# LANGUAGE FlexibleContexts #
# LANGUAGE ScopedTypeVariables #

module HERMIT.Dictionary.AlphaConversion
    ( -- * Alpha-Renaming and Shadowing
      externals
      -- ** Alpha-Renaming
    , alphaR
    , alphaLamR
    , alphaCaseBinderR
    , alphaAltWithR
    , alphaAltVarsR
    , alphaAltR
    , alphaCaseR
    , alphaLetWithR
    , alphaLetVarsR
    , alphaLetR
    , alphaProgConsWithR
    , alphaProgConsIdsR
    , alphaProgConsR
    , alphaProgR
      -- ** Shadow Detection and Unshadowing
    , unshadowR
    , unshadowExprR
    , unshadowAltR
    , unshadowProgR
    , visibleVarsT
    , cloneVarAvoidingT
    , freshNameGenAvoiding
    , detectShadowsM
    , replaceVarR
    ) where

import Control.Arrow
import Control.Monad (liftM, liftM2)
import Data.Char (isDigit)
import Data.Function (on)
import Data.List (intersect, delete, elemIndex)
import Data.Maybe (listToMaybe)

import HERMIT.Core
import HERMIT.Context
import HERMIT.Kure
import HERMIT.External
import HERMIT.GHC
import HERMIT.Name
import HERMIT.Utilities(dupsBy)

import HERMIT.Dictionary.GHC hiding (externals)
import HERMIT.Dictionary.Common

import Prelude hiding (exp)

-----------------------------------------------------------------------

-- | Externals for alpha-renaming.
externals :: [External]
externals = map (.+ Deep)
         [  external "alpha" (promoteCoreR alphaR :: RewriteH LCore)
               [ "Renames the bound variables at the current node."]
         ,  external "alpha-lam" (promoteExprR . alphaLamR . Just :: String -> RewriteH LCore)
               [ "Renames the bound variable in a Lambda expression to the given name."]
         ,  external "alpha-lam" (promoteExprR  (alphaLamR Nothing) :: RewriteH LCore)
               [ "Renames the bound variable in a Lambda expression."]
         ,  external "alpha-case-binder" (promoteExprR . alphaCaseBinderR . Just :: String -> RewriteH LCore)
               [ "Renames the binder in a Case expression to the given name."]
         ,  external "alpha-case-binder" (promoteExprR (alphaCaseBinderR Nothing) :: RewriteH LCore)
               [ "Renames the binder in a Case expression."]
         ,  external "alpha-alt" (promoteAltR alphaAltR :: RewriteH LCore)
               [ "Renames all binders in a Case alternative."]
         ,  external "alpha-alt" (promoteAltR . alphaAltWithR :: [String] -> RewriteH LCore)
               [ "Renames all binders in a Case alternative using the user-provided list of new names."]
         ,  external "alpha-case" (promoteExprR alphaCaseR :: RewriteH LCore)
               [ "Renames all binders in a Case alternative."]
         ,  external "alpha-let" (promoteExprR . alphaLetWithR :: [String] -> RewriteH LCore)
               [ "Renames the bound variables in a Let expression using a list of suggested names."]
         ,  external "alpha-let" (promoteExprR alphaLetR :: RewriteH LCore)
               [ "Renames the bound variables in a Let expression."]
         ,  external "alpha-top" (promoteProgR . alphaProgConsWithR :: [String] -> RewriteH LCore)
               [ "Renames the bound identifiers in the top-level binding group at the head of the program using a list of suggested names."]
         ,  external "alpha-top" (promoteProgR alphaProgConsR :: RewriteH LCore)
               [ "Renames the bound identifiers in the top-level binding at the head of the program."]
         ,  external "alpha-prog" (promoteProgR alphaProgR :: RewriteH LCore)
               [ "Rename all top-level identifiers in the program."]
         ,  external "unshadow" (promoteCoreR unshadowR :: RewriteH LCore)
                [ "Rename local variables with manifestly unique names (x, x0, x1, ...)."]
         ]

-----------------------------------------------------------------------
--
  freshNameGen is a function used in conjunction with cloneVarH , which clones an existing ' Var ' .
-- But, what name should the new Id have?
  cloneVarH generates a new Unique -- so we are positive that the new Var will be new ,
-- but freshNameGen tries to assign a Name that will be meaningful to the user, and
-- not shadow other names in scope.
-- So,  we start with the name of the original Id, and add an integer suffix
   x   goes to  or x1 or ...
-- and we do not want this newly generated name to shadow either:
  1 .   Any free variable name in the active  ; or
  2 .   Any bound variables in context .

-- | Collect all visible variables (in the expression or the context).
visibleVarsT :: (BoundVars c, Monad m) => Transform c m CoreTC VarSet
visibleVarsT = -- TODO: implement freeVarsLCoreTC
               liftM2 unionVarSet boundVarsT (promoteT $ arr freeVarsCoreTC)

-- | If a name is provided, use that as the name of the new variable.
    Otherwise modify the variable name making sure to /not/ clash with the given variables or any visible variables .
cloneVarAvoidingT :: (BoundVars c, MonadUnique m) => Var -> Maybe String -> [Var] -> Transform c m CoreTC Var
cloneVarAvoidingT v mn vs =
  do vvs <- visibleVarsT
     let nameModifier = freshNameGenAvoiding mn (extendVarSetList vvs vs)
     constT (cloneVarH nameModifier v)

-- | Use the optional argument if given, otherwise generate a new name avoiding clashes with the set of variables.
freshNameGenAvoiding :: Maybe String -> VarSet -> (String -> String)
freshNameGenAvoiding mn vs str = maybe (inventNames vs str) ((\(c:cs) -> reverse (c:(takeWhile (/='.') cs))) . reverse) mn
-- The 'Just' case above gives the unqualified portion of the name (properly handling the compose operator '.')

