%
% (c) The University of Glasgow 2006
% (c) The GRASP/AQUA Project, Glasgow University, 2000
%

FunDeps - functional dependencies

It's better to read it as: "if we know these, then we're going to know these"

\begin{code}
module FunDeps (
 	Equation, pprEquation,
	oclose, grow, improveOne,
	checkInstCoverage, checkFunDeps,
	pprFundeps
    ) where

#include "HsVersions.h"

import Name
import Var
import Class
import TcGadt
import TcType
import InstEnv
import VarSet
import VarEnv
import Outputable
import Util
import Data.Maybe	( isJust )
\end{code}


%************************************************************************
%*									*
\subsection{Close type variables}
%*									*
%************************************************************************

(oclose preds tvs) closes the set of type variables tvs, 
wrt functional dependencies in preds.  The result is a superset
of the argument set.  For example, if we have
	class C a b | a->b where ...
then
	oclose [C (x,y) z, C (x,p) q] {x,y} = {x,y,z}
because if we know x and y then that fixes z.

Using oclose
~~~~~~~~~~~~
oclose is used

a) When determining ambiguity.  The type
	forall a,b. C a b => a
is not ambiguous (given the above class decl for C) because
a determines b.  

b) When generalising a type T.  Usually we take FV(T) \ FV(Env),
but in fact we need
	FV(T) \ (FV(Env)+)
where the '+' is the oclosure operation.  Notice that we do not 
take FV(T)+.  This puzzled me for a bit.  Consider

	f = E

and suppose e have that E :: C a b => a, and suppose that b is
free in the environment. Then we quantify over 'a' only, giving
the type forall a. C a b => a.  Since a->b but we don't have b->a,
we might have instance decls like
	instance C Bool Int where ...
	instance C Char Int where ...
so knowing that b=Int doesn't fix 'a'; so we quantify over it.

		---------------
		A WORRY: ToDo!
		---------------
If we have	class C a b => D a b where ....
     		class D a b | a -> b where ...
and the preds are [C (x,y) z], then we want to see the fd in D,
even though it is not explicit in C, giving [({x,y},{z})]

Similarly for instance decls?  E.g. Suppose we have
	instance C a b => Eq (T a b) where ...
and we infer a type t with constraints Eq (T a b) for a particular
expression, and suppose that 'a' is free in the environment.  
We could generalise to
	forall b. Eq (T a b) => t
but if we reduced the constraint, to C a b, we'd see that 'a' determines
b, so that a better type might be
	t (with free constraint C a b) 
Perhaps it doesn't matter, because we'll still force b to be a
particular type at the call sites.  Generalising over too many
variables (provided we don't shadow anything by quantifying over a
variable that is actually free in the envt) may postpone errors; it
won't hide them altogether.


\begin{code}
oclose :: [PredType] -> TyVarSet -> TyVarSet
oclose preds fixed_tvs
  | null tv_fds = fixed_tvs	-- Fast escape hatch for common case
  | otherwise   = loop fixed_tvs
  where
    loop fixed_tvs
	| new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs
	| otherwise		  	      = loop new_fixed_tvs
	where
	  new_fixed_tvs = foldl extend fixed_tvs tv_fds

    extend fixed_tvs (ls,rs) | ls `subVarSet` fixed_tvs = fixed_tvs `unionVarSet` rs
			     | otherwise		= fixed_tvs

    tv_fds  :: [(TyVarSet,TyVarSet)]
	-- In our example, tv_fds will be [ ({x,y}, {z}), ({x,p},{q}) ]
	-- Meaning "knowing x,y fixes z, knowing x,p fixes q"
    tv_fds  = [ (tyVarsOfTypes xs, tyVarsOfTypes ys)
	      | ClassP cls tys <- preds,		-- Ignore implicit params
		let (cls_tvs, cls_fds) = classTvsFds cls,
		fd <- cls_fds,
		let (xs,ys) = instFD fd cls_tvs tys
	      ]
\end{code}

Note [Growing the tau-tvs using constraints]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(grow preds tvs) is the result of extend the set of tyvars tvs
		 using all conceivable links from pred

E.g. tvs = {a}, preds = {H [a] b, K (b,Int) c, Eq e}
Then grow precs tvs = {a,b,c}

All the type variables from an implicit parameter are added, whether or
not they are mentioned in tvs; see Note [Implicit parameters and ambiguity] 
in TcSimplify.

See also Note [Ambiguity] in TcSimplify

\begin{code}
grow :: [PredType] -> TyVarSet -> TyVarSet
grow preds fixed_tvs 
  | null preds = real_fixed_tvs
  | otherwise  = loop real_fixed_tvs
  where
	-- Add the implicit parameters; 
	-- see Note [Implicit parameters and ambiguity] in TcSimplify
