\begin{code}
module TcCanonical(
mkCanonical, mkCanonicals, canWanteds, canGivens, canOccursCheck, canEq,
) where
#include "HsVersions.h"
import BasicTypes
import Type
import TcRnTypes
import TcType
import TcErrors
import Coercion
import Class
import TyCon
import TypeRep
import Name
import Var
import Outputable
import Control.Monad ( when, zipWithM )
import MonadUtils
import Control.Applicative ( (<|>) )
import VarSet
import Bag
import HsBinds
import Control.Monad ( unless )
import TcSMonad
\end{code}
Note [Canonicalisation]
~~~~~~~~~~~~~~~~~~~~~~~
* Converts (Constraint f) _which_does_not_contain_proper_implications_ to CanonicalCts
* Unary: treats individual constraints one at a time
* Does not do any zonking
* Lives in TcS monad so that it can create new skolem variables
%************************************************************************
%* *
%* Flattening (eliminating all function symbols) *
%* *
%************************************************************************
Note [Flattening]
~~~~~~~~~~~~~~~~~~~~
flatten ty ==> (xi, cc)
where
xi has no type functions
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.
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.
TODO: caching the information about whether transitive synonym
expansions contain any type function applications would speed things
up a bit; right now we waste a lot of energy traversing the same types
multiple times.
\begin{code}
flattenMany :: CtFlavor -> [Type] -> TcS ([Xi], [Coercion], CanonicalCts)
flattenMany ctxt tys
= do { (xis, cos, cts_s) <- mapAndUnzip3M (flatten ctxt) tys
; return (xis, cos, andCCans cts_s) }
flatten :: CtFlavor -> TcType -> TcS (Xi, Coercion, CanonicalCts)
flatten ctxt ty
| Just ty' <- tcView ty
= do { (xi, co, ccs) <- flatten ctxt ty'
; if isEmptyCCan ccs then
return (ty, ty, emptyCCan)
else
return (xi, co, ccs) }
flatten _ v@(TyVarTy _)
= return (v, v, emptyCCan)
flatten ctxt (AppTy ty1 ty2)
= do { (xi1,co1,c1) <- flatten ctxt ty1
; (xi2,co2,c2) <- flatten ctxt ty2
; return (mkAppTy xi1 xi2, mkAppCoercion co1 co2, c1 `andCCan` c2) }
flatten ctxt (FunTy ty1 ty2)
= do { (xi1,co1,c1) <- flatten ctxt ty1
; (xi2,co2,c2) <- flatten ctxt ty2
; return (mkFunTy xi1 xi2, mkFunCoercion co1 co2, c1 `andCCan` c2) }
flatten fl (TyConApp tc tys)
| not (isSynFamilyTyCon tc)
= do { (xis,cos,ccs) <- flattenMany fl tys
; return (mkTyConApp tc xis, mkTyConCoercion tc cos, ccs) }
| otherwise
= ASSERT( tyConArity tc <= length tys )
do { (xis, cos, ccs) <- flattenMany fl tys
; let (xi_args, xi_rest) = splitAt (tyConArity tc) xis
(cos_args, cos_rest) = splitAt (tyConArity tc) cos
fam_ty = mkTyConApp tc xi_args
fam_co = fam_ty
; (ret_co, rhs_var, ct) <-
if isGiven fl then
do { rhs_var <- newFlattenSkolemTy fam_ty
; cv <- newGivOrDerCoVar fam_ty rhs_var fam_co
; let ct = CFunEqCan { cc_id = cv
