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 [diderot] / branches / ein16 / src / compiler / high-il / normalize-ein.sml

# View of /branches/ein16/src/compiler/high-il/normalize-ein.sml

Thu Apr 17 04:30:15 2014 UTC (5 years, 5 months ago) by cchiw
Original Path: branches/charisee/src/compiler/high-il/normalize-ein.sml
File size: 24650 byte(s)
`normalize`
```structure NormalizeEin = struct

local

structure E = Ein
structure P=Printer(*
structure O =OrderEin*)
in

(*Flattens Add constructor: change, expression *)
|flatten(i,((E.Const c):: l'))=
if (c>0 orelse c<0) then let
val(b,a)=flatten(i,l') in (b,[E.Const c]@a) end
else flatten(1,l')
| flatten(i,[])=(i,[])
| flatten (i,e::l') =  let
val(b,a)=flatten(i,l') in (b,[e]@a) end

val (b,a)=flatten(0,e)
in case a
of [] => (1,E.Const(1))
| [e] => (1,e)
(* end case *)
end

fun mkProd [e]=(1,e)
| mkProd(e)=let
fun flatten(i,((E.Prod l)::l'))= flatten(1,l@l')
|flatten(i,((E.Const c)::l'))=
if(c>0 orelse  0>c) then (3,[E.Const 0])
else flatten(i,l')
| flatten(i,[])=(i,[])
| flatten (i,e::l') =  let val(a,b)=flatten(i,l') in (a,[e]@b) end
val (change,a)=flatten(0,e)
in if(change=3) then (1,E.Const(0))
else case a
of [] => (1,E.Const(0))
| [e] => (1,e)
| es => (change, E.Prod es)
(* end case *)
end

(* filter function shifts constant/greeks to outside product*)
fun filter2([],pre,eps,dels,post)=(pre,eps,dels,post)
| filter2(E.Const c::es,pre, eps,dels,post)=filter2(es, pre@[E.Const c],eps,dels,post)
| filter2(E.Delta d::es,pre,eps,dels,post)= filter2(es,pre,eps,dels@[E.Delta d],post)
| filter2(E.Value v::es, pre, eps,dels,post)=filter2(es, pre@[E.Value v],eps,dels,post)
| filter2(E.Epsilon e::es, pre,eps,dels, post)=filter2(es, pre,eps@[E.Epsilon e],dels,post)
| filter2(E.Tensor(id,[])::es, pre,eps, dels,post)=filter2(es, pre@[E.Tensor(id,[])],eps,dels,post)
| filter2(E.Prod p::es, pre,eps,dels, post)=filter2(p@es,pre,eps,dels,post)
| filter2(e::es, pre,eps,dels, post)= filter2(es, pre, eps,dels,post@[e])

(*Only used to find eps, and embedded sums*)
fun findeps(e,(E.Epsilon eps)::es,rest)=  findeps(e@[E.Epsilon eps],es,rest)
| findeps(e, E.Sum(sx,E.Prod(E.Epsilon eps::ps))::es,rest)= (e@[E.Epsilon eps], rest@ps@es,sx)
| findeps(e, E.Prod p::es,rest)=findeps(e, p@es,rest)
| findeps(e, E.Field f::es,rest)=findeps(e, es,rest@[E.Field f])
| findeps(e, E.Tensor t::es,rest)=findeps(e, es,rest@[E.Tensor t])
| findeps(e,es,rest)= (e, rest@es,[])

fun prodAppPartial ([e1],p1)= E.Apply(E.Partial p1,e1)
| prodAppPartial((e1::e2),p1)=let
val l= prodAppPartial(e2,p1)
val (_,e2')= mkProd[e1,l]
val (_,e1')=mkProd(e2@ [E.Apply(E.Partial p1, e1)])
in
end

(*remove eps Index*)

fun rmEpsIndex(i,[],[],[])= []
| rmEpsIndex(i,[],x,[])= [x]
| rmEpsIndex(i,[],x,e::es)= rmEpsIndex(i,e,[],es)@[x]
| rmEpsIndex(i,  ( c ,lb, ub)::b,x, es)=
if (i=c) then let
val z=[(x@b)]
in (case z of [] => es |_=>z@es) end
