    {-
    (c) The GRASP/AQUA Project, Glasgow University, 1992-1998

    \section[CoreRules]{Transformation rules}
    -}

    {-# LANGUAGE CPP #-}

    -- | Functions for collecting together and applying rewrite rules to a module.
    -- The 'CoreRule' datatype itself is declared elsewhere.
    module Rules (
            -- * RuleBase
            RuleBase,

            -- ** Constructing
            emptyRuleBase, mkRuleBase, extendRuleBaseList,
            unionRuleBase, pprRuleBase,

            -- ** Checking rule applications
            ruleCheckProgram,

            -- ** Manipulating 'SpecInfo' rules
            mkSpecInfo, extendSpecInfo, addSpecInfo,
            addIdSpecialisations,

            -- * Misc. CoreRule helpers
            rulesOfBinds, getRules, pprRulesForUser,

            lookupRule, mkRule, roughTopNames
        ) where

    #include "HsVersions.h"

    import CoreSyn          -- All of it
    import CoreSubst
    import OccurAnal        ( occurAnalyseExpr )
    import CoreFVs          ( exprFreeVars, exprsFreeVars, bindFreeVars, rulesFreeVars )
    import CoreUtils        ( exprType, eqExpr, mkTick, mkTicks,
                              stripTicksTopT, stripTicksTopE )
    import PprCore          ( pprRules )
    import Type             ( Type )
    import TcType           ( tcSplitTyConApp_maybe )
    import Coercion
    import CoreTidy         ( tidyRules )
    import Id
    import IdInfo           ( SpecInfo( SpecInfo ) )
    import VarEnv
    import VarSet
    import Name             ( Name, NamedThing(..) )
    import NameEnv
    import Unify            ( ruleMatchTyX, MatchEnv(..) )
    import BasicTypes       ( Activation, CompilerPhase, isActive )
    import StaticFlags      ( opt_PprStyle_Debug )
    import DynFlags         ( DynFlags )
    import Outputable
    import FastString
    import Maybes
    import Bag
    import Util
    import Data.List
    import Data.Ord

    {-
    Note [Overall plumbing for rules]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    * After the desugarer:
       - The ModGuts initially contains mg_rules :: [CoreRule] of
         locally-declared rules for imported Ids.
       - Locally-declared rules for locally-declared Ids are attached to
         the IdInfo for that Id.  See Note [Attach rules to local ids] in
         DsBinds

    * TidyPgm strips off all the rules from local Ids and adds them to
      mg_rules, so that the ModGuts has *all* the locally-declared rules.

    * The HomePackageTable contains a ModDetails for each home package
      module.  Each contains md_rules :: [CoreRule] of rules declared in
      that module.  The HomePackageTable grows as ghc --make does its
      up-sweep.  In batch mode (ghc -c), the HPT is empty; all imported modules
      are treated by the "external" route, discussed next, regardless of
      which package they come from.

    * The ExternalPackageState has a single eps_rule_base :: RuleBase for
      Ids in other packages.  This RuleBase simply grow monotonically, as
      ghc --make compiles one module after another.

      During simplification, interface files may get demand-loaded,
      as the simplifier explores the unfoldings for Ids it has in
      its hand.  (Via an unsafePerformIO; the EPS is really a cache.)
      That in turn may make the EPS rule-base grow.  In contrast, the
      HPT never grows in this way.

    * The result of all this is that during Core-to-Core optimisation
      there are four sources of rules:

        (a) Rules in the IdInfo of the Id they are a rule for.  These are
            easy: fast to look up, and if you apply a substitution then
            it'll be applied to the IdInfo as a matter of course.

        (b) Rules declared in this module for imported Ids, kept in the
            ModGuts. If you do a substitution, you'd better apply the
            substitution to these.  There are seldom many of these.

        (c) Rules declared in the HomePackageTable.  These never change.

        (d) Rules in the ExternalPackageTable. These can grow in response
            to lazy demand-loading of interfaces.

    * At the moment (c) is carried in a reader-monad way by the CoreMonad.
      The HomePackageTable doesn't have a single RuleBase because technically
      we should only be able to "see" rules "below" this module; so we
      generate a RuleBase for (c) by combing rules from all the modules
      "below" us.  That's why we can't just select the home-package RuleBase
      from HscEnv.

      [NB: we are inconsistent here.  We should do the same for external
      packages, but we don't.  Same for type-class instances.]

    * So in the outer simplifier loop, we combine (b-d) into a single
      RuleBase, reading
         (b) from the ModGuts,
         (c) from the CoreMonad, and
         (d) from its mutable variable
      [Of coures this means that we won't see new EPS rules that come in
      during a single simplifier iteration, but that probably does not
      matter.]

    ************************************************************************
    *                                                                      *
    \subsection[specialisation-IdInfo]{Specialisation info about an @Id@}
    *                                                                      *
    ************************************************************************

    A @CoreRule@ holds details of one rule for an @Id@, which
    includes its specialisations.

    For example, if a rule for @f@ contains the mapping:
    \begin{verbatim}
            forall a b d. [Type (List a), Type b, Var d]  ===>  f' a b
    \end{verbatim}
    then when we find an application of f to matching types, we simply replace
    it by the matching RHS:
    \begin{verbatim}
            f (List Int) Bool dict ===>  f' Int Bool
    \end{verbatim}
    All the stuff about how many dictionaries to discard, and what types
    to apply the specialised function to, are handled by the fact that the
    Rule contains a template for the result of the specialisation.

