%
% (c) The University of Glasgow 2006
% (c) The GRASP/AQUA Project, Glasgow University, 19921998
%
TcSimplify
\begin{code}
module TcSimplify (
tcSimplifyInfer, tcSimplifyInferCheck,
tcSimplifyCheck, tcSimplifyRestricted,
tcSimplifyRuleLhs, tcSimplifyIPs,
tcSimplifySuperClasses,
tcSimplifyTop, tcSimplifyInteractive,
tcSimplifyBracket, tcSimplifyCheckPat,
tcSimplifyDeriv, tcSimplifyDefault,
bindInstsOfLocalFuns, bindIrreds,
) where
#include "HsVersions.h"
import {# SOURCE #} TcUnify( unifyType )
import HsSyn
import TcRnMonad
import Inst
import TcEnv
import InstEnv
import TcGadt
import TcType
import TcMType
import TcIface
import Var
import Name
import NameSet
import Class
import FunDeps
import PrelInfo
import PrelNames
import Type
import TysWiredIn
import ErrUtils
import BasicTypes
import VarSet
import VarEnv
import FiniteMap
import Bag
import Outputable
import ListSetOps
import Util
import SrcLoc
import DynFlags
import Data.List
\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

Note [Inheriting 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.
Note [Implicit parameters and ambiguity]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
What type should we infer for this?
f x = (show ?y, x::Int)
Since we must quantify over the ?y, the most plausible type is
f :: (Show a, ?y::a) => Int > (String, Int)
But notice that the type of the RHS is (String,Int), with no type
varibables mentioned at all! The type of f looks ambiguous. But
it isn't, because at a call site we might have
let ?y = 5::Int in f 7
and all is well. In effect, implicit parameters are, well, parameters,
so we can take their type variables into account as part of the
"tautvs" stuff. This is done in the function 'FunDeps.grow'.
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 and quantified)
[Inst],  Dict Ids that must be bound here (zonked)
TcDictBinds)  Bindings
 Any free (escaping) Insts are tossed into the environment
\end{code}
\begin{code}
tcSimplifyInfer doc tau_tvs wanted
= do { tau_tvs' < zonkTcTyVarsAndFV (varSetElems tau_tvs)
; wanted' < mappM zonkInst wanted  Zonk before deciding quantified tyvars
; gbl_tvs < tcGetGlobalTyVars
; let preds = fdPredsOfInsts wanted'
qtvs = grow preds tau_tvs' `minusVarSet` oclose preds gbl_tvs
(free, bound) = partition (isFreeWhenInferring qtvs) wanted'
; traceTc (text "infer" <+> (ppr preds $$ ppr (grow preds tau_tvs') $$ ppr gbl_tvs $$ ppr (oclose preds gbl_tvs) $$ ppr free $$ ppr bound))
; extendLIEs free
 To make types simple, reduce as much as possible
; let try_me inst = ReduceMe AddSCs
; (irreds, binds) < checkLoop (mkRedEnv doc try_me []) bound
; qtvs' < zonkQuantifiedTyVars (varSetElems qtvs)
 We can't abstract over implications
; let (dicts, implics) = partition isDict irreds
; loc < getInstLoc (ImplicOrigin doc)
; implic_bind < bindIrreds loc qtvs' dicts implics
; return (qtvs', dicts, binds `unionBags` implic_bind) }
 NB: when we are done, we might have some bindings, but
 the final qtvs might be empty. See Note [NO TYVARS] below.
\end{code}
\begin{code}

 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
:: InstLoc
> TcTyVarSet  fv(T)
> [Inst]  Given
> [Inst]  Wanted
> TcM ([TyVar],  Fully zonked, and quantified
TcDictBinds)  Bindings
tcSimplifyInferCheck loc tau_tvs givens wanteds
= do { (irreds, binds) < innerCheckLoop loc givens wanteds
 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.
; let all_tvs = varSetElems (tau_tvs `unionVarSet` tyVarsOfInsts givens)
; all_tvs < zonkTcTyVarsAndFV all_tvs
; gbl_tvs < tcGetGlobalTyVars
; let qtvs = varSetElems (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
; qtvs' < zonkQuantifiedTyVars qtvs
 Now we are back to normal (c.f. tcSimplCheck)
; implic_bind < bindIrreds loc qtvs' givens irreds
; return (qtvs', binds `unionBags` implic_bind) }
\end{code}
Note [Squashing methods]
~~~~~~~~~~~~~~~~~~~~~~~~~
Be careful if you want to float methods more:
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)
may continue to float out!
Note [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 Note [Inheriting implicit parameters]
{ No longer used (with implication constraints)
isFreeWhenChecking :: TyVarSet  Quantified tyvars
> NameSet  Quantified implicit parameters
> Inst > Bool
isFreeWhenChecking qtvs ips inst
= isFreeWrtTyVars qtvs inst
&& isFreeWrtIPs ips inst
}
isFreeWrtTyVars qtvs inst = tyVarsOfInst inst `disjointVarSet` 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 is used when checking expression type signatures,
 class decls, instance decls etc.