else rmEpsIndex(i,b,x@[(c ,lb, ub)],es)

fun doubleEps(count,E.Epsilon (a,b,c),E.Epsilon(d,e,f))=let
(*Function is called when eps are being changed to deltas*)
fun createDeltas(i,s,t,u,v)= let
val c'= rmEpsIndex(E.V i,[],[],count)
val d1=[E.Delta(E.V s,E.V u), E.Delta(E.V t,E.V v)]
val d2= [E.Delta(E.V s,E.V v), E.Delta(E.V t,E.V u)]

in (1,c',d1,d2)
end

in if(a=d) then createDeltas(a,b,c,e,f)
else if(a=e) then createDeltas(a,b,c,f,d)
else if(a=f) then createDeltas(a,b,c,d,e)
else if(b=d) then createDeltas(b,c,a,e,f)
else if(b=e) then createDeltas(b,c,a,f,d)
else if(b=f) then createDeltas(b,c,a,d,e)
else if(c=d) then createDeltas(c,a,b,e,f)
else if(c=e) then createDeltas(c,a,b,f,d)
else if(c=f) then createDeltas(c,a,b,d,e)
else (0,[],[],[])
end

fun distEps([],eps,_,_)=(0,[],[],[],[])
| distEps([e],eps,_,_)=(0,[],[],[],[])
| distEps(e1::e2::[],eps,c1::count,sx)=let
val(change,c',d1,d2)= doubleEps([c1@sx]@count,e1,e2)
in (case change
of 1=>(1, c', eps, d1,d2)
|_=> (0,[],[],[],[])
(*end case*))
end

| distEps(e1::e2::current,eps,count,sx)=let
val(change,c',d1,d2)= doubleEps(count,e1,e2)
in (case change
of 1=>(1, c', eps@current, d1,d2)
|_=> distEps(e2::current, eps@[e1],count,sx)
(*end case*))
end

(* Transform eps to deltas*)
fun epsToDels(count,E.Prod e)= let
val (epsA,es,sx)=findeps([],e,[])
val (change, s', eps,d1,d2)= distEps(epsA,[],count,sx)
val deltas=E.Sub(E.Prod d1,E.Prod d2)

in (case (change,eps,es)
of (0,_,_)=>(print "nooo";(0,[],epsA,es))
|(_,[],[]) =>(1,s',[deltas],[])
| _ =>(1,s',[E.Sub( E.Prod(eps@d1@es), E.Prod(eps@d2@es))],[])
(*end case *))
end

(*Another strategy. Go through entire expression inside summation and jsut examine index to apply deltas*)

(* Apply deltas to tensors/fields*)
fun reduceDelta(c, eps, dels, es)=let
fun distribute(change,d,dels,[],done)=(change,dels@d,done)
| distribute(change,[],[],e,done)=(change,[],done@e)
| distribute(change,[],dels,e::es,done)=distribute(change,dels,[],es,done@[e])
| distribute(change,E.Delta(i,j)::ds,dels,e::es,done)=(case e
of  E.Tensor(id,[tx])=>
if(j=tx) then distribute(change@[j],dels@ds,[] ,es ,done@[E.Tensor(id,[i])])
else distribute(change,ds,dels@[E.Delta(i,j)],E.Tensor(id,[tx])::es,done)
|  E.Field(id,[tx])=>
if(j=tx) then distribute(change@[j],dels@ds,[] ,es ,done@[E.Field(id,[i])])
else distribute(change,ds,dels@[E.Delta(i,j)],E.Field(id,[tx])::es,done)
| E.Apply(E.Partial d,e)=>let
fun distPart([],rest) =(0 ,rest)
| distPart(p::pd,rest)=
if(p=j) then (1,rest@[i]@pd)
else (distPart(pd,rest@[p]))
val (change'',p')=distPart(d,[])
in (case change''
of 0=>distribute(change, ds,dels@[E.Delta(i,j)], [E.Apply(E.Partial d, e)]@es,done)
|_=> distribute(change@[j], dels@ds,[], es,done@[E.Apply(E.Partial p', e)])
(*end case*))
end
| _=>distribute(change,dels@[E.Delta(i,j)]@ds,[],es,done@[e])
(*end case*))

val (change,dels',done)=distribute([],dels,[],es,[])
fun m([],c')=c'
