%
% (c) The GRASP/AQUA Project, Glasgow University, 19921998
%
\section[TcSimplify]{TcSimplify}
\begin{code}
module TcSimplify (
tcSimplifyInfer, tcSimplifyInferCheck,
tcSimplifyCheck, tcSimplifyRestricted,
tcSimplifyRuleLhs, tcSimplifyIPs,
tcSimplifySuperClasses,
tcSimplifyTop, tcSimplifyInteractive,
tcSimplifyBracket,
tcSimplifyDeriv, tcSimplifyDefault,
bindInstsOfLocalFuns
) where
#include "HsVersions.h"
import {# SOURCE #} TcUnify( unifyType )
import HsSyn ( HsBind(..), HsExpr(..), LHsExpr, emptyLHsBinds )
import TcHsSyn ( mkHsApp, mkHsTyApp, mkHsDictApp )
import TcRnMonad
import Inst ( lookupInst, LookupInstResult(..),
tyVarsOfInst, fdPredsOfInsts, newDicts,
isDict, isClassDict, isLinearInst, linearInstType,
isMethodFor, isMethod,
instToId, tyVarsOfInsts, cloneDict,
ipNamesOfInsts, ipNamesOfInst, dictPred,
fdPredsOfInst,
newDictsAtLoc, tcInstClassOp,
getDictClassTys, isTyVarDict, instLoc,
zonkInst, tidyInsts, tidyMoreInsts,
pprInsts, pprDictsInFull, pprInstInFull, tcGetInstEnvs,
isInheritableInst, pprDictsTheta
)
import TcEnv ( tcGetGlobalTyVars, tcLookupId, findGlobals, pprBinders,
lclEnvElts, tcMetaTy )
import InstEnv ( lookupInstEnv, classInstances, pprInstances )
import TcMType ( zonkTcTyVarsAndFV, tcInstTyVars, zonkTcPredType )
import TcType ( TcTyVar, TcTyVarSet, ThetaType, TcPredType, tidyPred,
mkClassPred, isOverloadedTy, mkTyConApp, isSkolemTyVar,
mkTyVarTy, tcGetTyVar, isTyVarClassPred, mkTyVarTys,
tyVarsOfPred, tcEqType, pprPred, mkPredTy, tcIsTyVarTy )
import TcIface ( checkWiredInTyCon )
import Id ( idType, mkUserLocal )
import Var ( TyVar )
import TyCon ( TyCon )
import Name ( Name, getOccName, getSrcLoc )
import NameSet ( NameSet, mkNameSet, elemNameSet )
import Class ( classBigSig, classKey )
import FunDeps ( oclose, grow, improve, pprEquation )
import PrelInfo ( isNumericClass, isStandardClass )
import PrelNames ( splitName, fstName, sndName, integerTyConName,
showClassKey, eqClassKey, ordClassKey )
import Type ( zipTopTvSubst, substTheta, substTy )
import TysWiredIn ( pairTyCon, doubleTy, doubleTyCon )
import ErrUtils ( Message )
import BasicTypes ( TopLevelFlag, isNotTopLevel )
import VarSet
import VarEnv ( TidyEnv )
import FiniteMap
import Bag
import Outputable
import ListSetOps ( equivClasses )
import Util ( zipEqual, isSingleton )
import List ( partition )
import SrcLoc ( Located(..) )
import DynFlags ( DynFlags(ctxtStkDepth),
DynFlag( Opt_GlasgowExts, Opt_AllowUndecidableInstances,
Opt_WarnTypeDefaults, Opt_ExtendedDefaultRules ) )
\end{code}
%************************************************************************
%* *
\subsection{NOTES}
%* *
%************************************************************************

Notes on functional dependencies (a bug)

Consider this:
class C a b  a > b
class D a b  a > b
instance D a b => C a b  Undecidable
 (Not sure if it's crucial to this eg)
f :: C a b => a > Bool
f _ = True
g :: C a b => a > Bool
g = f
Here f typechecks, but g does not!! Reason: before doing improvement,
we reduce the (C a b1) constraint from the call of f to (D a b1).
Here is a more complicated example:
 > class Foo a b  a>b
 >
 > class Bar a b  a>b
 >
 > data Obj = Obj
 >
 > instance Bar Obj Obj
 >
 > instance (Bar a b) => Foo a b
 >
 > foo:: (Foo a b) => a > String
 > foo _ = "works"
 >
 > runFoo:: (forall a b. (Foo a b) => a > w) > w
 > runFoo f = f Obj

 *Test> runFoo foo

 :1:
 Could not deduce (Bar a b) from the context (Foo a b)
 arising from use of `foo' at :1
 Probable fix:
 Add (Bar a b) to the expected type of an expression
 In the first argument of `runFoo', namely `foo'
 In the definition of `it': it = runFoo foo

 Why all of the sudden does GHC need the constraint Bar a b? The
 function foo didn't ask for that...
The trouble is that to type (runFoo foo), GHC has to solve the problem:
Given constraint Foo a b
Solve constraint Foo a b'
Notice that b and b' aren't the same. To solve this, just do
improvement and then they are the same. But GHC currently does
simplify constraints
apply improvement
and loop
That is usually fine, but it isn't here, because it sees that Foo a b is
not the same as Foo a b', and so instead applies the instance decl for
instance Bar a b => Foo a b. And that's where the Bar constraint comes
from.
The Right Thing is to improve whenever the constraint set changes at
all. Not hard in principle, but it'll take a bit of fiddling to do.

Notes on quantification

Suppose we are about to do a generalisation step.
We have in our hand
G the environment
T the type of the RHS
C the constraints from that RHS
The game is to figure out
Q the set of type variables over which to quantify
Ct the constraints we will *not* quantify over
Cq the constraints we will quantify over
So we're going to infer the type
forall Q. Cq => T
and float the constraints Ct further outwards.
Here are the things that *must* be true:
(A) Q intersect fv(G) = EMPTY limits how big Q can be
(B) Q superset fv(Cq union T) \ oclose(fv(G),C) limits how small Q can be
(A) says we can't quantify over a variable that's free in the
environment. (B) says we must quantify over all the truly free
variables in T, else we won't get a sufficiently general type. We do
not *need* to quantify over any variable that is fixed by the free
vars of the environment G.
BETWEEN THESE TWO BOUNDS, ANY Q WILL DO!
Example: class H x y  x>y where ...
fv(G) = {a} C = {H a b, H c d}
T = c > b
(A) Q intersect {a} is empty
(B) Q superset {a,b,c,d} \ oclose({a}, C) = {a,b,c,d} \ {a,b} = {c,d}
So Q can be {c,d}, {b,c,d}
Other things being equal, however, we'd like to quantify over as few
variables as possible: smaller types, fewer type applications, more
constraints can get into Ct instead of Cq.

We will make use of
fv(T) the free type vars of T
oclose(vs,C) The result of extending the set of tyvars vs
using the functional dependencies from C
grow(vs,C) The result of extend the set of tyvars vs
using all conceivable links from C.
E.g. vs = {a}, C = {H [a] b, K (b,Int) c, Eq e}
Then grow(vs,C) = {a,b,c}
Note that grow(vs,C) `superset` grow(vs,simplify(C))
That is, simplfication can only shrink the result of grow.
Notice that
oclose is conservative one way: v `elem` oclose(vs,C) => v is definitely fixed by vs
grow is conservative the other way: if v might be fixed by vs => v `elem` grow(vs,C)

Choosing Q
~~~~~~~~~~
Here's a good way to choose Q:
Q = grow( fv(T), C ) \ oclose( fv(G), C )
That is, quantify over all variable that that MIGHT be fixed by the
call site (which influences T), but which aren't DEFINITELY fixed by
G. This choice definitely quantifies over enough type variables,
albeit perhaps too many.
Why grow( fv(T), C ) rather than fv(T)? Consider
class H x y  x>y where ...
T = c>c
C = (H c d)
If we used fv(T) = {c} we'd get the type
forall c. H c d => c > b
And then if the fn was called at several different c's, each of
which fixed d differently, we'd get a unification error, because
d isn't quantified. Solution: quantify d. So we must quantify
everything that might be influenced by c.
Why not oclose( fv(T), C )? Because we might not be able to see
all the functional dependencies yet:
class H x y  x>y where ...
instance H x y => Eq (T x y) where ...
T = c>c
C = (Eq (T c d))
Now oclose(fv(T),C) = {c}, because the functional dependency isn't
apparent yet, and that's wrong. We must really quantify over d too.
There really isn't any point in quantifying over any more than
grow( fv(T), C ), because the call sites can't possibly influence
any other type variables.

Note [Ambiguity]

It's very hard to be certain when a type is ambiguous. Consider
class K x
class H x y  x > y
instance H x y => K (x,y)
Is this type ambiguous?
forall a b. (K (a,b), Eq b) => a > a
Looks like it! But if we simplify (K (a,b)) we get (H a b) and
now we see that a fixes b. So we can't tell about ambiguity for sure
without doing a full simplification. And even that isn't possible if
the context has some free vars that may get unified. Urgle!
Here's another example: is this ambiguous?
forall a b. Eq (T b) => a > a
Not if there's an insance decl (with no context)
instance Eq (T b) where ...
You may say of this example that we should use the instance decl right
away, but you can't always do that:
class J a b where ...
instance J Int b where ...
f :: forall a b. J a b => a > a
(Notice: no functional dependency in J's class decl.)
Here f's type is perfectly fine, provided f is only called at Int.
It's premature to complain when meeting f's signature, or even
when inferring a type for f.
However, we don't *need* to report ambiguity right away. It'll always
show up at the call site.... and eventually at main, which needs special
treatment. Nevertheless, reporting ambiguity promptly is an excellent thing.
So here's the plan. We WARN about probable ambiguity if
fv(Cq) is not a subset of oclose(fv(T) union fv(G), C)
(all tested before quantification).
That is, all the type variables in Cq must be fixed by the the variables
in the environment, or by the variables in the type.
Notice that we union before calling oclose. Here's an example:
class J a b c  a b > c
fv(G) = {a}
Is this ambiguous?
forall b c. (J a b c) => b > b
Only if we union {a} from G with {b} from T before using oclose,
do we see that c is fixed.
It's a bit vague exactly which C we should use for this oclose call. If we
don't fix enough variables we might complain when we shouldn't (see
the above nasty example). Nothing will be perfect. That's why we can
only issue a warning.
Can we ever be *certain* about ambiguity? Yes: if there's a constraint
c in C such that fv(c) intersect (fv(G) union fv(T)) = EMPTY
then c is a "bubble"; there's no way it can ever improve, and it's
certainly ambiguous. UNLESS it is a constant (sigh). And what about
the nasty example?
class K x
class H x y  x > y
instance H x y => K (x,y)
Is this type ambiguous?
forall a b. (K (a,b), Eq b) => a > a
Urk. The (Eq b) looks "definitely ambiguous" but it isn't. What we are after
is a "bubble" that's a set of constraints
Cq = Ca union Cq' st fv(Ca) intersect (fv(Cq') union fv(T) union fv(G)) = EMPTY
Hence another idea. To decide Q start with fv(T) and grow it
by transitive closure in Cq (no functional dependencies involved).