tcSimplifyCheck :: InstLoc
> [TcTyVar]  Quantify over these
> [Inst]  Given
> [Inst]  Wanted
> TcM TcDictBinds  Bindings
tcSimplifyCheck loc qtvs givens wanteds
= ASSERT( all isTcTyVar qtvs && all isSkolemTyVar qtvs )
do { (irreds, binds) < innerCheckLoop loc givens wanteds
; implic_bind < bindIrreds loc qtvs givens irreds
; return (binds `unionBags` implic_bind) }

 tcSimplifyCheckPat is used for existential pattern match
tcSimplifyCheckPat :: InstLoc
> [CoVar] > Refinement
> [TcTyVar]  Quantify over these
> [Inst]  Given
> [Inst]  Wanted
> TcM TcDictBinds  Bindings
tcSimplifyCheckPat loc co_vars reft qtvs givens wanteds
= ASSERT( all isTcTyVar qtvs && all isSkolemTyVar qtvs )
do { (irreds, binds) < innerCheckLoop loc givens wanteds
; implic_bind < bindIrredsR loc qtvs co_vars reft
givens irreds
; return (binds `unionBags` implic_bind) }

bindIrreds :: InstLoc > [TcTyVar]
> [Inst] > [Inst]
> TcM TcDictBinds
bindIrreds loc qtvs givens irreds
= bindIrredsR loc qtvs [] emptyRefinement givens irreds
bindIrredsR :: InstLoc > [TcTyVar] > [CoVar]
> Refinement > [Inst] > [Inst]
> TcM TcDictBinds
 Make a binding that binds 'irreds', by generating an implication
 constraint for them, *and* throwing the constraint into the LIE
bindIrredsR loc qtvs co_vars reft givens irreds
 null irreds
= return emptyBag
 otherwise
= do { let givens' = filter isDict givens
 The givens can include methods
 See Note [Pruning the givens in an implication constraint]
 If there are no 'givens' *and* the refinement is empty
 (the refinement is like more givens), then it's safe to
 partition the 'wanteds' by their qtvs, thereby trimming irreds
 See Note [Freeness and implications]
; irreds' < if null givens' && isEmptyRefinement reft
then do
{ let qtv_set = mkVarSet qtvs
(frees, real_irreds) = partition (isFreeWrtTyVars qtv_set) irreds
; extendLIEs frees
; return real_irreds }
else return irreds
; let all_tvs = qtvs ++ co_vars  Abstract over all these
; (implics, bind) < makeImplicationBind loc all_tvs reft givens' irreds'
 This call does the real work
 If irreds' is empty, it does something sensible
; extendLIEs implics
; return bind }
makeImplicationBind :: InstLoc > [TcTyVar] > Refinement
> [Inst] > [Inst]
> TcM ([Inst], TcDictBinds)
 Make a binding that binds 'irreds', by generating an implication
 constraint for them, *and* throwing the constraint into the LIE
 The binding looks like
 (ir1, .., irn) = f qtvs givens
 where f is (evidence for) the new implication constraint
 f :: forall qtvs. {reft} givens => (ir1, .., irn)
 qtvs includes coercion variables

 This binding must line up the 'rhs' in reduceImplication
makeImplicationBind loc all_tvs reft
givens  Guaranteed all Dicts
irreds
 null irreds  If there are no irreds, we are done
= return ([], emptyBag)
 otherwise  Otherwise we must generate a binding
= do { uniq < newUnique
; span < getSrcSpanM
; let name = mkInternalName uniq (mkVarOcc "ic") (srcSpanStart span)
implic_inst = ImplicInst { tci_name = name, tci_reft = reft,
tci_tyvars = all_tvs,
tci_given = givens,
tci_wanted = irreds, tci_loc = loc }
; let n_irreds = length irreds
irred_ids = map instToId irreds
tup_ty = mkTupleTy Boxed n_irreds (map idType irred_ids)
pat = TuplePat (map nlVarPat irred_ids) Boxed tup_ty
rhs = L span (mkHsWrap co (HsVar (instToId implic_inst)))
co = mkWpApps (map instToId givens) <.> mkWpTyApps (mkTyVarTys all_tvs)
bind  n_irreds==1 = VarBind (head irred_ids) rhs
 otherwise = PatBind { pat_lhs = L span pat,
pat_rhs = unguardedGRHSs rhs,
pat_rhs_ty = tup_ty,
bind_fvs = placeHolderNames }
;  pprTrace "Make implic inst" (ppr implic_inst) $
return ([implic_inst], unitBag (L span bind)) }

topCheckLoop :: SDoc
> [Inst]  Wanted
> TcM ([Inst], TcDictBinds)
topCheckLoop doc wanteds
= checkLoop (mkRedEnv doc try_me []) wanteds
where
try_me inst = ReduceMe AddSCs

innerCheckLoop :: InstLoc
> [Inst]  Given
> [Inst]  Wanted
> TcM ([Inst], TcDictBinds)
innerCheckLoop inst_loc givens wanteds
= checkLoop env wanteds
where
env = mkRedEnv (pprInstLoc inst_loc) try_me givens
try_me inst  isMethodOrLit inst = ReduceMe AddSCs
 otherwise = Stop
 When checking against a given signature
 we MUST be very gentle: Note [Check gently]
\end{code}
Note [Check gently]
~~~~~~~~~~~~~~~~~~~~
We have to very careful about not simplifying too vigorously
Example:
data T a where
MkT :: a > T [a]
f :: Show b => T b > b
f (MkT x) = show [x]
Inside the pattern match, which binds (a:*, x:a), we know that
b ~ [a]
Hence we have a dictionary for Show [a] available; and indeed we
need it. We are going to build an implication contraint
forall a. (b~[a]) => Show [a]
Later, we will solve this constraint using the knowledge (Show b)
But we MUST NOT reduce (Show [a]) to (Show a), else the whole
thing becomes insoluble. So we simplify gently (get rid of literals
and methods only, plus common up equal things), deferring the real
work until top level, when we solve the implication constraint
with topCheckLooop.
\begin{code}

checkLoop :: RedEnv
> [Inst]  Wanted
> TcM ([Inst], TcDictBinds)
 Precondition: givens are completely rigid
checkLoop env wanteds
= do {  Givens are skolems, so no need to zonk them
wanteds' < mappM zonkInst wanteds
; (improved, binds, irreds) < reduceContext env wanteds'
; if not improved then
return (irreds, binds)
else do
 If improvement did some unification, we go round again.