| m(e::es,c')= let val s=rmEpsIndex(e,[],[],c')
in m(es, s) end
val index= m(change, c)
in
(length change, index,E.Prod (eps@dels'@done))
end

(*Apply*)
fun mkApply(E.Apply(E.Partial d,e))=(case e
of E.Tensor(a,[])=>(1,E.Const 0)
| E.Const _ =>(1,E.Const 0)
| E.Delta _ =>(1,E.Const 0)
| E.Value _ =>(1,E.Const 0)
| E.Epsilon _ =>(1,E.Const 0)
| E.Conv (fid,alpha,tid, delta)=> (1, E.Conv(fid,alpha, tid, delta@d))
| E.Add l => (1,E.Add(List.map (fn e => E.Apply(E.Partial d, e)) l))
| E.Sub(e2, e3) =>(1, E.Sub(E.Apply(E.Partial d, e2), E.Apply(E.Partial d, e3)))
| E.Div(e2, e3) =>(1, E.Div(E.Apply(E.Partial d, e2),  e3))(********FIXX******)
| E.Apply(E.Partial d2,e2)=>(1,E.Apply(E.Partial(d@d2), e2))
| E.Prod [e1]=>(1,E.Apply(E.Partial d,e1))
| E.Prod es=> let
val (pre,eps,dels, post)= filter2(es,[],[],[],[])
val (_,x)=mkProd(pre@eps@dels@[prodAppPartial(post,d)])
in (1,x) end
|_=>(0,E.Apply(E.Partial d,e))
(* end case*))

(*Sum Apply*)

fun matchEps(2,_,_,_)= 1 (*matched 2*)
| matchEps(num,_,_,[])=0
| matchEps(0,_,_,[eps])=0
| matchEps(num,[],rest,eps::epsx)=
matchEps(num,rest,[],epsx)
| matchEps(num,E.V p::px,rest,eps::epsx)=
if(p=eps) then (matchEps(num+1,rest@px,[],epsx))
else matchEps(num,px,rest@[E.V p], eps::epsx)
| matchEps(num,p::px,rest,eps)=
matchEps(num,px,rest,eps)

(*

fun epsapply(c,eps,dels,post)=let
fun  applyEps(change,count,[],[],rest,done)= (print "kkk";(0,E.Const 0))
| applyEps(change,count,eps,epsrest,[],done)=(print "yyyy";(0,E.Const 0))
| applyEps(change,count,[],epsrest,r::rest,done)=(print "bb";applyEps(change,count,epsrest,[],rest,done@[r]))
| applyEps(change,count,eps1::eps,epsrest,r::rest,done)=( print "lrr";(case (r,eps1)
of (E.Sum(c2,E.Prod(E.Epsilon eps2::s2)),_)=> let
val (change', s',_,d1,d2)= distEps([eps1,E.Epsilon eps2],[],count@c2)
in (case change'
of 1=> let
val (_,p1)=mkProd(epsrest@eps@d1@dels@done@s2@rest)
val (_,p2)=mkProd(epsrest@eps@d2@dels@done@s2@rest)
in
(1,E.Sum(s',E.Sub(p1,p2))) end
| _=>applyEps(change,count,eps, epsrest@[eps1],r::rest,done)
(*end case*))
end
| (E.Conv(v,vx, h ,d),E.Epsilon(i,j,k))=> let
val change'= matchEps(0,d,[],[i,j,k])
in (case change' of 1=>  (1,E.Const 0)
|_=>  applyEps(0,count,epsrest@[eps1],[],rest,done@[r]))
end
|_=>applyEps(0,count,epsrest@[eps1],[],rest,done@[r])
(*end case*)))

val (change, s', eps',d1,d2)= distEps(eps,[],c)
in (case change
of 1 =>  let
val (_,p1)=mkProd(eps'@d1@dels@post)
val (_,p2)=mkProd(eps'@d2@dels@post)
in  (print "in changed";(1,E.Sub(E.Sum(s',p1), E.Sum(s',p2)))) end
|_=> (print "in apply eps";applyEps(0,c,eps,[],post,[]))
(*end case*))
end

*)

(*print summation range*)
fun handleIndex e= (case e
of E.C(cx)=> String.concat["'",Int.toString(cx),"'"]
|  E.V(ix)=> Int.toString(ix)
)
fun handleSumRange (mu,lb,ub)= print(String.concat[(handleIndex mu),"[",Int.toString(lb),"-",Int.toString(ub),"]"])
fun printSx e=(print "\n \$";List.map handleSumRange e; print "\$")

