TcSimplify.lhs 67.3 KB
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%
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% (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
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%
\section[TcSimplify]{TcSimplify}

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\begin{code}
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module TcSimplify (
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	tcSimplifyInfer, tcSimplifyInferCheck,
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	tcSimplifyCheck, tcSimplifyRestricted,
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	tcSimplifyToDicts, tcSimplifyIPs, tcSimplifyTop,
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	tcSimplifyDeriv, tcSimplifyDefault,
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	bindInstsOfLocalFuns
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    ) where

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#include "HsVersions.h"
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import {-# SOURCE #-} TcUnify( unifyTauTy )

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import HsSyn		( MonoBinds(..), HsExpr(..), andMonoBinds, andMonoBindList )
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import TcHsSyn		( TcExpr, TcId,
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			  TcMonoBinds, TcDictBinds
			)
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import TcMonad
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import Inst		( lookupInst, LookupInstResult(..),
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			  tyVarsOfInst, predsOfInsts, predsOfInst, newDicts,
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			  isDict, isClassDict, isLinearInst, linearInstType,
			  isStdClassTyVarDict, isMethodFor, isMethod,
			  instToId, tyVarsOfInsts,  cloneDict,
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			  ipNamesOfInsts, ipNamesOfInst, dictPred,
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			  instBindingRequired, instCanBeGeneralised,
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			  newDictsFromOld, newMethodAtLoc,
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			  getDictClassTys, isTyVarDict,
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			  instLoc, pprInst, zonkInst, tidyInsts, tidyMoreInsts,
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			  Inst, LIE, pprInsts, pprInstsInFull,
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			  mkLIE, lieToList
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			)
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import TcEnv		( tcGetGlobalTyVars, tcGetInstEnv, tcLookupGlobalId )
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import InstEnv		( lookupInstEnv, classInstEnv, InstLookupResult(..) )
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import TcMType		( zonkTcTyVarsAndFV, tcInstTyVars, checkAmbiguity )
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import TcType		( TcTyVar, TcTyVarSet, ThetaType, TyVarDetails(VanillaTv),
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			  mkClassPred, isOverloadedTy, mkTyConApp,
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			  mkTyVarTy, tcGetTyVar, isTyVarClassPred, mkTyVarTys,
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			  tyVarsOfPred, isIPPred, isInheritablePred, predHasFDs )
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import Id		( idType, mkUserLocal )
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import Var		( TyVar )
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import Name		( getOccName, getSrcLoc )
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import NameSet		( NameSet, mkNameSet, elemNameSet )
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import Class		( classBigSig )
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import FunDeps		( oclose, grow, improve, pprEquationDoc )
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import PrelInfo		( isNumericClass, isCreturnableClass, isCcallishClass, 
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			  splitName, fstName, sndName )
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import Subst		( mkTopTyVarSubst, substTheta, substTy )
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import TysWiredIn	( unitTy, pairTyCon )
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import VarSet
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import FiniteMap
import Outputable
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import ListSetOps	( equivClasses )
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import Util		( zipEqual )
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import List		( partition )
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import CmdLineOpts
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\end{code}


%************************************************************************
%*									*
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\subsection{NOTES}
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%*									*
%************************************************************************

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	--------------------------------------
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		Notes on quantification
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	--------------------------------------
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Suppose we are about to do a generalisation step.
We have in our hand

	G	the environment
	T	the type of the RHS
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	C	the constraints from that RHS
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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

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and float the constraints Ct further outwards.
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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
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		using all conceivable links from C.
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		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.

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Notice that
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   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 ...
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	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

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  And then if the fn was called at several different c's, each of
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  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.



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	--------------------------------------
		Notes on ambiguity
	--------------------------------------
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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.