Now partition Cq using Q, leaving the definitelyambiguous and probablyok.
The definitelyambiguous can then float out, and get smashed at top level
(which squashes out the constants, like Eq (T a) above)

Notes on principal types

class C a where
op :: a > a
f x = let g y = op (y::Int) in True
Here the principal type of f is (forall a. a>a)
but we'll produce the nonprincipal type
f :: forall a. C Int => a > a

The need for forall's in constraints

[Exchange on Haskell Cafe 5/6 Dec 2000]
class C t where op :: t > Bool
instance C [t] where op x = True
p y = (let f :: c > Bool; f x = op (y >> return x) in f, y ++ [])
q y = (y ++ [], let f :: c > Bool; f x = op (y >> return x) in f)
The definitions of p and q differ only in the order of the components in
the pair on their righthand sides. And yet:
ghc and "Typing Haskell in Haskell" reject p, but accept q;
Hugs rejects q, but accepts p;
hbc rejects both p and q;
nhc98 ... (Malcolm, can you fill in the blank for us!).
The type signature for f forces context reduction to take place, and
the results of this depend on whether or not the type of y is known,
which in turn depends on which component of the pair the type checker
analyzes first.
Solution: if y::m a, float out the constraints
Monad m, forall c. C (m c)
When m is later unified with [], we can solve both constraints.

Notes on implicit parameters

Question 1: can we "inherit" implicit parameters
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider this:
f x = (x::Int) + ?y
where f is *not* a toplevel binding.
From the RHS of f we'll get the constraint (?y::Int).
There are two types we might infer for f:
f :: Int > Int
(so we get ?y from the context of f's definition), or
f :: (?y::Int) => Int > Int
At first you might think the first was better, becuase then
?y behaves like a free variable of the definition, rather than
having to be passed at each call site. But of course, the WHOLE
IDEA is that ?y should be passed at each call site (that's what
dynamic binding means) so we'd better infer the second.
BOTTOM LINE: when *inferring types* you *must* quantify
over implicit parameters. See the predicate isFreeWhenInferring.
Question 2: type signatures
~~~~~~~~~~~~~~~~~~~~~~~~~~~
BUT WATCH OUT: When you supply a type signature, we can't force you
to quantify over implicit parameters. For example:
(?x + 1) :: Int
This is perfectly reasonable. We do not want to insist on
(?x + 1) :: (?x::Int => Int)
That would be silly. Here, the definition site *is* the occurrence site,
so the above strictures don't apply. Hence the difference between
tcSimplifyCheck (which *does* allow implicit paramters to be inherited)
and tcSimplifyCheckBind (which does not).
What about when you supply a type signature for a binding?
Is it legal to give the following explicit, user type
signature to f, thus:
f :: Int > Int
f x = (x::Int) + ?y
At first sight this seems reasonable, but it has the nasty property
that adding a type signature changes the dynamic semantics.
Consider this:
(let f x = (x::Int) + ?y
in (f 3, f 3 with ?y=5)) with ?y = 6
returns (3+6, 3+5)
vs
(let f :: Int > Int
f x = x + ?y
in (f 3, f 3 with ?y=5)) with ?y = 6
returns (3+6, 3+6)
Indeed, simply inlining f (at the Haskell source level) would change the
dynamic semantics.
Nevertheless, as Launchbury says (email Oct 01) we can't really give the
semantics for a Haskell program without knowing its typing, so if you
change the typing you may change the semantics.
To make things consistent in all cases where we are *checking* against
a supplied signature (as opposed to inferring a type), we adopt the
rule:
a signature does not need to quantify over implicit params.
[This represents a (rather marginal) change of policy since GHC 5.02,
which *required* an explicit signature to quantify over all implicit
params for the reasons mentioned above.]
But that raises a new question. Consider
Given (signature) ?x::Int
Wanted (inferred) ?x::Int, ?y::Bool
Clearly we want to discharge the ?x and float the ?y out. But
what is the criterion that distinguishes them? Clearly it isn't
what free type variables they have. The Right Thing seems to be
to float a constraint that
neither mentions any of the quantified type variables
nor any of the quantified implicit parameters
See the predicate isFreeWhenChecking.
Question 3: monomorphism
~~~~~~~~~~~~~~~~~~~~~~~~
There's a nasty corner case when the monomorphism restriction bites:
z = (x::Int) + ?y
The argument above suggests that we *must* generalise
over the ?y parameter, to get
z :: (?y::Int) => Int,
but the monomorphism restriction says that we *must not*, giving
z :: Int.
Why does the momomorphism restriction say this? Because if you have
let z = x + ?y in z+z
you might not expect the addition to be done twice  but it will if
we follow the argument of Question 2 and generalise over ?y.
Question 4: top level
~~~~~~~~~~~~~~~~~~~~~
At the top level, monomorhism makes no sense at all.
module Main where
main = let ?x = 5 in print foo
foo = woggle 3
woggle :: (?x :: Int) => Int > Int
woggle y = ?x + y
We definitely don't want (foo :: Int) with a toplevel implicit parameter
(?x::Int) becuase there is no way to bind it.
Possible choices
~~~~~~~~~~~~~~~~
(A) Always generalise over implicit parameters
Bindings that fall under the monomorphism restriction can't
be generalised
Consequences:
* Inlining remains valid
* No unexpected loss of sharing
* But simple bindings like
z = ?y + 1
will be rejected, unless you add an explicit type signature
(to avoid the monomorphism restriction)
z :: (?y::Int) => Int
z = ?y + 1
This seems unacceptable
(B) Monomorphism restriction "wins"
Bindings that fall under the monomorphism restriction can't
be generalised
Always generalise over implicit parameters *except* for bindings
that fall under the monomorphism restriction
Consequences
* Inlining isn't valid in general
* No unexpected loss of sharing
* Simple bindings like
z = ?y + 1
accepted (get value of ?y from binding site)
(C) Always generalise over implicit parameters
Bindings that fall under the monomorphism restriction can't
be generalised, EXCEPT for implicit parameters
Consequences
* Inlining remains valid
* Unexpected loss of sharing (from the extra generalisation)
* Simple bindings like
z = ?y + 1
accepted (get value of ?y from occurrence sites)
Discussion
~~~~~~~~~~
None of these choices seems very satisfactory. But at least we should
decide which we want to do.
It's really not clear what is the Right Thing To Do. If you see
z = (x::Int) + ?y
would you expect the value of ?y to be got from the *occurrence sites*
of 'z', or from the valuue of ?y at the *definition* of 'z'? In the
case of function definitions, the answer is clearly the former, but
less so in the case of nonfucntion definitions. On the other hand,
if we say that we get the value of ?y from the definition site of 'z',
then inlining 'z' might change the semantics of the program.
Choice (C) really says "the monomorphism restriction doesn't apply
to implicit parameters". Which is fine, but remember that every
innocent binding 'x = ...' that mentions an implicit parameter in
the RHS becomes a *function* of that parameter, called at each
use of 'x'. Now, the chances are that there are no intervening 'with'
clauses that bind ?y, so a decent compiler should common up all
those function calls. So I think I strongly favour (C). Indeed,
one could make a similar argument for abolishing the monomorphism
restriction altogether.
BOTTOM LINE: we choose (B) at present. See tcSimplifyRestricted
%************************************************************************
%* *
\subsection{tcSimplifyInfer}
%* *
%************************************************************************
tcSimplify is called when we *inferring* a type. Here's the overall game plan:
1. Compute Q = grow( fvs(T), C )
2. Partition C based on Q into Ct and Cq. Notice that ambiguous
predicates will end up in Ct; we deal with them at the top level
3. Try improvement, using functional dependencies
4. If Step 3 did any unification, repeat from step 1
(Unification can change the result of 'grow'.)
Note: we don't reduce dictionaries in step 2. For example, if we have
Eq (a,b), we don't simplify to (Eq a, Eq b). So Q won't be different
after step 2. However note that we may therefore quantify over more
type variables than we absolutely have to.
For the guts, we need a loop, that alternates context reduction and
improvement with unification. E.g. Suppose we have
class C x y  x>y where ...
and tcSimplify is called with:
(C Int a, C Int b)
Then improvement unifies a with b, giving
(C Int a, C Int a)
If we need to unify anything, we rattle round the whole thing all over
again.
\begin{code}
tcSimplifyInfer
:: SDoc
> TcTyVarSet  fv(T); type vars
> [Inst]  Wanted
> TcM ([TcTyVar],  Tyvars to quantify (zonked)
TcDictBinds,  Bindings
[TcId])  Dict Ids that must be bound here (zonked)
 Any free (escaping) Insts are tossed into the environment
\end{code}
\begin{code}
tcSimplifyInfer doc tau_tvs wanted_lie
= inferLoop doc (varSetElems tau_tvs)
wanted_lie `thenM` \ (qtvs, frees, binds, irreds) >
extendLIEs frees `thenM_`
returnM (qtvs, binds, map instToId irreds)
inferLoop doc tau_tvs wanteds
=  Step 1
zonkTcTyVarsAndFV tau_tvs `thenM` \ tau_tvs' >
mappM zonkInst wanteds `thenM` \ wanteds' >
tcGetGlobalTyVars `thenM` \ gbl_tvs >
let
preds = fdPredsOfInsts wanteds'
qtvs = grow preds tau_tvs' `minusVarSet` oclose preds gbl_tvs
try_me inst
 isFreeWhenInferring qtvs inst = Free
 isClassDict inst = DontReduceUnlessConstant  Dicts
 otherwise = ReduceMe NoSCs  Lits and Methods
in
traceTc (text "infloop" <+> vcat [ppr tau_tvs', ppr wanteds', ppr preds,
ppr (grow preds tau_tvs'), ppr qtvs]) `thenM_`
 Step 2
reduceContext doc try_me [] wanteds' `thenM` \ (no_improvement, frees, binds, irreds) >
 Step 3
if no_improvement then
returnM (varSetElems qtvs, frees, binds, irreds)
else
 If improvement did some unification, we go round again. There
 are two subtleties:
 a) We start again with irreds, not wanteds
 Using an instance decl might have introduced a fresh type variable
 which might have been unified, so we'd get an infinite loop
 if we started again with wanteds! See example [LOOP]

 b) It's also essential to reprocess frees, because unification
 might mean that a type variable that looked free isn't now.

 Hence the (irreds ++ frees)
 However, NOTICE that when we are done, we might have some bindings, but
 the final qtvs might be empty. See [NO TYVARS] below.
inferLoop doc tau_tvs (irreds ++ frees) `thenM` \ (qtvs1, frees1, binds1, irreds1) >
returnM (qtvs1, frees1, binds `unionBags` binds1, irreds1)
\end{code}
Example [LOOP]
class If b t e r  b t e > r
instance If T t e t
instance If F t e e
class Lte a b c  a b > c where lte :: a > b > c
instance Lte Z b T
instance (Lte a b l,If l b a c) => Max a b c
Wanted: Max Z (S x) y
Then we'll reduce using the Max instance to:
(Lte Z (S x) l, If l (S x) Z y)
and improve by binding l>T, after which we can do some reduction
on both the Lte and If constraints. What we *can't* do is start again
with (Max Z (S x) y)!
