CoreSubst.lhs 40.3 KB
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% (c) The University of Glasgow 2006
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% (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
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Utility functions on @Core@ syntax
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\begin{code}
module CoreSubst (
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	-- * Main data types
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	Subst(..), -- Implementation exported for supercompiler's Renaming.hs only
	TvSubstEnv, IdSubstEnv, InScopeSet,
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        -- ** Substituting into expressions and related types
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	deShadowBinds, substSpec, substRulesForImportedIds,
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	substTy, substCo, substExpr, substExprSC, substBind, substBindSC,
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        substUnfolding, substUnfoldingSC,
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	substUnfoldingSource, lookupIdSubst, lookupTvSubst, lookupCvSubst, substIdOcc,
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        -- ** Operations on substitutions
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	emptySubst, mkEmptySubst, mkSubst, mkOpenSubst, substInScope, isEmptySubst, 
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 	extendIdSubst, extendIdSubstList, extendTvSubst, extendTvSubstList,
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        extendCvSubst, extendCvSubstList,
	extendSubst, extendSubstList, extendSubstWithVar, zapSubstEnv,
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        addInScopeSet, extendInScope, extendInScopeList, extendInScopeIds,
        isInScope, setInScope,
        delBndr, delBndrs,
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	-- ** Substituting and cloning binders
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	substBndr, substBndrs, substRecBndrs,
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	cloneBndr, cloneBndrs, cloneIdBndr, cloneIdBndrs, cloneRecIdBndrs,
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	-- ** Simple expression optimiser
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        simpleOptPgm, simpleOptExpr, simpleOptExprWith
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    ) where

#include "HsVersions.h"

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import CoreSyn
import CoreFVs
import CoreUtils
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import OccurAnal( occurAnalyseExpr, occurAnalysePgm )
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import qualified Type
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import qualified Coercion

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

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import OptCoercion ( optCoercion )
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import PprCore     ( pprCoreBindings, pprRules )
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import PrelNames   ( eqBoxDataConKey )
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import Module	   ( Module )
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import VarSet
import VarEnv
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import Id
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import Name	( Name )
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import Var
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import IdInfo
import Unique
import UniqSupply
import Maybes
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import ErrUtils
import DynFlags   ( DynFlags, DynFlag(..) )
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import BasicTypes ( isAlwaysActive )
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import Outputable
import PprCore		()		-- Instances
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import FastString
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import Data.List
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\end{code}


%************************************************************************
%*									*
\subsection{Substitutions}
%*									*
%************************************************************************

\begin{code}
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-- | A substitution environment, containing both 'Id' and 'TyVar' 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
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data Subst 
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  = Subst InScopeSet  -- Variables in in scope (both Ids and TyVars) /after/
                      -- applying the substitution
          IdSubstEnv  -- Substitution for Ids
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          TvSubstEnv  -- Substitution from TyVars to Types
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          CvSubstEnv  -- Substitution from CoVars to Coercions
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	-- INVARIANT 1: See #in_scope_invariant#
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	-- This is what lets us deal with name capture properly
	-- It's a hard invariant to check...
	--
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	-- INVARIANT 2: The substitution is apply-once; see Note [Apply once] with
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	--		Types.TvSubstEnv
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	--
	-- INVARIANT 3: See Note [Extending the Subst]
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\end{code}
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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 TvSubst] 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:

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* If the TvSubstEnv and IdSubstEnv are both 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.
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* In substIdBndr, we extend the IdSubstEnv only when the unique changes
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* 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.)

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* 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.

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

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Why do we make a different choice for the IdSubstEnv than the
TvSubstEnv and CvSubstEnv?
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* 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
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\begin{code}
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-- | An environment for substituting for 'Id's
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type IdSubstEnv = IdEnv CoreExpr

