\begin{code}
module TcCanonical(
canonicalize, emitWorkNC,
StopOrContinue (..)
) where
#include "HsVersions.h"
import TcRnTypes
import TcType
import Type
import Kind
import TcEvidence
import Class
import TyCon
import TypeRep
import Var
import VarEnv
import OccName( OccName )
import Outputable
import Control.Monad ( when )
import DynFlags( DynFlags )
import VarSet
import TcSMonad
import FastString
import Util
import BasicTypes
import Maybes( catMaybes )
\end{code}
%************************************************************************
%* *
%* The Canonicaliser *
%* *
%************************************************************************
Note [Canonicalization]
~~~~~~~~~~~~~~~~~~~~~~~
Canonicalization converts a flat constraint to a canonical form. It is
unary (i.e. treats individual constraints one at a time), does not do
any zonking, but lives in TcS monad because it needs to create fresh
variables (for flattening) and consult the inerts (for efficiency).
The execution plan for canonicalization is the following:
1) Decomposition of equalities happens as necessary until we reach a
variable or type family in one side. There is no decomposition step
for other forms of constraints.
2) If, when we decompose, we discover a variable on the head then we
look at inert_eqs from the current inert for a substitution for this
variable and contine decomposing. Hence we lazily apply the inert
substitution if it is needed.
3) If no more decomposition is possible, we deeply apply the substitution
from the inert_eqs and continue with flattening.
4) During flattening, we examine whether we have already flattened some
function application by looking at all the CTyFunEqs with the same
function in the inert set. The reason for deeply applying the inert
substitution at step (3) is to maximise our chances of matching an
already flattened family application in the inert.
The net result is that a constraint coming out of the canonicalization
phase cannot be rewritten any further from the inerts (but maybe /it/ can
rewrite an inert or still interact with an inert in a further phase in the
simplifier.
\begin{code}
data StopOrContinue
= ContinueWith Ct
| Stop
instance Outputable StopOrContinue where
ppr Stop = ptext (sLit "Stop")
ppr (ContinueWith w) = ptext (sLit "ContinueWith") <+> ppr w
continueWith :: Ct -> TcS StopOrContinue
continueWith = return . ContinueWith
andWhenContinue :: TcS StopOrContinue
-> (Ct -> TcS StopOrContinue)
-> TcS StopOrContinue
andWhenContinue tcs1 tcs2
= do { r <- tcs1
; case r of
Stop -> return Stop
ContinueWith ct -> tcs2 ct }
\end{code}
Note [Caching for canonicals]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Our plan with pre-canonicalization is to be able to solve a constraint
really fast from existing bindings in TcEvBinds. So one may think that
the condition (isCNonCanonical) is not necessary. However consider
the following setup:
InertSet = { [W] d1 : Num t }
WorkList = { [W] d2 : Num t, [W] c : t ~ Int}
Now, we prioritize equalities, but in our concrete example
(should_run/mc17.hs) the first (d2) constraint is dealt with first,
because (t ~ Int) is an equality that only later appears in the
worklist since it is pulled out from a nested implication
constraint. So, let's examine what happens:
- We encounter work item (d2 : Num t)
- Nothing is yet in EvBinds, so we reach the interaction with inerts
and set:
d2 := d1
and we discard d2 from the worklist. The inert set remains unaffected.
- Now the equation ([W] c : t ~ Int) is encountered and kicks-out
(d1 : Num t) from the inerts. Then that equation gets
spontaneously solved, perhaps. We end up with:
InertSet : { [G] c : t ~ Int }
WorkList : { [W] d1 : Num t}
- Now we examine (d1), we observe that there is a binding for (Num
t) in the evidence binds and we set:
d1 := d2
and end up in a loop!
Now, the constraints that get kicked out from the inert set are always
Canonical, so by restricting the use of the pre-canonicalizer to
NonCanonical constraints we eliminate this danger. Moreover, for
canonical constraints we already have good caching mechanisms
(effectively the interaction solver) and we are interested in reducing
things like superclasses of the same non-canonical constraint being
generated hence I don't expect us to lose a lot by introducing the
(isCNonCanonical) restriction.
A similar situation can arise in TcSimplify, at the end of the
solve_wanteds function, where constraints from the inert set are
returned as new work -- our substCt ensures however that if they are
not rewritten by subst, they remain canonical and hence we will not
attempt to solve them from the EvBinds. If on the other hand they did
get rewritten and are now non-canonical they will still not match the
EvBinds, so we are again good.
\begin{code}
canonicalize :: Ct -> TcS StopOrContinue
canonicalize ct@(CNonCanonical { cc_ev = ev })
= do { traceTcS "canonicalize (non-canonical)" (ppr ct)
;
canEvNC ev }
canonicalize (CDictCan { cc_ev = ev
, cc_class = cls
, cc_tyargs = xis })
=
canClass ev cls xis
canonicalize (CTyEqCan { cc_ev = ev
, cc_tyvar = tv
, cc_rhs = xi })
=
canEqTyVar ev NotSwapped tv xi xi
canonicalize (CFunEqCan { cc_ev = ev
, cc_fun = fn
, cc_tyargs = xis1
, cc_rhs = xi2 })
=
canEqLeafFun ev NotSwapped fn xis1 xi2 xi2
canonicalize (CIrredEvCan { cc_ev = ev })
= canIrred ev
canonicalize (CHoleCan { cc_ev = ev, cc_occ = occ })
= canHole ev occ
canEvNC :: CtEvidence -> TcS StopOrContinue
canEvNC ev
= case classifyPredType (ctEvPred ev) of
ClassPred cls tys -> traceTcS "canEvNC:cls" (ppr cls <+> ppr tys) >> canClassNC ev cls tys
EqPred ty1 ty2 -> traceTcS "canEvNC:eq" (ppr ty1 $$ ppr ty2) >> canEqNC ev ty1 ty2
TuplePred tys -> traceTcS "canEvNC:tup" (ppr tys) >> canTuple ev tys
IrredPred {} -> traceTcS "canEvNC:irred" (ppr (ctEvPred ev)) >> canIrred ev
\end{code}
%************************************************************************
%* *
%* Tuple Canonicalization
%* *
%************************************************************************
\begin{code}
canTuple :: CtEvidence -> [PredType] -> TcS StopOrContinue
canTuple ev tys
= do { traceTcS "can_pred" (text "TuplePred!")
