coreSyn/CoreSubst.hs

    {-
    (c) The University of Glasgow 2006
    (c) The GRASP/AQUA Project, Glasgow University, 1992-1998

    Utility functions on @Core@ syntax
    -}

    {-# LANGUAGE CPP #-}
    module CoreSubst (
            -- * Main data types
            Subst(..), -- Implementation exported for supercompiler's Renaming.hs only
            TvSubstEnv, IdSubstEnv, InScopeSet,

            -- ** Substituting into expressions and related types
            deShadowBinds, substSpec, substRulesForImportedIds,
            substTy, substCo, substExpr, substExprSC, substBind, substBindSC,
            substUnfolding, substUnfoldingSC,
            lookupIdSubst, lookupTCvSubst, substIdOcc,
            substTickish, substDVarSet, substIdInfo,

            -- ** Operations on substitutions
            emptySubst, mkEmptySubst, mkSubst, mkOpenSubst, substInScope, isEmptySubst,
            extendIdSubst, extendIdSubstList, extendTCvSubst, extendTvSubstList,
            extendSubst, extendSubstList, extendSubstWithVar, zapSubstEnv,
            addInScopeSet, extendInScope, extendInScopeList, extendInScopeIds,
            isInScope, setInScope, getTCvSubst, extendTvSubst, extendCvSubst,
            delBndr, delBndrs,

            -- ** Substituting and cloning binders
            substBndr, substBndrs, substRecBndrs, substTyVarBndr, substCoVarBndr,
            cloneBndr, cloneBndrs, cloneIdBndr, cloneIdBndrs, cloneRecIdBndrs,

        ) where

    #include "HsVersions.h"

    import CoreSyn
    import CoreFVs
    import CoreSeq
    import CoreUtils
    import qualified Type
    import qualified Coercion

            -- We are defining local versions
    import Type     hiding ( substTy, extendTvSubst, extendCvSubst, extendTvSubstList
                           , isInScope, substTyVarBndr, cloneTyVarBndr )
    import Coercion hiding ( substCo, substCoVarBndr )

    import PrelNames
    import VarSet
    import VarEnv
    import Id
    import Name     ( Name )
    import Var
    import IdInfo
    import UniqSupply
    import Maybes
    import Util
    import Outputable
    import PprCore          ()              -- Instances
    import Data.List

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Substitutions}
    *                                                                      *
    ************************************************************************
    -}

    -- | A substitution environment, containing 'Id', 'TyVar', and 'CoVar'
    -- substitutions.
    --
    -- Some invariants apply to how you use the substitution:
    --
    -- 1. #in_scope_invariant# The in-scope set contains at least those 'Id's and 'TyVar's that will be in scope /after/
    -- applying the substitution to a term. Precisely, the in-scope set must be a superset of the free vars of the
    -- substitution range that might possibly clash with locally-bound variables in the thing being substituted in.
    --
    -- 2. #apply_once# You may apply the substitution only /once/
    --
    -- There are various ways of setting up the in-scope set such that the first of these invariants hold:
    --
    -- * Arrange that the in-scope set really is all the things in scope
    --
    -- * Arrange that it's the free vars of the range of the substitution
    --
    -- * Make it empty, if you know that all the free vars of the substitution are fresh, and hence can't possibly clash
    data Subst
      = Subst InScopeSet  -- Variables in in scope (both Ids and TyVars) /after/
                          -- applying the substitution
              IdSubstEnv  -- Substitution from NcIds to CoreExprs
              TvSubstEnv  -- Substitution from TyVars to Types
              CvSubstEnv  -- Substitution from CoVars to Coercions

            -- INVARIANT 1: See #in_scope_invariant#
            -- This is what lets us deal with name capture properly
            -- It's a hard invariant to check...
            --
            -- INVARIANT 2: The substitution is apply-once; see Note [Apply once] with
            --              Types.TvSubstEnv
            --
            -- INVARIANT 3: See Note [Extending the Subst]

    {-
    Note [Extending the Subst]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    For a core Subst, which binds Ids as well, we make a different choice for Ids
    than we do for TyVars.

    For TyVars, see Note [Extending the TCvSubst] with Type.TvSubstEnv

    For Ids, we have a different invariant
            The IdSubstEnv is extended *only* when the Unique on an Id changes
            Otherwise, we just extend the InScopeSet

    In consequence:

    * If all subst envs are empty, substExpr would be a
      no-op, so substExprSC ("short cut") does nothing.