-- | Invent a new String based on the old one, but avoiding clashing with the given list of identifiers.
inventNames :: VarSet -> String -> String
inventNames curr old = head
                     [ nm
                     | nm <- old : [ base ++ show uq | uq <- [start ..] :: [Int] ]
                     , nm `notElem` names
                     ]
   where
           names = varSetToStrings curr
           nums = reverse $ takeWhile isDigit (reverse old)
           baseLeng = length $ drop (length nums) old
           base = take baseLeng old
           start = case reads nums of
                     [(v,_)] -> v + 1
                     _       -> 0


  | Discard variables from the first set that do not shadow a variable in the second set .
shadowedBy :: VarSet -> VarSet -> VarSet
shadowedBy vs fvs = let fvNames = varSetToStrings fvs
                     in filterVarSet (\ v -> unqualifiedName v `elem` fvNames) vs

-- | Shadows are any duplicates in the list, or any occurrences of the list elements in the set.
detectShadowsM :: Monad m => [Var] -> VarSet -> m VarSet
detectShadowsM bs fvs = let ss = shadowedBy (mkVarSet bs) fvs `extendVarSetList` dupVars bs
                         in do guardMsg (not $ isEmptyVarSet ss) "No shadows detected."
                               return ss

  | Rename local variables with manifestly unique names ( x ,  , x1 , ... ) .
--   Does not rename top-level definitions.
unshadowR :: ( AddBindings c, BoundVars c, ExtendPath c Crumb, HasEmptyContext c
             , ReadPath c Crumb, MonadCatch m, MonadUnique m )
          => Rewrite c m Core
unshadowR = setFailMsg "No shadows to eliminate." $
    anytdR (promoteExprR unshadowExprR <+ promoteAltR unshadowAltR <+ promoteProgR unshadowProgR)

unshadowExprR :: (AddBindings c, BoundVars c, ExtendPath c Crumb, ReadPath c Crumb, MonadCatch m, MonadUnique m)
              => Rewrite c m CoreExpr
unshadowExprR = do
    bs  <- letVarsT <+ (liftM return (caseBinderIdT <+ lamVarT))
    fvs <- liftM2 unionVarSet boundVarsT (arr freeVarsExpr)
    ss  <- detectShadowsM bs fvs
    alphaLamR Nothing <+ alphaLetVarsR (varSetElems ss) <+ alphaCaseBinderR Nothing

unshadowAltR :: (BoundVars c, MonadCatch m, MonadUnique m)
             => Rewrite c m CoreAlt
unshadowAltR = do
    bs  <- arr altVars
    fvs <- liftM2 unionVarSet boundVarsT (arr freeVarsAlt)
    ss  <- detectShadowsM bs fvs
    alphaAltVarsR (varSetElems ss)

unshadowProgR :: (AddBindings c, BoundVars c, ExtendPath c Crumb, ReadPath c Crumb, MonadCatch m, MonadUnique m)
              => Rewrite c m CoreProg
unshadowProgR = do
    bs  <- progConsIdsT
    fvs <- liftM2 unionVarSet boundVarsT (arr freeVarsProg)
    ss  <- detectShadowsM bs fvs
    alphaProgConsIdsR (varSetElems ss)

dupVars :: [Var] -> [Var]
dupVars = dupsBy ((==) `on` unqualifiedName)

-----------------------------------------------------------------------

  Maybe this should be defined in Dictionary . GHC .

-- | Replace all occurrences of a specified variable.
--   Arguments are the variable to replace and the replacement variable, respectively.
replaceVarR :: (Injection a Core, MonadCatch m) => Var -> Var -> Rewrite c m a
replaceVarR v v' = extractR $ tryR $ substR v $ varToCoreExpr v'

-- TODO: Experimental
replaceRecBindVarR :: Monad m => Id -> Id -> Rewrite c m CoreBind
replaceRecBindVarR v v' =
   do Rec ies <- idR
      let (is,es) = unzip ies
      case elemIndex v is of
        Nothing -> fail "Specified identifier does not occur in the current recursive binding group."
        Just n  -> let is0       = delete v is
                       (is1,is2) = splitAt n is0
                       is'       = is1 ++ v' : is2
                       es'       = map (substCoreExpr v (Var v')) es
  TODO .   Do we need to initialize the emptySubst with bindFreeVars ?
                       sub       = extendSubst emptySubst v (Var v')
                   in return $ snd $ substBind sub (Rec (zip is' es'))

                   -- let is0       = delete v is
      emptySub   = mkEmptySubst $ mkInScopeSet $ unionVarSets ( map ( localFreeVarsExpr .  ) is0 )
      sub        = extendSubst emptySub v ( Var v ' )
      ( is1,is2 ) = splitAt n ( snd $ substRecBndrs sub is0 )
                   --     is'       = is1 ++ v' : is2
      es '        = map ( substCoreExpr v ( Var v ' ) ) es
                   -- in return $ Rec (zip is' es')