    real_fixed_tvs = foldr unionVarSet fixed_tvs ip_tvs
 
    loop fixed_tvs
	| new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs
	| otherwise		  	      = loop new_fixed_tvs
	where
	  new_fixed_tvs = foldl extend fixed_tvs non_ip_tvs

    extend fixed_tvs pred_tvs 
	| fixed_tvs `intersectsVarSet` pred_tvs = fixed_tvs `unionVarSet` pred_tvs
	| otherwise			        = fixed_tvs

    (ip_tvs, non_ip_tvs) = partitionWith get_ip preds
    get_ip (IParam _ ty) = Left (tyVarsOfType ty)
    get_ip other         = Right (tyVarsOfPred other)
\end{code}
    
%************************************************************************
%*									*
\subsection{Generate equations from functional dependencies}
%*									*
%************************************************************************


\begin{code}
type Equation = (TyVarSet, [(Type, Type)])
-- These pairs of types should be equal, for some
-- substitution of the tyvars in the tyvar set
-- INVARIANT: corresponding types aren't already equal

-- It's important that we have a *list* of pairs of types.  Consider
-- 	class C a b c | a -> b c where ...
--	instance C Int x x where ...
-- Then, given the constraint (C Int Bool v) we should improve v to Bool,
-- via the equation ({x}, [(Bool,x), (v,x)])
-- This would not happen if the class had looked like
--	class C a b c | a -> b, a -> c

-- To "execute" the equation, make fresh type variable for each tyvar in the set,
-- instantiate the two types with these fresh variables, and then unify.
--
-- For example, ({a,b}, (a,Int,b), (Int,z,Bool))
-- We unify z with Int, but since a and b are quantified we do nothing to them
-- We usually act on an equation by instantiating the quantified type varaibles
-- to fresh type variables, and then calling the standard unifier.

pprEquation (qtvs, pairs) 
  = vcat [ptext SLIT("forall") <+> braces (pprWithCommas ppr (varSetElems qtvs)),
	  nest 2 (vcat [ ppr t1 <+> ptext SLIT(":=:") <+> ppr t2 | (t1,t2) <- pairs])]
\end{code}

Given a bunch of predicates that must hold, such as

	C Int t1, C Int t2, C Bool t3, ?x::t4, ?x::t5

improve figures out what extra equations must hold.
For example, if we have

	class C a b | a->b where ...

then improve will return

	[(t1,t2), (t4,t5)]

NOTA BENE:

  * improve does not iterate.  It's possible that when we make
    t1=t2, for example, that will in turn trigger a new equation.
    This would happen if we also had
	C t1 t7, C t2 t8
    If t1=t2, we also get t7=t8.

    improve does *not* do this extra step.  It relies on the caller
    doing so.

  * The equations unify types that are not already equal.  So there
    is no effect iff the result of improve is empty



\begin{code}
type Pred_Loc = (PredType, SDoc)	-- SDoc says where the Pred comes from

improveOne :: (Class -> [Instance])		-- Gives instances for given class
	   -> Pred_Loc				-- Do improvement triggered by this
	   -> [Pred_Loc]			-- Current constraints 
	   -> [(Equation,Pred_Loc,Pred_Loc)]	-- Derived equalities that must also hold
						-- (NB the above INVARIANT for type Equation)
						-- The Pred_Locs explain which two predicates were
						-- combined (for error messages)
-- Just do improvement triggered by a single, distinguised predicate

improveOne inst_env pred@(IParam ip ty, _) preds
  = [ ((emptyVarSet, [(ty,ty2)]), pred, p2) 
    | p2@(IParam ip2 ty2, _) <- preds
    , ip==ip2
    , not (ty `tcEqType` ty2)]

improveOne inst_env pred@(ClassP cls tys, _) preds
  | tys `lengthAtLeast` 2
  = instance_eqns ++ pairwise_eqns
	-- NB: we put the instance equations first.   This biases the 
	-- order so that we first improve individual constraints against the
	-- instances (which are perhaps in a library and less likely to be
	-- wrong; and THEN perform the pairwise checks.
	-- The other way round, it's possible for the pairwise check to succeed
	-- and cause a subsequent, misleading failure of one of the pair with an
	-- instance declaration.  See tcfail143.hs for an example
  where
    (cls_tvs, cls_fds) = classTvsFds cls
    instances	       = inst_env cls
    rough_tcs 	       = roughMatchTcs tys

	-- NOTE that we iterate over the fds first; they are typically
	-- empty, which aborts the rest of the loop.
    pairwise_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
    pairwise_eqns	-- This group comes from pairwise comparison
      = [ (eqn, pred, p2)
	| fd <- cls_fds
	, p2@(ClassP cls2 tys2, _) <- preds