; let xcomp = EvTupleMk
xdecomp x = zipWith (\_ i -> EvTupleSel x i) tys [0..]
; ctevs <- xCtEvidence ev (XEvTerm tys xcomp xdecomp)
; canEvVarsCreated ctevs }
\end{code}
%************************************************************************
%* *
%* Class Canonicalization
%* *
%************************************************************************
\begin{code}
canClass, canClassNC
:: CtEvidence
-> Class -> [Type] -> TcS StopOrContinue
canClassNC ev cls tys
= canClass ev cls tys
`andWhenContinue` emitSuperclasses
canClass ev cls tys
= do { (xis, cos) <- flattenMany FMFullFlatten ev tys
; let co = mkTcTyConAppCo Nominal (classTyCon cls) cos
xi = mkClassPred cls xis
; mb <- rewriteEvidence ev xi co
; traceTcS "canClass" (vcat [ ppr ev <+> ppr cls <+> ppr tys
, ppr xi, ppr mb ])
; case mb of
Nothing -> return Stop
Just new_ev -> continueWith $
CDictCan { cc_ev = new_ev
, cc_tyargs = xis, cc_class = cls } }
emitSuperclasses :: Ct -> TcS StopOrContinue
emitSuperclasses ct@(CDictCan { cc_ev = ev , cc_tyargs = xis_new, cc_class = cls })
= do { newSCWorkFromFlavored ev cls xis_new
; continueWith ct }
emitSuperclasses _ = panic "emit_superclasses of non-class!"
\end{code}
Note [Adding superclasses]
~~~~~~~~~~~~~~~~~~~~~~~~~~
Since dictionaries are canonicalized only once in their lifetime, the
place to add their superclasses is canonicalisation (The alternative
would be to do it during constraint solving, but we'd have to be
extremely careful to not repeatedly introduced the same superclass in
our worklist). Here is what we do:
For Givens:
We add all their superclasses as Givens.
For Wanteds:
Generally speaking we want to be able to add superclasses of
wanteds for two reasons:
(1) Oportunities for improvement. Example:
class (a ~ b) => C a b
Wanted constraint is: C alpha beta
We'd like to simply have C alpha alpha. Similar
situations arise in relation to functional dependencies.
(2) To have minimal constraints to quantify over:
For instance, if our wanted constraint is (Eq a, Ord a)
we'd only like to quantify over Ord a.
To deal with (1) above we only add the superclasses of wanteds
which may lead to improvement, that is: equality superclasses or
superclasses with functional dependencies.
We deal with (2) completely independently in TcSimplify. See
Note [Minimize by SuperClasses] in TcSimplify.
Moreover, in all cases the extra improvement constraints are
Derived. Derived constraints have an identity (for now), but
we don't do anything with their evidence. For instance they
are never used to rewrite other constraints.
See also [New Wanted Superclass Work] in TcInteract.
For Deriveds:
We do nothing.
Here's an example that demonstrates why we chose to NOT add
superclasses during simplification: [Comes from ticket #4497]
class Num (RealOf t) => Normed t
type family RealOf x
Assume the generated wanted constraint is:
RealOf e ~ e, Normed e
If we were to be adding the superclasses during simplification we'd get:
Num uf, Normed e, RealOf e ~ e, RealOf e ~ uf
==>
e ~ uf, Num uf, Normed e, RealOf e ~ e
==> [Spontaneous solve]
Num uf, Normed uf, RealOf uf ~ uf
While looks exactly like our original constraint. If we add the superclass again we'd loop.
By adding superclasses definitely only once, during canonicalisation, this situation can't
happen.
\begin{code}
newSCWorkFromFlavored :: CtEvidence -> Class -> [Xi] -> TcS ()
newSCWorkFromFlavored flavor cls xis
| isDerived flavor
= return ()
| isGiven flavor
= do { let sc_theta = immSuperClasses cls xis
xev_decomp x = zipWith (\_ i -> EvSuperClass x i) sc_theta [0..]
xev = XEvTerm { ev_preds = sc_theta
, ev_comp = panic "Can't compose for given!"