[NO TYVARS]
class Y a b  a > b where
y :: a > X b
instance Y [[a]] a where
y ((x:_):_) = X x
k :: X a > X a > X a
g :: Num a => [X a] > [X a]
g xs = h xs
where
h ys = ys ++ map (k (y [[0]])) xs
The excitement comes when simplifying the bindings for h. Initially
try to simplify {y @ [[t1]] t2, 0 @ t1}, with initial qtvs = {t2}.
From this we get t1:=:t2, but also various bindings. We can't forget
the bindings (because of [LOOP]), but in fact t1 is what g is
polymorphic in.
The net effect of [NO TYVARS]
\begin{code}
isFreeWhenInferring :: TyVarSet > Inst > Bool
isFreeWhenInferring qtvs inst
= isFreeWrtTyVars qtvs inst  Constrains no quantified vars
&& isInheritableInst inst  And no implicit parameter involved
 (see "Notes on implicit parameters")
isFreeWhenChecking :: TyVarSet  Quantified tyvars
> NameSet  Quantified implicit parameters
> Inst > Bool
isFreeWhenChecking qtvs ips inst
= isFreeWrtTyVars qtvs inst
&& isFreeWrtIPs ips inst
isFreeWrtTyVars qtvs inst = not (tyVarsOfInst inst `intersectsVarSet` qtvs)
isFreeWrtIPs ips inst = not (any (`elemNameSet` ips) (ipNamesOfInst inst))
\end{code}
%************************************************************************
%* *
\subsection{tcSimplifyCheck}
%* *
%************************************************************************
@tcSimplifyCheck@ is used when we know exactly the set of variables
we are going to quantify over. For example, a class or instance declaration.
\begin{code}
tcSimplifyCheck
:: SDoc
> [TcTyVar]  Quantify over these
> [Inst]  Given
> [Inst]  Wanted
> TcM TcDictBinds  Bindings
 tcSimplifyCheck is used when checking expression type signatures,
 class decls, instance decls etc.

 NB: tcSimplifyCheck does not consult the
 global type variables in the environment; so you don't
 need to worry about setting them before calling tcSimplifyCheck
tcSimplifyCheck doc qtvs givens wanted_lie
= ASSERT( all isSkolemTyVar qtvs )
do { (qtvs', frees, binds) < tcSimplCheck doc get_qtvs AddSCs givens wanted_lie
; extendLIEs frees
; return binds }
where
 get_qtvs = zonkTcTyVarsAndFV qtvs
get_qtvs = return (mkVarSet qtvs)  All skolems
 tcSimplifyInferCheck is used when we know the constraints we are to simplify
 against, but we don't know the type variables over which we are going to quantify.
 This happens when we have a type signature for a mutually recursive group
tcSimplifyInferCheck
:: SDoc
> TcTyVarSet  fv(T)
> [Inst]  Given
> [Inst]  Wanted
> TcM ([TcTyVar],  Variables over which to quantify
TcDictBinds)  Bindings
tcSimplifyInferCheck doc tau_tvs givens wanted_lie
= do { (qtvs', frees, binds) < tcSimplCheck doc get_qtvs AddSCs givens wanted_lie
; extendLIEs frees
; return (qtvs', binds) }
where
 Figure out which type variables to quantify over
 You might think it should just be the signature tyvars,
 but in bizarre cases you can get extra ones
 f :: forall a. Num a => a > a
 f x = fst (g (x, head [])) + 1
 g a b = (b,a)
 Here we infer g :: forall a b. a > b > (b,a)
 We don't want g to be monomorphic in b just because
 f isn't quantified over b.
all_tvs = varSetElems (tau_tvs `unionVarSet` tyVarsOfInsts givens)
get_qtvs = zonkTcTyVarsAndFV all_tvs `thenM` \ all_tvs' >
tcGetGlobalTyVars `thenM` \ gbl_tvs >
let
qtvs = all_tvs' `minusVarSet` gbl_tvs
 We could close gbl_tvs, but its not necessary for
 soundness, and it'll only affect which tyvars, not which
 dictionaries, we quantify over
in
returnM qtvs
\end{code}
Here is the workhorse function for all three wrappers.
\begin{code}
tcSimplCheck doc get_qtvs want_scs givens wanted_lie
= do { (qtvs, frees, binds, irreds) < check_loop givens wanted_lie
 Complain about any irreducible ones
; if not (null irreds)
then do { givens' < mappM zonkInst given_dicts_and_ips
; groupErrs (addNoInstanceErrs (Just doc) givens') irreds }
else return ()
; returnM (qtvs, frees, binds) }
where
given_dicts_and_ips = filter (not . isMethod) givens
 For error reporting, filter out methods, which are
 only added to the given set as an optimisation
ip_set = mkNameSet (ipNamesOfInsts givens)
check_loop givens wanteds
=  Step 1
mappM zonkInst givens `thenM` \ givens' >
mappM zonkInst wanteds `thenM` \ wanteds' >
get_qtvs `thenM` \ qtvs' >
 Step 2
let
 When checking against a given signature we always reduce
 until we find a match against something given, or can't reduce
try_me inst  isFreeWhenChecking qtvs' ip_set inst = Free
 otherwise = ReduceMe want_scs
in
reduceContext doc try_me givens' wanteds' `thenM` \ (no_improvement, frees, binds, irreds) >
 Step 3
if no_improvement then
returnM (varSetElems qtvs', frees, binds, irreds)
else
check_loop givens' (irreds ++ frees) `thenM` \ (qtvs', frees1, binds1, irreds1) >
returnM (qtvs', frees1, binds `unionBags` binds1, irreds1)
\end{code}
%************************************************************************
%* *
tcSimplifySuperClasses
%* *
%************************************************************************
Note [SUPERCLASSLOOP 1]
~~~~~~~~~~~~~~~~~~~~~~~~
We have to be very, very careful when generating superclasses, lest we
accidentally build a loop. Here's an example:
class S a
class S a => C a where { opc :: a > a }
class S b => D b where { opd :: b > b }
instance C Int where
opc = opd
instance D Int where
opd = opc
From (instance C Int) we get the constraint set {ds1:S Int, dd:D Int}
Simplifying, we may well get:
$dfCInt = :C ds1 (opd dd)
dd = $dfDInt
ds1 = $p1 dd
Notice that we spot that we can extract ds1 from dd.
Alas! Alack! We can do the same for (instance D Int):
$dfDInt = :D ds2 (opc dc)
dc = $dfCInt
ds2 = $p1 dc
And now we've defined the superclass in terms of itself.
Solution: never generate a superclass selectors at all when
satisfying the superclass context of an instance declaration.
Two more nasty cases are in
tcrun021
tcrun033
\begin{code}
tcSimplifySuperClasses qtvs givens sc_wanteds
= ASSERT( all isSkolemTyVar qtvs )
do { (_, frees, binds1) < tcSimplCheck doc get_qtvs NoSCs givens sc_wanteds
; ext_default < doptM Opt_ExtendedDefaultRules
; binds2 < tc_simplify_top doc ext_default NoSCs frees
; return (binds1 `unionBags` binds2) }
where
get_qtvs = return (mkVarSet qtvs)
doc = ptext SLIT("instance declaration superclass context")
\end{code}
%************************************************************************
%* *
\subsection{tcSimplifyRestricted}
%* *
%************************************************************************
tcSimplifyRestricted infers which type variables to quantify for a
group of restricted bindings. This isn't trivial.
Eg1: id = \x > x
We want to quantify over a to get id :: forall a. a>a
Eg2: eq = (==)
We do not want to quantify over a, because there's an Eq a
constraint, so we get eq :: a>a>Bool (notice no forall)
So, assume:
RHS has type 'tau', whose free tyvars are tau_tvs
RHS has constraints 'wanteds'
Plan A (simple)
Quantify over (tau_tvs \ ftvs(wanteds))
This is bad. The constraints may contain (Monad (ST s))
where we have instance Monad (ST s) where...
so there's no need to be monomorphic in s!
Also the constraint might be a method constraint,
whose type mentions a perfectly innocent tyvar:
op :: Num a => a > b > a
Here, b is unconstrained. A good example would be
foo = op (3::Int)
We want to infer the polymorphic type
foo :: forall b. b > b
Plan B (cunning, used for a long time up to and including GHC 6.2)
Step 1: Simplify the constraints as much as possible (to deal
with Plan A's problem). Then set
qtvs = tau_tvs \ ftvs( simplify( wanteds ) )
Step 2: Now simplify again, treating the constraint as 'free' if
it does not mention qtvs, and trying to reduce it otherwise.
The reasons for this is to maximise sharing.
This fails for a very subtle reason. Suppose that in the Step 2
a constraint (Foo (Succ Zero) (Succ Zero) b) gets thrown upstairs as 'free'.
In the Step 1 this constraint might have been simplified, perhaps to
(Foo Zero Zero b), AND THEN THAT MIGHT BE IMPROVED, to bind 'b' to 'T'.
This won't happen in Step 2... but that in turn might prevent some other
constraint (Baz [a] b) being simplified (e.g. via instance Baz [a] T where {..})
and that in turn breaks the invariant that no constraints are quantified over.
Test typecheck/should_compile/tc177 (which failed in GHC 6.2) demonstrates
the problem.
Plan C (brutal)
Step 1: Simplify the constraints as much as possible (to deal
with Plan A's problem). Then set
qtvs = tau_tvs \ ftvs( simplify( wanteds ) )
Return the bindings from Step 1.
A note about Plan C (arising from "bug" reported by George Russel March 2004)
Consider this:
instance (HasBinary ty IO) => HasCodedValue ty
foo :: HasCodedValue a => String > IO a
doDecodeIO :: HasCodedValue a => () > () > IO a
doDecodeIO codedValue view
= let { act = foo "foo" } in act
You might think this should work becuase the call to foo gives rise to a constraint
(HasCodedValue t), which can be satisfied by the type sig for doDecodeIO. But the
restricted binding act = ... calls tcSimplifyRestricted, and PlanC simplifies the
constraint using the (rather bogus) instance declaration, and now we are stuffed.
I claim this is not really a bug  but it bit Sergey as well as George. So here's
plan D
Plan D (a variant of plan B)
Step 1: Simplify the constraints as much as possible (to deal
with Plan A's problem), BUT DO NO IMPROVEMENT. Then set
qtvs = tau_tvs \ ftvs( simplify( wanteds ) )
Step 2: Now simplify again, treating the constraint as 'free' if
it does not mention qtvs, and trying to reduce it otherwise.
The point here is that it's generally OK to have too few qtvs; that is,
to make the thing more monomorphic than it could be. We don't want to
do that in the common cases, but in wierd cases it's ok: the programmer
can always add a signature.
