Simplify.lhs 86.4 KB
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%
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% (c) The AQUA Project, Glasgow University, 1993-1998
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%
\section[Simplify]{The main module of the simplifier}

\begin{code}
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module Simplify ( simplTopBinds, simplExpr ) where
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#include "HsVersions.h"
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Wibble  
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import DynFlags
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import SimplMonad
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import Type hiding      ( substTy, extendTvSubst )
import SimplEnv
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import SimplUtils
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import FamInstEnv	( FamInstEnv )
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import Id
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import MkId		( mkImpossibleExpr, seqId )
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import Var
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import IdInfo
import Coercion
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import FamInstEnv       ( topNormaliseType )
import DataCon          ( dataConRepStrictness, dataConUnivTyVars )
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import CoreSyn
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import NewDemand        ( isStrictDmd, splitStrictSig )
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import PprCore          ( pprParendExpr, pprCoreExpr )
import CoreUnfold       ( mkUnfolding, callSiteInline, CallCtxt(..) )
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import CoreUtils
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import CoreArity	( exprArity )
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import Rules            ( lookupRule, getRules )
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import BasicTypes       ( isMarkedStrict, Arity )
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import CostCentre       ( currentCCS, pushCCisNop )
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import TysPrim          ( realWorldStatePrimTy )
import PrelInfo         ( realWorldPrimId )
import BasicTypes       ( TopLevelFlag(..), isTopLevel,
                          RecFlag(..), isNonRuleLoopBreaker )
import Maybes           ( orElse )
import Data.List        ( mapAccumL )
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import Outputable
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import FastString
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\end{code}


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The guts of the simplifier is in this module, but the driver loop for
the simplifier is in SimplCore.lhs.
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-----------------------------------------
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        *** IMPORTANT NOTE ***
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-----------------------------------------
The simplifier used to guarantee that the output had no shadowing, but
it does not do so any more.   (Actually, it never did!)  The reason is
documented with simplifyArgs.


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-----------------------------------------
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        *** IMPORTANT NOTE ***
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-----------------------------------------
Many parts of the simplifier return a bunch of "floats" as well as an
expression. This is wrapped as a datatype SimplUtils.FloatsWith.

All "floats" are let-binds, not case-binds, but some non-rec lets may
be unlifted (with RHS ok-for-speculation).



-----------------------------------------
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        ORGANISATION OF FUNCTIONS
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-----------------------------------------
simplTopBinds
  - simplify all top-level binders
  - for NonRec, call simplRecOrTopPair
  - for Rec,    call simplRecBind

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        ------------------------------
simplExpr (applied lambda)      ==> simplNonRecBind
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simplExpr (Let (NonRec ...) ..) ==> simplNonRecBind
simplExpr (Let (Rec ...)    ..) ==> simplify binders; simplRecBind

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        ------------------------------
simplRecBind    [binders already simplfied]
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  - use simplRecOrTopPair on each pair in turn

simplRecOrTopPair [binder already simplified]
  Used for: recursive bindings (top level and nested)
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            top-level non-recursive bindings
  Returns:
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  - check for PreInlineUnconditionally
  - simplLazyBind

simplNonRecBind
  Used for: non-top-level non-recursive bindings
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            beta reductions (which amount to the same thing)
  Because it can deal with strict arts, it takes a
        "thing-inside" and returns an expression
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  - check for PreInlineUnconditionally
  - simplify binder, including its IdInfo
  - if strict binding
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        simplStrictArg
        mkAtomicArgs
        completeNonRecX
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    else
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        simplLazyBind
        addFloats
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simplNonRecX:   [given a *simplified* RHS, but an *unsimplified* binder]
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  Used for: binding case-binder and constr args in a known-constructor case
  - check for PreInLineUnconditionally
  - simplify binder
  - completeNonRecX
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        ------------------------------
simplLazyBind:  [binder already simplified, RHS not]
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  Used for: recursive bindings (top level and nested)
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            top-level non-recursive bindings
            non-top-level, but *lazy* non-recursive bindings
        [must not be strict or unboxed]
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  Returns floats + an augmented environment, not an expression
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  - substituteIdInfo and add result to in-scope
        [so that rules are available in rec rhs]
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  - simplify rhs
  - mkAtomicArgs
  - float if exposes constructor or PAP
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  - completeBind
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completeNonRecX:        [binder and rhs both simplified]
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  - if the the thing needs case binding (unlifted and not ok-for-spec)
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        build a Case
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   else
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        completeBind
        addFloats
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completeBind:   [given a simplified RHS]
        [used for both rec and non-rec bindings, top level and not]
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  - try PostInlineUnconditionally
  - add unfolding [this is the only place we add an unfolding]
  - add arity