----------------------------
isEmptySubst :: Subst -> Bool
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isEmptySubst (Subst _ id_env tv_env cv_env) 
  = isEmptyVarEnv id_env && isEmptyVarEnv tv_env && isEmptyVarEnv cv_env
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emptySubst :: Subst
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emptySubst = Subst emptyInScopeSet emptyVarEnv emptyVarEnv emptyVarEnv
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mkEmptySubst :: InScopeSet -> Subst
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mkEmptySubst in_scope = Subst in_scope emptyVarEnv emptyVarEnv emptyVarEnv
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mkSubst :: InScopeSet -> TvSubstEnv -> CvSubstEnv -> IdSubstEnv -> Subst
mkSubst in_scope tvs cvs ids = Subst in_scope ids tvs cvs
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-- | Find the in-scope set: see "CoreSubst#in_scope_invariant"
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substInScope :: Subst -> InScopeSet
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substInScope (Subst in_scope _ _ _) = in_scope
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-- | Remove all substitutions for 'Id's and 'Var's that might have been built up
-- while preserving the in-scope set
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zapSubstEnv :: Subst -> Subst
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zapSubstEnv (Subst in_scope _ _ _) = Subst in_scope emptyVarEnv emptyVarEnv emptyVarEnv
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-- | 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
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extendIdSubst :: Subst -> Id -> CoreExpr -> Subst
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-- ToDo: add an ASSERT that fvs(subst-result) is already in the in-scope set
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extendIdSubst (Subst in_scope ids tvs cvs) v r = Subst in_scope (extendVarEnv ids v r) tvs cvs
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-- | Adds multiple 'Id' substitutions to the 'Subst': see also 'extendIdSubst'
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extendIdSubstList :: Subst -> [(Id, CoreExpr)] -> Subst
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extendIdSubstList (Subst in_scope ids tvs cvs) prs = Subst in_scope (extendVarEnvList ids prs) tvs cvs
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-- | Add a substitution for a 'TyVar' 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
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extendTvSubst :: Subst -> TyVar -> Type -> Subst
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extendTvSubst (Subst in_scope ids tvs cvs) v r = Subst in_scope ids (extendVarEnv tvs v r) cvs
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-- | Adds multiple 'TyVar' substitutions to the 'Subst': see also 'extendTvSubst'
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extendTvSubstList :: Subst -> [(TyVar,Type)] -> Subst
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extendTvSubstList (Subst in_scope ids tvs cvs) prs = Subst in_scope ids (extendVarEnvList tvs prs) cvs
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-- | Add a substitution from a 'CoVar' to a 'Coercion' to the 'Subst': you must ensure that the in-scope set is
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-- such that the "CoreSubst#in_scope_invariant" is true after extending the substitution like this
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extendCvSubst :: Subst -> CoVar -> Coercion -> Subst
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extendCvSubst (Subst in_scope ids tvs cvs) v r = Subst in_scope ids tvs (extendVarEnv cvs v r)

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-- | Adds multiple 'CoVar' -> 'Coercion' substitutions to the
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-- 'Subst': see also 'extendCvSubst'
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extendCvSubstList :: Subst -> [(CoVar,Coercion)] -> Subst
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extendCvSubstList (Subst in_scope ids tvs cvs) prs = Subst in_scope ids tvs (extendVarEnvList cvs prs)
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-- | Add a substitution appropriate to the thing being substituted
--   (whether an expression, type, or coercion). See also
--   'extendIdSubst', 'extendTvSubst', and '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'.
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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'
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lookupIdSubst :: SDoc -> Subst -> Id -> CoreExpr
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lookupIdSubst doc (Subst in_scope ids _ _) v
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  | not (isLocalId v) = Var v
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  | Just e  <- lookupVarEnv ids       v = e
  | Just v' <- lookupInScope in_scope v = Var v'
	-- Vital! See Note [Extending the Subst]
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  | otherwise = WARN( True, ptext (sLit "CoreSubst.lookupIdSubst") <+> doc <+> ppr v 
                            $$ ppr in_scope) 
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		Var v
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-- | Find the substitution for a 'TyVar' in the 'Subst'
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lookupTvSubst :: Subst -> TyVar -> Type
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lookupTvSubst (Subst _ _ tvs _) v = ASSERT( isTyVar v) lookupVarEnv tvs v `orElse` Type.mkTyVarTy v