, ev_decomp = xev_decomp }
; ctevs <- xCtEvidence flavor xev
; emitWorkNC ctevs }
| isEmptyVarSet (tyVarsOfTypes xis)
= return ()
| otherwise
= do { let sc_rec_theta = transSuperClasses cls xis
impr_theta = filter is_improvement_pty sc_rec_theta
loc = ctev_loc flavor
; traceTcS "newSCWork/Derived" $ text "impr_theta =" <+> ppr impr_theta
; mb_der_evs <- mapM (newDerived loc) impr_theta
; emitWorkNC (catMaybes mb_der_evs) }
is_improvement_pty :: PredType -> Bool
is_improvement_pty ty = go (classifyPredType ty)
where
go (EqPred {}) = True
go (ClassPred cls _tys) = not $ null fundeps
where (_,fundeps) = classTvsFds cls
go (TuplePred ts) = any is_improvement_pty ts
go (IrredPred {}) = True
\end{code}
%************************************************************************
%* *
%* Irreducibles canonicalization
%* *
%************************************************************************
\begin{code}
canIrred :: CtEvidence -> TcS StopOrContinue
canIrred old_ev
= do { let old_ty = ctEvPred old_ev
; traceTcS "can_pred" (text "IrredPred = " <+> ppr old_ty)
; (xi,co) <- flatten FMFullFlatten old_ev old_ty
; mb <- rewriteEvidence old_ev xi co
; case mb of {
Nothing -> return Stop ;
Just new_ev ->
do {
; case classifyPredType (ctEvPred new_ev) of
ClassPred cls tys -> canClassNC new_ev cls tys
TuplePred tys -> canTuple new_ev tys
EqPred ty1 ty2
| something_changed old_ty ty1 ty2 -> canEqNC new_ev ty1 ty2
_ -> continueWith $
CIrredEvCan { cc_ev = new_ev } } } }
where
something_changed old_ty new_ty1 new_ty2
| EqPred old_ty1 old_ty2 <- classifyPredType old_ty
= not ( new_ty1 `tcEqType` old_ty1
&& typeKind new_ty1 `tcEqKind` typeKind old_ty1
&& new_ty2 `tcEqType` old_ty2
&& typeKind new_ty2 `tcEqKind` typeKind old_ty2)
| otherwise
= True
canHole :: CtEvidence -> OccName -> TcS StopOrContinue
canHole ev occ
= do { let ty = ctEvPred ev
; (xi,co) <- flatten FMFullFlatten ev ty
; mb <- rewriteEvidence ev xi co
; case mb of
Just new_ev -> emitInsoluble (CHoleCan { cc_ev = new_ev, cc_occ = occ })
Nothing -> return ()
; return Stop }
\end{code}
%************************************************************************
%* *
%* Flattening (eliminating all function symbols) *
%* *
%************************************************************************
Note [Flattening]
~~~~~~~~~~~~~~~~~~~~
flatten ty ==> (xi, cc)
where
xi has no type functions, unless they appear under ForAlls
cc = Auxiliary given (equality) constraints constraining
the fresh type variables in xi. Evidence for these
is always the identity coercion, because internally the
fresh flattening skolem variables are actually identified
with the types they have been generated to stand in for.
Note that it is flatten's job to flatten *every type function it sees*.
flatten is only called on *arguments* to type functions, by canEqGiven.
Recall that in comments we use alpha[flat = ty] to represent a
flattening skolem variable alpha which has been generated to stand in
for ty.
----- Example of flattening a constraint: ------
flatten (List (F (G Int))) ==> (xi, cc)
where
xi = List alpha
cc = { G Int ~ beta[flat = G Int],
F beta ~ alpha[flat = F beta] }
Here
* alpha and beta are 'flattening skolem variables'.
* All the constraints in cc are 'given', and all their coercion terms
are the identity.
NB: Flattening Skolems only occur in canonical constraints, which
are never zonked, so we don't need to worry about zonking doing
accidental unflattening.
Note that we prefer to leave type synonyms unexpanded when possible,
so when the flattener encounters one, it first asks whether its
transitive expansion contains any type function applications. If so,
it expands the synonym and proceeds; if not, it simply returns the
unexpanded synonym.
\begin{code}
data FlattenMode = FMSubstOnly | FMFullFlatten
flattenMany :: FlattenMode
-> CtEvidence
-> [Type] -> TcS ([Xi], [TcCoercion])
flattenMany f ctxt tys
=
go tys
where go [] = return ([],[])
go (ty:tys) = do { (xi,co) <- flatten f ctxt ty
; (xis,cos) <- go tys
; return (xi:xis,co:cos) }
flatten :: FlattenMode
-> CtEvidence -> TcType -> TcS (Xi, TcCoercion)
flatten f ctxt ty
| Just ty' <- tcView ty
= do { (xi, co) <- flatten f ctxt ty'
; if xi `tcEqType` ty' then return (ty,co)
else return (xi,co) }
flatten _ _ xi@(LitTy {}) = return (xi, mkTcNomReflCo xi)
flatten f ctxt (TyVarTy tv)
= flattenTyVar f ctxt tv
flatten f ctxt (AppTy ty1 ty2)
= do { (xi1,co1) <- flatten f ctxt ty1
; (xi2,co2) <- flatten f ctxt ty2
; traceTcS "flatten/appty" (ppr ty1 $$ ppr ty2 $$ ppr xi1 $$ ppr co1 $$ ppr xi2 $$ ppr co2)
; return (mkAppTy xi1 xi2, mkTcAppCo co1 co2) }
flatten f ctxt (FunTy ty1 ty2)
= do { (xi1,co1) <- flatten f ctxt ty1
; (xi2,co2) <- flatten f ctxt ty2
; return (mkFunTy xi1 xi2, mkTcFunCo Nominal co1 co2) }
flatten f ctxt (TyConApp tc tys)
| not (isSynFamilyTyCon tc)
= do { (xis,cos) <- flattenMany f ctxt tys
; return (mkTyConApp tc xis, mkTcTyConAppCo Nominal tc cos) }
| otherwise
= ASSERT( tyConArity tc <= length tys )
do { (xis, cos) <- flattenMany f ctxt tys
; let (xi_args, xi_rest) = splitAt (tyConArity tc) xis
(cos_args, cos_rest) = splitAt (tyConArity tc) cos
; (rhs_xi, ret_co) <- flattenNestedFamApp f ctxt tc xi_args
; return ( mkAppTys rhs_xi xi_rest
, mkTcAppCos (mkTcSymCo ret_co `mkTcTransCo` mkTcTyConAppCo Nominal tc cos_args) $
cos_rest
)
}
flatten _f ctxt ty@(ForAllTy {})
= do { let (tvs, rho) = splitForAllTys ty
; (rho', co) <- flatten FMSubstOnly ctxt rho
; return (mkForAllTys tvs rho', foldr mkTcForAllCo co tvs) }
\end{code}
Note [Flattening under a forall]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Under a forall, we
(a) MUST apply the inert subsitution
(b) MUST NOT flatten type family applications
Hence FMSubstOnly.
For (a) consider c ~ a, a ~ T (forall b. (b, [c])
If we don't apply the c~a substitution to the second constraint
we won't see the occurs-check error.
