -> Bool
forall (t :: * -> *). Foldable t => t Bool -> Bool
and (VarSet -> Bool
isEmptyVarSet (VarSet -> Bool) -> Pair VarSet -> Pair Bool
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Pair VarSet
liberal_undet_tvs)) (SDoc -> SDoc) -> SDoc -> SDoc
forall a b. (a -> b) -> a -> b
$
                      String -> SDoc
text "Using UndecidableInstances might help" ]

{- Note [Closing over kinds in coverage]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we have a fundep  (a::k) -> b
Then if 'a' is instantiated to (x y), where x:k2->*, y:k2,
then fixing x really fixes k2 as well, and so k2 should be added to
the lhs tyvars in the fundep check.

Example (Trac #8391), using liberal coverage
      data Foo a = ...  -- Foo :: forall k. k -> *
      class Bar a b | a -> b
      instance Bar a (Foo a)

    In the instance decl, (a:k) does fix (Foo k a), but only if we notice
    that (a:k) fixes k.  Trac #10109 is another example.

Here is a more subtle example, from HList-0.4.0.0 (Trac #10564)

  class HasFieldM (l :: k) r (v :: Maybe *)
        | l r -> v where ...
  class HasFieldM1 (b :: Maybe [*]) (l :: k) r v
        | b l r -> v where ...
  class HMemberM (e1 :: k) (l :: [k]) (r :: Maybe [k])
        | e1 l -> r

  data Label :: k -> *
  type family LabelsOf (a :: [*]) ::  *

  instance (HMemberM (Label {k} (l::k)) (LabelsOf xs) b,
            HasFieldM1 b l (r xs) v)
         => HasFieldM l (r xs) v where

Is the instance OK? Does {l,r,xs} determine v?  Well:

  * From the instance constraint HMemberM (Label k l) (LabelsOf xs) b,
    plus the fundep "| el l -> r" in class HMameberM,
    we get {l,k,xs} -> b

  * Note the 'k'!! We must call closeOverKinds on the seed set
    ls_tvs = {l,r,xs}, BEFORE doing oclose, else the {l,k,xs}->b
    fundep won't fire.  This was the reason for #10564.

  * So starting from seeds {l,r,xs,k} we do oclose to get
    first {l,r,xs,k,b}, via the HMemberM constraint, and then
    {l,r,xs,k,b,v}, via the HasFieldM1 constraint.

  * And that fixes v.

However, we must closeOverKinds whenever augmenting the seed set
in oclose!  Consider Trac #10109:

  data Succ a   -- Succ :: forall k. k -> *
  class Add (a :: k1) (b :: k2) (ab :: k3) | a b -> ab
  instance (Add a b ab) => Add (Succ {k1} (a :: k1))
                               b
                               (Succ {k3} (ab :: k3})

We start with seed set {a:k1,b:k2} and closeOverKinds to {a,k1,b,k2}.
Now use the fundep to extend to {a,k1,b,k2,ab}.  But we need to
closeOverKinds *again* now to {a,k1,b,k2,ab,k3}, so that we fix all
the variables free in (Succ {k3} ab).

Bottom line:
  * closeOverKinds on initial seeds (done automatically
    by tyCoVarsOfTypes in checkInstCoverage)
  * and closeOverKinds whenever extending those seeds (in oclose)

Note [The liberal coverage condition]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(oclose preds tvs) closes the set of type variables tvs,
wrt functional dependencies in preds.  The result is a superset
of the argument set.  For example, if we have
        class C a b | a->b where ...
then
        oclose [C (x,y) z, C (x,p) q] {x,y} = {x,y,z}
because if we know x and y then that fixes z.

We also use equality predicates in the predicates; if we have an
assumption `t1 ~ t2`, then we use the fact that if we know `t1` we
also know `t2` and the other way.
  eg    oclose [C (x,y) z, a ~ x] {a,y} = {a,y,z,x}

oclose is used (only) when checking the coverage condition for
an instance declaration

Note [Equality superclasses]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we have
  class (a ~ [b]) => C a b

Remember from Note [The equality types story] in TysPrim, that
  * (a ~~ b) is a superclass of (a ~ b)
  * (a ~# b) is a superclass of (a ~~ b)

So when oclose expands superclasses we'll get a (a ~# [b]) superclass.
But that's an EqPred not a ClassPred, and we jolly well do want to
account for the mutual functional dependencies implied by (t1 ~# t2).
Hence the EqPred handling in oclose.  See Trac #10778.