-----------------------------------------------------------------------

-- | Alpha rename a lambda binder.  Optionally takes a suggested new name.
alphaLamR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
          => Maybe String -> Rewrite c m CoreExpr
alphaLamR mn = setFailMsg (wrongFormForAlpha "Lam v e") $
              do v  <- lamVarT
                 v' <- extractT (cloneVarAvoidingT v mn [v])
                 lamAnyR (return v') (replaceVarR v v')

-----------------------------------------------------------------------

-- | Alpha rename a case binder.  Optionally takes a suggested new name.
alphaCaseBinderR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                 => Maybe String -> Rewrite c m CoreExpr
alphaCaseBinderR mn = setFailMsg (wrongFormForAlpha "Case e i ty alts") $
                     do i  <- caseBinderIdT
                        i' <- extractT (cloneVarAvoidingT i mn [i])
                        caseAnyR idR (return i') idR (\ _ -> replaceVarR i i')

-----------------------------------------------------------------------

-- | Rename the specified variable in a case alternative.  Optionally takes a suggested new name.
alphaAltVarR :: (BoundVars c, MonadCatch m, MonadUnique m)
             => Maybe String -> Var -> Rewrite c m CoreAlt
alphaAltVarR mn v = do
    (con, vs, rhs) <- idR
    v' <- extractT (cloneVarAvoidingT v mn vs)

    -- This is a bit of a hack. We include all the binders *after* v in the call to substAltR,
    -- then put the binders before v, and v', back on the front. The use of substAltR this way,
    -- handles the case where v is a type binder which substitutes into the types of bs'.
    -- It's a hack because we depend on substAltR not noticing that the constructor is not applied
    -- to enough binders.
    case break (==v) vs of
        (bs,_:bs') -> let (con',bs'',rhs') = substCoreAlt v (varToCoreExpr v') (con,bs',rhs)
                       in return (con',bs ++ (v':bs''),rhs')
        _ -> fail "pattern binder not present."

-- | Rename the specified variables in a case alternative, using the suggested names where provided.
-- Suggested names *must* be provided in left-to-right order matching the order of the alt binders.
alphaAltVarsWithR :: (BoundVars c, MonadCatch m, MonadUnique m)
                  => [(Maybe String,Var)] -> Rewrite c m CoreAlt
alphaAltVarsWithR = andR . map (uncurry alphaAltVarR) . reverse -- note: right-to-left so type subst aren't undone

-- | Rename the variables bound in a case alternative with the given list of suggested names.
alphaAltWithR :: (BoundVars c, MonadCatch m, MonadUnique m)
              => [String] -> Rewrite c m CoreAlt
alphaAltWithR ns =
  do vs <- arr altVars
     alphaAltVarsWithR $ zip (map Just ns) vs

-- | Rename the specified variables in a case alternative.
alphaAltVarsR :: (BoundVars c, MonadCatch m, MonadUnique m)
              => [Var] -> Rewrite c m CoreAlt
alphaAltVarsR vs =
  do bs <- arr altVars
     alphaAltVarsWithR (zip (repeat Nothing) (bs `intersect` vs))

-- | Rename all identifiers bound in a case alternative.
alphaAltR :: (BoundVars c, MonadCatch m, MonadUnique m)
          => Rewrite c m CoreAlt
alphaAltR = arr altVars >>= alphaAltVarsR

-----------------------------------------------------------------------

-- | Rename all identifiers bound in a case expression.
alphaCaseR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
           => Rewrite c m CoreExpr
alphaCaseR = alphaCaseBinderR Nothing >+> caseAllR idR idR idR (const alphaAltR)

-----------------------------------------------------------------------

-- | Alpha rename a non-recursive let binder.  Optionally takes a suggested new name.
alphaLetNonRecR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                => Maybe String -> Rewrite c m CoreExpr
alphaLetNonRecR mn = setFailMsg (wrongFormForAlpha "Let (NonRec v e1) e2") $
                    do v  <- letNonRecVarT
                       v' <- extractT (cloneVarAvoidingT v mn [v])
                       letNonRecAnyR (return v') idR (replaceVarR v v')

-- | Alpha rename a non-recursive let binder if the variable appears in the argument list.  Optionally takes a suggested new name.
alphaLetNonRecVarsR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                    => Maybe String -> [Var] -> Rewrite c m CoreExpr
alphaLetNonRecVarsR mn vs = whenM (liftM (`elem` vs) letNonRecVarT) (alphaLetNonRecR mn)


-- TODO: Maybe it would be more efficient to rename all the Ids at once, rather than one by one?

-- | Rename the specified identifiers in a recursive let, using the suggested names where provided.
alphaLetRecIdsWithR :: forall c m. ( ExtendPath c Crumb, ReadPath c Crumb, AddBindings c
                                   , BoundVars c, MonadCatch m, MonadUnique m )
                    => [(Maybe String,Id)] -> Rewrite c m CoreExpr
alphaLetRecIdsWithR = andR . map (uncurry alphaLetRecIdR)
  where
    -- | Rename the specified identifier bound in a recursive let.  Optionally takes a suggested new name.
    alphaLetRecIdR :: Maybe String -> Id -> Rewrite c m CoreExpr
    alphaLetRecIdR mn i = setFailMsg (wrongFormForAlpha "Let (Rec bs) e") $
                     do is <- letRecIdsT
                        i' <- extractT (cloneVarAvoidingT i mn is)
                        letAnyR (replaceRecBindVarR i i') (replaceVarR i i')


