{-# LANGUAGE DerivingStrategies #-} {-# LANGUAGE RankNTypes #-} {-# LANGUAGE TypeApplications #-} {-# OPTIONS_GHC -Wno-incomplete-uni-patterns #-} module GHC.Tc.Solver.InertSet ( -- * The work list WorkList(..), isEmptyWorkList, emptyWorkList, extendWorkListNonEq, extendWorkListCt, extendWorkListCts, extendWorkListEq, appendWorkList, extendWorkListImplic, workListSize, selectWorkItem, -- * The inert set InertSet(..), InertCans(..), InertEqs, emptyInert, addInertItem, noMatchableGivenDicts, noGivenNewtypeReprEqs, mightEqualLater, prohibitedSuperClassSolve, -- * Inert equalities foldTyEqs, delEq, findEq, partitionInertEqs, partitionFunEqs, -- * Kick-out kickOutRewritableLHS, -- * Cycle breaker vars CycleBreakerVarStack, pushCycleBreakerVarStack, insertCycleBreakerBinding, forAllCycleBreakerBindings_ ) where import GHC.Prelude import GHC.Tc.Types.Constraint import GHC.Tc.Types.Origin import GHC.Tc.Solver.Types import GHC.Tc.Utils.TcType import GHC.Types.Var import GHC.Types.Var.Env import GHC.Core.Reduction import GHC.Core.Predicate import GHC.Core.TyCo.FVs import qualified GHC.Core.TyCo.Rep as Rep import GHC.Core.Class( Class ) import GHC.Core.TyCon import GHC.Core.Unify import GHC.Data.Bag import GHC.Utils.Misc ( partitionWith ) import GHC.Utils.Outputable import GHC.Utils.Panic import Data.List ( partition ) import Data.List.NonEmpty ( NonEmpty(..), (<|) ) import qualified Data.List.NonEmpty as NE import GHC.Utils.Panic.Plain import GHC.Data.Maybe import Control.Monad ( forM_ ) {- ************************************************************************ * * * Worklists * * Canonical and non-canonical constraints that the simplifier has to * * work on. Including their simplification depths. * * * * * ************************************************************************ Note [WorkList priorities] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ A WorkList contains canonical and non-canonical items (of all flavours). Notice that each Ct now has a simplification depth. We may consider using this depth for prioritization as well in the future. As a simple form of priority queue, our worklist separates out * equalities (wl_eqs); see Note [Prioritise equalities] * all the rest (wl_rest) Note [Prioritise equalities] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It's very important to process equalities /first/: * (Efficiency) The general reason to do so is that if we process a class constraint first, we may end up putting it into the inert set and then kicking it out later. That's extra work compared to just doing the equality first. * (Avoiding fundep iteration) As #14723 showed, it's possible to get non-termination if we - Emit the fundep equalities for a class constraint, generating some fresh unification variables. - That leads to some unification - Which kicks out the class constraint - Which isn't solved (because there are still some more equalities in the work-list), but generates yet more fundeps Solution: prioritise equalities over class constraints * (Class equalities) We need to prioritise equalities even if they are hidden inside a class constraint; see Note [Prioritise class equalities] * (Kick-out) We want to apply this priority scheme to kicked-out constraints too (see the call to extendWorkListCt in kick_out_rewritable E.g. a CIrredCan can be a hetero-kinded (t1 ~ t2), which may become homo-kinded when kicked out, and hence we want to prioritise it. Note [Prioritise class equalities] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We prioritise equalities in the solver (see selectWorkItem). But class constraints like (a ~ b) and (a ~~ b) are actually equalities too; see Note [The equality types story] in GHC.Builtin.Types.Prim. Failing to prioritise these is inefficient (more kick-outs etc). But, worse, it can prevent us spotting a "recursive knot" among Wanted constraints. See comment:10 of #12734 for a worked-out example. So we arrange to put these particular class constraints in the wl_eqs. NB: since we do not currently apply the substitution to the inert_solved_dicts, the knot-tying still seems a bit fragile. But this makes it better. Note [Residual implications] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The wl_implics in the WorkList are the residual implication constraints that are generated while solving or canonicalising the current worklist. Specifically, when canonicalising (forall a. t1 ~ forall a. t2) from which we get the implication (forall a. t1 ~ t2) See GHC.Tc.Solver.Monad.deferTcSForAllEq -} -- See Note [WorkList priorities] data WorkList = WL { WorkList -> [Ct] wl_eqs :: [Ct] -- CEqCan, CDictCan, CIrredCan -- Given and Wanted -- Contains both equality constraints and their -- class-level variants (a~b) and (a~~b); -- See Note [Prioritise equalities] -- See Note [Prioritise class equalities] , WorkList -> [Ct] wl_rest :: [Ct] , WorkList -> Bag Implication wl_implics :: Bag Implication -- See Note [Residual implications] } appendWorkList :: WorkList -> WorkList -> WorkList appendWorkList :: WorkList -> WorkList -> WorkList appendWorkList (WL { wl_eqs :: WorkList -> [Ct] wl_eqs = [Ct] eqs1, wl_rest :: WorkList -> [Ct] wl_rest = [Ct] rest1 , wl_implics :: WorkList -> Bag Implication wl_implics = Bag Implication implics1 }) (WL { wl_eqs :: WorkList -> [Ct] wl_eqs = [Ct] eqs2, wl_rest :: WorkList -> [Ct] wl_rest = [Ct] rest2 , wl_implics :: WorkList -> Bag Implication wl_implics = Bag Implication implics2 }) = WL { wl_eqs :: [Ct] wl_eqs = [Ct] eqs1 [Ct] -> [Ct] -> [Ct] forall a. [a] -> [a] -> [a] ++ [Ct] eqs2 , wl_rest :: [Ct] wl_rest = [Ct] rest1 [Ct] -> [Ct] -> [Ct] forall a. [a] -> [a] -> [a] ++ [Ct] rest2 , wl_implics :: Bag Implication wl_implics = Bag Implication implics1 Bag Implication -> Bag Implication -> Bag Implication forall a. Bag a -> Bag a -> Bag a `unionBags` Bag Implication implics2 } workListSize :: WorkList -> Int workListSize :: WorkList -> Int workListSize (WL { wl_eqs :: WorkList -> [Ct] wl_eqs = [Ct] eqs, wl_rest :: WorkList -> [Ct] wl_rest = [Ct] rest }) = [Ct] -> Int forall a. [a] -> Int forall (t :: * -> *) a. Foldable t => t a -> Int length [Ct] eqs Int -> Int -> Int forall a. Num a => a -> a -> a + [Ct] -> Int forall a. [a] -> Int forall (t :: * -> *) a. Foldable t => t a -> Int length [Ct] rest extendWorkListEq :: Ct -> WorkList -> WorkList extendWorkListEq :: Ct -> WorkList -> WorkList extendWorkListEq Ct ct WorkList wl = WorkList wl { wl_eqs = ct : wl_eqs wl } extendWorkListNonEq :: Ct -> WorkList -> WorkList -- Extension by non equality extendWorkListNonEq :: Ct -> WorkList -> WorkList extendWorkListNonEq Ct ct WorkList wl = WorkList wl { wl_rest = ct : wl_rest wl } extendWorkListImplic :: Implication -> WorkList -> WorkList extendWorkListImplic :: Implication -> WorkList -> WorkList extendWorkListImplic Implication implic WorkList wl = WorkList wl { wl_implics = implic `consBag` wl_implics wl } extendWorkListCt :: Ct -> WorkList -> WorkList -- Agnostic extendWorkListCt :: Ct -> WorkList -> WorkList extendWorkListCt Ct ct WorkList wl = case TcType -> Pred classifyPredType (Ct -> TcType ctPred Ct ct) of EqPred {} -> Ct -> WorkList -> WorkList extendWorkListEq Ct ct WorkList wl ClassPred Class cls [TcType] _ -- See Note [Prioritise class equalities] | Class -> Bool isEqPredClass Class cls -> Ct -> WorkList -> WorkList extendWorkListEq Ct ct WorkList wl Pred _ -> Ct -> WorkList -> WorkList extendWorkListNonEq Ct ct WorkList wl extendWorkListCts :: [Ct] -> WorkList -> WorkList -- Agnostic extendWorkListCts :: [Ct] -> WorkList -> WorkList extendWorkListCts [Ct] cts WorkList wl = (Ct -> WorkList -> WorkList) -> WorkList -> [Ct] -> WorkList forall a b. (a -> b -> b) -> b -> [a] -> b forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr Ct -> WorkList -> WorkList extendWorkListCt WorkList wl [Ct] cts isEmptyWorkList :: WorkList -> Bool isEmptyWorkList :: WorkList -> Bool isEmptyWorkList (WL { wl_eqs :: WorkList -> [Ct] wl_eqs = [Ct] eqs, wl_rest :: WorkList -> [Ct] wl_rest = [Ct] rest, wl_implics :: WorkList -> Bag Implication wl_implics = Bag Implication implics }) = [Ct] -> Bool forall a. [a] -> Bool forall (t :: * -> *) a. Foldable t => t a -> Bool null [Ct] eqs Bool -> Bool -> Bool && [Ct] -> Bool forall a. [a] -> Bool forall (t :: * -> *) a. Foldable t => t a -> Bool null [Ct] rest Bool -> Bool -> Bool && Bag Implication -> Bool forall a. Bag a -> Bool isEmptyBag Bag Implication implics emptyWorkList :: WorkList emptyWorkList :: WorkList emptyWorkList = WL { wl_eqs :: [Ct] wl_eqs = [], wl_rest :: [Ct] wl_rest = [], wl_implics :: Bag Implication wl_implics = Bag Implication forall a. Bag a emptyBag } selectWorkItem :: WorkList -> Maybe (Ct, WorkList) -- See Note [Prioritise equalities] selectWorkItem :: WorkList -> Maybe (Ct, WorkList) selectWorkItem wl :: WorkList wl@(WL { wl_eqs :: WorkList -> [Ct] wl_eqs = [Ct] eqs, wl_rest :: WorkList -> [Ct] wl_rest = [Ct] rest }) | Ct ct:[Ct] cts <- [Ct] eqs = (Ct, WorkList) -> Maybe (Ct, WorkList) forall a. a -> Maybe a Just (Ct ct, WorkList wl { wl_eqs = cts }) | Ct ct:[Ct] cts <- [Ct] rest = (Ct, WorkList) -> Maybe (Ct, WorkList) forall a. a -> Maybe a Just (Ct ct, WorkList wl { wl_rest = cts }) | Bool otherwise = Maybe (Ct, WorkList) forall a. Maybe a Nothing -- Pretty printing instance Outputable WorkList where ppr :: WorkList -> SDoc ppr (WL { wl_eqs :: WorkList -> [Ct] wl_eqs = [Ct] eqs, wl_rest :: WorkList -> [Ct] wl_rest = [Ct] rest, wl_implics :: WorkList -> Bag Implication wl_implics = Bag Implication implics }) = String -> SDoc forall doc. IsLine doc => String -> doc text String "WL" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> (SDoc -> SDoc forall doc. IsLine doc => doc -> doc braces (SDoc -> SDoc) -> SDoc -> SDoc forall a b. (a -> b) -> a -> b $ [SDoc] -> SDoc forall doc. IsDoc doc => [doc] -> doc vcat [ Bool -> SDoc -> SDoc forall doc. IsOutput doc => Bool -> doc -> doc ppUnless ([Ct] -> Bool forall a. [a] -> Bool forall (t :: * -> *) a. Foldable t => t a -> Bool null [Ct] eqs) (SDoc -> SDoc) -> SDoc -> SDoc forall a b. (a -> b) -> a -> b $ String -> SDoc forall doc. IsLine doc => String -> doc text String "Eqs =" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> [SDoc] -> SDoc forall doc. IsDoc doc => [doc] -> doc vcat ((Ct -> SDoc) -> [Ct] -> [SDoc] forall a b. (a -> b) -> [a] -> [b] map Ct -> SDoc forall a. Outputable a => a -> SDoc ppr [Ct] eqs) , Bool -> SDoc -> SDoc forall doc. IsOutput doc => Bool -> doc -> doc ppUnless ([Ct] -> Bool forall a. [a] -> Bool forall (t :: * -> *) a. Foldable t => t a -> Bool null [Ct] rest) (SDoc -> SDoc) -> SDoc -> SDoc forall a b. (a -> b) -> a -> b $ String -> SDoc forall doc. IsLine doc => String -> doc text String "Non-eqs =" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> [SDoc] -> SDoc forall doc. IsDoc doc => [doc] -> doc vcat ((Ct -> SDoc) -> [Ct] -> [SDoc] forall a b. (a -> b) -> [a] -> [b] map Ct -> SDoc forall a. Outputable a => a -> SDoc ppr [Ct] rest) , Bool -> SDoc -> SDoc forall doc. IsOutput doc => Bool -> doc -> doc ppUnless (Bag Implication -> Bool forall a. Bag a -> Bool isEmptyBag Bag Implication implics) (SDoc -> SDoc) -> SDoc -> SDoc forall a b. (a -> b) -> a -> b $ SDoc -> SDoc -> SDoc forall doc. IsOutput doc => doc -> doc -> doc ifPprDebug (String -> SDoc forall doc. IsLine doc => String -> doc text String "Implics =" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> [SDoc] -> SDoc forall doc. IsDoc doc => [doc] -> doc vcat ((Implication -> SDoc) -> [Implication] -> [SDoc] forall a b. (a -> b) -> [a] -> [b] map Implication -> SDoc forall a. Outputable a => a -> SDoc ppr (Bag Implication -> [Implication] forall a. Bag a -> [a] bagToList Bag Implication implics))) (String -> SDoc forall doc. IsLine doc => String -> doc text String "(Implics omitted)") ]) {- ********************************************************************* * * InertSet: the inert set * * * * ********************************************************************* -} type CycleBreakerVarStack = NonEmpty [(TcTyVar, TcType)] -- ^ a stack of (CycleBreakerTv, original family applications) lists -- first element in the stack corresponds to current implication; -- later elements correspond to outer implications -- used to undo the cycle-breaking needed to handle -- Note [Type equality cycles] in GHC.Tc.Solver.Canonical -- Why store the outer implications? For the use in mightEqualLater (only) data InertSet = IS { InertSet -> InertCans inert_cans :: InertCans -- Canonical Given, Wanted -- Sometimes called "the inert set" , InertSet -> CycleBreakerVarStack inert_cycle_breakers :: CycleBreakerVarStack , InertSet -> FunEqMap Reduction inert_famapp_cache :: FunEqMap Reduction -- Just a hash-cons cache for use when reducing family applications -- only -- -- If F tys :-> (co, rhs, flav), -- then co :: F tys ~N rhs -- all evidence is from instances or Givens; no coercion holes here -- (We have no way of "kicking out" from the cache, so putting -- wanteds here means we can end up solving a Wanted with itself. Bad) , InertSet -> DictMap CtEvidence inert_solved_dicts :: DictMap CtEvidence -- All Wanteds, of form ev :: C t1 .. tn -- See Note [Solved dictionaries] -- and Note [Do not add superclasses of solved dictionaries] } instance Outputable InertSet where ppr :: InertSet -> SDoc ppr (IS { inert_cans :: InertSet -> InertCans inert_cans = InertCans ics , inert_solved_dicts :: InertSet -> DictMap CtEvidence inert_solved_dicts = DictMap CtEvidence solved_dicts }) = [SDoc] -> SDoc forall doc. IsDoc doc => [doc] -> doc vcat [ InertCans -> SDoc forall a. Outputable a => a -> SDoc ppr InertCans ics , Bool -> SDoc -> SDoc forall doc. IsOutput doc => Bool -> doc -> doc ppUnless ([CtEvidence] -> Bool forall a. [a] -> Bool forall (t :: * -> *) a. Foldable t => t a -> Bool null [CtEvidence] dicts) (SDoc -> SDoc) -> SDoc -> SDoc forall a b. (a -> b) -> a -> b $ String -> SDoc forall doc. IsLine doc => String -> doc text String "Solved dicts =" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> [SDoc] -> SDoc forall doc. IsDoc doc => [doc] -> doc vcat ((CtEvidence -> SDoc) -> [CtEvidence] -> [SDoc] forall a b. (a -> b) -> [a] -> [b] map CtEvidence -> SDoc forall a. Outputable a => a -> SDoc ppr [CtEvidence] dicts) ] where dicts :: [CtEvidence] dicts = Bag CtEvidence -> [CtEvidence] forall a. Bag a -> [a] bagToList (DictMap CtEvidence -> Bag CtEvidence forall a. DictMap a -> Bag a dictsToBag DictMap CtEvidence solved_dicts) emptyInertCans :: InertCans emptyInertCans :: InertCans emptyInertCans = IC { inert_eqs :: InertEqs inert_eqs = InertEqs forall a. DVarEnv a emptyDVarEnv , inert_given_eq_lvl :: TcLevel inert_given_eq_lvl = TcLevel topTcLevel , inert_given_eqs :: Bool inert_given_eqs = Bool False , inert_dicts :: DictMap Ct inert_dicts = DictMap Ct forall a. DictMap a emptyDictMap , inert_safehask :: DictMap Ct inert_safehask = DictMap Ct forall a. DictMap a emptyDictMap , inert_funeqs :: FunEqMap [Ct] inert_funeqs = FunEqMap [Ct] forall a. DictMap a emptyFunEqs , inert_insts :: [QCInst] inert_insts = [] , inert_irreds :: Cts inert_irreds = Cts emptyCts } emptyInert :: InertSet emptyInert :: InertSet emptyInert = IS { inert_cans :: InertCans inert_cans = InertCans emptyInertCans , inert_cycle_breakers :: CycleBreakerVarStack inert_cycle_breakers = [] [(TcTyVar, TcType)] -> [[(TcTyVar, TcType)]] -> CycleBreakerVarStack forall a. a -> [a] -> NonEmpty a :| [] , inert_famapp_cache :: FunEqMap Reduction inert_famapp_cache = FunEqMap Reduction forall a. DictMap a emptyFunEqs , inert_solved_dicts :: DictMap CtEvidence inert_solved_dicts = DictMap CtEvidence forall a. DictMap a emptyDictMap } {- Note [Solved dictionaries] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ When we apply a top-level instance declaration, we add the "solved" dictionary to the inert_solved_dicts. In general, we use it to avoid creating a new EvVar when we have a new goal that we have solved in the past. But in particular, we can use it to create *recursive* dictionaries. The simplest, degenerate case is instance C [a] => C [a] where ... If we have [W] d1 :: C [x] then we can apply the instance to get d1 = $dfCList d [W] d2 :: C [x] Now 'd1' goes in inert_solved_dicts, and we can solve d2 directly from d1. d1 = $dfCList d d2 = d1 See Note [Example of recursive dictionaries] VERY IMPORTANT INVARIANT: (Solved Dictionary Invariant) Every member of the inert_solved_dicts is the result of applying an instance declaration that "takes a step" An instance "takes a step" if it has the form dfunDList d1 d2 = MkD (...) (...) (...) That is, the dfun is lazy in its arguments, and guarantees to immediately return a dictionary constructor. NB: all dictionary data constructors are lazy in their arguments. This property is crucial to ensure that all dictionaries are non-bottom, which in turn ensures that the whole "recursive dictionary" idea works at all, even if we get something like rec { d = dfunDList d dx } See Note [Recursive superclasses] in GHC.Tc.TyCl.Instance. Reason: - All instances, except two exceptions listed below, "take a step" in the above sense - Exception 1: local quantified constraints have no such guarantee; indeed, adding a "solved dictionary" when applying a quantified constraint led to the ability to define unsafeCoerce in #17267. - Exception 2: the magic built-in instance for (~) has no such guarantee. It behaves as if we had class (a ~# b) => (a ~ b) where {} instance (a ~# b) => (a ~ b) where {} The "dfun" for the instance is strict in the coercion. Anyway there's no point in recording a "solved dict" for (t1 ~ t2); it's not going to allow a recursive dictionary to be constructed. Ditto (~~) and Coercible. THEREFORE we only add a "solved dictionary" - when applying an instance declaration - subject to Exceptions 1 and 2 above In implementation terms - GHC.Tc.Solver.Monad.addSolvedDict adds a new solved dictionary, conditional on the kind of instance - It is only called when applying an instance decl, in GHC.Tc.Solver.Interact.doTopReactDict - ClsInst.InstanceWhat says what kind of instance was used to solve the constraint. In particular * LocalInstance identifies quantified constraints * BuiltinEqInstance identifies the strange built-in instances for equality. - ClsInst.instanceReturnsDictCon says which kind of instance guarantees to return a dictionary constructor Other notes about solved dictionaries * See also Note [Do not add superclasses of solved dictionaries] * The inert_solved_dicts field is not rewritten by equalities, so it may get out of date. * The inert_solved_dicts are all Wanteds, never givens * We only cache dictionaries from top-level instances, not from local quantified constraints. Reason: if we cached the latter we'd need to purge the cache when bringing new quantified constraints into scope, because quantified constraints "shadow" top-level instances. Note [Do not add superclasses of solved dictionaries] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Every member of inert_solved_dicts is the result of applying a dictionary function, NOT of applying superclass selection to anything. Consider class Ord a => C a where instance Ord [a] => C [a] where ... Suppose we are trying to solve [G] d1 : Ord a [W] d2 : C [a] Then we'll use the instance decl to give [G] d1 : Ord a Solved: d2 : C [a] = $dfCList d3 [W] d3 : Ord [a] We must not add d4 : Ord [a] to the 'solved' set (by taking the superclass of d2), otherwise we'll use it to solve d3, without ever using d1, which would be a catastrophe. Solution: when extending the solved dictionaries, do not add superclasses. That's why each element of the inert_solved_dicts is the result of applying a dictionary function. Note [Example of recursive dictionaries] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ --- Example 1 data D r = ZeroD | SuccD (r (D r)); instance (Eq (r (D r))) => Eq (D r) where ZeroD == ZeroD = True (SuccD a) == (SuccD b) = a == b _ == _ = False; equalDC :: D [] -> D [] -> Bool; equalDC = (==); We need to prove (Eq (D [])). Here's how we go: [W] d1 : Eq (D []) By instance decl of Eq (D r): [W] d2 : Eq [D []] where d1 = dfEqD d2 By instance decl of Eq [a]: [W] d3 : Eq (D []) where d2 = dfEqList d3 d1 = dfEqD d2 Now this wanted can interact with our "solved" d1 to get: d3 = d1 -- Example 2: This code arises in the context of "Scrap Your Boilerplate with Class" class Sat a class Data ctx a instance Sat (ctx Char) => Data ctx Char -- dfunData1 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a] -- dfunData2 class Data Maybe a => Foo a instance Foo t => Sat (Maybe t) -- dfunSat instance Data Maybe a => Foo a -- dfunFoo1 instance Foo a => Foo [a] -- dfunFoo2 instance Foo [Char] -- dfunFoo3 Consider generating the superclasses of the instance declaration instance Foo a => Foo [a] So our problem is this [G] d0 : Foo t [W] d1 : Data Maybe [t] -- Desired superclass We may add the given in the inert set, along with its superclasses Inert: [G] d0 : Foo t [G] d01 : Data Maybe t -- Superclass of d0 WorkList [W] d1 : Data Maybe [t] Solve d1 using instance dfunData2; d1 := dfunData2 d2 d3 Inert: [G] d0 : Foo t [G] d01 : Data Maybe t -- Superclass of d0 Solved: d1 : Data Maybe [t] WorkList: [W] d2 : Sat (Maybe [t]) [W] d3 : Data Maybe t Now, we may simplify d2 using dfunSat; d2 := dfunSat d4 Inert: [G] d0 : Foo t [G] d01 : Data Maybe t -- Superclass of d0 Solved: d1 : Data Maybe [t] d2 : Sat (Maybe [t]) WorkList: [W] d3 : Data Maybe t [W] d4 : Foo [t] Now, we can just solve d3 from d01; d3 := d01 Inert [G] d0 : Foo t [G] d01 : Data Maybe t -- Superclass of d0 Solved: d1 : Data Maybe [t] d2 : Sat (Maybe [t]) WorkList [W] d4 : Foo [t] Now, solve d4 using dfunFoo2; d4 := dfunFoo2 d5 Inert [G] d0 : Foo t [G] d01 : Data Maybe t -- Superclass of d0 Solved: d1 : Data Maybe [t] d2 : Sat (Maybe [t]) d4 : Foo [t] WorkList: [W] d5 : Foo t Now, d5 can be solved! d5 := d0 Result d1 := dfunData2 d2 d3 d2 := dfunSat d4 d3 := d01 d4 := dfunFoo2 d5 d5 := d0 -} {- ********************************************************************* * * InertCans: the canonical inerts * * * * ********************************************************************* -} {- Note [Tracking Given equalities] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ For reasons described in (UNTOUCHABLE) in GHC.Tc.Utils.Unify Note [Unification preconditions], we can't unify alpha[2] ~ Int under a level-4 implication if there are any Given equalities bound by the implications at level 3 of 4. To that end, the InertCans tracks inert_given_eq_lvl :: TcLevel -- The TcLevel of the innermost implication that has a Given -- equality of the sort that make a unification variable untouchable -- (see Note [Unification preconditions] in GHC.Tc.Utils.Unify). We update inert_given_eq_lvl whenever we add a Given to the inert set, in updateGivenEqs. Then a unification variable alpha[n] is untouchable iff n < inert_given_eq_lvl that is, if the unification variable was born outside an enclosing Given equality. Exactly which constraints should trigger (UNTOUCHABLE), and hence should update inert_given_eq_lvl? * We do /not/ need to worry about let-bound skolems, such ast forall[2] a. a ~ [b] => blah See Note [Let-bound skolems] * Consider an implication forall[2]. beta[1] => alpha[1] ~ Int where beta is a unification variable that has already been unified to () in an outer scope. Then alpha[1] is perfectly touchable and we can unify alpha := Int. So when deciding whether the givens contain an equality, we should canonicalise first, rather than just looking at the /original/ givens (#8644). * However, we must take account of *potential* equalities. Consider the same example again, but this time we have /not/ yet unified beta: forall[2] beta[1] => ...blah... Because beta might turn into an equality, updateGivenEqs conservatively treats it as a potential equality, and updates inert_give_eq_lvl * What about something like forall[2] a b. a ~ F b => [W] alpha[1] ~ X y z? That Given cannot affect the Wanted, because the Given is entirely *local*: it mentions only skolems bound in the very same implication. Such equalities need not make alpha untouchable. (Test case typecheck/should_compile/LocalGivenEqs has a real-life motivating example, with some detailed commentary.) Hence the 'mentionsOuterVar' test in updateGivenEqs. However, solely to support better error messages (see Note [HasGivenEqs] in GHC.Tc.Types.Constraint) we also track these "local" equalities in the boolean inert_given_eqs field. This field is used only to set the ic_given_eqs field to LocalGivenEqs; see the function getHasGivenEqs. Here is a simpler case that triggers this behaviour: data T where MkT :: F a ~ G b => a -> b -> T f (MkT _ _) = True Because of this behaviour around local equality givens, we can infer the type of f. This is typecheck/should_compile/LocalGivenEqs2. * We need not look at the equality relation involved (nominal vs representational), because representational equalities can still imply nominal ones. For example, if (G a ~R G b) and G's argument's role is nominal, then we can deduce a ~N b. Note [Let-bound skolems] ~~~~~~~~~~~~~~~~~~~~~~~~ If * the inert set contains a canonical Given CEqCan (a ~ ty) and * 'a' is a skolem bound in this very implication, then: a) The Given is pretty much a let-binding, like f :: (a ~ b->c) => a -> a Here the equality constraint is like saying let a = b->c in ... It is not adding any new, local equality information, and hence can be ignored by has_given_eqs b) 'a' will have been completely substituted out in the inert set, so we can safely discard it. For an example, see #9211. See also GHC.Tc.Utils.Unify Note [Deeper level on the left] for how we ensure that the right variable is on the left of the equality when both are tyvars. You might wonder whether the skolem really needs to be bound "in the very same implication" as the equality constraint. Consider this (c.f. #15009): data S a where MkS :: (a ~ Int) => S a g :: forall a. S a -> a -> blah g x y = let h = \z. ( z :: Int , case x of MkS -> [y,z]) in ... From the type signature for `g`, we get `y::a` . Then when we encounter the `\z`, we'll assign `z :: alpha[1]`, say. Next, from the body of the lambda we'll get [W] alpha[1] ~ Int -- From z::Int [W] forall[2]. (a ~ Int) => [W] alpha[1] ~ a -- From [y,z] Now, unify alpha := a. Now we are stuck with an unsolved alpha~Int! So we must treat alpha as untouchable under the forall[2] implication. Note [Detailed InertCans Invariants] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The InertCans represents a collection of constraints with the following properties: * All canonical * No two dictionaries with the same head * No two CIrreds with the same type * Family equations inert wrt top-level family axioms * Dictionaries have no matching top-level instance * Given family or dictionary constraints don't mention touchable unification variables * Non-CEqCan constraints are fully rewritten with respect to the CEqCan equalities (modulo eqCanRewrite of course; eg a wanted cannot rewrite a given) * CEqCan equalities: see Note [inert_eqs: the inert equalities] Also see documentation in Constraint.Ct for a list of invariants Note [inert_eqs: the inert equalities] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Definition [Can-rewrite relation] A "can-rewrite" relation between flavours, written f1 >= f2, is a binary relation with the following properties (R1) >= is transitive (R2) If f1 >= f, and f2 >= f, then either f1 >= f2 or f2 >= f1 (See Note [Why R2?].) Lemma (L0). If f1 >= f then f1 >= f1 Proof. By property (R2), with f1=f2 Definition [Generalised substitution] A "generalised substitution" S is a set of triples (lhs -f-> t), where lhs is a type variable or an exactly-saturated type family application (that is, lhs is a CanEqLHS) t is a type f is a flavour such that (WF1) if (lhs1 -f1-> t1) in S (lhs2 -f2-> t2) in S then (f1 >= f2) implies that lhs1 does not appear within lhs2 (WF2) if (lhs -f-> t) is in S, then t /= lhs Definition [Applying a generalised substitution] If S is a generalised substitution S(f,t0) = t, if (t0 -fs-> t) in S, and fs >= f = apply S to components of t0, otherwise See also Note [Flavours with roles]. Theorem: S(f,t0) is well defined as a function. Proof: Suppose (lhs -f1-> t1) and (lhs -f2-> t2) are both in S, and f1 >= f and f2 >= f Then by (R2) f1 >= f2 or f2 >= f1, which contradicts (WF1) Notation: repeated application. S^0(f,t) = t S^(n+1)(f,t) = S(f, S^n(t)) Definition: terminating generalised substitution A generalised substitution S is *terminating* iff (IG1) there is an n such that for every f,t, S^n(f,t) = S^(n+1)(f,t) By (IG1) we define S*(f,t) to be the result of exahaustively applying S(f,_) to t. ----------------------------------------------------------------------------- Our main invariant: the CEqCans in inert_eqs should be a terminating generalised substitution ----------------------------------------------------------------------------- Note that termination is not the same as idempotence. To apply S to a type, you may have to apply it recursively. But termination does guarantee that this recursive use will terminate. Note [Why R2?] ~~~~~~~~~~~~~~ R2 states that, if we have f1 >= f and f2 >= f, then either f1 >= f2 or f2 >= f1. If we do not have R2, we will easily fall into a loop. To see why, imagine we have f1 >= f, f2 >= f, and that's it. Then, let our inert set S = {a -f1-> b, b -f2-> a}. Computing S(f,a) does not terminate. And yet, we have a hard time noticing an occurs-check problem when building S, as the two equalities cannot rewrite one another. R2 actually restricts our ability to accept user-written programs. See Note [Avoiding rewriting cycles] in GHC.Tc.Types.Constraint for an example. Note [Rewritable] ~~~~~~~~~~~~~~~~~ This Note defines what it means for a type variable or type family application (that is, a CanEqLHS) to be rewritable in a type. This definition is used by the anyRewritableXXX family of functions and is meant to model the actual behaviour in GHC.Tc.Solver.Rewrite. Ignoring roles (for now): A CanEqLHS lhs is *rewritable* in a type t if the lhs tree appears as a subtree within t without traversing any of the following components of t: * coercions (whether they appear in casts CastTy or as arguments CoercionTy) * kinds of variable occurrences The check for rewritability *does* look in kinds of the bound variable of a ForAllTy. Goal: If lhs is not rewritable in t, then t is a fixpoint of the generalised substitution containing only {lhs -f*-> t'}, where f* is a flavour such that f* >= f for all f. The reason for this definition is that the rewriter does not rewrite in coercions or variables' kinds. In turn, the rewriter does not need to rewrite there because those places are never used for controlling the behaviour of the solver: these places are not used in matching instances or in decomposing equalities. There is one exception to the claim that non-rewritable parts of the tree do not affect the solver: we sometimes do an occurs-check to decide e.g. how to orient an equality. (See the comments on GHC.Tc.Solver.Canonical.canEqTyVarFunEq.) Accordingly, the presence of a variable in a kind or coercion just might influence the solver. Here is an example: type family Const x y where Const x y = x AxConst :: forall x y. Const x y ~# x alpha :: Const Type Nat [W] alpha ~ Int |> (sym (AxConst Type alpha) ;; AxConst Type alpha ;; sym (AxConst Type Nat)) The cast is clearly ludicrous (it ties together a cast and its symmetric version), but we can't quite rule it out. (See (EQ1) from Note [Respecting definitional equality] in GHC.Core.TyCo.Rep to see why we need the Const Type Nat bit.) And yet this cast will (quite rightly) prevent alpha from unifying with the RHS. I (Richard E) don't have an example of where this problem can arise from a Haskell program, but we don't have an air-tight argument for why the definition of *rewritable* given here is correct. Taking roles into account: we must consider a rewrite at a given role. That is, a rewrite arises from some equality, and that equality has a role associated with it. As we traverse a type, we track what role we are allowed to rewrite with. For example, suppose we have an inert [G] b ~R# Int. Then b is rewritable in Maybe b but not in F b, where F is a type function. This role-aware logic is present in both the anyRewritableXXX functions and in the rewriter. See also Note [anyRewritableTyVar must be role-aware] in GHC.Tc.Utils.TcType. Note [Extending the inert equalities] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Main Theorem [Stability under extension] Suppose we have a "work item" lhs -fw-> t and a terminating generalised substitution S, THEN the extended substitution T = S+(lhs -fw-> t) is a terminating generalised substitution PROVIDED (T1) S(fw,lhs) = lhs -- LHS of work-item is a fixpoint of S(fw,_) (T2) S(fw,t) = t -- RHS of work-item is a fixpoint of S(fw,_) (T3) lhs not in t -- No occurs check in the work item -- If lhs is a type family application, we require only that -- lhs is not *rewritable* in t. See Note [Rewritable] and -- Note [CEqCan occurs check] in GHC.Tc.Types.Constraint. AND, for every (lhs1 -fs-> s) in S: (K0) not (fw >= fs) Reason: suppose we kick out (lhs1 -fs-> s), and add (lhs -fw-> t) to the inert set. The latter can't rewrite the former, so the kick-out achieved nothing -- From here, we can assume fw >= fs OR (K4) lhs1 is a tyvar AND fs >= fw OR { (K1) lhs is not rewritable in lhs1. See Note [Rewritable]. Reason: if fw >= fs, WF1 says we can't have both lhs0 -fw-> t and F lhs0 -fs-> s AND (K2): guarantees termination of the new substitution { (K2a) not (fs >= fs) OR (K2b) lhs not in s } AND (K3) See Note [K3: completeness of solving] { (K3a) If the role of fs is nominal: s /= lhs (K3b) If the role of fs is representational: s is not of form (lhs t1 .. tn) } } Conditions (T1-T3) are established by the canonicaliser Conditions (K1-K3) are established by GHC.Tc.Solver.Monad.kickOutRewritable The idea is that * T1 and T2 are guaranteed by exhaustively rewriting the work-item with S(fw,_). * T3 is guaranteed by an occurs-check on the work item. This is done during canonicalisation, in checkTypeEq; invariant (TyEq:OC) of CEqCan. See also Note [CEqCan occurs check] in GHC.Tc.Types.Constraint. * (K1-3) are the "kick-out" criteria. (As stated, they are really the "keep" criteria.) If the current inert S contains a triple that does not satisfy (K1-3), then we remove it from S by "kicking it out", and re-processing it. * Note that kicking out is a Bad Thing, because it means we have to re-process a constraint. The less we kick out, the better. TODO: Make sure that kicking out really *is* a Bad Thing. We've assumed this but haven't