    There is one more exciting case, which is dealt with in exactly the same
    way.  If the specialised value is unboxed then it is lifted at its
    definition site and unlifted at its uses.  For example:

            pi :: forall a. Num a => a

    might have a specialisation

            [Int#] ===>  (case pi' of Lift pi# -> pi#)

    where pi' :: Lift Int# is the specialised version of pi.
    -}

    mkRule :: Bool -> Bool -> RuleName -> Activation
           -> Name -> [CoreBndr] -> [CoreExpr] -> CoreExpr -> CoreRule
    -- ^ Used to make 'CoreRule' for an 'Id' defined in the module being
    -- compiled. See also 'CoreSyn.CoreRule'
    mkRule is_auto is_local name act fn bndrs args rhs
      = Rule { ru_name = name, ru_fn = fn, ru_act = act,
               ru_bndrs = bndrs, ru_args = args,
               ru_rhs = occurAnalyseExpr rhs,
               ru_rough = roughTopNames args,
               ru_auto = is_auto, ru_local = is_local }

    --------------
    roughTopNames :: [CoreExpr] -> [Maybe Name]
    -- ^ Find the \"top\" free names of several expressions.
    -- Such names are either:
    --
    -- 1. The function finally being applied to in an application chain
    --    (if that name is a GlobalId: see "Var#globalvslocal"), or
    --
    -- 2. The 'TyCon' if the expression is a 'Type'
    --
    -- This is used for the fast-match-check for rules;
    --      if the top names don't match, the rest can't
    roughTopNames args = map roughTopName args

    roughTopName :: CoreExpr -> Maybe Name
    roughTopName (Type ty) = case tcSplitTyConApp_maybe ty of
                                   Just (tc,_) -> Just (getName tc)
                                   Nothing     -> Nothing
    roughTopName (Coercion _) = Nothing
    roughTopName (App f _) = roughTopName f
    roughTopName (Var f)   | isGlobalId f   -- Note [Care with roughTopName]
                           , isDataConWorkId f || idArity f > 0
                           = Just (idName f)
    roughTopName (Tick t e) | tickishFloatable t
                            = roughTopName e
    roughTopName _ = Nothing

    ruleCantMatch :: [Maybe Name] -> [Maybe Name] -> Bool
    -- ^ @ruleCantMatch tpl actual@ returns True only if @actual@
    -- definitely can't match @tpl@ by instantiating @tpl@.
    -- It's only a one-way match; unlike instance matching we
    -- don't consider unification.
    --
    -- Notice that [_$_]
    --      @ruleCantMatch [Nothing] [Just n2] = False@
    --      Reason: a template variable can be instantiated by a constant
    -- Also:
    --      @ruleCantMatch [Just n1] [Nothing] = False@
    --      Reason: a local variable @v@ in the actuals might [_$_]

    ruleCantMatch (Just n1 : ts) (Just n2 : as) = n1 /= n2 || ruleCantMatch ts as
    ruleCantMatch (_       : ts) (_       : as) = ruleCantMatch ts as
    ruleCantMatch _              _              = False

    {-
    Note [Care with roughTopName]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider this
        module M where { x = a:b }
        module N where { ...f x...
                         RULE f (p:q) = ... }
    You'd expect the rule to match, because the matcher can
    look through the unfolding of 'x'.  So we must avoid roughTopName
    returning 'M.x' for the call (f x), or else it'll say "can't match"
    and we won't even try!!

    However, suppose we have
             RULE g (M.h x) = ...
             foo = ...(g (M.k v))....
    where k is a *function* exported by M.  We never really match
    functions (lambdas) except by name, so in this case it seems like
    a good idea to treat 'M.k' as a roughTopName of the call.
    -}

    pprRulesForUser :: [CoreRule] -> SDoc
    -- (a) tidy the rules
    -- (b) sort them into order based on the rule name
    -- (c) suppress uniques (unless -dppr-debug is on)
    -- This combination makes the output stable so we can use in testing
    -- It's here rather than in PprCore because it calls tidyRules
    pprRulesForUser rules
      = withPprStyle defaultUserStyle $
        pprRules $
        sortBy (comparing ru_name) $
        tidyRules emptyTidyEnv rules

    {-
    ************************************************************************
    *                                                                      *
                    SpecInfo: the rules in an IdInfo
    *                                                                      *
    ************************************************************************
    -}

    -- | Make a 'SpecInfo' containing a number of 'CoreRule's, suitable
    -- for putting into an 'IdInfo'
    mkSpecInfo :: [CoreRule] -> SpecInfo
    mkSpecInfo rules = SpecInfo rules (rulesFreeVars rules)

    extendSpecInfo :: SpecInfo -> [CoreRule] -> SpecInfo
    extendSpecInfo (SpecInfo rs1 fvs1) rs2
      = SpecInfo (rs2 ++ rs1) (rulesFreeVars rs2 `unionVarSet` fvs1)

    addSpecInfo :: SpecInfo -> SpecInfo -> SpecInfo
    addSpecInfo (SpecInfo rs1 fvs1) (SpecInfo rs2 fvs2)
      = SpecInfo (rs1 ++ rs2) (fvs1 `unionVarSet` fvs2)

    addIdSpecialisations :: Id -> [CoreRule] -> Id
    addIdSpecialisations id []
      = id
    addIdSpecialisations id rules
      = setIdSpecialisation id $
        extendSpecInfo (idSpecialisation id) rules

    -- | Gather all the rules for locally bound identifiers from the supplied bindings
    rulesOfBinds :: [CoreBind] -> [CoreRule]
    rulesOfBinds binds = concatMap (concatMap idCoreRules . bindersOf) binds

    getRules :: RuleBase -> Id -> [CoreRule]
    -- See Note [Where rules are found]
    getRules rule_base fn
      = idCoreRules fn ++ imp_rules
      where
        imp_rules = lookupNameEnv rule_base (idName fn) `orElse` []

    {-
    Note [Where rules are found]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The rules for an Id come from two places:
      (a) the ones it is born with, stored inside the Id iself (idCoreRules fn),
      (b) rules added in other modules, stored in the global RuleBase (imp_rules)

    It's tempting to think that
         - LocalIds have only (a)
         - non-LocalIds have only (b)

    but that isn't quite right:

         - PrimOps and ClassOps are born with a bunch of rules inside the Id,
           even when they are imported

         - The rules in PrelRules.builtinRules should be active even
           in the module defining the Id (when it's a LocalId), but
           the rules are kept in the global RuleBase

    ************************************************************************
    *                                                                      *
                    RuleBase
    *                                                                      *
    ************************************************************************
    -}