For (b) consider (a ~ forall b. F a b), we don't want to flatten
to (a ~ forall b.fsk, F a b ~ fsk)
because now the 'b' has escaped its scope. We'd have to flatten to
(a ~ forall b. fsk b, forall b. F a b ~ fsk b)
and we have not begun to think about how to make that work!
\begin{code}
flattenNestedFamApp :: FlattenMode -> CtEvidence
-> TyCon -> [TcType]
-> TcS (Xi, TcCoercion)
flattenNestedFamApp FMSubstOnly _ tc xi_args
= do { let fam_ty = mkTyConApp tc xi_args
; return (fam_ty, mkTcNomReflCo fam_ty) }
flattenNestedFamApp FMFullFlatten ctxt tc xi_args
= do { let fam_ty = mkTyConApp tc xi_args
; mb_ct <- lookupFlatEqn tc xi_args
; case mb_ct of
Just (ctev, rhs_ty)
| ctev `canRewriteOrSame `ctxt
->
do { (rhs_xi,co) <- flatten FMFullFlatten ctev rhs_ty
; let final_co = evTermCoercion (ctEvTerm ctev)
`mkTcTransCo` mkTcSymCo co
; traceTcS "flatten/flat-cache hit" $ (ppr ctev $$ ppr rhs_xi $$ ppr final_co)
; return (rhs_xi, final_co) }
_ -> do { (ctev, rhs_xi) <- newFlattenSkolem ctxt fam_ty
; extendFlatCache tc xi_args ctev rhs_xi
; let ct = CFunEqCan { cc_ev = ctev
, cc_fun = tc
, cc_tyargs = xi_args
, cc_rhs = rhs_xi }
; updWorkListTcS $ extendWorkListFunEq ct
; traceTcS "flatten/flat-cache miss" $ (ppr fam_ty $$ ppr rhs_xi $$ ppr ctev)
; return (rhs_xi, evTermCoercion (ctEvTerm ctev)) }
}
\end{code}
\begin{code}
flattenTyVar :: FlattenMode -> CtEvidence -> TcTyVar -> TcS (Xi, TcCoercion)
flattenTyVar f ctxt tv
= do { mb_yes <- flattenTyVarOuter f ctxt tv
; case mb_yes of
Left tv' ->
return (ty, mkTcNomReflCo ty)
where
ty = mkTyVarTy tv'
Right (ty1, co1) ->
do { (ty2, co2) <- flatten f ctxt ty1
; return (ty2, co2 `mkTcTransCo` co1) }
}
flattenTyVarOuter, flattenTyVarFinal
:: FlattenMode -> CtEvidence
-> TcTyVar
-> TcS (Either TyVar (TcType, TcCoercion))
flattenTyVarOuter f ctxt tv
| not (isTcTyVar tv)
= flattenTyVarFinal f ctxt tv
| otherwise
= do { mb_ty <- isFilledMetaTyVar_maybe tv
; case mb_ty of {
Just ty -> do { traceTcS "Following filled tyvar" (ppr tv <+> equals <+> ppr ty)
; return (Right (ty, mkTcNomReflCo ty)) } ;
Nothing ->
do { ty_binds <- getTcSTyBindsMap
; case lookupVarEnv ty_binds tv of {
Just (_tv,ty) -> do { traceTcS "Following bound tyvar" (ppr tv <+> equals <+> ppr ty)
; return (Right (ty, mkTcNomReflCo ty)) } ;
Nothing ->
do { ieqs <- getInertEqs
; case lookupVarEnv ieqs tv of
Just (ct:_)
| let ctev = ctEvidence ct
rhs_ty = cc_rhs ct
, ctev `canRewrite` ctxt
-> do { traceTcS "Following inert tyvar" (ppr tv <+> equals <+> ppr rhs_ty $$ ppr ctev)
; return (Right (rhs_ty, mkTcSymCo (evTermCoercion (ctEvTerm ctev)))) }
_other -> flattenTyVarFinal f ctxt tv
} } } } }
flattenTyVarFinal f ctxt tv
=
do { let knd = tyVarKind tv
; (new_knd, _kind_co) <- flatten f ctxt knd
; return (Left (setVarType tv new_knd)) }
\end{code}
Note [Non-idempotent inert substitution]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The inert substitution is not idempotent in the broad sense. It is only idempotent in
that it cannot rewrite the RHS of other inert equalities any further. An example of such
an inert substitution is:
[G] g1 : ta8 ~ ta4
[W] g2 : ta4 ~ a5Fj
Observe that the wanted cannot rewrite the solved goal, despite the fact that ta4 appears on
an RHS of an equality. Now, imagine a constraint:
[W] g3: ta8 ~ Int
coming in. If we simply apply once the inert substitution we will get:
[W] g3_1: ta4 ~ Int
and because potentially ta4 is untouchable we will try to insert g3_1 in the inert set,
getting a panic since the inert only allows ONE equation per LHS type variable (as it
should).
For this reason, when we reach to flatten a type variable, we flatten it recursively,
so that we can make sure that the inert substitution /is/ fully applied.
Insufficient (non-recursive) rewriting was the reason for #5668.