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So here's the plan.  We WARN about probable ambiguity if
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	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
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in the environment, or by the variables in the type.
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Notice that we union before calling oclose.  Here's an example:

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	class J a b c | a b -> c
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	fv(G) = {a}

Is this ambiguous?
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	forall b c. (J a b c) => b -> b
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Only if we union {a} from G with {b} from T before using oclose,
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do we see that c is fixed.
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It's a bit vague exactly which C we should use for this oclose call.  If we
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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

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then c is a "bubble"; there's no way it can ever improve, and it's
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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 definitely-ambiguous and probably-ok.
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The definitely-ambiguous can then float out, and get smashed at top level
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(which squashes out the constants, like Eq (T a) above)


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	--------------------------------------
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		Notes on principal types
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    class C a where
      op :: a -> a
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    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 non-principal type
    f :: forall a. C Int => a -> a


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		Notes on implicit parameters
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Question 1: can we "inherit" implicit parameters
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider this:

	f x = (x::Int) + ?y
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where f is *not* a top-level binding.
From the RHS of f we'll get the constraint (?y::Int).
There are two types we might infer for f:
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	f :: Int -> Int

(so we get ?y from the context of f's definition), or
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	f :: (?y::Int) => Int -> Int

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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.

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BOTTOM LINE: when *inferring types* you *must* quantify 
over implicit parameters. See the predicate isFreeWhenInferring.
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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:
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	(?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).
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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:
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	f :: Int -> Int
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	f x = (x::Int) + ?y
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At first sight this seems reasonable, but it has the nasty property
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that adding a type signature changes the dynamic semantics.
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Consider this:
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	(let f x = (x::Int) + ?y
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 	 in (f 3, f 3 with ?y=5))  with ?y = 6

		returns (3+6, 3+5)
vs
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	(let f :: Int -> Int
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	     f x = x + ?y
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	 in (f 3, f 3 with ?y=5))  with ?y = 6

		returns (3+6, 3+6)

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Indeed, simply inlining f (at the Haskell source level) would change the
dynamic semantics.
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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.
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Question 3: monomorphism
~~~~~~~~~~~~~~~~~~~~~~~~
There's a nasty corner case when the monomorphism restriction bites:
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	z = (x::Int) + ?y

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The argument above suggests that we *must* generalise
over the ?y parameter, to get
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	z :: (?y::Int) => Int,
but the monomorphism restriction says that we *must not*, giving
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	z :: Int.
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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.



Possible choices
~~~~~~~~~~~~~~~~
(A) Always generalise over implicit parameters
    Bindings that fall under the monomorphism restriction can't
	be generalised

    Consequences:
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	* Inlining remains valid
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	* 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.
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It's really not clear what is the Right Thing To Do.  If you see
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	z = (x::Int) + ?y
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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 non-fucntion 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.
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Choice (C) really says "the monomorphism restriction doesn't apply
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to implicit parameters".  Which is fine, but remember that every
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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'
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clauses that bind ?y, so a decent compiler should common up all
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those function calls.  So I think I strongly favour (C).  Indeed,
one could make a similar argument for abolishing the monomorphism
restriction altogether.
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BOTTOM LINE: we choose (B) at present.  See tcSimplifyRestricted
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%************************************************************************
%*									*
\subsection{tcSimplifyInfer}
%*									*
%************************************************************************

tcSimplify is called when we *inferring* a type.  Here's the overall game plan:

    1. Compute Q = grow( fvs(T), C )
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    2. Partition C based on Q into Ct and Cq.  Notice that ambiguous
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       predicates will end up in Ct; we deal with them at the top level
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    3. Try improvement, using functional dependencies
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    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
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Eq (a,b), we don't simplify to (Eq a, Eq b).  So Q won't be different
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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 ...
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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
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again.
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\begin{code}
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tcSimplifyInfer
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	:: SDoc
	-> TcTyVarSet		-- fv(T); type vars
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	-> LIE			-- Wanted
	-> TcM ([TcTyVar],	-- Tyvars to quantify (zonked)
		LIE,		-- Free
		TcDictBinds,	-- Bindings
		[TcId])		-- Dict Ids that must be bound here (zonked)
\end{code}
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\begin{code}
tcSimplifyInfer doc tau_tvs wanted_lie
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  = inferLoop doc (varSetElems tau_tvs)
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	      (lieToList wanted_lie)	`thenTc` \ (qtvs, frees, binds, irreds) ->
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	-- Check for non-generalisable insts
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    mapTc_ addCantGenErr (filter (not . instCanBeGeneralised) irreds)	`thenTc_`

