(* low-to-tree-fn.sml
 *
 * COPYRIGHT (c) 2011 The Diderot Project (http://diderot-language.cs.uchicago.edu)
 * All rights reserved.
 *
 * This module translates the LowIL representation of a program (i.e., a pure CFG) to
 * a block-structured AST with nested expressions.
 *
 * NOTE: this translation is pretty dumb about variable coalescing (i.e., it doesn't do any).
 *)

functor LowToTreeFn (Target : sig

    val supportsPrinting : unit -> bool (* does the target support the Print op? *)

  (* tests for whether various expression forms can appear inline *)
    val inlineCons : int -> bool        (* can n'th-order tensor construction appear inline *)
    val inlineMatrixExp : bool          (* can matrix-valued expressions appear inline? *)

  end) : sig

    val translate : LowIL.program -> TreeIL.program

  end = struct

    structure IL = LowIL
    structure Ty = LowILTypes
    structure V = LowIL.Var
    structure StV = LowIL.StateVar
    structure Op = LowOps
    structure Nd = LowIL.Node
    structure CFG = LowIL.CFG
    structure T = TreeIL
    structure VA = VarAnalysis
    structure InP = Inputs

  (* create new tree IL variables *)
    local
      val newVar = T.Var.new
      val cnt = ref 0
      fun genName prefix = let
            val n = !cnt
            in
              cnt := n+1;
              String.concat[prefix, "_", Int.toString n]
            end
    in
    fun newInput x = newVar (V.name x, T.VK_Input, V.ty x)
    fun newGlobal x = newVar (V.name x, T.VK_Global, V.ty x)
    fun newParam x = newVar (genName("p_" ^ V.name x), T.VK_Local, V.ty x)
    fun newLocal x = newVar (genName("l_" ^ V.name x), T.VK_Local, V.ty x)
    fun newIter x = newVar (genName("i_" ^ V.name x), T.VK_Local, V.ty x)
    end

  (* associate Tree IL state variables with Low IL variables using properties *)
    local
      fun mkStateVar x = T.SV{
              name = StV.name x,
              id = Stamp.new(),
              ty = StV.ty x,
              varying = VA.isVarying x,
              output = StV.isOutput x
            }
    in
    val {getFn = getStateVar, ...} = StV.newProp mkStateVar
    end

    fun mkBlock stms = T.Block{locals=[], body=stms}
    fun mkIf (x, stms, []) = T.S_IfThen(x, mkBlock stms)
      | mkIf (x, stms1, stms2) = T.S_IfThenElse(x, mkBlock stms1, mkBlock stms2)

  (* an environment that tracks bindings of variables to target expressions and the list
   * of locals that have been defined.
   *)
    local
      structure VT = V.Tbl
      fun decCount (IL.V{useCnt, ...}) = let
            val n = !useCnt - 1
            in
              useCnt := n;  (n <= 0)
            end
      datatype target_binding
        = GLOB of T.var         (* variable is global *)
        | TREE of T.exp         (* variable bound to target expression tree *)
        | DEF of T.exp          (* either a target variable or constant for a defined variable *)
      datatype env = E of {
          tbl : target_binding VT.hash_table,
          locals : T.var list
        }
    in
(* DEBUG *)
fun bindToString binding = (case binding
       of GLOB y => "GLOB " ^ T.Var.name y
        | TREE e => "TREE"
        | DEF(T.E_Var y) => "DEF " ^ T.Var.name y
        | DEF e => "DEF"
      (* end case *))
fun dumpEnv (E{tbl, ...}) = let
      fun prEntry (x, binding) =
            print(concat["  ", IL.Var.toString x, " --> ", bindToString binding, "\n"])
      in
        print "*** dump environment\n";
        VT.appi prEntry tbl;
        print "***\n"
      end
(* DEBUG *)

    fun newEnv () = E{tbl = VT.mkTable (512, Fail "tbl"), locals=[]}

  (* use a variable.  If it is a pending expression, we remove it from the table *)
    fun useVar (env as E{tbl, ...}) x = (case VT.find tbl x
           of SOME(GLOB x') => T.E_Var x'
            | SOME(TREE e) => (
(*print(concat["useVar ", V.toString x, " ==> TREE\n"]);*)
                ignore(VT.remove tbl x);
                e)
            | SOME(DEF e) => (
(*print(concat["useVar ", V.toString x, " ==> ", bindToString(DEF e), "; use count = ", Int.toString(V.useCount x), "\n"]);*)
              (* if this is the last use of x, then remove it from the table *)
                if (decCount x) then ignore(VT.remove tbl x) else ();
                e)
            | NONE => (
dumpEnv env;
raise Fail(concat ["useVar(", V.toString x, ")"])
)
          (* end case *))

