%
% (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 (
        FDEq (..),
 	Equation(..), pprEquation,
	oclose, improveFromInstEnv, improveFromAnother,
	checkInstCoverage, checkFunDeps,
	pprFundeps
    ) where

#include "HsVersions.h"

import Name
import Var
import Class
import TcType
import Unify
import InstEnv
import VarSet
import VarEnv
import Outputable
import Util
import FastString

import Data.List	( nubBy )
import Data.Maybe	( isJust )
\end{code}


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

  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 	v `elem` oclose(vs,C)
          one way:     		 => v is definitely fixed by vs

   grow is conservative		if v might be fixed by vs 
          the other way:	=> v `elem` grow(vs,C)

----------------------------------------------------------
(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.

oclose is used (only) when generalising a type T; see extensive
notes in TcSimplify.

Note [Important subtlety in oclose]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider (oclose (C Int t) {}), where class C a b | a->b
Then, since a->b, 't' is fully determined by Int, and the
uniform thing is to return {t}.

However, consider
	class D a b c | b->c
	f x = e	  -- 'e' generates constraint (D s Int t)
		  -- \x.e has type s->s
Then, if (oclose (D s Int t) {}) = {t}, we'll make the function
monomorphic in 't', thus
	f :: forall s. D s Int t => s -> s

But if this function is never called, 't' will never be instantiated;
the functional dependencies that fix 't' may well be instance decls in
some importing module.  But the top-level defaulting of unconstrained
type variables will fix t=GHC.Prim.Any, and that's simply a bug.

Conclusion: oclose only returns a type variable as "fixed" if it 
depends on at least one type variable in the input fixed_tvs.

Remember, it's always sound for oclose to return a smaller set.
An interesting example is tcfail093, where we get this inferred type:
    class C a b | a->b
    dup :: forall h. (Call (IO Int) h) => () -> Int -> h
This is perhaps a bit silly, because 'h' is fixed by the (IO Int);
previously GHC rejected this saying 'no instance for Call (IO Int) h'.
But it's right on the borderline. If there was an extra, otherwise
uninvolved type variable, like 's' in the type of 'f' above, then
we must accept the function.  So, for now anyway, we accept 'dup' too.

\begin{code}
oclose :: [PredType] -> TyVarSet -> TyVarSet
oclose preds fixed_tvs
  | null tv_fds 	    = fixed_tvs	   -- Fast escape hatch for common case
  | isEmptyVarSet fixed_tvs = emptyVarSet  -- Note [Important subtlety in oclose]
  | 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) 
	| not (isEmptyVarSet ls)	-- Note [Important subtlety in oclose]
	, 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}

    
%************************************************************************
%*									*
\subsection{Generate equations from functional dependencies}
%*									*
%************************************************************************


Each functional dependency with one variable in the RHS is responsible
for generating a single equality. For instance:
     class C a b | a -> b
The constraints ([Wanted] C Int Bool) and [Wanted] C Int alpha 
     FDEq { fd_pos      = 1
          , fd_ty_left  = Bool 
          , fd_ty_right = alpha }
However notice that a functional dependency may have more than one variable
in the RHS which will create more than one FDEq. Example: 
     class C a b c | a -> b c 
     [Wanted] C Int alpha alpha 
     [Wanted] C Int Bool beta 
Will generate: 
        fd1 = FDEq { fd_pos = 1, fd_ty_left = alpha, fd_ty_right = Bool } and
        fd2 = FDEq { fd_pos = 2, fd_ty_left = alpha, fd_ty_right = beta }

We record the paremeter position so that can immediately rewrite a constraint
using the produced FDEqs and remove it from our worklist.


INVARIANT: Corresponding types aren't already equal 
That is, there exists at least one non-identity equality in FDEqs. 