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    returnTc (qtvs, mkLIE frees, binds, map instToId irreds)
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inferLoop doc tau_tvs wanteds
  =   	-- Step 1
    zonkTcTyVarsAndFV tau_tvs		`thenNF_Tc` \ tau_tvs' ->
    mapNF_Tc zonkInst wanteds		`thenNF_Tc` \ wanteds' ->
    tcGetGlobalTyVars			`thenNF_Tc` \ gbl_tvs ->
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    let
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 	preds = predsOfInsts wanteds'
	qtvs  = grow preds tau_tvs' `minusVarSet` oclose preds gbl_tvs
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	try_me inst
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	  | isFreeWhenInferring qtvs inst = Free
	  | isClassDict inst 		  = DontReduceUnlessConstant	-- Dicts
	  | otherwise	    		  = ReduceMe 			-- Lits and Methods
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    in
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		-- Step 2
    reduceContext doc try_me [] wanteds'    `thenTc` \ (no_improvement, frees, binds, irreds) ->
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		-- Step 3
    if no_improvement then
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	returnTc (varSetElems qtvs, frees, binds, irreds)
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    else
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	-- 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 re-process frees, because unification
	--      might mean that a type variable that looked free isn't now.
	--
	-- Hence the (irreds ++ frees)

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	-- However, NOTICE that when we are done, we might have some bindings, but
	-- the final qtvs might be empty.  See [NO TYVARS] below.
				
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	inferLoop doc tau_tvs (irreds ++ frees)	`thenTc` \ (qtvs1, frees1, binds1, irreds1) ->
	returnTc (qtvs1, frees1, binds `AndMonoBinds` binds1, irreds1)
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\end{code}
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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)
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and improve by binding l->T, after which we can do some reduction
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on both the Lte and If constraints.  What we *can't* do is start again
with (Max Z (S x) y)!

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[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
630
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632
polymorphic in.  

The net effect of [NO TYVARS] 
633

634
\begin{code}
635
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isFreeWhenInferring :: TyVarSet -> Inst	-> Bool
isFreeWhenInferring qtvs inst
  =  isFreeWrtTyVars qtvs inst			-- Constrains no quantified vars
638
  && all isInheritablePred (predsOfInst inst)	-- And no implicit parameter involved
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						-- (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))
650
\end{code}
651

652

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%************************************************************************
%*									*
\subsection{tcSimplifyCheck}
%*									*
%************************************************************************
658

659
@tcSimplifyCheck@ is used when we know exactly the set of variables
660
we are going to quantify over.  For example, a class or instance declaration.
661
662

\begin{code}
663
tcSimplifyCheck
664
	 :: SDoc
665
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	 -> [TcTyVar]		-- Quantify over these
	 -> [Inst]		-- Given
667
	 -> LIE			-- Wanted
668
	 -> TcM (LIE,		-- Free
669
		 TcDictBinds)	-- Bindings
670

671
-- tcSimplifyCheck is used when checking expression type signatures,
672
-- class decls, instance decls etc.
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--
-- 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
677
tcSimplifyCheck doc qtvs givens wanted_lie
678
  = tcSimplCheck doc get_qtvs
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		 givens wanted_lie	`thenTc` \ (qtvs', frees, binds) ->
    returnTc (frees, binds)
  where
    get_qtvs = zonkTcTyVarsAndFV qtvs


-- 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
689
	 :: SDoc
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	 -> TcTyVarSet		-- fv(T)
	 -> [Inst]		-- Given
	 -> LIE			-- Wanted
	 -> TcM ([TcTyVar],	-- Variables over which to quantify
		 LIE,		-- Free
		 TcDictBinds)	-- Bindings

tcSimplifyInferCheck doc tau_tvs givens wanted_lie
698
  = tcSimplCheck doc get_qtvs givens wanted_lie
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  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	`thenNF_Tc` \ all_tvs' ->
	       tcGetGlobalTyVars		`thenNF_Tc` \ gbl_tvs ->
	       let
	          qtvs = all_tvs' `minusVarSet` gbl_tvs
			-- We could close gbl_tvs, but its not necessary for
716
			-- soundness, and it'll only affect which tyvars, not which
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723
			-- dictionaries, we quantify over
	       in
	       returnNF_Tc qtvs
\end{code}

Here is the workhorse function for all three wrappers.