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-- | Find the coercion substitution for a 'CoVar' in the 'Subst'
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lookupCvSubst :: Subst -> CoVar -> Coercion
lookupCvSubst (Subst _ _ _ cvs) v = ASSERT( isCoVar v ) lookupVarEnv cvs v `orElse` mkCoVarCo v
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delBndr :: Subst -> Var -> Subst
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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
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delBndrs :: Subst -> [Var] -> Subst
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delBndrs (Subst in_scope ids tvs cvs) vs
  = Subst in_scope (delVarEnvList ids vs) (delVarEnvList tvs vs) (delVarEnvList cvs vs)
      -- Easist thing is just delete all from all!
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-- | 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
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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])
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                                   (mkVarEnv [(v,co)  | (v, Coercion co) <- pairs])
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------------------------------
isInScope :: Var -> Subst -> Bool
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isInScope v (Subst in_scope _ _ _) = v `elemInScopeSet` in_scope
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-- | Add the 'Var' to the in-scope set, but do not remove
-- any existing substitutions for it
addInScopeSet :: Subst -> VarSet -> Subst
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addInScopeSet (Subst in_scope ids tvs cvs) vs
  = Subst (in_scope `extendInScopeSetSet` vs) ids tvs cvs
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-- | Add the 'Var' to the in-scope set: as a side effect,
-- and remove any existing substitutions for it
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extendInScope :: Subst -> Var -> Subst
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extendInScope (Subst in_scope ids tvs cvs) v
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  = Subst (in_scope `extendInScopeSet` v) 
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	  (ids `delVarEnv` v) (tvs `delVarEnv` v) (cvs `delVarEnv` v)
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-- | Add the 'Var's to the in-scope set: see also 'extendInScope'
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extendInScopeList :: Subst -> [Var] -> Subst
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extendInScopeList (Subst in_scope ids tvs cvs) vs
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  = Subst (in_scope `extendInScopeSetList` vs) 
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	  (ids `delVarEnvList` vs) (tvs `delVarEnvList` vs) (cvs `delVarEnvList` vs)
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-- | Optimized version of 'extendInScopeList' that can be used if you are certain 
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-- all the things being added are 'Id's and hence none are 'TyVar's or 'CoVar's
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extendInScopeIds :: Subst -> [Id] -> Subst
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extendInScopeIds (Subst in_scope ids tvs cvs) vs 
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  = Subst (in_scope `extendInScopeSetList` vs) 
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	  (ids `delVarEnvList` vs) tvs cvs
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setInScope :: Subst -> InScopeSet -> Subst
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setInScope (Subst _ ids tvs cvs) in_scope = Subst in_scope ids tvs cvs
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\end{code}

Pretty printing, for debugging only

\begin{code}
instance Outputable Subst where
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  ppr (Subst in_scope ids tvs cvs) 
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	=  ptext (sLit "<InScope =") <+> braces (fsep (map ppr (varEnvElts (getInScopeVars in_scope))))
	$$ ptext (sLit " IdSubst   =") <+> ppr ids
	$$ ptext (sLit " TvSubst   =") <+> ppr tvs
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        $$ ptext (sLit " CvSubst   =") <+> ppr cvs   
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 	 <> char '>'
\end{code}


%************************************************************************
%*									*
	Substituting expressions
%*									*
%************************************************************************

\begin{code}
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-- | Apply a substititon to an entire 'CoreExpr'. Rememeber, you may only 
-- apply the substitution /once/: see "CoreSubst#apply_once"
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--
-- Do *not* attempt to short-cut in the case of an empty substitution!
-- See Note [Extending the Subst]
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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 subst orig_expr

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

subst_expr :: Subst -> CoreExpr -> CoreExpr
subst_expr subst expr
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  = go expr
  where
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    go (Var v)	       = lookupIdSubst (text "subst_expr") subst v 
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    go (Type ty)       = Type (substTy subst ty)
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    go (Coercion co)   = Coercion (substCo subst co)
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    go (Lit lit)       = Lit lit
    go (App fun arg)   = App (go fun) (go arg)
    go (Note note e)   = Note (go_note note) (go e)
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    go (Cast e co)     = Cast (go e) (substCo subst co)
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       -- 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
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    go (Lam bndr body) = Lam bndr' (subst_expr subst' body)
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		       where
			 (subst', bndr') = substBndr subst bndr

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    go (Let bind body) = Let bind' (subst_expr subst' body)
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		       where
			 (subst', bind') = substBind subst bind
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    go (Case scrut bndr ty alts) = Case (go scrut) bndr' (substTy subst ty) (map (go_alt subst') alts)
			         where
			  	 (subst', bndr') = substBndr subst bndr

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

    go_note note	     = note
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-- | Apply a substititon to an entire 'CoreBind', additionally returning an updated 'Subst'
-- that should be used by subsequent substitutons.
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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 subst') rhss

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

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substBind subst (Rec pairs) = (subst', Rec (bndrs' `zip` rhss'))
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			    where
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                                (bndrs, rhss)    = unzip pairs
				(subst', bndrs') = substRecBndrs subst bndrs
				rhss' = map (subst_expr subst') rhss
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\end{code}

\begin{code}
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-- | De-shadowing the program is sometimes a useful pre-pass. It can be done simply
-- by running over the bindings with an empty substitution, becuase 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.)
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--
-- [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
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deShadowBinds :: [CoreBind] -> [CoreBind]
deShadowBinds binds = snd (mapAccumL substBind emptySubst binds)
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\end{code}


%************************************************************************
%*									*
	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.