fun K gg=String.concatWith "," (List.map (fn (E.V e1,_,_)=> (Int.toString(e1))) gg)
fun Kt gg=List.map (fn e1=> print(String.concat["[", (K e1),"]"])) gg

(*Apply normalize to each term in product list
or Apply normalize to tail of each list*)
fun normalize (Ein.EIN{params, index, body}) = let
(* val _ = print(String.concat["\n IN NORMALIZE@", P.printbody(body),"@\n"])*)
val changed = ref false
val sumIndex=ref []

fun rewriteBody body =
(case body
of E.Const _=> body
| E.Tensor _ =>body
| E.Field _=> body
| E.Delta _ => body
| E.Value _ =>body
| E.Epsilon _=>body
| E.Conv _=>body

| E.Neg(E.Neg e)=> rewriteBody e
| E.Neg e => E.Neg(rewriteBody e)
in if (change=1) then ( changed:=true;body') else body' end
| E.Sub(a, E.Field f)=> (changed:=true;E.Add[a, E.Neg(E.Field(f))])
| E.Sub (a,b)=>  E.Sub(rewriteBody a, rewriteBody b)
| E.Div(E.Div(a,b),E.Div(c,d))=> rewriteBody (E.Div(E.Prod[a,d],E.Prod[b,c]))
| E.Div(E.Div(a,b),c)=> rewriteBody (E.Div(a, E.Prod[b,c]))
| E.Div(a,E.Div(b,c))=>  rewriteBody (E.Div(E.Prod[a,c],b))
| E.Div (a, b) => E.Div(rewriteBody a, rewriteBody b)
| E.Partial _=>body
| E.Krn(tid,deltas,pos)=> E.Krn(tid,deltas, (rewriteBody pos))
| E.Img(fid,alpha,pos)=> E.Img(fid,alpha, (List.map rewriteBody pos))

(*************Product**************)
| E.Prod [e1] => rewriteBody e1
| E.Prod((E.Div(e2,e3))::e4)=>
(changed :=true; E.Div(E.Prod([e2]@e4), e3 ))
(changed := true; E.Add(List.map (fn e=> E.Prod([e]@e3)) e2))
(changed := true; E.Add(List.map (fn e=> E.Prod([e1,e]@e3)) e2))
| E.Prod((E.Sub(e2,e3))::e4)=>
(changed :=true; E.Sub(E.Prod([e2]@e4), E.Prod([e3]@e4 )))
| E.Prod(e1::E.Sub(e2,e3)::e4)=>
(changed :=true; E.Sub(E.Prod([e1,e2]@e4), E.Prod([e1,e3]@e4 )))

| E.Prod [E.Partial r1,E.Partial r2]=>
(changed:=true;E.Partial(r1@r2))
| E.Prod(E.Partial r1::E.Partial r2::p)=>
(changed:=true;E.Prod([E.Partial(r1@r2)]@p))

(*************Product EPS **************)

(* Apply (d, e) shoudl be convereted to Conv operator *)
| E.Prod(E.Epsilon(i,j,k)::E.Apply(E.Partial d,e)::es)=>let
val change= matchEps(0,d,[],[i,j,k])
in case (change,es)
of (1,_) =>(changed:=true; E.Const 0)
| (_,[]) =>E.Prod[E.Epsilon(i,j,k),rewriteBody (E.Apply(E.Partial d,e))]
|(_,_)=> let
val a=rewriteBody(E.Prod([E.Apply(E.Partial d,e)]@ es))
val (_,b)=mkProd [E.Epsilon(i,j,k),a]
in b end
end
| E.Prod(E.Epsilon(i,j,k)::E.Conv(V,alpha, h, d)::es)=>let

val change= matchEps(0,d,[],[i,j,k])
in case (change,es)
of (1,_) =>(changed:=true; E.Const 0)
| (_,[]) =>E.Prod[E.Epsilon(i,j,k),E.Conv(V,alpha, h, d)]
| (_,_) =>let
val a=rewriteBody(E.Prod([E.Conv(V,alpha, h, d)]@ es))
val (_,b) = mkProd [E.Epsilon(i,j,k),a]
in b end
end

| E.Prod[(E.Epsilon(e1,e2,e3)), E.Tensor(_,[E.V i1,E.V i2])]=>
if(e2=i1 andalso e3=i2) then (changed :=true;E.Const(0))
else body

| E.Prod(E.Epsilon eps1::ps)=>
let

val ref x=sumIndex
val (i,s',e,rest)=epsToDels(x,body)
in (case (i, e,rest)