Note [Care with type functions]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider (Trac #12803)
  class C x y | x -> y
  type family F a b
  type family G c d = r | r -> d

Now consider
  oclose (C (F a b) (G c d)) {a,b}

Knowing {a,b} fixes (F a b) regardless of the injectivity of F.
But knowing (G c d) fixes only {d}, because G is only injective
in its second parameter.

Hence the tyCoVarsOfTypes/injTyVarsOfTypes dance in tv_fds.
-}

oclose :: [PredType] -> TyCoVarSet -> TyCoVarSet
-- See Note [The liberal coverage condition]
oclose :: [PredType] -> VarSet -> VarSet
oclose preds :: [PredType]
preds fixed_tvs :: VarSet
fixed_tvs
  | [(VarSet, VarSet)] -> Bool
forall (t :: * -> *) a. Foldable t => t a -> Bool
null [(VarSet, VarSet)]
tv_fds = VarSet
fixed_tvs -- Fast escape hatch for common case.
  | Bool
otherwise   = (VarSet -> VarSet) -> VarSet -> VarSet
fixVarSet VarSet -> VarSet
extend VarSet
fixed_tvs
  where
    extend :: VarSet -> VarSet
extend fixed_tvs :: VarSet
fixed_tvs = (VarSet -> (VarSet, VarSet) -> VarSet)
-> VarSet -> [(VarSet, VarSet)] -> VarSet
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl' VarSet -> (VarSet, VarSet) -> VarSet
add VarSet
fixed_tvs [(VarSet, VarSet)]
tv_fds
       where
          add :: VarSet -> (VarSet, VarSet) -> VarSet
add fixed_tvs :: VarSet
fixed_tvs (ls :: VarSet
ls,rs :: VarSet
rs)
            | VarSet
ls VarSet -> VarSet -> Bool
`subVarSet` VarSet
fixed_tvs = VarSet
fixed_tvs VarSet -> VarSet -> VarSet
`unionVarSet` VarSet -> VarSet
closeOverKinds VarSet
rs
            | Bool
otherwise                = VarSet
fixed_tvs
            -- closeOverKinds: see Note [Closing over kinds in coverage]

    tv_fds  :: [(TyCoVarSet,TyCoVarSet)]
    tv_fds :: [(VarSet, VarSet)]
tv_fds  = [ ([PredType] -> VarSet
tyCoVarsOfTypes [PredType]
ls, [PredType] -> VarSet
injTyVarsOfTypes [PredType]
rs)
                  -- See Note [Care with type functions]
              | PredType
pred <- [PredType]
preds
              , PredType
pred' <- PredType
pred PredType -> [PredType] -> [PredType]
forall a. a -> [a] -> [a]
: PredType -> [PredType]
transSuperClasses PredType
pred
                   -- Look for fundeps in superclasses too
              , (ls :: [PredType]
ls, rs :: [PredType]
rs) <- PredType -> [FunDep PredType]
determined PredType
pred' ]

    determined :: PredType -> [([Type],[Type])]
    determined :: PredType -> [FunDep PredType]
determined pred :: PredType
pred
       = case PredType -> PredTree
classifyPredType PredType
pred of
            EqPred NomEq t1 :: PredType
t1 t2 :: PredType
t2 -> [([PredType
t1],[PredType
t2]), ([PredType
t2],[PredType
t1])]
               -- See Note [Equality superclasses]
            ClassPred cls :: Class
cls tys :: [PredType]
tys  -> [ FunDep TyVar -> [TyVar] -> [PredType] -> FunDep PredType
instFD FunDep TyVar
fd [TyVar]
cls_tvs [PredType]
tys
                                  | let (cls_tvs :: [TyVar]
cls_tvs, cls_fds :: [FunDep TyVar]
cls_fds) = Class -> ([TyVar], [FunDep TyVar])
classTvsFds Class
cls
                                  , FunDep TyVar
fd <- [FunDep TyVar]
cls_fds ]
            _ -> []


{- *********************************************************************
*                                                                      *
        Check that a new instance decl is OK wrt fundeps
*                                                                      *
************************************************************************

Here is the bad case:
        class C a b | a->b where ...
        instance C Int Bool where ...
        instance C Int Char where ...