      However, substExpr still goes ahead and substitutes.  Reason: we may
      want to replace existing Ids with new ones from the in-scope set, to
      avoid space leaks.

    * In substIdBndr, we extend the IdSubstEnv only when the unique changes

    * If the CvSubstEnv, TvSubstEnv and IdSubstEnv are all empty,
      substExpr does nothing (Note that the above rule for substIdBndr
      maintains this property.  If the incoming envts are both empty, then
      substituting the type and IdInfo can't change anything.)

    * In lookupIdSubst, we *must* look up the Id in the in-scope set, because
      it may contain non-trivial changes.  Example:
            (/\a. \x:a. ...x...) Int
      We extend the TvSubstEnv with [a |-> Int]; but x's unique does not change
      so we only extend the in-scope set.  Then we must look up in the in-scope
      set when we find the occurrence of x.

    * The requirement to look up the Id in the in-scope set means that we
      must NOT take no-op short cut when the IdSubst is empty.
      We must still look up every Id in the in-scope set.

    * (However, we don't need to do so for expressions found in the IdSubst
      itself, whose range is assumed to be correct wrt the in-scope set.)

    Why do we make a different choice for the IdSubstEnv than the
    TvSubstEnv and CvSubstEnv?

    * For Ids, we change the IdInfo all the time (e.g. deleting the
      unfolding), and adding it back later, so using the TyVar convention
      would entail extending the substitution almost all the time

    * The simplifier wants to look up in the in-scope set anyway, in case it
      can see a better unfolding from an enclosing case expression

    * For TyVars, only coercion variables can possibly change, and they are
      easy to spot
    -}

    -- | An environment for substituting for 'Id's
    type IdSubstEnv = IdEnv CoreExpr   -- Domain is NcIds, i.e. not coercions

    ----------------------------
    isEmptySubst :: Subst -> Bool
    isEmptySubst (Subst _ id_env tv_env cv_env)
      = isEmptyVarEnv id_env && isEmptyVarEnv tv_env && isEmptyVarEnv cv_env

    emptySubst :: Subst
    emptySubst = Subst emptyInScopeSet emptyVarEnv emptyVarEnv emptyVarEnv

    mkEmptySubst :: InScopeSet -> Subst
    mkEmptySubst in_scope = Subst in_scope emptyVarEnv emptyVarEnv emptyVarEnv

    mkSubst :: InScopeSet -> TvSubstEnv -> CvSubstEnv -> IdSubstEnv -> Subst
    mkSubst in_scope tvs cvs ids = Subst in_scope ids tvs cvs

    -- | Find the in-scope set: see "CoreSubst#in_scope_invariant"
    substInScope :: Subst -> InScopeSet
    substInScope (Subst in_scope _ _ _) = in_scope

    -- | Remove all substitutions for 'Id's and 'Var's that might have been built up
    -- while preserving the in-scope set
    zapSubstEnv :: Subst -> Subst
    zapSubstEnv (Subst in_scope _ _ _) = Subst in_scope emptyVarEnv emptyVarEnv emptyVarEnv

    -- | Add a substitution for an 'Id' to the 'Subst': you must ensure that the in-scope set is
    -- such that the "CoreSubst#in_scope_invariant" is true after extending the substitution like this
    extendIdSubst :: Subst -> Id -> CoreExpr -> Subst
    -- ToDo: add an ASSERT that fvs(subst-result) is already in the in-scope set
    extendIdSubst (Subst in_scope ids tvs cvs) v r
      = ASSERT2( isNonCoVarId v, ppr v $$ ppr r )
        Subst in_scope (extendVarEnv ids v r) tvs cvs

    -- | Adds multiple 'Id' substitutions to the 'Subst': see also 'extendIdSubst'
    extendIdSubstList :: Subst -> [(Id, CoreExpr)] -> Subst
    extendIdSubstList (Subst in_scope ids tvs cvs) prs
      = ASSERT( all (isNonCoVarId . fst) prs )
        Subst in_scope (extendVarEnvList ids prs) tvs cvs

    -- | Add a substitution for a 'TyVar' to the 'Subst'
    -- The 'TyVar' *must* be a real TyVar, and not a CoVar
    -- You must ensure that the in-scope set is such that
    -- the "CoreSubst#in_scope_invariant" is true after extending
    -- the substitution like this.
    extendTvSubst :: Subst -> TyVar -> Type -> Subst
    extendTvSubst (Subst in_scope ids tvs cvs) tv ty
      = ASSERT( isTyVar tv )
        Subst in_scope ids (extendVarEnv tvs tv ty) cvs