, cc_flavor = fl
, cc_fun = tc
, cc_tyargs = xi_args
, cc_rhs = rhs_var }
; return $ (mkCoVarCoercion cv, rhs_var, ct) }
else
do { rhs_var <- newFlexiTcSTy (typeKind fam_ty)
; cv <- newWantedCoVar fam_ty rhs_var
; let ct = CFunEqCan { cc_id = cv
, cc_flavor = mkWantedFlavor fl
, cc_fun = tc
, cc_tyargs = xi_args
, cc_rhs = rhs_var }
; return $ (mkCoVarCoercion cv, rhs_var, ct) }
; return ( foldl AppTy rhs_var xi_rest
, foldl AppTy (mkSymCoercion ret_co
`mkTransCoercion` mkTyConCoercion tc cos_args) cos_rest
, ccs `extendCCans` ct) }
flatten ctxt (PredTy pred)
= do { (pred', co, ccs) <- flattenPred ctxt pred
; return (PredTy pred', co, ccs) }
flatten ctxt ty@(ForAllTy {})
= do { let (tvs, rho) = splitForAllTys ty
; (rho', co, ccs) <- flatten ctxt rho
; let bad_eqs = filterBag is_bad ccs
is_bad c = tyVarsOfCanonical c `intersectsVarSet` tv_set
tv_set = mkVarSet tvs
; unless (isEmptyBag bad_eqs)
(flattenForAllErrorTcS ctxt ty bad_eqs)
; return (mkForAllTys tvs rho', mkForAllTys tvs co, ccs) }
flattenPred :: CtFlavor -> TcPredType -> TcS (TcPredType, Coercion, CanonicalCts)
flattenPred ctxt (ClassP cls tys)
= do { (tys', cos, ccs) <- flattenMany ctxt tys
; return (ClassP cls tys', mkClassPPredCo cls cos, ccs) }
flattenPred ctxt (IParam nm ty)
= do { (ty', co, ccs) <- flatten ctxt ty
; return (IParam nm ty', mkIParamPredCo nm co, ccs) }
flattenPred ctxt (EqPred ty1 ty2)
= do { (ty1', co1, ccs1) <- flatten ctxt ty1
; (ty2', co2, ccs2) <- flatten ctxt ty2
; return (EqPred ty1' ty2', mkEqPredCo co1 co2, ccs1 `andCCan` ccs2) }
\end{code}
%************************************************************************
%* *
%* Canonicalising given constraints *
%* *
%************************************************************************
\begin{code}
canWanteds :: [WantedEvVar] -> TcS CanonicalCts
canWanteds = fmap andCCans . mapM (\(WantedEvVar ev loc) -> mkCanonical (Wanted loc) ev)
canGivens :: GivenLoc -> [EvVar] -> TcS CanonicalCts
canGivens loc givens = do { ccs <- mapM (mkCanonical (Given loc)) givens
; return (andCCans ccs) }
mkCanonicals :: CtFlavor -> [EvVar] -> TcS CanonicalCts
mkCanonicals fl vs = fmap andCCans (mapM (mkCanonical fl) vs)
mkCanonical :: CtFlavor -> EvVar -> TcS CanonicalCts
mkCanonical fl ev = case evVarPred ev of
ClassP clas tys -> canClass fl ev clas tys
IParam ip ty -> canIP fl ev ip ty
EqPred ty1 ty2 -> canEq fl ev ty1 ty2
canClass :: CtFlavor -> EvVar -> Class -> [TcType] -> TcS CanonicalCts
canClass fl v cn tys
= do { (xis,cos,ccs) <- flattenMany fl tys
; let no_flattening_happened = isEmptyCCan ccs
dict_co = mkTyConCoercion (classTyCon cn) cos
; v_new <- if no_flattening_happened then return v
else if isGiven fl then return v
else do { v' <- newDictVar cn xis
; if isWanted fl
then setDictBind v (EvCast v' dict_co)
else setDictBind v' (EvCast v (mkSymCoercion dict_co))