Assume:
       class C a b c | a -> b c
       instance C Int x x
And:   [Wanted] C Int Bool alpha
We will /match/ the LHS of fundep equations, producing a matching substitution
and create equations for the RHS sides. In our last example we'd have generated:
      ({x}, [fd1,fd2])
where 
       fd1 = FDEq 1 Bool x
       fd2 = FDEq 2 alpha x
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 or generate 
a new constraint. In the above example we would generate a new unification 
variable 'beta' for x and produce the following constraints:
     [Wanted] (Bool ~ beta)
     [Wanted] (alpha ~ beta)

Notice the subtle difference between the above class declaration and:
       class C a b c | a -> b, a -> c 
where we would generate: 
      ({x},[fd1]),({x},[fd2]) 
This means that the template variable would be instantiated to different 
unification variables when producing the FD constraints. 

Finally, the position parameters will help us rewrite the wanted constraint ``on the spot''

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

data Equation 
   = FDEqn { fd_qtvs :: TyVarSet		-- Instantiate these to fresh unification vars
           , fd_eqs  :: [FDEq]			--   and then make these equal
           , fd_pred1, fd_pred2 :: Pred_Loc }	-- The Equation arose from
	     	       		   	    	-- combining these two constraints

data FDEq = FDEq { fd_pos      :: Int -- We use '0' for the first position
                 , fd_ty_left  :: Type
                 , fd_ty_right :: Type }
\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}
instFD_WithPos :: FunDep TyVar -> [TyVar] -> [Type] -> ([Type], [(Int,Type)]) 
-- Returns a FunDep between the types accompanied along with their 
-- position (<=0) in the types argument list.
instFD_WithPos (ls,rs) tvs tys
  = (map (snd . lookup) ls, map lookup rs)
  where
    ind_tys   = zip [0..] tys 
    env       = zipVarEnv tvs ind_tys
    lookup tv = lookupVarEnv_NF env tv

zipAndComputeFDEqs :: (Type -> Type -> Bool) -- Discard this FDEq if true
                   -> [Type] 
                   -> [(Int,Type)] 
                   -> [FDEq]
-- Create a list of FDEqs from two lists of types, making sure
-- that the types are not equal.
zipAndComputeFDEqs discard (ty1:tys1) ((i2,ty2):tys2)
 | discard ty1 ty2 = zipAndComputeFDEqs discard tys1 tys2
 | otherwise = FDEq { fd_pos      = i2
                    , fd_ty_left  = ty1
                    , fd_ty_right = ty2 } : zipAndComputeFDEqs discard tys1 tys2
zipAndComputeFDEqs _ _ _ = [] 

-- Improve a class constraint from another class constraint
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
improveFromAnother :: Pred_Loc -- Template item (usually given, or inert) 
                   -> Pred_Loc -- Workitem [that can be improved]
                   -> [Equation]
-- Post: FDEqs always oriented from the other to the workitem 
--       Equations have empty quantified variables 
improveFromAnother pred1@(ClassP cls1 tys1, _) pred2@(ClassP cls2 tys2, _)
  | tys1 `lengthAtLeast` 2 && cls1 == cls2
  = [ FDEqn { fd_qtvs = emptyVarSet, fd_eqs = eqs, fd_pred1 = pred1, fd_pred2 = pred2 }
    | let (cls_tvs, cls_fds) = classTvsFds cls1
    , fd <- cls_fds
    , let (ltys1, rs1)  = instFD         fd cls_tvs tys1
          (ltys2, irs2) = instFD_WithPos fd cls_tvs tys2
    , tcEqTypes ltys1 ltys2		-- The LHSs match
    , let eqs = zipAndComputeFDEqs tcEqType rs1 irs2
    , not (null eqs) ]

improveFromAnother _ _ = []


