(*printer Function returns String*)
structure Printer = struct

    local

      structure E = Ein

    in 

fun intList l = String.concat[String.concatWith "," (List.map Int.toString l)]

fun handleIndex e= (case e
    of E.C(cx)=> String.concat["'",Int.toString(cx),"'"]
    |  E.V(ix)=> Int.toString(ix)
)

fun handleAlpha alpha= String.concat[String.concatWith "," (List.map handleIndex alpha)]

    
fun handleBeta(a,b)=String.concat["δ_(",handleIndex a, ",", handleIndex b,")"]

fun handleSumRange (mu,lb,ub)= String.concat[(handleIndex mu),"[",Int.toString(lb),"-",Int.toString(ub),"]"]
    
fun printbody term = (case term
    of E.Const r => Int.toString(r)
    | E.Tensor(id, []) =>String.concat[" S",Int.toString(id)]
    | E.Tensor(id, alpha) =>String.concat[" T",Int.toString(id),"_",handleAlpha alpha]
    | E.Field(id, []) =>String.concat[" F",Int.toString(id)]
    | E.Field(id, alpha) =>String.concat[" F",Int.toString(id),"_",handleAlpha alpha]
    | E.Krn(tid,[],pos) =>String.concat[" H ",Int.toString(tid),"[",  (printbody pos),"]"]
    | E.Krn(tid,betas,pos) => String.concat[" H",Int.toString(tid),"^{", String.concat (List.map handleBeta betas),"} [",(printbody pos),"]"]
    | E.Delta(ix) =>  handleBeta ix
    | E.Value(ix)=> String.concat["_",Int.toString(ix),"_"]
    | E.Epsilon(ix, jx, kx) => String.concat["E_",Int.toString(ix), Int.toString(jx), Int.toString(kx)]
    | E.Sum (sumindex,e1)=>String.concat[" Σ_",String.concatWith ","(List.map handleSumRange sumindex),"~" ,printbody e1,"~"]
    | E.Neg e1 => String.concat["-NEG-", printbody e1]
    | E.Add el => String.concat["(",String.concatWith "+" (List.map printbody el),")"]
    | E.Sub(e1, e2) => String.concat ["(",printbody(e1),"- ",printbody(e2), ")"]
    | E.Prod el => String.concat["{{",String.concatWith "* " (List.map printbody el),"}}"]
    | E.Div(e1,e2) => String.concat ["(",printbody(e1),"/ ",printbody (e2), ")"]
    | E.Partial alpha => String.concat["d/dx_",handleAlpha alpha]
    | E.Apply(e1, e2)=> String.concat [ printbody(e1),"@{", printbody(e2),"} "]
    | E.Conv(fid,alpha, tid ,[])=> String.concat["|v",Int.toString(fid),"_{",handleAlpha alpha, "}★h",Int.toString(tid),"|"]
    | E.Conv(fid,alpha, tid, beta)=> String.concat["|v",Int.toString(fid),"_{",handleAlpha alpha, "}★d/dx_{",handleAlpha beta,"}h",Int.toString(tid),"|"]
    | E.Probe (e1,e2)=> String.concat ["",printbody(e1), "","[", printbody(e2),"]"]
    | E.Img (fid,alpha,pos)=> String.concat [" V", Int.toString(fid),"_",handleAlpha alpha,"[",
                (String.concatWith "," (List.map printbody pos)),"]"]
     

           
            (* end case *))
        fun printerE (Ein.EIN{params, index, body}) = let
        fun Index (dim::i, count) = String.concat["(", Int.toString count,
                " DIM:", Int.toString dim, ")", Index(i,count+1)]
            | Index (_, count) = ""
        fun Param(E.TEN(t,shape)::param, i)=let 
                val shape'=List.map(fn e1=>Int.toString(e1)) shape
                in String.concat[Int.toString(i), ":TEN", Int.toString t," ", String.concatWith"," shape'," --",Param(param, i+1)]
                end
            | Param(E.FLD(d)::param, i)= String.concat[Int.toString(i), ":FLD-", Int.toString d," ",Param(param, i+1)]
               | Param(E.IMG(d)::param, i)= String.concat[Int.toString(i), ":IMG-", Int.toString d," ",Param(param, i+1)]
               | Param(E.KRN::param, i)= String.concat[Int.toString(i), ":KRN ",Param(param, i+1)]
            | Param(_,_)=""
   
        val str=String.concat ["\n" ,Param(params, 0)," <",printbody(body),">"," _{",Index(index,0),"}  \n "]
        in
            str
        end

       (* fun printerApp(R.App(e,l))= printerE(e)
            | printerApp(_)= ""*)
                    
    end (* local *)
  end