724
\begin{code}
725
tcSimplCheck doc get_qtvs givens wanted_lie
726
  = check_loop givens (lieToList wanted_lie)	`thenTc` \ (qtvs, frees, binds, irreds) ->
727

728
	-- Complain about any irreducible ones
729
    complainCheck doc givens irreds		`thenNF_Tc_`
730

731
	-- Done
732
    returnTc (qtvs, mkLIE frees, binds)
733

734
  where
735
736
    ip_set = mkNameSet (ipNamesOfInsts givens)

737
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739
740
    check_loop givens wanteds
      =		-- Step 1
    	mapNF_Tc zonkInst givens	`thenNF_Tc` \ givens' ->
    	mapNF_Tc zonkInst wanteds	`thenNF_Tc` \ wanteds' ->
741
742
    	get_qtvs 			`thenNF_Tc` \ qtvs' ->

743
744
745
746
 		    -- Step 2
    	let
 	    -- When checking against a given signature we always reduce
 	    -- until we find a match against something given, or can't reduce
747
748
 	    try_me inst | isFreeWhenChecking qtvs' ip_set inst = Free
 			| otherwise  			       = ReduceMe
749
750
    	in
    	reduceContext doc try_me givens' wanteds'	`thenTc` \ (no_improvement, frees, binds, irreds) ->
751

752
753
754
755
756
757
 		    -- Step 3
    	if no_improvement then
 	    returnTc (varSetElems qtvs', frees, binds, irreds)
    	else
 	    check_loop givens' (irreds ++ frees) 	`thenTc` \ (qtvs', frees1, binds1, irreds1) ->
 	    returnTc (qtvs', frees1, binds `AndMonoBinds` binds1, irreds1)
758
759
760
\end{code}


761
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766
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768
%************************************************************************
%*									*
\subsection{tcSimplifyRestricted}
%*									*
%************************************************************************

\begin{code}
tcSimplifyRestricted 	-- Used for restricted binding groups
769
			-- i.e. ones subject to the monomorphism restriction
770
	:: SDoc
771
	-> TcTyVarSet		-- Free in the type of the RHSs
772
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774
775
776
777
778
	-> LIE			-- Free in the RHSs
	-> TcM ([TcTyVar],	-- Tyvars to quantify (zonked)
		LIE,		-- Free
		TcDictBinds)	-- Bindings

tcSimplifyRestricted doc tau_tvs wanted_lie
  = 	-- First squash out all methods, to find the constrained tyvars
779
   	-- We can't just take the free vars of wanted_lie because that'll
780
781
782
783
784
785
786
	-- have methods that may incidentally mention entirely unconstrained variables
	--  	e.g. a call to 	f :: Eq a => a -> b -> b
	-- Here, b is unconstrained.  A good example would be
	--	foo = f (3::Int)
	-- We want to infer the polymorphic type
	--	foo :: forall b. b -> b
    let
787
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792
	wanteds = lieToList wanted_lie
	try_me inst = 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.
793
    in
794
    simpleReduceLoop doc try_me wanteds		`thenTc` \ (_, _, constrained_dicts) ->
795
796

	-- Next, figure out the tyvars we will quantify over
797
798
    zonkTcTyVarsAndFV (varSetElems tau_tvs)	`thenNF_Tc` \ tau_tvs' ->
    tcGetGlobalTyVars				`thenNF_Tc` \ gbl_tvs ->
799
    let
800
801
	constrained_tvs = tyVarsOfInsts constrained_dicts
	qtvs = (tau_tvs' `minusVarSet` oclose (predsOfInsts constrained_dicts) gbl_tvs)
802
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804
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806
807
808
			 `minusVarSet` constrained_tvs
    in

	-- The first step may have squashed more methods than
	-- necessary, so try again, this time knowing the exact
	-- set of type variables to quantify over.
	--
809
	-- We quantify only over constraints that are captured by qtvs;
810
	-- these will just be a subset of non-dicts.  This in contrast
811
	-- to normal inference (using isFreeWhenInferring) in which we quantify over
812
	-- all *non-inheritable* constraints too.  This implements choice
813
	-- (B) under "implicit parameter and monomorphism" above.
814
815
816
817
	--
	-- 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
818
819
    mapNF_Tc zonkInst (lieToList wanted_lie)	`thenNF_Tc` \ wanteds' ->
    let
820
821
        try_me inst | isFreeWrtTyVars qtvs inst = Free
	            | otherwise                 = ReduceMe
822
823
824
825
    in
    reduceContext doc try_me [] wanteds'	`thenTc` \ (no_improvement, frees, binds, irreds) ->
    ASSERT( no_improvement )
    ASSERT( null irreds )
826
	-- No need to loop because simpleReduceLoop will have
827
828
829
830
831
	-- already done any improvement necessary