    -- | Gathers a collection of 'CoreRule's. Maps (the name of) an 'Id' to its rules
    type RuleBase = NameEnv [CoreRule]
            -- The rules are are unordered;
            -- we sort out any overlaps on lookup

    emptyRuleBase :: RuleBase
    emptyRuleBase = emptyNameEnv

    mkRuleBase :: [CoreRule] -> RuleBase
    mkRuleBase rules = extendRuleBaseList emptyRuleBase rules

    extendRuleBaseList :: RuleBase -> [CoreRule] -> RuleBase
    extendRuleBaseList rule_base new_guys
      = foldl extendRuleBase rule_base new_guys

    unionRuleBase :: RuleBase -> RuleBase -> RuleBase
    unionRuleBase rb1 rb2 = plusNameEnv_C (++) rb1 rb2

    extendRuleBase :: RuleBase -> CoreRule -> RuleBase
    extendRuleBase rule_base rule
      = extendNameEnv_Acc (:) singleton rule_base (ruleIdName rule) rule

    pprRuleBase :: RuleBase -> SDoc
    pprRuleBase rules = vcat [ pprRules (tidyRules emptyTidyEnv rs)
                             | rs <- nameEnvElts rules ]

    {-
    ************************************************************************
    *                                                                      *
                            Matching
    *                                                                      *
    ************************************************************************
    -}

    -- | The main rule matching function. Attempts to apply all (active)
    -- supplied rules to this instance of an application in a given
    -- context, returning the rule applied and the resulting expression if
    -- successful.
    lookupRule :: DynFlags -> InScopeEnv
               -> (Activation -> Bool)      -- When rule is active
               -> Id -> [CoreExpr]
               -> [CoreRule] -> Maybe (CoreRule, CoreExpr)

    -- See Note [Extra args in rule matching]
    -- See comments on matchRule
    lookupRule dflags in_scope is_active fn args rules
      = -- pprTrace "matchRules" (ppr fn <+> ppr args $$ ppr rules ) $
        case go [] rules of
            []     -> Nothing
            (m:ms) -> Just (findBest (fn,args') m ms)
      where
        rough_args = map roughTopName args

        -- Strip ticks from arguments, see note [Tick annotations in RULE
        -- matching]. We only collect ticks if a rule actually matches -
        -- this matters for performance tests.
        args' = map (stripTicksTopE tickishFloatable) args
        ticks = concatMap (stripTicksTopT tickishFloatable) args

        go :: [(CoreRule,CoreExpr)] -> [CoreRule] -> [(CoreRule,CoreExpr)]
        go ms [] = ms
        go ms (r:rs)
          | Just e <- matchRule dflags in_scope is_active fn args' rough_args r
          = go ((r,mkTicks ticks e):ms) rs
          | otherwise
          = -- pprTrace "match failed" (ppr r $$ ppr args $$
            --   ppr [ (arg_id, unfoldingTemplate unf)
            --       | Var arg_id <- args
            --       , let unf = idUnfolding arg_id
            --       , isCheapUnfolding unf] )
            go ms rs

    findBest :: (Id, [CoreExpr])
             -> (CoreRule,CoreExpr) -> [(CoreRule,CoreExpr)] -> (CoreRule,CoreExpr)
    -- All these pairs matched the expression
    -- Return the pair the the most specific rule
    -- The (fn,args) is just for overlap reporting

    findBest _      (rule,ans)   [] = (rule,ans)
    findBest target (rule1,ans1) ((rule2,ans2):prs)
      | rule1 `isMoreSpecific` rule2 = findBest target (rule1,ans1) prs
      | rule2 `isMoreSpecific` rule1 = findBest target (rule2,ans2) prs
      | debugIsOn = let pp_rule rule
                            | opt_PprStyle_Debug = ppr rule
                            | otherwise          = doubleQuotes (ftext (ru_name rule))
                    in pprTrace "Rules.findBest: rule overlap (Rule 1 wins)"
                             (vcat [if opt_PprStyle_Debug then
                                       ptext (sLit "Expression to match:") <+> ppr fn <+> sep (map ppr args)
                                    else empty,
                                    ptext (sLit "Rule 1:") <+> pp_rule rule1,
                                    ptext (sLit "Rule 2:") <+> pp_rule rule2]) $
                    findBest target (rule1,ans1) prs
      | otherwise = findBest target (rule1,ans1) prs
      where
        (fn,args) = target

    isMoreSpecific :: CoreRule -> CoreRule -> Bool
    -- This tests if one rule is more specific than another
    -- We take the view that a BuiltinRule is less specific than
    -- anything else, because we want user-define rules to "win"
    -- In particular, class ops have a built-in rule, but we
    -- any user-specific rules to win
    --   eg (Trac #4397)
    --      truncate :: (RealFrac a, Integral b) => a -> b
    --      {-# RULES "truncate/Double->Int" truncate = double2Int #-}
    --      double2Int :: Double -> Int
    --   We want the specific RULE to beat the built-in class-op rule
    isMoreSpecific (BuiltinRule {}) _                = False
    isMoreSpecific (Rule {})        (BuiltinRule {}) = True
    isMoreSpecific (Rule { ru_bndrs = bndrs1, ru_args = args1 })
                   (Rule { ru_bndrs = bndrs2, ru_args = args2 })
      = isJust (matchN (in_scope, id_unfolding_fun) bndrs2 args2 args1)
      where
       id_unfolding_fun _ = NoUnfolding     -- Don't expand in templates
       in_scope = mkInScopeSet (mkVarSet bndrs1)
            -- Actually we should probably include the free vars
            -- of rule1's args, but I can't be bothered

    noBlackList :: Activation -> Bool
    noBlackList _ = False           -- Nothing is black listed

    {-
    Note [Extra args in rule matching]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    If we find a matching rule, we return (Just (rule, rhs)),
    but the rule firing has only consumed as many of the input args
    as the ruleArity says.  It's up to the caller to keep track
    of any left-over args.  E.g. if you call
            lookupRule ... f [e1, e2, e3]
    and it returns Just (r, rhs), where r has ruleArity 2
    then the real rewrite is
            f e1 e2 e3 ==> rhs e3