  (* record a local variable *)
    fun addLocal (E{tbl, locals}, x) = E{tbl=tbl, locals=x::locals}

    fun global (E{tbl, ...}, x, x') = VT.insert tbl (x, GLOB x')

  (* insert a pending expression into the table.  Note that x should only be used once! *)
    fun insert (env as E{tbl, ...}, x, exp) = (
          VT.insert tbl (x, TREE exp);
          env)

    fun rename (env as E{tbl, ...}, x, x') = (
          VT.insert tbl (x, DEF(T.E_Var x'));
          env)

    fun peekGlobal (E{tbl, ...}, x) = (case VT.find tbl x
           of SOME(GLOB x') => SOME x'
            | _ => NONE
          (* end case *))

    fun bindLocal (env, lhs, rhs) = if (V.useCount lhs = 1)
          then (insert(env, lhs, rhs), [])
          else let
            val t = newLocal lhs
            in
              (rename(addLocal(env, t), lhs, t), [T.S_Assign([t], rhs)])
            end

    fun bind (env, lhs, rhs) = (case peekGlobal (env, lhs)
           of SOME x => (env, [T.S_Assign([x], rhs)])
            | NONE => bindLocal (env, lhs, rhs)
          (* end case *))

  (* set the definition of a variable, where the RHS is either a literal constant or a variable *)
    fun bindSimple (env as E{tbl, ...}, lhs, rhs) = (
          case peekGlobal (env, lhs)
           of SOME x => (env, [T.S_Assign([x], rhs)])
            | NONE => (VT.insert tbl (lhs, DEF rhs); (env, []))
          (* end case *))

  (* at the end of a block, we need to assign any pending expressions to locals.  The
   * blkStms list and the resulting statement list are in reverse order.
   *)
    fun flushPending (E{tbl, locals}, blkStms) = let
          fun doVar (x, TREE e, (locals, stms)) = let
                val t = newLocal x
                in
                  VT.insert tbl (x, DEF(T.E_Var t));
                  (t::locals, T.S_Assign([t], e)::stms)
                end
            | doVar (_, _, acc) = acc
          val (locals, stms) = VT.foldi doVar (locals, blkStms) tbl
          in
            (E{tbl=tbl, locals=locals}, stms)
          end

    fun doPhi ((lhs, rhs), (env, predBlks : T.stm list list)) = let
        (* t will be the variable in the continuation of the JOIN *)
          val t = newLocal lhs
          val predBlks = ListPair.map
                (fn (x, stms) => T.S_Assign([t], useVar env x)::stms)
                  (rhs, predBlks)
          in
            (rename (addLocal(env, t), lhs, t), predBlks)
          end

    fun endScope (E{locals, ...}, stms) = T.Block{
            locals = List.rev locals,
            body = stms
          }

    end

  (* Certain IL operators cannot be compiled to inline expressions.  Return
   * false for those and true for all others.
   *)
    fun isInlineOp rator = let
          fun chkTensorTy (Ty.TensorTy[]) = true
            | chkTensorTy (Ty.TensorTy[_]) = true
            | chkTensorTy (Ty.TensorTy[_, _]) = Target.inlineMatrixExp
            | chkTensorTy _ = false
          in
           case rator
             of Op.LoadVoxels(_, 1) => true
              | Op.LoadVoxels _ => false
              | Op.Add ty => chkTensorTy ty
              | Op.Sub ty => chkTensorTy ty
              | Op.Neg ty => chkTensorTy ty
              | Op.Scale ty => chkTensorTy ty
              | Op.MulMatMat _ => Target.inlineMatrixExp
              | Op.MulVecTen3 _ => false
              | Op.MulTen3Vec _ => false
              | Op.ColonMul(Ty.TensorTy dd1, Ty.TensorTy dd2) =>
                (* if the result is a vector or scalar, then it is inline *)
                  (List.length dd1 + List.length dd2 > 5)
              | Op.EigenVecs2x2 => false
              | Op.EigenVecs3x3 => false
              | Op.EigenVals2x2 => false
              | Op.EigenVals3x3 => false
              | Op.Identity _ => Target.inlineMatrixExp
              | Op.Zero _ => Target.inlineMatrixExp
              | Op.Transpose _ => false
              | Op.TensorToWorldSpace(_, ty) => chkTensorTy ty
              | _ => true
            (* end case *)
          end