; return v' }
; return (ccs `extendCCans` CDictCan { cc_id = v_new
, cc_flavor = fl
, cc_class = cn
, cc_tyargs = xis }) }
canIP :: CtFlavor -> EvVar -> IPName Name -> TcType -> TcS CanonicalCts
canIP fl v nm ty
= return $ singleCCan $ CIPCan { cc_id = v
, cc_flavor = fl
, cc_ip_nm = nm
, cc_ip_ty = ty }
canEq :: CtFlavor -> EvVar -> Type -> Type -> TcS CanonicalCts
canEq fl cv ty1 ty2
| tcEqType ty1 ty2
= do { when (isWanted fl) (setWantedCoBind cv ty1)
; return emptyCCan }
canEq fl cv ty1@(TyVarTy {}) ty2
= do { untch <- getUntouchables
; canEqLeaf untch fl cv (classify ty1) (classify ty2) }
canEq fl cv ty1 ty2@(TyVarTy {})
= do { untch <- getUntouchables
; canEqLeaf untch fl cv (classify ty1) (classify ty2) }
canEq fl cv (TyConApp fn tys) ty2
| isSynFamilyTyCon fn, length tys == tyConArity fn
= do { untch <- getUntouchables
; canEqLeaf untch fl cv (FunCls fn tys) (classify ty2) }
canEq fl cv ty1 (TyConApp fn tys)
| isSynFamilyTyCon fn, length tys == tyConArity fn
= do { untch <- getUntouchables
; canEqLeaf untch fl cv (classify ty1) (FunCls fn tys) }
canEq fl cv s1 s2
| Just (t1a,t1b,t1c) <- splitCoPredTy_maybe s1,
Just (t2a,t2b,t2c) <- splitCoPredTy_maybe s2
= do { (v1,v2,v3) <- if isWanted fl then
do { v1 <- newWantedCoVar t1a t2a
; v2 <- newWantedCoVar t1b t2b
; v3 <- newWantedCoVar t1c t2c
; let res_co = mkCoPredCo (mkCoVarCoercion v1)
(mkCoVarCoercion v2) (mkCoVarCoercion v3)
; setWantedCoBind cv res_co
; return (v1,v2,v3) }
else let co_orig = mkCoVarCoercion cv
coa = mkCsel1Coercion co_orig
cob = mkCsel2Coercion co_orig
coc = mkCselRCoercion co_orig
in do { v1 <- newGivOrDerCoVar t1a t2a coa
; v2 <- newGivOrDerCoVar t1b t2b cob
; v3 <- newGivOrDerCoVar t1c t2c coc
; return (v1,v2,v3) }
; cc1 <- canEq fl v1 t1a t2a
; cc2 <- canEq fl v2 t1b t2b
; cc3 <- canEq fl v3 t1c t2c
; return (cc1 `andCCan` cc2 `andCCan` cc3) }
canEq fl cv (FunTy s1 t1) (FunTy s2 t2)
= do { (argv, resv) <-
if isWanted fl then
do { argv <- newWantedCoVar s1 s2
; resv <- newWantedCoVar t1 t2
; setWantedCoBind cv $
mkFunCoercion (mkCoVarCoercion argv) (mkCoVarCoercion resv)
; return (argv,resv) }
else let [arg,res] = decomposeCo 2 (mkCoVarCoercion cv)
in do { argv <- newGivOrDerCoVar s1 s2 arg
; resv <- newGivOrDerCoVar t1 t2 res
; return (argv,resv) }
; cc1 <- canEq fl argv s1 s2
; cc2 <- canEq fl resv t1 t2
; return (cc1 `andCCan` cc2) }
canEq fl cv (PredTy (IParam n1 t1)) (PredTy (IParam n2 t2))
| n1 == n2
= if isWanted fl then
do { v <- newWantedCoVar t1 t2
; setWantedCoBind cv $ mkIParamPredCo n1 (mkCoVarCoercion cv)
; canEq fl v t1 t2 }
else return emptyCCan
canEq fl cv (PredTy (ClassP c1 tys1)) (PredTy (ClassP c2 tys2))
| c1 == c2
= if isWanted fl then
do { vs <- zipWithM newWantedCoVar tys1 tys2
; setWantedCoBind cv $ mkClassPPredCo c1 (map mkCoVarCoercion vs)