-- Improve a class constraint from instance declarations
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

pprEquation :: Equation -> SDoc
pprEquation (FDEqn { fd_qtvs = qtvs, fd_eqs = pairs }) 
  = vcat [ptext (sLit "forall") <+> braces (pprWithCommas ppr (varSetElems qtvs)),
	  nest 2 (vcat [ ppr t1 <+> ptext (sLit "~") <+> ppr t2 | (FDEq _ t1 t2) <- pairs])]

improveFromInstEnv :: (InstEnv,InstEnv)
                   -> Pred_Loc
                   -> [Equation] -- Needs to be an Equation because
                                 -- of quantified variables
-- Post: Equations oriented from the template (matching instance) to the workitem!
improveFromInstEnv _inst_env (pred,_loc)
  | not (isClassPred pred)
  = panic "improveFromInstEnv: not a class predicate"
improveFromInstEnv inst_env pred@(ClassP cls tys, _)
  | tys `lengthAtLeast` 2
  = [ FDEqn { fd_qtvs = qtvs, fd_eqs = eqs, fd_pred1 = p_inst, fd_pred2=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)
    , let p_inst = (mkClassPred cls tys_inst,
		    sep [ ptext (sLit "arising from the dependency") <+> quotes (pprFunDep fd)	
		        , ptext (sLit "in the instance declaration at")
			            <+> ppr (getSrcLoc ispec)])
    , (qtvs, eqs) <- checkClsFD qtvs fd cls_tvs tys_inst tys -- NB: orientation
    , not (null eqs)
    ]
  where 
     (cls_tvs, cls_fds) = classTvsFds cls
     instances          = classInstances inst_env cls
     rough_tcs          = roughMatchTcs tys
improveFromInstEnv _ _ = []


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

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 ltys1 ltys2 of
	Nothing  -> []
	Just subst | isJust (tcUnifyTys bind_fn rtys1' rtys2')
			-- 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
                        -- NB: We can't do this 'is-useful-equation' check element-wise 
                        --     because of:
                        --           class C a b c | a -> b c
                        --           instance C Int x x
                        --           [Wanted] C Int alpha Int
                        -- We would get that  x -> alpha  (isJust) and x -> Int (isJust)
                        -- so we would produce no FDs, which is clearly wrong. 
                  -> [] 

                  | otherwise
                  -> [(qtvs', fdeqs)]
		  	-- 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
                    rtys1' = map (substTy subst) rtys1
                    irs2'  = map (\(i,x) -> (i,substTy subst x)) irs2
                    rtys2' = map snd irs2'
 
                    fdeqs = zipAndComputeFDEqs (\_ _ -> False) rtys1' irs2'
                        -- Don't discard anything! 
                        -- We could discard equal types but it's an overkill to call 
                        -- tcEqType again, since we know for sure that /at least one/ 
                        -- equation in there is useful)

		    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

    (ltys1, rtys1) = instFD         fd clas_tvs tys1
    (ltys2, irs2)  = instFD_WithPos fd clas_tvs tys2
\end{code}


\begin{code}
instFD :: FunDep TyVar -> [TyVar] -> [Type] -> FunDep Type
-- A simpler version of instFD_WithPos to be used in checking instance coverage etc.
instFD (ls,rs) tvs tys
  = (map lookup ls, map lookup rs)
  where
    env       = zipVarEnv tvs tys
    lookup tv = lookupVarEnv_NF env tv

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 
  = nubBy eq_inst $
    [ ispec | fd <- fds,	-- fds is often empty, so do this first!
	      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
    eq_inst i1 i2 = instanceDFunId i1 == instanceDFunId i2
	-- An single instance may appear twice in the un-nubbed conflict list
	-- because it may conflict with more than one fundep.  E.g.
	--	class C a b c | a -> b, a -> c
	--	instance C Int Bool Bool
	--	instance C Int Char Char
	-- The second instance conflicts with the first by *both* fundeps

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 type ta; so our
-- rough-match thing must similarly be filtered.  
-- Hence, we Nothing-ise the tb and tc types right here
trimRoughMatchTcs clas_tvs (ltvs, _) mb_tcs
  = zipWith select clas_tvs mb_tcs
  where
    select clas_tv mb_tc | clas_tv `elem` ltvs = mb_tc
                         | otherwise           = Nothing
\end{code}