  (* is a CONS inline? *)
    fun isInlineCons ty = (case ty
           of Ty.SeqTy(Ty.IntTy, _) => true
            | Ty.TensorTy dd => Target.inlineCons(List.length dd)
            | Ty.SeqTy _ => false
            | Ty.DynSeqTy ty => false
            | _ => raise Fail(concat["invalid CONS<", Ty.toString ty, ">"])
          (* end case *))

  (* translate input-variable initialization to a TreeIL expression *)
    fun trInitialization (InP.String s) = ([], T.E_Lit(Literal.String s))
      | trInitialization (InP.Int n) = ([], T.E_Lit(Literal.Int n))
      | trInitialization (InP.Real f) = ([], T.E_Lit(Literal.Float f))
      | trInitialization (InP.Bool b) = ([], T.E_Lit(Literal.Bool b))
      | trInitialization (InP.Tensor(shp, vs)) = let
          fun mk i = T.E_Lit(Literal.Float(Vector.sub(vs, i)))
          fun mkCons (i, [d]) =
                (T.E_Cons(Ty.TensorTy[d], List.tabulate(d, fn j => mk(i+j))), i+d)
            | mkCons (i, d::dd) = let
                fun f (i, j, args) = if (j < d)
                      then let
                        val (arg, i) = mkCons(i, dd)
                        in
                          f (i, j+1, arg::args)
                        end
                      else (List.rev args, i)
                val (args, i) = f (i, 0, [])
                val cons = T.E_Cons(Ty.TensorTy(d::dd), args)
                in
                  if Target.inlineCons(List.length dd + 1)
                    then (cons, i)
                    else raise Fail "non-inline initialization not supported yet"
                end
          val (exp, _) = mkCons(0, shp)
          in
            ([], exp)
          end
      | trInitialization (InP.Seq vs) = raise Fail "trInitialization: Seq"
      | trInitialization _ = raise Fail "trInitialization: impossible"