    -- | Adds multiple 'TyVar' substitutions to the 'Subst': see also 'extendTvSubst'
    extendTvSubstList :: Subst -> [(TyVar,Type)] -> Subst
    extendTvSubstList subst vrs
      = foldl' extend subst vrs
      where
        extend subst (v, r) = extendTvSubst subst v r

    -- | Add a substitution from a 'CoVar' to a 'Coercion' to the 'Subst': you must ensure that the in-scope set is
    -- such that the "CoreSubst#in_scope_invariant" is true after extending the substitution like this
    extendCvSubst :: Subst -> CoVar -> Coercion -> Subst
    extendCvSubst (Subst in_scope ids tvs cvs) v r
      = ASSERT( isCoVar v )
        Subst in_scope ids tvs (extendVarEnv cvs v r)

    -- | Add a substitution appropriate to the thing being substituted
    --   (whether an expression, type, or coercion). See also
    --   'extendIdSubst', 'extendTvSubst', 'extendCvSubst'
    extendSubst :: Subst -> Var -> CoreArg -> Subst
    extendSubst subst var arg
      = case arg of
          Type ty     -> ASSERT( isTyVar var ) extendTvSubst subst var ty
          Coercion co -> ASSERT( isCoVar var ) extendCvSubst subst var co
          _           -> ASSERT( isId    var ) extendIdSubst subst var arg

    extendSubstWithVar :: Subst -> Var -> Var -> Subst
    extendSubstWithVar subst v1 v2
      | isTyVar v1 = ASSERT( isTyVar v2 ) extendTvSubst subst v1 (mkTyVarTy v2)
      | isCoVar v1 = ASSERT( isCoVar v2 ) extendCvSubst subst v1 (mkCoVarCo v2)
      | otherwise  = ASSERT( isId    v2 ) extendIdSubst subst v1 (Var v2)

    -- | Add a substitution as appropriate to each of the terms being
    --   substituted (whether expressions, types, or coercions). See also
    --   'extendSubst'.
    extendSubstList :: Subst -> [(Var,CoreArg)] -> Subst
    extendSubstList subst []              = subst
    extendSubstList subst ((var,rhs):prs) = extendSubstList (extendSubst subst var rhs) prs

    -- | Find the substitution for an 'Id' in the 'Subst'
    lookupIdSubst :: SDoc -> Subst -> Id -> CoreExpr
    lookupIdSubst doc (Subst in_scope ids _ _) v
      | not (isLocalId v) = Var v
      | Just e  <- lookupVarEnv ids       v = e
      | Just v' <- lookupInScope in_scope v = Var v'
            -- Vital! See Note [Extending the Subst]
      | otherwise = WARN( True, text "CoreSubst.lookupIdSubst" <+> doc <+> ppr v
                                $$ ppr in_scope)
                    Var v

    -- | Find the substitution for a 'TyVar' in the 'Subst'
    lookupTCvSubst :: Subst -> TyVar -> Type
    lookupTCvSubst (Subst _ _ tvs cvs) v
      | isTyVar v
      = lookupVarEnv tvs v `orElse` Type.mkTyVarTy v
      | otherwise
      = mkCoercionTy $ lookupVarEnv cvs v `orElse` mkCoVarCo v

    delBndr :: Subst -> Var -> Subst
    delBndr (Subst in_scope ids tvs cvs) v
      | isCoVar v = Subst in_scope ids tvs (delVarEnv cvs v)
      | isTyVar v = Subst in_scope ids (delVarEnv tvs v) cvs
      | otherwise = Subst in_scope (delVarEnv ids v) tvs cvs

    delBndrs :: Subst -> [Var] -> Subst
    delBndrs (Subst in_scope ids tvs cvs) vs
      = Subst in_scope (delVarEnvList ids vs) (delVarEnvList tvs vs) (delVarEnvList cvs vs)
          -- Easiest thing is just delete all from all!