of (1,[e1],_) =>(changed:=true;sumIndex:=s';e1)
|(0,eps,[])=>body
|(0,eps,rest)=> let
val p'=rewriteBody(E.Prod rest)
val p''= (case p' of E.Prod p=>p |e=>[e])
val(_,b)= mkProd (eps@p'')
in b end
(*end case*))
end
| E.Prod(E.Sum(c1,E.Prod(E.Epsilon e1::es1))::E.Sum(c2,E.Prod(E.Epsilon e2::es2))::es)=>let
val ref x=sumIndex

val m= Kt x

val c'= [c1@c2]@x
val (i,s',e,rest)=epsToDels(c', E.Prod([E.Epsilon e1, E.Epsilon e2]@es1@es2@es))
val gsg=Kt s'

in (case (i, e,rest)
of (1,[e1],_)=> (changed:=true;sumIndex:=s';let
val ss=List.nth(s',((length s')-2))
in
E.Sum(ss,e1) end )
| _=>let
val eA=rewriteBody(E.Sum(c1,E.Prod(E.Epsilon e1::es1)))
val eB=rewriteBody(E.Prod(E.Sum(c2,E.Prod(E.Epsilon e2::es2))::es))
val (_,e)=mkProd([eA,eB])
in e
end
(*end case*))
end

| E.Prod(E.Delta d::es)=>let
val (pre',eps, dels,post)= filter2(E.Delta d::es,[],[],[],[])
val ref x=sumIndex
val (change,i',a)=reduceDelta(x, eps, dels, post)

in (case (change,a)
of (0, _)=> E.Prod [E.Delta d,rewriteBody(E.Prod es)]
| (_, E.Prod p)=>let
val (_, p') = mkProd p
in (changed:=true;sumIndex:=i';p') end
| _ => (changed:=true;sumIndex:=i';a )
(*end case*))
end

| E.Prod[e1,e2]=> let val (_,b)=mkProd[rewriteBody e1, rewriteBody e2] in b end
| E.Prod(e::es)=>let
val e'=rewriteBody e
val e2=rewriteBody(E.Prod es)
val(_,b)=(case e2
of E.Prod p'=> mkProd([e']@p')
|_=>mkProd [e',e2])
in b
end
(**************Apply**************)

(* Apply, Sum*)
| E.Apply(E.Partial d,E.Sum (c,e))=> let
val ref x=sumIndex
val x'=[c]@x
val e' = (sumIndex:=x';rewriteBody(E.Apply(E.Partial d, e)))
val ref s=sumIndex
in
(sumIndex:=tl(s);E.Sum(hd(s), e'))
end

| E.Apply(E.Partial [],e)=> e
| E.Apply(E.Partial p,E.Probe(E.Conv(fid,alpha,tid,d),x))=>
(changed:=true;E.Probe(E.Conv(fid,alpha,tid,d@p),x))
| E.Apply(E.Partial p,E.Conv(fid,alpha,tid,d))=>
(changed:=true;E.Conv(fid,alpha,tid,d@p))
| E.Apply(E.Partial p, e)=>let
val body'=E.Apply(E.Partial p, rewriteBody e)
val (c, e')=mkApply(body')
in (case c
of 1=>(changed:=true;e')
| _ =>e') end
| E.Apply(e1,e2)=>E.Apply(rewriteBody e1, rewriteBody e2)

(************** Sum *****************)
| E.Sum([],e)=> (changed:=true;rewriteBody e)
| E.Sum(_,E.Const c)=>(changed:=true;E.Const c)
| E.Sum(c, E.Sum(c', e))=> (changed:=true; E.Sum(c@c', e))
| E.Sum(c, E.Sub(e1,e2))=>(changed:=true; E.Sub(E.Sum(c,e1), E.Sum(c, e2)))
| E.Sum(c,E.Div(e1,e2))=>(changed:=true; E.Div(E.Sum(c,e1),E.Sum(c,e2)))
| E.Sum(c, E.Prod(E.Const e::es))=>(changed:=true;E.Prod[E.Const e,E.Sum(c, E.Prod es)])
| E.Sum(c, E.Prod(E.Value v::es))=>(changed:=true; E.Prod [E.Value v, E.Sum(c, E.Prod es)])
| E.Sum(c, E.Prod(E.Tensor(id,[])::es))=> (changed:=true;E.Prod [E.Tensor(id,[]), E.Sum(c, E.Prod es)])

| E.Sum(c,E.Prod e)=> let
val e' =rewriteBody(E.Prod e)
(*val _=print (String.concat["\n change \n",P.printbody(body ),"\n ==>\n",P.printbody(E.Sum(c,e')),"\n"])*)
val b'= (case e'
of E.Prod p=>let