\begin{code}
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-- | Substitutes a 'Var' for another one according to the 'Subst' given, returning
-- the result and an updated 'Subst' that should be used by subsequent substitutons.
-- 'IdInfo' is preserved by this process, although it is substituted into appropriately.
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substBndr :: Subst -> Var -> (Subst, Var)
substBndr subst bndr
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  | isTyVar bndr  = substTyVarBndr subst bndr
  | isCoVar bndr  = substCoVarBndr subst bndr
  | otherwise     = substIdBndr (text "var-bndr") subst subst bndr
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-- | Applies 'substBndr' to a number of 'Var's, accumulating a new 'Subst' left-to-right
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substBndrs :: Subst -> [Var] -> (Subst, [Var])
substBndrs subst bndrs = mapAccumL substBndr subst bndrs

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-- | Substitute in a mutually recursive group of 'Id's
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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
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    (new_subst, new_bndrs) = mapAccumL (substIdBndr (text "rec-bndr") new_subst) subst bndrs
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\end{code}


\begin{code}
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substIdBndr :: SDoc 
            -> Subst		-- ^ Substitution to use for the IdInfo
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	    -> Subst -> Id 	-- ^ Substitition and Id to transform
	    -> (Subst, Id)	-- ^ Transformed pair
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				-- NB: unfolding may be zapped
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substIdBndr _doc rec_subst subst@(Subst in_scope env tvs cvs) old_id
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  = -- pprTrace "substIdBndr" (doc $$ ppr old_id $$ ppr in_scope) $
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    (Subst (in_scope `extendInScopeSet` new_id) new_env tvs cvs, new_id)
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  where
    id1 = uniqAway in_scope old_id	-- id1 is cloned if necessary
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    id2 | no_type_change = id1
	| otherwise	 = setIdType id1 (substTy subst old_ty)

    old_ty = idType old_id
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    no_type_change = isEmptyVarEnv tvs || 
                     isEmptyVarSet (Type.tyVarsOfType old_ty)
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	-- 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
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    new_id = maybeModifyIdInfo mb_new_info id2
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    mb_new_info = substIdInfo rec_subst id2 (idInfo id2)
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	-- NB: unfolding info may be zapped
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	-- Extend the substitution if the unique has changed
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	-- See the notes with substTyVarBndr for the delVarEnv
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    new_env | no_change = delVarEnv env old_id
	    | otherwise = extendVarEnv env old_id (Var new_id)

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

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

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

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

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

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

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-- | Clone a mutually recursive group of 'Id's
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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)	-- Substitition and Id to transform
	    -> (Subst, Id)		-- Transformed pair

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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)
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  where
    id1	    = setVarUnique old_id uniq
    id2     = substIdType subst id1
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    new_id  = maybeModifyIdInfo (substIdInfo rec_subst id2 (idInfo old_id)) id2
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    (new_idvs, new_cvs) | isCoVar old_id = (idvs, extendVarEnv cvs old_id (mkCoVarCo new_id))
                        | otherwise      = (extendVarEnv idvs old_id (Var new_id), cvs)
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\end{code}


%************************************************************************
%*									*
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		Types and Coercions
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%*									*
%************************************************************************

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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 TvSubst.
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\begin{code}
substTyVarBndr :: Subst -> TyVar -> (Subst, TyVar)
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substTyVarBndr (Subst in_scope id_env tv_env cv_env) tv
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  = case Type.substTyVarBndr (TvSubst in_scope tv_env) tv of
	(TvSubst in_scope' tv_env', tv') 
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	   -> (Subst in_scope' id_env tv_env' cv_env, tv')

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

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substCoVarBndr :: Subst -> TyVar -> (Subst, TyVar)
substCoVarBndr (Subst in_scope id_env tv_env cv_env) cv
  = case Coercion.substCoVarBndr (CvSubst in_scope tv_env cv_env) cv of
	(CvSubst in_scope' tv_env' cv_env', cv') 
	   -> (Subst in_scope' id_env tv_env' cv_env', cv')
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-- | See 'Type.substTy'
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substTy :: Subst -> Type -> Type 
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substTy subst ty = Type.substTy (getTvSubst subst) ty

getTvSubst :: Subst -> TvSubst
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getTvSubst (Subst in_scope _ tenv _) = TvSubst in_scope tenv

getCvSubst :: Subst -> CvSubst
getCvSubst (Subst in_scope _ tenv cenv) = CvSubst in_scope tenv cenv

-- | See 'Coercion.substCo'
substCo :: Subst -> Coercion -> Coercion
substCo subst co = Coercion.substCo (getCvSubst subst) co
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\end{code}