%************************************************************************
%* *
%* Equalities
%* *
%************************************************************************
\begin{code}
canEvVarsCreated :: [CtEvidence] -> TcS StopOrContinue
canEvVarsCreated [] = return Stop
canEvVarsCreated (ev : evs)
= do { emitWorkNC evs; canEvNC ev }
emitWorkNC :: [CtEvidence] -> TcS ()
emitWorkNC evs
| null evs = return ()
| otherwise = updWorkListTcS (extendWorkListCts (map mk_nc evs))
where
mk_nc ev = mkNonCanonical ev
canEqNC :: CtEvidence -> Type -> Type -> TcS StopOrContinue
canEqNC ev ty1 ty2 = can_eq_nc ev ty1 ty1 ty2 ty2
can_eq_nc, can_eq_nc'
:: CtEvidence
-> Type -> Type
-> Type -> Type
-> TcS StopOrContinue
can_eq_nc ev ty1 ps_ty1 ty2 ps_ty2
= do { traceTcS "can_eq_nc" $
vcat [ ppr ev, ppr ty1, ppr ps_ty1, ppr ty2, ppr ps_ty2 ]
; can_eq_nc' ev ty1 ps_ty1 ty2 ps_ty2 }
can_eq_nc' ev ty1 ps_ty1 ty2 ps_ty2
| Just ty1' <- tcView ty1 = can_eq_nc ev ty1' ps_ty1 ty2 ps_ty2
| Just ty2' <- tcView ty2 = can_eq_nc ev ty1 ps_ty1 ty2' ps_ty2
can_eq_nc' ev (TyConApp fn tys) _ ty2 ps_ty2
| isSynFamilyTyCon fn
= canEqLeafFun ev NotSwapped fn tys ty2 ps_ty2
can_eq_nc' ev ty1 ps_ty1 (TyConApp fn tys) _
| isSynFamilyTyCon fn
= canEqLeafFun ev IsSwapped fn tys ty1 ps_ty1
can_eq_nc' ev (TyVarTy tv1) _ ty2 ps_ty2
= canEqTyVar ev NotSwapped tv1 ty2 ps_ty2
can_eq_nc' ev ty1 ps_ty1 (TyVarTy tv2) _
= canEqTyVar ev IsSwapped tv2 ty1 ps_ty1
can_eq_nc' ev ty1@(LitTy l1) _ (LitTy l2) _
| l1 == l2
= do { when (isWanted ev) $
setEvBind (ctev_evar ev) (EvCoercion (mkTcNomReflCo ty1))
; return Stop }
can_eq_nc' ev (TyConApp tc1 tys1) _ (TyConApp tc2 tys2) _
| isDecomposableTyCon tc1
, isDecomposableTyCon tc2
= canDecomposableTyConApp ev tc1 tys1 tc2 tys2
can_eq_nc' ev (TyConApp tc1 _) ps_ty1 (FunTy {}) ps_ty2
| isDecomposableTyCon tc1
= canEqFailure ev ps_ty1 ps_ty2
can_eq_nc' ev (FunTy s1 t1) _ (FunTy s2 t2) _
= canDecomposableTyConAppOK ev funTyCon [s1,t1] [s2,t2]
can_eq_nc' ev (FunTy {}) ps_ty1 (TyConApp tc2 _) ps_ty2
| isDecomposableTyCon tc2
= canEqFailure ev ps_ty1 ps_ty2
can_eq_nc' ev s1@(ForAllTy {}) _ s2@(ForAllTy {}) _
| CtWanted { ctev_loc = loc, ctev_evar = orig_ev } <- ev
= do { let (tvs1,body1) = tcSplitForAllTys s1
(tvs2,body2) = tcSplitForAllTys s2
; if not (equalLength tvs1 tvs2) then
canEqFailure ev s1 s2
else
do { traceTcS "Creating implication for polytype equality" $ ppr ev
; ev_term <- deferTcSForAllEq Nominal loc (tvs1,body1) (tvs2,body2)
; setEvBind orig_ev ev_term
; return Stop } }
| otherwise
= do { traceTcS "Ommitting decomposition of given polytype equality" $
pprEq s1 s2
; return Stop }
can_eq_nc' ev (AppTy s1 t1) ps_ty1 ty2 ps_ty2
= can_eq_app ev NotSwapped s1 t1 ps_ty1 ty2 ps_ty2
can_eq_nc' ev ty1 ps_ty1 (AppTy s2 t2) ps_ty2
= can_eq_app ev IsSwapped s2 t2 ps_ty2 ty1 ps_ty1
can_eq_nc' ev _ ps_ty1 _ ps_ty2
= canEqFailure ev ps_ty1 ps_ty2
can_eq_app, can_eq_flat_app
:: CtEvidence -> SwapFlag
-> Type -> Type -> Type
-> Type -> Type
-> TcS StopOrContinue
can_eq_app ev swapped s1 t1 ps_ty1 ty2 ps_ty2
= do { traceTcS "can_eq_app 1" $
vcat [ ppr ev, ppr swapped, ppr s1, ppr t1, ppr ty2 ]
; (xi_s1, co_s1) <- flatten FMSubstOnly ev s1
; traceTcS "can_eq_app 2" $ vcat [ ppr ev, ppr xi_s1 ]
; if s1 `tcEqType` xi_s1
then can_eq_flat_app ev swapped s1 t1 ps_ty1 ty2 ps_ty2
else
do { (xi_t1, co_t1) <- flatten FMSubstOnly ev t1
; let xi1 = mkAppTy xi_s1 xi_t1
co1 = mkTcAppCo co_s1 co_t1
; traceTcS "can_eq_app 3" $ vcat [ ppr ev, ppr xi1, ppr co1 ]
; mb_ct <- rewriteEqEvidence ev swapped xi1 ps_ty2
co1 (mkTcNomReflCo ps_ty2)
; traceTcS "can_eq_app 4" $ vcat [ ppr ev, ppr xi1, ppr co1 ]
; case mb_ct of
Nothing -> return Stop
Just new_ev -> can_eq_nc new_ev xi1 xi1 ty2 ps_ty2 }}
can_eq_flat_app ev swapped s1 t1 ps_ty1 ty2 ps_ty2
| Just (s2,t2) <- tcSplitAppTy_maybe ty2
= unSwap swapped decompose_it (s1,t1) (s2,t2)
| otherwise
= unSwap swapped (canEqFailure ev) ps_ty1 ps_ty2
where
decompose_it (s1,t1) (s2,t2)
= do { let xevcomp [x,y] = EvCoercion (mkTcAppCo (evTermCoercion x) (evTermCoercion y))
xevcomp _ = error "canEqAppTy: can't happen"
xevdecomp x = let xco = evTermCoercion x
in [ EvCoercion (mkTcLRCo CLeft xco)
, EvCoercion (mkTcLRCo CRight xco)]
; ctevs <- xCtEvidence ev (XEvTerm [mkTcEqPred s1 s2, mkTcEqPred t1 t2] xevcomp xevdecomp)
; canEvVarsCreated ctevs }
canDecomposableTyConApp :: CtEvidence
-> TyCon -> [TcType]
-> TyCon -> [TcType]
-> TcS StopOrContinue
canDecomposableTyConApp ev tc1 tys1 tc2 tys2
| tc1 /= tc2 || length tys1 /= length tys2
= canEqFailure ev (mkTyConApp tc1 tys1) (mkTyConApp tc2 tys2)
| otherwise
= canDecomposableTyConAppOK ev tc1 tys1 tys2
canDecomposableTyConAppOK :: CtEvidence
-> TyCon -> [TcType] -> [TcType]
-> TcS StopOrContinue
canDecomposableTyConAppOK ev tc1 tys1 tys2
= do { let xcomp xs = EvCoercion (mkTcTyConAppCo Nominal tc1 (map evTermCoercion xs))
xdecomp x = zipWith (\_ i -> EvCoercion $ mkTcNthCo i (evTermCoercion x)) tys1 [0..]