Too few qtvs => too many wanteds, which is what happens if you do less
improvement.
\begin{code}
tcSimplifyRestricted  Used for restricted binding groups
 i.e. ones subject to the monomorphism restriction
:: SDoc
> TopLevelFlag
> [Name]  Things bound in this group
> TcTyVarSet  Free in the type of the RHSs
> [Inst]  Free in the RHSs
> TcM ([TcTyVar],  Tyvars to quantify (zonked)
TcDictBinds)  Bindings
 tcSimpifyRestricted returns no constraints to
 quantify over; by definition there are none.
 They are all thrown back in the LIE
tcSimplifyRestricted doc top_lvl bndrs tau_tvs wanteds
 Zonk everything in sight
= mappM zonkInst wanteds `thenM` \ wanteds' >
 'reduceMe': Reduce as far as we can. Don't stop at
 dicts; the idea is to get rid of as many type
 variables as possible, and we don't want to stop
 at (say) Monad (ST s), because that reduces
 immediately, with no constraint on s.

 BUT do no improvement! See Plan D above
 HOWEVER, some unification may take place, if we instantiate
 a method Inst with an equality constraint
reduceContextWithoutImprovement
doc reduceMe wanteds' `thenM` \ (_frees, _binds, constrained_dicts) >
 Next, figure out the tyvars we will quantify over
zonkTcTyVarsAndFV (varSetElems tau_tvs) `thenM` \ tau_tvs' >
tcGetGlobalTyVars `thenM` \ gbl_tvs' >
mappM zonkInst constrained_dicts `thenM` \ constrained_dicts' >
let
constrained_tvs' = tyVarsOfInsts constrained_dicts'
qtvs' = (tau_tvs' `minusVarSet` oclose (fdPredsOfInsts constrained_dicts) gbl_tvs')
`minusVarSet` constrained_tvs'
in
traceTc (text "tcSimplifyRestricted" <+> vcat [
pprInsts wanteds, pprInsts _frees, pprInsts constrained_dicts',
ppr _binds,
ppr constrained_tvs', ppr tau_tvs', ppr qtvs' ]) `thenM_`
 The first step may have squashed more methods than
 necessary, so try again, this time more gently, knowing the exact
 set of type variables to quantify over.

 We quantify only over constraints that are captured by qtvs';
 these will just be a subset of nondicts. This in contrast
 to normal inference (using isFreeWhenInferring) in which we quantify over
 all *noninheritable* constraints too. This implements choice
 (B) under "implicit parameter and monomorphism" above.

 Remember that we may need to do *some* simplification, to
 (for example) squash {Monad (ST s)} into {}. It's not enough
 just to float all constraints

 At top level, we *do* squash methods becuase we want to
 expose implicit parameters to the test that follows
let
is_nested_group = isNotTopLevel top_lvl
try_me inst  isFreeWrtTyVars qtvs' inst,
(is_nested_group  isDict inst) = Free
 otherwise = ReduceMe AddSCs
in
reduceContextWithoutImprovement
doc try_me wanteds' `thenM` \ (frees, binds, irreds) >
ASSERT( null irreds )
 See "Notes on implicit parameters, Question 4: top level"
if is_nested_group then
extendLIEs frees `thenM_`
returnM (varSetElems qtvs', binds)
else
let
(non_ips, bad_ips) = partition isClassDict frees
in
addTopIPErrs bndrs bad_ips `thenM_`
extendLIEs non_ips `thenM_`
returnM (varSetElems qtvs', binds)
\end{code}
%************************************************************************
%* *
tcSimplifyRuleLhs
%* *
%************************************************************************
On the LHS of transformation rules we only simplify methods and constants,
getting dictionaries. We want to keep all of them unsimplified, to serve
as the available stuff for the RHS of the rule.
Example. Consider the following lefthand side of a rule
f (x == y) (y > z) = ...
If we typecheck this expression we get constraints
d1 :: Ord a, d2 :: Eq a
We do NOT want to "simplify" to the LHS
forall x::a, y::a, z::a, d1::Ord a.
f ((==) (eqFromOrd d1) x y) ((>) d1 y z) = ...
Instead we want
forall x::a, y::a, z::a, d1::Ord a, d2::Eq a.
f ((==) d2 x y) ((>) d1 y z) = ...
Here is another example:
fromIntegral :: (Integral a, Num b) => a > b
{# RULES "foo" fromIntegral = id :: Int > Int #}
In the rule, a=b=Int, and Num Int is a superclass of Integral Int. But
we *dont* want to get
forall dIntegralInt.
fromIntegral Int Int dIntegralInt (scsel dIntegralInt) = id Int
because the scsel will mess up RULE matching. Instead we want
forall dIntegralInt, dNumInt.
fromIntegral Int Int dIntegralInt dNumInt = id Int
Even if we have
g (x == y) (y == z) = ..
where the two dictionaries are *identical*, we do NOT WANT
forall x::a, y::a, z::a, d1::Eq a
f ((==) d1 x y) ((>) d1 y z) = ...
because that will only match if the dict args are (visibly) equal.
Instead we want to quantify over the dictionaries separately.
In short, tcSimplifyRuleLhs must *only* squash LitInst and MethInts, leaving
all dicts unchanged, with absolutely no sharing. It's simpler to do this
from scratch, rather than further parameterise simpleReduceLoop etc
\begin{code}
tcSimplifyRuleLhs :: [Inst] > TcM ([Inst], TcDictBinds)
tcSimplifyRuleLhs wanteds
= go [] emptyBag wanteds
where
go dicts binds []
= return (dicts, binds)
go dicts binds (w:ws)
 isDict w
= go (w:dicts) binds ws
 otherwise
= do { w' < zonkInst w  So that (3::Int) does not generate a call
 to fromInteger; this looks fragile to me
; lookup_result < lookupInst w'
; case lookup_result of
GenInst ws' rhs > go dicts (addBind binds w rhs) (ws' ++ ws)
SimpleInst rhs > go dicts (addBind binds w rhs) ws
NoInstance > pprPanic "tcSimplifyRuleLhs" (ppr w)
}
\end{code}
tcSimplifyBracket is used when simplifying the constraints arising from
a Template Haskell bracket [ ... ]. We want to check that there aren't
any constraints that can't be satisfied (e.g. Show Foo, where Foo has no
Show instance), but we aren't otherwise interested in the results.
Nor do we care about ambiguous dictionaries etc. We will type check
this bracket again at its usage site.
\begin{code}
tcSimplifyBracket :: [Inst] > TcM ()
tcSimplifyBracket wanteds
= simpleReduceLoop doc reduceMe wanteds `thenM_`
returnM ()
where
doc = text "tcSimplifyBracket"
\end{code}
%************************************************************************
%* *
\subsection{Filtering at a dynamic binding}
%* *
%************************************************************************
When we have
let ?x = R in B
we must discharge all the ?x constraints from B. We also do an improvement
step; if we have ?x::t1 and ?x::t2 we must unify t1, t2.
Actually, the constraints from B might improve the types in ?x. For example
f :: (?x::Int) => Char > Char
let ?x = 3 in f 'c'
then the constraint (?x::Int) arising from the call to f will
force the binding for ?x to be of type Int.
\begin{code}
tcSimplifyIPs :: [Inst]  The implicit parameters bound here
> [Inst]  Wanted
> TcM TcDictBinds
tcSimplifyIPs given_ips wanteds
= simpl_loop given_ips wanteds `thenM` \ (frees, binds) >
extendLIEs frees `thenM_`
returnM binds
where
doc = text "tcSimplifyIPs" <+> ppr given_ips
ip_set = mkNameSet (ipNamesOfInsts given_ips)
 Simplify any methods that mention the implicit parameter
try_me inst  isFreeWrtIPs ip_set inst = Free
 otherwise = ReduceMe NoSCs
simpl_loop givens wanteds
= mappM zonkInst givens `thenM` \ givens' >
mappM zonkInst wanteds `thenM` \ wanteds' >
reduceContext doc try_me givens' wanteds' `thenM` \ (no_improvement, frees, binds, irreds) >
if no_improvement then
ASSERT( null irreds )
returnM (frees, binds)
else
simpl_loop givens' (irreds ++ frees) `thenM` \ (frees1, binds1) >
returnM (frees1, binds `unionBags` binds1)
\end{code}
%************************************************************************
%* *
\subsection[bindsforlocalfuns]{@bindInstsOfLocalFuns@}
%* *
%************************************************************************
When doing a binding group, we may have @Insts@ of local functions.
For example, we might have...
\begin{verbatim}
let f x = x + 1  orig local function (overloaded)
f.1 = f Int  two instances of f
f.2 = f Float
in
(f.1 5, f.2 6.7)
\end{verbatim}
The point is: we must drop the bindings for @f.1@ and @f.2@ here,
where @f@ is in scope; those @Insts@ must certainly not be passed
upwards towards the toplevel. If the @Insts@ were bindingified up
there, they would have unresolvable references to @f@.
We pass in an @init_lie@ of @Insts@ and a list of locallybound @Ids@.
For each method @Inst@ in the @init_lie@ that mentions one of the
@Ids@, we create a binding. We return the remaining @Insts@ (in an
@LIE@), as well as the @HsBinds@ generated.
\begin{code}
bindInstsOfLocalFuns :: [Inst] > [TcId] > TcM TcDictBinds
 Simlifies only MethodInsts, and generate only bindings of form
 fm = f tys dicts
 We're careful not to even generate bindings of the form
 d1 = d2
 You'd think that'd be fine, but it interacts with what is
 arguably a bug in Match.tidyEqnInfo (see notes there)
bindInstsOfLocalFuns wanteds local_ids
 null overloaded_ids
 Common case
= extendLIEs wanteds `thenM_`
returnM emptyLHsBinds
 otherwise
= simpleReduceLoop doc try_me for_me `thenM` \ (frees, binds, irreds) >
ASSERT( null irreds )
extendLIEs not_for_me `thenM_`
extendLIEs frees `thenM_`
returnM binds
where
doc = text "bindInsts" <+> ppr local_ids
overloaded_ids = filter is_overloaded local_ids
is_overloaded id = isOverloadedTy (idType id)
(for_me, not_for_me) = partition (isMethodFor overloaded_set) wanteds
overloaded_set = mkVarSet overloaded_ids  There can occasionally be a lot of them
 so it's worth building a set, so that
 lookup (in isMethodFor) is faster
try_me inst  isMethod inst = ReduceMe NoSCs
 otherwise = Free
\end{code}
%************************************************************************
%* *
\subsection{Data types for the reduction mechanism}
%* *
%************************************************************************
The main control over context reduction is here
\begin{code}
data WhatToDo
= ReduceMe WantSCs  Try to reduce this
 If there's no instance, behave exactly like
 DontReduce: add the inst to the irreductible ones,
 but don't produce an error message of any kind.
 It might be quite legitimate such as (Eq a)!