%************************************************************************
%*									*
\section{IdInfo substitution}
%*									*
%************************************************************************

\begin{code}
substIdType :: Subst -> Id -> Id
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substIdType subst@(Subst _ _ tv_env cv_env) id
  | (isEmptyVarEnv tv_env && isEmptyVarEnv cv_env) || isEmptyVarSet (Type.tyVarsOfType old_ty) = id
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  | otherwise	= setIdType id (substTy subst old_ty)
		-- The tyVarsOfType 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

------------------
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-- | Substitute into some 'IdInfo' with regard to the supplied new 'Id'.
substIdInfo :: Subst -> Id -> IdInfo -> Maybe IdInfo
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substIdInfo subst new_id info
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  | nothing_to_do = Nothing
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  | otherwise     = Just (info `setSpecInfo`      substSpec subst new_id old_rules
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			       `setUnfoldingInfo` substUnfolding subst old_unf)
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  where
    old_rules 	  = specInfo info
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    old_unf	  = unfoldingInfo info
    nothing_to_do = isEmptySpecInfo old_rules && isClosedUnfolding old_unf
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------------------
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-- | Substitutes for the 'Id's within an unfolding
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substUnfolding, substUnfoldingSC :: Subst -> Unfolding -> Unfolding
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	-- Seq'ing on the returned Unfolding is enough to cause
	-- all the substitutions to happen completely
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substUnfoldingSC subst unf 	 -- Short-cut version
  | isEmptySubst subst = unf
  | otherwise          = substUnfolding subst unf

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substUnfolding subst (DFunUnfolding ar con args)
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  = DFunUnfolding ar con (map subst_arg args)
  where
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    subst_arg = substExpr (text "dfun-unf") subst
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substUnfolding subst unf@(CoreUnfolding { uf_tmpl = tmpl, uf_src = src })
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	-- Retain an InlineRule!
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  | not (isStableSource src)  -- Zap an unstable unfolding, to save substitution work
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  = NoUnfolding
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  | otherwise                 -- But keep a stable one!
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  = seqExpr new_tmpl `seq` 
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    new_src `seq`
    unf { uf_tmpl = new_tmpl, uf_src = new_src }
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  where
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    new_tmpl = substExpr (text "subst-unf") subst tmpl
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    new_src  = substUnfoldingSource subst src
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substUnfolding _ unf = unf	-- NoUnfolding, OtherCon
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-------------------
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substUnfoldingSource :: Subst -> UnfoldingSource -> UnfoldingSource
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substUnfoldingSource (Subst in_scope ids _ _) (InlineWrapper wkr)
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  | Just wkr_expr <- lookupVarEnv ids wkr 
  = case wkr_expr of
      Var w1 -> InlineWrapper w1
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      _other -> -- WARN( True, text "Interesting! CoreSubst.substWorker1:" <+> ppr wkr 
                --             <+> ifPprDebug (equals <+> ppr wkr_expr) )   
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			      -- Note [Worker inlining]
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                InlineStable  -- It's not a wrapper any more, but still inline it!
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  | Just w1  <- lookupInScope in_scope wkr = InlineWrapper w1
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  | otherwise = -- WARN( True, text "Interesting! CoreSubst.substWorker2:" <+> ppr wkr )
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    	      	-- This can legitimately happen.  The worker has been inlined and
		-- dropped as dead code, because we don't treat the UnfoldingSource
		-- as an "occurrence".
                -- Note [Worker inlining]
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      	        InlineStable
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substUnfoldingSource _ src = src
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------------------
substIdOcc :: Subst -> Id -> Id
-- These Ids should not be substituted to non-Ids
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substIdOcc subst v = case lookupIdSubst (text "substIdOcc") subst v of
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	   	        Var v' -> v'
			other  -> pprPanic "substIdOcc" (vcat [ppr v <+> ppr other, ppr subst])
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------------------
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-- | Substitutes for the 'Id's within the 'WorkerInfo' given the new function 'Id'
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substSpec :: Subst -> Id -> SpecInfo -> SpecInfo
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substSpec subst new_id (SpecInfo rules rhs_fvs)
  = seqSpecInfo new_spec `seq` new_spec
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  where
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    subst_ru_fn = const (idName new_id)
    new_spec = SpecInfo (map (substRule subst subst_ru_fn) rules)
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                        (substVarSet subst rhs_fvs)
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------------------
substRulesForImportedIds :: Subst -> [CoreRule] -> [CoreRule]
substRulesForImportedIds subst rules 
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  = map (substRule subst not_needed) rules
  where
    not_needed name = pprPanic "substRulesForImportedIds" (ppr name)
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------------------
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 
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--      of the Id
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substRule _ _ rule@(BuiltinRule {}) = rule
substRule subst subst_ru_fn rule@(Rule { ru_bndrs = bndrs, ru_args = args
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                                       , ru_fn = fn_name, ru_rhs = rhs
                                       , ru_local = is_local })
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  = rule { ru_bndrs = bndrs', 
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           ru_fn    = if is_local 
                        then subst_ru_fn fn_name 
                        else fn_name,
           ru_args  = map (substExpr (text "subst-rule" <+> ppr fn_name) subst') args,
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           ru_rhs   = simpleOptExprWith subst' rhs }
           -- Do simple optimisation on RHS, in case substitution lets
           -- you improve it.  The real simplifier never gets to look at it.
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  where
    (subst', bndrs') = substBndrs subst bndrs
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------------------
substVects :: Subst -> [CoreVect] -> [CoreVect]
substVects subst = map (substVect subst)