-- | Rename the identifiers bound in a Let with the given list of suggested names.
alphaLetWithR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
              => [String] -> Rewrite c m CoreExpr
alphaLetWithR ns = alphaLetNonRecR (listToMaybe ns)
                  <+ (letRecIdsT >>= (alphaLetRecIdsWithR . zip (map Just ns)))

-- | Rename the specified variables bound in a let.
alphaLetVarsR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
              => [Var] -> Rewrite c m CoreExpr
alphaLetVarsR vs = alphaLetNonRecVarsR Nothing vs
                   <+ (do bs <- letT (arr bindVars) successT const
                          alphaLetRecIdsWithR (zip (repeat Nothing) (bs `intersect` vs))
                      )

-- | Rename all identifiers bound in a Let.
alphaLetR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
          => Rewrite c m CoreExpr
alphaLetR = letVarsT >>= alphaLetVarsR

-----------------------------------------------------------------------

-- | Alpha rename a non-recursive top-level binder.  Optionally takes a suggested new name.
alphaProgConsNonRecR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                     => Maybe String -> Rewrite c m CoreProg
alphaProgConsNonRecR mn = setFailMsg (wrongFormForAlpha "ProgCons (NonRec v e) p") $
                    do i <- progConsNonRecIdT
                       guardMsg (not $ isExportedId i) ("Identifier " ++ unqualifiedName i ++ " is exported, and thus cannot be alpha-renamed.")
                       i' <- extractT (cloneVarAvoidingT i mn [i])
                       consNonRecAnyR (return i') idR (replaceVarR i i')

-- | Alpha rename a non-recursive top-level binder if the identifier appears in the argument list.  Optionally takes a suggested new name.
alphaProgConsNonRecIdsR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                        => Maybe String -> [Id] -> Rewrite c m CoreProg
alphaProgConsNonRecIdsR mn is = whenM (liftM (`elem` is) progConsNonRecIdT) (alphaProgConsNonRecR mn)

-- TODO: Maybe it would be more efficient to rename all the Ids at once, rather than one by one?

-- | Rename the specified identifiers in a recursive top-level binding at the head of a program, using the suggested names where provided.
alphaProgConsRecIdsWithR :: forall c m. ( ExtendPath c Crumb, ReadPath c Crumb, AddBindings c
                                        , BoundVars c, MonadCatch m, MonadUnique m )
                         => [(Maybe String,Id)] -> Rewrite c m CoreProg
alphaProgConsRecIdsWithR = andR . map (uncurry alphaProgConsRecIdR) . filter (not . isExportedId . snd)
  where
    -- | Rename the specified identifier bound in a recursive top-level binder.  Optionally takes a suggested new name.
    alphaProgConsRecIdR :: Maybe String -> Id -> Rewrite c m CoreProg
    alphaProgConsRecIdR mn i =  setFailMsg (wrongFormForAlpha "ProgCons (Rec bs) p") $
                      do is <- progConsRecIdsT
                         i' <- extractT (cloneVarAvoidingT i mn is)
                         progConsAnyR (replaceRecBindVarR i i') (replaceVarR i i')


-- | Rename the identifiers bound in the top-level binding at the head of the program with the given list of suggested names.
alphaProgConsWithR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                   => [String] -> Rewrite c m CoreProg
alphaProgConsWithR ns = alphaProgConsNonRecR (listToMaybe ns)
                        <+ (progConsRecIdsT >>= (alphaProgConsRecIdsWithR . zip (map Just ns)))

-- | Rename the specified variables bound in the top-level binding at the head of the program.
alphaProgConsIdsR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                  => [Id] -> Rewrite c m CoreProg
alphaProgConsIdsR vs = alphaProgConsNonRecIdsR Nothing vs
                       <+ (do bs <- progConsT (arr bindVars) successT const
                              alphaProgConsRecIdsWithR (zip (repeat Nothing) (bs `intersect` vs))
                          )

-- | Rename all identifiers bound in the top-level binding at the head of the program.
alphaProgConsR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
               => Rewrite c m CoreProg
alphaProgConsR = progConsIdsT >>= alphaProgConsIdsR

-----------------------------------------------------------------------

-- | Rename all identifiers bound at the top-level.
alphaProgR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
           => Rewrite c m CoreProg
alphaProgR = alphaProgConsR >+> progConsAllR idR alphaProgR

-----------------------------------------------------------------------

-- | Alpha rename any bindings at this node.  Note: does not rename case alternatives unless invoked on the alternative.
alphaR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
       => Rewrite c m Core
alphaR = setFailMsg "Cannot alpha-rename here." $
           promoteExprR (alphaLamR Nothing <+ alphaCaseBinderR Nothing <+ alphaLetR)
        <+ promoteAltR alphaAltR
        <+ promoteProgR alphaProgConsR

-- TODO: Alpha rewrites need better error messages.  Currently the use of (<+) leads to incorrect error reporting.
        Though really , we first need to improve KURE to have a version of ( < + ) that maintains the existing error message in the case of non - matching constructors henceforth .

  TODO 2 : Also , we should be able to rename inside types and coercions .