    You might think it'd be cleaner for lookupRule to deal with the
    leftover arguments, by applying 'rhs' to them, but the main call
    in the Simplifier works better as it is.  Reason: the 'args' passed
    to lookupRule are the result of a lazy substitution
    -}

    ------------------------------------
    matchRule :: DynFlags -> InScopeEnv -> (Activation -> Bool)
              -> Id -> [CoreExpr] -> [Maybe Name]
              -> CoreRule -> Maybe CoreExpr

    -- If (matchRule rule args) returns Just (name,rhs)
    -- then (f args) matches the rule, and the corresponding
    -- rewritten RHS is rhs
    --
    -- The bndrs and rhs is occurrence-analysed
    --
    --      Example
    --
    -- The rule
    --      forall f g x. map f (map g x) ==> map (f . g) x
    -- is stored
    --      CoreRule "map/map"
    --               [f,g,x]                -- tpl_vars
    --               [f,map g x]            -- tpl_args
    --               map (f.g) x)           -- rhs
    --
    -- Then the call: matchRule the_rule [e1,map e2 e3]
    --        = Just ("map/map", (\f,g,x -> rhs) e1 e2 e3)
    --
    -- Any 'surplus' arguments in the input are simply put on the end
    -- of the output.

    matchRule dflags rule_env _is_active fn args _rough_args
              (BuiltinRule { ru_try = match_fn })
    -- Built-in rules can't be switched off, it seems
      = case match_fn dflags rule_env fn args of
            Just expr -> Just expr
            Nothing   -> Nothing

    matchRule _ in_scope is_active _ args rough_args
              (Rule { ru_act = act, ru_rough = tpl_tops
                    , ru_bndrs = tpl_vars, ru_args = tpl_args
                    , ru_rhs = rhs })
      | not (is_active act)               = Nothing
      | ruleCantMatch tpl_tops rough_args = Nothing
      | otherwise
      = case matchN in_scope tpl_vars tpl_args args of
            Nothing                        -> Nothing
            Just (bind_wrapper, tpl_vals) -> Just (bind_wrapper $
                                                   rule_fn `mkApps` tpl_vals)
      where
        rule_fn = occurAnalyseExpr (mkLams tpl_vars rhs)
            -- We could do this when putting things into the rulebase, I guess

    ---------------------------------------
    matchN  :: InScopeEnv
            -> [Var]                -- ^ Match template type variables
            -> [CoreExpr]           -- ^ Match template
            -> [CoreExpr]           -- ^ Target; can have more elements than the template
            -> Maybe (BindWrapper,  -- Floated bindings; see Note [Matching lets]
                      [CoreExpr])
    -- For a given match template and context, find bindings to wrap around
    -- the entire result and what should be substituted for each template variable.
    -- Fail if there are two few actual arguments from the target to match the template

    matchN (in_scope, id_unf) tmpl_vars tmpl_es target_es
      = do  { subst <- go init_menv emptyRuleSubst tmpl_es target_es
            ; return (rs_binds subst,
                      map (lookup_tmpl subst) tmpl_vars') }
      where
        (init_rn_env, tmpl_vars') = mapAccumL rnBndrL (mkRnEnv2 in_scope) tmpl_vars
            -- See Note [Template binders]

        init_menv = RV { rv_tmpls = mkVarSet tmpl_vars', rv_lcl = init_rn_env
                       , rv_fltR = mkEmptySubst (rnInScopeSet init_rn_env)
                       , rv_unf = id_unf }

        go _    subst []     _      = Just subst
        go _    _     _      []     = Nothing       -- Fail if too few actual args
        go menv subst (t:ts) (e:es) = do { subst1 <- match menv subst t e
                                         ; go menv subst1 ts es }

        lookup_tmpl :: RuleSubst -> Var -> CoreExpr
        lookup_tmpl (RS { rs_tv_subst = tv_subst, rs_id_subst = id_subst }) tmpl_var'
            | isId tmpl_var' = case lookupVarEnv id_subst tmpl_var' of
                                 Just e -> e
                                 _      -> unbound tmpl_var'
            | otherwise      = case lookupVarEnv tv_subst tmpl_var' of
                                 Just ty -> Type ty
                                 Nothing -> unbound tmpl_var'

        unbound var = pprPanic "Template variable unbound in rewrite rule"
                            (ppr var $$ ppr tmpl_vars $$ ppr tmpl_vars' $$ ppr tmpl_es $$ ppr target_es)

    {-
    Note [Template binders]
    ~~~~~~~~~~~~~~~~~~~~~~~
    Consider the following match:
            Template:  forall x.  f x
            Target:     f (x+1)
    This should succeed, because the template variable 'x' has
    nothing to do with the 'x' in the target.

    On reflection, this case probably does just work, but this might not
            Template:  forall x. f (\x.x)
            Target:    f (\y.y)
    Here we want to clone when we find the \x, but to know that x must be in scope

    To achive this, we use rnBndrL to rename the template variables if
    necessary; the renamed ones are the tmpl_vars'

    ************************************************************************
    *                                                                      *
                       The main matcher
    *                                                                      *
    ************************************************************************

            ---------------------------------------------
                    The inner workings of matching
            ---------------------------------------------
    -}

    -- * The domain of the TvSubstEnv and IdSubstEnv are the template
    --   variables passed into the match.
    --
    -- * The BindWrapper in a RuleSubst are the bindings floated out
    --   from nested matches; see the Let case of match, below
    --
    data RuleMatchEnv
      = RV { rv_tmpls :: VarSet          -- Template variables
           , rv_lcl   :: RnEnv2          -- Renamings for *local bindings*
                                         --   (lambda/case)
           , rv_fltR  :: Subst           -- Renamings for floated let-bindings
                                         --   domain disjoint from envR of rv_lcl
                                         -- See Note [Matching lets]
           , rv_unf :: IdUnfoldingFun
           }

    rvInScopeEnv :: RuleMatchEnv -> InScopeEnv
    rvInScopeEnv renv = (rnInScopeSet (rv_lcl renv), rv_unf renv)

    data RuleSubst = RS { rs_tv_subst :: TvSubstEnv      -- Range is the
                        , rs_id_subst :: IdEnv CoreExpr  --   template variables
                        , rs_binds    :: BindWrapper     -- Floated bindings
                        , rs_bndrs    :: VarSet          -- Variables bound by floated lets
                        }

    type BindWrapper = CoreExpr -> CoreExpr
      -- See Notes [Matching lets] and [Matching cases]
      -- we represent the floated bindings as a core-to-core function

    emptyRuleSubst :: RuleSubst
    emptyRuleSubst = RS { rs_tv_subst = emptyVarEnv, rs_id_subst = emptyVarEnv
                        , rs_binds = \e -> e, rs_bndrs = emptyVarSet }

    --      At one stage I tried to match even if there are more
    --      template args than real args.