------------------
substVect :: Subst -> CoreVect -> CoreVect
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substVect _subst (Vect   v Nothing)    = Vect   v Nothing
substVect subst  (Vect   v (Just rhs)) = Vect   v (Just (simpleOptExprWith subst rhs))
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substVect _subst vd@(NoVect _)         = vd
substVect _subst vd@(VectType _ _)     = vd
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------------------
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substVarSet :: Subst -> VarSet -> VarSet
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substVarSet subst fvs
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  = foldVarSet (unionVarSet . subst_fv subst) emptyVarSet fvs
  where
    subst_fv subst fv 
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        | isId fv   = exprFreeVars (lookupIdSubst (text "substVarSet") subst fv)
        | otherwise = Type.tyVarsOfType (lookupTvSubst subst fv)
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\end{code}
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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 occurence 
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.


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%************************************************************************
%*									*
	The Very Simple Optimiser
%*									*
%************************************************************************

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Note [Optimise coercion boxes agressively]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The simple expression optimiser has special cases for Eq# boxes as follows:
 1. If the result of optimising the RHS of a non-recursive binding is an
    Eq# box, that box is substituted rather than turned into a let, just as
    if it were trivial.

 2. If the result of optimising a case scrutinee is a Eq# box and the case
    deconstructs it in a trivial way, we evaluate the case then and there.

We do this for two reasons:

 1. Bindings/case scrutinisation of this form is often created by the
    evidence-binding mechanism and we need them to be inlined to be able
    desugar RULE LHSes that involve equalities (see e.g. T2291)

 2. The test T4356 fails Lint because it creates a coercion between types
    of kind (* -> * -> *) and (?? -> ? -> *), which differ. If we do this
    inlining agressively we can collapse away the intermediate coercion between
    these two types and hence pass Lint again. (This is a sort of a hack.)

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\begin{code}
simpleOptExpr :: CoreExpr -> CoreExpr
-- Do simple optimisation on an expression
-- The optimisation is very straightforward: just
-- inline non-recursive bindings that are used only once, 
-- or where the RHS is trivial
--
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-- We also inline bindings that bind a Eq# box: see
-- See Note [Optimise coercion boxes agressively].
--
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-- The result is NOT guaranteed occurence-analysed, becuase
-- in  (let x = y in ....) we substitute for x; so y's occ-info
-- may change radically

simpleOptExpr expr
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  = -- pprTrace "simpleOptExpr" (ppr init_subst $$ ppr expr)
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    simpleOptExprWith init_subst expr
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  where
    init_subst = mkEmptySubst (mkInScopeSet (exprFreeVars expr))
	-- It's potentially important to make a proper in-scope set
	-- Consider  let x = ..y.. in \y. ...x...
	-- Then we should remember to clone y before substituting
	-- for x.  It's very unlikely to occur, because we probably
	-- won't *be* substituting for x if it occurs inside a
	-- lambda.  
	--
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        -- It's a bit painful to call exprFreeVars, because it makes
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	-- three passes instead of two (occ-anal, and go)

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simpleOptExprWith :: Subst -> InExpr -> OutExpr
simpleOptExprWith subst expr = simple_opt_expr subst (occurAnalyseExpr expr)

