NFSimplifyExp.mo

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encapsulated package NFSimplifyExp

import Expression = NFExpression;
import Operator = NFOperator;
import Type = NFType;
import Call = NFCall;
import Subscript = NFSubscript;
import NFOperator.Op;
import NFPrefixes.{Variability, Purity};
import NFInstNode.InstNode;

protected

import Dimension = NFDimension;
import Ceval = NFCeval;
import NFCeval.EvalTarget;
import NFFunction.Function;
import ComponentRef = NFComponentRef;
import ExpandExp = NFExpandExp;
import TypeCheck = NFTypeCheck;
import Absyn;
import AbsynUtil;
import ErrorExt;
import Flags;
import Debug;
import Array;
import MetaModelica.Dangerous.listReverseInPlace;

public

function simplifyDump
  "wrapper function for simplification to allow dumping before and afterwards"
  input Expression exp;
  input Boolean backend;
  output Expression res;
  input String name = "";
  input String indent = "";
algorithm
  res := simplify(exp, backend);
  if Flags.isSet(Flags.DUMP_SIMPLIFY) and not Expression.isEqual(exp, res) then
    print(indent + "### dumpSimplify | " + name + " ###\n");
    print(indent + "[BEFORE] " + Expression.toString(exp) + "\n");
    print(indent + "[AFTER ] " + Expression.toString(res) + "\n\n");
  end if;
end simplifyDump;

function simplify
  input output Expression exp;
  input Boolean backend = false;
algorithm
  exp := match exp
    case Expression.CREF()
      algorithm
        exp.cref := ComponentRef.simplifySubscripts(exp.cref);
        exp.ty := ComponentRef.getSubscriptedType(exp.cref, backend);
      then
        exp;

    case Expression.ARRAY()
      guard not exp.literal
      algorithm
        exp.elements := Array.map(exp.elements, function simplify(backend = false));
      then
        exp;

    case Expression.RANGE()
      then simplifyRange(exp);

    case Expression.RECORD()
      algorithm
        exp.elements := list(simplify(e) for e in exp.elements);
      then
        exp;

    case Expression.CALL()              then simplifyCall(exp);
    case Expression.SIZE()              then simplifySize(exp);
    case Expression.MULTARY()           then simplifyMultary(exp);
    case Expression.BINARY()            then simplifyBinary(exp);
    case Expression.UNARY()             then simplifyUnary(exp);
    case Expression.LBINARY()           then simplifyLogicBinary(exp);
    case Expression.LUNARY()            then simplifyLogicUnary(exp);
    case Expression.RELATION()          then simplifyRelation(exp);
    case Expression.IF()                then simplifyIf(exp);
    case Expression.CAST()              then simplifyCast(simplify(exp.exp), exp.ty);
    case Expression.UNBOX()             then Expression.UNBOX(simplify(exp.exp), exp.ty);
    case Expression.SUBSCRIPTED_EXP()   then simplifySubscriptedExp(exp);
    case Expression.TUPLE_ELEMENT()     then simplifyTupleElement(exp);
    case Expression.RECORD_ELEMENT()    then simplifyRecordElement(exp);
    case Expression.BOX()               then Expression.BOX(simplify(exp.exp));
    case Expression.MUTABLE()           then simplify(Mutable.access(exp.exp));
                                        else exp;
  end match;
end simplify;

function simplifyOpt
  input output Option<Expression> exp;
protected
  Expression e;
algorithm
  exp := match exp
    case SOME(e) then SOME(simplify(e));
    else exp;
  end match;
end simplifyOpt;

function simplifyRange
  input Expression range;
  output Expression exp;
protected
  Expression start_exp1, stop_exp1, start_exp2, stop_exp2;
  Option<Expression> step_exp1, step_exp2;
  Type ty, ty2;
algorithm
  Expression.RANGE(ty = ty, start = start_exp1, step = step_exp1, stop = stop_exp1) := range;