The point is that a->b, so Int in the first parameter must uniquely
determine the second.  In general, given the same class decl, and given

        instance C s1 s2 where ...
        instance C t1 t2 where ...

Then the criterion is: if U=unify(s1,t1) then U(s2) = U(t2).

Matters are a little more complicated if there are free variables in
the s2/t2.

        class D a b c | a -> b
        instance D a b => D [(a,a)] [b] Int
        instance D a b => D [a]     [b] Bool

The instance decls don't overlap, because the third parameter keeps
them separate.  But we want to make sure that given any constraint
        D s1 s2 s3
if s1 matches

Note [Bogus consistency check]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In checkFunDeps we check that a new ClsInst is consistent with all the
ClsInsts in the environment.

The bogus aspect is discussed in Trac #10675. Currenty it if the two
types are *contradicatory*, using (isNothing . tcUnifyTys).  But all
the papers say we should check if the two types are *equal* thus
   not (substTys subst rtys1 `eqTypes` substTys subst rtys2)
For now I'm leaving the bogus form because that's the way it has
been for years.
-}

checkFunDeps :: InstEnvs -> ClsInst -> [ClsInst]
-- The Consistency Check.
-- Check whether adding DFunId would break functional-dependency constraints
-- Used only for instance decls defined in the module being compiled
-- Returns a list of the ClsInst in InstEnvs that are inconsistent
-- with the proposed new ClsInst
checkFunDeps :: InstEnvs -> ClsInst -> [ClsInst]
checkFunDeps inst_envs :: InstEnvs
inst_envs (ClsInst { is_tvs :: ClsInst -> [TyVar]
is_tvs = [TyVar]
qtvs1, is_cls :: ClsInst -> Class
is_cls = Class
cls
                                , is_tys :: ClsInst -> [PredType]
is_tys = [PredType]
tys1, is_tcs :: ClsInst -> [Maybe Name]
is_tcs = [Maybe Name]
rough_tcs1 })
  | [FunDep TyVar] -> Bool
forall (t :: * -> *) a. Foldable t => t a -> Bool
null [FunDep TyVar]
fds
  = []
  | Bool
otherwise
  = (ClsInst -> ClsInst -> Bool) -> [ClsInst] -> [ClsInst]
forall a. (a -> a -> Bool) -> [a] -> [a]
nubBy ClsInst -> ClsInst -> Bool
eq_inst ([ClsInst] -> [ClsInst]) -> [ClsInst] -> [ClsInst]
forall a b. (a -> b) -> a -> b
$
    [ ClsInst
ispec | ClsInst
ispec <- [ClsInst]
cls_insts
            , FunDep TyVar
fd    <- [FunDep TyVar]
fds
            , FunDep TyVar -> ClsInst -> Bool
is_inconsistent FunDep TyVar
fd ClsInst
ispec ]
  where
    cls_insts :: [ClsInst]
cls_insts      = InstEnvs -> Class -> [ClsInst]
classInstances InstEnvs
inst_envs Class
cls
    (cls_tvs :: [TyVar]
cls_tvs, fds :: [FunDep TyVar]
fds) = Class -> ([TyVar], [FunDep TyVar])
classTvsFds Class
cls
    qtv_set1 :: VarSet
qtv_set1       = [TyVar] -> VarSet
mkVarSet [TyVar]
qtvs1

    is_inconsistent :: FunDep TyVar -> ClsInst -> Bool
is_inconsistent fd :: FunDep TyVar
fd (ClsInst { is_tvs :: ClsInst -> [TyVar]
is_tvs = [TyVar]
qtvs2, is_tys :: ClsInst -> [PredType]
is_tys = [PredType]
tys2, is_tcs :: ClsInst -> [Maybe Name]
is_tcs = [Maybe Name]
rough_tcs2 })
      | [Maybe Name] -> [Maybe Name] -> Bool
instanceCantMatch [Maybe Name]
trimmed_tcs [Maybe Name]
rough_tcs2
      = Bool
False
      | Bool
otherwise
      = case (TyVar -> BindFlag) -> [PredType] -> [PredType] -> Maybe TCvSubst
tcUnifyTyKis TyVar -> BindFlag
bind_fn [PredType]
ltys1 [PredType]
ltys2 of
          Nothing         -> Bool
False
          Just subst :: TCvSubst
subst
            -> Maybe TCvSubst -> Bool
forall a. Maybe a -> Bool
isNothing (Maybe TCvSubst -> Bool) -> Maybe TCvSubst -> Bool
forall a b. (a -> b) -> a -> b
$   -- Bogus legacy test (Trac #10675)
                             -- See Note [Bogus consistency check]
               (TyVar -> BindFlag) -> [PredType] -> [PredType] -> Maybe TCvSubst
tcUnifyTyKis TyVar -> BindFlag
bind_fn (TCvSubst -> [PredType] -> [PredType]
substTysUnchecked TCvSubst
subst [PredType]
rtys1) (TCvSubst -> [PredType] -> [PredType]
substTysUnchecked TCvSubst
subst [PredType]
rtys2)

