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

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Revision 2508 - (download) (annotate)
Tue Nov 12 17:14:33 2013 UTC (5 years, 10 months ago) by cchiw
Original Path: branches/charisee/src/compiler/high-il/normalize-ein.sml
File size: 23674 byte(s)
Added Tests
structure NormalizeEin = struct

    local

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

      
(*Flattens Add constructor: change, expression *)
fun mkAdd [e]=(1,e)
    | mkAdd(e)=let
    fun flatten((i, (E.Add l)::l'))= flatten(1,l@l')
        |flatten(i,((E.Const c):: l'))=
            if (c>0.0 orelse c<0.0) 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(1.0))
                | [e] => (1,e)
                | es => (b,E.Add es)
                (* 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>0.0 orelse  0.0>c) then (3,[E.Const 0.0])
                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(0.0))
        else case a
        of [] => (1,E.Const(0.0))
        | [e] => (1,e)
        | es => (change, E.Prod es)
        (* end case *)
         end
                
(* filter function shifts constant/greeks to outside product*)
fun filter([],pre,dels,post)=(pre,dels,post)
    | filter(E.Const c::es, pre, dels,post)=filter(es, pre@[E.Const c],dels,post)
    | filter(E.Delta d::es,pre,dels,post)=filter(es,pre,dels@[E.Delta d],post)
    | filter(E.Value v::es, pre, dels,post)=filter(es, pre@[E.Value v],dels,post)
    | filter(E.Epsilon e::es, pre,dels, post)=filter(es, pre@[E.Epsilon e],dels,post)
    | filter(E.Tensor(id,[])::es, pre, dels,post)=filter(es, pre@[E.Tensor(id,[])],dels,post)
    | filter(E.Prod p::es, pre,dels, post)=filter(p@es,pre,dels,post)
    | filter(e::es, pre,dels, post)= filter(es, pre, dels,post@[e])

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

                
        
(*remove eps Index*)
fun rmEpsIndex(i,[],rest)=rest
  | rmEpsIndex(i, (E.V c ,lb, ub)::es,rest)=
    if (i=c) then rest@es
    else rmEpsIndex(i, es, rest@[(E.V c, lb, ub)])
                
                
(*remove index variable from list*)
fun rmIndex(_,_,[])=[]
    | rmIndex([],[],cs)=cs
    | rmIndex([],m ,e1::cs)=[e1]@rmIndex(m,[],cs)
    | rmIndex(i::ix,rest ,(c,lb,ub)::cs)=
        if(i=c) then rmIndex(rest@ix,[],cs)
        else rmIndex(ix,rest@[i],(c,lb,ub)::cs)

    
        
                   
(* Transform eps to deltas*)
fun epsToDels(E.Sum(count,E.Prod e))= let
    fun doubleEps((E.Epsilon (a,b,c))::(E.Epsilon(d,e,f))::es,eps,e3)=
        let

        (*Function is called when eps are being changed to deltas*)
        fun createDeltas(i,s,t,u,v, e3)= let

            (*remove index from original index list*)
                   
            val s'= rmEpsIndex(i,count,[])
   
            val deltas= E.Sub(
                    E.Prod([E.Delta(E.V s,E.V u), E.Delta(E.V t,E.V v)] @e3),
                    E.Prod([E.Delta(E.V s,E.V v), E.Delta(E.V t,E.V u)]@e3))
                   
                in (case (eps,es,s')
                of ([],[],[]) =>(1,deltas)
                |([],_,[]) =>(1,E.Prod( es@[deltas]))
                |([],[],_)=>(1,E.Sum(s',deltas))
                |([],_,_)=>(1,E.Sum(s',E.Prod(es@[deltas])))
                |(_,_,[])=>(1,E.Prod(eps@es@[deltas]))
                |_ =>(1, E.Sum(s', E.Prod(eps@es@[deltas])))
                   )
             end 
                
        in if(a=d) then createDeltas(a,b,c,e,f, e3)
           else if(a=e) then createDeltas(a,b,c,f,d, e3)
           else if(a=f) then createDeltas(a,b,c,d,e, e3)
           else if(b=d) then createDeltas(b,c,a,e,f, e3)
           else if(b=e) then createDeltas(b,c,a,f,d,e3)
           else if(b=f) then createDeltas(b,c,a,d,e,e3)
           else if(c=d) then createDeltas(c,a,b,e,f,e3)
           else if(c=e) then createDeltas(c,a,b,f,d,e3)
           else if(c=f) then createDeltas(c,a,b,d,e,e3)
           else (0,E.Const 0.0)
        end 
    fun findeps(e,[])= (e,[])
      | findeps(e,(E.Epsilon eps)::es)=  findeps(e@[E.Epsilon eps],es)
      | findeps(e,es)= (e, es)
           