  start_exp2 := simplify(start_exp1);
  step_exp2 := simplifyOpt(step_exp1);
  stop_exp2 := simplify(stop_exp1);
  ty2 := Type.simplify(ty);

  if referenceEq(start_exp1, start_exp2) and
     referenceEq(step_exp1, step_exp2) and
     referenceEq(stop_exp1, stop_exp2) and
     referenceEq(ty, ty2) then
    exp := range;
  else
    ty := TypeCheck.getRangeType(start_exp2, step_exp2, stop_exp2,
      Type.arrayElementType(ty), AbsynUtil.dummyInfo);
    exp := Expression.RANGE(ty, start_exp2, step_exp2, stop_exp2);
  end if;
end simplifyRange;

function simplifyCall
  input output Expression callExp;
protected
  Call call;
  list<Expression> args;
  Boolean builtin, is_pure, scalarize;
algorithm
  Expression.CALL(call = call) := callExp;

  callExp := match call
    case Call.TYPED_CALL(arguments = args) guard not Call.isExternal(call)
      algorithm
        if Flags.isSet(Flags.NF_EXPAND_FUNC_ARGS) then
          args := list(if Expression.hasArrayCall(arg) then arg else ExpandExp.expand(arg) for arg in args);
        end if;

        args := list(simplify(arg) for arg in args);
        call.arguments := args;
        builtin := Function.isBuiltin(call.fn);
        is_pure := not Function.isImpure(call.fn);

        // Use Ceval for builtin pure functions with literal arguments.
        if builtin then
          scalarize := Flags.isSet(Flags.NF_SCALARIZE);

          if is_pure and List.all(args, Expression.isLiteral) and (scalarize or Type.isScalar(call.ty)) then
            try
              callExp := Ceval.evalCall(call, EvalTarget.IGNORE_ERRORS());
            else
              callExp := Expression.CALL(call);
            end try;
          else
            callExp := simplifyBuiltinCall(Function.nameConsiderBuiltin(call.fn), args, call, expand = scalarize);
          end if;
        elseif Flags.isSet(Flags.NF_EVAL_CONST_ARG_FUNCS) and is_pure and List.all(args, Expression.isLiteral) then
          callExp := simplifyCall2(call);
        else
          callExp := Expression.CALL(call);
        end if;
      then
        callExp;

    case Call.TYPED_CALL(arguments = args)
      algorithm
        args := list(simplify(arg) for arg in args);
        call.arguments := args;
      then
        Expression.CALL(call);

    case Call.TYPED_ARRAY_CONSTRUCTOR() then simplifyArrayConstructor(call);
    case Call.TYPED_REDUCTION() then simplifyReduction(call);
    else callExp;
  end match;
end simplifyCall;

function simplifyCall2
  input Call call;
  output Expression outExp;
algorithm
  ErrorExt.setCheckpoint(getInstanceName());

  try
    outExp := Ceval.evalCall(call, EvalTarget.IGNORE_ERRORS());
    ErrorExt.delCheckpoint(getInstanceName());
  else
    if Flags.isSet(Flags.FAILTRACE) then
      ErrorExt.delCheckpoint(getInstanceName());
      Debug.traceln("- " + getInstanceName() + " failed to evaluate " + Call.toString(call) + "\n");
    else
      ErrorExt.rollBack(getInstanceName());
    end if;

    outExp := Expression.CALL(call);
  end try;
end simplifyCall2;

function simplifyBuiltinCall
  input Absyn.Path name;
  input list<Expression> args;
  input Call call;
  input Boolean expand;
  output Expression exp;
algorithm
  exp := match AbsynUtil.pathFirstIdent(name)
    case "cat"
      algorithm
        exp := ExpandExp.expandBuiltinCat(args, call);
      then
        exp;