    --      I now think this is probably a bad idea.
    --      Should the template (map f xs) match (map g)?  I think not.
    --      For a start, in general eta expansion wastes work.
    --      SLPJ July 99

    match :: RuleMatchEnv
          -> RuleSubst
          -> CoreExpr               -- Template
          -> CoreExpr               -- Target
          -> Maybe RuleSubst

    -- We look through certain ticks. See note [Tick annotations in RULE matching]
    match renv subst e1 (Tick t e2)
      | tickishFloatable t
      = match renv subst' e1 e2
      where subst' = subst { rs_binds = rs_binds subst . mkTick t }
    match _ _ e@Tick{} _
      = pprPanic "Tick in rule" (ppr e)

    -- See the notes with Unify.match, which matches types
    -- Everything is very similar for terms

    -- Interesting examples:
    -- Consider matching
    --      \x->f      against    \f->f
    -- When we meet the lambdas we must remember to rename f to f' in the
    -- second expresion.  The RnEnv2 does that.
    --
    -- Consider matching
    --      forall a. \b->b    against   \a->3
    -- We must rename the \a.  Otherwise when we meet the lambdas we
    -- might substitute [a/b] in the template, and then erroneously
    -- succeed in matching what looks like the template variable 'a' against 3.

    -- The Var case follows closely what happens in Unify.match
    match renv subst (Var v1)    e2 = match_var renv subst v1 e2

    match renv subst e1 (Var v2)      -- Note [Expanding variables]
      | not (inRnEnvR rn_env v2) -- Note [Do not expand locally-bound variables]
      , Just e2' <- expandUnfolding_maybe (rv_unf renv v2')
      = match (renv { rv_lcl = nukeRnEnvR rn_env }) subst e1 e2'
      where
        v2'    = lookupRnInScope rn_env v2
        rn_env = rv_lcl renv
            -- Notice that we look up v2 in the in-scope set
            -- See Note [Lookup in-scope]
            -- No need to apply any renaming first (hence no rnOccR)
            -- because of the not-inRnEnvR

    match renv subst e1 (Let bind e2)
      | -- pprTrace "match:Let" (vcat [ppr bind, ppr $ okToFloat (rv_lcl renv) (bindFreeVars bind)]) $
        okToFloat (rv_lcl renv) (bindFreeVars bind)        -- See Note [Matching lets]
      = match (renv { rv_fltR = flt_subst' })
              (subst { rs_binds = rs_binds subst . Let bind'
                     , rs_bndrs = extendVarSetList (rs_bndrs subst) new_bndrs })
              e1 e2
      where
        flt_subst = addInScopeSet (rv_fltR renv) (rs_bndrs subst)
        (flt_subst', bind') = substBind flt_subst bind
        new_bndrs = bindersOf bind'

    {- Disabled: see Note [Matching cases] below
    match renv (tv_subst, id_subst, binds) e1
          (Case scrut case_bndr ty [(con, alt_bndrs, rhs)])
      | exprOkForSpeculation scrut  -- See Note [Matching cases]
      , okToFloat rn_env bndrs (exprFreeVars scrut)
      = match (renv { me_env = rn_env' })
              (tv_subst, id_subst, binds . case_wrap)
              e1 rhs
      where
        rn_env   = me_env renv
        rn_env'  = extendRnInScopeList rn_env bndrs
        bndrs    = case_bndr : alt_bndrs
        case_wrap rhs' = Case scrut case_bndr ty [(con, alt_bndrs, rhs')]
    -}

    match _ subst (Lit lit1) (Lit lit2)
      | lit1 == lit2
      = Just subst

    match renv subst (App f1 a1) (App f2 a2)
      = do  { subst' <- match renv subst f1 f2
            ; match renv subst' a1 a2 }

    match renv subst (Lam x1 e1) e2
      | Just (x2, e2, ts) <- exprIsLambda_maybe (rvInScopeEnv renv) e2
      = let renv' = renv { rv_lcl = rnBndr2 (rv_lcl renv) x1 x2
                         , rv_fltR = delBndr (rv_fltR renv) x2 }
            subst' = subst { rs_binds = rs_binds subst . flip (foldr mkTick) ts }
        in  match renv' subst' e1 e2

    match renv subst (Case e1 x1 ty1 alts1) (Case e2 x2 ty2 alts2)
      = do  { subst1 <- match_ty renv subst ty1 ty2
            ; subst2 <- match renv subst1 e1 e2
            ; let renv' = rnMatchBndr2 renv subst x1 x2
            ; match_alts renv' subst2 alts1 alts2   -- Alts are both sorted
            }

    match renv subst (Type ty1) (Type ty2)
      = match_ty renv subst ty1 ty2
    match renv subst (Coercion co1) (Coercion co2)
      = match_co renv subst co1 co2

    match renv subst (Cast e1 co1) (Cast e2 co2)
      = do  { subst1 <- match_co renv subst co1 co2
            ; match renv subst1 e1 e2 }

    -- Everything else fails
    match _ _ _e1 _e2 = -- pprTrace "Failing at" ((text "e1:" <+> ppr _e1) $$ (text "e2:" <+> ppr _e2)) $
                        Nothing