      
    fun dist([],eps,rest)=(0,eps,rest)
     | dist([e],eps,rest)=(0,eps@[e],rest)
     | dist(c1::current,eps,rest)=let
            val(i, exp)= doubleEps(c1::current,eps,rest)
        in  (case i of 1=>(i,[exp],[E.Const 2.0])
            |_=> dist(current, eps@[c1],rest))
        end               
        
    val (es,rest)=findeps([],e)
    in
        dist(es,[],rest)
    end

(*Another strategy. Go through entire expression inside summation and jsut examine index to apply deltas*)
                
(* Apply deltas to tensors/fields*)
fun reduceDelta(E.Sum(c,E.Prod p))=let
            
    fun findDeltas(dels,rest,E.Delta d::es)= findDeltas(dels@[E.Delta d], rest, es)
    | findDeltas(dels,rest,E.Epsilon eps::es)=findDeltas(dels,rest@[E.Epsilon eps],es)
    | findDeltas(dels,rest,es)=  (dels,rest,es)

    fun distribute(change,d,dels,[],done)=(change,dels@d,done)
    | distribute(change,[],[],e,done)=(change,[],done@e)
    | distribute(change,E.Delta(i,j)::ds,dels,E.Tensor(id,[tx])::es,done)=
        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)
    | distribute(change,E.Delta(i,j)::ds,dels,E.Field(id,[tx])::es,done)=
        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)
    | distribute(change,E.Delta(i,j)::ds,dels,E.Apply(E.Partial d,e)::es,done)=
        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,[])
            val x=print "in here "
        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
                
                (*
        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)
             *)
                
    | distribute(change,d,dels,e::es,done)=distribute(change,dels@d,[],es,done@[e])
 
    val (dels,eps,es)=findDeltas([],[],p)
    val (change,dels',done)=distribute([],dels,[],es,[])
    val index=rmIndex(change,[],c)

  in
       (length change, E.Sum(index,E.Prod (eps@dels'@done)))
  end


(*Apply Sum*)
fun mkApplySum(E.Apply(E.Partial d,E.Sum(c,e)))=(case e
    of E.Tensor(a,[])=>(1,E.Const 0.0)
    | E.Const _ =>(1,E.Const 0.0)
    | E.Delta _ =>(1,E.Const 0.0)
    | E.Value _ =>(1,E.Const 0.0)
    | E.Epsilon _ =>(1,E.Const 0.0)
            
    | E.Add l => (1,E.Add(List.map (fn e => E.Apply(E.Partial d, E.Sum(c,e))) l))
    | E.Sub(e2, e3) =>(1, E.Sub(E.Apply(E.Partial d, E.Sum(c,e2)), E.Apply(E.Partial d, E.Sum(c,e3))))
    | E.Conv (fid,alpha,tid, delta)=> let
        val e'=E.Conv(fid,alpha, tid, delta@d)
        in (1,E.Sum(c,e')) end
  
    | E.Prod [e1]=>(1,E.Apply(E.Partial d,E.Sum(c,e1)))
    | E.Prod es'=> let
        val y=print "in apply sum"
        val (change,m)=reduceDelta(E.Sum(c,e))
        val t=print(Int.toString(change))
        val (sumc,es)=(case (change,m) of (0,_)=>(c,es')
                | (_,E.Sum( c', E.Prod p)) =>(c',p)
                (*end case*))
        val (pre', dels,post)= filter(es,[],[],[])
        val pre=pre'@dels
        val x1= prodAppPartial(post,d)
        in  (case x1
                of E.Add a=> (1,E.Add(List.map (fn e =>  E.Sum(sumc,E.Prod(pre@[e]))) a))
                | _ => (1,E.Sum(sumc, E.Prod(pre@[x1])))
            (*end case*))
        end
    |_=>(0,E.Apply(E.Partial d,E.Sum(c,e)))
    (* end case*))
                