xev = XEvTerm (zipWith mkTcEqPred tys1 tys2) xcomp xdecomp
; ctevs <- xCtEvidence ev xev
; canEvVarsCreated ctevs }
canEqFailure :: CtEvidence -> TcType -> TcType -> TcS StopOrContinue
canEqFailure ev ty1 ty2
= do { (s1, co1) <- flatten FMSubstOnly ev ty1
; (s2, co2) <- flatten FMSubstOnly ev ty2
; mb_ct <- rewriteEqEvidence ev NotSwapped s1 s2 co1 co2
; case mb_ct of
Just new_ev -> emitInsoluble (mkNonCanonical new_ev)
Nothing -> pprPanic "canEqFailure" (ppr ev $$ ppr ty1 $$ ppr ty2)
; return Stop }
\end{code}
Note [Canonicalising type applications]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given (s1 t1) ~ ty2, how should we proceed?
The simple things is to see if ty2 is of form (s2 t2), and
decompose. By this time s1 and s2 can't be saturated type
function applications, because those have been dealt with
by an earlier equation in can_eq_nc, so it is always sound to
decompose.
However, over-eager decomposition gives bad error messages
for things like
a b ~ Maybe c
e f ~ p -> q
Suppose (in the first example) we already know a~Array. Then if we
decompose the application eagerly, yielding
a ~ Maybe
b ~ c
we get an error "Can't match Array ~ Maybe",
but we'd prefer to get "Can't match Array b ~ Maybe c".
So instead can_eq_app flattens s1. If flattening does something, it
rewrites, and goes round can_eq_nc again. If flattening
does nothing, then (at least with our present state of knowledge)
we can only decompose, and that is what can_eq_flat_app attempts
to do.
Note [Make sure that insolubles are fully rewritten]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When an equality fails, we still want to rewrite the equality
all the way down, so that it accurately reflects
(a) the mutable reference substitution in force at start of solving
(b) any ty-binds in force at this point in solving
See Note [Kick out insolubles] in TcInteract.
And if we don't do this there is a bad danger that
TcSimplify.applyTyVarDefaulting will find a variable
that has in fact been substituted.
Note [Do not decompose Given polytype equalities]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider [G] (forall a. t1 ~ forall a. t2). Can we decompose this?
No -- what would the evidence look like? So instead we simply discard
this given evidence.
Note [Combining insoluble constraints]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
As this point we have an insoluble constraint, like Int~Bool.
* If it is Wanted, delete it from the cache, so that subsequent
Int~Bool constraints give rise to separate error messages
* But if it is Derived, DO NOT delete from cache. A class constraint
may get kicked out of the inert set, and then have its functional
dependency Derived constraints generated a second time. In that
case we don't want to get two (or more) error messages by
generating two (or more) insoluble fundep constraints from the same
class constraint.
Note [Canonical ordering for equality constraints]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Implemented as (<+=) below:
- Type function applications always come before anything else.
- Variables always come before non-variables (other than type
function applications).
Note that we don't need to unfold type synonyms on the RHS to check
the ordering; that is, in the rules above it's OK to consider only
whether something is *syntactically* a type function application or
not. To illustrate why this is OK, suppose we have an equality of the
form 'tv ~ S a b c', where S is a type synonym which expands to a
top-level application of the type function F, something like
type S a b c = F d e
Then to canonicalize 'tv ~ S a b c' we flatten the RHS, and since S's
expansion contains type function applications the flattener will do
the expansion and then generate a skolem variable for the type
function application, so we end up with something like this:
tv ~ x
F d e ~ x
where x is the skolem variable. This is one extra equation than
absolutely necessary (we could have gotten away with just 'F d e ~ tv'
if we had noticed that S expanded to a top-level type function
application and flipped it around in the first place) but this way
keeps the code simpler.
Unlike the OutsideIn(X) draft of May 7, 2010, we do not care about the
ordering of tv ~ tv constraints. There are several reasons why we
might:
(1) In order to be able to extract a substitution that doesn't
mention untouchable variables after we are done solving, we might
prefer to put touchable variables on the left. However, in and
of itself this isn't necessary; we can always re-orient equality
constraints at the end if necessary when extracting a substitution.
(2) To ensure termination we might think it necessary to put
variables in lexicographic order. However, this isn't actually
necessary as outlined below.
While building up an inert set of canonical constraints, we maintain
the invariant that the equality constraints in the inert set form an
acyclic rewrite system when viewed as L-R rewrite rules. Moreover,
the given constraints form an idempotent substitution (i.e. none of
the variables on the LHS occur in any of the RHS's, and type functions
never show up in the RHS at all), the wanted constraints also form an
idempotent substitution, and finally the LHS of a given constraint
never shows up on the RHS of a wanted constraint. There may, however,
be a wanted LHS that shows up in a given RHS, since we do not rewrite
given constraints with wanted constraints.