done the empirical study to check. * Assume we have G>=G, G>=W and that's all. Then, when performing a unification we add a new given a -G-> ty. But doing so does NOT require us to kick out an inert wanted that mentions a, because of (K2a). This is a common case, hence good not to kick out. See also (K2a) below. * Lemma (L1): The conditions of the Main Theorem imply that there is no (lhs -fs-> t) in S, s.t. (fs >= fw). Proof. Suppose the contrary (fs >= fw). Then because of (T1), S(fw,lhs)=lhs. But since fs>=fw, S(fw,lhs) = t, hence t=lhs. But now we have (lhs -fs-> lhs) in S, which contradicts (WF2). * The extended substitution satisfies (WF1) and (WF2) - (K1) plus (L1) guarantee that the extended substitution satisfies (WF1). - (T3) guarantees (WF2). * (K2) and (K4) are about termination. Intuitively, any infinite chain S^0(f,t), S^1(f,t), S^2(f,t).... must pass through the new work item infinitely often, since the substitution without the work item is terminating; and must pass through at least one of the triples in S infinitely often. - (K2a): if not(fs>=fs) then there is no f that fs can rewrite (fs>=f) (this is Lemma (L0)), and hence this triple never plays a role in application S(f,t). It is always safe to extend S with such a triple. (NB: we could strengthen K1) in this way too, but see K3. - (K2b): if lhs not in s, we have no further opportunity to apply the work item - (K4): See Note [K4] * Lemma (L3). Suppose we have f* such that, for all f, f* >= f. Then if we are adding lhs -fw-> t (where T1, T2, and T3 hold), we will keep a -f*-> s. Proof. K4 holds; thus, we keep. Key lemma to make it watertight. Under the conditions of the Main Theorem, forall f st fw >= f, a is not in S^k(f,t), for any k Also, consider roles more carefully. See Note [Flavours with roles] Note [K4] ~~~~~~~~~ K4 is a "keep" condition of Note [Extending the inert equalities]. Here is the scenario: * We are considering adding (lhs -fw-> t) to the inert set S. * S already has (lhs1 -fs-> s). * We know S(fw, lhs) = lhs, S(fw, t) = t, and lhs is not rewritable in t. See Note [Rewritable]. These are (T1), (T2), and (T3). * We further know fw >= fs. (If not, then we short-circuit via (K0).) K4 says that we may keep lhs1 -fs-> s in S if: lhs1 is a tyvar AND fs >= fw Why K4 guarantees termination: * If fs >= fw, we know a is not rewritable in t, because of (T2). * We further know lhs /= a, because of (T1). * Accordingly, a use of the new inert item lhs -fw-> t cannot create the conditions for a use of a -fs-> s (precisely because t does not mention a), and hence, the extended substitution (with lhs -fw-> t in it) is a terminating generalised substitution. Recall that the termination generalised substitution includes only mappings that pass an occurs check. This is (T3). At one point, we worried that the argument here would fail if s mentioned a, but (T3) rules out this possibility. Put another way: the terminating generalised substitution considers only the inert_eqs, not other parts of the inert set (such as the irreds). Can we liberalise K4? No. Why we cannot drop the (fs >= fw) condition: * Suppose not (fs >= fw). It might be the case that t mentions a, and this can cause a loop. Example: Work: [G] b ~ a Inert: [W] a ~ b (where G >= G, G >= W, and W >= W) If we don't kick out the inert, then we get a loop on e.g. [W] a ~ Int. * Note that the above example is different if the inert is a Given G, because (T1) won't hold. Why we cannot drop the tyvar condition: * Presume fs >= fw. Thus, F tys is not rewritable in t, because of (T2). * Can the use of lhs -fw-> t create the conditions for a use of F tys -fs-> s? Yes! This can happen if t appears within tys. Here is an example: Work: [G] a ~ Int Inert: [G] F Int ~ F a Now, if we have [W] F a ~ Bool, we will rewrite ad infinitum on the left-hand side. The key reason why K2b works in the tyvar case is that tyvars are atomic: if the right-hand side of an equality does not mention a variable a, then it cannot allow an equality with an LHS of a to fire. This is not the case for type family applications. Bottom line: K4 can keep only inerts with tyvars on the left. Put differently, K4 will never prevent an inert with a type family on the left from being kicked out. Consequence: We never kick out a Given/Nominal equality with a tyvar on the left. This is Lemma (L3) of Note [Extending the inert equalities]. It is good because it means we can effectively model the mutable filling of metavariables with Given/Nominal equalities. That is: it should be the case that we could rewrite our solver never to fill in a metavariable; instead, it would "solve" a wanted like alpha ~ Int by turning it into a Given, allowing it to be used in rewriting. We would want the solver to behave the same whether it uses metavariables or Givens. And (L3) says that no Given/Nominals over tyvars are ever kicked out, just like we never unfill a metavariable. Nice. Getting this wrong (that is, allowing K4 to apply to situations with the type family on the left) led to #19042. (At that point, K4 was known as K2b.) Originally, this condition was part of K2, but #17672 suggests it should be a top-level K condition. Note [K3: completeness of solving] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (K3) is not necessary for the extended substitution to be terminating. In fact K1 could be made stronger by saying ... then (not (fw >= fs) or not (fs >= fs)) But it's not enough for S to be terminating; we also want completeness. That is, we want to be able to solve all soluble wanted equalities. Suppose we have work-item b -G-> a inert-item a -W-> b Assuming (G >= W) but not (W >= W), this fulfills all the conditions, so we could extend the inerts, thus: inert-items b -G-> a a -W-> b But if we kicked-out the inert item, we'd get work-item a -W-> b inert-item b -G-> a Then rewrite the work-item gives us (a -W-> a), which is soluble via Refl. So we add one more clause to the kick-out criteria Another way to understand (K3) is that we treat an inert item a -f-> b in the same way as b -f-> a So if we kick out one, we should kick out the other. The orientation is somewhat accidental. When considering roles, we also need the second clause (K3b). Consider work-item c -G/N-> a inert-item a -W/R-> b c The work-item doesn't get rewritten by the inert, because (>=) doesn't hold. But we don't kick out the inert item because not (W/R >= W/R). So we just add the work item. But then, consider if we hit the following: work-item b -G/N-> Id inert-items a -W/R-> b c c -G/N-> a where newtype Id x = Id x For similar reasons, if we only had (K3a), we wouldn't kick the representational inert out. And then, we'd miss solving the inert, which now reduced to reflexivity. The solution here is to kick out representational inerts whenever the lhs of a work item is "exposed", where exposed means being at the head of the top-level application chain (lhs t1 .. tn). See is_can_eq_lhs_head. This is encoded in (K3b). Beware: if we make this test succeed too often, we kick out too much, and the solver might loop. Consider (#14363) work item: [G] a ~R f b inert item: [G] b ~R f a In GHC 8.2 the completeness tests more aggressive, and kicked out the inert item; but no rewriting happened and there was an infinite loop. All we need is to have the tyvar at the head. Note [Flavours with roles] ~~~~~~~~~~~~~~~~~~~~~~~~~~ The system described in Note [inert_eqs: the inert equalities] discusses an abstract set of flavours. In GHC, flavours have two components: the flavour proper, taken from {Wanted, Given} and the equality relation (often called role), taken from {NomEq, ReprEq}. When substituting w.r.t. the inert set, as described in Note [inert_eqs: the inert equalities], we must be careful to respect all components of a flavour. For example, if we have inert set: a -G/R-> Int b -G/R-> Bool type role T nominal representational and we wish to compute S(W/R, T a b), the correct answer is T a Bool, NOT T Int Bool. The reason is that T's first parameter has a nominal role, and thus rewriting a to Int in T a b is wrong. Indeed, this non-congruence of substitution means that the proof in Note [inert_eqs: the inert equalities] may need to be revisited, but we don't think that the end conclusion is wrong. -} data InertCans -- See Note [Detailed InertCans Invariants] for more = IC { InertCans -> InertEqs inert_eqs :: InertEqs -- See Note [inert_eqs: the inert equalities] -- All CEqCans with a TyVarLHS; index is the LHS tyvar -- Domain = skolems and untouchables; a touchable would be unified , InertCans -> FunEqMap [Ct] inert_funeqs :: FunEqMap EqualCtList -- All CEqCans with a TyFamLHS; index is the whole family head type. -- LHS is fully rewritten (modulo eqCanRewrite constraints) -- wrt inert_eqs -- Can include both [G] and [W] , InertCans -> DictMap Ct inert_dicts :: DictMap Ct -- Dictionaries only -- All fully rewritten (modulo flavour constraints) -- wrt inert_eqs , InertCans -> [QCInst] inert_insts :: [QCInst] , InertCans -> DictMap Ct inert_safehask :: DictMap Ct -- Failed dictionary resolution due to Safe Haskell overlapping -- instances restriction. We keep this separate from inert_dicts -- as it doesn't cause compilation failure, just safe inference -- failure. -- -- ^ See Note [Safe Haskell Overlapping Instances Implementation] -- in GHC.Tc.Solver , InertCans -> Cts inert_irreds :: Cts -- Irreducible predicates that cannot be made canonical, -- and which don't interact with others (e.g. (c a)) -- and insoluble predicates (e.g. Int ~ Bool, or a ~ [a]) , InertCans -> TcLevel inert_given_eq_lvl :: TcLevel -- The TcLevel of the innermost implication that has a Given -- equality of the sort that make a unification variable untouchable -- (see Note [Unification preconditions] in GHC.Tc.Utils.Unify). -- See Note [Tracking Given equalities] , InertCans -> Bool inert_given_eqs :: Bool -- True <=> The inert Givens *at this level* (tcl_tclvl) -- could includes at least one equality /other than/ a -- let-bound skolem equality. -- Reason: report these givens when reporting a failed equality -- See Note [Tracking Given equalities] } type InertEqs = DTyVarEnv EqualCtList instance Outputable InertCans where ppr :: InertCans -> SDoc ppr (IC { inert_eqs :: InertCans -> InertEqs inert_eqs = InertEqs eqs , inert_funeqs :: InertCans -> FunEqMap [Ct] inert_funeqs = FunEqMap [Ct] funeqs , inert_dicts :: InertCans -> DictMap Ct inert_dicts = DictMap Ct dicts , inert_safehask :: InertCans -> DictMap Ct inert_safehask = DictMap Ct safehask , inert_irreds :: InertCans -> Cts inert_irreds = Cts irreds , inert_given_eq_lvl :: InertCans -> TcLevel inert_given_eq_lvl = TcLevel ge_lvl , inert_given_eqs :: InertCans -> Bool inert_given_eqs = Bool given_eqs , inert_insts :: InertCans -> [QCInst] inert_insts = [QCInst] insts }) = SDoc -> SDoc forall doc. IsLine doc => doc -> doc braces (SDoc -> SDoc) -> SDoc -> SDoc forall a b. (a -> b) -> a -> b $ [SDoc] -> SDoc forall doc. IsDoc doc => [doc] -> doc vcat [ Bool -> SDoc -> SDoc forall doc. IsOutput doc => Bool -> doc -> doc ppUnless (InertEqs -> Bool forall a. DVarEnv a -> Bool isEmptyDVarEnv InertEqs eqs) (SDoc -> SDoc) -> SDoc -> SDoc forall a b. (a -> b) -> a -> b $ String -> SDoc forall doc. IsLine doc => String -> doc text String "Equalities:" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> Cts -> SDoc pprCts (([Ct] -> Cts -> Cts) -> Cts -> InertEqs -> Cts forall a b. (a -> b -> b) -> b -> DVarEnv a -> b foldDVarEnv [Ct] -> Cts -> Cts folder Cts emptyCts InertEqs eqs) , Bool -> SDoc -> SDoc forall doc. IsOutput doc => Bool -> doc -> doc ppUnless (FunEqMap [Ct] -> Bool forall a. TcAppMap a -> Bool isEmptyTcAppMap FunEqMap [Ct] funeqs) (SDoc -> SDoc) -> SDoc -> SDoc forall a b. (a -> b) -> a -> b $ String -> SDoc forall doc. IsLine doc => String -> doc text String "Type-function equalities =" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> Cts -> SDoc pprCts (([Ct] -> Cts -> Cts) -> FunEqMap [Ct] -> Cts -> Cts forall a b. (a -> b -> b) -> FunEqMap a -> b -> b foldFunEqs [Ct] -> Cts -> Cts folder FunEqMap [Ct] funeqs Cts emptyCts) , Bool -> SDoc -> SDoc forall doc. IsOutput doc => Bool -> doc -> doc ppUnless (DictMap Ct -> Bool forall a. TcAppMap a -> Bool isEmptyTcAppMap DictMap Ct dicts) (SDoc -> SDoc) -> SDoc -> SDoc forall a b. (a -> b) -> a -> b $ String -> SDoc forall doc. IsLine doc => String -> doc text String "Dictionaries =" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> Cts -> SDoc pprCts (DictMap Ct -> Cts forall a. DictMap a -> Bag a dictsToBag DictMap Ct dicts) , Bool -> SDoc -> SDoc forall doc. IsOutput doc => Bool -> doc -> doc ppUnless (DictMap Ct -> Bool forall a. TcAppMap a -> Bool isEmptyTcAppMap DictMap Ct safehask) (SDoc -> SDoc) -> SDoc -> SDoc forall a b. (a -> b) -> a -> b $ String -> SDoc forall doc. IsLine doc => String -> doc text String "Safe Haskell unsafe overlap =" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> Cts -> SDoc pprCts (DictMap Ct -> Cts forall a. DictMap a -> Bag a dictsToBag DictMap Ct safehask) , Bool -> SDoc -> SDoc forall doc. IsOutput doc => Bool -> doc -> doc ppUnless (Cts -> Bool isEmptyCts Cts irreds) (SDoc -> SDoc) -> SDoc -> SDoc forall a b. (a -> b) -> a -> b $ String -> SDoc forall doc. IsLine doc => String -> doc text String "Irreds =" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> Cts -> SDoc pprCts Cts irreds , Bool -> SDoc -> SDoc forall doc. IsOutput doc => Bool -> doc -> doc ppUnless ([QCInst] -> Bool forall a. [a] -> Bool forall (t :: * -> *) a. Foldable t => t a -> Bool null [QCInst] insts) (SDoc -> SDoc) -> SDoc -> SDoc forall a b. (a -> b) -> a -> b $ String -> SDoc forall doc. IsLine doc => String -> doc text String "Given instances =" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> [SDoc] -> SDoc forall doc. IsDoc doc => [doc] -> doc vcat ((QCInst -> SDoc) -> [QCInst] -> [SDoc] forall a b. (a -> b) -> [a] -> [b] map QCInst -> SDoc forall a. Outputable a => a -> SDoc ppr [QCInst] insts) , String -> SDoc forall doc. IsLine doc => String -> doc text String "Innermost given equalities =" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> TcLevel -> SDoc forall a. Outputable a => a -> SDoc ppr TcLevel ge_lvl , String -> SDoc forall doc. IsLine doc => String -> doc text String "Given eqs at this level =" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> Bool -> SDoc forall a. Outputable a => a -> SDoc ppr Bool given_eqs ] where folder :: [Ct] -> Cts -> Cts folder [Ct] eqs Cts rest = [Ct] -> Cts forall a. [a] -> Bag a listToBag [Ct] eqs Cts -> Cts -> Cts `andCts` Cts rest {- ********************************************************************* * * Inert equalities * * ********************************************************************* -} addTyEq :: InertEqs -> TcTyVar -> Ct -> InertEqs addTyEq :: InertEqs -> TcTyVar -> Ct -> InertEqs addTyEq InertEqs old_eqs TcTyVar tv Ct ct = ([Ct] -> [Ct] -> [Ct]) -> InertEqs -> TcTyVar -> [Ct] -> InertEqs forall a. (a -> a -> a) -> DVarEnv a -> TcTyVar -> a -> DVarEnv a extendDVarEnv_C [Ct] -> [Ct] -> [Ct] add_eq InertEqs old_eqs TcTyVar tv [Ct ct] where add_eq :: [Ct] -> [Ct] -> [Ct] add_eq [Ct] old_eqs [Ct] _ = Ct -> [Ct] -> [Ct] addToEqualCtList Ct ct [Ct] old_eqs addCanFunEq :: FunEqMap EqualCtList -> TyCon -> [TcType] -> Ct -> FunEqMap EqualCtList addCanFunEq :: FunEqMap [Ct] -> TyCon -> [TcType] -> Ct -> FunEqMap [Ct] addCanFunEq FunEqMap [Ct] old_eqs TyCon fun_tc [TcType] fun_args Ct ct = FunEqMap [Ct] -> TyCon -> [TcType] -> XT [Ct] -> FunEqMap [Ct] forall a. TcAppMap a -> TyCon -> [TcType] -> XT a -> TcAppMap a alterTcApp FunEqMap [Ct] old_eqs TyCon fun_tc [TcType] fun_args XT [Ct] upd where upd :: XT [Ct] upd (Just [Ct] old_equal_ct_list) = [Ct] -> Maybe [Ct] forall a. a -> Maybe a Just ([Ct] -> Maybe [Ct]) -> [Ct] -> Maybe [Ct] forall a b. (a -> b) -> a -> b $ Ct -> [Ct] -> [Ct] addToEqualCtList Ct ct [Ct] old_equal_ct_list upd Maybe [Ct] Nothing = [Ct] -> Maybe [Ct] forall a. a -> Maybe a Just [Ct ct] foldTyEqs :: (Ct -> b -> b) -> InertEqs -> b -> b foldTyEqs :: forall b. (Ct -> b -> b) -> InertEqs -> b -> b foldTyEqs Ct -> b -> b k InertEqs eqs b z = ([Ct] -> b -> b) -> b -> InertEqs -> b forall a b. (a -> b -> b) -> b -> DVarEnv a -> b foldDVarEnv (\[Ct] cts b z -> (Ct -> b -> b) -> b -> [Ct] -> b forall a b. (a -> b -> b) -> b -> [a] -> b forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr Ct -> b -> b k b z [Ct] cts) b z InertEqs eqs findTyEqs :: InertCans -> TyVar -> [Ct] findTyEqs :: InertCans -> TcTyVar -> [Ct] findTyEqs InertCans icans TcTyVar tv = forall (t :: * -> *) a. Foldable t => t [a] -> [a] concat @Maybe (InertEqs -> TcTyVar -> Maybe [Ct] forall a. DVarEnv a -> TcTyVar -> Maybe a lookupDVarEnv (InertCans -> InertEqs inert_eqs InertCans icans) TcTyVar tv) delEq :: InertCans -> CanEqLHS -> TcType -> InertCans delEq :: InertCans -> CanEqLHS -> TcType -> InertCans delEq InertCans ic CanEqLHS lhs TcType rhs = case CanEqLHS lhs of TyVarLHS TcTyVar tv -> InertCans ic { inert_eqs = alterDVarEnv upd (inert_eqs ic) tv } TyFamLHS TyCon tf [TcType] args -> InertCans ic { inert_funeqs = alterTcApp (inert_funeqs ic) tf args upd } where isThisOne :: Ct -> Bool isThisOne :: Ct -> Bool isThisOne (CEqCan { cc_rhs :: Ct -> TcType cc_rhs = TcType t1 }) = TcType -> TcType -> Bool tcEqTypeNoKindCheck TcType rhs TcType t1 isThisOne Ct other = String -> SDoc -> Bool forall a. HasCallStack => String -> SDoc -> a pprPanic String "delEq" (CanEqLHS -> SDoc forall a. Outputable a => a -> SDoc ppr CanEqLHS lhs SDoc -> SDoc -> SDoc forall doc. IsDoc doc => doc -> doc -> doc $$ InertCans -> SDoc forall a. Outputable a => a -> SDoc ppr InertCans ic SDoc -> SDoc -> SDoc forall doc. IsDoc doc => doc -> doc -> doc $$ Ct -> SDoc forall a. Outputable a => a -> SDoc ppr Ct other) upd :: Maybe EqualCtList -> Maybe EqualCtList upd :: XT [Ct] upd (Just [Ct] eq_ct_list) = (Ct -> Bool) -> [Ct] -> Maybe [Ct] filterEqualCtList (Bool -> Bool not (Bool -> Bool) -> (Ct -> Bool) -> Ct -> Bool forall b c a. (b -> c) -> (a -> b) -> a -> c . Ct -> Bool isThisOne) [Ct] eq_ct_list upd Maybe [Ct] Nothing = Maybe [Ct] forall a. Maybe a Nothing findEq :: InertCans -> CanEqLHS -> [Ct] findEq :: InertCans -> CanEqLHS -> [Ct] findEq InertCans icans (TyVarLHS TcTyVar tv) = InertCans -> TcTyVar -> [Ct] findTyEqs InertCans icans TcTyVar tv findEq InertCans icans (TyFamLHS TyCon fun_tc [TcType] fun_args) = forall (t :: * -> *) a. Foldable t => t [a] -> [a] concat @Maybe (FunEqMap [Ct] -> TyCon -> [TcType] -> Maybe [Ct] forall a. FunEqMap a -> TyCon -> [TcType] -> Maybe a findFunEq (InertCans -> FunEqMap [Ct] inert_funeqs InertCans icans) TyCon fun_tc [TcType] fun_args) {-# INLINE partition_eqs_container #-} partition_eqs_container :: forall container . container -- empty container -> (forall b. (EqualCtList -> b -> b) -> b -> container -> b) -- folder -> (container -> CanEqLHS -> EqualCtList -> container) -- extender -> (Ct -> Bool) -> container -> ([Ct], container) partition_eqs_container :: forall container. container -> (forall b. ([Ct] -> b -> b) -> b -> container -> b) -> (container -> CanEqLHS -> [Ct] -> container) -> (Ct -> Bool) -> container -> ([Ct], container) partition_eqs_container container empty_container forall b. ([Ct] -> b -> b) -> b -> container -> b fold_container container -> CanEqLHS -> [Ct] -> container extend_container Ct -> Bool pred container orig_inerts = ([Ct] -> ([Ct], container) -> ([Ct], container)) -> ([Ct], container) -> container -> ([Ct], container) forall b. ([Ct] -> b -> b) -> b -> container -> b fold_container [Ct] -> ([Ct], container) -> ([Ct], container) folder ([], container empty_container) container orig_inerts where folder :: EqualCtList -> ([Ct], container) -> ([Ct], container) folder :: [Ct] -> ([Ct], container) -> ([Ct], container) folder [Ct] eqs ([Ct] acc_true, container acc_false) = ([Ct] eqs_true [Ct] -> [Ct] -> [Ct] forall a. [a] -> [a] -> [a] ++ [Ct] acc_true, container acc_false') where ([Ct] eqs_true, [Ct] eqs_false) = (Ct -> Bool) -> [Ct] -> ([Ct], [Ct]) forall a. (a -> Bool) -> [a] -> ([a], [a]) partition Ct -> Bool pred [Ct] eqs acc_false' :: container acc_false' | CEqCan { cc_lhs :: Ct -> CanEqLHS cc_lhs = CanEqLHS lhs } : [Ct] _ <- [Ct] eqs_false = container -> CanEqLHS -> [Ct] -> container extend_container container acc_false CanEqLHS lhs [Ct] eqs_false | Bool otherwise = container acc_false partitionInertEqs :: (Ct -> Bool) -- Ct will always be a CEqCan with a TyVarLHS -> InertEqs -> ([Ct], InertEqs) partitionInertEqs :: (Ct -> Bool) -> InertEqs -> ([Ct], InertEqs) partitionInertEqs = InertEqs -> (forall b. ([Ct] -> b -> b) -> b -> InertEqs -> b) -> (InertEqs -> CanEqLHS -> [Ct] -> InertEqs) -> (Ct -> Bool) -> InertEqs -> ([Ct], InertEqs) forall container. container -> (forall b. ([Ct] -> b -> b) -> b -> container -> b) -> (container -> CanEqLHS -> [Ct] -> container) -> (Ct -> Bool) -> container -> ([Ct], container) partition_eqs_container InertEqs forall a. DVarEnv a emptyDVarEnv ([Ct] -> b -> b) -> b -> InertEqs -> b forall b. ([Ct] -> b -> b) -> b -> InertEqs -> b forall a b. (a -> b -> b) -> b -> DVarEnv a -> b foldDVarEnv InertEqs -> CanEqLHS -> [Ct] -> InertEqs extendInertEqs -- precondition: CanEqLHS is a TyVarLHS extendInertEqs :: InertEqs -> CanEqLHS -> EqualCtList -> InertEqs extendInertEqs :: InertEqs -> CanEqLHS -> [Ct] -> InertEqs extendInertEqs InertEqs eqs (TyVarLHS TcTyVar tv) [Ct] new_eqs = InertEqs -> TcTyVar -> [Ct] -> InertEqs forall a. DVarEnv a -> TcTyVar -> a -> DVarEnv a extendDVarEnv InertEqs eqs TcTyVar tv [Ct] new_eqs extendInertEqs InertEqs _ CanEqLHS other [Ct] _ = String -> SDoc -> InertEqs forall a. HasCallStack => String -> SDoc -> a pprPanic String "extendInertEqs" (CanEqLHS -> SDoc forall a. Outputable a => a -> SDoc ppr CanEqLHS other) partitionFunEqs :: (Ct -> Bool) -- Ct will always be a CEqCan with a TyFamLHS -> FunEqMap EqualCtList -> ([Ct], FunEqMap EqualCtList) partitionFunEqs :: (Ct -> Bool) -> FunEqMap [Ct] -> ([Ct], FunEqMap [Ct]) partitionFunEqs = FunEqMap [Ct] -> (forall b. ([Ct] -> b -> b) -> b -> FunEqMap [Ct] -> b) -> (FunEqMap [Ct] -> CanEqLHS -> [Ct] -> FunEqMap [Ct]) -> (Ct -> Bool) -> FunEqMap [Ct] -> ([Ct], FunEqMap [Ct]) forall container. container -> (forall b. ([Ct] -> b -> b) -> b -> container -> b) -> (container -> CanEqLHS -> [Ct] -> container) -> (Ct -> Bool) -> container -> ([Ct], container) partition_eqs_container FunEqMap [Ct] forall a. DictMap a emptyFunEqs (\ [Ct] -> b -> b f b z FunEqMap [Ct] eqs -> ([Ct] -> b -> b) -> FunEqMap [Ct] -> b -> b forall a b. (a -> b -> b) -> FunEqMap a -> b -> b foldFunEqs [Ct] -> b -> b f FunEqMap [Ct] eqs b z) FunEqMap [Ct] -> CanEqLHS -> [Ct] -> FunEqMap [Ct] extendFunEqs -- precondition: CanEqLHS is a TyFamLHS extendFunEqs :: FunEqMap EqualCtList -> CanEqLHS -> EqualCtList -> FunEqMap EqualCtList extendFunEqs :: FunEqMap [Ct] -> CanEqLHS -> [Ct] -> FunEqMap [Ct] extendFunEqs FunEqMap [Ct] eqs (TyFamLHS TyCon tf [TcType] args) [Ct] new_eqs = FunEqMap [Ct] -> TyCon -> [TcType] -> [Ct] -> FunEqMap [Ct] forall a. TcAppMap a -> TyCon -> [TcType] -> a -> TcAppMap a insertTcApp FunEqMap [Ct] eqs TyCon tf [TcType] args [Ct] new_eqs