 DontReduceUnlessConstant  Return as irreducible unless it can
 be reduced to a constant in one step
 Free  Return as free
reduceMe :: Inst > WhatToDo
reduceMe inst = ReduceMe AddSCs
data WantSCs = NoSCs  AddSCs  Tells whether we should add the superclasses
 of a predicate when adding it to the avails
 The reason for this flag is entirely the superclass loop problem
 Note [SUPERCLASS LOOP 1]
\end{code}
\begin{code}
type Avails = FiniteMap Inst Avail
emptyAvails = emptyFM
data Avail
= IsFree  Used for free Insts
 Irred  Used for irreducible dictionaries,
 which are going to be lambda bound
 Given TcId  Used for dictionaries for which we have a binding
 e.g. those "given" in a signature
Bool  True <=> actually consumed (splittable IPs only)
 Rhs  Used when there is a RHS
(LHsExpr TcId)  The RHS
[Inst]  Insts free in the RHS; we need these too
 Linear  Splittable Insts only.
Int  The Int is always 2 or more; indicates how
 many copies are required
Inst  The splitter
Avail  Where the "master copy" is
 LinRhss  Splittable Insts only; this is used only internally
 by extractResults, where a Linear
 is turned into an LinRhss
[LHsExpr TcId]  A supply of suitable RHSs
pprAvails avails = vcat [sep [ppr inst, nest 2 (equals <+> pprAvail avail)]
 (inst,avail) < fmToList avails ]
instance Outputable Avail where
ppr = pprAvail
pprAvail IsFree = text "Free"
pprAvail Irred = text "Irred"
pprAvail (Given x b) = text "Given" <+> ppr x <+>
if b then text "(used)" else empty
pprAvail (Rhs rhs bs) = text "Rhs" <+> ppr rhs <+> braces (ppr bs)
pprAvail (Linear n i a) = text "Linear" <+> ppr n <+> braces (ppr i) <+> ppr a
pprAvail (LinRhss rhss) = text "LinRhss" <+> ppr rhss
\end{code}
Extracting the bindings from a bunch of Avails.
The bindings do *not* come back sorted in dependency order.
We assume that they'll be wrapped in a big Rec, so that the
dependency analyser can sort them out later
The loop startes
\begin{code}
extractResults :: Avails
> [Inst]  Wanted
> TcM (TcDictBinds,  Bindings
[Inst],  Irreducible ones
[Inst])  Free ones
extractResults avails wanteds
= go avails emptyBag [] [] wanteds
where
go avails binds irreds frees []
= returnM (binds, irreds, frees)
go avails binds irreds frees (w:ws)
= case lookupFM avails w of
Nothing > pprTrace "Urk: extractResults" (ppr w) $
go avails binds irreds frees ws
Just IsFree > go (add_free avails w) binds irreds (w:frees) ws
Just Irred > go (add_given avails w) binds (w:irreds) frees ws
Just (Given id _) > go avails new_binds irreds frees ws
where
new_binds  id == instToId w = binds
 otherwise = addBind binds w (L (instSpan w) (HsVar id))
 The sought Id can be one of the givens, via a superclass chain
 and then we definitely don't want to generate an x=x binding!
Just (Rhs rhs ws') > go (add_given avails w) new_binds irreds frees (ws' ++ ws)
where
new_binds = addBind binds w rhs
Just (Linear n split_inst avail)  Transform Linear > LinRhss
> get_root irreds frees avail w `thenM` \ (irreds', frees', root_id) >
split n (instToId split_inst) root_id w `thenM` \ (binds', rhss) >
go (addToFM avails w (LinRhss rhss))
(binds `unionBags` binds')
irreds' frees' (split_inst : w : ws)
Just (LinRhss (rhs:rhss))  Consume one of the Rhss
> go new_avails new_binds irreds frees ws
where
new_binds = addBind binds w rhs
new_avails = addToFM avails w (LinRhss rhss)
get_root irreds frees (Given id _) w = returnM (irreds, frees, id)
get_root irreds frees Irred w = cloneDict w `thenM` \ w' >
returnM (w':irreds, frees, instToId w')
get_root irreds frees IsFree w = cloneDict w `thenM` \ w' >
returnM (irreds, w':frees, instToId w')
add_given avails w = addToFM avails w (Given (instToId w) True)
add_free avails w  isMethod w = avails
 otherwise = add_given avails w
 NB: Hack alert!
 Do *not* replace Free by Given if it's a method.
 The following situation shows why this is bad:
 truncate :: forall a. RealFrac a => forall b. Integral b => a > b
 From an application (truncate f i) we get
 t1 = truncate at f
 t2 = t1 at i
 If we have also have a second occurrence of truncate, we get
 t3 = truncate at f
 t4 = t3 at i
 When simplifying with i,f free, we might still notice that
 t1=t3; but alas, the binding for t2 (which mentions t1)
 will continue to float out!
split :: Int > TcId > TcId > Inst
> TcM (TcDictBinds, [LHsExpr TcId])
 (split n split_id root_id wanted) returns
 * a list of 'n' expressions, all of which witness 'avail'
 * a bunch of auxiliary bindings to support these expressions
 * one or zero insts needed to witness the whole lot
 (maybe be zero if the initial Inst is a Given)

 NB: 'wanted' is just a template
split n split_id root_id wanted
= go n
where
ty = linearInstType wanted
pair_ty = mkTyConApp pairTyCon [ty,ty]
id = instToId wanted
occ = getOccName id
loc = getSrcLoc id
span = instSpan wanted
go 1 = returnM (emptyBag, [L span $ HsVar root_id])
go n = go ((n+1) `div` 2) `thenM` \ (binds1, rhss) >
expand n rhss `thenM` \ (binds2, rhss') >
returnM (binds1 `unionBags` binds2, rhss')
 (expand n rhss)
 Given ((n+1)/2) rhss, make n rhss, using auxiliary bindings
 e.g. expand 3 [rhs1, rhs2]
 = ( { x = split rhs1 },
 [fst x, snd x, rhs2] )
expand n rhss
 n `rem` 2 == 0 = go rhss  n is even
 otherwise = go (tail rhss) `thenM` \ (binds', rhss') >
returnM (binds', head rhss : rhss')
where
go rhss = mapAndUnzipM do_one rhss `thenM` \ (binds', rhss') >
returnM (listToBag binds', concat rhss')
do_one rhs = newUnique `thenM` \ uniq >
tcLookupId fstName `thenM` \ fst_id >
tcLookupId sndName `thenM` \ snd_id >
let
x = mkUserLocal occ uniq pair_ty loc
in
returnM (L span (VarBind x (mk_app span split_id rhs)),
[mk_fs_app span fst_id ty x, mk_fs_app span snd_id ty x])
mk_fs_app span id ty var = L span (HsVar id) `mkHsTyApp` [ty,ty] `mkHsApp` (L span (HsVar var))
mk_app span id rhs = L span (HsApp (L span (HsVar id)) rhs)
addBind binds inst rhs = binds `unionBags` unitBag (L (instLocSrcSpan (instLoc inst))
(VarBind (instToId inst) rhs))
instSpan wanted = instLocSrcSpan (instLoc wanted)
\end{code}
%************************************************************************
%* *
\subsection[reduce]{@reduce@}
%* *
%************************************************************************
When the "what to do" predicate doesn't depend on the quantified type variables,
matters are easier. We don't need to do any zonking, unless the improvement step
does something, in which case we zonk before iterating.
The "given" set is always empty.
\begin{code}
simpleReduceLoop :: SDoc
> (Inst > WhatToDo)  What to do, *not* based on the quantified type variables
> [Inst]  Wanted
> TcM ([Inst],  Free
TcDictBinds,
[Inst])  Irreducible
simpleReduceLoop doc try_me wanteds
= mappM zonkInst wanteds `thenM` \ wanteds' >
reduceContext doc try_me [] wanteds' `thenM` \ (no_improvement, frees, binds, irreds) >
if no_improvement then
returnM (frees, binds, irreds)
else
simpleReduceLoop doc try_me (irreds ++ frees) `thenM` \ (frees1, binds1, irreds1) >
returnM (frees1, binds `unionBags` binds1, irreds1)
\end{code}
\begin{code}
reduceContext :: SDoc
> (Inst > WhatToDo)
> [Inst]  Given
> [Inst]  Wanted
> TcM (Bool,  True <=> improve step did no unification
[Inst],  Free
TcDictBinds,  Dictionary bindings
[Inst])  Irreducible
reduceContext doc try_me givens wanteds
=
traceTc (text "reduceContext" <+> (vcat [
text "",
doc,
text "given" <+> ppr givens,
text "wanted" <+> ppr wanteds,
text ""
])) `thenM_`
 Build the Avail mapping from "givens"
foldlM addGiven emptyAvails givens `thenM` \ init_state >
 Do the real work
reduceList (0,[]) try_me wanteds init_state `thenM` \ avails >
 Do improvement, using everything in avails
 In particular, avails includes all superclasses of everything
tcImprove avails `thenM` \ no_improvement >
extractResults avails wanteds `thenM` \ (binds, irreds, frees) >
traceTc (text "reduceContext end" <+> (vcat [
text "",
doc,
text "given" <+> ppr givens,
text "wanted" <+> ppr wanteds,
text "",
text "avails" <+> pprAvails avails,
text "frees" <+> ppr frees,
text "no_improvement =" <+> ppr no_improvement,
text ""
])) `thenM_`
returnM (no_improvement, frees, binds, irreds)
 reduceContextWithoutImprovement differs from reduceContext
 (a) no improvement
 (b) 'givens' is assumed empty
reduceContextWithoutImprovement doc try_me wanteds
=
traceTc (text "reduceContextWithoutImprovement" <+> (vcat [
text "",
doc,
text "wanted" <+> ppr wanteds,
text ""
])) `thenM_`
 Do the real work
reduceList (0,[]) try_me wanteds emptyAvails `thenM` \ avails >
extractResults avails wanteds `thenM` \ (binds, irreds, frees) >
traceTc (text "reduceContextWithoutImprovement end" <+> (vcat [
text "",
doc,
text "wanted" <+> ppr wanteds,
text "",
text "avails" <+> pprAvails avails,
text "frees" <+> ppr frees,
text ""
])) `thenM_`
returnM (frees, binds, irreds)
tcImprove :: Avails > TcM Bool  False <=> no change
 Perform improvement using all the predicates in Avails
tcImprove avails
= tcGetInstEnvs `thenM` \ inst_envs >
let
preds = [ (pred, pp_loc)
 (inst, avail) < fmToList avails,
pred < get_preds inst avail,
let pp_loc = pprInstLoc (instLoc inst)
]
 Avails has all the superclasses etc (good)
 It also has all the intermediates of the deduction (good)
 It does not have duplicates (good)
 NB that (?x::t1) and (?x::t2) will be held separately in avails
 so that improve will see them separate
 For free Methods, we want to take predicates from their context,
 but for Methods that have been squished their context will already
 be in Avails, and we don't want duplicates. Hence this rather
 horrid get_preds function
get_preds inst IsFree = fdPredsOfInst inst
get_preds inst other  isDict inst = [dictPred inst]
 otherwise = []
eqns = improve get_insts preds
get_insts clas = classInstances inst_envs clas
in
if null eqns then
returnM True
else
traceTc (ptext SLIT("Improve:") <+> vcat (map pprEquationDoc eqns)) `thenM_`
mappM_ unify eqns `thenM_`
returnM False
where
unify ((qtvs, pairs), what1, what2)
= addErrCtxtM (mkEqnMsg what1 what2) $
tcInstTyVars (varSetElems qtvs) `thenM` \ (_, _, tenv) >
mapM_ (unif_pr tenv) pairs
unif_pr tenv (ty1,ty2) = unifyType (substTy tenv ty1) (substTy tenv ty2)
pprEquationDoc (eqn, (p1,w1), (p2,w2)) = vcat [pprEquation eqn, nest 2 (ppr p1), nest 2 (ppr p2)]
mkEqnMsg (pred1,from1) (pred2,from2) tidy_env
= do { pred1' < zonkTcPredType pred1; pred2' < zonkTcPredType pred2
; let { pred1'' = tidyPred tidy_env pred1'; pred2'' = tidyPred tidy_env pred2' }
; let msg = vcat [ptext SLIT("When using functional dependencies to combine"),
nest 2 (sep [ppr pred1'' <> comma, nest 2 from1]),
nest 2 (sep [ppr pred2'' <> comma, nest 2 from2])]
; return (tidy_env, msg) }
\end{code}
The main contextreduction function is @reduce@. Here's its game plan.