Right hand sides and arguments
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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In many ways we want to treat
        (a) the right hand side of a let(rec), and
        (b) a function argument
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in the same way.  But not always!  In particular, we would
like to leave these arguments exactly as they are, so they
will match a RULE more easily.
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        f (g x, h x)
        g (+ x)
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It's harder to make the rule match if we ANF-ise the constructor,
or eta-expand the PAP:

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        f (let { a = g x; b = h x } in (a,b))
        g (\y. + x y)
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On the other hand if we see the let-defns

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        p = (g x, h x)
        q = + x
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then we *do* want to ANF-ise and eta-expand, so that p and q
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can be safely inlined.
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Even floating lets out is a bit dubious.  For let RHS's we float lets
out if that exposes a value, so that the value can be inlined more vigorously.
For example

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        r = let x = e in (x,x)
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Here, if we float the let out we'll expose a nice constructor. We did experiments
that showed this to be a generally good thing.  But it was a bad thing to float
lets out unconditionally, because that meant they got allocated more often.

For function arguments, there's less reason to expose a constructor (it won't
get inlined).  Just possibly it might make a rule match, but I'm pretty skeptical.
So for the moment we don't float lets out of function arguments either.


Eta expansion
~~~~~~~~~~~~~~
For eta expansion, we want to catch things like

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        case e of (a,b) -> \x -> case a of (p,q) -> \y -> r
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If the \x was on the RHS of a let, we'd eta expand to bring the two
lambdas together.  And in general that's a good thing to do.  Perhaps
we should eta expand wherever we find a (value) lambda?  Then the eta
expansion at a let RHS can concentrate solely on the PAP case.
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%************************************************************************
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%*                                                                      *
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\subsection{Bindings}
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%*                                                                      *
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%************************************************************************

\begin{code}
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simplTopBinds :: SimplEnv -> [InBind] -> SimplM [OutBind]
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simplTopBinds env0 binds0
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  = do  {       -- Put all the top-level binders into scope at the start
                -- so that if a transformation rule has unexpectedly brought
                -- anything into scope, then we don't get a complaint about that.
                -- It's rather as if the top-level binders were imported.
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        ; env1 <- simplRecBndrs env0 (bindersOfBinds binds0)
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        ; dflags <- getDOptsSmpl
        ; let dump_flag = dopt Opt_D_dump_inlinings dflags ||
                          dopt Opt_D_dump_rule_firings dflags
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        ; env2 <- simpl_binds dump_flag env1 binds0
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        ; freeTick SimplifierDone
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        ; return (getFloats env2) }
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  where
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        -- We need to track the zapped top-level binders, because
        -- they should have their fragile IdInfo zapped (notably occurrence info)
        -- That's why we run down binds and bndrs' simultaneously.
        --
        -- The dump-flag emits a trace for each top-level binding, which
        -- helps to locate the tracing for inlining and rule firing
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    simpl_binds :: Bool -> SimplEnv -> [InBind] -> SimplM SimplEnv
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    simpl_binds _    env []           = return env
    simpl_binds dump env (bind:binds) = do { env' <- trace_bind dump bind $
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                                                     simpl_bind env bind
                                           ; simpl_binds dump env' binds }
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    trace_bind True  bind = pprTrace "SimplBind" (ppr (bindersOf bind))
    trace_bind False _    = \x -> x
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    simpl_bind env (Rec pairs)  = simplRecBind      env  TopLevel pairs
    simpl_bind env (NonRec b r) = simplRecOrTopPair env' TopLevel b b' r
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        where
          (env', b') = addBndrRules env b (lookupRecBndr env b)
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\end{code}


%************************************************************************
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%*                                                                      *
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\subsection{Lazy bindings}
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%*                                                                      *
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%************************************************************************

simplRecBind is used for
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        * recursive bindings only
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\begin{code}
simplRecBind :: SimplEnv -> TopLevelFlag
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             -> [(InId, InExpr)]
             -> SimplM SimplEnv
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simplRecBind env0 top_lvl pairs0
  = do  { let (env_with_info, triples) = mapAccumL add_rules env0 pairs0
        ; env1 <- go (zapFloats env_with_info) triples
        ; return (env0 `addRecFloats` env1) }
        -- addFloats adds the floats from env1,
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        -- _and_ updates env0 with the in-scope set from env1