(*Apply*)
fun mkApply(E.Apply(E.Partial d,e))=(case e
    of E.Tensor(a,[])=>(1,E.Const 0.0)
    | E.Const _ =>(1,E.Const 0.0)
    | E.Delta _ =>(1,E.Const 0.0)
    | E.Value _ =>(1,E.Const 0.0)
    | E.Epsilon _ =>(1,E.Const 0.0)
    | E.Conv (fid,alpha,tid, delta)=> let
        val e'=E.Conv(fid,alpha, tid, delta@d)
        in (1,e') end 
    | 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))
    | 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,dels, post)= filter(es,[],[],[])
        val (_,x)=mkProd(pre@[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 mkSumApply(E.Sum(c,E.Apply(E.Partial d,e)))=(case e
    of E.Const _=>(1,E.Const 0.0)
    | E.Tensor(_,[])=> (1,E.Const 0.0)
    | E.Delta _ =>(1,E.Const 0.0)
    | E.Value _ =>(1,E.Const 0.0)
    | E.Epsilon _ =>(1,E.Const 0.0)
    | E.Conv (fid,alpha,tid, delta)=> let
        val e'=E.Conv(fid,alpha, tid, delta@d)
        in (1,E.Sum(c,e')) end 
    | E.Apply(E.Partial d1,e2)=>(1,E.Sum(c,E.Apply(E.Partial(d@d1),e2)))
    | E.Add l => (1,E.Add(List.map (fn e => E.Sum(c,E.Apply(E.Partial d, e))) l))
    | E.Sub(e1, e2) => (1, E.Sub(E.Sum(c,E.Apply(E.Partial d, e1)), E.Sum(c,E.Apply(E.Partial d, e2))))

    | E.Prod [e1]=>(1,E.Sum(c,E.Apply(E.Partial d,e1)))
                
             
    | E.Prod(E.Tensor(a,[])::e2)=>(1, E.Prod[E.Tensor(a,[]),E.Sum(c,E.Apply(E.Partial d,E.Prod e2))])
    
    | E.Prod es =>(let
        fun prod (change,rest, sum,partial,[]) = (change,E.Sum(sum,E.Apply(E.Partial partial,E.Prod rest)))
        | prod (change,rest, sum,partial,E.Epsilon(i,j,k)::ps)= let
            val change'= matchEps(0,d,[],[i,j,k])
            in (case change'
                of 1 => (1,E.Const 0.0)
                | _ =>prod(change,rest@[E.Epsilon(i,j,k)],sum,partial,ps)
                (*end case*))
            end
        | prod (change,rest, sum,partial,E.Delta(i,j)::ps)=let
            fun applyDelPartial([],_)=(0,[])
            | applyDelPartial(p::px,r)=
                if(j=p) then (1,r@[i]@px)
                else  applyDelPartial(px,r@[p])
                
            val (change',px)=applyDelPartial(d,[])
                
            in (case change'
                of 1 => (let val index=rmIndex([j],[],sum)
                    in prod(1,rest, index,px, ps) end )
                | _ => prod(change,rest@[E.Delta(i,j)], sum,partial, ps)
                (*end case*)) end
                
        | prod (change,rest,sum, partial,e::es)= prod(change,rest@[e],sum,partial,es)
                
        in  prod(0,[],c, d, es)
                
            
        end)
        | _=>(0,E.Sum(c,E.Apply(E.Partial d,e)))
        (* end case*))

              
(*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 changed = ref false
     
      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 => E.Neg(rewriteBody e)
              | E.Add es => let val (change,body')= mkAdd(List.map rewriteBody es)
                   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,E.Sub(b,c))=> (changed:=true;E.Add[E.Sub(a,b),c])*)
              | E.Sub (a,b)=>  E.Sub(rewriteBody a, rewriteBody 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.Add(e2))::e3)=>
                   (changed := true; E.Add(List.map (fn e=> E.Prod([e]@e3)) e2))
              | E.Prod((E.Sub(e2,e3))::e4)=>
                   (changed :=true; E.Sub(E.Prod([e2]@e4), E.Prod([e3]@e4 )))
                
              | E.Prod((E.Div(e2,e3))::e4)=>
                (changed :=true; E.Div(E.Prod([e2]@e4), e3 ))
                