    -------------
    match_co :: RuleMatchEnv
             -> RuleSubst
             -> Coercion
             -> Coercion
             -> Maybe RuleSubst
    match_co renv subst (CoVarCo cv) co
      = match_var renv subst cv (Coercion co)
    match_co renv subst (Refl r1 ty1) co
      = case co of
           Refl r2 ty2
             | r1 == r2 -> match_ty renv subst ty1 ty2
           _            -> Nothing
    match_co renv subst (TyConAppCo r1 tc1 cos1) co2
      = case co2 of
           TyConAppCo r2 tc2 cos2
             | r1 == r2 && tc1 == tc2
             -> match_cos renv subst cos1 cos2
           _ -> Nothing
    match_co _ _ _co1 _co2
        -- Currently just deals with CoVarCo, TyConAppCo and Refl
    #ifdef DEBUG
      = pprTrace "match_co: needs more cases" (ppr _co1 $$ ppr _co2) Nothing
    #else
      = Nothing
    #endif

    match_cos :: RuleMatchEnv
             -> RuleSubst
             -> [Coercion]
             -> [Coercion]
             -> Maybe RuleSubst
    match_cos renv subst (co1:cos1) (co2:cos2) =
        case match_co renv subst co1 co2 of
           Just subst' -> match_cos renv subst' cos1 cos2
           Nothing -> Nothing
    match_cos _ subst [] [] = Just subst
    match_cos _ _ cos1 cos2 = pprTrace "match_cos: not same length" (ppr cos1 $$ ppr cos2) Nothing

    -------------
    rnMatchBndr2 :: RuleMatchEnv -> RuleSubst -> Var -> Var -> RuleMatchEnv
    rnMatchBndr2 renv subst x1 x2
      = renv { rv_lcl  = rnBndr2 rn_env x1 x2
             , rv_fltR = delBndr (rv_fltR renv) x2 }
      where
        rn_env = addRnInScopeSet (rv_lcl renv) (rs_bndrs subst)
        -- Typically this is a no-op, but it may matter if
        -- there are some floated let-bindings

    ------------------------------------------
    match_alts :: RuleMatchEnv
               -> RuleSubst
               -> [CoreAlt]         -- Template
               -> [CoreAlt]         -- Target
               -> Maybe RuleSubst
    match_alts _ subst [] []
      = return subst
    match_alts renv subst ((c1,vs1,r1):alts1) ((c2,vs2,r2):alts2)
      | c1 == c2
      = do  { subst1 <- match renv' subst r1 r2
            ; match_alts renv subst1 alts1 alts2 }
      where
        renv' = foldl mb renv (vs1 `zip` vs2)
        mb renv (v1,v2) = rnMatchBndr2 renv subst v1 v2

    match_alts _ _ _ _
      = Nothing

    ------------------------------------------
    okToFloat :: RnEnv2 -> VarSet -> Bool
    okToFloat rn_env bind_fvs
      = foldVarSet ((&&) . not_captured) True bind_fvs
      where
        not_captured fv = not (inRnEnvR rn_env fv)

    ------------------------------------------
    match_var :: RuleMatchEnv
              -> RuleSubst
              -> Var                -- Template
              -> CoreExpr        -- Target
              -> Maybe RuleSubst
    match_var renv@(RV { rv_tmpls = tmpls, rv_lcl = rn_env, rv_fltR = flt_env })
              subst v1 e2
      | v1' `elemVarSet` tmpls
      = match_tmpl_var renv subst v1' e2

      | otherwise   -- v1' is not a template variable; check for an exact match with e2
      = case e2 of  -- Remember, envR of rn_env is disjoint from rv_fltR
           Var v2 | v1' == rnOccR rn_env v2
                  -> Just subst

                  | Var v2' <- lookupIdSubst (text "match_var") flt_env v2
                  , v1' == v2'
                  -> Just subst

           _ -> Nothing

      where
        v1' = rnOccL rn_env v1
            -- If the template is
            --      forall x. f x (\x -> x) = ...
            -- Then the x inside the lambda isn't the
            -- template x, so we must rename first!

    ------------------------------------------
    match_tmpl_var :: RuleMatchEnv
                   -> RuleSubst
                   -> Var                -- Template
                   -> CoreExpr              -- Target
                   -> Maybe RuleSubst

    match_tmpl_var renv@(RV { rv_lcl = rn_env, rv_fltR = flt_env })
                   subst@(RS { rs_id_subst = id_subst, rs_bndrs = let_bndrs })
                   v1' e2
      | any (inRnEnvR rn_env) (varSetElems (exprFreeVars e2))
      = Nothing     -- Occurs check failure
                    -- e.g. match forall a. (\x-> a x) against (\y. y y)

      | Just e1' <- lookupVarEnv id_subst v1'
      = if eqExpr (rnInScopeSet rn_env) e1' e2'
        then Just subst
        else Nothing

      | otherwise
      =             -- Note [Matching variable types]
                    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
                    -- However, we must match the *types*; e.g.
                    --   forall (c::Char->Int) (x::Char).
                    --      f (c x) = "RULE FIRED"
                    -- We must only match on args that have the right type
                    -- It's actually quite difficult to come up with an example that shows
                    -- you need type matching, esp since matching is left-to-right, so type
                    -- args get matched first.  But it's possible (e.g. simplrun008) and
                    -- this is the Right Thing to do
        do { subst' <- match_ty renv subst (idType v1') (exprType e2)
           ; return (subst' { rs_id_subst = id_subst' }) }
      where
        -- e2' is the result of applying flt_env to e2
        e2' | isEmptyVarSet let_bndrs = e2
            | otherwise = substExpr (text "match_tmpl_var") flt_env e2

        id_subst' = extendVarEnv (rs_id_subst subst) v1' e2'
             -- No further renaming to do on e2',
             -- because no free var of e2' is in the rnEnvR of the envt

    ------------------------------------------
    match_ty :: RuleMatchEnv
             -> RuleSubst
             -> Type                -- Template
             -> Type                -- Target
             -> Maybe RuleSubst
    -- Matching Core types: use the matcher in TcType.
    -- Notice that we treat newtypes as opaque.  For example, suppose
    -- we have a specialised version of a function at a newtype, say
    --      newtype T = MkT Int
    -- We only want to replace (f T) with f', not (f Int).

    match_ty renv subst ty1 ty2
      = do  { tv_subst' <- Unify.ruleMatchTyX menv tv_subst ty1 ty2
            ; return (subst { rs_tv_subst = tv_subst' }) }
      where
        tv_subst = rs_tv_subst subst
        menv = ME { me_tmpls = rv_tmpls renv, me_env = rv_lcl renv }

    {-
    Note [Expanding variables]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    Here is another Very Important rule: if the term being matched is a
    variable, we expand it so long as its unfolding is "expandable". (Its
    occurrence information is not necessarily up to date, so we don't use
    it.)  By "expandable" we mean a WHNF or a "constructor-like" application.
    This is the key reason for "constructor-like" Ids.  If we have
         {-# NOINLINE [1] CONLIKE g #-}
         {-# RULE f (g x) = h x #-}
    then in the term
       let v = g 3 in ....(f v)....
    we want to make the rule fire, to replace (f v) with (h 3).