    case "delay"           then simplifyDelay(args, call);
    case "der"             then simplifyDer(listHead(args), call);
    case "fill"            then simplifyFill(listHead(args), listRest(args), call, expand);
    case "homotopy"        then simplifyHomotopy(args, call);
    case "max"             then simplifyMinMax(args, call, isMin = false);
    case "min"             then simplifyMinMax(args, call, isMin = true);
    case "ones"            then simplifyFill(Expression.INTEGER(1), args, call, expand);
    case "product"         then simplifySumProduct(listHead(args), call, expand, isSum = false);
    case "sum"             then simplifySumProduct(listHead(args), call, expand, isSum = true);
    case "transpose"       then simplifyTranspose(listHead(args), call, expand);
    case "vector"          then simplifyVector(listHead(args), call);
    case "zeros"           then simplifyFill(Expression.INTEGER(0), args, call, expand);
    case "semiLinear"      then simplifySemiLinear(args, call);
    case "getInstanceName" then Ceval.evalGetInstanceName(listHead(args));

    else Expression.CALL(call);
  end match;
end simplifyBuiltinCall;

function simplifySemiLinear
  input list<Expression> args;
  input Call call;
  output Expression exp;
protected
  Expression x, m1, m2;
  Type ty;
algorithm
  {x, m1, m2} := args;
  ty := Expression.typeOf(x);
  if Expression.isZero(x) or (Expression.isZero(m1) and Expression.isZero(m2)) then
    // both slopes x*m1, x*m2 return 0
    exp := Expression.makeZero(ty);
  elseif Expression.isEqual(m1, m2) then
    // both slopes x*m1, x*m2 are equal
    exp := Expression.BINARY(x, Operator.makeMul(ty), m1);
  else
    // no simplification, just return
    exp := Expression.CALL(call);
  end if;
end simplifySemiLinear;

function simplifyMinMax
  input list<Expression> args;
  input Call call;
  input Boolean isMin;
  output Expression exp;
protected
  Expression arg;
  Type ty;
algorithm
  if listLength(args) == 1 then
    arg := listHead(args);
    ty := Expression.typeOf(arg);

    if Type.isEmptyArray(ty) then
      ty := Type.arrayElementType(ty);
      exp := if isMin then Expression.makeMaxValue(ty) else
                           Expression.makeMinValue(ty);
    else
      exp := simplifyReducedArrayConstructor(arg, call);
    end if;
  else
    exp := Expression.CALL(call);
  end if;
end simplifyMinMax;

function simplifySumProduct
  input Expression arg;
  input Call call;
  input Boolean expand;
  input Boolean isSum;
  output Expression exp;
protected
  Boolean expanded;
  list<Expression> args;
  Type ty;
  Operator op;
algorithm
  if expand then
    (exp, expanded) := ExpandExp.expand(arg);

    if expanded then
      args := Expression.arrayScalarElements(exp);
      ty := Type.arrayElementType(Expression.typeOf(arg));

      if listEmpty(args) then
        exp := if isSum then Expression.makeZero(ty) else Expression.makeOne(ty);
      else
        exp :: args := args;
        op := if isSum then Operator.makeAdd(ty) else
                            Operator.makeMul(ty);

        for e in args loop
          exp := Expression.BINARY(exp, op, e);
        end for;
      end if;

      return;
    end if;
  end if;

  exp := simplifyReducedArrayConstructor(arg, call);
end simplifySumProduct;

function simplifyReducedArrayConstructor
  input Expression arg;
  input Call call;
  output Expression exp;
algorithm
  exp := match arg
    local
      Call arr_call;
      Function fn;
      Type ty;
      Variability var;
      Purity purity;

    case Expression.CALL(call = arr_call as Call.TYPED_ARRAY_CONSTRUCTOR())
      guard Type.dimensionCount(arr_call.ty) == 1
      algorithm
        Call.TYPED_CALL(fn = fn, ty = ty, var = var, purity = purity) := call;
      then
        Expression.CALL(Call.makeTypedReduction(fn, ty, var, purity, arr_call.exp, arr_call.iters, AbsynUtil.dummyInfo));