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  where
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    add_rules :: SimplEnv -> (InBndr,InExpr) -> (SimplEnv, (InBndr, OutBndr, InExpr))
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        -- Add the (substituted) rules to the binder
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    add_rules env (bndr, rhs) = (env', (bndr, bndr', rhs))
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        where
          (env', bndr') = addBndrRules env bndr (lookupRecBndr env bndr)
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    go env [] = return env
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    go env ((old_bndr, new_bndr, rhs) : pairs)
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        = do { env' <- simplRecOrTopPair env top_lvl old_bndr new_bndr rhs
             ; go env' pairs }
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\end{code}

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simplOrTopPair is used for
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        * recursive bindings (whether top level or not)
        * top-level non-recursive bindings
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It assumes the binder has already been simplified, but not its IdInfo.

\begin{code}
simplRecOrTopPair :: SimplEnv
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                  -> TopLevelFlag
                  -> InId -> OutBndr -> InExpr  -- Binder and rhs
                  -> SimplM SimplEnv    -- Returns an env that includes the binding
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simplRecOrTopPair env top_lvl old_bndr new_bndr rhs
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  | preInlineUnconditionally env top_lvl old_bndr rhs   -- Check for unconditional inline
  = do  { tick (PreInlineUnconditionally old_bndr)
        ; return (extendIdSubst env old_bndr (mkContEx env rhs)) }
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  | otherwise
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  = simplLazyBind env top_lvl Recursive old_bndr new_bndr rhs env
        -- May not actually be recursive, but it doesn't matter
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\end{code}


simplLazyBind is used for
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  * [simplRecOrTopPair] recursive bindings (whether top level or not)
  * [simplRecOrTopPair] top-level non-recursive bindings
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  * [simplNonRecE]      non-top-level *lazy* non-recursive bindings
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Nota bene:
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    1. It assumes that the binder is *already* simplified,
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       and is in scope, and its IdInfo too, except unfolding
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    2. It assumes that the binder type is lifted.

    3. It does not check for pre-inline-unconditionallly;
       that should have been done already.

\begin{code}
simplLazyBind :: SimplEnv
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              -> TopLevelFlag -> RecFlag
              -> InId -> OutId          -- Binder, both pre-and post simpl
                                        -- The OutId has IdInfo, except arity, unfolding
              -> InExpr -> SimplEnv     -- The RHS and its environment
              -> SimplM SimplEnv
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simplLazyBind env top_lvl is_rec bndr bndr1 rhs rhs_se
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  = do  { let   rhs_env     = rhs_se `setInScope` env
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		(tvs, body) = case collectTyBinders rhs of
			        (tvs, body) | not_lam body -> (tvs,body)
					    | otherwise	   -> ([], rhs)
		not_lam (Lam _ _) = False
		not_lam _	  = True
			-- Do not do the "abstract tyyvar" thing if there's
			-- a lambda inside, becuase it defeats eta-reduction
			--    f = /\a. \x. g a x  
			-- should eta-reduce

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        ; (body_env, tvs') <- simplBinders rhs_env tvs
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                -- See Note [Floating and type abstraction] in SimplUtils
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        -- Simplify the RHS
        ; (body_env1, body1) <- simplExprF body_env body mkBoringStop
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        -- ANF-ise a constructor or PAP rhs
        ; (body_env2, body2) <- prepareRhs body_env1 body1

        ; (env', rhs')
            <-  if not (doFloatFromRhs top_lvl is_rec False body2 body_env2)
                then                            -- No floating, just wrap up!
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                     do { rhs' <- mkLam env tvs' (wrapFloats body_env2 body2)
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                        ; return (env, rhs') }

                else if null tvs then           -- Simple floating
                     do { tick LetFloatFromLet
                        ; return (addFloats env body_env2, body2) }

                else                            -- Do type-abstraction first
                     do { tick LetFloatFromLet
                        ; (poly_binds, body3) <- abstractFloats tvs' body_env2 body2
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                        ; rhs' <- mkLam env tvs' body3
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                        ; let env' = foldl (addPolyBind top_lvl) env poly_binds
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                        ; return (env', rhs') }
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        ; completeBind env' top_lvl bndr bndr1 rhs' }
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\end{code}
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A specialised variant of simplNonRec used when the RHS is already simplified,
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notably in knownCon.  It uses case-binding where necessary.

\begin{code}
simplNonRecX :: SimplEnv
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             -> InId            -- Old binder
             -> OutExpr         -- Simplified RHS
             -> SimplM SimplEnv
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simplNonRecX env bndr new_rhs
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  | isDeadBinder bndr	-- Not uncommon; e.g. case (a,b) of b { (p,q) -> p }
  = return env		-- 		 Here b is dead, and we avoid creating
  | otherwise		--		 the binding b = (a,b)
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  = do  { (env', bndr') <- simplBinder env bndr
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        ; completeNonRecX env' (isStrictId bndr) bndr bndr' new_rhs }
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completeNonRecX :: SimplEnv