  TODO 3 : Also , we should be able to rename lemma quantifiers

-----------------------------------------------------------------------

wrongFormForAlpha :: String -> String
wrongFormForAlpha s = "Cannot alpha-rename, " ++ wrongExprForm s

-----------------------------------------------------------------------

 * Alpha-Renaming and Shadowing
 ** Alpha-Renaming
 ** Shadow Detection and Unshadowing
---------------------------------------------------------------------
 | Externals for alpha-renaming.
---------------------------------------------------------------------

 But, what name should the new Id have?
 so we are positive that the new Var will be new ,
 but freshNameGen tries to assign a Name that will be meaningful to the user, and
 not shadow other names in scope.
 So,  we start with the name of the original Id, and add an integer suffix
 and we do not want this newly generated name to shadow either:
 | Collect all visible variables (in the expression or the context).
 TODO: implement freeVarsLCoreTC
 | If a name is provided, use that as the name of the new variable.
 | Use the optional argument if given, otherwise generate a new name avoiding clashes with the set of variables.
 The 'Just' case above gives the unqualified portion of the name (properly handling the compose operator '.')
 | Invent a new String based on the old one, but avoiding clashing with the given list of identifiers.
 | Shadows are any duplicates in the list, or any occurrences of the list elements in the set.
   Does not rename top-level definitions.
---------------------------------------------------------------------
 | Replace all occurrences of a specified variable.
   Arguments are the variable to replace and the replacement variable, respectively.
 TODO: Experimental
 let is0       = delete v is
     is'       = is1 ++ v' : is2
 in return $ Rec (zip is' es')
---------------------------------------------------------------------
 | Alpha rename a lambda binder.  Optionally takes a suggested new name.
---------------------------------------------------------------------
 | Alpha rename a case binder.  Optionally takes a suggested new name.
---------------------------------------------------------------------
 | Rename the specified variable in a case alternative.  Optionally takes a suggested new name.
 This is a bit of a hack. We include all the binders *after* v in the call to substAltR,
 then put the binders before v, and v', back on the front. The use of substAltR this way,
 handles the case where v is a type binder which substitutes into the types of bs'.
 It's a hack because we depend on substAltR not noticing that the constructor is not applied
 to enough binders.
 | Rename the specified variables in a case alternative, using the suggested names where provided.
 Suggested names *must* be provided in left-to-right order matching the order of the alt binders.
 note: right-to-left so type subst aren't undone
 | Rename the variables bound in a case alternative with the given list of suggested names.
 | Rename the specified variables in a case alternative.
 | Rename all identifiers bound in a case alternative.
---------------------------------------------------------------------
 | Rename all identifiers bound in a case expression.
---------------------------------------------------------------------
 | Alpha rename a non-recursive let binder.  Optionally takes a suggested new name.
 | Alpha rename a non-recursive let binder if the variable appears in the argument list.  Optionally takes a suggested new name.
 TODO: Maybe it would be more efficient to rename all the Ids at once, rather than one by one?
 | Rename the specified identifiers in a recursive let, using the suggested names where provided.
 | Rename the specified identifier bound in a recursive let.  Optionally takes a suggested new name.
 | Rename the identifiers bound in a Let with the given list of suggested names.
 | Rename the specified variables bound in a let.
 | Rename all identifiers bound in a Let.
---------------------------------------------------------------------
 | Alpha rename a non-recursive top-level binder.  Optionally takes a suggested new name.
 | Alpha rename a non-recursive top-level binder if the identifier appears in the argument list.  Optionally takes a suggested new name.
 TODO: Maybe it would be more efficient to rename all the Ids at once, rather than one by one?
 | Rename the specified identifiers in a recursive top-level binding at the head of a program, using the suggested names where provided.
 | Rename the specified identifier bound in a recursive top-level binder.  Optionally takes a suggested new name.
 | Rename the identifiers bound in the top-level binding at the head of the program with the given list of suggested names.
 | Rename the specified variables bound in the top-level binding at the head of the program.
 | Rename all identifiers bound in the top-level binding at the head of the program.
---------------------------------------------------------------------
 | Rename all identifiers bound at the top-level.
---------------------------------------------------------------------
 | Alpha rename any bindings at this node.  Note: does not rename case alternatives unless invoked on the alternative.
 TODO: Alpha rewrites need better error messages.  Currently the use of (<+) leads to incorrect error reporting.
---------------------------------------------------------------------
---------------------------------------------------------------------
# LANGUAGE FlexibleContexts #
# LANGUAGE ScopedTypeVariables #

module HERMIT.Dictionary.AlphaConversion
      externals
    , alphaR
    , alphaLamR
    , alphaCaseBinderR
    , alphaAltWithR
    , alphaAltVarsR
    , alphaAltR
    , alphaCaseR
    , alphaLetWithR
    , alphaLetVarsR
    , alphaLetR
    , alphaProgConsWithR
    , alphaProgConsIdsR
    , alphaProgConsR
    , alphaProgR
    , unshadowR
    , unshadowExprR
    , unshadowAltR
    , unshadowProgR
    , visibleVarsT
    , cloneVarAvoidingT
    , freshNameGenAvoiding
    , detectShadowsM
    , replaceVarR
    ) where

import Control.Arrow
import Control.Monad (liftM, liftM2)
import Data.Char (isDigit)
import Data.Function (on)
import Data.List (intersect, delete, elemIndex)
import Data.Maybe (listToMaybe)

import HERMIT.Core
import HERMIT.Context
import HERMIT.Kure
import HERMIT.External
import HERMIT.GHC
import HERMIT.Name
import HERMIT.Utilities(dupsBy)