    Note [Do not expand locally-bound variables]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Do *not* expand locally-bound variables, else there's a worry that the
    unfolding might mention variables that are themselves renamed.
    Example
              case x of y { (p,q) -> ...y... }
    Don't expand 'y' to (p,q) because p,q might themselves have been
    renamed.  Essentially we only expand unfoldings that are "outside"
    the entire match.

    Hence, (a) the guard (not (isLocallyBoundR v2))
           (b) when we expand we nuke the renaming envt (nukeRnEnvR).

    Note [Tick annotations in RULE matching]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    We used to unconditionally look through Notes in both template and
    expression being matched. This is actually illegal for counting or
    cost-centre-scoped ticks, because we have no place to put them without
    changing entry counts and/or costs. So now we just fail the match in
    these cases.

    On the other hand, where we are allowed to insert new cost into the
    tick scope, we can float them upwards to the rule application site.

    cf Note [Notes in call patterns] in SpecConstr

    Note [Matching lets]
    ~~~~~~~~~~~~~~~~~~~~
    Matching a let-expression.  Consider
            RULE forall x.  f (g x) = <rhs>
    and target expression
            f (let { w=R } in g E))
    Then we'd like the rule to match, to generate
            let { w=R } in (\x. <rhs>) E
    In effect, we want to float the let-binding outward, to enable
    the match to happen.  This is the WHOLE REASON for accumulating
    bindings in the RuleSubst

    We can only do this if the free variables of R are not bound by the
    part of the target expression outside the let binding; e.g.
            f (\v. let w = v+1 in g E)
    Here we obviously cannot float the let-binding for w.  Hence the
    use of okToFloat.

    There are a couple of tricky points.
      (a) What if floating the binding captures a variable?
            f (let v = x+1 in v) v
          --> NOT!
            let v = x+1 in f (x+1) v

      (b) What if two non-nested let bindings bind the same variable?
            f (let v = e1 in b1) (let v = e2 in b2)
          --> NOT!
            let v = e1 in let v = e2 in (f b2 b2)
          See testsuite test "RuleFloatLet".

    Our cunning plan is this:
      * Along with the growing substitution for template variables
        we maintain a growing set of floated let-bindings (rs_binds)
        plus the set of variables thus bound.

      * The RnEnv2 in the MatchEnv binds only the local binders
        in the term (lambdas, case)

      * When we encounter a let in the term to be matched, we
        check that does not mention any locally bound (lambda, case)
        variables.  If so we fail

      * We use CoreSubst.substBind to freshen the binding, using an
        in-scope set that is the original in-scope variables plus the
        rs_bndrs (currently floated let-bindings).  So in (a) above
        we'll freshen the 'v' binding; in (b) above we'll freshen
        the *second* 'v' binding.

      * We apply that freshening substitution, in a lexically-scoped
        way to the term, although lazily; this is the rv_fltR field.

    Note [Matching cases]
    ~~~~~~~~~~~~~~~~~~~~~
    {- NOTE: This idea is currently disabled.  It really only works if
             the primops involved are OkForSpeculation, and, since
             they have side effects readIntOfAddr and touch are not.
             Maybe we'll get back to this later .  -}

    Consider
       f (case readIntOffAddr# p# i# realWorld# of { (# s#, n# #) ->
          case touch# fp s# of { _ ->
          I# n# } } )
    This happened in a tight loop generated by stream fusion that
    Roman encountered.  We'd like to treat this just like the let
    case, because the primops concerned are ok-for-speculation.
    That is, we'd like to behave as if it had been
       case readIntOffAddr# p# i# realWorld# of { (# s#, n# #) ->
       case touch# fp s# of { _ ->
       f (I# n# } } )

    Note [Lookup in-scope]
    ~~~~~~~~~~~~~~~~~~~~~~
    Consider this example
            foo :: Int -> Maybe Int -> Int
            foo 0 (Just n) = n
            foo m (Just n) = foo (m-n) (Just n)

    SpecConstr sees this fragment:

            case w_smT of wild_Xf [Just A] {
              Data.Maybe.Nothing -> lvl_smf;
              Data.Maybe.Just n_acT [Just S(L)] ->
                case n_acT of wild1_ams [Just A] { GHC.Base.I# y_amr [Just L] ->
                \$wfoo_smW (GHC.Prim.-# ds_Xmb y_amr) wild_Xf
                }};

    and correctly generates the rule

            RULES: "SC:$wfoo1" [0] __forall {y_amr [Just L] :: GHC.Prim.Int#
                                              sc_snn :: GHC.Prim.Int#}
              \$wfoo_smW sc_snn (Data.Maybe.Just @ GHC.Base.Int (GHC.Base.I# y_amr))
              = \$s\$wfoo_sno y_amr sc_snn ;]

    BUT we must ensure that this rule matches in the original function!
    Note that the call to \$wfoo is
                \$wfoo_smW (GHC.Prim.-# ds_Xmb y_amr) wild_Xf

    During matching we expand wild_Xf to (Just n_acT).  But then we must also
    expand n_acT to (I# y_amr).  And we can only do that if we look up n_acT
    in the in-scope set, because in wild_Xf's unfolding it won't have an unfolding
    at all.