    -- | Simultaneously substitute for a bunch of variables
    --   No left-right shadowing
    --   ie the substitution for   (\x \y. e) a1 a2
    --      so neither x nor y scope over a1 a2
    mkOpenSubst :: InScopeSet -> [(Var,CoreArg)] -> Subst
    mkOpenSubst in_scope pairs = Subst in_scope
                                       (mkVarEnv [(id,e)  | (id, e) <- pairs, isId id])
                                       (mkVarEnv [(tv,ty) | (tv, Type ty) <- pairs])
                                       (mkVarEnv [(v,co)  | (v, Coercion co) <- pairs])

    ------------------------------
    isInScope :: Var -> Subst -> Bool
    isInScope v (Subst in_scope _ _ _) = v `elemInScopeSet` in_scope

    -- | Add the 'Var' to the in-scope set, but do not remove
    -- any existing substitutions for it
    addInScopeSet :: Subst -> VarSet -> Subst
    addInScopeSet (Subst in_scope ids tvs cvs) vs
      = Subst (in_scope `extendInScopeSetSet` vs) ids tvs cvs

    -- | Add the 'Var' to the in-scope set: as a side effect,
    -- and remove any existing substitutions for it
    extendInScope :: Subst -> Var -> Subst
    extendInScope (Subst in_scope ids tvs cvs) v
      = Subst (in_scope `extendInScopeSet` v)
              (ids `delVarEnv` v) (tvs `delVarEnv` v) (cvs `delVarEnv` v)

    -- | Add the 'Var's to the in-scope set: see also 'extendInScope'
    extendInScopeList :: Subst -> [Var] -> Subst
    extendInScopeList (Subst in_scope ids tvs cvs) vs
      = Subst (in_scope `extendInScopeSetList` vs)
              (ids `delVarEnvList` vs) (tvs `delVarEnvList` vs) (cvs `delVarEnvList` vs)

    -- | Optimized version of 'extendInScopeList' that can be used if you are certain
    -- all the things being added are 'Id's and hence none are 'TyVar's or 'CoVar's
    extendInScopeIds :: Subst -> [Id] -> Subst
    extendInScopeIds (Subst in_scope ids tvs cvs) vs
      = Subst (in_scope `extendInScopeSetList` vs)
              (ids `delVarEnvList` vs) tvs cvs

    setInScope :: Subst -> InScopeSet -> Subst
    setInScope (Subst _ ids tvs cvs) in_scope = Subst in_scope ids tvs cvs

    -- Pretty printing, for debugging only

    instance Outputable Subst where
      ppr (Subst in_scope ids tvs cvs)
            =  text "<InScope =" <+> in_scope_doc
            $$ text " IdSubst   =" <+> ppr ids
            $$ text " TvSubst   =" <+> ppr tvs
            $$ text " CvSubst   =" <+> ppr cvs
             <> char '>'
        where
        in_scope_doc = pprVarSet (getInScopeVars in_scope) (braces . fsep . map ppr)

    {-
    ************************************************************************
    *                                                                      *
            Substituting expressions
    *                                                                      *
    ************************************************************************
    -}

    -- | Apply a substitution to an entire 'CoreExpr'. Remember, you may only
    -- apply the substitution /once/: see "CoreSubst#apply_once"
    --
    -- Do *not* attempt to short-cut in the case of an empty substitution!
    -- See Note [Extending the Subst]
    substExprSC :: SDoc -> Subst -> CoreExpr -> CoreExpr
    substExprSC doc subst orig_expr
      | isEmptySubst subst = orig_expr
      | otherwise          = -- pprTrace "enter subst-expr" (doc $$ ppr orig_expr) $
                             subst_expr doc subst orig_expr

    substExpr :: SDoc -> Subst -> CoreExpr -> CoreExpr
    substExpr doc subst orig_expr = subst_expr doc subst orig_expr

    subst_expr :: SDoc -> Subst -> CoreExpr -> CoreExpr
    subst_expr doc subst expr
      = go expr
      where
        go (Var v)         = lookupIdSubst (doc $$ text "subst_expr") subst v
        go (Type ty)       = Type (substTy subst ty)
        go (Coercion co)   = Coercion (substCo subst co)
        go (Lit lit)       = Lit lit
        go (App fun arg)   = App (go fun) (go arg)
        go (Tick tickish e) = mkTick (substTickish subst tickish) (go e)
        go (Cast e co)     = Cast (go e) (substCo subst co)
           -- Do not optimise even identity coercions
           -- Reason: substitution applies to the LHS of RULES, and
           --         if you "optimise" an identity coercion, you may
           --         lose a binder. We optimise the LHS of rules at
           --         construction time

        go (Lam bndr body) = Lam bndr' (subst_expr doc subst' body)
                           where
                             (subst', bndr') = substBndr subst bndr

        go (Let bind body) = Let bind' (subst_expr doc subst' body)
                           where
                             (subst', bind') = substBind subst bind

        go (Case scrut bndr ty alts) = Case (go scrut) bndr' (substTy subst ty) (map (go_alt subst') alts)
                                     where
                                     (subst', bndr') = substBndr subst bndr

        go_alt subst (con, bndrs, rhs) = (con, bndrs', subst_expr doc subst' rhs)
                                     where
                                       (subst', bndrs') = substBndrs subst bndrs