Suppose we have an inert constraint set
tg_1 ~ xig_1 -- givens
tg_2 ~ xig_2
...
tw_1 ~ xiw_1 -- wanteds
tw_2 ~ xiw_2
...
where each t_i can be either a type variable or a type function
application. Now suppose we take a new canonical equality constraint,
t' ~ xi' (note among other things this means t' does not occur in xi')
and try to react it with the existing inert set. We show by induction
on the number of t_i which occur in t' ~ xi' that this process will
terminate.
There are several ways t' ~ xi' could react with an existing constraint:
TODO: finish this proof. The below was for the case where the entire
inert set is an idempotent subustitution...
(b) We could have t' = t_j for some j. Then we obtain the new
equality xi_j ~ xi'; note that neither xi_j or xi' contain t_j. We
now canonicalize the new equality, which may involve decomposing it
into several canonical equalities, and recurse on these. However,
none of the new equalities will contain t_j, so they have fewer
occurrences of the t_i than the original equation.
(a) We could have t_j occurring in xi' for some j, with t' /=
t_j. Then we substitute xi_j for t_j in xi' and continue. However,
since none of the t_i occur in xi_j, we have decreased the
number of t_i that occur in xi', since we eliminated t_j and did not
introduce any new ones.
\begin{code}
canEqLeafFun :: CtEvidence
-> SwapFlag
-> TyCon -> [TcType]
-> TcType -> TcType
-> TcS StopOrContinue
canEqLeafFun ev swapped fn tys1 ty2 ps_ty2
| length tys1 > tyConArity fn
=
do { (xi1, co1) <- flatten FMFullFlatten ev (mkTyConApp fn tys1)
; mb <- rewriteEqEvidence ev swapped xi1 ps_ty2
co1 (mkTcNomReflCo ps_ty2)
; case mb of
Nothing -> return Stop
Just new_ev -> can_eq_nc new_ev xi1 xi1 ty2 ps_ty2 }
| otherwise
=
ASSERT( length tys1 == tyConArity fn )
do { traceTcS "canEqLeafFun" $ pprEq (mkTyConApp fn tys1) ps_ty2
; (xis1,cos1) <- flattenMany FMFullFlatten ev tys1
; (xi2, co2) <- flatten FMFullFlatten ev ps_ty2
; let fam_head = mkTyConApp fn xis1
co1 = mkTcTyConAppCo Nominal fn cos1
; mb <- rewriteEqEvidence ev swapped fam_head xi2 co1 co2
; let k1 = typeKind fam_head
k2 = typeKind xi2
; case mb of
Nothing -> return Stop
Just new_ev | k1 `isSubKind` k2
-> continueWith (CFunEqCan { cc_ev = new_ev, cc_fun = fn
, cc_tyargs = xis1, cc_rhs = xi2 })
| otherwise
-> checkKind new_ev fam_head k1 xi2 k2 }
canEqTyVar :: CtEvidence -> SwapFlag
-> TcTyVar
-> TcType -> TcType
-> TcS StopOrContinue
canEqTyVar ev swapped tv1 ty2 ps_ty2
= do { traceTcS "canEqTyVar" (ppr tv1 $$ ppr ty2 $$ ppr swapped)
; mb_yes <- flattenTyVarOuter FMFullFlatten ev tv1
; case mb_yes of
Right (ty1, co1) ->
do { mb <- rewriteEqEvidence ev swapped ty1 ps_ty2
co1 (mkTcNomReflCo ps_ty2)
; traceTcS "canEqTyVar2" (vcat [ppr tv1, ppr ty2, ppr swapped, ppr ty1,
ppUnless (isDerived ev) (ppr co1)])
; case mb of
Nothing -> return Stop
Just new_ev -> can_eq_nc new_ev ty1 ty1 ty2 ps_ty2 }
Left tv1' -> do { (xi2, co2) <- flatten FMFullFlatten ev ps_ty2
; dflags <- getDynFlags
; canEqTyVar2 dflags ev swapped tv1' xi2 co2 } }
canEqTyVar2 :: DynFlags
-> CtEvidence
-> SwapFlag
-> TcTyVar
-> TcType
-> TcCoercion
-> TcS StopOrContinue
canEqTyVar2 dflags ev swapped tv1 xi2 co2
| Just tv2 <- getTyVar_maybe xi2
= canEqTyVarTyVar ev swapped tv1 tv2 co2
| OC_OK xi2' <- occurCheckExpand dflags tv1 xi2
= do { mb <- rewriteEqEvidence ev swapped xi1 xi2' co1 co2
; let k1 = tyVarKind tv1
k2 = typeKind xi2'
; case mb of
Nothing -> return Stop
Just new_ev | k2 `isSubKind` k1
-> continueWith (CTyEqCan { cc_ev = new_ev
, cc_tyvar = tv1, cc_rhs = xi2' })
| otherwise
-> checkKind new_ev xi1 k1 xi2' k2 }
| otherwise
= do { mb <- rewriteEqEvidence ev swapped xi1 xi2 co1 co2
; case mb of
Nothing -> return ()
Just new_ev -> emitInsoluble (mkNonCanonical new_ev)
; return Stop }
where
xi1 = mkTyVarTy tv1
co1 = mkTcNomReflCo xi1
canEqTyVarTyVar :: CtEvidence
-> SwapFlag
-> TyVar -> TyVar
-> TcCoercion
-> TcS StopOrContinue
canEqTyVarTyVar ev swapped tv1 tv2 co2
| tv1 == tv2
= do { when (isWanted ev) $
ASSERT( tcCoercionRole co2 == Nominal )
setEvBind (ctev_evar ev) (EvCoercion (maybeSym swapped co2))
; return Stop }
| reorient_me
= do { mb <- rewriteEqEvidence ev (flipSwap swapped) xi2 xi1
co2 (mkTcNomReflCo xi1)
; case mb of
Nothing -> return Stop
Just new_ev -> continueWith (CTyEqCan { cc_ev = new_ev
, cc_tyvar = tv2, cc_rhs = xi1 }) }
| otherwise
= do { mb <- rewriteEqEvidence ev swapped xi1 xi2
(mkTcNomReflCo xi1) co2
; case mb of
Nothing -> return Stop
Just new_ev | k2 `isSubKind` k1
-> continueWith (CTyEqCan { cc_ev = new_ev
, cc_tyvar = tv1, cc_rhs = xi2 })
| otherwise
-> checkKind ev xi1 k1 xi2 k2 }
where
reorient_me
| k1 `tcEqKind` k2 = tv2 `better_than` tv1
| k1 `isSubKind` k2 = True
| otherwise = False
xi1 = mkTyVarTy tv1
xi2 = mkTyVarTy tv2
k1 = tyVarKind tv1
k2 = tyVarKind tv2
tv2 `better_than` tv1
| isMetaTyVar tv1 = False
| isFlatSkolTyVar tv1 = isMetaTyVar tv2
| otherwise = isMetaTyVar tv2 || isFlatSkolTyVar tv2
checkKind :: CtEvidence
-> TcType -> TcKind
-> TcType -> TcKind
-> TcS StopOrContinue
checkKind new_ev s1 k1 s2 k2
= ASSERT( isKind k1 && isKind k2 )
do { traceTcS "canEqLeaf: incompatible kinds" (vcat [ppr k1, ppr k2])