    else Expression.CALL(call);
  end match;
end simplifyReducedArrayConstructor;

function simplifyTranspose
  input Expression arg;
  input Call call;
  input Boolean expand;
  output Expression exp;
protected
  Expression e;
algorithm
  e := if not expand or Expression.hasArrayCall(arg) then arg else ExpandExp.expand(arg);

  exp := match e
    case Expression.ARRAY()
      guard Array.all(e.elements, Expression.isArray)
      then Expression.transposeArray(e);

    else Expression.CALL(call);
  end match;
end simplifyTranspose;

function simplifyVector
  input Expression arg;
  input Call call;
  output Expression exp;
protected
  list<Expression> expl;
  Boolean is_literal;
  Type ty;
algorithm
  expl := Expression.arrayScalarElements(arg);
  is_literal := Expression.isLiteral(arg);

  if is_literal then
    // Ranges count as literals, make sure they're expanded.
    expl := ExpandExp.expandList(expl);
  end if;

  if is_literal or List.all(expl, Expression.isScalar) then
    ty := Type.arrayElementType(Expression.typeOf(arg));
    exp := Expression.makeExpArray(listArray(expl), ty);
  else
    exp := Expression.CALL(call);
  end if;
end simplifyVector;

function simplifyFill
  input Expression fillArg;
  input list<Expression> dimArgs;
  input Call call;
  input Boolean expand;
  output Expression exp;
algorithm
  if List.all(dimArgs, Expression.isLiteral) and expand then
    exp := Expression.fillArgs(fillArg, dimArgs);
  else
    exp := Expression.CALL(call);
  end if;
end simplifyFill;

function simplifyHomotopy
  input list<Expression> args;
  input Call call;
  output Expression exp;
algorithm
  exp := match Flags.getConfigString(Flags.REPLACE_HOMOTOPY)
    case "actual" then listHead(args);
    case "simplified" then listHead(listRest(args));
    else Expression.CALL(call);
  end match;
end simplifyHomotopy;

function simplifyDelay
  input list<Expression> args;
  input Call call;
  output Expression callExp;
protected
  Expression exp, delayTime;
algorithm
  exp :: delayTime :: _ := args;

  if Expression.variability(delayTime) <= Variability.PARAMETER then
    delayTime := Ceval.tryEvalExp(delayTime);

    if Expression.isZero(delayTime) then
      callExp := exp;
      return;
    end if;
  end if;

  callExp := Expression.CALL(call);
end simplifyDelay;

function simplifyDer
  input Expression arg;
  input Call call;
  output Expression exp;
algorithm
  if Call.variability(call) < Variability.DISCRETE then
    exp := Expression.makeZero(Expression.typeOf(arg));
  else
    exp := Expression.CALL(call);
  end if;
end simplifyDer;

function simplifyArrayConstructor
  input Call call;
  output Expression outExp;
protected
  Type ty;
  Variability var;
  Purity pur;
  Expression exp, e;
  list<tuple<InstNode, Expression>> iters;
  InstNode iter;
  Dimension dim;
  Integer dim_size;
  Boolean expanded;
algorithm
  Call.TYPED_ARRAY_CONSTRUCTOR(ty, var, pur, exp, iters) := call;
  iters := list((Util.tuple21(i), simplify(Util.tuple22(i))) for i in iters);

  outExp := matchcontinue (iters)
    case {(iter, e)}
      algorithm
        Type.ARRAY(dimensions = {dim}) := Expression.typeOf(e);
        dim_size := Dimension.size(dim);