    returnTc (varSetElems qtvs, mkLIE frees, binds)
\end{code}

832
833
834
835
836
837
838

%************************************************************************
%*									*
\subsection{tcSimplifyToDicts}
%*									*
%************************************************************************

839
840
841
842
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.

843
The same thing is used for specialise pragmas. Consider
844

845
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847
848
849
850
851
852
853
854
855
856
	f :: Num a => a -> a
	{-# SPECIALISE f :: Int -> Int #-}
	f = ...

The type checker generates a binding like:

	f_spec = (f :: Int -> Int)

and we want to end up with

	f_spec = _inline_me_ (f Int dNumInt)

857
But that means that we must simplify the Method for f to (f Int dNumInt)!
858
859
So tcSimplifyToDicts squeezes out all Methods.

860
861
862
863
864
IMPORTANT NOTE:  we *don't* want to do superclass commoning up.  Consider

	fromIntegral :: (Integral a, Num b) => a -> b
	{-# RULES "foo"  fromIntegral = id :: Int -> Int #-}

865
Here, a=b=Int, and Num Int is a superclass of Integral Int. But we *dont*
866
867
868
869
870
871
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873
874
875
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877
want to get

	forall dIntegralInt.
	fromIntegral Int Int dIntegralInt (scsel dIntegralInt) = id Int

because the scsel will mess up matching.  Instead we want

	forall dIntegralInt, dNumInt.
	fromIntegral Int Int dIntegralInt dNumInt = id Int

Hence "DontReduce NoSCs"

878
\begin{code}
879
tcSimplifyToDicts :: LIE -> TcM ([Inst], TcDictBinds)
880
tcSimplifyToDicts wanted_lie
881
  = simpleReduceLoop doc try_me wanteds		`thenTc` \ (frees, binds, irreds) ->
882
	-- Since try_me doesn't look at types, we don't need to
883
	-- do any zonking, so it's safe to call reduceContext directly
884
    ASSERT( null frees )
885
886
    returnTc (irreds, binds)

887
  where
888
    doc = text "tcSimplifyToDicts"
889
    wanteds = lieToList wanted_lie
890
891

	-- Reduce methods and lits only; stop as soon as we get a dictionary
892
893
    try_me inst	| isDict inst = DontReduce NoSCs
		| otherwise   = ReduceMe
894
895
\end{code}

896

897
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899
900
901
902
903
904
905
906
%************************************************************************
%*									*
\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
907
step; if we have ?x::t1 and ?x::t2 we must unify t1, t2.
908
909
910
911
912
913

Actually, the constraints from B might improve the types in ?x. For example

	f :: (?x::Int) => Char -> Char
	let ?x = 3 in f 'c'

914
then the constraint (?x::Int) arising from the call to f will
915
force the binding for ?x to be of type Int.
916
917

\begin{code}
918
tcSimplifyIPs :: [Inst]		-- The implicit parameters bound here
919
920
	      -> LIE
	      -> TcM (LIE, TcDictBinds)
921
922
tcSimplifyIPs given_ips wanted_lie
  = simpl_loop given_ips wanteds	`thenTc` \ (frees, binds) ->
923
    returnTc (mkLIE frees, binds)
924
  where
925
    doc	     = text "tcSimplifyIPs" <+> ppr given_ips
926
    wanteds  = lieToList wanted_lie
927
    ip_set   = mkNameSet (ipNamesOfInsts given_ips)
928

929
	-- Simplify any methods that mention the implicit parameter
930
931
    try_me inst | isFreeWrtIPs ip_set inst = Free
		| otherwise		   = ReduceMe
932
933
934
935

    simpl_loop givens wanteds
      = mapNF_Tc zonkInst givens		`thenNF_Tc` \ givens' ->
        mapNF_Tc zonkInst wanteds		`thenNF_Tc` \ wanteds' ->
936