\begin{code}
reduceList :: (Int,[Inst])  Stack (for err msgs)
 along with its depth
> (Inst > WhatToDo)
> [Inst]
> Avails
> TcM Avails
\end{code}
@reduce@ is passed
try_me: given an inst, this function returns
Reduce reduce this
DontReduce return this in "irreds"
Free return this in "frees"
wanteds: The list of insts to reduce
state: An accumulating parameter of type Avails
that contains the state of the algorithm
It returns a Avails.
The (n,stack) pair is just used for error reporting.
n is always the depth of the stack.
The stack is the stack of Insts being reduced: to produce X
I had to produce Y, to produce Y I had to produce Z, and so on.
\begin{code}
reduceList (n,stack) try_me wanteds state
= do { dopts < getDOpts
#ifdef DEBUG
; if n > 8 then
dumpTcRn (text "Interesting! Context reduction stack deeper than 8:"
<+> (int n $$ ifPprDebug (nest 2 (pprStack stack))))
else return ()
#endif
; if n >= ctxtStkDepth dopts then
failWithTc (reduceDepthErr n stack)
else
go wanteds state }
where
go [] state = return state
go (w:ws) state = do { state' < reduce (n+1, w:stack) try_me w state
; go ws state' }
 Base case: we're done!
reduce stack try_me wanted avails
 It's the same as an existing inst, or a superclass thereof
 Just avail < isAvailable avails wanted
= if isLinearInst wanted then
addLinearAvailable avails avail wanted `thenM` \ (avails', wanteds') >
reduceList stack try_me wanteds' avails'
else
returnM avails  No op for nonlinear things
 otherwise
= case try_me wanted of {
; DontReduceUnlessConstant >  It's irreducible (or at least should not be reduced)
 First, see if the inst can be reduced to a constant in one step
try_simple (addIrred AddSCs)  Assume want superclasses
; Free >  It's free so just chuck it upstairs
 First, see if the inst can be reduced to a constant in one step
try_simple addFree
; ReduceMe want_scs >  It should be reduced
lookupInst wanted `thenM` \ lookup_result >
case lookup_result of
GenInst wanteds' rhs > addIrred NoSCs avails wanted `thenM` \ avails1 >
reduceList stack try_me wanteds' avails1 `thenM` \ avails2 >
addWanted want_scs avails2 wanted rhs wanteds'
 Experiment with temporarily doing addIrred *before* the reduceList,
 which has the effect of adding the thing we are trying
 to prove to the database before trying to prove the things it
 needs. See note [RECURSIVE DICTIONARIES]
 NB: we must not do an addWanted before, because that adds the
 superclasses too, and thaat can lead to a spurious loop; see
 the examples in [SUPERCLASSLOOP]
 So we do an addIrred before, and then overwrite it afterwards with addWanted
SimpleInst rhs > addWanted want_scs avails wanted rhs []
NoInstance >  No such instance!
 Add it and its superclasses
addIrred want_scs avails wanted
}
where
try_simple do_this_otherwise
= lookupInst wanted `thenM` \ lookup_result >
case lookup_result of
SimpleInst rhs > addWanted AddSCs avails wanted rhs []
other > do_this_otherwise avails wanted
\end{code}
\begin{code}

isAvailable :: Avails > Inst > Maybe Avail
isAvailable avails wanted = lookupFM avails wanted
 NB 1: the Ord instance of Inst compares by the class/type info
 *not* by unique. So
 d1::C Int == d2::C Int
addLinearAvailable :: Avails > Avail > Inst > TcM (Avails, [Inst])
addLinearAvailable avails avail wanted
 avails currently maps [wanted > avail]
 Extend avails to reflect a neeed for an extra copy of avail
 Just avail' < split_avail avail
= returnM (addToFM avails wanted avail', [])
 otherwise
= tcLookupId splitName `thenM` \ split_id >
tcInstClassOp (instLoc wanted) split_id
[linearInstType wanted] `thenM` \ split_inst >
returnM (addToFM avails wanted (Linear 2 split_inst avail), [split_inst])
where
split_avail :: Avail > Maybe Avail
 (Just av) if there's a modified version of avail that
 we can use to replace avail in avails
 Nothing if there isn't, so we need to create a Linear
split_avail (Linear n i a) = Just (Linear (n+1) i a)
split_avail (Given id used)  not used = Just (Given id True)
 otherwise = Nothing
split_avail Irred = Nothing
split_avail IsFree = Nothing
split_avail other = pprPanic "addLinearAvailable" (ppr avail $$ ppr wanted $$ ppr avails)

addFree :: Avails > Inst > TcM Avails
 When an Inst is tossed upstairs as 'free' we nevertheless add it
 to avails, so that any other equal Insts will be commoned up right
 here rather than also being tossed upstairs. This is really just
 an optimisation, and perhaps it is more trouble that it is worth,
 as the following comments show!

 NB: do *not* add superclasses. If we have
 df::Floating a
 dn::Num a
 but a is not bound here, then we *don't* want to derive
 dn from df here lest we lose sharing.

addFree avails free = returnM (addToFM avails free IsFree)
addWanted :: WantSCs > Avails > Inst > LHsExpr TcId > [Inst] > TcM Avails
addWanted want_scs avails wanted rhs_expr wanteds
= addAvailAndSCs want_scs avails wanted avail
where
avail = Rhs rhs_expr wanteds
addGiven :: Avails > Inst > TcM Avails
addGiven avails given = addAvailAndSCs AddSCs avails given (Given (instToId given) False)
 Always add superclasses for 'givens'

 No ASSERT( not (given `elemFM` avails) ) because in an instance
 decl for Ord t we can add both Ord t and Eq t as 'givens',
 so the assert isn't true
addIrred :: WantSCs > Avails > Inst > TcM Avails
addIrred want_scs avails irred = ASSERT2( not (irred `elemFM` avails), ppr irred $$ ppr avails )
addAvailAndSCs want_scs avails irred Irred
addAvailAndSCs :: WantSCs > Avails > Inst > Avail > TcM Avails
addAvailAndSCs want_scs avails inst avail
 not (isClassDict inst) = return avails_with_inst
 NoSCs < want_scs = return avails_with_inst
 otherwise = do { traceTc (text "addAvailAndSCs" <+> vcat [ppr inst, ppr deps])
; addSCs is_loop avails_with_inst inst }
where
avails_with_inst = addToFM avails inst avail
is_loop pred = any (`tcEqType` mkPredTy pred) dep_tys
 Note: this compares by *type*, not by Unique
deps = findAllDeps (unitVarSet (instToId inst)) avail
dep_tys = map idType (varSetElems deps)
findAllDeps :: IdSet > Avail > IdSet
 Find all the Insts that this one depends on
 See Note [SUPERCLASSLOOP 2]
 Watch out, though. Since the avails may contain loops
 (see Note [RECURSIVE DICTIONARIES]), so we need to track the ones we've seen so far
findAllDeps so_far (Rhs _ kids) = foldl find_all so_far kids
findAllDeps so_far other = so_far
find_all :: IdSet > Inst > IdSet
find_all so_far kid
 kid_id `elemVarSet` so_far = so_far
 Just avail < lookupFM avails kid = findAllDeps so_far' avail
 otherwise = so_far'
where
so_far' = extendVarSet so_far kid_id  Add the new kid to so_far
kid_id = instToId kid
addSCs :: (TcPredType > Bool) > Avails > Inst > TcM Avails
 Add all the superclasses of the Inst to Avails
 The first param says "dont do this because the original thing
 depends on this one, so you'd build a loop"
 Invariant: the Inst is already in Avails.
addSCs is_loop avails dict
= do { sc_dicts < newDictsAtLoc (instLoc dict) sc_theta'
; foldlM add_sc avails (zipEqual "add_scs" sc_dicts sc_sels) }
where
(clas, tys) = getDictClassTys dict
(tyvars, sc_theta, sc_sels, _) = classBigSig clas
sc_theta' = substTheta (zipTopTvSubst tyvars tys) sc_theta
add_sc avails (sc_dict, sc_sel)
 is_loop (dictPred sc_dict) = return avails  See Note [SUPERCLASSLOOP 2]
 is_given sc_dict = return avails
 otherwise = addSCs is_loop avails' sc_dict
where
sc_sel_rhs = mkHsDictApp (mkHsTyApp (L (instSpan dict) (HsVar sc_sel)) tys) [instToId dict]
avails' = addToFM avails sc_dict (Rhs sc_sel_rhs [dict])
is_given :: Inst > Bool
is_given sc_dict = case lookupFM avails sc_dict of
Just (Given _ _) > True  Given is cheaper than superclass selection
other > False
\end{code}
Note [SUPERCLASSLOOP 2]
~~~~~~~~~~~~~~~~~~~~~~~~
But the above isn't enough. Suppose we are *given* d1:Ord a,
and want to deduce (d2:C [a]) where
class Ord a => C a where
instance Ord [a] => C [a] where ...
Then we'll use the instance decl to deduce C [a] from Ord [a], and then add the
superclasses of C [a] to avails. But we must not overwrite the binding
for Ord [a] (which is obtained from Ord a) with a superclass selection or we'll just
build a loop!
Here's another variant, immortalised in tcrun020
class Monad m => C1 m
class C1 m => C2 m x
instance C2 Maybe Bool
For the instance decl we need to build (C1 Maybe), and it's no good if
we run around and add (C2 Maybe Bool) and its superclasses to the avails
before we search for C1 Maybe.
Here's another example
class Eq b => Foo a b
instance Eq a => Foo [a] a
If we are reducing
(Foo [t] t)
we'll first deduce that it holds (via the instance decl). We must not
then overwrite the Eq t constraint with a superclass selection!