    -- | Apply a substitution to an entire 'CoreBind', additionally returning an updated 'Subst'
    -- that should be used by subsequent substitutions.
    substBind, substBindSC :: Subst -> CoreBind -> (Subst, CoreBind)

    substBindSC subst bind    -- Short-cut if the substitution is empty
      | not (isEmptySubst subst)
      = substBind subst bind
      | otherwise
      = case bind of
           NonRec bndr rhs -> (subst', NonRec bndr' rhs)
              where
                (subst', bndr') = substBndr subst bndr
           Rec pairs -> (subst', Rec (bndrs' `zip` rhss'))
              where
                (bndrs, rhss)    = unzip pairs
                (subst', bndrs') = substRecBndrs subst bndrs
                rhss' | isEmptySubst subst'
                      = rhss
                      | otherwise
                      = map (subst_expr (text "substBindSC") subst') rhss

    substBind subst (NonRec bndr rhs)
      = (subst', NonRec bndr' (subst_expr (text "substBind") subst rhs))
      where
        (subst', bndr') = substBndr subst bndr

    substBind subst (Rec pairs)
       = (subst', Rec (bndrs' `zip` rhss'))
       where
           (bndrs, rhss)    = unzip pairs
           (subst', bndrs') = substRecBndrs subst bndrs
           rhss' = map (subst_expr (text "substBind") subst') rhss

    -- | De-shadowing the program is sometimes a useful pre-pass. It can be done simply
    -- by running over the bindings with an empty substitution, because substitution
    -- returns a result that has no-shadowing guaranteed.
    --
    -- (Actually, within a single /type/ there might still be shadowing, because
    -- 'substTy' is a no-op for the empty substitution, but that's probably OK.)
    --
    -- [Aug 09] This function is not used in GHC at the moment, but seems so
    --          short and simple that I'm going to leave it here
    deShadowBinds :: CoreProgram -> CoreProgram
    deShadowBinds binds = snd (mapAccumL substBind emptySubst binds)

    {-
    ************************************************************************
    *                                                                      *
            Substituting binders
    *                                                                      *
    ************************************************************************

    Remember that substBndr and friends are used when doing expression
    substitution only.  Their only business is substitution, so they
    preserve all IdInfo (suitably substituted).  For example, we *want* to
    preserve occ info in rules.
    -}

    -- | Substitutes a 'Var' for another one according to the 'Subst' given, returning
    -- the result and an updated 'Subst' that should be used by subsequent substitutions.
    -- 'IdInfo' is preserved by this process, although it is substituted into appropriately.
    substBndr :: Subst -> Var -> (Subst, Var)
    substBndr subst bndr
      | isTyVar bndr  = substTyVarBndr subst bndr
      | isCoVar bndr  = substCoVarBndr subst bndr
      | otherwise     = substIdBndr (text "var-bndr") subst subst bndr

    -- | Applies 'substBndr' to a number of 'Var's, accumulating a new 'Subst' left-to-right
    substBndrs :: Subst -> [Var] -> (Subst, [Var])
    substBndrs subst bndrs = mapAccumL substBndr subst bndrs

    -- | Substitute in a mutually recursive group of 'Id's
    substRecBndrs :: Subst -> [Id] -> (Subst, [Id])
    substRecBndrs subst bndrs
      = (new_subst, new_bndrs)
      where         -- Here's the reason we need to pass rec_subst to subst_id
        (new_subst, new_bndrs) = mapAccumL (substIdBndr (text "rec-bndr") new_subst) subst bndrs

    substIdBndr :: SDoc
                -> Subst            -- ^ Substitution to use for the IdInfo
                -> Subst -> Id      -- ^ Substitution and Id to transform
                -> (Subst, Id)      -- ^ Transformed pair
                                    -- NB: unfolding may be zapped

    substIdBndr _doc rec_subst subst@(Subst in_scope env tvs cvs) old_id
      = -- pprTrace "substIdBndr" (doc $$ ppr old_id $$ ppr in_scope) $
        (Subst (in_scope `extendInScopeSet` new_id) new_env tvs cvs, new_id)
      where
        id1 = uniqAway in_scope old_id      -- id1 is cloned if necessary
        id2 | no_type_change = id1
            | otherwise      = setIdType id1 (substTy subst old_ty)

        old_ty = idType old_id
        no_type_change = (isEmptyVarEnv tvs && isEmptyVarEnv cvs) ||
                         noFreeVarsOfType old_ty