937
938
939
940
941
942
943
944
        reduceContext doc try_me givens' wanteds'    `thenTc` \ (no_improvement, frees, binds, irreds) ->

        if no_improvement then
	    ASSERT( null irreds )
	    returnTc (frees, binds)
	else
	    simpl_loop givens' (irreds ++ frees)	`thenTc` \ (frees1, binds1) ->
	    returnTc (frees1, binds `AndMonoBinds` binds1)
945
946
947
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952
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961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
\end{code}


%************************************************************************
%*									*
\subsection[binds-for-local-funs]{@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 top-level.	If the @Insts@ were binding-ified up
there, they would have unresolvable references to @f@.

We pass in an @init_lie@ of @Insts@ and a list of locally-bound @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 ::	LIE -> [TcId] -> TcM (LIE, TcMonoBinds)

bindInstsOfLocalFuns init_lie local_ids
977
  | null overloaded_ids
978
979
980
981
	-- Common case
  = returnTc (init_lie, EmptyMonoBinds)

  | otherwise
982
  = simpleReduceLoop doc try_me wanteds		`thenTc` \ (frees, binds, irreds) ->
983
    ASSERT( null irreds )
984
    returnTc (mkLIE frees, binds)
985
986
987
988
  where
    doc		     = text "bindInsts" <+> ppr local_ids
    wanteds	     = lieToList init_lie
    overloaded_ids   = filter is_overloaded local_ids
989
    is_overloaded id = isOverloadedTy (idType id)
990
991

    overloaded_set = mkVarSet overloaded_ids	-- There can occasionally be a lot of them
992
						-- so it's worth building a set, so that
993
994
						-- lookup (in isMethodFor) is faster

995
    try_me inst | isMethodFor overloaded_set inst = ReduceMe
996
		| otherwise		          = Free
997
\end{code}
998

999

1000
1001
%************************************************************************
%*									*
1002
\subsection{Data types for the reduction mechanism}
1003
1004
1005
%*									*
%************************************************************************

1006
1007
The main control over context reduction is here

1008
\begin{code}
1009
data WhatToDo
1010
1011
 = ReduceMe		-- Try to reduce this
			-- If there's no instance, behave exactly like
1012
1013
			-- DontReduce: add the inst to
			-- the irreductible ones, but don't
1014
1015
			-- produce an error message of any kind.
			-- It might be quite legitimate such as (Eq a)!
1016

1017
 | DontReduce WantSCs		-- Return as irreducible
1018
1019
1020

 | DontReduceUnlessConstant	-- Return as irreducible unless it can
				-- be reduced to a constant in one step
1021

1022
 | Free			  -- Return as free
1023

1024
1025
1026
reduceMe :: Inst -> WhatToDo
reduceMe inst = ReduceMe

1027
1028
data WantSCs = NoSCs | AddSCs	-- Tells whether we should add the superclasses
				-- of a predicate when adding it to the avails
1029
\end{code}
1030
1031
1032
1033



\begin{code}
1034
type Avails = FiniteMap Inst Avail
1035

1036
data Avail
1037
1038
  = IsFree		-- Used for free Insts
  | Irred		-- Used for irreducible dictionaries,
1039
1040
			-- which are going to be lambda bound

1041
  | Given TcId 		-- Used for dictionaries for which we have a binding
1042
			-- e.g. those "given" in a signature
1043
	  Bool		-- True <=> actually consumed (splittable IPs only)
1044
1045

  | NoRhs 		-- Used for Insts like (CCallable f)
1046
1047
			-- where no witness is required.

1048
  | Rhs 		-- Used when there is a RHS
1049
1050
	TcExpr	 	-- The RHS
	[Inst]		-- Insts free in the RHS; we need these too
1051

1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
  | 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
	[TcExpr]	-- A supply of suitable RHSs

1063
pprAvails avails = vcat [sep [ppr inst, nest 2 (equals <+> pprAvail avail)]
1064
			| (inst,avail) <- fmToList avails ]
1065
1066
1067
1068

instance Outputable Avail where
    ppr = pprAvail

1069
1070
1071
1072
1073
1074
1075
1076
pprAvail NoRhs	       	= text "<no rhs>"
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
1077
1078
1079
1080
1081
1082
1083
1084
1085
\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}
1086
extractResults :: Avails
1087
	       -> [Inst]		-- Wanted
1088
1089
1090
	       -> NF_TcM (TcDictBinds, 	-- Bindings
			  [Inst],	-- Irreducible ones
			  [Inst])	-- Free ones
1091