At first I had a gross hack, whereby I simply did not add superclass constraints
in addWanted, though I did for addGiven and addIrred. This was suboptimal,
becuase it lost legitimate superclass sharing, and it still didn't do the job:
I found a very obscure program (now tcrun021) in which improvement meant the
simplifier got two bites a the cherry... so something seemed to be an Irred
first time, but reducible next time.
Now we implement the Right Solution, which is to check for loops directly
when adding superclasses. It's a bit like the occurs check in unification.
Note [RECURSIVE DICTIONARIES]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider
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:
d1 : Eq (D [])
by instance decl, holds if
d2 : Eq [D []]
where d1 = dfEqD d2
by instance decl of Eq, holds if
d3 : D []
where d2 = dfEqList d3
d1 = dfEqD d2
But now we can "tie the knot" to give
d3 = d1
d2 = dfEqList d3
d1 = dfEqD d2
and it'll even run! The trick is to put the thing we are trying to prove
(in this case Eq (D []) into the database before trying to prove its
contributing clauses.
%************************************************************************
%* *
\section{tcSimplifyTop: defaulting}
%* *
%************************************************************************
@tcSimplifyTop@ is called once per module to simplify all the constant
and ambiguous Insts.
We need to be careful of one case. Suppose we have
instance Num a => Num (Foo a b) where ...
and @tcSimplifyTop@ is given a constraint (Num (Foo x y)). Then it'll simplify
to (Num x), and default x to Int. But what about y??
It's OK: the final zonking stage should zap y to (), which is fine.
\begin{code}
tcSimplifyTop, tcSimplifyInteractive :: [Inst] > TcM TcDictBinds
tcSimplifyTop wanteds
= do { ext_default < doptM Opt_ExtendedDefaultRules
; tc_simplify_top doc ext_default AddSCs wanteds }
where
doc = text "tcSimplifyTop"
tcSimplifyInteractive wanteds
= tc_simplify_top doc True { Interactive loop } AddSCs wanteds
where
doc = text "tcSimplifyTop"
 The TcLclEnv should be valid here, solely to improve
 error message generation for the monomorphism restriction
tc_simplify_top doc use_extended_defaulting want_scs wanteds
= do { lcl_env < getLclEnv
; traceTc (text "tcSimplifyTop" <+> ppr (lclEnvElts lcl_env))
; let try_me inst = ReduceMe want_scs
; (frees, binds, irreds) < simpleReduceLoop doc try_me wanteds
; let
 First get rid of implicit parameters
(non_ips, bad_ips) = partition isClassDict irreds
 All the nontv or multiparam ones are definite errors
(unary_tv_dicts, non_tvs) = partition is_unary_tyvar_dict non_ips
bad_tyvars = unionVarSets (map tyVarsOfInst non_tvs)
 Group by type variable
tv_groups = equivClasses cmp_by_tyvar unary_tv_dicts
 Pick the ones which its worth trying to disambiguate
 namely, the ones whose type variable isn't bound
 up with one of the nontyvar classes
(default_gps, non_default_gps) = partition defaultable_group tv_groups
defaultable_group ds
= not (bad_tyvars `intersectsVarSet` tyVarsOfInst (head ds))
&& defaultable_classes (map get_clas ds)
defaultable_classes clss
 use_extended_defaulting = any isInteractiveClass clss
 otherwise = all isStandardClass clss && any isNumericClass clss
isInteractiveClass cls = isNumericClass cls
 (classKey cls `elem` [showClassKey, eqClassKey, ordClassKey])
 In interactive mode, or with fextendeddefaultrules,
 we default Show a to Show () to avoid graututious errors on "show []"
 Collect together all the bad guys
bad_guys = non_tvs ++ concat non_default_gps
(ambigs, no_insts) = partition isTyVarDict bad_guys
 If the dict has no type constructors involved, it must be ambiguous,
 except I suppose that another error with fundeps maybe should have
 constrained those type variables
 Report definite errors
; ASSERT( null frees )
groupErrs (addNoInstanceErrs Nothing []) no_insts
; strangeTopIPErrs bad_ips
 Deal with ambiguity errors, but only if
 if there has not been an error so far:
 errors often give rise to spurious ambiguous Insts.
 For example:
 f = (*)  Monomorphic
 g :: Num a => a > a
 g x = f x x
 Here, we get a complaint when checking the type signature for g,
 that g isn't polymorphic enough; but then we get another one when
 dealing with the (Num a) context arising from f's definition;
 we try to unify a with Int (to default it), but find that it's
 already been unified with the rigid variable from g's type sig
; binds_ambig < ifErrsM (returnM []) $
do {  Complain about the ones that don't fall under
 the Haskell rules for disambiguation
 This group includes both nonexistent instances
 e.g. Num (IO a) and Eq (Int > Int)
 and ambiguous dictionaries
 e.g. Num a
addTopAmbigErrs ambigs
 Disambiguate the ones that look feasible
; mappM disambigGroup default_gps }
; return (binds `unionBags` unionManyBags binds_ambig) }

d1 `cmp_by_tyvar` d2 = get_tv d1 `compare` get_tv d2
is_unary_tyvar_dict :: Inst > Bool  Dicts of form (C a)
 Invariant: argument is a ClassDict, not IP or method
is_unary_tyvar_dict d = case getDictClassTys d of
(_, [ty]) > tcIsTyVarTy ty
other > False
get_tv d = case getDictClassTys d of
(clas, [ty]) > tcGetTyVar "tcSimplify" ty
get_clas d = case getDictClassTys d of
(clas, _) > clas
\end{code}
If a dictionary constrains a type variable which is
* not mentioned in the environment
* and not mentioned in the type of the expression
then it is ambiguous. No further information will arise to instantiate
the type variable; nor will it be generalised and turned into an extra
parameter to a function.
It is an error for this to occur, except that Haskell provided for
certain rules to be applied in the special case of numeric types.
Specifically, if
* at least one of its classes is a numeric class, and
* all of its classes are numeric or standard
then the type variable can be defaulted to the first type in the
defaulttype list which is an instance of all the offending classes.
So here is the function which does the work. It takes the ambiguous
dictionaries and either resolves them (producing bindings) or
complains. It works by splitting the dictionary list by type
variable, and using @disambigOne@ to do the real business.
@disambigOne@ assumes that its arguments dictionaries constrain all
the same type variable.
ADR Comment 20/6/94: I've changed the @CReturnable@ case to default to
@()@ instead of @Int@. I reckon this is the Right Thing to do since
the most common use of defaulting is code like:
\begin{verbatim}
_ccall_ foo `seqPrimIO` bar
\end{verbatim}
Since we're not using the result of @foo@, the result if (presumably)
@void@.
\begin{code}
disambigGroup :: [Inst]  All standard classes of form (C a)
> TcM TcDictBinds
disambigGroup dicts
=  THE DICTS OBEY THE DEFAULTABLE CONSTRAINT
 SO, TRY DEFAULT TYPES IN ORDER
 Failure here is caused by there being no type in the
 default list which can satisfy all the ambiguous classes.
 For example, if Real a is reqd, but the only type in the
 default list is Int.
get_default_tys `thenM` \ default_tys >
let
try_default []  No defaults work, so fail
= failM
try_default (default_ty : default_tys)
= tryTcLIE_ (try_default default_tys) $  If default_ty fails, we try
 default_tys instead
tcSimplifyDefault theta `thenM` \ _ >
returnM default_ty
where
theta = [mkClassPred clas [default_ty]  clas < classes]
in
 See if any default works
tryM (try_default default_tys) `thenM` \ mb_ty >
case mb_ty of
Left _ > bomb_out
Right chosen_default_ty > choose_default chosen_default_ty
where
tyvar = get_tv (head dicts)  Should be nonempty
classes = map get_clas dicts
choose_default default_ty  Commit to tyvar = default_ty
=  Bind the type variable
unifyType default_ty (mkTyVarTy tyvar) `thenM_`
 and reduce the context, for real this time
simpleReduceLoop (text "disambig" <+> ppr dicts)
reduceMe dicts `thenM` \ (frees, binds, ambigs) >
WARN( not (null frees && null ambigs), ppr frees $$ ppr ambigs )
warnDefault dicts default_ty `thenM_`
returnM binds
bomb_out = addTopAmbigErrs dicts `thenM_`
returnM emptyBag
get_default_tys
= do { mb_defaults < getDefaultTys
; case mb_defaults of
Just tys > return tys
Nothing >  No usesupplied default;
 use [Integer, Double]
do { integer_ty < tcMetaTy integerTyConName
; checkWiredInTyCon doubleTyCon
; return [integer_ty, doubleTy] } }
\end{code}
[Aside  why the defaulting mechanism is turned off when
dealing with arguments and results to ccalls.
When typechecking _ccall_s, TcExpr ensures that the external
function is only passed arguments (and in the other direction,
results) of a restricted set of 'native' types.
The interaction between the defaulting mechanism for numeric
values and CC & CR can be a bit puzzling to the user at times.
For example,
x < _ccall_ f
if (x /= 0) then
_ccall_ g x
else
return ()
What type has 'x' got here? That depends on the default list
in operation, if it is equal to Haskell 98's defaultdefault
of (Integer, Double), 'x' has type Double, since Integer
is not an instance of CR. If the default list is equal to
Haskell 1.4's defaultdefault of (Int, Double), 'x' has type
Int.
End of aside]
%************************************************************************
%* *
\subsection[simple]{@Simple@ versions}
%* *
%************************************************************************
Much simpler versions when there are no bindings to make!
@tcSimplifyThetas@ simplifies classtype constraints formed by
@deriving@ declarations and when specialising instances. We are
only interested in the simplified bunch of class/type constraints.
It simplifies to constraints of the form (C a b c) where
a,b,c are type variables. This is required for the context of
instance declarations.
\begin{code}
tcSimplifyDeriv :: TyCon
> [TyVar]
> ThetaType  Wanted
> TcM ThetaType  Needed
tcSimplifyDeriv tc tyvars theta
= tcInstTyVars tyvars `thenM` \ (tvs, _, tenv) >
 The main loop may do unification, and that may crash if
 it doesn't see a TcTyVar, so we have to instantiate. Sigh
 ToDo: what if two of them do get unified?
newDicts DerivOrigin (substTheta tenv theta) `thenM` \ wanteds >
simpleReduceLoop doc reduceMe wanteds `thenM` \ (frees, _, irreds) >
ASSERT( null frees )  reduceMe never returns Free
doptM Opt_GlasgowExts `thenM` \ gla_exts >
doptM Opt_AllowUndecidableInstances `thenM` \ undecidable_ok >
let
tv_set = mkVarSet tvs
(bad_insts, ok_insts) = partition is_bad_inst irreds
is_bad_inst dict
= let pred = dictPred dict  reduceMe squashes all nondicts
in isEmptyVarSet (tyVarsOfPred pred)
 Things like (Eq T) are bad
 (not gla_exts && not (isTyVarClassPred pred))
simpl_theta = map dictPred ok_insts
weird_preds = [pred  pred < simpl_theta
, not (tyVarsOfPred pred `subVarSet` tv_set)]
 Check for a bizarre corner case, when the derived instance decl should
 have form instance C a b => D (T a) where ...