; andCCans <$> zipWith3M (canEq fl) vs tys1 tys2
}
else return emptyCCan
canEq fl cv (TyConApp tc1 tys1) (TyConApp tc2 tys2)
| isAlgTyCon tc1 && isAlgTyCon tc2
, tc1 == tc2
, length tys1 == length tys2
=
do { argsv <- if isWanted fl then
do { argsv <- zipWithM newWantedCoVar tys1 tys2
; setWantedCoBind cv $ mkTyConCoercion tc1 (map mkCoVarCoercion argsv)
; return argsv }
else
let cos = decomposeCo (length tys1) (mkCoVarCoercion cv)
in zipWith3M newGivOrDerCoVar tys1 tys2 cos
; andCCans <$> zipWith3M (canEq fl) argsv tys1 tys2 }
canEq fl cv ty1 ty2
| Just (s1,t1) <- tcSplitAppTy_maybe ty1
, Just (s2,t2) <- tcSplitAppTy_maybe ty2
= do { (cv1,cv2) <-
if isWanted fl
then do { cv1 <- newWantedCoVar s1 s2
; cv2 <- newWantedCoVar t1 t2
; setWantedCoBind cv $
mkAppCoercion (mkCoVarCoercion cv1) (mkCoVarCoercion cv2)
; return (cv1,cv2) }
else let co1 = mkLeftCoercion $ mkCoVarCoercion cv
co2 = mkRightCoercion $ mkCoVarCoercion cv
in do { cv1 <- newGivOrDerCoVar s1 s2 co1
; cv2 <- newGivOrDerCoVar t1 t2 co2
; return (cv1,cv2) }
; cc1 <- canEq fl cv1 s1 s2
; cc2 <- canEq fl cv2 t1 t2
; return (cc1 `andCCan` cc2) }
canEq fl _ s1@(ForAllTy {}) s2@(ForAllTy {})
| tcIsForAllTy s1, tcIsForAllTy s2,
Wanted {} <- fl
= canEqFailure fl s1 s2
| otherwise
= do { traceTcS "Ommitting decomposition of given polytype equality" (pprEq s1 s2)
; return emptyCCan }
canEq fl cv ty1 ty2 | Just ty1' <- tcView ty1 = canEq fl cv ty1' ty2
canEq fl cv ty1 ty2 | Just ty2' <- tcView ty2 = canEq fl cv ty1 ty2'
canEq fl _ ty1 ty2 = canEqFailure fl ty1 ty2
canEqFailure :: CtFlavor -> Type -> Type -> TcS CanonicalCts
canEqFailure fl ty1 ty2
= do { addErrorTcS MisMatchError fl ty1 ty2
; return emptyCCan }
\end{code}
Note [Equality between type applications]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If we see an equality of the form s1 t1 ~ s2 t2 we can always split
it up into s1 ~ s2 /\ t1 ~ t2, since s1 and s2 can't be type
functions (type functions use the TyConApp constructor, which never
shows up as the LHS of an AppTy). Other than type functions, types
in Haskell are always
(1) generative: a b ~ c d implies a ~ c, since different type
constructors always generate distinct types
(2) injective: a b ~ a d implies b ~ d; we never generate the
same type from different type arguments.
Note [Canonical ordering for equality constraints]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Implemented as (<+=) below:
Type function applications always come before anything else.
Variables always come before nonvariables (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
toplevel 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 toplevel 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 reorient 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 LR 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
tg_2 ~ xig_2
...