import HERMIT.Dictionary.GHC hiding (externals)
import HERMIT.Dictionary.Common

import Prelude hiding (exp)


externals :: [External]
externals = map (.+ Deep)
         [  external "alpha" (promoteCoreR alphaR :: RewriteH LCore)
               [ "Renames the bound variables at the current node."]
         ,  external "alpha-lam" (promoteExprR . alphaLamR . Just :: String -> RewriteH LCore)
               [ "Renames the bound variable in a Lambda expression to the given name."]
         ,  external "alpha-lam" (promoteExprR  (alphaLamR Nothing) :: RewriteH LCore)
               [ "Renames the bound variable in a Lambda expression."]
         ,  external "alpha-case-binder" (promoteExprR . alphaCaseBinderR . Just :: String -> RewriteH LCore)
               [ "Renames the binder in a Case expression to the given name."]
         ,  external "alpha-case-binder" (promoteExprR (alphaCaseBinderR Nothing) :: RewriteH LCore)
               [ "Renames the binder in a Case expression."]
         ,  external "alpha-alt" (promoteAltR alphaAltR :: RewriteH LCore)
               [ "Renames all binders in a Case alternative."]
         ,  external "alpha-alt" (promoteAltR . alphaAltWithR :: [String] -> RewriteH LCore)
               [ "Renames all binders in a Case alternative using the user-provided list of new names."]
         ,  external "alpha-case" (promoteExprR alphaCaseR :: RewriteH LCore)
               [ "Renames all binders in a Case alternative."]
         ,  external "alpha-let" (promoteExprR . alphaLetWithR :: [String] -> RewriteH LCore)
               [ "Renames the bound variables in a Let expression using a list of suggested names."]
         ,  external "alpha-let" (promoteExprR alphaLetR :: RewriteH LCore)
               [ "Renames the bound variables in a Let expression."]
         ,  external "alpha-top" (promoteProgR . alphaProgConsWithR :: [String] -> RewriteH LCore)
               [ "Renames the bound identifiers in the top-level binding group at the head of the program using a list of suggested names."]
         ,  external "alpha-top" (promoteProgR alphaProgConsR :: RewriteH LCore)
               [ "Renames the bound identifiers in the top-level binding at the head of the program."]
         ,  external "alpha-prog" (promoteProgR alphaProgR :: RewriteH LCore)
               [ "Rename all top-level identifiers in the program."]
         ,  external "unshadow" (promoteCoreR unshadowR :: RewriteH LCore)
                [ "Rename local variables with manifestly unique names (x, x0, x1, ...)."]
         ]

  freshNameGen is a function used in conjunction with cloneVarH , which clones an existing ' Var ' .
   x   goes to  or x1 or ...
  1 .   Any free variable name in the active  ; or
  2 .   Any bound variables in context .

visibleVarsT :: (BoundVars c, Monad m) => Transform c m CoreTC VarSet
               liftM2 unionVarSet boundVarsT (promoteT $ arr freeVarsCoreTC)

    Otherwise modify the variable name making sure to /not/ clash with the given variables or any visible variables .
cloneVarAvoidingT :: (BoundVars c, MonadUnique m) => Var -> Maybe String -> [Var] -> Transform c m CoreTC Var
cloneVarAvoidingT v mn vs =
  do vvs <- visibleVarsT
     let nameModifier = freshNameGenAvoiding mn (extendVarSetList vvs vs)
     constT (cloneVarH nameModifier v)

freshNameGenAvoiding :: Maybe String -> VarSet -> (String -> String)
freshNameGenAvoiding mn vs str = maybe (inventNames vs str) ((\(c:cs) -> reverse (c:(takeWhile (/='.') cs))) . reverse) mn

inventNames :: VarSet -> String -> String
inventNames curr old = head
                     [ nm
                     | nm <- old : [ base ++ show uq | uq <- [start ..] :: [Int] ]
                     , nm `notElem` names
                     ]
   where
           names = varSetToStrings curr
           nums = reverse $ takeWhile isDigit (reverse old)
           baseLeng = length $ drop (length nums) old
           base = take baseLeng old
           start = case reads nums of
                     [(v,_)] -> v + 1
                     _       -> 0


  | Discard variables from the first set that do not shadow a variable in the second set .
shadowedBy :: VarSet -> VarSet -> VarSet
shadowedBy vs fvs = let fvNames = varSetToStrings fvs
                     in filterVarSet (\ v -> unqualifiedName v `elem` fvNames) vs

detectShadowsM :: Monad m => [Var] -> VarSet -> m VarSet
detectShadowsM bs fvs = let ss = shadowedBy (mkVarSet bs) fvs `extendVarSetList` dupVars bs
                         in do guardMsg (not $ isEmptyVarSet ss) "No shadows detected."
                               return ss

  | Rename local variables with manifestly unique names ( x ,  , x1 , ... ) .
unshadowR :: ( AddBindings c, BoundVars c, ExtendPath c Crumb, HasEmptyContext c
             , ReadPath c Crumb, MonadCatch m, MonadUnique m )
          => Rewrite c m Core
unshadowR = setFailMsg "No shadows to eliminate." $
    anytdR (promoteExprR unshadowExprR <+ promoteAltR unshadowAltR <+ promoteProgR unshadowProgR)