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                -> Bool
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                -> InId                 -- Old binder
                -> OutId                -- New binder
                -> OutExpr              -- Simplified RHS
                -> SimplM SimplEnv
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completeNonRecX env is_strict old_bndr new_bndr new_rhs
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  = do  { (env1, rhs1) <- prepareRhs (zapFloats env) new_rhs
        ; (env2, rhs2) <-
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                if doFloatFromRhs NotTopLevel NonRecursive is_strict rhs1 env1
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                then do { tick LetFloatFromLet
                        ; return (addFloats env env1, rhs1) }   -- Add the floats to the main env
                else return (env, wrapFloats env1 rhs1)         -- Wrap the floats around the RHS
        ; completeBind env2 NotTopLevel old_bndr new_bndr rhs2 }
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\end{code}

{- No, no, no!  Do not try preInlineUnconditionally in completeNonRecX
   Doing so risks exponential behaviour, because new_rhs has been simplified once already
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   In the cases described by the folowing commment, postInlineUnconditionally will
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   catch many of the relevant cases.
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        -- This happens; for example, the case_bndr during case of
        -- known constructor:  case (a,b) of x { (p,q) -> ... }
        -- Here x isn't mentioned in the RHS, so we don't want to
        -- create the (dead) let-binding  let x = (a,b) in ...
        --
        -- Similarly, single occurrences can be inlined vigourously
        -- e.g.  case (f x, g y) of (a,b) -> ....
        -- If a,b occur once we can avoid constructing the let binding for them.
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   Furthermore in the case-binding case preInlineUnconditionally risks extra thunks
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        -- Consider     case I# (quotInt# x y) of
        --                I# v -> let w = J# v in ...
        -- If we gaily inline (quotInt# x y) for v, we end up building an
        -- extra thunk:
        --                let w = J# (quotInt# x y) in ...
        -- because quotInt# can fail.
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  | preInlineUnconditionally env NotTopLevel bndr new_rhs
  = thing_inside (extendIdSubst env bndr (DoneEx new_rhs))
-}

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----------------------------------
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prepareRhs takes a putative RHS, checks whether it's a PAP or
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constructor application and, if so, converts it to ANF, so that the
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resulting thing can be inlined more easily.  Thus
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        x = (f a, g b)
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becomes
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        t1 = f a
        t2 = g b
        x = (t1,t2)
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We also want to deal well cases like this
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        v = (f e1 `cast` co) e2
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Here we want to make e1,e2 trivial and get
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        x1 = e1; x2 = e2; v = (f x1 `cast` co) v2
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That's what the 'go' loop in prepareRhs does

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\begin{code}
prepareRhs :: SimplEnv -> OutExpr -> SimplM (SimplEnv, OutExpr)
-- Adds new floats to the env iff that allows us to return a good RHS
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prepareRhs env (Cast rhs co)    -- Note [Float coercions]
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  | (ty1, _ty2) <- coercionKind co       -- Do *not* do this if rhs has an unlifted type
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  , not (isUnLiftedType ty1)            -- see Note [Float coercions (unlifted)]
  = do  { (env', rhs') <- makeTrivial env rhs
        ; return (env', Cast rhs' co) }
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prepareRhs env0 rhs0
  = do  { (_is_val, env1, rhs1) <- go 0 env0 rhs0
        ; return (env1, rhs1) }
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  where
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    go n_val_args env (Cast rhs co)
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        = do { (is_val, env', rhs') <- go n_val_args env rhs
             ; return (is_val, env', Cast rhs' co) }
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    go n_val_args env (App fun (Type ty))
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        = do { (is_val, env', rhs') <- go n_val_args env fun
             ; return (is_val, env', App rhs' (Type ty)) }
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    go n_val_args env (App fun arg)
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        = do { (is_val, env', fun') <- go (n_val_args+1) env fun
             ; case is_val of
                True -> do { (env'', arg') <- makeTrivial env' arg
                           ; return (True, env'', App fun' arg') }
                False -> return (False, env, App fun arg) }
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    go n_val_args env (Var fun)
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        = return (is_val, env, Var fun)
        where
          is_val = n_val_args > 0       -- There is at least one arg
                                        -- ...and the fun a constructor or PAP
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                 && (isConLikeId fun || n_val_args < idArity fun)
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    go _ env other
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        = return (False, env, other)
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\end{code}

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Note [Float coercions]
~~~~~~~~~~~~~~~~~~~~~~
When we find the binding
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        x = e `cast` co
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we'd like to transform it to
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        x' = e
        x = x `cast` co         -- A trivial binding
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There's a chance that e will be a constructor application or function, or something
like that, so moving the coerion to the usage site may well cancel the coersions
and lead to further optimisation.  Example:

     data family T a :: *
     data instance T Int = T Int

     foo :: Int -> Int -> Int
     foo m n = ...
        where
          x = T m
          go 0 = 0
          go n = case x of { T m -> go (n-m) }
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                -- This case should optimise
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Note [Float coercions (unlifted)]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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BUT don't do [Float coercions] if 'e' has an unlifted type.
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This *can* happen:

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     foo :: Int = (error (# Int,Int #) "urk")
                  `cast` CoUnsafe (# Int,Int #) Int
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If do the makeTrivial thing to the error call, we'll get
    foo = case error (# Int,Int #) "urk" of v -> v `cast` ...
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But 'v' isn't in scope!
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These strange casts can happen as a result of case-of-case
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        bar = case (case x of { T -> (# 2,3 #); F -> error "urk" }) of
                (# p,q #) -> p+q
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\begin{code}
makeTrivial :: SimplEnv -> OutExpr -> SimplM (SimplEnv, OutExpr)
-- Binds the expression to a variable, if it's not trivial, returning the variable
makeTrivial env expr
  | exprIsTrivial expr
  = return (env, expr)
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  | otherwise           -- See Note [Take care] below
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  = do  { var <- newId (fsLit "a") (exprType expr)
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        ; env' <- completeNonRecX env False var var expr
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--	  pprTrace "makeTrivial" (vcat [ppr var <+> ppr (exprArity (substExpr env' (Var var)))
--	  	   		       , ppr expr
--	  	   		       , ppr (substExpr env' (Var var))
--				       , ppr (idArity (fromJust (lookupInScope (seInScope env') var))) ]) $
	; return (env', substExpr env' (Var var)) }
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	-- The substitution is needed becase we're constructing a new binding
	--     a = rhs
	-- And if rhs is of form (rhs1 |> co), then we might get
	--     a1 = rhs1
	--     a = a1 |> co
	-- and now a's RHS is trivial and can be substituted out, and that
	-- is what completeNonRecX will do
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\end{code}
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%************************************************************************
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%*                                                                      *
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\subsection{Completing a lazy binding}
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%*                                                                      *
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%************************************************************************

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completeBind
  * deals only with Ids, not TyVars
  * takes an already-simplified binder and RHS
  * is used for both recursive and non-recursive bindings
  * is used for both top-level and non-top-level bindings
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It does the following:
  - tries discarding a dead binding
  - tries PostInlineUnconditionally
  - add unfolding [this is the only place we add an unfolding]
  - add arity

It does *not* attempt to do let-to-case.  Why?  Because it is used for
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  - top-level bindings (when let-to-case is impossible)
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  - many situations where the "rhs" is known to be a WHNF
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                (so let-to-case is inappropriate).
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Nor does it do the atomic-argument thing

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\begin{code}
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completeBind :: SimplEnv
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             -> TopLevelFlag            -- Flag stuck into unfolding
             -> InId                    -- Old binder
             -> OutId -> OutExpr        -- New binder and RHS
             -> SimplM SimplEnv
-- completeBind may choose to do its work
--      * by extending the substitution (e.g. let x = y in ...)
--      * or by adding to the floats in the envt
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completeBind env top_lvl old_bndr new_bndr new_rhs
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  | postInlineUnconditionally env top_lvl new_bndr occ_info new_rhs unfolding
                -- Inline and discard the binding
  = do  { tick (PostInlineUnconditionally old_bndr)
        ; -- pprTrace "postInlineUnconditionally" (ppr old_bndr <+> ppr new_bndr <+> ppr new_rhs) $
          return (extendIdSubst env old_bndr (DoneEx new_rhs)) }
        -- Use the substitution to make quite, quite sure that the
        -- substitution will happen, since we are going to discard the binding
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  | otherwise
  = return (addNonRecWithUnf env new_bndr new_rhs unfolding wkr)
  where
    unfolding | omit_unfolding = NoUnfolding
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	      | otherwise      = mkUnfolding (isTopLevel top_lvl) new_rhs
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    old_info    = idInfo old_bndr
    occ_info    = occInfo old_info
    wkr		= substWorker env (workerInfo old_info)
    omit_unfolding = isNonRuleLoopBreaker occ_info 
		   --       or not (activeInline env old_bndr)
    		   -- Do *not* trim the unfolding in SimplGently, else
		   -- the specialiser can't see it!

-----------------
addPolyBind :: TopLevelFlag -> SimplEnv -> OutBind -> SimplEnv
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-- Add a new binding to the environment, complete with its unfolding
-- but *do not* do postInlineUnconditionally, because we have already
-- processed some of the scope of the binding
-- We still want the unfolding though.  Consider
--	let 
--	      x = /\a. let y = ... in Just y
--	in body
-- Then we float the y-binding out (via abstractFloats and addPolyBind)
-- but 'x' may well then be inlined in 'body' in which case we'd like the 
-- opportunity to inline 'y' too.

addPolyBind top_lvl env (NonRec poly_id rhs)
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  = addNonRecWithUnf env poly_id rhs unfolding NoWorker
  where
    unfolding | not (activeInline env poly_id) = NoUnfolding
	      | otherwise		       = mkUnfolding (isTopLevel top_lvl) rhs
		-- addNonRecWithInfo adds the new binding in the
		-- proper way (ie complete with unfolding etc),
		-- and extends the in-scope set
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addPolyBind _ env bind@(Rec _) = extendFloats env bind
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		-- Hack: letrecs are more awkward, so we extend "by steam"
		-- without adding unfoldings etc.  At worst this leads to
		-- more simplifier iterations