  (* translate a LowIL assignment to a list of zero or more target statements in reverse
   * order.
   *)
    fun doAssign (env, (lhs, rhs)) = let
          fun doLHS () = (case peekGlobal(env, lhs)
                 of SOME lhs' => (env, lhs')
                  | NONE => let
                      val t = newLocal lhs
                      in
                        (rename (addLocal(env, t), lhs, t), t)
                      end
                (* end case *))
        (* for expressions that are going to be compiled to a call statement *)
          fun assignExp (env, exp) = let
              (* operations that return matrices may not be supported inline *)
                val (env, t) = doLHS()
                in
                  (env, [T.S_Assign([t], exp)])
                end
        (* force an argument to be stored in something that will be mapped to an l-value *)
          fun bindVar (env, x) = (case useVar env x
                 of x' as T.E_State _ => (env, x', [])
                  | x' as T.E_Var _ => (env, x', [])
                  | e => let
                      val x' = newLocal x
                      in
                        (addLocal(env, x'), T.E_Var x', [T.S_Assign([x'], e)])
                      end
                (* end case *))
          in
            case rhs
             of IL.STATE x => bindSimple (env, lhs, T.E_State(getStateVar x))
              | IL.VAR x => bindSimple (env, lhs, useVar env x)
              | IL.LIT lit => bindSimple (env, lhs, T.E_Lit lit)
              | IL.OP(Op.Prepend ty, [item, seq]) => let
                  val (env, t) = doLHS()
                  val (env, item', stms) = bindVar (env, item)
                  val exp = T.E_Op(Op.Prepend ty, [item', useVar env seq])
                  in
                    (env, T.S_Assign([t], exp) :: stms)
                  end
              | IL.OP(Op.Append ty, [seq, item]) => let
                  val (env, t) = doLHS()
                  val (env, item', stms) = bindVar (env, item)
                  val exp = T.E_Op(Op.Append ty, [useVar env seq, item'])
                  in
                    (env, T.S_Assign([t], exp) :: stms)
                  end
              | IL.OP(Op.LoadSeq(ty, nrrd), []) => let
                  val (env, t) = doLHS()
                  in
                    (env, [T.S_LoadNrrd(t, ty, nrrd)])
                  end
              | IL.OP(Op.LoadImage(ty, nrrd, info), []) => let
                  val (env, t) = doLHS()
                  in
                    (env, [T.S_LoadNrrd(t, ty, nrrd)])
                  end
              | IL.OP(Op.Input(InP.INP{ty=Ty.DynSeqTy _, name, desc, init}), []) => let
                  val (env, t) = doLHS()
                  in
                    case init
                     of NONE => (env, [T.S_InputNrrd(t, name, desc, NONE)])
                      | SOME(InP.DynSeq nrrd) => (env, [T.S_InputNrrd(t, name, desc, SOME nrrd)])
                      | _ => raise Fail "bogus initialization for dynamic sequence"
                    (* end case *)
                  end
              | IL.OP(Op.Input(InP.INP{ty=Ty.ImageTy _, name, desc, init}), []) => let
                  val (env, t) = doLHS()
                  in
                    case init
                     of SOME(InP.Proxy(nrrd, _)) => (env, [T.S_InputNrrd(t, name, desc, SOME nrrd)])
                      | SOME(InP.Image _) => (env, [T.S_InputNrrd(t, name, desc, NONE)])
                      | _ => raise Fail "bogus initialization for image"
                    (* end case *)
                  end
              | IL.OP(Op.Input(InP.INP{ty, name, desc, init=NONE}), []) => let
                  val (env, t) = doLHS()
                  in
                    (env, [T.S_Input(t, name, desc, NONE)])
                  end
              | IL.OP(Op.Input(InP.INP{ty, name, desc, init=SOME init}), []) => let
                  val (env, t) = doLHS()
                  val (stms, exp) = trInitialization init
                  in
                    (env, stms@[T.S_Input(t, name, desc, SOME exp)])
                  end
              | IL.OP(rator, args) => let
                  val exp = T.E_Op(rator, List.map (useVar env) args)
                  in
                    if isInlineOp rator
                      then bind (env, lhs, exp)
                      else assignExp (env, exp)
                  end
              | IL.APPLY(f, args) =>
                  bind (env, lhs, T.E_Apply(f, List.map (useVar env) args))
              | IL.CONS(ty, args) => let
                  val exp = T.E_Cons(ty, List.map (useVar env) args)
                  in
                    if isInlineCons ty
                      then bind (env, lhs, exp)
                      else assignExp (env, exp)
                  end
            (* end case *)
          end

  (* In order to reconstruct the block-structure from the CFG, we keep a stack of open ifs.
   * the items on this stack distinguish between when we are processing the then and else
   * branches of the if.
   *)
    datatype open_if
    (* working on the "then" branch.  The fields are statments that preceed the if, the condition,
     * and the else-branch node.
     *)
      = THEN_BR of T.stm list * T.exp * IL.node
    (* working on the "else" branch.  The fields are statments that preceed the if, the condition,
     * the "then" branch statements, and the node that terminated the "then" branch (will be
     * a JOIN, DIE, or STABILIZE).
     *)
      | ELSE_BR of T.stm list * T.exp * T.stm list * IL.node_kind