            -- new_id has the right IdInfo
            -- The lazy-set is because we're in a loop here, with
            -- rec_subst, when dealing with a mutually-recursive group
        new_id = maybeModifyIdInfo mb_new_info id2
        mb_new_info = substIdInfo rec_subst id2 (idInfo id2)
            -- NB: unfolding info may be zapped

            -- Extend the substitution if the unique has changed
            -- See the notes with substTyVarBndr for the delVarEnv
        new_env | no_change = delVarEnv env old_id
                | otherwise = extendVarEnv env old_id (Var new_id)

        no_change = id1 == old_id
            -- See Note [Extending the Subst]
            -- it's /not/ necessary to check mb_new_info and no_type_change

    {-
    Now a variant that unconditionally allocates a new unique.
    It also unconditionally zaps the OccInfo.
    -}

    -- | Very similar to 'substBndr', but it always allocates a new 'Unique' for
    -- each variable in its output.  It substitutes the IdInfo though.
    cloneIdBndr :: Subst -> UniqSupply -> Id -> (Subst, Id)
    cloneIdBndr subst us old_id
      = clone_id subst subst (old_id, uniqFromSupply us)

    -- | Applies 'cloneIdBndr' to a number of 'Id's, accumulating a final
    -- substitution from left to right
    cloneIdBndrs :: Subst -> UniqSupply -> [Id] -> (Subst, [Id])
    cloneIdBndrs subst us ids
      = mapAccumL (clone_id subst) subst (ids `zip` uniqsFromSupply us)

    cloneBndrs :: Subst -> UniqSupply -> [Var] -> (Subst, [Var])
    -- Works for all kinds of variables (typically case binders)
    -- not just Ids
    cloneBndrs subst us vs
      = mapAccumL (\subst (v, u) -> cloneBndr subst u v) subst (vs `zip` uniqsFromSupply us)

    cloneBndr :: Subst -> Unique -> Var -> (Subst, Var)
    cloneBndr subst uniq v
      | isTyVar v = cloneTyVarBndr subst v uniq
      | otherwise = clone_id subst subst (v,uniq)  -- Works for coercion variables too

    -- | Clone a mutually recursive group of 'Id's
    cloneRecIdBndrs :: Subst -> UniqSupply -> [Id] -> (Subst, [Id])
    cloneRecIdBndrs subst us ids
      = (subst', ids')
      where
        (subst', ids') = mapAccumL (clone_id subst') subst
                                   (ids `zip` uniqsFromSupply us)

    -- Just like substIdBndr, except that it always makes a new unique
    -- It is given the unique to use
    clone_id    :: Subst                    -- Substitution for the IdInfo
                -> Subst -> (Id, Unique)    -- Substitution and Id to transform
                -> (Subst, Id)              -- Transformed pair

    clone_id rec_subst subst@(Subst in_scope idvs tvs cvs) (old_id, uniq)
      = (Subst (in_scope `extendInScopeSet` new_id) new_idvs tvs new_cvs, new_id)
      where
        id1     = setVarUnique old_id uniq
        id2     = substIdType subst id1
        new_id  = maybeModifyIdInfo (substIdInfo rec_subst id2 (idInfo old_id)) id2
        (new_idvs, new_cvs) | isCoVar old_id = (idvs, extendVarEnv cvs old_id (mkCoVarCo new_id))
                            | otherwise      = (extendVarEnv idvs old_id (Var new_id), cvs)

    {-
    ************************************************************************
    *                                                                      *
                    Types and Coercions
    *                                                                      *
    ************************************************************************