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-----------------
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addNonRecWithUnf :: SimplEnv
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             	  -> OutId -> OutExpr        -- New binder and RHS
		  -> Unfolding -> WorkerInfo -- and unfolding
             	  -> SimplEnv
-- Add suitable IdInfo to the Id, add the binding to the floats, and extend the in-scope set
addNonRecWithUnf env new_bndr rhs unfolding wkr
  = ASSERT( isId new_bndr )
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    WARN( new_arity < old_arity || new_arity < dmd_arity, 
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          (ptext (sLit "Arity decrease:") <+> ppr final_id <+> ppr old_arity
		<+> ppr new_arity <+> ppr dmd_arity) $$ ppr rhs )
	-- Note [Arity decrease]
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    final_id `seq`      -- This seq forces the Id, and hence its IdInfo,
	                -- and hence any inner substitutions
    addNonRec env final_id rhs
	-- The addNonRec adds it to the in-scope set too
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  where
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	dmd_arity = length $ fst $ splitStrictSig $ idNewStrictness new_bndr
	old_arity = idArity new_bndr

        --      Arity info
	new_arity = exprArity rhs
        new_bndr_info = idInfo new_bndr `setArityInfo` new_arity

        --      Unfolding info
        -- Add the unfolding *only* for non-loop-breakers
        -- Making loop breakers not have an unfolding at all
        -- means that we can avoid tests in exprIsConApp, for example.
        -- This is important: if exprIsConApp says 'yes' for a recursive
        -- thing, then we can get into an infinite loop

        --      Demand info
        -- If the unfolding is a value, the demand info may
        -- go pear-shaped, so we nuke it.  Example:
        --      let x = (a,b) in
        --      case x of (p,q) -> h p q x
        -- Here x is certainly demanded. But after we've nuked
        -- the case, we'll get just
        --      let x = (a,b) in h a b x
        -- and now x is not demanded (I'm assuming h is lazy)
        -- This really happens.  Similarly
        --      let f = \x -> e in ...f..f...
        -- After inlining f at some of its call sites the original binding may
        -- (for example) be no longer strictly demanded.
        -- The solution here is a bit ad hoc...
        info_w_unf = new_bndr_info `setUnfoldingInfo` unfolding
				   `setWorkerInfo`    wkr

        final_info | isEvaldUnfolding unfolding = zapDemandInfo info_w_unf `orElse` info_w_unf
                   | otherwise                  = info_w_unf
	