    fun trCFG (env, prefix, finish, cfg) = let
          fun join (env, [], _, IL.JOIN _) = raise Fail "JOIN with no open if"
            | join (env, [], stms, _) = endScope (env, prefix @ List.rev stms)
            | join (env, THEN_BR(stms1, cond, elseBr)::stk, thenBlk, k) = let
                val (env, thenBlk) = flushPending (env, thenBlk)
                in
                  doNode (env, ELSE_BR(stms1, cond, thenBlk, k)::stk, [], elseBr)
                end
            | join (env, ELSE_BR(stms, cond, thenBlk, k1)::stk, elseBlk, k2) = let
                val (env, elseBlk) = flushPending (env, elseBlk)
                in
                  case (k1, k2)
                   of (IL.JOIN{phis, succ, ...}, IL.JOIN _) => let
                        val (env, [thenBlk, elseBlk]) =
                              List.foldl doPhi (env, [thenBlk, elseBlk]) (!phis)
                        val stm = mkIf(cond, List.rev thenBlk, List.rev elseBlk)
                        in
                          doNode (env, stk, stm::stms, !succ)
                        end
                    | (IL.JOIN{phis, succ, ...}, _) => let
                        val (env, [thenBlk]) = List.foldl doPhi (env, [thenBlk]) (!phis)
                        val stm = mkIf(cond, List.rev thenBlk, List.rev elseBlk)
                        in
                          doNode (env, stk, stm::stms, !succ)
                        end
                    | (_, IL.JOIN{phis, succ, ...}) => let
                        val (env, [elseBlk]) = List.foldl doPhi (env, [elseBlk]) (!phis)
                        val stm = mkIf(cond, List.rev thenBlk, List.rev elseBlk)
                        in
                          doNode (env, stk, stm::stms, !succ)
                        end
                    | (_, _) => raise Fail "no path to exit unimplemented" (* FIXME *)
                  (* end case *)
                end
          and doNode (env, ifStk : open_if list, stms, nd) = (
                case Nd.kind nd
                 of IL.NULL => raise Fail "unexpected NULL"
                  | IL.ENTRY{succ} => doNode (env, ifStk, stms, !succ)
                  | k as IL.JOIN{phis, succ, ...} => join (env, ifStk, stms, k)
                  | IL.COND{cond, trueBranch, falseBranch, ...} => let
                      val cond = useVar env cond
                      val (env, stms) = flushPending (env, stms)
                      in
                        doNode (env, THEN_BR(stms, cond, !falseBranch)::ifStk, [], !trueBranch)
                      end
                  | IL.COM {text, succ, ...} =>
                      doNode (env, ifStk, T.S_Comment text :: stms, !succ)
                  | IL.ASSIGN{stm, succ, ...} => let
                      val (env, stms') = doAssign (env, stm)
                      in
                        doNode (env, ifStk, stms' @ stms, !succ)
                      end
                  | IL.MASSIGN{stm=(ys, rator, xs), succ, ...} => let
                      fun doit () = let
                            fun doLHSVar (y, (env, ys)) = (case peekGlobal(env, y)
                                   of SOME y' => (env, y'::ys)
                                    | NONE => let
                                        val t = newLocal y
                                        in
                                          (rename (addLocal(env, t), y, t), t::ys)
                                        end
                                  (* end case *))
                            val (env, ys) = List.foldr doLHSVar (env, []) ys
                            val exp = T.E_Op(rator, List.map (useVar env) xs)
                            val stm = T.S_Assign(ys, exp)
                            in
                              doNode (env, ifStk, stm :: stms, !succ)
                            end
                      in
                        case rator
                         of Op.Print _ => if Target.supportsPrinting()
                              then doit ()
                              else doNode (env, ifStk, stms, !succ)
                          | _ => doit()
                        (* end case *)
                      end
                  | IL.NEW{strand, args, succ, ...} => raise Fail "NEW unimplemented"
                  | IL.SAVE{lhs, rhs, succ, ...} => let
                      val stm = T.S_Save([getStateVar lhs], useVar env rhs)
                      in
                        doNode (env, ifStk, stm::stms, !succ)
                      end
                  | k as IL.EXIT{kind, live, ...} => (case kind
                       of ExitKind.FRAGMENT =>
                            endScope (env, prefix @ List.revAppend(stms, finish env))
                        | ExitKind.SINIT => let
(* FIXME: we should probably call flushPending here! *)
                            val suffix = finish env @ [T.S_Exit[]]
                            in
                              endScope (env, prefix @ List.revAppend(stms, suffix))
                            end
                        | ExitKind.RETURN => let
(* FIXME: we should probably call flushPending here! *)
                            val suffix = finish env @ [T.S_Exit(List.map (useVar env) live)]
                            in
                              endScope (env, prefix @ List.revAppend(stms, suffix))
                            end
                        | ExitKind.ACTIVE => let
(* FIXME: we should probably call flushPending here! *)
                            val suffix = finish env @ [T.S_Active]
                            in
                              endScope (env, prefix @ List.revAppend(stms, suffix))
                            end
                        | ExitKind.STABILIZE => let
(* FIXME: we should probably call flushPending here! *)
                            val stms = T.S_Stabilize :: stms
                            in
(* FIXME: we should probably call flushPending here! *)
                              join (env, ifStk, stms, k)
                            end
                        | ExitKind.DIE => join (env, ifStk, T.S_Die :: stms, k)
                      (* end case *))
                (* end case *))
          in
            doNode (env, [], [], CFG.entry cfg)
          end