              | E.Prod(e1::E.Add(e2)::e3)=>
                (changed := true; E.Add(List.map (fn e=> E.Prod([e1,e]@e3)) e2))
              | 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.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 0.0)
                    | (_,[]) =>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(e1,e2,e3)), E.Tensor(_,[E.V i1,E.V i2])]=>
                    if(e2=i1 andalso e3=i2) then (changed :=true;E.Const(0.0))
                    else body
              | E.Prod [E.Partial r1, E.Tensor(_,[])]=> (changed:=true;E.Const(0.0))
              | 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))
              | E.Prod(E.Sum(c1,E.Prod(E.Epsilon e1::es1))::E.Sum(c2,E.Prod(E.Epsilon e2::es2))::es)=>let
                  val (change,e,rest)=epsToDels(E.Sum(c1@c2, E.Prod([E.Epsilon e1, E.Epsilon e2]@es1@es2@es)))
                in (case (change,e, rest)
                    of (1,[e1],_)=> (changed:=true;e1)
                    | _=>let
                        val e1=rewriteBody(E.Sum(c1,E.Prod(E.Epsilon e1::es1)))
                        val es'=rewriteBody(E.Prod(E.Sum(c2,E.Prod(E.Epsilon e2::es2))::es))
                        val (_,e)=(case es' of E.Prod p=>mkProd([e1]@p)
                            |_=> mkProd([e1]@e)
                            (*end case*))
                        in e 
                        end
                    (*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 e)=>let
                    val s'=rewriteBody(E.Sum  e)
                    val (c, e')=(case s'
                        of E.Sum e1=> mkApplySum(E.Apply(E.Partial d,s'))
                        | _=>(0, E.Apply(E.Partial d, s'))
                        (*end case*))
                    in (case c
                        of 1=>(changed:=true;e')
                        |_=> e'
                    (*end case*))
                    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.Add l))=> (changed:=true;E.Add(List.map (fn e => E.Sum(c,e)) l))
              | 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.Epsilon eps1::E.Epsilon eps2::ps))=>
                let val (i,e,rest)=epsToDels(body)
                in (case (i, e,rest)
                    of (1,[e1],r) =>(changed:=true;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 E.Sum(c,b) end
                    |_=>body
                    (*end case*))
                   end
                
              | E.Sum(c1,E.Prod(E.Epsilon eps1::E.Sum(c2,E.Prod(E.Epsilon eps2::s2))::ps))=>let 
                    val (i, e, rest)=epsToDels(E.Sum(c1@c2, E.Prod([E.Epsilon eps1, E.Epsilon eps2]@ s2@ps)))
                  in (case (i,e,rest)
                    of (1,[e1],_) =>(changed:=true; e1)
                    |_ => E.Sum(c1,rewriteBody(E.Prod(E.Epsilon eps1::E.Sum(c2,E.Prod(E.Epsilon eps2::s2))::ps)))
                    (* end case*))
                  end
                
              | E.Sum(c,E.Prod(E.Delta d::es))=>let
                    val (change,a)=reduceDelta(body)
                    in (case (change,a)
                of (0, _)=> E.Sum(c,rewriteBody(E.Prod([E.Delta d]@es)))
                        | (_, E.Prod p)=>let
                            val (_, p') = mkProd p
                            in (changed:=true;p') end
                        | _ => (changed:=true;a )
                        (*end case*))
                    end 
  

              | E.Sum(c,E.Apply(E.Partial p,e))=>let
                    val (change,exp)=mkSumApply(body)
                    val exp'=(case change
                        of 1=> (changed:=true;exp)
                        | _ => E.Sum(c,rewriteBody(E.Apply(E.Partial p,e))))
                    in exp' end 
                    

                | E.Sum(c,e)=>E.Sum(c,rewriteBody e)
            
            (*Probe*)
            | E.Probe(E.Sum(c,s),x)=>(changed:=true;E.Sum(c,E.Probe(s,x)))
            | E.Probe(E.Neg e1,x)=>(changed:=true;E.Neg(E.Probe(e1,x)))
            | E.Probe(E.Add es,x) =>
                (changed:=true;E.Add(List.map (fn(e1)=>E.Probe(e1,x)) es))
            | 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 (p',x')= (rewriteBody (E.Prod p), rewriteBody x)
                fun  probeprod([],rest) =
                        (print "err-Did not find field/Conv"; body)
                  | 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;E.Prod(rest@[E.Probe(E.Field f, x')] @es))
                  | probeprod(E.Conv f::es,rest)=
                        (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(_,[])=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
           
               (* val y=(print "Counter:";print(Int.toString(count));print"\n")*)
            in 
              if !changed
                then (changed := false ;loop(body',count+1))
                else (body',count)
            end

    val (b,count) = loop(body,0)
    (*val j=(print "Final Counter:";print(Int.toString(count));print"\n")*)
    in
                (Ein.EIN{params=params, index=index, body=b},count)
    end
end
                


end (* local *)

root@smlnj-gforge.cs.uchicago.edu
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