 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 Note [LOOP]
{ (irreds1, binds1) < checkLoop env irreds
; return (irreds1, binds `unionBags` binds1) } }
\end{code}
Note [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)!
%************************************************************************
%* *
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
:: InstLoc
> [Inst]  Given
> [Inst]  Wanted
> TcM TcDictBinds
tcSimplifySuperClasses loc givens sc_wanteds
= do { (irreds, binds1) < checkLoop env sc_wanteds
; let (tidy_env, tidy_irreds) = tidyInsts irreds
; reportNoInstances tidy_env (Just (loc, givens)) tidy_irreds
; return binds1 }
where
env = mkRedEnv (pprInstLoc loc) try_me givens
try_me inst = ReduceMe NoSCs
 Like topCheckLoop, but with NoSCs
\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 ([TyVar],  Tyvars to quantify (zonked and quantified)
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
= do { wanteds' < mappM zonkInst 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
; let env = mkNoImproveRedEnv doc (\i > ReduceMe AddSCs)
; (_imp, _binds, constrained_dicts) < reduceContext env wanteds'
 Next, figure out the tyvars we will quantify over
; tau_tvs' < zonkTcTyVarsAndFV (varSetElems tau_tvs)
; gbl_tvs' < tcGetGlobalTyVars
; constrained_dicts' < mappM zonkInst constrained_dicts
; let constrained_tvs' = tyVarsOfInsts constrained_dicts'
qtvs = (tau_tvs' `minusVarSet` oclose (fdPredsOfInsts constrained_dicts) gbl_tvs')
`minusVarSet` constrained_tvs'
; traceTc (text "tcSimplifyRestricted" <+> vcat [
pprInsts wanteds, pprInsts constrained_dicts',
ppr _binds,
ppr constrained_tvs', ppr tau_tvs', ppr qtvs ])
 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) = Stop
 otherwise = ReduceMe AddSCs
env = mkNoImproveRedEnv doc try_me
; (_imp, binds, irreds) < reduceContext env wanteds'
 See "Notes on implicit parameters, Question 4: top level"
; ASSERT( all (isFreeWrtTyVars qtvs) irreds )  None should be captured
if is_nested_group then
extendLIEs irreds
else do { let (bad_ips, non_ips) = partition isIPDict irreds
; addTopIPErrs bndrs bad_ips
; extendLIEs non_ips }
; qtvs' < zonkQuantifiedTyVars (varSetElems qtvs)
; return (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 < lookupSimpleInst w'
; case lookup_result of
GenInst ws' rhs > go dicts (addBind binds w rhs) (ws' ++ 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
= do { topCheckLoop doc wanteds
; return () }
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
 We need a loop so that we do improvement, and then
 (next time round) generate a binding to connect the two
 let ?x = e in ?x
 Here the two ?x's have different types, and improvement
 makes them the same.
tcSimplifyIPs given_ips wanteds
= do { wanteds' < mappM zonkInst wanteds
; given_ips' < mappM zonkInst given_ips
 Unusually for checking, we *must* zonk the given_ips
; let env = mkRedEnv doc try_me given_ips'
; (improved, binds, irreds) < reduceContext env wanteds'
; if not improved then
ASSERT( all is_free irreds )
do { extendLIEs irreds
; return binds }
else
tcSimplifyIPs given_ips wanteds }
where
doc = text "tcSimplifyIPs" <+> ppr given_ips
ip_set = mkNameSet (ipNamesOfInsts given_ips)
is_free inst = isFreeWrtIPs ip_set inst
 Simplify any methods that mention the implicit parameter
try_me inst  is_free inst = Stop
 otherwise = ReduceMe NoSCs
\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
= do { (irreds, binds) < checkLoop env for_me
; extendLIEs not_for_me
; extendLIEs irreds
; return binds }
where
env = mkRedEnv doc try_me []
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 = Stop
\end{code}
%************************************************************************
%* *
\subsection{Data types for the reduction mechanism}
%* *
%************************************************************************
The main control over context reduction is here
\begin{code}
data RedEnv
= RedEnv { red_doc :: SDoc  The context
, red_try_me :: Inst > WhatToDo
, red_improve :: Bool  True <=> do improvement
, red_givens :: [Inst]  All guaranteed rigid
 Always dicts
 but see Note [Rigidity]
, red_stack :: (Int, [Inst])  Recursion stack (for err msg)
 See Note [RedStack]
}
 Note [Rigidity]
 The red_givens are rigid so far as cmpInst is concerned.
 There is one case where they are not totally rigid, namely in tcSimplifyIPs
 let ?x = e in ...
 Here, the given is (?x::a), where 'a' is not necy a rigid type
 But that doesn't affect the comparison, which is based only on mame.
 Note [RedStack]
 The red_stack pair (n,insts) pair is just used for error reporting.
 'n' is always the depth of the stack.
 The 'insts' 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.
mkRedEnv :: SDoc > (Inst > WhatToDo) > [Inst] > RedEnv
mkRedEnv doc try_me givens
= RedEnv { red_doc = doc, red_try_me = try_me,
red_givens = givens, red_stack = (0,[]),
red_improve = True }
mkNoImproveRedEnv :: SDoc > (Inst > WhatToDo) > RedEnv
 Do not do improvement; no givens
mkNoImproveRedEnv doc try_me
= RedEnv { red_doc = doc, red_try_me = try_me,
red_givens = [], red_stack = (0,[]),
red_improve = True }
data WhatToDo
= ReduceMe WantSCs  Try to reduce this
 If there's no instance, 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)!