unshadowExprR :: (AddBindings c, BoundVars c, ExtendPath c Crumb, ReadPath c Crumb, MonadCatch m, MonadUnique m)
              => Rewrite c m CoreExpr
unshadowExprR = do
    bs  <- letVarsT <+ (liftM return (caseBinderIdT <+ lamVarT))
    fvs <- liftM2 unionVarSet boundVarsT (arr freeVarsExpr)
    ss  <- detectShadowsM bs fvs
    alphaLamR Nothing <+ alphaLetVarsR (varSetElems ss) <+ alphaCaseBinderR Nothing

unshadowAltR :: (BoundVars c, MonadCatch m, MonadUnique m)
             => Rewrite c m CoreAlt
unshadowAltR = do
    bs  <- arr altVars
    fvs <- liftM2 unionVarSet boundVarsT (arr freeVarsAlt)
    ss  <- detectShadowsM bs fvs
    alphaAltVarsR (varSetElems ss)

unshadowProgR :: (AddBindings c, BoundVars c, ExtendPath c Crumb, ReadPath c Crumb, MonadCatch m, MonadUnique m)
              => Rewrite c m CoreProg
unshadowProgR = do
    bs  <- progConsIdsT
    fvs <- liftM2 unionVarSet boundVarsT (arr freeVarsProg)
    ss  <- detectShadowsM bs fvs
    alphaProgConsIdsR (varSetElems ss)

dupVars :: [Var] -> [Var]
dupVars = dupsBy ((==) `on` unqualifiedName)


  Maybe this should be defined in Dictionary . GHC .

replaceVarR :: (Injection a Core, MonadCatch m) => Var -> Var -> Rewrite c m a
replaceVarR v v' = extractR $ tryR $ substR v $ varToCoreExpr v'

replaceRecBindVarR :: Monad m => Id -> Id -> Rewrite c m CoreBind
replaceRecBindVarR v v' =
   do Rec ies <- idR
      let (is,es) = unzip ies
      case elemIndex v is of
        Nothing -> fail "Specified identifier does not occur in the current recursive binding group."
        Just n  -> let is0       = delete v is
                       (is1,is2) = splitAt n is0
                       is'       = is1 ++ v' : is2
                       es'       = map (substCoreExpr v (Var v')) es
  TODO .   Do we need to initialize the emptySubst with bindFreeVars ?
                       sub       = extendSubst emptySubst v (Var v')
                   in return $ snd $ substBind sub (Rec (zip is' es'))

      emptySub   = mkEmptySubst $ mkInScopeSet $ unionVarSets ( map ( localFreeVarsExpr .  ) is0 )
      sub        = extendSubst emptySub v ( Var v ' )
      ( is1,is2 ) = splitAt n ( snd $ substRecBndrs sub is0 )
      es '        = map ( substCoreExpr v ( Var v ' ) ) es


alphaLamR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
          => Maybe String -> Rewrite c m CoreExpr
alphaLamR mn = setFailMsg (wrongFormForAlpha "Lam v e") $
              do v  <- lamVarT
                 v' <- extractT (cloneVarAvoidingT v mn [v])
                 lamAnyR (return v') (replaceVarR v v')


alphaCaseBinderR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                 => Maybe String -> Rewrite c m CoreExpr
alphaCaseBinderR mn = setFailMsg (wrongFormForAlpha "Case e i ty alts") $
                     do i  <- caseBinderIdT
                        i' <- extractT (cloneVarAvoidingT i mn [i])
                        caseAnyR idR (return i') idR (\ _ -> replaceVarR i i')


alphaAltVarR :: (BoundVars c, MonadCatch m, MonadUnique m)
             => Maybe String -> Var -> Rewrite c m CoreAlt
alphaAltVarR mn v = do
    (con, vs, rhs) <- idR
    v' <- extractT (cloneVarAvoidingT v mn vs)

    case break (==v) vs of
        (bs,_:bs') -> let (con',bs'',rhs') = substCoreAlt v (varToCoreExpr v') (con,bs',rhs)
                       in return (con',bs ++ (v':bs''),rhs')
        _ -> fail "pattern binder not present."

alphaAltVarsWithR :: (BoundVars c, MonadCatch m, MonadUnique m)
                  => [(Maybe String,Var)] -> Rewrite c m CoreAlt

alphaAltWithR :: (BoundVars c, MonadCatch m, MonadUnique m)
              => [String] -> Rewrite c m CoreAlt
alphaAltWithR ns =
  do vs <- arr altVars
     alphaAltVarsWithR $ zip (map Just ns) vs

alphaAltVarsR :: (BoundVars c, MonadCatch m, MonadUnique m)
              => [Var] -> Rewrite c m CoreAlt
alphaAltVarsR vs =
  do bs <- arr altVars
     alphaAltVarsWithR (zip (repeat Nothing) (bs `intersect` vs))

alphaAltR :: (BoundVars c, MonadCatch m, MonadUnique m)
          => Rewrite c m CoreAlt
alphaAltR = arr altVars >>= alphaAltVarsR


alphaCaseR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
           => Rewrite c m CoreExpr
alphaCaseR = alphaCaseBinderR Nothing >+> caseAllR idR idR idR (const alphaAltR)