; updWorkListTcS $ extendWorkListNonEq $
CIrredEvCan { cc_ev = new_ev }
; mw <- newDerived kind_co_loc (mkEqPred k1 k2)
; case mw of
Nothing -> return Stop
Just kev -> canEqNC kev k1 k2 }
where
loc = ctev_loc new_ev
kind_co_loc = setCtLocOrigin loc (KindEqOrigin s1 s2 (ctLocOrigin loc))
\end{code}
Note [Eliminate flat-skols]
~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we have [G] Num (F [a])
then we flatten to
[G] Num fsk
[G] F [a] ~ fsk
where fsk is a flatten-skolem (FlatSkol). Suppose we have
type instance F [a] = a
then we'll reduce the second constraint to
[G] a ~ fsk
and then replace all uses of 'a' with fsk. That's bad because
in error messages intead of saying 'a' we'll say (F [a]). In all
places, including those where the programmer wrote 'a' in the first
place. Very confusing! See Trac #7862.
Solution: re-orient a~fsk to fsk~a, so that we preferentially eliminate
the fsk.
Note [Equalities with incompatible kinds]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
canEqLeaf is about to make a CTyEqCan or CFunEqCan; but both have the
invariant that LHS and RHS satisfy the kind invariants for CTyEqCan,
CFunEqCan. What if we try to unify two things with incompatible
kinds?
eg a ~ b where a::*, b::*->*
or a ~ b where a::*, b::k, k is a kind variable
The CTyEqCan compatKind invariant is important. If we make a CTyEqCan
for a~b, then we might well *substitute* 'b' for 'a', and that might make
a well-kinded type ill-kinded; and that is bad (eg typeKind can crash, see
Trac #7696).
So instead for these ill-kinded equalities we generate a CIrredCan,
which keeps it out of the way until a subsequent substitution (on kind
variables, say) re-activates it.
NB: it is important that the types s1,s2 are flattened and zonked
so that their kinds k1, k2 are inert wrt the substitution. That
means that they can only become the same if we change the inert
set, which in turn will kick out the irreducible equality
E.g. it is WRONG to make an irred (a:k1)~(b:k2)
if we already have a substitution k1:=k2
See also Note [Kind orientation for CTyEqCan] and
Note [Kind orientation for CFunEqCan] in TcRnTypes
Note [Type synonyms and canonicalization]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We treat type synonym applications as xi types, that is, they do not
count as type function applications. However, we do need to be a bit
careful with type synonyms: like type functions they may not be
generative or injective. However, unlike type functions, they are
parametric, so there is no problem in expanding them whenever we see
them, since we do not need to know anything about their arguments in
order to expand them; this is what justifies not having to treat them
as specially as type function applications. The thing that causes
some subtleties is that we prefer to leave type synonym applications
*unexpanded* whenever possible, in order to generate better error
messages.
If we encounter an equality constraint with type synonym applications
on both sides, or a type synonym application on one side and some sort
of type application on the other, we simply must expand out the type
synonyms in order to continue decomposing the equality constraint into
primitive equality constraints. For example, suppose we have
type F a = [Int]
and we encounter the equality
F a ~ [b]
In order to continue we must expand F a into [Int], giving us the
equality
[Int] ~ [b]
which we can then decompose into the more primitive equality
constraint
Int ~ b.
However, if we encounter an equality constraint with a type synonym
application on one side and a variable on the other side, we should
NOT (necessarily) expand the type synonym, since for the purpose of
good error messages we want to leave type synonyms unexpanded as much
as possible. Hence the ps_ty1, ps_ty2 argument passed to canEqTyVar.
Note [occurCheckExpand]
~~~~~~~~~~~~~~~~~~~~~~~
There is a subtle point with type synonyms and the occurs check that
takes place for equality constraints of the form tv ~ xi. As an
example, suppose we have
type F a = Int
and we come across the equality constraint
a ~ F a
This should not actually fail the occurs check, since expanding out
the type synonym results in the legitimate equality constraint a ~
Int. We must actually do this expansion, because unifying a with F a
will lead the type checker into infinite loops later. Put another
way, canonical equality constraints should never *syntactically*
contain the LHS variable in the RHS type. However, we don't always
need to expand type synonyms when doing an occurs check; for example,
the constraint
a ~ F b
is obviously fine no matter what F expands to. And in this case we
would rather unify a with F b (rather than F b's expansion) in order
to get better error messages later.
So, when doing an occurs check with a type synonym application on the
RHS, we use some heuristics to find an expansion of the RHS which does
not contain the variable from the LHS. In particular, given
a ~ F t1 ... tn
we first try expanding each of the ti to types which no longer contain
a. If this turns out to be impossible, we next try expanding F
itself, and so on. See Note [Occurs check expansion] in TcType