 Stop  Return as irreducible unless it can
 be reduced to a constant in one step
 Do not add superclasses; see
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}
%************************************************************************
%* *
\subsection[reduce]{@reduce@}
%* *
%************************************************************************
\begin{code}
reduceContext :: RedEnv
> [Inst]  Wanted
> TcM (ImprovementDone,
TcDictBinds,  Dictionary bindings
[Inst])  Irreducible
reduceContext env wanteds
= do { traceTc (text "reduceContext" <+> (vcat [
text "",
red_doc env,
text "given" <+> ppr (red_givens env),
text "wanted" <+> ppr wanteds,
text ""
]))
 Build the Avail mapping from "givens"
; init_state < foldlM addGiven emptyAvails (red_givens env)
 Do the real work
; avails < reduceList env wanteds init_state
; let improved = availsImproved avails
; (binds, irreds) < extractResults avails wanteds
; traceTc (text "reduceContext end" <+> (vcat [
text "",
red_doc env,
text "given" <+> ppr (red_givens env),
text "wanted" <+> ppr wanteds,
text "",
text "avails" <+> pprAvails avails,
text "improved =" <+> ppr improved,
text ""
]))
; return (improved, binds, irreds) }
tcImproveOne :: Avails > Inst > TcM ImprovementDone
tcImproveOne avails inst
 not (isDict inst) = return False
 otherwise
= do { inst_envs < tcGetInstEnvs
; let eqns = improveOne (classInstances inst_envs)
(dictPred inst, pprInstArising inst)
[ (dictPred p, pprInstArising p)
 p < availsInsts avails, isDict p ]
 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
; traceTc (text "improveOne" <+> ppr inst)
; unifyEqns eqns }
unifyEqns :: [(Equation,(PredType,SDoc),(PredType,SDoc))]
> TcM ImprovementDone
unifyEqns [] = return False
unifyEqns eqns
= do { traceTc (ptext SLIT("Improve:") <+> vcat (map pprEquationDoc eqns))
; mappM_ unify eqns
; return True }
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 :: RedEnv > [Inst] > Avails > TcM Avails
reduceList env@(RedEnv {red_stack = (n,stk)}) wanteds state
= do { dopts < getDOpts
#ifdef DEBUG
; if n > 8 then
dumpTcRn (hang (ptext SLIT("Interesting! Context reduction stack depth") <+> int n)
2 (ifPprDebug (nest 2 (pprStack stk))))
else return ()
#endif
; if n >= ctxtStkDepth dopts then
failWithTc (reduceDepthErr n stk)
else
go wanteds state }
where
go [] state = return state
go (w:ws) state = do { state' < reduce (env {red_stack = (n+1, w:stk)}) w state
; go ws state' }
 Base case: we're done!
reduce env wanted avails
 It's the same as an existing inst, or a superclass thereof
 Just avail < findAvail avails wanted
= returnM avails
 otherwise
= case red_try_me env wanted of {
; Stop > try_simple (addIrred NoSCs)  See Note [No superclasses for Stop]
; ReduceMe want_scs >  It should be reduced
reduceInst env avails wanted `thenM` \ (avails, lookup_result) >
case lookup_result of
NoInstance >  No such instance!
 Add it and its superclasses
addIrred want_scs avails wanted
GenInst [] rhs > addWanted want_scs avails wanted rhs []
GenInst wanteds' rhs > do { avails1 < addIrred NoSCs avails wanted
; avails2 < reduceList env wanteds' avails1
; addWanted want_scs avails2 wanted rhs wanteds' }
 Temporarily do 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
}
where
 First, see if the inst can be reduced to a constant in one step
 Works well for literals (1::Int) and constant dictionaries (d::Num Int)
 Don't bother for implication constraints, which take real work
try_simple do_this_otherwise
= do { res < lookupSimpleInst wanted
; case res of
GenInst [] rhs > addWanted AddSCs avails wanted rhs []
other > do_this_otherwise avails wanted }
\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 Stop
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.
%************************************************************************
%* *
Reducing a single constraint
%* *
%************************************************************************
\begin{code}

reduceInst :: RedEnv > Avails > Inst > TcM (Avails, LookupInstResult)
reduceInst env avails (ImplicInst { tci_tyvars = tvs, tci_reft = reft, tci_loc = loc,
tci_given = extra_givens, tci_wanted = wanteds })
= reduceImplication env avails reft tvs extra_givens wanteds loc
reduceInst env avails other_inst
= do { result < lookupSimpleInst other_inst
; return (avails, result) }
\end{code}
\begin{code}

reduceImplication :: RedEnv
> Avails
> Refinement  May refine the givens; often empty
> [TcTyVar]  Quantified type variables; all skolems
> [Inst]  Extra givens; all rigid
> [Inst]  Wanted
> InstLoc
> TcM (Avails, LookupInstResult)
\end{code}
Suppose we are simplifying the constraint
forall bs. extras => wanted
in the context of an overall simplification problem with givens 'givens',
and refinment 'reft'.
Note that
* The refinement is often empty
* The 'extra givens' need not mention any of the quantified type variables
e.g. forall {}. Eq a => Eq [a]
forall {}. C Int => D (Tree Int)
This happens when you have something like
data T a where
T1 :: Eq a => a > T a
f :: T a > Int
f x = ...(case x of { T1 v > v==v })...
\begin{code}
 ToDo: should we instantiate tvs? I think it's not necessary

 ToDo: what about improvement? There may be some improvement
 exposed as a result of the simplifications done by reduceList
 which are discarded if we back off.