      where
        trimmed_tcs :: [Maybe Name]
trimmed_tcs    = [TyVar] -> FunDep TyVar -> [Maybe Name] -> [Maybe Name]
trimRoughMatchTcs [TyVar]
cls_tvs FunDep TyVar
fd [Maybe Name]
rough_tcs1
        (ltys1 :: [PredType]
ltys1, rtys1 :: [PredType]
rtys1) = FunDep TyVar -> [TyVar] -> [PredType] -> FunDep PredType
instFD FunDep TyVar
fd [TyVar]
cls_tvs [PredType]
tys1
        (ltys2 :: [PredType]
ltys2, rtys2 :: [PredType]
rtys2) = FunDep TyVar -> [TyVar] -> [PredType] -> FunDep PredType
instFD FunDep TyVar
fd [TyVar]
cls_tvs [PredType]
tys2
        qtv_set2 :: VarSet
qtv_set2       = [TyVar] -> VarSet
mkVarSet [TyVar]
qtvs2
        bind_fn :: TyVar -> BindFlag
bind_fn tv :: TyVar
tv | TyVar
tv TyVar -> VarSet -> Bool
`elemVarSet` VarSet
qtv_set1 = BindFlag
BindMe
                   | TyVar
tv TyVar -> VarSet -> Bool
`elemVarSet` VarSet
qtv_set2 = BindFlag
BindMe
                   | Bool
otherwise                = BindFlag
Skolem

    eq_inst :: ClsInst -> ClsInst -> Bool
eq_inst i1 :: ClsInst
i1 i2 :: ClsInst
i2 = ClsInst -> TyVar
instanceDFunId ClsInst
i1 TyVar -> TyVar -> Bool
forall a. Eq a => a -> a -> Bool
== ClsInst -> TyVar
instanceDFunId ClsInst
i2
        -- A single instance may appear twice in the un-nubbed conflict list
        -- because it may conflict with more than one fundep.  E.g.
        --      class C a b c | a -> b, a -> c
        --      instance C Int Bool Bool
        --      instance C Int Char Char
        -- The second instance conflicts with the first by *both* fundeps

trimRoughMatchTcs :: [TyVar] -> FunDep TyVar -> [Maybe Name] -> [Maybe Name]
-- Computing rough_tcs for a particular fundep
--     class C a b c | a -> b where ...
-- For each instance .... => C ta tb tc
-- we want to match only on the type ta; so our
-- rough-match thing must similarly be filtered.
-- Hence, we Nothing-ise the tb and tc types right here
--
-- Result list is same length as input list, just with more Nothings
trimRoughMatchTcs :: [TyVar] -> FunDep TyVar -> [Maybe Name] -> [Maybe Name]
trimRoughMatchTcs clas_tvs :: [TyVar]
clas_tvs (ltvs :: [TyVar]
ltvs, _) mb_tcs :: [Maybe Name]
mb_tcs
  = (TyVar -> Maybe Name -> Maybe Name)
-> [TyVar] -> [Maybe Name] -> [Maybe Name]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith TyVar -> Maybe Name -> Maybe Name
forall a. TyVar -> Maybe a -> Maybe a
select [TyVar]
clas_tvs [Maybe Name]
mb_tcs
  where
    select :: TyVar -> Maybe a -> Maybe a
select clas_tv :: TyVar
clas_tv mb_tc :: Maybe a
mb_tc | TyVar
clas_tv TyVar -> [TyVar] -> Bool
forall (t :: * -> *) a. (Foldable t, Eq a) => a -> t a -> Bool
`elem` [TyVar]
ltvs = Maybe a
mb_tc
                         | Bool
otherwise           = Maybe a
forall a. Maybe a
Nothing