1092
1093
extractResults avails wanteds
  = go avails EmptyMonoBinds [] [] wanteds
1094
  where
1095
1096
    go avails binds irreds frees [] 
      = returnNF_Tc (binds, irreds, frees)
1097

1098
    go avails binds irreds frees (w:ws)
1099
      = case lookupFM avails w of
1100
1101
	  Nothing    -> pprTrace "Urk: extractResults" (ppr w) $
			go avails binds irreds frees ws
1102

1103
1104
1105
	  Just NoRhs  -> 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
1106

1107
	  Just (Given id _) -> go avails new_binds irreds frees ws
1108
			    where
1109
1110
1111
1112
			       new_binds | id == instToId w = binds
					 | otherwise        = addBind binds 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!
1113

1114
1115
1116
1117
	  Just (Rhs rhs ws') -> go (add_given avails w) new_binds irreds frees (ws' ++ ws)
			     where
				new_binds = addBind binds w rhs

1118
1119
1120
1121
1122
1123
1124
1125
	  Just (Linear n split_inst avail)	-- Transform Linear --> LinRhss
	    -> get_root irreds frees avail w		`thenNF_Tc` \ (irreds', frees', root_id) ->
	       split n (instToId split_inst) root_id w	`thenNF_Tc` \ (binds', rhss) ->
	       go (addToFM avails w (LinRhss rhss))
		  (binds `AndMonoBinds` binds')
		  irreds' frees' (split_inst : w : ws)

	  Just (LinRhss (rhs:rhss))		-- Consume one of the Rhss
1126
1127
1128
1129
1130
		-> go new_avails new_binds irreds frees ws
		where		
		   new_binds  = addBind binds w rhs
		   new_avails = addToFM avails w (LinRhss rhss)

1131
1132
1133
1134
1135
    get_root irreds frees (Given id _) w = returnNF_Tc (irreds, frees, id)
    get_root irreds frees Irred	       w = cloneDict w	`thenNF_Tc` \ w' ->
					   returnNF_Tc (w':irreds, frees, instToId w')
    get_root irreds frees IsFree       w = cloneDict w	`thenNF_Tc` \ w' ->
					   returnNF_Tc (irreds, w':frees, instToId w')
1136
1137
1138
1139
1140
1141
1142
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    add_given avails w 
	| instBindingRequired w = addToFM avails w (Given (instToId w) True)
	| otherwise		= addToFM avails w NoRhs
	-- NB: make sure that CCallable/CReturnable use NoRhs rather
	--	than Given, else we end up with bogus bindings.

    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 n i a) returns: n rhss
	--			  auxiliary bindings
	--			  1 or 0 insts to add to irreds


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split :: Int -> TcId -> TcId -> Inst 
      -> NF_TcM (TcDictBinds, [TcExpr])
-- (split n split_id root_id wanted) returns
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--	* 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)
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--
-- NB: 'wanted' is just a template

split n split_id root_id wanted
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  = go n
  where
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    ty      = linearInstType wanted
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    pair_ty = mkTyConApp pairTyCon [ty,ty]
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    id      = instToId wanted
    occ     = getOccName id
    loc     = getSrcLoc id
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    go 1 = returnNF_Tc (EmptyMonoBinds, [HsVar root_id])
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    go n = go ((n+1) `div` 2)		`thenNF_Tc` \ (binds1, rhss) ->
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	   expand n rhss		`thenNF_Tc` \ (binds2, rhss') ->
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	   returnNF_Tc (binds1 `AndMonoBinds` binds2, rhss')
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	-- (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)	`thenNF_Tc` \ (binds', rhss') ->
			   returnNF_Tc (binds', head rhss : rhss')
	where
	  go rhss = mapAndUnzipNF_Tc do_one rhss	`thenNF_Tc` \ (binds', rhss') ->
		    returnNF_Tc (andMonoBindList binds', concat rhss')