 This is almost certainly Wrong, but we'll fix it when dealing
 better with equality constraints
reduceImplication env orig_avails reft tvs extra_givens wanteds inst_loc
= do {  Add refined givens, and the extra givens
(refined_red_givens, avails)
< if isEmptyRefinement reft then return (red_givens env, orig_avails)
else foldlM (addRefinedGiven reft) ([], orig_avails) (red_givens env)
; avails < foldlM addGiven avails extra_givens
 Solve the subproblem
; let try_me inst = ReduceMe AddSCs  Note [Freeness and implications]
env' = env { red_givens = refined_red_givens ++ extra_givens
, red_try_me = try_me }
; traceTc (text "reduceImplication" <+> vcat
[ ppr orig_avails,
ppr (red_givens env), ppr extra_givens,
ppr reft, ppr wanteds, ppr avails ])
; avails < reduceList env' wanteds avails
 Extract the binding
; (binds, irreds) < extractResults avails wanteds
 We always discard the extra avails we've generated;
 but we remember if we have done any (global) improvement
; let ret_avails = updateImprovement orig_avails avails
; if isEmptyLHsBinds binds then  No progress
return (ret_avails, NoInstance)
else do
{ (implic_insts, bind) < makeImplicationBind inst_loc tvs reft extra_givens irreds
 This binding is useless if the recursive simplification
 made no progress; but currently we don't try to optimise that
 case. After all, we only try hard to reduce at top level, or
 when inferring types.
; let dict_ids = map instToId extra_givens
co = mkWpTyLams tvs <.> mkWpLams dict_ids <.> WpLet (binds `unionBags` bind)
rhs = mkHsWrap co payload
loc = instLocSpan inst_loc
payload  isSingleton wanteds = HsVar (instToId (head wanteds))
 otherwise = ExplicitTuple (map (L loc . HsVar . instToId) wanteds) Boxed
 If there are any irreds, we back off and return NoInstance
; return (ret_avails, GenInst implic_insts (L loc rhs))
} }
\end{code}
Note [Freeness and implications]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
It's hard to say when an implication constraint can be floated out. Consider
forall {} Eq a => Foo [a]
The (Foo [a]) doesn't mention any of the quantified variables, but it
still might be partially satisfied by the (Eq a).
There is a useful special case when it *is* easy to partition the
constraints, namely when there are no 'givens'. Consider
forall {a}. () => Bar b
There are no 'givens', and so there is no reason to capture (Bar b).
We can let it float out. But if there is even one constraint we
must be much more careful:
forall {a}. C a b => Bar (m b)
because (C a b) might have a superclass (D b), from which we might
deduce (Bar [b]) when m later gets instantiated to []. Ha!
Here is an even more exotic example
class C a => D a b
Now consider the constraint
forall b. D Int b => C Int
We can satisfy the (C Int) from the superclass of D, so we don't want
to float the (C Int) out, even though it mentions no type variable in
the constraints!
Note [Pruning the givens in an implication constraint]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we are about to form the implication constraint
forall tvs. Eq a => Ord b
The (Eq a) cannot contribute to the (Ord b), because it has no access to
the type variable 'b'. So we could filter out the (Eq a) from the givens.
Doing so would be a bit tidier, but all the implication constraints get
simplified away by the optimiser, so it's no great win. So I don't take
advantage of that at the moment.
If you do, BE CAREFUL of wobbly type variables.
%************************************************************************
%* *
Avails and AvailHow: the pool of evidence
%* *
%************************************************************************
\begin{code}
data Avails = Avails !ImprovementDone !AvailEnv
type ImprovementDone = Bool  True <=> some unification has happened
 so some Irreds might now be reducible
 keys that are now
type AvailEnv = FiniteMap Inst AvailHow
data AvailHow
= IsIrred  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
 Rhs  Used when there is a RHS
(LHsExpr TcId)  The RHS
[Inst]  Insts free in the RHS; we need these too
instance Outputable Avails where
ppr = pprAvails
pprAvails (Avails imp avails)
= vcat [ ptext SLIT("Avails") <> (if imp then ptext SLIT("[improved]") else empty)
, nest 2 (vcat [sep [ppr inst, nest 2 (equals <+> ppr avail)]
 (inst,avail) < fmToList avails ])]
instance Outputable AvailHow where
ppr = pprAvail

pprAvail :: AvailHow > SDoc
pprAvail IsIrred = text "Irred"
pprAvail (Given x) = text "Given" <+> ppr x
pprAvail (Rhs rhs bs) = text "Rhs" <+> ppr rhs <+> braces (ppr bs)

extendAvailEnv :: AvailEnv > Inst > AvailHow > AvailEnv
extendAvailEnv env inst avail = addToFM env inst avail
findAvailEnv :: AvailEnv > Inst > Maybe AvailHow
findAvailEnv env wanted = lookupFM env wanted
 NB 1: the Ord instance of Inst compares by the class/type info
 *not* by unique. So
 d1::C Int == d2::C Int
emptyAvails :: Avails
emptyAvails = Avails False emptyFM
findAvail :: Avails > Inst > Maybe AvailHow
findAvail (Avails _ avails) wanted = findAvailEnv avails wanted
elemAvails :: Inst > Avails > Bool
elemAvails wanted (Avails _ avails) = wanted `elemFM` avails
extendAvails :: Avails > Inst > AvailHow > TcM Avails
 Does improvement
extendAvails avails@(Avails imp env) inst avail
= do { imp1 < tcImproveOne avails inst  Do any improvement
; return (Avails (imp  imp1) (extendAvailEnv env inst avail)) }
availsInsts :: Avails > [Inst]
availsInsts (Avails _ avails) = keysFM avails
availsImproved (Avails imp _) = imp
updateImprovement :: Avails > Avails > Avails
 (updateImprovement a1 a2) sets a1's improvement flag from a2
updateImprovement (Avails _ avails1) (Avails imp2 _) = Avails imp2 avails1
\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
\begin{code}
extractResults :: Avails
> [Inst]  Wanted
> TcM ( TcDictBinds,  Bindings
[Inst])  Irreducible ones
extractResults (Avails _ avails) wanteds
= go avails emptyBag [] wanteds
where
go :: AvailEnv > TcDictBinds > [Inst] > [Inst]
> TcM (TcDictBinds, [Inst])
go avails binds irreds []
= returnM (binds, irreds)
go avails binds irreds (w:ws)
= case findAvailEnv avails w of
Nothing > pprTrace "Urk: extractResults" (ppr w) $
go avails binds irreds ws
Just IsIrred > go (add_given avails w) binds (w:irreds) ws
Just (Given id)
 id == instToId w
> go avails binds irreds ws
 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!