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----------------------
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simpleOptPgm :: DynFlags -> Module 
             -> [CoreBind] -> [CoreRule] -> [CoreVect] 
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             -> IO ([CoreBind], [CoreRule], [CoreVect])
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simpleOptPgm dflags this_mod binds rules vects
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  = do { dumpIfSet_dyn dflags Opt_D_dump_occur_anal "Occurrence analysis"
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                       (pprCoreBindings occ_anald_binds $$ pprRules rules );
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       ; return (reverse binds', substRulesForImportedIds subst' rules, substVects subst' vects) }
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  where
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    occ_anald_binds  = occurAnalysePgm this_mod (\_ -> False) {- No rules active -}
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                                       rules vects binds
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    (subst', binds') = foldl do_one (emptySubst, []) occ_anald_binds
                       
    do_one (subst, binds') bind 
      = case simple_opt_bind subst bind of
          (subst', Nothing)    -> (subst', binds')
          (subst', Just bind') -> (subst', bind':binds')

----------------------
type InVar   = Var
type OutVar  = Var
type InId    = Id
type OutId   = Id
type InExpr  = CoreExpr
type OutExpr = CoreExpr

-- In these functions the substitution maps InVar -> OutExpr

----------------------
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simple_opt_expr, simple_opt_expr' :: Subst -> InExpr -> OutExpr
simple_opt_expr s e = simple_opt_expr' s e

simple_opt_expr' subst expr
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  = go expr
  where
    go (Var v)          = lookupIdSubst (text "simpleOptExpr") subst v
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    go (App e1 e2)      = simple_app subst e1 [go e2]
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    go (Type ty)        = Type     (substTy subst ty)
    go (Coercion co)    = Coercion (optCoercion (getCvSubst subst) co)
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    go (Lit lit)        = Lit lit
    go (Note note e)    = Note note (go e)
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    go (Cast e co)      | isReflCo co' = go e
       	                | otherwise    = Cast (go e) co' 
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                        where
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                          co' = optCoercion (getCvSubst subst) co
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    go (Let bind body) = case simple_opt_bind subst bind of
                           (subst', Nothing)   -> simple_opt_expr subst' body
                           (subst', Just bind) -> Let bind (simple_opt_expr subst' body)

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    go lam@(Lam {})     = go_lam [] subst lam
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    go (Case e b ty as)
      | [(DataAlt dc, [cov], e_alt)] <- as -- See Note [Optimise coercion boxes agressively]
      , dc `hasKey` eqBoxDataConKey
      , (Var fun, [Type _, Type _, Coercion co]) <- collectArgs e'
      , isDataConWorkId fun
      , isDeadBinder b
      = simple_opt_expr (extendCvSubst subst cov co) e_alt
      | otherwise
      = Case (go e) b' (substTy subst ty)
       		       (map (go_alt subst') as)
        where
          e' = go e
          (subst', b') = subst_opt_bndr subst b
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    ----------------------
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    go_alt subst (con, bndrs, rhs) 
      = (con, bndrs', simple_opt_expr subst' rhs)
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      where
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	(subst', bndrs') = subst_opt_bndrs subst bndrs
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    ----------------------
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    -- go_lam tries eta reduction
    go_lam bs' subst (Lam b e) 
       = go_lam (b':bs') subst' e
       where
         (subst', b') = subst_opt_bndr subst b
    go_lam bs' subst e 
       | Just etad_e <- tryEtaReduce bs e' = etad_e
       | otherwise                         = mkLams bs e'
       where
         bs = reverse bs'
         e' = simple_opt_expr subst e

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----------------------
-- simple_app collects arguments for beta reduction
simple_app :: Subst -> InExpr -> [OutExpr] -> CoreExpr
simple_app subst (App e1 e2) as   
  = simple_app subst e1 (simple_opt_expr subst e2 : as)
simple_app subst (Lam b e) (a:as) 
  = case maybe_substitute subst b a of
      Just ext_subst -> simple_app ext_subst e as
      Nothing        -> Let (NonRec b2 a) (simple_app subst' e as)
  where
    (subst', b') = subst_opt_bndr subst b
    b2 = add_info subst' b b'
simple_app subst e as
  = foldl App (simple_opt_expr subst e) as

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simple_opt_bind,simple_opt_bind' :: Subst -> CoreBind -> (Subst, Maybe CoreBind)
simple_opt_bind s b 		  -- Can add trace stuff here
  = simple_opt_bind' s b