tw_1 ~ xiw_1
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}
data TypeClassifier
= FskCls TcTyVar
| VarCls TcTyVar
| FunCls TyCon [Type]
| OtherCls TcType
unClassify :: TypeClassifier -> TcType
unClassify (VarCls tv) = TyVarTy tv
unClassify (FskCls tv) = TyVarTy tv
unClassify (FunCls fn tys) = TyConApp fn tys
unClassify (OtherCls ty) = ty
classify :: TcType -> TypeClassifier
classify (TyVarTy tv)
| isTcTyVar tv,
FlatSkol {} <- tcTyVarDetails tv = FskCls tv
| otherwise = VarCls tv
classify (TyConApp tc tys) | isSynFamilyTyCon tc
, tyConArity tc == length tys
= FunCls tc tys
classify ty | Just ty' <- tcView ty
= case classify ty' of
OtherCls {} -> OtherCls ty
var_or_fn -> var_or_fn
| otherwise
= OtherCls ty
reOrient :: Untouchables -> TypeClassifier -> TypeClassifier -> Bool
reOrient _untch (OtherCls {}) (FunCls {}) = True
reOrient _untch (OtherCls {}) (FskCls {}) = True
reOrient _untch (OtherCls {}) (VarCls {}) = True
reOrient _untch (OtherCls {}) (OtherCls {}) = panic "reOrient"
reOrient _untch (FunCls {}) (VarCls {}) = False
reOrient _untch (FunCls {}) _ = False
reOrient _untch (VarCls {}) (FunCls {}) = True
reOrient _untch (VarCls {}) (FskCls {}) = False
reOrient _untch (VarCls {}) (OtherCls {}) = False
reOrient _untch (VarCls tv1) (VarCls tv2)
| isMetaTyVar tv2 && not (isMetaTyVar tv1) = True
| otherwise = False
reOrient _untch (FskCls {}) (VarCls tv2) = isMetaTyVar tv2
reOrient _untch (FskCls {}) (FskCls {}) = False
reOrient _untch (FskCls {}) (FunCls {}) = True
reOrient _untch (FskCls {}) (OtherCls {}) = False
canEqLeaf :: Untouchables
-> CtFlavor -> CoVar
-> TypeClassifier -> TypeClassifier -> TcS CanonicalCts
canEqLeaf untch fl cv cls1 cls2
| cls1 `re_orient` cls2
= do { cv' <- if isWanted fl
then do { cv' <- newWantedCoVar s2 s1
; setWantedCoBind cv $ mkSymCoercion (mkCoVarCoercion cv')
; return cv' }
else newGivOrDerCoVar s2 s1 (mkSymCoercion (mkCoVarCoercion cv))
; canEqLeafOriented fl cv' cls2 s1 }
| otherwise
= canEqLeafOriented fl cv cls1 s2
where
re_orient = reOrient untch
s1 = unClassify cls1
s2 = unClassify cls2
canEqLeafOriented :: CtFlavor -> CoVar
-> TypeClassifier -> TcType -> TcS CanonicalCts
canEqLeafOriented fl cv cls1@(FunCls fn tys1) s2
| let k1 = kindAppResult (tyConKind fn) tys1,
let k2 = typeKind s2,
isGiven fl && not (k1 `compatKind` k2)
= addErrorTcS KindError fl (unClassify cls1) s2 >> return emptyCCan
| otherwise
= ASSERT2( isSynFamilyTyCon fn, ppr (unClassify cls1) )
do { (xis1,cos1,ccs1) <- flattenMany fl tys1
; (xi2, co2, ccs2) <- flatten fl s2
; let ccs = ccs1 `andCCan` ccs2
no_flattening_happened = isEmptyCCan ccs
; cv_new <- if no_flattening_happened then return cv
else if isGiven fl then return cv
else do { cv' <- newWantedCoVar (unClassify (FunCls fn xis1)) xi2
; let
fun_co = mkTyConCoercion fn cos1
want_co = mkSymCoercion fun_co
`mkTransCoercion` mkCoVarCoercion cv'
`mkTransCoercion` co2
der_co = fun_co
`mkTransCoercion` mkCoVarCoercion cv
`mkTransCoercion` mkSymCoercion co2
; if isWanted fl
then setWantedCoBind cv want_co
else setWantedCoBind cv' der_co
; return cv' }
; let final_cc = CFunEqCan { cc_id = cv_new
, cc_flavor = fl
, cc_fun = fn
, cc_tyargs = xis1
, cc_rhs = xi2 }
; return $ ccs `extendCCans` final_cc }
canEqLeafOriented fl cv (FskCls tv) s2