 otherwise
> go avails (addBind binds w (nlHsVar id)) irreds ws
Just (Rhs rhs ws') > go (add_given avails w) new_binds irreds (ws' ++ ws)
where
new_binds = addBind binds w rhs
add_given avails w = extendAvailEnv avails w (Given (instToId w))
addBind binds inst rhs = binds `unionBags` unitBag (L (instSpan inst)
(VarBind (instToId inst) rhs))
\end{code}
Note [No superclasses for Stop]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When we decide not to reduce an Inst  the 'WhatToDo'  we still
add it to avails, so that any other equal Insts will be commoned up
right here. However, we 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.
\begin{code}
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))
 Always add superclasses for 'givens'

 No ASSERT( not (given `elemAvails` 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
addRefinedGiven :: Refinement > ([Inst], Avails) > Inst > TcM ([Inst], Avails)
addRefinedGiven reft (refined_givens, avails) given
 isDict given  We sometimes have 'given' methods, but they
 are always optional, so we can drop them
, let pred = dictPred given
, isRefineablePred pred  See Note [ImplicInst rigidity]
, Just (co, pred) < refinePred reft pred
= do { new_given < newDictBndr (instLoc given) pred
; let rhs = L (instSpan given) $
HsWrap (WpCo co) (HsVar (instToId given))
; avails < addAvailAndSCs AddSCs avails new_given (Rhs rhs [given])
; return (new_given:refined_givens, avails) }
 ToDo: the superclasses of the original given all exist in Avails
 so we could really just cast them, but it's more awkward to do,
 and hopefully the optimiser will spot the duplicated work
 otherwise
= return (refined_givens, avails)
\end{code}
Note [ImplicInst rigidity]
~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider
C :: forall ab. (Eq a, Ord b) => b > T a
...(case x of C v > )...
From the case (where x::T ty) we'll get an implication constraint
forall b. (Eq ty, Ord b) =>
Now suppose itself has an implication constraint
of form
forall c. =>
Then, we can certainly apply the refinement to the Ord b, becuase it is
existential, but we probably should not apply it to the (Eq ty) because it may
be wobbly. Hence the isRigidInst
@Insts@ are ordered by their class/type info, rather than by their
unique. This allows the contextreduction mechanism to use standard finite
maps to do their stuff. It's horrible that this code is here, rather
than with the Avails handling stuff in TcSimplify
\begin{code}
addIrred :: WantSCs > Avails > Inst > TcM Avails
addIrred want_scs avails irred = ASSERT2( not (irred `elemAvails` avails), ppr irred $$ ppr avails )
addAvailAndSCs want_scs avails irred IsIrred
addAvailAndSCs :: WantSCs > Avails > Inst > AvailHow > TcM Avails
addAvailAndSCs want_scs avails inst avail
 not (isClassDict inst) = extendAvails avails inst avail
 NoSCs < want_scs = extendAvails avails inst avail
 otherwise = do { traceTc (text "addAvailAndSCs" <+> vcat [ppr inst, ppr deps])
; avails' < extendAvails avails inst avail
; addSCs is_loop avails' inst }
where
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 > AvailHow > 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 < findAvail 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
= ASSERT( isDict dict )
do { sc_dicts < newDictBndrs (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 = do { avails' < extendAvails avails sc_dict (Rhs sc_sel_rhs [dict])
; addSCs is_loop avails' sc_dict }
where
sc_sel_rhs = L (instSpan dict) (HsWrap co_fn (HsVar sc_sel))
co_fn = WpApp (instToId dict) <.> mkWpTyApps tys
is_given :: Inst > Bool
is_given sc_dict = case findAvail avails sc_dict of
Just (Given _) > True  Given is cheaper than superclass selection
other > False
\end{code}
%************************************************************************
%* *
\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
= tc_simplify_top doc False wanteds
where
doc = text "tcSimplifyTop"
tcSimplifyInteractive wanteds
= tc_simplify_top doc True wanteds
where
doc = text "tcSimplifyInteractive"
 The TcLclEnv should be valid here, solely to improve
 error message generation for the monomorphism restriction
tc_simplify_top doc interactive wanteds
= do { wanteds < mapM zonkInst wanteds
; mapM_ zonkTopTyVar (varSetElems (tyVarsOfInsts wanteds))
; (irreds1, binds1) < topCheckLoop doc wanteds
; if null irreds1 then
return binds1
else do
 OK, so there are some errors
{  Use the defaulting rules to do extra unification
 NB: irreds are already zonked
; dflags < getDOpts
; disambiguate interactive dflags irreds1  Does unification
; (irreds2, binds2) < topCheckLoop doc irreds1
 Deal with implicit parameter
; let (bad_ips, non_ips) = partition isIPDict irreds2
(ambigs, others) = partition isTyVarDict non_ips
; topIPErrs bad_ips  Can arise from f :: Int > Int