simple_opt_bind' subst (Rec prs)
  = (subst'', res_bind)
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  where
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    res_bind            = Just (Rec (reverse rev_prs'))
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    (subst', bndrs')    = subst_opt_bndrs subst (map fst prs)
    (subst'', rev_prs') = foldl do_pr (subst', []) (prs `zip` bndrs')
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    do_pr (subst, prs) ((b,r), b') 
       = case maybe_substitute subst b r2 of
           Just subst' -> (subst', prs)
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           Nothing     -> (subst,  (b2,r2):prs)
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       where
         b2 = add_info subst b b'
         r2 = simple_opt_expr subst r
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simple_opt_bind' subst (NonRec b r)
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  = case maybe_substitute subst b r' of
      Just ext_subst -> (ext_subst, Nothing)
      Nothing        -> (subst', Just (NonRec b2 r'))
  where
    r' = simple_opt_expr subst r
    (subst', b') = subst_opt_bndr subst b
    b2 = add_info subst' b b'
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----------------------
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maybe_substitute :: Subst -> InVar -> OutExpr -> Maybe Subst
    -- (maybe_substitute subst in_var out_rhs)  
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    --   either extends subst with (in_var -> out_rhs)
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    --   or     returns Nothing
maybe_substitute subst b r
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  | Type ty <- r 	-- let a::* = TYPE ty in <body>
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  = ASSERT( isTyVar b )
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    Just (extendTvSubst subst b ty)
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  | Coercion co <- r
  = ASSERT( isCoVar b )
    Just (extendCvSubst subst b co)

  | isId b              -- let x = e in <body>
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  , safe_to_inline (idOccInfo b) 
  , isAlwaysActive (idInlineActivation b)	-- Note [Inline prag in simplOpt]
  , not (isStableUnfolding (idUnfolding b))
  , not (isExportedId b)
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  = Just (extendIdSubst subst b r)
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  | otherwise
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  = Nothing
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  where
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	-- Unconditionally safe to inline
    safe_to_inline :: OccInfo -> Bool
    safe_to_inline (IAmALoopBreaker {})     = False
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    safe_to_inline IAmDead                  = True
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    safe_to_inline (OneOcc in_lam one_br _) = (not in_lam && one_br) || trivial
    safe_to_inline NoOccInfo                = trivial

    trivial | exprIsTrivial r = True
            | (Var fun, _args) <- collectArgs r
            , Just dc <- isDataConWorkId_maybe fun
            , dc `hasKey` eqBoxDataConKey = True -- See Note [Optimise coercion boxes agressively]
            | otherwise = False
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----------------------
subst_opt_bndr :: Subst -> InVar -> (Subst, OutVar)
subst_opt_bndr subst bndr
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  | isTyVar bndr  = substTyVarBndr subst bndr
  | isCoVar bndr  = substCoVarBndr subst bndr
  | otherwise     = subst_opt_id_bndr subst bndr
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subst_opt_id_bndr :: Subst -> InId -> (Subst, OutId)
-- Nuke all fragile IdInfo, unfolding, and RULES; 
--    it gets added back later by add_info
-- Rather like SimplEnv.substIdBndr
--
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-- It's important to zap fragile OccInfo (which CoreSubst.substIdBndr 
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-- carefully does not do) because simplOptExpr invalidates it

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subst_opt_id_bndr subst@(Subst in_scope id_subst tv_subst cv_subst) old_id
  = (Subst new_in_scope new_id_subst tv_subst cv_subst, new_id)
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  where
    id1	   = uniqAway in_scope old_id
    id2    = setIdType id1 (substTy subst (idType old_id))
    new_id = zapFragileIdInfo id2	-- Zaps rules, worker-info, unfolding
					-- and fragile OccInfo
    new_in_scope = in_scope `extendInScopeSet` new_id

	-- Extend the substitution if the unique has changed,
	-- or there's some useful occurrence information
	-- See the notes with substTyVarBndr for the delSubstEnv
    new_id_subst | new_id /= old_id
	         = extendVarEnv id_subst old_id (Var new_id)
	         | otherwise 
	         = delVarEnv id_subst old_id

----------------------
subst_opt_bndrs :: Subst -> [InVar] -> (Subst, [OutVar])
subst_opt_bndrs subst bndrs
  = mapAccumL subst_opt_bndr subst bndrs

----------------------
add_info :: Subst -> InVar -> OutVar -> OutVar
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add_info subst old_bndr new_bndr
 | isTyVar old_bndr = new_bndr
 | otherwise        = maybeModifyIdInfo mb_new_info new_bndr
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 where
   mb_new_info = substIdInfo subst new_bndr (idInfo old_bndr)
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\end{code}
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Note [Inline prag in simplOpt]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If there's an INLINE/NOINLINE pragma that restricts the phase in 
which the binder can be inlined, we don't inline here; after all,
we don't know what phase we're in.  Here's an example

  foo :: Int -> Int -> Int
  {-# INLINE foo #-}
  foo m n = inner m
     where
       {-# INLINE [1] inner #-}
       inner m = m+n

  bar :: Int -> Int
  bar n = foo n 1

When inlining 'foo' in 'bar' we want the let-binding for 'inner' 
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to remain visible until Phase 1

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