extendFunEqs FunEqMap [Ct] _ CanEqLHS other [Ct] _ = String -> SDoc -> FunEqMap [Ct] forall a. HasCallStack => String -> SDoc -> a pprPanic String "extendFunEqs" (CanEqLHS -> SDoc forall a. Outputable a => a -> SDoc ppr CanEqLHS other) {- ********************************************************************* * * Adding to and removing from the inert set * * * * ********************************************************************* -} addInertItem :: TcLevel -> InertCans -> Ct -> InertCans addInertItem :: TcLevel -> InertCans -> Ct -> InertCans addInertItem TcLevel tc_lvl ics :: InertCans ics@(IC { inert_funeqs :: InertCans -> FunEqMap [Ct] inert_funeqs = FunEqMap [Ct] funeqs, inert_eqs :: InertCans -> InertEqs inert_eqs = InertEqs eqs }) item :: Ct item@(CEqCan { cc_lhs :: Ct -> CanEqLHS cc_lhs = CanEqLHS lhs }) = TcLevel -> Ct -> InertCans -> InertCans updateGivenEqs TcLevel tc_lvl Ct item (InertCans -> InertCans) -> InertCans -> InertCans forall a b. (a -> b) -> a -> b $ case CanEqLHS lhs of TyFamLHS TyCon tc [TcType] tys -> InertCans ics { inert_funeqs = addCanFunEq funeqs tc tys item } TyVarLHS TcTyVar tv -> InertCans ics { inert_eqs = addTyEq eqs tv item } addInertItem TcLevel tc_lvl ics :: InertCans ics@(IC { inert_irreds :: InertCans -> Cts inert_irreds = Cts irreds }) item :: Ct item@(CIrredCan {}) = TcLevel -> Ct -> InertCans -> InertCans updateGivenEqs TcLevel tc_lvl Ct item (InertCans -> InertCans) -> InertCans -> InertCans forall a b. (a -> b) -> a -> b $ -- An Irred might turn out to be an -- equality, so we play safe InertCans ics { inert_irreds = irreds `snocBag` item } addInertItem TcLevel _ InertCans ics item :: Ct item@(CDictCan { cc_class :: Ct -> Class cc_class = Class cls, cc_tyargs :: Ct -> [TcType] cc_tyargs = [TcType] tys }) = InertCans ics { inert_dicts = addDict (inert_dicts ics) cls tys item } addInertItem TcLevel _ InertCans _ Ct item = String -> SDoc -> InertCans forall a. HasCallStack => String -> SDoc -> a pprPanic String "upd_inert set: can't happen! Inserting " (SDoc -> InertCans) -> SDoc -> InertCans forall a b. (a -> b) -> a -> b $ Ct -> SDoc forall a. Outputable a => a -> SDoc ppr Ct item -- Can't be CNonCanonical because they only land in inert_irreds updateGivenEqs :: TcLevel -> Ct -> InertCans -> InertCans -- Set the inert_given_eq_level to the current level (tclvl) -- if the constraint is a given equality that should prevent -- filling in an outer unification variable. -- See Note [Tracking Given equalities] updateGivenEqs :: TcLevel -> Ct -> InertCans -> InertCans updateGivenEqs TcLevel tclvl Ct ct inerts :: InertCans inerts@(IC { inert_given_eq_lvl :: InertCans -> TcLevel inert_given_eq_lvl = TcLevel ge_lvl }) | Bool -> Bool not (Ct -> Bool isGivenCt Ct ct) = InertCans inerts | Ct -> Bool not_equality Ct ct = InertCans inerts -- See Note [Let-bound skolems] | Bool otherwise = InertCans inerts { inert_given_eq_lvl = ge_lvl' , inert_given_eqs = True } where ge_lvl' :: TcLevel ge_lvl' | TcLevel -> CtEvidence -> Bool mentionsOuterVar TcLevel tclvl (Ct -> CtEvidence ctEvidence Ct ct) -- Includes things like (c a), which *might* be an equality = TcLevel tclvl | Bool otherwise = TcLevel ge_lvl not_equality :: Ct -> Bool -- True <=> definitely not an equality of any kind -- except for a let-bound skolem, which doesn't count -- See Note [Let-bound skolems] -- NB: no need to spot the boxed CDictCan (a ~ b) because its -- superclass (a ~# b) will be a CEqCan not_equality :: Ct -> Bool not_equality (CEqCan { cc_lhs :: Ct -> CanEqLHS cc_lhs = TyVarLHS TcTyVar tv }) = Bool -> Bool not (TcLevel -> TcTyVar -> Bool isOuterTyVar TcLevel tclvl TcTyVar tv) not_equality (CDictCan {}) = Bool True not_equality Ct _ = Bool False kickOutRewritableLHS :: CtFlavourRole -- Flavour/role of the equality that -- is being added to the inert set -> CanEqLHS -- The new equality is lhs ~ ty -> InertCans -> (WorkList, InertCans) -- See Note [kickOutRewritable] kickOutRewritableLHS :: CtFlavourRole -> CanEqLHS -> InertCans -> (WorkList, InertCans) kickOutRewritableLHS CtFlavourRole new_fr CanEqLHS new_lhs ics :: InertCans ics@(IC { inert_eqs :: InertCans -> InertEqs inert_eqs = InertEqs tv_eqs , inert_dicts :: InertCans -> DictMap Ct inert_dicts = DictMap Ct dictmap , inert_funeqs :: InertCans -> FunEqMap [Ct] inert_funeqs = FunEqMap [Ct] funeqmap , inert_irreds :: InertCans -> Cts inert_irreds = Cts irreds , inert_insts :: InertCans -> [QCInst] inert_insts = [QCInst] old_insts }) = (WorkList kicked_out, InertCans inert_cans_in) where -- inert_safehask stays unchanged; is that right? inert_cans_in :: InertCans inert_cans_in = InertCans ics { inert_eqs = tv_eqs_in , inert_dicts = dicts_in , inert_funeqs = feqs_in , inert_irreds = irs_in , inert_insts = insts_in } kicked_out :: WorkList -- NB: use extendWorkList to ensure that kicked-out equalities get priority -- See Note [Prioritise equalities] (Kick-out). -- The irreds may include non-canonical (hetero-kinded) equality -- constraints, which perhaps may have become soluble after new_lhs -- is substituted; ditto the dictionaries, which may include (a~b) -- or (a~~b) constraints. kicked_out :: WorkList kicked_out = (Ct -> WorkList -> WorkList) -> WorkList -> Cts -> WorkList forall a b. (a -> b -> b) -> b -> Bag a -> b forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr Ct -> WorkList -> WorkList extendWorkListCt (WorkList emptyWorkList { wl_eqs = tv_eqs_out ++ feqs_out }) ((Cts dicts_out Cts -> Cts -> Cts `andCts` Cts irs_out) Cts -> [Ct] -> Cts `extendCtsList` [Ct] insts_out) ([Ct] tv_eqs_out, InertEqs tv_eqs_in) = (Ct -> Bool) -> InertEqs -> ([Ct], InertEqs) partitionInertEqs Ct -> Bool kick_out_eq InertEqs tv_eqs ([Ct] feqs_out, FunEqMap [Ct] feqs_in) = (Ct -> Bool) -> FunEqMap [Ct] -> ([Ct], FunEqMap [Ct]) partitionFunEqs Ct -> Bool kick_out_eq FunEqMap [Ct] funeqmap (Cts dicts_out, DictMap Ct dicts_in) = (Ct -> Bool) -> DictMap Ct -> (Cts, DictMap Ct) partitionDicts Ct -> Bool kick_out_ct DictMap Ct dictmap (Cts irs_out, Cts irs_in) = (Ct -> Bool) -> Cts -> (Cts, Cts) forall a. (a -> Bool) -> Bag a -> (Bag a, Bag a) partitionBag Ct -> Bool kick_out_ct Cts irreds -- Kick out even insolubles: See Note [Rewrite insolubles] -- Of course we must kick out irreducibles like (c a), in case -- we can rewrite 'c' to something more useful -- Kick-out for inert instances -- See Note [Quantified constraints] in GHC.Tc.Solver.Canonical insts_out :: [Ct] insts_in :: [QCInst] ([Ct] insts_out, [QCInst] insts_in) | CtFlavourRole -> Bool fr_may_rewrite (CtFlavour Given, EqRel NomEq) -- All the insts are Givens = (QCInst -> Either Ct QCInst) -> [QCInst] -> ([Ct], [QCInst]) forall a b c. (a -> Either b c) -> [a] -> ([b], [c]) partitionWith QCInst -> Either Ct QCInst kick_out_qci [QCInst] old_insts | Bool otherwise = ([], [QCInst] old_insts) kick_out_qci :: QCInst -> Either Ct QCInst kick_out_qci QCInst qci | let ev :: CtEvidence ev = QCInst -> CtEvidence qci_ev QCInst qci , EqRel -> TcType -> Bool fr_can_rewrite_ty EqRel NomEq (CtEvidence -> TcType ctEvPred (QCInst -> CtEvidence qci_ev QCInst qci)) = Ct -> Either Ct QCInst forall a b. a -> Either a b Left (CtEvidence -> Ct mkNonCanonical CtEvidence ev) | Bool otherwise = QCInst -> Either Ct QCInst forall a b. b -> Either a b Right QCInst qci (CtFlavour _, EqRel new_role) = CtFlavourRole new_fr fr_tv_can_rewrite_ty :: TyVar -> EqRel -> Type -> Bool fr_tv_can_rewrite_ty :: TcTyVar -> EqRel -> TcType -> Bool fr_tv_can_rewrite_ty TcTyVar new_tv EqRel role TcType ty = EqRel -> (EqRel -> TcTyVar -> Bool) -> TcType -> Bool anyRewritableTyVar EqRel role EqRel -> TcTyVar -> Bool can_rewrite TcType ty where can_rewrite :: EqRel -> TyVar -> Bool can_rewrite :: EqRel -> TcTyVar -> Bool can_rewrite EqRel old_role TcTyVar tv = EqRel new_role EqRel -> EqRel -> Bool `eqCanRewrite` EqRel old_role Bool -> Bool -> Bool && TcTyVar tv TcTyVar -> TcTyVar -> Bool forall a. Eq a => a -> a -> Bool == TcTyVar new_tv fr_tf_can_rewrite_ty :: TyCon -> [TcType] -> EqRel -> Type -> Bool fr_tf_can_rewrite_ty :: TyCon -> [TcType] -> EqRel -> TcType -> Bool fr_tf_can_rewrite_ty TyCon new_tf [TcType] new_tf_args EqRel role TcType ty = EqRel -> (EqRel -> TyCon -> [TcType] -> Bool) -> TcType -> Bool anyRewritableTyFamApp EqRel role EqRel -> TyCon -> [TcType] -> Bool can_rewrite TcType ty where can_rewrite :: EqRel -> TyCon -> [TcType] -> Bool can_rewrite :: EqRel -> TyCon -> [TcType] -> Bool can_rewrite EqRel old_role TyCon old_tf [TcType] old_tf_args = EqRel new_role EqRel -> EqRel -> Bool `eqCanRewrite` EqRel old_role Bool -> Bool -> Bool && TyCon -> [TcType] -> TyCon -> [TcType] -> Bool tcEqTyConApps TyCon new_tf [TcType] new_tf_args TyCon old_tf [TcType] old_tf_args -- it's possible for old_tf_args to have too many. This is fine; -- we'll only check what we need to. {-# INLINE fr_can_rewrite_ty #-} -- perform the check here only once fr_can_rewrite_ty :: EqRel -> Type -> Bool fr_can_rewrite_ty :: EqRel -> TcType -> Bool fr_can_rewrite_ty = case CanEqLHS new_lhs of TyVarLHS TcTyVar new_tv -> TcTyVar -> EqRel -> TcType -> Bool fr_tv_can_rewrite_ty TcTyVar new_tv TyFamLHS TyCon new_tf [TcType] new_tf_args -> TyCon -> [TcType] -> EqRel -> TcType -> Bool fr_tf_can_rewrite_ty TyCon new_tf [TcType] new_tf_args fr_may_rewrite :: CtFlavourRole -> Bool fr_may_rewrite :: CtFlavourRole -> Bool fr_may_rewrite CtFlavourRole fs = CtFlavourRole new_fr CtFlavourRole -> CtFlavourRole -> Bool `eqCanRewriteFR` CtFlavourRole fs -- Can the new item rewrite the inert item? {-# INLINE kick_out_ct #-} -- perform case on new_lhs here only once kick_out_ct :: Ct -> Bool -- Kick it out if the new CEqCan can rewrite the inert one -- See Note [kickOutRewritable] kick_out_ct :: Ct -> Bool kick_out_ct = case CanEqLHS new_lhs of TyVarLHS TcTyVar new_tv -> \Ct ct -> let fs :: CtFlavourRole fs@(CtFlavour _,EqRel role) = Ct -> CtFlavourRole ctFlavourRole Ct ct in CtFlavourRole -> Bool fr_may_rewrite CtFlavourRole fs Bool -> Bool -> Bool && TcTyVar -> EqRel -> TcType -> Bool fr_tv_can_rewrite_ty TcTyVar new_tv EqRel role (Ct -> TcType ctPred Ct ct) TyFamLHS TyCon new_tf [TcType] new_tf_args -> \Ct ct -> let fs :: CtFlavourRole fs@(CtFlavour _, EqRel role) = Ct -> CtFlavourRole ctFlavourRole Ct ct in CtFlavourRole -> Bool fr_may_rewrite CtFlavourRole fs Bool -> Bool -> Bool && TyCon -> [TcType] -> EqRel -> TcType -> Bool fr_tf_can_rewrite_ty TyCon new_tf [TcType] new_tf_args EqRel role (Ct -> TcType ctPred Ct ct) -- Implements criteria K1-K3 in Note [Extending the inert equalities] kick_out_eq :: Ct -> Bool kick_out_eq :: Ct -> Bool kick_out_eq (CEqCan { cc_lhs :: Ct -> CanEqLHS cc_lhs = CanEqLHS lhs, cc_rhs :: Ct -> TcType cc_rhs = TcType rhs_ty , cc_ev :: Ct -> CtEvidence cc_ev = CtEvidence ev, cc_eq_rel :: Ct -> EqRel cc_eq_rel = EqRel eq_rel }) | Bool -> Bool not (CtFlavourRole -> Bool fr_may_rewrite CtFlavourRole fs) = Bool False -- (K0) Keep it in the inert set if the new thing can't rewrite it -- Below here (fr_may_rewrite fs) is True | TyVarLHS TcTyVar _ <- CanEqLHS lhs , CtFlavourRole fs CtFlavourRole -> CtFlavourRole -> Bool `eqCanRewriteFR` CtFlavourRole new_fr = Bool False -- (K4) Keep it in the inert set if the LHS is a tyvar and -- it can rewrite the work item. See Note [K4] | EqRel -> TcType -> Bool fr_can_rewrite_ty EqRel eq_rel (CanEqLHS -> TcType canEqLHSType CanEqLHS lhs) = Bool True -- (K1) -- The above check redundantly checks the role & flavour, -- but it's very convenient | Bool kick_out_for_inertness = Bool True -- (K2) | Bool kick_out_for_completeness = Bool True -- (K3) | Bool otherwise = Bool False where fs :: CtFlavourRole fs = (CtEvidence -> CtFlavour ctEvFlavour CtEvidence ev, EqRel eq_rel) kick_out_for_inertness :: Bool kick_out_for_inertness = (CtFlavourRole fs CtFlavourRole -> CtFlavourRole -> Bool `eqCanRewriteFR` CtFlavourRole fs) -- (K2a) Bool -> Bool -> Bool && EqRel -> TcType -> Bool fr_can_rewrite_ty EqRel eq_rel TcType rhs_ty -- (K2b) kick_out_for_completeness :: Bool kick_out_for_completeness -- (K3) and Note [K3: completeness of solving] = case EqRel eq_rel of EqRel NomEq -> TcType rhs_ty TcType -> TcType -> Bool `eqType` CanEqLHS -> TcType canEqLHSType CanEqLHS new_lhs -- (K3a) EqRel ReprEq -> CanEqLHS -> TcType -> Bool is_can_eq_lhs_head CanEqLHS new_lhs TcType rhs_ty -- (K3b) kick_out_eq Ct ct = String -> SDoc -> Bool forall a. HasCallStack => String -> SDoc -> a pprPanic String "kick_out_eq" (Ct -> SDoc forall a. Outputable a => a -> SDoc ppr Ct ct) is_can_eq_lhs_head :: CanEqLHS -> TcType -> Bool is_can_eq_lhs_head (TyVarLHS TcTyVar tv) = TcType -> Bool go where go :: TcType -> Bool go (Rep.TyVarTy TcTyVar tv') = TcTyVar tv TcTyVar -> TcTyVar -> Bool forall a. Eq a => a -> a -> Bool == TcTyVar tv' go (Rep.AppTy TcType fun TcType _) = TcType -> Bool go TcType fun go (Rep.CastTy TcType ty KindCoercion _) = TcType -> Bool go TcType ty go (Rep.TyConApp {}) = Bool False go (Rep.LitTy {}) = Bool False go (Rep.ForAllTy {}) = Bool False go (Rep.FunTy {}) = Bool False go (Rep.CoercionTy {}) = Bool False is_can_eq_lhs_head (TyFamLHS TyCon fun_tc [TcType] fun_args) = TcType -> Bool go where go :: TcType -> Bool go (Rep.TyVarTy {}) = Bool False go (Rep.AppTy {}) = Bool False -- no TyConApp to the left of an AppTy go (Rep.CastTy TcType ty KindCoercion _) = TcType -> Bool go TcType ty go (Rep.TyConApp TyCon tc [TcType] args) = TyCon -> [TcType] -> TyCon -> [TcType] -> Bool tcEqTyConApps TyCon fun_tc [TcType] fun_args TyCon tc [TcType] args go (Rep.LitTy {}) = Bool False go (Rep.ForAllTy {}) = Bool False go (Rep.FunTy {}) = Bool False go (Rep.CoercionTy {}) = Bool False {- Note [kickOutRewritable] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ See also Note [inert_eqs: the inert equalities]. When we add a new inert equality (lhs ~N ty) to the inert set, we must kick out any inert items that could be rewritten by the new equality, to maintain the inert-set invariants. - We want to kick out an existing inert constraint if a) the new constraint can rewrite the inert one b) 'lhs' is free in the inert constraint (so that it *will*) rewrite it if we kick it out. For (b) we use anyRewritableCanLHS, which examines the types /and kinds/ that are directly visible in the type. Hence we will have exposed all the rewriting we care about to make the most precise kinds visible for matching classes etc. No need to kick out constraints that mention type variables whose kinds contain this LHS! - We don't kick out constraints from inert_solved_dicts, and inert_solved_funeqs optimistically. But when we lookup we have to take the substitution into account NB: we could in principle avoid kick-out: a) When unifying a meta-tyvar from an outer level, because then the entire implication will be iterated; see Note [The Unification Level Flag] in GHC.Tc.Solver.Monad. b) For Givens, after a unification. By (GivenInv) in GHC.Tc.Utils.TcType Note [TcLevel invariants], a Given can't include a meta-tyvar from its own level, so it falls under (a). Of course, we must still kick out Givens when adding a new non-unification Given. But kicking out more vigorously may lead to earlier unification and fewer iterations, so we don't take advantage of these possibilities. Note [Rewrite insolubles] ~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have an insoluble alpha ~ [alpha], which is insoluble because an occurs check. And then we unify alpha := [Int]. Then we really want to rewrite the insoluble to [Int] ~ [[Int]]. Now it can be decomposed. Otherwise we end up with a "Can't match [Int] ~ [[Int]]" which is true, but a bit confusing because the outer type constructors match. Hence: * In the main simplifier loops in GHC.Tc.Solver (solveWanteds, simpl_loop), we feed the insolubles in solveSimpleWanteds, so that they get rewritten (albeit not solved). * We kick insolubles out of the inert set, if they can be rewritten (see GHC.Tc.Solver.Monad.kick_out_rewritable) * We rewrite those insolubles in GHC.Tc.Solver.Canonical. See Note [Make sure that insolubles are fully rewritten] in GHC.Tc.Solver.Canonical. -} {- ********************************************************************* * * Queries * * * * ********************************************************************* -} mentionsOuterVar :: TcLevel -> CtEvidence -> Bool mentionsOuterVar :: TcLevel -> CtEvidence -> Bool mentionsOuterVar TcLevel tclvl CtEvidence ev = (TcTyVar -> Bool) -> TcType -> Bool anyFreeVarsOfType (TcLevel -> TcTyVar -> Bool isOuterTyVar TcLevel tclvl) (TcType -> Bool) -> TcType -> Bool forall a b. (a -> b) -> a -> b $ CtEvidence -> TcType ctEvPred CtEvidence ev isOuterTyVar :: TcLevel -> TyCoVar -> Bool -- True of a type variable that comes from a -- shallower level than the ambient level (tclvl) isOuterTyVar :: TcLevel -> TcTyVar -> Bool isOuterTyVar TcLevel tclvl TcTyVar tv | TcTyVar -> Bool isTyVar TcTyVar tv = Bool -> SDoc -> Bool -> Bool forall a. HasCallStack => Bool -> SDoc -> a -> a assertPpr (Bool -> Bool not (TcLevel -> TcTyVar -> Bool isTouchableMetaTyVar TcLevel tclvl TcTyVar tv)) (TcTyVar -> SDoc forall a. Outputable a => a -> SDoc ppr TcTyVar tv SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> TcLevel -> SDoc forall a. Outputable a => a -> SDoc ppr TcLevel tclvl) (Bool -> Bool) -> Bool -> Bool forall a b. (a -> b) -> a -> b $ TcLevel tclvl TcLevel -> TcLevel -> Bool `strictlyDeeperThan` TcTyVar -> TcLevel tcTyVarLevel TcTyVar tv -- ASSERT: we are dealing with Givens here, and invariant (GivenInv) from -- Note Note [TcLevel invariants] in GHC.Tc.Utils.TcType ensures that there can't -- be a touchable meta tyvar. If this wasn't true, you might worry that, -- at level 3, a meta-tv alpha[3] gets unified with skolem b[2], and thereby -- becomes "outer" even though its level numbers says it isn't. | Bool otherwise = Bool False -- Coercion variables; doesn't much matter noGivenNewtypeReprEqs :: TyCon -> InertSet -> Bool -- True <=> there is no Irred looking like (N tys1 ~ N tys2) -- See Note [Decomposing newtype equalities] (EX2) in GHC.Tc.Solver.Canonical -- This is the only call site. noGivenNewtypeReprEqs :: TyCon -> InertSet -> Bool noGivenNewtypeReprEqs TyCon tc InertSet inerts = Bool -> Bool not ((Ct -> Bool) -> Cts -> Bool forall a. (a -> Bool) -> Bag a -> Bool anyBag Ct -> Bool might_help (InertCans -> Cts inert_irreds (InertSet -> InertCans inert_cans InertSet inerts))) where might_help :: Ct -> Bool might_help Ct ct = case TcType -> Pred classifyPredType (Ct -> TcType ctPred Ct ct) of EqPred EqRel ReprEq TcType t1 TcType t2 | Just (TyCon tc1,[TcType] _) <- HasCallStack => TcType -> Maybe (TyCon, [TcType]) TcType -> Maybe (TyCon, [TcType]) tcSplitTyConApp_maybe TcType t1 , TyCon tc TyCon -> TyCon -> Bool forall a. Eq a => a -> a -> Bool == TyCon tc1 , Just (TyCon tc2,[TcType] _) <- HasCallStack => TcType -> Maybe (TyCon, [TcType]) TcType -> Maybe (TyCon, [TcType]) tcSplitTyConApp_maybe TcType t2 , TyCon tc TyCon -> TyCon -> Bool forall a. Eq a => a -> a -> Bool == TyCon tc2 -> Bool True Pred _ -> Bool False -- | Returns True iff there are no Given constraints that might, -- potentially, match the given class consraint. This is used when checking to see if a -- Given might overlap with an instance. See Note [Instance and Given overlap] -- in "GHC.Tc.Solver.Interact" noMatchableGivenDicts :: InertSet -> CtLoc -> Class -> [TcType] -> Bool noMatchableGivenDicts :: InertSet -> CtLoc -> Class -> [TcType] -> Bool noMatchableGivenDicts inerts :: InertSet inerts@(IS { inert_cans :: InertSet -> InertCans inert_cans = InertCans inert_cans }) CtLoc loc_w Class clas [TcType] tys = Bool -> Bool not (Bool -> Bool) -> Bool -> Bool forall a b. (a -> b) -> a -> b $ (Ct -> Bool) -> Cts -> Bool forall a. (a -> Bool) -> Bag a -> Bool anyBag Ct -> Bool matchable_given (Cts -> Bool) -> Cts -> Bool forall a b. (a -> b) -> a -> b $ DictMap Ct -> Class -> Cts forall a. DictMap a -> Class -> Bag a findDictsByClass (InertCans -> DictMap Ct inert_dicts InertCans inert_cans) Class clas where pred_w :: TcType pred_w = Class -> [TcType] -> TcType mkClassPred Class clas [TcType] tys matchable_given :: Ct -> Bool matchable_given :: Ct -> Bool matchable_given Ct ct | CtGiven { ctev_loc :: CtEvidence -> CtLoc ctev_loc = CtLoc loc_g, ctev_pred :: CtEvidence -> TcType ctev_pred = TcType pred_g } <- Ct -> CtEvidence ctEvidence Ct ct = Maybe Subst -> Bool forall a. Maybe a -> Bool isJust (Maybe Subst -> Bool) -> Maybe Subst -> Bool forall a b. (a -> b) -> a -> b $ InertSet -> TcType -> CtLoc -> TcType -> CtLoc -> Maybe Subst mightEqualLater InertSet inerts TcType pred_g CtLoc loc_g TcType pred_w CtLoc loc_w | Bool otherwise = Bool False mightEqualLater :: InertSet -> TcPredType -> CtLoc -> TcPredType -> CtLoc -> Maybe Subst -- See Note [What might equal later?] -- Used to implement logic in Note [Instance and Given overlap] in GHC.Tc.Solver.Interact mightEqualLater :: InertSet -> TcType -> CtLoc -> TcType -> CtLoc -> Maybe Subst mightEqualLater InertSet inert_set TcType given_pred CtLoc given_loc TcType wanted_pred CtLoc wanted_loc | CtLoc -> CtLoc -> Bool prohibitedSuperClassSolve CtLoc given_loc CtLoc wanted_loc = Maybe Subst forall a. Maybe a Nothing | Bool otherwise = case BindFun -> [TcType] -> [TcType] -> UnifyResult tcUnifyTysFG BindFun bind_fun [TcType flattened_given] [TcType flattened_wanted] of Unifiable Subst subst -> Subst -> Maybe Subst forall a. a -> Maybe a Just Subst subst MaybeApart MaybeApartReason reason Subst subst | MaybeApartReason MARInfinite <- MaybeApartReason reason -- see Example 7 in the Note. -> Maybe Subst forall a. Maybe a Nothing | Bool otherwise -> Subst -> Maybe Subst forall a. a -> Maybe a Just Subst subst UnifyResult SurelyApart -> Maybe Subst forall a. Maybe a Nothing where in_scope :: InScopeSet in_scope = VarSet -> InScopeSet mkInScopeSet (VarSet -> InScopeSet) -> VarSet -> InScopeSet forall a b. (a -> b) -> a -> b $ [TcType] -> VarSet tyCoVarsOfTypes [TcType given_pred, TcType wanted_pred] -- NB: flatten both at the same time, so that we can share mappings -- from type family applications to variables, and also to guarantee -- that the fresh variables are really fresh between the given and -- the wanted. Flattening both at the same time is needed to get -- Example 10 from the Note. ([TcType flattened_given, TcType flattened_wanted], TyVarEnv (TyCon, [TcType]) var_mapping) = InScopeSet -> [TcType] -> ([TcType], TyVarEnv (TyCon, [TcType])) flattenTysX InScopeSet in_scope [TcType given_pred, TcType wanted_pred] bind_fun :: BindFun bind_fun :: BindFun bind_fun TcTyVar tv TcType rhs_ty | TcTyVar -> Bool isMetaTyVar TcTyVar tv , TcTyVar -> MetaInfo -> TcType -> Bool can_unify TcTyVar tv (TcTyVar -> MetaInfo metaTyVarInfo TcTyVar tv) TcType rhs_ty -- this checks for CycleBreakerTvs and TyVarTvs; forgetting -- the latter was #19106. = BindFlag BindMe -- See Examples 4, 5, and 6 from the Note | Just (TyCon _fam_tc, [TcType] fam_args) <- TyVarEnv (TyCon, [TcType]) -> TcTyVar -> Maybe (TyCon, [TcType]) forall a. VarEnv a -> TcTyVar -> Maybe a lookupVarEnv TyVarEnv (TyCon, [TcType]) var_mapping TcTyVar tv , (TcTyVar -> Bool) -> [TcType] -> Bool anyFreeVarsOfTypes TcTyVar -> Bool mentions_meta_ty_var [TcType] fam_args = BindFlag BindMe | Bool otherwise = BindFlag Apart -- True for TauTv and TyVarTv (and RuntimeUnkTv) meta-tyvars -- (as they can be unified) -- and also for CycleBreakerTvs that mentions meta-tyvars mentions_meta_ty_var :: TyVar -> Bool mentions_meta_ty_var :: TcTyVar -> Bool mentions_meta_ty_var TcTyVar tv | TcTyVar -> Bool isMetaTyVar TcTyVar tv = case TcTyVar -> MetaInfo metaTyVarInfo TcTyVar tv of -- See Examples 8 and 9 in the Note MetaInfo CycleBreakerTv -> (TcTyVar -> Bool) -> TcType -> Bool anyFreeVarsOfType TcTyVar -> Bool mentions_meta_ty_var (TcTyVar -> InertSet -> TcType lookupCycleBreakerVar TcTyVar tv InertSet inert_set) MetaInfo _ -> Bool True | Bool otherwise = Bool False -- like startSolvingByUnification, but allows cbv variables to unify can_unify :: TcTyVar -> MetaInfo -> Type -> Bool can_unify :: TcTyVar -> MetaInfo -> TcType -> Bool can_unify TcTyVar _lhs_tv MetaInfo TyVarTv TcType rhs_ty -- see Example 3 from the Note | Just TcTyVar rhs_tv <- TcType -> Maybe TcTyVar getTyVar_maybe TcType rhs_ty = case TcTyVar -> TcTyVarDetails tcTyVarDetails TcTyVar rhs_tv of MetaTv { mtv_info :: TcTyVarDetails -> MetaInfo mtv_info = MetaInfo TyVarTv } -> Bool True MetaTv {} -> Bool False -- could unify with anything SkolemTv {} -> Bool True TcTyVarDetails RuntimeUnk -> Bool True | Bool otherwise -- not a var on the RHS = Bool False can_unify TcTyVar lhs_tv MetaInfo _other TcType _rhs_ty = TcTyVar -> Bool mentions_meta_ty_var TcTyVar lhs_tv -- | Is it (potentially) loopy to use the first @ct1@ to solve @ct2@? -- -- Necessary (but not sufficient) conditions for this function to return @True@: -- -- - @ct1@ and @ct2@ both arise from superclass expansion, -- - @ct1@ is a Given and @ct2@ is a Wanted. -- -- See Note [Solving superclass constraints] in GHC.Tc.TyCl.Instance, (sc2). prohibitedSuperClassSolve :: CtLoc -- ^ is it loopy to use this one ... -> CtLoc -- ^ ... to solve this one? -> Bool -- ^ True ==> don't solve it prohibitedSuperClassSolve :: CtLoc -> CtLoc -> Bool prohibitedSuperClassSolve CtLoc given_loc CtLoc wanted_loc | GivenSCOrigin SkolemInfoAnon _ Int _ Bool blocked <- CtLoc -> CtOrigin ctLocOrigin CtLoc given_loc , Bool blocked , ScOrigin ClsInstOrQC _ NakedScFlag NakedSc <- CtLoc -> CtOrigin ctLocOrigin CtLoc wanted_loc = Bool True -- Prohibited if the Wanted is a superclass -- and the Given has come via a superclass selection from -- a predicate bigger than the head | Bool otherwise = Bool False {- Note [What might equal later?] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We must determine whether a Given might later equal a Wanted. We definitely need to account for the possibility that any metavariable might be arbitrarily instantiated. Yet we do *not* want to allow skolems in to be instantiated, as we've already rewritten with respect to any Givens. (We're solving a Wanted here, and so all Givens have already been processed.) This is best understood by example. 1. C alpha ~? C Int That given certainly might match later. 2. C a ~? C Int No. No new givens are going to arise that will get the `a` to rewrite to Int. 3. C alpha[tv] ~? C Int That alpha[tv] is a TyVarTv, unifiable only with other type variables. It cannot equal later. 4. C (F alpha) ~? C Int Sure -- that can equal later, if we learn something useful about alpha. 5. C (F alpha[tv]) ~? C Int This, too, might equal later. Perhaps we have [G] F b ~ Int elsewhere. Or maybe we have C (F alpha[tv] beta[tv]), these unify with each other, and F x x = Int. Remember: returning True doesn't commit ourselves to anything. 6. C (F a) ~? C a No, this won't match later. If we could rewrite (F a) or a, we would have by now. But see also Red Herring below. 7. C (Maybe alpha) ~? C alpha We say this cannot equal later, because it would require alpha := Maybe (Maybe (Maybe ...)). While such a type can be contrived, we choose not to worry about it. See Note [Infinitary substitution in lookup] in GHC.Core.InstEnv. Getting this wrong let to #19107, tested in typecheck/should_compile/T19107. 8. C cbv ~? C Int where cbv = F a The cbv is a cycle-breaker var which stands for F a. See Note [Type equality cycles] in GHC.Tc.Solver.Canonical. This is just like case 6, and we say "no". Saying "no" here is essential in getting the parser to type-check, with its use of DisambECP. 9. C cbv ~? C Int where cbv = F alpha Here, we might indeed equal later. Distinguishing between this case and Example 8 is why we need the InertSet in mightEqualLater. 10. C (F alpha, Int) ~? C (Bool, F alpha) This cannot equal later, because F a would have to equal both Bool and Int. To deal with type family applications, we use the Core flattener. See Note [Flattening type-family applications when matching instances] in GHC.Core.Unify. The Core flattener replaces all type family applications with fresh variables. The next question: should we allow these fresh variables in the domain of a unifying substitution? A type family application that mentions only skolems (example 6) is settled: any skolems would have been rewritten w.r.t. Givens by now. These type family applications match only themselves. A type family application that mentions metavariables, on the other hand, can match anything. So, if the original type family application contains a metavariable, we use BindMe to tell the unifier to allow it in the substitution. On the other hand, a type family application with only skolems is considered rigid. This treatment fixes #18910 and is tested in typecheck/should_compile/InstanceGivenOverlap{,2} Red Herring ~~~~~~~~~~~ In #21208, we have this scenario: instance forall b. C b [G] C a[sk] [W] C (F a[sk]) What should we do with that wanted? According to the logic above, the Given cannot match later (this is example 6), and so we use the global instance. But wait, you say: What if we learn later (say by a future type instance F a = a) that F a unifies with a? That looks like the Given might really match later! This mechanism described in this Note is *not* about this kind of situation, however. It is all asking whether a Given might match the Wanted *in this run of the solver*. It is *not* about whether a variable might be instantiated so that the Given matches, or whether a type instance introduced in a downstream module might make the Given match. The reason we care about what might match later is only about avoiding order-dependence. That is, we don't want to commit to a course of action that depends on seeing constraints in a certain order. But an instantiation of a variable and a later type instance don't introduce order dependency in this way, and so mightMatchLater is right to ignore these possibilities. Here is an example, with no type families, that is perhaps clearer: instance forall b. C (Maybe b) [G] C (Maybe Int) [W] C (Maybe a) What to do? We *might* say that the Given could match later and should thus block us from using the global instance. But we don't do this. Instead, we rely on class coherence to say that choosing the global instance is just fine, even if later we call a function with (a := Int). After all, in this run of the solver, [G] C (Maybe Int) will definitely never match [W] C (Maybe a). (Recall that we process Givens before Wanteds, so there is no [G] a ~ Int hanging about unseen.) Interestingly, in the first case (from #21208), the behavior changed between GHC 8.10.7 and GHC 9.2, with the latter behaving correctly and the former reporting overlapping instances. Test case: typecheck/should_compile/T21208. -} {- ********************************************************************* * * Cycle breakers * * ********************************************************************* -} -- | Return the type family application a CycleBreakerTv maps to. lookupCycleBreakerVar :: TcTyVar -- ^ cbv, must be a CycleBreakerTv -> InertSet -> TcType -- ^ type family application the cbv maps to lookupCycleBreakerVar :: TcTyVar -> InertSet -> TcType lookupCycleBreakerVar TcTyVar cbv (IS { inert_cycle_breakers :: InertSet -> CycleBreakerVarStack inert_cycle_breakers = CycleBreakerVarStack cbvs_stack }) -- This function looks at every environment in the stack. This is necessary -- to avoid #20231. This function (and its one usage site) is the only reason -- that we store a stack instead of just the top environment. | Just TcType tyfam_app <- Bool -> Maybe TcType -> Maybe TcType forall a. HasCallStack => Bool -> a -> a assert (TcTyVar -> Bool isCycleBreakerTyVar TcTyVar cbv) (Maybe TcType -> Maybe TcType) -> Maybe TcType -> Maybe TcType forall a b. (a -> b) -> a -> b $ NonEmpty (Maybe TcType) -> Maybe TcType forall (f :: * -> *) a. Foldable f => f (Maybe a) -> Maybe a firstJusts (([(TcTyVar, TcType)] -> Maybe TcType) -> CycleBreakerVarStack -> NonEmpty (Maybe TcType) forall a b. (a -> b) -> NonEmpty a -> NonEmpty b NE.map (TcTyVar -> [(TcTyVar, TcType)] -> Maybe TcType forall a b. Eq a => a -> [(a, b)] -> Maybe b lookup TcTyVar cbv) CycleBreakerVarStack cbvs_stack) = TcType tyfam_app | Bool otherwise = String -> SDoc -> TcType forall a. HasCallStack => String -> SDoc -> a pprPanic String "lookupCycleBreakerVar found an unbound cycle breaker" (TcTyVar -> SDoc forall a. Outputable a => a -> SDoc ppr TcTyVar cbv SDoc -> SDoc -> SDoc forall doc. IsDoc doc => doc -> doc -> doc $$ CycleBreakerVarStack -> SDoc forall a. Outputable a => a -> SDoc ppr CycleBreakerVarStack cbvs_stack) -- | Push a fresh environment onto the cycle-breaker var stack. Useful -- when entering a nested implication. pushCycleBreakerVarStack :: CycleBreakerVarStack -> CycleBreakerVarStack pushCycleBreakerVarStack :: CycleBreakerVarStack -> CycleBreakerVarStack pushCycleBreakerVarStack = ([] [(TcTyVar, TcType)] -> CycleBreakerVarStack -> CycleBreakerVarStack forall a. a -> NonEmpty a -> NonEmpty a <|) -- | Add a new cycle-breaker binding to the top environment on the stack. insertCycleBreakerBinding :: TcTyVar -- ^ cbv, must be a CycleBreakerTv -> TcType -- ^ cbv's expansion -> CycleBreakerVarStack -> CycleBreakerVarStack insertCycleBreakerBinding :: TcTyVar -> TcType -> CycleBreakerVarStack -> CycleBreakerVarStack insertCycleBreakerBinding TcTyVar cbv TcType expansion ([(TcTyVar, TcType)] top_env :| [[(TcTyVar, TcType)]] rest_envs) = Bool -> CycleBreakerVarStack -> CycleBreakerVarStack forall a. HasCallStack => Bool -> a -> a assert (TcTyVar -> Bool isCycleBreakerTyVar TcTyVar cbv) (CycleBreakerVarStack -> CycleBreakerVarStack) -> CycleBreakerVarStack -> CycleBreakerVarStack forall a b. (a -> b) -> a -> b $ ((TcTyVar cbv, TcType expansion) (TcTyVar, TcType) -> [(TcTyVar, TcType)] -> [(TcTyVar, TcType)] forall a. a -> [a] -> [a] : [(TcTyVar, TcType)] top_env) [(TcTyVar, TcType)] -> [[(TcTyVar, TcType)]] -> CycleBreakerVarStack forall a. a -> [a] -> NonEmpty a :| [[(TcTyVar, TcType)]] rest_envs -- | Perform a monadic operation on all pairs in the top environment -- in the stack. forAllCycleBreakerBindings_ :: Monad m => CycleBreakerVarStack -> (TcTyVar -> TcType -> m ()) -> m () forAllCycleBreakerBindings_ :: forall (m :: * -> *). Monad m => CycleBreakerVarStack -> (TcTyVar -> TcType -> m ()) -> m () forAllCycleBreakerBindings_ ([(TcTyVar, TcType)] top_env :| [[(TcTyVar, TcType)]] _rest_envs) TcTyVar -> TcType -> m () action = [(TcTyVar, TcType)] -> ((TcTyVar, TcType) -> m ()) -> m () forall (t :: * -> *) (m :: * -> *) a b. (Foldable t, Monad m) => t a -> (a -> m b) -> m () forM_ [(TcTyVar, TcType)] top_env ((TcTyVar -> TcType -> m ()) -> (TcTyVar, TcType) -> m () forall a b c. (a -> b -> c) -> (a, b) -> c uncurry TcTyVar -> TcType -> m () action) {-# INLINABLE forAllCycleBreakerBindings_ #-} -- to allow SPECIALISE later