	, cls == cls2
	, eqn <- checkClsFD emptyVarSet fd cls_tvs tys tys2
	]

    instance_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
    instance_eqns	-- This group comes from comparing with instance decls
      = [ (eqn, p_inst, pred)
	| fd <- cls_fds		-- Iterate through the fundeps first, 
				-- because there often are none!
	, let trimmed_tcs = trimRoughMatchTcs cls_tvs fd rough_tcs
		-- Trim the rough_tcs based on the head of the fundep.
		-- Remember that instanceCantMatch treats both argumnents
		-- symmetrically, so it's ok to trim the rough_tcs,
		-- rather than trimming each inst_tcs in turn
	, ispec@(Instance { is_tvs = qtvs, is_tys = tys_inst, 
		 	    is_tcs = inst_tcs }) <- instances
	, not (instanceCantMatch inst_tcs trimmed_tcs)
	, eqn <- checkClsFD qtvs fd cls_tvs tys_inst tys
	, let p_inst = (mkClassPred cls tys_inst, 
		        ptext SLIT("arising from the instance declaration at")
			<+> ppr (getSrcLoc ispec))
	]

improveOne inst_env eq_pred preds
  = []


checkClsFD :: TyVarSet 			-- Quantified type variables; see note below
	   -> FunDep TyVar -> [TyVar] 	-- One functional dependency from the class
	   -> [Type] -> [Type]
	   -> [Equation]

checkClsFD qtvs fd clas_tvs tys1 tys2
-- 'qtvs' are the quantified type variables, the ones which an be instantiated 
-- to make the types match.  For example, given
--	class C a b | a->b where ...
--	instance C (Maybe x) (Tree x) where ..
--
-- and an Inst of form (C (Maybe t1) t2), 
-- then we will call checkClsFD with
--
--	qtvs = {x}, tys1 = [Maybe x,  Tree x]
--		    tys2 = [Maybe t1, t2]
--
-- We can instantiate x to t1, and then we want to force
-- 	(Tree x) [t1/x]  :=:   t2
--
-- This function is also used when matching two Insts (rather than an Inst
-- against an instance decl. In that case, qtvs is empty, and we are doing
-- an equality check
-- 
-- This function is also used by InstEnv.badFunDeps, which needs to *unify*
-- For the one-sided matching case, the qtvs are just from the template,
-- so we get matching
--
  = ASSERT2( length tys1 == length tys2     && 
	     length tys1 == length clas_tvs 
	    , ppr tys1 <+> ppr tys2 )

    case tcUnifyTys bind_fn ls1 ls2 of
	Nothing  -> []
	Just subst | isJust (tcUnifyTys bind_fn rs1' rs2') 
			-- Don't include any equations that already hold. 
			-- Reason: then we know if any actual improvement has happened,
			-- 	   in which case we need to iterate the solver
			-- In making this check we must taking account of the fact that any 
			-- qtvs that aren't already instantiated can be instantiated to anything 
			-- at all
		  -> []

		  | otherwise	-- Aha!  A useful equation
		  -> [ (qtvs', zip rs1' rs2')]
		  	-- We could avoid this substTy stuff by producing the eqn
		  	-- (qtvs, ls1++rs1, ls2++rs2)
		  	-- which will re-do the ls1/ls2 unification when the equation is
		  	-- executed.  What we're doing instead is recording the partial
		  	-- work of the ls1/ls2 unification leaving a smaller unification problem
		  where
		    rs1'  = substTys subst rs1 
	 	    rs2'  = substTys subst rs2
		    qtvs' = filterVarSet (`notElemTvSubst` subst) qtvs
			-- qtvs' are the quantified type variables
			-- that have not been substituted out
			--	
			-- Eg. 	class C a b | a -> b
			--	instance C Int [y]
			-- Given constraint C Int z
			-- we generate the equation
			--	({y}, [y], z)
  where
    bind_fn tv | tv `elemVarSet` qtvs = BindMe
	       | otherwise	      = Skolem

    (ls1, rs1) = instFD fd clas_tvs tys1
    (ls2, rs2) = instFD fd clas_tvs tys2

instFD :: FunDep TyVar -> [TyVar] -> [Type] -> FunDep Type
instFD (ls,rs) tvs tys
  = (map lookup ls, map lookup rs)
  where
    env       = zipVarEnv tvs tys
    lookup tv = lookupVarEnv_NF env tv
\end{code}

\begin{code}
checkInstCoverage :: Class -> [Type] -> Bool
-- Check that the Coverage Condition is obeyed in an instance decl
-- For example, if we have 
--	class theta => C a b | a -> b
-- 	instance C t1 t2 
-- Then we require fv(t2) `subset` fv(t1)
-- See Note [Coverage Condition] below

checkInstCoverage clas inst_taus
  = all fundep_ok fds
  where
    (tyvars, fds) = classTvsFds clas
    fundep_ok fd  = tyVarsOfTypes rs `subVarSet` tyVarsOfTypes ls
		 where
		   (ls,rs) = instFD fd tyvars inst_taus
\end{code}

Note [Coverage condition]
~~~~~~~~~~~~~~~~~~~~~~~~~
For the coverage condition, we used to require only that 
	fv(t2) `subset` oclose(fv(t1), theta)