alphaLetNonRecR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                => Maybe String -> Rewrite c m CoreExpr
alphaLetNonRecR mn = setFailMsg (wrongFormForAlpha "Let (NonRec v e1) e2") $
                    do v  <- letNonRecVarT
                       v' <- extractT (cloneVarAvoidingT v mn [v])
                       letNonRecAnyR (return v') idR (replaceVarR v v')

alphaLetNonRecVarsR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                    => Maybe String -> [Var] -> Rewrite c m CoreExpr
alphaLetNonRecVarsR mn vs = whenM (liftM (`elem` vs) letNonRecVarT) (alphaLetNonRecR mn)



alphaLetRecIdsWithR :: forall c m. ( ExtendPath c Crumb, ReadPath c Crumb, AddBindings c
                                   , BoundVars c, MonadCatch m, MonadUnique m )
                    => [(Maybe String,Id)] -> Rewrite c m CoreExpr
alphaLetRecIdsWithR = andR . map (uncurry alphaLetRecIdR)
  where
    alphaLetRecIdR :: Maybe String -> Id -> Rewrite c m CoreExpr
    alphaLetRecIdR mn i = setFailMsg (wrongFormForAlpha "Let (Rec bs) e") $
                     do is <- letRecIdsT
                        i' <- extractT (cloneVarAvoidingT i mn is)
                        letAnyR (replaceRecBindVarR i i') (replaceVarR i i')


alphaLetWithR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
              => [String] -> Rewrite c m CoreExpr
alphaLetWithR ns = alphaLetNonRecR (listToMaybe ns)
                  <+ (letRecIdsT >>= (alphaLetRecIdsWithR . zip (map Just ns)))

alphaLetVarsR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
              => [Var] -> Rewrite c m CoreExpr
alphaLetVarsR vs = alphaLetNonRecVarsR Nothing vs
                   <+ (do bs <- letT (arr bindVars) successT const
                          alphaLetRecIdsWithR (zip (repeat Nothing) (bs `intersect` vs))
                      )

alphaLetR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
          => Rewrite c m CoreExpr
alphaLetR = letVarsT >>= alphaLetVarsR


alphaProgConsNonRecR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                     => Maybe String -> Rewrite c m CoreProg
alphaProgConsNonRecR mn = setFailMsg (wrongFormForAlpha "ProgCons (NonRec v e) p") $
                    do i <- progConsNonRecIdT
                       guardMsg (not $ isExportedId i) ("Identifier " ++ unqualifiedName i ++ " is exported, and thus cannot be alpha-renamed.")
                       i' <- extractT (cloneVarAvoidingT i mn [i])
                       consNonRecAnyR (return i') idR (replaceVarR i i')

alphaProgConsNonRecIdsR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                        => Maybe String -> [Id] -> Rewrite c m CoreProg
alphaProgConsNonRecIdsR mn is = whenM (liftM (`elem` is) progConsNonRecIdT) (alphaProgConsNonRecR mn)


alphaProgConsRecIdsWithR :: forall c m. ( ExtendPath c Crumb, ReadPath c Crumb, AddBindings c
                                        , BoundVars c, MonadCatch m, MonadUnique m )
                         => [(Maybe String,Id)] -> Rewrite c m CoreProg
alphaProgConsRecIdsWithR = andR . map (uncurry alphaProgConsRecIdR) . filter (not . isExportedId . snd)
  where
    alphaProgConsRecIdR :: Maybe String -> Id -> Rewrite c m CoreProg
    alphaProgConsRecIdR mn i =  setFailMsg (wrongFormForAlpha "ProgCons (Rec bs) p") $
                      do is <- progConsRecIdsT
                         i' <- extractT (cloneVarAvoidingT i mn is)
                         progConsAnyR (replaceRecBindVarR i i') (replaceVarR i i')


alphaProgConsWithR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                   => [String] -> Rewrite c m CoreProg
alphaProgConsWithR ns = alphaProgConsNonRecR (listToMaybe ns)
                        <+ (progConsRecIdsT >>= (alphaProgConsRecIdsWithR . zip (map Just ns)))

alphaProgConsIdsR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
                  => [Id] -> Rewrite c m CoreProg
alphaProgConsIdsR vs = alphaProgConsNonRecIdsR Nothing vs
                       <+ (do bs <- progConsT (arr bindVars) successT const
                              alphaProgConsRecIdsWithR (zip (repeat Nothing) (bs `intersect` vs))
                          )

alphaProgConsR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
               => Rewrite c m CoreProg
alphaProgConsR = progConsIdsT >>= alphaProgConsIdsR


alphaProgR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
           => Rewrite c m CoreProg
alphaProgR = alphaProgConsR >+> progConsAllR idR alphaProgR


alphaR :: (ExtendPath c Crumb, ReadPath c Crumb, AddBindings c, BoundVars c, MonadCatch m, MonadUnique m)
       => Rewrite c m Core
alphaR = setFailMsg "Cannot alpha-rename here." $
           promoteExprR (alphaLamR Nothing <+ alphaCaseBinderR Nothing <+ alphaLetR)
        <+ promoteAltR alphaAltR
        <+ promoteProgR alphaProgConsR

        Though really , we first need to improve KURE to have a version of ( < + ) that maintains the existing error message in the case of non - matching constructors henceforth .

  TODO 2 : Also , we should be able to rename inside types and coercions .

  TODO 3 : Also , we should be able to rename lemma quantifiers


wrongFormForAlpha :: String -> String
wrongFormForAlpha s = "Cannot alpha-rename, " ++ wrongExprForm s