 Note that 'b' isn't a parameter of T. This gives rise to all sorts
 of problems; in particular, it's hard to compare solutions for
 equality when finding the fixpoint. So I just rule it out for now.
rev_env = zipTopTvSubst tvs (mkTyVarTys tyvars)
 This reversemapping is a Royal Pain,
 but the result should mention TyVars not TcTyVars
in
addNoInstanceErrs Nothing [] bad_insts `thenM_`
mapM_ (addErrTc . badDerivedPred) weird_preds `thenM_`
returnM (substTheta rev_env simpl_theta)
where
doc = ptext SLIT("deriving classes for a data type")
\end{code}
@tcSimplifyDefault@ just checks classtype constraints, essentially;
used with \tr{default} declarations. We are only interested in
whether it worked or not.
\begin{code}
tcSimplifyDefault :: ThetaType  Wanted; has no type variables in it
> TcM ()
tcSimplifyDefault theta
= newDicts DefaultOrigin theta `thenM` \ wanteds >
simpleReduceLoop doc reduceMe wanteds `thenM` \ (frees, _, irreds) >
ASSERT( null frees )  try_me never returns Free
addNoInstanceErrs Nothing [] irreds `thenM_`
if null irreds then
returnM ()
else
failM
where
doc = ptext SLIT("default declaration")
\end{code}
%************************************************************************
%* *
\section{Errors and contexts}
%* *
%************************************************************************
ToDo: for these error messages, should we note the location as coming
from the insts, or just whatever seems to be around in the monad just
now?
\begin{code}
groupErrs :: ([Inst] > TcM ())  Deal with one group
> [Inst]  The offending Insts
> TcM ()
 Group together insts with the same origin
 We want to report them together in error messages
groupErrs report_err []
= returnM ()
groupErrs report_err (inst:insts)
= do_one (inst:friends) `thenM_`
groupErrs report_err others
where
 (It may seem a bit crude to compare the error messages,
 but it makes sure that we combine just what the user sees,
 and it avoids need equality on InstLocs.)
(friends, others) = partition is_friend insts
loc_msg = showSDoc (pprInstLoc (instLoc inst))
is_friend friend = showSDoc (pprInstLoc (instLoc friend)) == loc_msg
do_one insts = addInstCtxt (instLoc (head insts)) (report_err insts)
 Add location and context information derived from the Insts
 Add the "arising from..." part to a message about bunch of dicts
addInstLoc :: [Inst] > Message > Message
addInstLoc insts msg = msg $$ nest 2 (pprInstLoc (instLoc (head insts)))
addTopIPErrs :: [Name] > [Inst] > TcM ()
addTopIPErrs bndrs []
= return ()
addTopIPErrs bndrs ips
= addErrTcM (tidy_env, mk_msg tidy_ips)
where
(tidy_env, tidy_ips) = tidyInsts ips
mk_msg ips = vcat [sep [ptext SLIT("Implicit parameters escape from"),
nest 2 (ptext SLIT("the monomorphic toplevel binding(s) of")
<+> pprBinders bndrs <> colon)],
nest 2 (vcat (map ppr_ip ips)),
monomorphism_fix]
ppr_ip ip = pprPred (dictPred ip) <+> pprInstLoc (instLoc ip)
strangeTopIPErrs :: [Inst] > TcM ()
strangeTopIPErrs dicts  Strange, becuase addTopIPErrs should have caught them all
= groupErrs report tidy_dicts
where
(tidy_env, tidy_dicts) = tidyInsts dicts
report dicts = addErrTcM (tidy_env, mk_msg dicts)
mk_msg dicts = addInstLoc dicts (ptext SLIT("Unbound implicit parameter") <>
plural tidy_dicts <+> pprDictsTheta tidy_dicts)
addNoInstanceErrs :: Maybe SDoc  Nothing => top level
 Just d => d describes the construct
> [Inst]  What is given by the context or type sig
> [Inst]  What is wanted
> TcM ()
addNoInstanceErrs mb_what givens []
= returnM ()
addNoInstanceErrs mb_what givens dicts
=  Some of the dicts are here because there is no instances
 and some because there are too many instances (overlap)
tcGetInstEnvs `thenM` \ inst_envs >
let
(tidy_env1, tidy_givens) = tidyInsts givens
(tidy_env2, tidy_dicts) = tidyMoreInsts tidy_env1 dicts
 Run through the dicts, generating a message for each
 overlapping one, but simply accumulating all the
 noinstance ones so they can be reported as a group
(overlap_doc, no_inst_dicts) = foldl check_overlap (empty, []) tidy_dicts
check_overlap (overlap_doc, no_inst_dicts) dict
 not (isClassDict dict) = (overlap_doc, dict : no_inst_dicts)
 otherwise
= case lookupInstEnv inst_envs clas tys of
 The case of exactly one match and no unifiers means
 a successful lookup. That can't happen here, becuase
 dicts only end up here if they didn't match in Inst.lookupInst
#ifdef DEBUG
([m],[]) > pprPanic "addNoInstanceErrs" (ppr dict)
#endif
([], _) > (overlap_doc, dict : no_inst_dicts)  No match
res > (mk_overlap_msg dict res $$ overlap_doc, no_inst_dicts)
where
(clas,tys) = getDictClassTys dict
in
 Now generate a good message for the noinstance bunch
mk_probable_fix tidy_env2 no_inst_dicts `thenM` \ (tidy_env3, probable_fix) >
let
no_inst_doc  null no_inst_dicts = empty
 otherwise = vcat [addInstLoc no_inst_dicts heading, probable_fix]
heading  null givens = ptext SLIT("No instance") <> plural no_inst_dicts <+>
ptext SLIT("for") <+> pprDictsTheta no_inst_dicts
 otherwise = sep [ptext SLIT("Could not deduce") <+> pprDictsTheta no_inst_dicts,
nest 2 $ ptext SLIT("from the context") <+> pprDictsTheta tidy_givens]
in
 And emit both the noninstance and overlap messages
addErrTcM (tidy_env3, no_inst_doc $$ overlap_doc)
where
mk_overlap_msg dict (matches, unifiers)
= vcat [ addInstLoc [dict] ((ptext SLIT("Overlapping instances for")
<+> pprPred (dictPred dict))),
sep [ptext SLIT("Matching instances") <> colon,
nest 2 (vcat [pprInstances ispecs, pprInstances unifiers])],
ASSERT( not (null matches) )
if not (isSingleton matches)
then  Two or more matches
empty
else  One match, plus some unifiers
ASSERT( not (null unifiers) )
parens (vcat [ptext SLIT("The choice depends on the instantiation of") <+>
quotes (pprWithCommas ppr (varSetElems (tyVarsOfInst dict))),
ptext SLIT("Use fallowincoherentinstances to use the first choice above")])]
where
ispecs = [ispec  (_, ispec) < matches]
mk_probable_fix tidy_env dicts
= returnM (tidy_env, sep [ptext SLIT("Possible fix:"), nest 2 (vcat fixes)])
where
fixes = add_ors (fix1 ++ fix2)
fix1 = case mb_what of
Nothing > []  Top level
Just what >  Nested (type signatures, instance decls)
[ sep [ ptext SLIT("add") <+> pprDictsTheta dicts,
ptext SLIT("to the") <+> what] ]
fix2  null instance_dicts = []
 otherwise = [ sep [ptext SLIT("add an instance declaration for"),
pprDictsTheta instance_dicts] ]
instance_dicts = [d  d < dicts, isClassDict d, not (isTyVarDict d)]
 Insts for which it is worth suggesting an adding an instance declaration
 Exclude implicit parameters, and tyvar dicts
add_ors :: [SDoc] > [SDoc]  The empty case should not happen
add_ors [] = [ptext SLIT("[No suggested fixes]")]  Strange
add_ors (f1:fs) = f1 : map (ptext SLIT("or") <+>) fs
addTopAmbigErrs dicts
 Divide into groups that share a common set of ambiguous tyvars
= mapM report (equivClasses cmp [(d, tvs_of d)  d < tidy_dicts])
where
(tidy_env, tidy_dicts) = tidyInsts dicts
tvs_of :: Inst > [TcTyVar]
tvs_of d = varSetElems (tyVarsOfInst d)
cmp (_,tvs1) (_,tvs2) = tvs1 `compare` tvs2
report :: [(Inst,[TcTyVar])] > TcM ()
report pairs@((inst,tvs) : _)  The pairs share a common set of ambiguous tyvars
= mkMonomorphismMsg tidy_env tvs `thenM` \ (tidy_env, mono_msg) >
setSrcSpan (instLocSrcSpan (instLoc inst)) $
 the location of the first one will do for the err message
addErrTcM (tidy_env, msg $$ mono_msg)
where
dicts = map fst pairs
msg = sep [text "Ambiguous type variable" <> plural tvs <+>
pprQuotedList tvs <+> in_msg,
nest 2 (pprDictsInFull dicts)]
in_msg = text "in the constraint" <> plural dicts <> colon
mkMonomorphismMsg :: TidyEnv > [TcTyVar] > TcM (TidyEnv, Message)
 There's an error with these Insts; if they have free type variables
 it's probably caused by the monomorphism restriction.
 Try to identify the offending variable
 ASSUMPTION: the Insts are fully zonked
mkMonomorphismMsg tidy_env inst_tvs
= findGlobals (mkVarSet inst_tvs) tidy_env `thenM` \ (tidy_env, docs) >
returnM (tidy_env, mk_msg docs)
where
mk_msg [] = ptext SLIT("Probable fix: add a type signature that fixes these type variable(s)")
 This happens in things like
 f x = show (read "foo")
 whre monomorphism doesn't play any role
mk_msg docs = vcat [ptext SLIT("Possible cause: the monomorphism restriction applied to the following:"),
nest 2 (vcat docs),
monomorphism_fix
]
monomorphism_fix :: SDoc
monomorphism_fix = ptext SLIT("Probable fix:") <+>
(ptext SLIT("give these definition(s) an explicit type signature")
$$ ptext SLIT("or use fnomonomorphismrestriction"))
warnDefault dicts default_ty
= doptM Opt_WarnTypeDefaults `thenM` \ warn_flag >
addInstCtxt (instLoc (head dicts)) (warnTc warn_flag warn_msg)
where
 Tidy them first
(_, tidy_dicts) = tidyInsts dicts
warn_msg = vcat [ptext SLIT("Defaulting the following constraint(s) to type") <+>
quotes (ppr default_ty),
pprDictsInFull tidy_dicts]
 Used for the ...Thetas variants; all top level
badDerivedPred pred
= vcat [ptext SLIT("Can't derive instances where the instance context mentions"),
ptext SLIT("type variables that are not data type parameters"),
nest 2 (ptext SLIT("Offending constraint:") <+> ppr pred)]
reduceDepthErr n stack
= vcat [ptext SLIT("Context reduction stack overflow; size =") <+> int n,
ptext SLIT("Use fcontextstack=N to increase stack size to N"),
nest 4 (pprStack stack)]
pprStack stack = vcat (map pprInstInFull stack)
\end{code}