    For types and coercions we just call the corresponding functions in
    Type and Coercion, but we have to repackage the substitution, from a
    Subst to a TCvSubst.
    -}

    substTyVarBndr :: Subst -> TyVar -> (Subst, TyVar)
    substTyVarBndr (Subst in_scope id_env tv_env cv_env) tv
      = case Type.substTyVarBndr (TCvSubst in_scope tv_env cv_env) tv of
            (TCvSubst in_scope' tv_env' cv_env', tv')
               -> (Subst in_scope' id_env tv_env' cv_env', tv')

    cloneTyVarBndr :: Subst -> TyVar -> Unique -> (Subst, TyVar)
    cloneTyVarBndr (Subst in_scope id_env tv_env cv_env) tv uniq
      = case Type.cloneTyVarBndr (TCvSubst in_scope tv_env cv_env) tv uniq of
            (TCvSubst in_scope' tv_env' cv_env', tv')
               -> (Subst in_scope' id_env tv_env' cv_env', tv')

    substCoVarBndr :: Subst -> TyVar -> (Subst, TyVar)
    substCoVarBndr (Subst in_scope id_env tv_env cv_env) cv
      = case Coercion.substCoVarBndr (TCvSubst in_scope tv_env cv_env) cv of
            (TCvSubst in_scope' tv_env' cv_env', cv')
               -> (Subst in_scope' id_env tv_env' cv_env', cv')

    -- | See 'Type.substTy'
    substTy :: Subst -> Type -> Type
    substTy subst ty = Type.substTyUnchecked (getTCvSubst subst) ty

    getTCvSubst :: Subst -> TCvSubst
    getTCvSubst (Subst in_scope _ tenv cenv) = TCvSubst in_scope tenv cenv

    -- | See 'Coercion.substCo'
    substCo :: Subst -> Coercion -> Coercion
    substCo subst co = Coercion.substCo (getTCvSubst subst) co

    {-
    ************************************************************************
    *                                                                      *
    \section{IdInfo substitution}
    *                                                                      *
    ************************************************************************
    -}

    substIdType :: Subst -> Id -> Id
    substIdType subst@(Subst _ _ tv_env cv_env) id
      | (isEmptyVarEnv tv_env && isEmptyVarEnv cv_env) || noFreeVarsOfType old_ty = id
      | otherwise   = setIdType id (substTy subst old_ty)
                    -- The tyCoVarsOfType is cheaper than it looks
                    -- because we cache the free tyvars of the type
                    -- in a Note in the id's type itself
      where
        old_ty = idType id

    ------------------
    -- | Substitute into some 'IdInfo' with regard to the supplied new 'Id'.
    substIdInfo :: Subst -> Id -> IdInfo -> Maybe IdInfo
    substIdInfo subst new_id info
      | nothing_to_do = Nothing
      | otherwise     = Just (info `setRuleInfo`      substSpec subst new_id old_rules
                                   `setUnfoldingInfo` substUnfolding subst old_unf)
      where
        old_rules     = ruleInfo info
        old_unf       = unfoldingInfo info
        nothing_to_do = isEmptyRuleInfo old_rules && not (isFragileUnfolding old_unf)

    ------------------
    -- | Substitutes for the 'Id's within an unfolding
    substUnfolding, substUnfoldingSC :: Subst -> Unfolding -> Unfolding
            -- Seq'ing on the returned Unfolding is enough to cause
            -- all the substitutions to happen completely

    substUnfoldingSC subst unf       -- Short-cut version
      | isEmptySubst subst = unf
      | otherwise          = substUnfolding subst unf

    substUnfolding subst df@(DFunUnfolding { df_bndrs = bndrs, df_args = args })
      = df { df_bndrs = bndrs', df_args = args' }
      where
        (subst',bndrs') = substBndrs subst bndrs
        args'           = map (substExpr (text "subst-unf:dfun") subst') args

    substUnfolding subst unf@(CoreUnfolding { uf_tmpl = tmpl, uf_src = src })
            -- Retain an InlineRule!
      | not (isStableSource src)  -- Zap an unstable unfolding, to save substitution work
      = NoUnfolding
      | otherwise                 -- But keep a stable one!
      = seqExpr new_tmpl `seq`
        unf { uf_tmpl = new_tmpl }
      where
        new_tmpl = substExpr (text "subst-unf") subst tmpl

    substUnfolding _ unf = unf      -- NoUnfolding, OtherCon

    ------------------
    substIdOcc :: Subst -> Id -> Id
    -- These Ids should not be substituted to non-Ids
    substIdOcc subst v = case lookupIdSubst (text "substIdOcc") subst v of
                            Var v' -> v'
                            other  -> pprPanic "substIdOcc" (vcat [ppr v <+> ppr other, ppr subst])