val (_,b)=mkProd p
in b end
|_=>e'
(* end case*))
val _ =print(P.printbody( b'))
in E.Sum(c,b')
end
| E.Sum(c,e)=>let

val ref x=sumIndex
val c'=[c]@x

val A= Kt c'
val e'=(sumIndex:=c';rewriteBody e)
val ref s=sumIndex

val C= Kt s
val z=hd(s)

val B= Kt [z]
val D=Kt (tl(s))
in (sumIndex:=tl(s);E.Sum(z, e')) end

(*******************Probe*****************)
| E.Probe(E.Sum(c,s),x)=>(changed:=true;E.Sum(c,E.Probe(s,x)))
| E.Probe(E.Tensor t,_)=> E.Tensor t
| E.Probe(E.Neg e1,x)=>(changed:=true;E.Neg(E.Probe(e1,x)))
| E.Probe(E.Sub (a,b),x)=>
(changed:=true;E.Sub(rewriteBody(E.Probe(a,x)), rewriteBody(E.Probe(b,x))))
| E.Probe(E.Div (a,b),x) =>
(changed:=true;E.Div(rewriteBody(E.Probe(a, x)),b))
| E.Probe(E.Prod p, x)=>let
val _=print ("\n probe of prod \n ")
val (p',x')= (rewriteBody (E.Prod p), rewriteBody x)
fun  probeprod([],[e1]) =e1
| probeprod([],rest) = E.Prod rest
| probeprod(E.Const c::es,rest)=
(changed:=true;probeprod(es,rest@[E.Const c]))
| probeprod(E.Tensor t::es,rest)=
(changed:=true;probeprod(es,rest@[E.Tensor t]))
| probeprod(E.Krn e::es, rest)=
(changed:=true;probeprod(es, rest@[E.Krn e]))
| probeprod(E.Delta e::es, rest)=
(changed:=true;probeprod(es, rest@[E.Delta e]))
| probeprod(E.Value e::es, rest)=
(changed:=true;probeprod(es, rest@[E.Value e]))
| probeprod(E.Epsilon e::es, rest)=
(changed:=true;probeprod(es, rest@[E.Epsilon e]))
| probeprod(E.Partial e::es, rest)=
(changed:=true;probeprod(es, rest@[E.Partial e]))
| probeprod(E.Field f::es,rest)=
(changed:=true;print "\n \$#\$ Found Field";probeprod(es,rest@[E.Probe(E.Field f, x')]))

(*  (changed:=true;E.Prod(rest@[E.Probe(E.Field f, x')] @es))*)
| probeprod(E.Conv f::es,rest)=
(changed:=true;print "\n \$#\$ Found Field";probeprod(es,rest@[E.Probe(E.Conv f, x')]))

(*(changed:=true;E.Prod(rest@[E.Probe(E.Conv f, x')] @es))*)
| probeprod(E.Prod p::es , rest)=
(changed:=true;probeprod(p@es,rest))
| probeprod(E.Sum(c,e)::es, rest)=
(changed:=true;print "\n \$#\$ Found Sum in probe product \n "  ;probeprod(es,rest@[E.Sum(c,E.Probe(e, x'))]))
| probeprod(E.Neg(e)::es, rest)=
(changed:=true;probeprod(es,rest@[E.Neg(E.Probe(e, x'))]))
| probeprod(_,[])=body
| probeprod(e1::es, rest)=let
val e'= rewriteBody(E.Prod(e1::es))
val e''= rewriteBody(E.Probe(e',x'))
in  (changed:=true;E.Prod(rest@[e'']))
end
in (case p'
of E.Prod pro=>probeprod(p,[])
|_=> E.Probe(p',x')
(*end case*))
end
| E.Probe(u,v)=>  (E.Probe(rewriteBody u, rewriteBody v))
(*end case*))

fun loop(body ,count) = let
val body' = rewriteBody body

in
if !changed
then (print(String.concat["\n=>",P.printbody(body')]);
changed := false ;sumIndex:=[];loop(body',count+1))
else (body',count)
end

val (b,count) = loop(body,0)
val _ = print(String.concat["\n out of normalize \n",P.printbody(b),"\n Final CounterXX:",Int.toString(count),"\n\n"])
in
(Ein.EIN{params=params, index=index, body=b},count)
end
end

end (* local *)```