 f x = x + ?y
; addNoInstanceErrs others
; addTopAmbigErrs ambigs
; return (binds1 `unionBags` binds2) }}
\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}
disambiguate :: Bool > DynFlags > [Inst] > TcM ()
 Just does unification to fix the default types
 The Insts are assumed to be prezonked
disambiguate interactive dflags insts
 null defaultable_groups
= do { traceTc (text "disambigutate" <+> vcat [ppr unaries, ppr bad_tvs, ppr defaultable_groups])
; return () }
 otherwise
= do {  Figure out what default types to use
; default_tys < getDefaultTys extended_defaulting ovl_strings
; traceTc (text "disambigutate" <+> vcat [ppr unaries, ppr bad_tvs, ppr defaultable_groups])
; mapM_ (disambigGroup default_tys) defaultable_groups }
where
extended_defaulting = interactive  dopt Opt_ExtendedDefaultRules dflags
ovl_strings = dopt Opt_OverloadedStrings dflags
unaries :: [(Inst,Class, TcTyVar)]  (C tv) constraints
bad_tvs :: TcTyVarSet  Tyvars mentioned by *other* constraints
(unaries, bad_tvs) = getDefaultableDicts insts
 Group by type variable
defaultable_groups :: [[(Inst,Class,TcTyVar)]]
defaultable_groups = filter defaultable_group (equivClasses cmp_tv unaries)
cmp_tv (_,_,tv1) (_,_,tv2) = tv1 `compare` tv2
defaultable_group :: [(Inst,Class,TcTyVar)] > Bool
defaultable_group ds@((_,_,tv):_)
= isTyConableTyVar tv  Note [Avoiding spurious errors]
&& not (tv `elemVarSet` bad_tvs)
&& defaultable_classes [c  (_,c,_) < ds]
defaultable_group [] = panic "defaultable_group"
defaultable_classes clss
 extended_defaulting = any isInteractiveClass clss
 otherwise = all is_std_class clss && (any is_num_class clss)
 In interactive mode, or with fextendeddefaultrules,
 we default Show a to Show () to avoid graututious errors on "show []"
isInteractiveClass cls
= is_num_class cls  (classKey cls `elem` [showClassKey, eqClassKey, ordClassKey])
is_num_class cls = isNumericClass cls  (ovl_strings && (cls `hasKey` isStringClassKey))
 is_num_class adds IsString to the standard numeric classes,
 when foverloadedstrings is enabled
is_std_class cls = isStandardClass cls  (ovl_strings && (cls `hasKey` isStringClassKey))
 Similarly is_std_class
disambigGroup :: [Type]  The default types
> [(Inst,Class,TcTyVar)]  All standard classes of form (C a)
> TcM ()  Just does unification, to fix the default types
disambigGroup default_tys dicts
= try_default default_tys
where
(_,_,tyvar) = head dicts  Should be nonempty
classes = [c  (_,c,_) < dicts]
try_default [] = return ()
try_default (default_ty : default_tys)
= tryTcLIE_ (try_default default_tys) $
do { tcSimplifyDefault [mkClassPred clas [default_ty]  clas < classes]
 This may fail; then the tryTcLIE_ kicks in
 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.
 After this we can't fail
; warnDefault dicts default_ty
; unifyType default_ty (mkTyVarTy tyvar) }
getDefaultTys :: Bool > Bool > TcM [Type]
getDefaultTys extended_deflts ovl_strings
= do { mb_defaults < getDeclaredDefaultTys
; case mb_defaults of
Just tys > return tys  Usersupplied defaults
Nothing > do
 No usesupplied default
 Use [Integer, Double], plus modifications
{ integer_ty < tcMetaTy integerTyConName
; checkWiredInTyCon doubleTyCon
; string_ty < tcMetaTy stringTyConName
; return (opt_deflt extended_deflts unitTy
 Note [Default unitTy]
++
[integer_ty,doubleTy]
++
opt_deflt ovl_strings string_ty) }}
where
opt_deflt True ty = [ty]
opt_deflt False ty = []
\end{code}
Note [Default unitTy]
~~~~~~~~~~~~~~~~~~~~~
In interative mode (or with fextendeddefaultrules) we add () as the first type we
try when defaulting. This has very little real impact, except in the following case.
Consider:
Text.Printf.printf "hello"
This has type (forall a. IO a); it prints "hello", and returns 'undefined'. We don't
want the GHCi repl loop to try to print that 'undefined'. The neatest thing is to
default the 'a' to (), rather than to Integer (which is what would otherwise happen;
and then GHCi doesn't attempt to print the (). So in interactive mode, we add
() to the list of defaulting types. See Trac #1200.
Note [Avoiding spurious errors]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When doing the unification for defaulting, we check for skolem
type variables, and simply don't default them. 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
%************************************************************************
%* *
\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 :: InstOrigin
> [TyVar]
> ThetaType  Wanted
> TcM ThetaType  Needed
 Given instance (wanted) => C inst_ty
 Simplify 'wanted' as much as possible
 The inst_ty is needed only for the termination check
tcSimplifyDeriv orig tyvars theta
= do { (tvs, _, tenv) < tcInstTyVars tyvars
 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?