= canEqLeafTyVarLeft fl cv tv s2
canEqLeafOriented fl cv (VarCls tv) s2
= canEqLeafTyVarLeft fl cv tv s2
canEqLeafOriented _ cv (OtherCls ty1) ty2
= pprPanic "canEqLeaf" (ppr cv $$ ppr ty1 $$ ppr ty2)
canEqLeafTyVarLeft :: CtFlavor -> CoVar -> TcTyVar -> TcType -> TcS CanonicalCts
canEqLeafTyVarLeft fl cv tv s2
| isGiven fl && not (k1 `compatKind` k2)
= addErrorTcS KindError fl (mkTyVarTy tv) s2 >> return emptyCCan
| otherwise
= do { (xi2, co, ccs2) <- flatten fl s2
; mxi2' <- canOccursCheck fl tv xi2
; case mxi2' of {
Nothing -> addErrorTcS OccCheckError fl (mkTyVarTy tv) xi2 >> return emptyCCan ;
Just xi2' ->
do { let no_flattening_happened = isEmptyCCan ccs2
; cv_new <- if no_flattening_happened then return cv
else if isGiven fl then return cv
else do { cv' <- newWantedCoVar (mkTyVarTy tv) xi2'
; if isWanted fl
then setWantedCoBind cv (mkCoVarCoercion cv' `mkTransCoercion` co)
else setWantedCoBind cv' (mkCoVarCoercion cv `mkTransCoercion`
mkSymCoercion co)
; return cv' }
; return $ ccs2 `extendCCans` CTyEqCan { cc_id = cv_new
, cc_flavor = fl
, cc_tyvar = tv
, cc_rhs = xi2' } } } }
where
k1 = tyVarKind tv
k2 = typeKind s2
canOccursCheck :: CtFlavor -> TcTyVar -> Xi -> TcS (Maybe Xi)
canOccursCheck _gw tv xi = return (expandAway tv xi)
\end{code}
@expandAway tv xi@ expands synonyms in xi just enough to get rid of
occurrences of tv, if that is possible; otherwise, it returns Nothing.
For example, suppose we have
type F a b = [a]
Then
expandAway b (F Int b) = Just [Int]
but
expandAway a (F a Int) = Nothing
We don't promise to do the absolute minimum amount of expanding
necessary, but we try not to do expansions we don't need to. We
prefer doing inner expansions first. For example,
type F a b = (a, Int, a, [a])
type G b = Char
We have
expandAway b (F (G b)) = F Char
even though we could also expand F to get rid of b.
\begin{code}
expandAway :: TcTyVar -> Xi -> Maybe Xi
expandAway tv t@(TyVarTy tv')
| tv == tv' = Nothing
| otherwise = Just t
expandAway tv xi
| not (tv `elemVarSet` tyVarsOfType xi) = Just xi
expandAway tv (AppTy ty1 ty2)
= do { ty1' <- expandAway tv ty1
; ty2' <- expandAway tv ty2
; return (mkAppTy ty1' ty2') }
expandAway tv (FunTy ty1 ty2)
= do { ty1' <- expandAway tv ty1
; ty2' <- expandAway tv ty2
; return (mkFunTy ty1' ty2') }
expandAway tv ty@(ForAllTy {})
= let (tvs,rho) = splitForAllTys ty
tvs_knds = map tyVarKind tvs
in if tv `elemVarSet` tyVarsOfTypes tvs_knds then
Nothing
else do { rho' <- expandAway tv rho
; return (mkForAllTys tvs rho') }
expandAway tv (PredTy pred)
= do { pred' <- expandAwayPred tv pred
; return (PredTy pred') }
expandAway tv ty@(TyConApp tc tys)
= (mkTyConApp tc <$> mapM (expandAway tv) tys) <|> (tcView ty >>= expandAway tv)
expandAwayPred :: TcTyVar -> TcPredType -> Maybe TcPredType
expandAwayPred tv (ClassP cls tys)
= do { tys' <- mapM (expandAway tv) tys; return (ClassP cls tys') }
expandAwayPred tv (EqPred ty1 ty2)
= do { ty1' <- expandAway tv ty1
; ty2' <- expandAway tv ty2
; return (EqPred ty1' ty2') }
expandAwayPred tv (IParam nm ty)
= do { ty' <- expandAway tv ty
; return (IParam nm ty') }
\end{code}
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.
However, 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.