    That is why the 'lookupRnInScope' call in the (Var v2) case of 'match'
    is so important.

    ************************************************************************
    *                                                                      *
                       Rule-check the program
    *                                                                      *
    ************************************************************************

       We want to know what sites have rules that could have fired but didn't.
       This pass runs over the tree (without changing it) and reports such.
    -}

    -- | Report partial matches for rules beginning with the specified
    -- string for the purposes of error reporting
    ruleCheckProgram :: CompilerPhase               -- ^ Rule activation test
                     -> String                      -- ^ Rule pattern
                     -> RuleBase                    -- ^ Database of rules
                     -> CoreProgram                 -- ^ Bindings to check in
                     -> SDoc                        -- ^ Resulting check message
    ruleCheckProgram phase rule_pat rule_base binds
      | isEmptyBag results
      = text "Rule check results: no rule application sites"
      | otherwise
      = vcat [text "Rule check results:",
              line,
              vcat [ p $$ line | p <- bagToList results ]
             ]
      where
        env = RuleCheckEnv { rc_is_active = isActive phase
                           , rc_id_unf    = idUnfolding     -- Not quite right
                                                            -- Should use activeUnfolding
                           , rc_pattern   = rule_pat
                           , rc_rule_base = rule_base }
        results = unionManyBags (map (ruleCheckBind env) binds)
        line = text (replicate 20 '-')

    data RuleCheckEnv = RuleCheckEnv {
        rc_is_active :: Activation -> Bool,
        rc_id_unf  :: IdUnfoldingFun,
        rc_pattern :: String,
        rc_rule_base :: RuleBase
    }

    ruleCheckBind :: RuleCheckEnv -> CoreBind -> Bag SDoc
       -- The Bag returned has one SDoc for each call site found
    ruleCheckBind env (NonRec _ r) = ruleCheck env r
    ruleCheckBind env (Rec prs)    = unionManyBags [ruleCheck env r | (_,r) <- prs]

    ruleCheck :: RuleCheckEnv -> CoreExpr -> Bag SDoc
    ruleCheck _   (Var _)       = emptyBag
    ruleCheck _   (Lit _)       = emptyBag
    ruleCheck _   (Type _)      = emptyBag
    ruleCheck _   (Coercion _)  = emptyBag
    ruleCheck env (App f a)     = ruleCheckApp env (App f a) []
    ruleCheck env (Tick _ e)  = ruleCheck env e
    ruleCheck env (Cast e _)    = ruleCheck env e
    ruleCheck env (Let bd e)    = ruleCheckBind env bd `unionBags` ruleCheck env e
    ruleCheck env (Lam _ e)     = ruleCheck env e
    ruleCheck env (Case e _ _ as) = ruleCheck env e `unionBags`
                                    unionManyBags [ruleCheck env r | (_,_,r) <- as]

    ruleCheckApp :: RuleCheckEnv -> Expr CoreBndr -> [Arg CoreBndr] -> Bag SDoc
    ruleCheckApp env (App f a) as = ruleCheck env a `unionBags` ruleCheckApp env f (a:as)
    ruleCheckApp env (Var f) as   = ruleCheckFun env f as
    ruleCheckApp env other _      = ruleCheck env other

    ruleCheckFun :: RuleCheckEnv -> Id -> [CoreExpr] -> Bag SDoc
    -- Produce a report for all rules matching the predicate
    -- saying why it doesn't match the specified application

    ruleCheckFun env fn args
      | null name_match_rules = emptyBag
      | otherwise             = unitBag (ruleAppCheck_help env fn args name_match_rules)
      where
        name_match_rules = filter match (getRules (rc_rule_base env) fn)
        match rule = (rc_pattern env) `isPrefixOf` unpackFS (ruleName rule)

    ruleAppCheck_help :: RuleCheckEnv -> Id -> [CoreExpr] -> [CoreRule] -> SDoc
    ruleAppCheck_help env fn args rules
      =     -- The rules match the pattern, so we want to print something
        vcat [text "Expression:" <+> ppr (mkApps (Var fn) args),
              vcat (map check_rule rules)]
      where
        n_args = length args
        i_args = args `zip` [1::Int ..]
        rough_args = map roughTopName args

        check_rule rule = sdocWithDynFlags $ \dflags ->
                          rule_herald rule <> colon <+> rule_info dflags rule

        rule_herald (BuiltinRule { ru_name = name })
            = ptext (sLit "Builtin rule") <+> doubleQuotes (ftext name)
        rule_herald (Rule { ru_name = name })
            = ptext (sLit "Rule") <+> doubleQuotes (ftext name)

        rule_info dflags rule
            | Just _ <- matchRule dflags (emptyInScopeSet, rc_id_unf env)
                                  noBlackList fn args rough_args rule
            = text "matches (which is very peculiar!)"

        rule_info _ (BuiltinRule {}) = text "does not match"

        rule_info _ (Rule { ru_act = act,
                            ru_bndrs = rule_bndrs, ru_args = rule_args})
            | not (rc_is_active env act)  = text "active only in later phase"
            | n_args < n_rule_args        = text "too few arguments"
            | n_mismatches == n_rule_args = text "no arguments match"
            | n_mismatches == 0           = text "all arguments match (considered individually), but rule as a whole does not"
            | otherwise                   = text "arguments" <+> ppr mismatches <+> text "do not match (1-indexing)"
            where
              n_rule_args  = length rule_args
              n_mismatches = length mismatches
              mismatches   = [i | (rule_arg, (arg,i)) <- rule_args `zip` i_args,
                                  not (isJust (match_fn rule_arg arg))]

              lhs_fvs = exprsFreeVars rule_args     -- Includes template tyvars
              match_fn rule_arg arg = match renv emptyRuleSubst rule_arg arg
                    where
                      in_scope = mkInScopeSet (lhs_fvs `unionVarSet` exprFreeVars arg)
                      renv = RV { rv_lcl   = mkRnEnv2 in_scope
                                , rv_tmpls = mkVarSet rule_bndrs
                                , rv_fltR  = mkEmptySubst in_scope
                                , rv_unf   = rc_id_unf env }