; wanteds < newDictBndrsO orig (substTheta tenv theta)
; (irreds, _) < topCheckLoop doc wanteds
; let rev_env = zipTopTvSubst tvs (mkTyVarTys tyvars)
simpl_theta = substTheta rev_env (map dictPred irreds)
 This reversemapping is a pain, but the result
 should mention the original TyVars not TcTyVars
 NB: the caller will further check the tv_dicts for
 legal instancedeclaration form
; return 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
= newDictBndrsO DefaultOrigin theta `thenM` \ wanteds >
topCheckLoop doc wanteds `thenM` \ (irreds, _) >
addNoInstanceErrs 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 (pprInstArising (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")
<> plural bndrs <+> ptext SLIT("of")
<+> pprBinders bndrs <> colon)],
nest 2 (vcat (map ppr_ip ips)),
monomorphism_fix]
ppr_ip ip = pprPred (dictPred ip) <+> pprInstArising ip
topIPErrs :: [Inst] > TcM ()
topIPErrs dicts
= 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 :: [Inst]  Wanted (can include implications)
> TcM ()
addNoInstanceErrs insts
= do { let (tidy_env, tidy_insts) = tidyInsts insts
; reportNoInstances tidy_env Nothing tidy_insts }
reportNoInstances
:: TidyEnv
> Maybe (InstLoc, [Inst])  Context
 Nothing => top level
 Just (d,g) => d describes the construct
 with givens g
> [Inst]  What is wanted (can include implications)
> TcM ()
reportNoInstances tidy_env mb_what insts
= groupErrs (report_no_instances tidy_env mb_what) insts
report_no_instances tidy_env mb_what insts
= do { inst_envs < tcGetInstEnvs
; let (implics, insts1) = partition isImplicInst insts
(insts2, overlaps) = partitionWith (check_overlap inst_envs) insts1
; traceTc (text "reportNoInstnces" <+> vcat
[ppr implics, ppr insts1, ppr insts2])
; mapM_ complain_implic implics
; mapM_ (\doc > addErrTcM (tidy_env, doc)) overlaps
; groupErrs complain_no_inst insts2 }
where
complain_no_inst insts = addErrTcM (tidy_env, mk_no_inst_err insts)
complain_implic inst  Recurse!
= reportNoInstances tidy_env
(Just (tci_loc inst, tci_given inst))
(tci_wanted inst)
check_overlap :: (InstEnv,InstEnv) > Inst > Either Inst SDoc
 Right msg => overlap message
 Left inst => no instance
check_overlap inst_envs wanted
 not (isClassDict wanted) = Left wanted
 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 "reportNoInstance" (ppr wanted)
#endif
([], _) > Left wanted  No match
res > Right (mk_overlap_msg wanted res)
where
(clas,tys) = getDictClassTys wanted
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_no_inst_err insts
 null insts = empty
 Just (loc, givens) < mb_what,  Nested (type signatures, instance decls)
not (isEmptyVarSet (tyVarsOfInsts insts))
= vcat [ addInstLoc insts $
sep [ ptext SLIT("Could not deduce") <+> pprDictsTheta insts
, nest 2 $ ptext SLIT("from the context") <+> pprDictsTheta givens]
, show_fixes (fix1 loc : fixes2) ]
 otherwise  Top level
= vcat [ addInstLoc insts $
ptext SLIT("No instance") <> plural insts
<+> ptext SLIT("for") <+> pprDictsTheta insts
, show_fixes fixes2 ]
where
fix1 loc = sep [ ptext SLIT("add") <+> pprDictsTheta insts
<+> ptext SLIT("to the context of"),
nest 2 (ppr (instLocOrigin loc)) ]
 I'm not sure it helps to add the location
 nest 2 (ptext SLIT("at") <+> ppr (instLocSpan loc)) ]
fixes2  null instance_dicts = []
 otherwise = [sep [ptext SLIT("add an instance declaration for"),
pprDictsTheta instance_dicts]]
instance_dicts = [d  d < insts, isClassDict d, not (isTyVarDict d)]
 Insts for which it is worth suggesting an adding an instance declaration
 Exclude implicit parameters, and tyvar dicts
show_fixes :: [SDoc] > SDoc
show_fixes [] = empty
show_fixes (f:fs) = sep [ptext SLIT("Possible fix:"),
nest 2 (vcat (f : map (ptext SLIT("or") <+>) fs))]
addTopAmbigErrs dicts
 Divide into groups that share a common set of ambiguous tyvars
= ifErrsM (return ()) $  Only report ambiguity if no other errors happened
 See Note [Avoiding spurious errors]
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 (instSpan inst) $
 the location of the first one will do for the err message
addErrTcM (tidy_env, msg $$ mono_msg)
where
dicts = map fst pairs
msg = sep [text "Ambiguous type variable" <> plural tvs <+>
pprQuotedList tvs <+> in_msg,
nest 2 (pprDictsInFull dicts)]
in_msg = text "in the constraint" <> plural dicts <> colon
report [] = panic "addTopAmbigErrs"
mkMonomorphismMsg :: TidyEnv > [TcTyVar] > TcM (TidyEnv, Message)
 There's an error with these Insts; if they have free type variables
 it's probably caused by the monomorphism restriction.
 Try to identify the offending variable
 ASSUMPTION: the Insts are fully zonked
mkMonomorphismMsg tidy_env inst_tvs
= findGlobals (mkVarSet inst_tvs) tidy_env `thenM` \ (tidy_env, docs) >
returnM (tidy_env, mk_msg docs)
where
mk_msg [] = ptext SLIT("Probable fix: add a type signature that fixes these type variable(s)")
 This happens in things like
 f x = show (read "foo")
 where monomorphism doesn't play any role
mk_msg docs = vcat [ptext SLIT("Possible cause: the monomorphism restriction applied to the following:"),
nest 2 (vcat docs),
monomorphism_fix
]
monomorphism_fix :: SDoc
monomorphism_fix = ptext SLIT("Probable fix:") <+>
(ptext SLIT("give these definition(s) an explicit type signature")
$$ ptext SLIT("or use fnomonomorphismrestriction"))
warnDefault ups default_ty
= doptM Opt_WarnTypeDefaults `thenM` \ warn_flag >
addInstCtxt (instLoc (head (dicts))) (warnTc warn_flag warn_msg)
where
dicts = [d  (d,_,_) < ups]
 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]
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}