        final_id = new_bndr `setIdInfo` final_info
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\end{code}
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Note [Arity decrease]
~~~~~~~~~~~~~~~~~~~~~
Generally speaking the arity of a binding should not decrease.  But it *can* 
legitimately happen becuase of RULES.  Eg
	f = g Int
where g has arity 2, will have arity 2.  But if there's a rewrite rule
	g Int --> h
where h has arity 1, then f's arity will decrease.  Here's a real-life example,
which is in the output of Specialise:

     Rec {
	$dm {Arity 2} = \d.\x. op d
	{-# RULES forall d. $dm Int d = $s$dm #-}
	
	dInt = MkD .... opInt ...
	opInt {Arity 1} = $dm dInt

	$s$dm {Arity 0} = \x. op dInt }

Here opInt has arity 1; but when we apply the rule its arity drops to 0.
That's why Specialise goes to a little trouble to pin the right arity
on specialised functions too.
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%************************************************************************
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%*                                                                      *
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\subsection[Simplify-simplExpr]{The main function: simplExpr}
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%*                                                                      *
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%************************************************************************

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The reason for this OutExprStuff stuff is that we want to float *after*
simplifying a RHS, not before.  If we do so naively we get quadratic
behaviour as things float out.

To see why it's important to do it after, consider this (real) example:

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        let t = f x
        in fst t
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==>
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        let t = let a = e1
                    b = e2
                in (a,b)
        in fst t
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==>
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        let a = e1
            b = e2
            t = (a,b)
        in
        a       -- Can't inline a this round, cos it appears twice
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==>
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        e1
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Each of the ==> steps is a round of simplification.  We'd save a
whole round if we float first.  This can cascade.  Consider

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        let f = g d
        in \x -> ...f...
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==>
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        let f = let d1 = ..d.. in \y -> e
        in \x -> ...f...
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==>
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        let d1 = ..d..
        in \x -> ...(\y ->e)...
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Only in this second round can the \y be applied, and it
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might do the same again.


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\begin{code}
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simplExpr :: SimplEnv -> CoreExpr -> SimplM CoreExpr
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simplExpr env expr = simplExprC env expr mkBoringStop
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simplExprC :: SimplEnv -> CoreExpr -> SimplCont -> SimplM CoreExpr
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        -- Simplify an expression, given a continuation
simplExprC env expr cont
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  = -- pprTrace "simplExprC" (ppr expr $$ ppr cont {- $$ ppr (seIdSubst env) -} $$ ppr (seFloats env) ) $
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    do  { (env', expr') <- simplExprF (zapFloats env) expr cont
        ; -- pprTrace "simplExprC ret" (ppr expr $$ ppr expr') $
          -- pprTrace "simplExprC ret3" (ppr (seInScope env')) $
          -- pprTrace "simplExprC ret4" (ppr (seFloats env')) $
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          return (wrapFloats env' expr') }

--------------------------------------------------
simplExprF :: SimplEnv -> InExpr -> SimplCont
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           -> SimplM (SimplEnv, OutExpr)
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simplExprF env e cont
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  = -- pprTrace "simplExprF" (ppr e $$ ppr cont $$ ppr (seTvSubst env) $$ ppr (seIdSubst env) {- $$ ppr (seFloats env) -} ) $
    simplExprF' env e cont
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simplExprF' :: SimplEnv -> InExpr -> SimplCont
            -> SimplM (SimplEnv, OutExpr)
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simplExprF' env (Var v)        cont = simplVar env v cont
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simplExprF' env (Lit lit)      cont = rebuild env (Lit lit) cont
simplExprF' env (Note n expr)  cont = simplNote env n expr cont
simplExprF' env (Cast body co) cont = simplCast env body co cont
simplExprF' env (App fun arg)  cont = simplExprF env fun $
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                                      ApplyTo NoDup arg env cont
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simplExprF' env expr@(Lam _ _) cont
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  = simplLam env (map zap bndrs) body cont
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        -- The main issue here is under-saturated lambdas
        --   (\x1. \x2. e) arg1
        -- Here x1 might have "occurs-once" occ-info, because occ-info
        -- is computed assuming that a group of lambdas is applied
        -- all at once.  If there are too few args, we must zap the
        -- occ-info.
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  where
    n_args   = countArgs cont
    n_params = length bndrs
    (bndrs, body) = collectBinders expr
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    zap | n_args >= n_params = \b -> b
        | otherwise          = \b -> if isTyVar b then b
                                     else zapLamIdInfo b
        -- NB: we count all the args incl type args
        -- so we must count all the binders (incl type lambdas)
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simplExprF' env (Type ty) cont
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  = ASSERT( contIsRhsOrArg cont )
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    do  { ty' <- simplType env ty
        ; rebuild env (Type ty') cont }
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simplExprF' env (Case scrut bndr _ alts) cont
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  | not (switchIsOn (getSwitchChecker env) NoCaseOfCase)
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  =     -- Simplify the scrutinee with a Select continuation
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    simplExprF env scrut (Select NoDup bndr alts env cont)
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  | otherwise
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  =     -- If case-of-case is off, simply simplify the case expression
        -- in a vanilla Stop context, and rebuild the result around it
    do  { case_expr' <- simplExprC env scrut case_cont
        ; rebuild env case_expr' cont }
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  where
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    case_cont = Select NoDup bndr alts env mkBoringStop
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simplExprF' env (Let (Rec pairs) body) cont
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  = do  { env' <- simplRecBndrs env (map fst pairs)
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                -- NB: bndrs' don't have unfoldings or rules
                -- We add them as we go down
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        ; env'' <- simplRecBind env' NotTopLevel pairs
        ; simplExprF env'' body cont }
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simplExprF' env (Let (NonRec bndr rhs) body) cont
  = simplNonRecE env bndr (rhs, env) ([], body) cont
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---------------------------------
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simplType :: SimplEnv -> InType -> SimplM OutType
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        -- Kept monadic just so we can do the seqType
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simplType env ty
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  = -- pprTrace "simplType" (ppr ty $$ ppr (seTvSubst env)) $
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    seqType new_ty   `seq`   return new_ty
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  where
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    new_ty = substTy env ty
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---------------------------------
simplCoercion :: SimplEnv -> InType -> SimplM OutType
simplCoercion env co
  = do { co' <- simplType env co
       ; return (optCoercion co') }
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\end{code}


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%************************************************************************