    fun trInitially (env, IL.Initially{isArray, rangeInit, iters, create=(createInit, strand, args)}) =
          let
          val iterPrefix = trCFG (env, [], fn _ => [], rangeInit)
          fun cvtIter ((param, lo, hi), (env, iters)) = let
                val param' = newIter param
                val env = rename (env, param, param')
                in
                  (env, (param', useVar env lo, useVar env hi)::iters)
                end
          val (env, iters) = List.foldr cvtIter (env, []) iters
          val createPrefix = trCFG (env, [], fn _ => [], createInit)
          in {
            isArray = isArray,
            iterPrefix = iterPrefix,
            iters = iters,
            createPrefix = createPrefix,
            strand = strand,
            args = List.map (useVar env) args
          } end

    fun trMethod env (IL.Method{name, body}) = T.Method{
            name = name,
            body = trCFG (env, [], fn _ => [], body)
          }

    fun trStrand globalEnv (IL.Strand{name, params, state, stateInit, methods}) = let
          val params' = List.map newParam params
          val env = ListPair.foldlEq (fn (x, x', env) => rename(env, x, x')) globalEnv (params, params')
          in
            T.Strand{
                name = name,
                params = params',
                state = List.map getStateVar state,
                stateInit = trCFG (env, [], fn _ => [], stateInit),
                methods = List.map (trMethod env) methods
              }
          end

  (* split the globalInit into the part that specifies the inputs and the rest of
   * the global initialization.
   *)
    fun splitGlobalInit globalInit = let
(* FIXME: can split as soon as we see a non-Input statement! *)
          fun walk (nd, lastInput, live) = (case Nd.kind nd
                 of IL.ENTRY{succ} => walk (!succ, lastInput, live)
                  | IL.COM{succ, ...} => walk (!succ, lastInput, live)
                  | IL.ASSIGN{stm=(lhs, rhs), succ, ...} => (case rhs
                       of IL.OP(Op.Input _, _) => walk (!succ, nd, lhs::live)
                        | _ => walk (!succ, lastInput, live)
                      (* end case *))
                  | _ => if Nd.isNULL lastInput
                      then let (* no inputs *)
                        val entry = Nd.mkENTRY()
                        val exit = Nd.mkEXIT(ExitKind.RETURN, [])
                        in
                          Nd.addEdge (entry, exit);
                          {inputInit = IL.CFG{entry=entry, exit=exit}, globalInit = globalInit}
                        end
                      else let (* split at lastInput *)
                        val inputExit = Nd.mkEXIT(ExitKind.RETURN, live)
                        val globalEntry = Nd.mkENTRY()
                        val [gFirst] = Nd.succs lastInput
                        in
                          Nd.replaceInEdge {src = lastInput, oldDst = gFirst, dst = inputExit};
                          Nd.replaceOutEdge {oldSrc = lastInput, src = globalEntry, dst = gFirst};
                          {
                            inputInit = IL.CFG{entry = IL.CFG.entry globalInit, exit = inputExit},
                            globalInit = IL.CFG{entry = globalEntry, exit = IL.CFG.exit globalInit}
                          }
                        end
                (* end case *))
          in
            walk (IL.CFG.entry globalInit, Nd.dummy, [])
          end

    fun translate prog = let
        (* first we do a variable analysis pass on the Low IL *)
          val prog as IL.Program{props, globalInit, initially, strands} = VA.optimize prog
(* FIXME: here we should do a contraction pass to eliminate unused variables that VA may have created *)
          val _ = (* DEBUG *)
                LowPP.output (Log.logFile(), "LowIL after variable analysis", prog)
          val env = newEnv()
          val globals = List.map
                (fn x => let val x' = newGlobal x in global(env, x, x'); x' end)
                  (IL.CFG.liveAtExit globalInit)
          val {inputInit, globalInit} = splitGlobalInit globalInit
          val strands = List.map (trStrand env) strands
          in
            T.Program{
                props = props,
                globals = globals,
                inputInit = trCFG (env, [], fn _ => [], inputInit),
                globalInit = trCFG (env, [], fn _ => [], globalInit),
                strands = strands,
                initially = trInitially (env, initially)
              }
          end

  end