    ------------------
    -- | Substitutes for the 'Id's within the 'WorkerInfo' given the new function 'Id'
    substSpec :: Subst -> Id -> RuleInfo -> RuleInfo
    substSpec subst new_id (RuleInfo rules rhs_fvs)
      = seqRuleInfo new_spec `seq` new_spec
      where
        subst_ru_fn = const (idName new_id)
        new_spec = RuleInfo (map (substRule subst subst_ru_fn) rules)
                            (substDVarSet subst rhs_fvs)

    ------------------
    substRulesForImportedIds :: Subst -> [CoreRule] -> [CoreRule]
    substRulesForImportedIds subst rules
      = map (substRule subst not_needed) rules
      where
        not_needed name = pprPanic "substRulesForImportedIds" (ppr name)

    ------------------
    substRule :: Subst -> (Name -> Name) -> CoreRule -> CoreRule

    -- The subst_ru_fn argument is applied to substitute the ru_fn field
    -- of the rule:
    --    - Rules for *imported* Ids never change ru_fn
    --    - Rules for *local* Ids are in the IdInfo for that Id,
    --      and the ru_fn field is simply replaced by the new name
    --      of the Id
    substRule _ _ rule@(BuiltinRule {}) = rule
    substRule subst subst_ru_fn rule@(Rule { ru_bndrs = bndrs, ru_args = args
                                           , ru_fn = fn_name, ru_rhs = rhs
                                           , ru_local = is_local })
      = rule { ru_bndrs = bndrs'
             , ru_fn    = if is_local
                            then subst_ru_fn fn_name
                            else fn_name
             , ru_args  = map (substExpr doc subst') args
             , ru_rhs   = substExpr (text "foo") subst' rhs }
               -- Do NOT optimise the RHS (previously we did simplOptExpr here)
               -- See Note [Substitute lazily]
      where
        doc = text "subst-rule" <+> ppr fn_name
        (subst', bndrs') = substBndrs subst bndrs

    ------------------
    substDVarSet :: Subst -> DVarSet -> DVarSet
    substDVarSet subst fvs
      = mkDVarSet $ fst $ foldr (subst_fv subst) ([], emptyVarSet) $ dVarSetElems fvs
      where
      subst_fv subst fv acc
         | isId fv = expr_fvs (lookupIdSubst (text "substDVarSet") subst fv) isLocalVar emptyVarSet $! acc
         | otherwise = tyCoFVsOfType (lookupTCvSubst subst fv) (const True) emptyVarSet $! acc

    ------------------
    substTickish :: Subst -> Tickish Id -> Tickish Id
    substTickish subst (Breakpoint n ids)
       = Breakpoint n (map do_one ids)
     where
        do_one = getIdFromTrivialExpr . lookupIdSubst (text "subst_tickish") subst
    substTickish _subst other = other

    {- Note [Substitute lazily]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The functions that substitute over IdInfo must be pretty lazy, because
    they are knot-tied by substRecBndrs.

    One case in point was Trac #10627 in which a rule for a function 'f'
    referred to 'f' (at a differnet type) on the RHS.  But instead of just
    substituting in the rhs of the rule, we were calling simpleOptExpr, which
    looked at the idInfo for 'f'; result <<loop>>.

    In any case we don't need to optimise the RHS of rules, or unfoldings,
    because the simplifier will do that.

    Note [substTickish]
    ~~~~~~~~~~~~~~~~~~~~~~
    A Breakpoint contains a list of Ids.  What happens if we ever want to
    substitute an expression for one of these Ids?

    First, we ensure that we only ever substitute trivial expressions for
    these Ids, by marking them as NoOccInfo in the occurrence analyser.
    Then, when substituting for the Id, we unwrap any type applications
    and abstractions to get back to an Id, with getIdFromTrivialExpr.

    Second, we have to ensure that we never try to substitute a literal
    for an Id in a breakpoint.  We ensure this by never storing an Id with
    an unlifted type in a Breakpoint - see Coverage.mkTickish.
    Breakpoints can't handle free variables with unlifted types anyway.
    -}

    {-
    Note [Worker inlining]
    ~~~~~~~~~~~~~~~~~~~~~~
    A worker can get sustituted away entirely.
            - it might be trivial
            - it might simply be very small
    We do not treat an InlWrapper as an 'occurrence' in the occurrence
    analyser, so it's possible that the worker is not even in scope any more.

    In all all these cases we simply drop the special case, returning to
    InlVanilla.  The WARN is just so I can see if it happens a lot.
    -}