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%*                                                                      *
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\subsection{The main rebuilder}
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%*                                                                      *
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%************************************************************************

\begin{code}
rebuild :: SimplEnv -> OutExpr -> SimplCont -> SimplM (SimplEnv, OutExpr)
-- At this point the substitution in the SimplEnv should be irrelevant
-- only the in-scope set and floats should matter
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rebuild env expr cont0
  = -- pprTrace "rebuild" (ppr expr $$ ppr cont0 $$ ppr (seFloats env)) $
    case cont0 of
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      Stop {}                      -> return (env, expr)
      CoerceIt co cont             -> rebuild env (mkCoerce co expr) cont
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      Select _ bndr alts se cont   -> rebuildCase (se `setFloats` env) expr bndr alts cont
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      StrictArg fun _ info cont    -> rebuildCall env (fun `App` expr) info cont
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      StrictBind b bs body se cont -> do { env' <- simplNonRecX (se `setFloats` env) b expr
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                                         ; simplLam env' bs body cont }
      ApplyTo _ arg se cont        -> do { arg' <- simplExpr (se `setInScope` env) arg
                                         ; rebuild env (App expr arg') cont }
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\end{code}


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%************************************************************************
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%*                                                                      *
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\subsection{Lambdas}
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%*                                                                      *
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%************************************************************************

\begin{code}
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simplCast :: SimplEnv -> InExpr -> Coercion -> SimplCont
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          -> SimplM (SimplEnv, OutExpr)
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simplCast env body co0 cont0
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  = do  { co1 <- simplCoercion env co0
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        ; simplExprF env body (addCoerce co1 cont0) }
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  where
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       addCoerce co cont = add_coerce co (coercionKind co) cont

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       add_coerce _co (s1, k1) cont     -- co :: ty~ty
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         | s1 `coreEqType` k1 = cont    -- is a no-op
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       add_coerce co1 (s1, _k2) (CoerceIt co2 cont)
         | (_l1, t1) <- coercionKind co2
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		-- 	e |> (g1 :: S1~L) |> (g2 :: L~T1)
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                -- ==>
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                --      e,                       if S1=T1
                --      e |> (g1 . g2 :: S1~T1)  otherwise
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                --
                -- For example, in the initial form of a worker
                -- we may find  (coerce T (coerce S (\x.e))) y
                -- and we'd like it to simplify to e[y/x] in one round
                -- of simplification
         , s1 `coreEqType` t1  = cont            -- The coerces cancel out
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         | otherwise           = CoerceIt (mkTransCoercion co1 co2) cont
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       add_coerce co (s1s2, _t1t2) (ApplyTo dup (Type arg_ty) arg_se cont)
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                -- (f |> g) ty  --->   (f ty) |> (g @ ty)
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                -- This implements the PushT rule from the paper
         | Just (tyvar,_) <- splitForAllTy_maybe s1s2
         , not (isCoVar tyvar)
         = ApplyTo dup (Type ty') (zapSubstEnv env) (addCoerce (mkInstCoercion co ty') cont)
         where
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           ty' = substTy (arg_se `setInScope` env) arg_ty
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        -- ToDo: the PushC rule is not implemented at all
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       add_coerce co (s1s2, _t1t2) (ApplyTo dup arg arg_se cont)
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         | not (isTypeArg arg)  -- This implements the Push rule from the paper
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         , isFunTy s1s2   -- t1t2 must be a function type, becuase it's applied
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                --      (e |> (g :: s1s2 ~ t1->t2)) f
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                -- ===>
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                --      (e (f |> (arg g :: t1~s1))
		--	|> (res g :: s2->t2)
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                --
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                -- t1t2 must be a function type, t1->t2, because it's applied
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                -- to something but s1s2 might conceivably not be
                --
                -- When we build the ApplyTo we can't mix the out-types
                -- with the InExpr in the argument, so we simply substitute
                -- to make it all consistent.  It's a bit messy.
                -- But it isn't a common case.
                --
                -- Example of use: Trac #995
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         = ApplyTo dup new_arg (zapSubstEnv env) (addCoerce co2 cont)
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         where
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           -- we split coercion t1->t2 ~ s1->s2 into t1 ~ s1 and
           -- t2 ~ s2 with left and right on the curried form:
           --    (->) t1 t2 ~ (->) s1 s2
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           [co1, co2] = decomposeCo 2 co
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           new_arg    = mkCoerce (mkSymCoercion co1) arg'
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           arg'       = substExpr (arg_se `setInScope` env) arg
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       add_coerce co _ cont = CoerceIt co cont
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\end{code}

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%************************************************************************
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%*                                                                      *
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\subsection{Lambdas}
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%*                                                                      *
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%************************************************************************
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\begin{code}
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simplLam :: SimplEnv -> [InId] -> InExpr -> SimplCont
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         -> SimplM (SimplEnv, OutExpr)
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simplLam env [] body cont = simplExprF env body cont
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        -- Beta reduction
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simplLam env (bndr:bndrs) body (ApplyTo _ arg arg_se cont)
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  = do  { tick (BetaReduction bndr)
        ; simplNonRecE env bndr (arg, arg_se) (bndrs, body) cont }
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        -- Not enough args, so there are real lambdas left to put in the result
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simplLam env bndrs body cont
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  = do  { (env', bndrs') <- simplLamBndrs env bndrs
        ; body' <- simplExpr env' body
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        ; new_lam <- mkLam env' bndrs' body'
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        ; rebuild env' new_lam cont }
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simplNonRecE :: SimplEnv
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             -> InId                    -- The binder
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             -> (InExpr, SimplEnv)      -- Rhs of binding (or arg of lambda)
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             -> ([InBndr], InExpr)      -- Body of the let/lambda
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