	  do_one rhs = tcGetUnique 			`thenNF_Tc` \ uniq -> 
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		       tcLookupGlobalId fstName		`thenNF_Tc` \ fst_id ->
		       tcLookupGlobalId sndName		`thenNF_Tc` \ snd_id ->
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		       let 
			  x = mkUserLocal occ uniq pair_ty loc
		       in
		       returnNF_Tc (VarMonoBind x (mk_app split_id rhs),
				    [mk_fs_app fst_id ty x, mk_fs_app snd_id ty x])

mk_fs_app id ty var = HsVar id `TyApp` [ty,ty] `HsApp` HsVar var

mk_app id rhs = HsApp (HsVar id) rhs

addBind binds inst rhs = binds `AndMonoBinds` VarMonoBind (instToId inst) rhs
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\end{code}


%************************************************************************
%*									*
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\subsection[reduce]{@reduce@}
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%*									*
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%************************************************************************

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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.
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\begin{code}
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simpleReduceLoop :: SDoc
	 	 -> (Inst -> WhatToDo)		-- What to do, *not* based on the quantified type variables
		 -> [Inst]			-- Wanted
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		 -> TcM ([Inst],		-- Free
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			 TcDictBinds,
			 [Inst])		-- Irreducible

simpleReduceLoop doc try_me wanteds
  = mapNF_Tc zonkInst wanteds			`thenNF_Tc` \ wanteds' ->
    reduceContext doc try_me [] wanteds'	`thenTc` \ (no_improvement, frees, binds, irreds) ->
    if no_improvement then
	returnTc (frees, binds, irreds)
    else
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	simpleReduceLoop doc try_me (irreds ++ frees)	`thenTc` \ (frees1, binds1, irreds1) ->
	returnTc (frees1, binds `AndMonoBinds` binds1, irreds1)
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\end{code}
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\begin{code}
reduceContext :: SDoc
	      -> (Inst -> WhatToDo)
	      -> [Inst]			-- Given
	      -> [Inst]			-- Wanted
	      -> NF_TcM (Bool, 		-- True <=> improve step did no unification
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			 [Inst],	-- Free
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			 TcDictBinds,	-- Dictionary bindings
			 [Inst])	-- Irreducible

reduceContext doc try_me givens wanteds
  =
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    traceTc (text "reduceContext" <+> (vcat [
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	     text "----------------------",
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	     doc,
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	     text "given" <+> ppr givens,
	     text "wanted" <+> ppr wanteds,
	     text "----------------------"
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	     ]))					`thenNF_Tc_`

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        -- Build the Avail mapping from "givens"
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    foldlNF_Tc addGiven emptyFM givens			`thenNF_Tc` \ init_state ->
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        -- Do the real work
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    reduceList (0,[]) try_me wanteds init_state		`thenNF_Tc` \ avails ->
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	-- Do improvement, using everything in avails
	-- In particular, avails includes all superclasses of everything
    tcImprove avails					`thenTc` \ no_improvement ->
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    extractResults avails wanteds			`thenNF_Tc` \ (binds, irreds, frees) ->

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    traceTc (text "reduceContext end" <+> (vcat [
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	     text "----------------------",
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	     doc,
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	     text "given" <+> ppr givens,
	     text "wanted" <+> ppr wanteds,
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	     text "----",
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	     text "avails" <+> pprAvails avails,
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	     text "frees" <+> ppr frees,
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	     text "no_improvement =" <+> ppr no_improvement,
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	     text "----------------------"
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	     ])) 					`thenNF_Tc_`
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    returnTc (no_improvement, frees, binds, irreds)
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tcImprove avails
 =  tcGetInstEnv 				`thenTc` \ inst_env ->
    let
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	preds = [ (pred, pp_loc)
		| inst <- keysFM avails,
		  let pp_loc = pprInstLoc (instLoc inst),
		  pred <- predsOfInst inst,
		  predHasFDs pred
		]
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		-- 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
	eqns  = improve (classInstEnv inst_env) preds
     in
     if null eqns then
	returnTc True
     else
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	traceTc (ptext SLIT("Improve:") <+> vcat (map pprEquationDoc eqns))	`thenNF_Tc_`
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        mapTc_ unify eqns	`thenTc_`
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	returnTc False
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  where