Example:
	class Mul a b c | a b -> c where
		(.*.) :: a -> b -> c

	instance Mul Int Int Int where (.*.) = (*)
	instance Mul Int Float Float where x .*. y = fromIntegral x * y
	instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v

In the third instance, it's not the case that fv([c]) `subset` fv(a,[b]).
But it is the case that fv([c]) `subset` oclose( theta, fv(a,[b]) )

But it is a mistake to accept the instance because then this defn:
	f = \ b x y -> if b then x .*. [y] else y
makes instance inference go into a loop, because it requires the constraint
	Mul a [b] b


%************************************************************************
%*									*
	Check that a new instance decl is OK wrt fundeps
%*									*
%************************************************************************

Here is the bad case:
	class C a b | a->b where ...
	instance C Int Bool where ...
	instance C Int Char where ...

The point is that a->b, so Int in the first parameter must uniquely
determine the second.  In general, given the same class decl, and given

	instance C s1 s2 where ...
	instance C t1 t2 where ...

Then the criterion is: if U=unify(s1,t1) then U(s2) = U(t2).

Matters are a little more complicated if there are free variables in
the s2/t2.  

	class D a b c | a -> b
	instance D a b => D [(a,a)] [b] Int
	instance D a b => D [a]     [b] Bool

The instance decls don't overlap, because the third parameter keeps
them separate.  But we want to make sure that given any constraint
	D s1 s2 s3
if s1 matches 


\begin{code}
checkFunDeps :: (InstEnv, InstEnv) -> Instance
	     -> Maybe [Instance]	-- Nothing  <=> ok
					-- Just dfs <=> conflict with dfs
-- Check wheher adding DFunId would break functional-dependency constraints
-- Used only for instance decls defined in the module being compiled
checkFunDeps inst_envs ispec
  | null bad_fundeps = Nothing
  | otherwise	     = Just bad_fundeps
  where
    (ins_tvs, _, clas, ins_tys) = instanceHead ispec
    ins_tv_set   = mkVarSet ins_tvs
    cls_inst_env = classInstances inst_envs clas
    bad_fundeps  = badFunDeps cls_inst_env clas ins_tv_set ins_tys

badFunDeps :: [Instance] -> Class
	   -> TyVarSet -> [Type]	-- Proposed new instance type
	   -> [Instance]
badFunDeps cls_insts clas ins_tv_set ins_tys 
  = [ ispec | fd <- fds,	-- fds is often empty
	      let trimmed_tcs = trimRoughMatchTcs clas_tvs fd rough_tcs,
	      ispec@(Instance { is_tcs = inst_tcs, is_tvs = tvs, 
				is_tys = tys }) <- cls_insts,
		-- Filter out ones that can't possibly match, 
		-- based on the head of the fundep
	      not (instanceCantMatch inst_tcs trimmed_tcs),	
	      notNull (checkClsFD (tvs `unionVarSet` ins_tv_set) 
				   fd clas_tvs tys ins_tys)
    ]
  where
    (clas_tvs, fds) = classTvsFds clas
    rough_tcs = roughMatchTcs ins_tys

trimRoughMatchTcs :: [TyVar] -> FunDep TyVar -> [Maybe Name] -> [Maybe Name]
-- Computing rough_tcs for a particular fundep
--	class C a b c | a -> b where ... 
-- For each instance .... => C ta tb tc
-- we want to match only on the types ta, tc; so our
-- rough-match thing must similarly be filtered.  
-- Hence, we Nothing-ise the tb type right here
trimRoughMatchTcs clas_tvs (_,rtvs) mb_tcs
  = zipWith select clas_tvs mb_tcs
  where
    select clas_tv mb_tc | clas_tv `elem` rtvs = Nothing
			 | otherwise	       = mb_tc
\end{code}