        if dim_size == 0 then
          // Result is Array[0], return empty array expression.
          outExp := Expression.makeEmptyArray(ty);
        elseif dim_size == 1 then
          // Result is Array[1], return array with the single element.
          e := ExpandExp.expand(e);
          e := Expression.arrayScalarElement(e);
          exp := Expression.replaceIterator(exp, iter, e);
          exp := Expression.makeArray(ty, listArray({exp}));
          outExp := simplify(exp);
        elseif Expression.isLiteral(e) and isIteratorSubscriptedArray(exp, iter) then
          // If the iterator is only used to subscript array expressions like
          // {{1, 2, 3}[i] for i in 1:3}, then we might as well expand it.
          (outExp, expanded) := ExpandExp.expandArrayConstructor(exp, ty, iters);

          if expanded then
            outExp := simplify(outExp);
          end if;
        else
          fail();
        end if;
      then
        outExp;

    else
      algorithm
        exp := simplify(exp);
        ty := Type.simplify(ty);
      then
        Expression.CALL(Call.TYPED_ARRAY_CONSTRUCTOR(ty, var, pur, exp, iters));
  end matchcontinue;
end simplifyArrayConstructor;

function isIteratorSubscriptedArray
  input Expression exp;
  input InstNode iterator;
  output Boolean res;
algorithm
  res := match exp
    case Expression.SUBSCRIPTED_EXP()
      then Expression.isArray(exp.exp) and
           List.all(exp.subscripts, function Subscript.equalsIterator(iterator = iterator));
    else false;
  end match;
end isIteratorSubscriptedArray;

function simplifyReduction
  input Call call;
  output Expression outExp;
algorithm
  outExp := match call
    local
      Expression exp, e;
      list<tuple<InstNode, Expression>> iters;
      InstNode iter;
      Dimension dim;
      Integer dim_size;

    case Call.TYPED_REDUCTION()
      algorithm
        iters := list((Util.tuple21(i), simplify(Util.tuple22(i))) for i in call.iters);
      then matchcontinue iters
        case {(iter, e)}
          algorithm
            Type.ARRAY(dimensions = {dim}) := Expression.typeOf(e);
            dim_size := Dimension.size(dim);

            if dim_size == 0 then
              // Iteration range is empty, return default value for reduction.
              SOME(outExp) := call.defaultExp;
            elseif dim_size == 1 then
              // Iteration range is one, return reduction expression with iterator value applied.
              e := ExpandExp.expand(e);
              e := Expression.arrayScalarElement(e);
              outExp := Expression.replaceIterator(call.exp, iter, e);
              outExp := simplify(outExp);
            else
              fail();
            end if;
          then
            outExp;

        case _
          guard call.var <= Variability.STRUCTURAL_PARAMETER
          then Ceval.tryEvalExp(Expression.CALL(call));

        case _
          guard Flags.isSet(Flags.NF_SCALARIZE)
          then simplifyReduction2(AbsynUtil.pathString(Function.name(call.fn)), call.exp, iters);

        else
          algorithm
            call.exp := simplify(call.exp);
            call.iters := iters;
          then
            Expression.CALL(call);

      end matchcontinue;
  end match;
end simplifyReduction;

function simplifyReduction2
  input String name;
  input Expression exp;
  input list<tuple<InstNode, Expression>> iterators;
  output Expression outExp;
protected
  InstNode iter;
  Expression range, default_exp;
  Boolean expanded = true;
  list<tuple<InstNode, Expression>> iters = {};
  Type ty;
  Operator op;
algorithm
  ty := Expression.typeOf(exp);
  // Operator records are problematic since the start value isn't simplified
  // away currently.
  false := Type.isRecord(Type.arrayElementType(ty));

  (default_exp, op) := match name
    case "sum" then (Expression.makeZero(ty), Operator.makeAdd(ty));
    case "product" then (Expression.makeOne(ty), Operator.makeMul(ty));
  end match;

  for i in iterators loop
    (iter, range) := i;
    (range, true) := ExpandExp.expand(range);
    iters := (iter, range) :: iters;
  end for;

  outExp := Expression.foldReduction(simplify(exp), listReverseInPlace(iters),
    default_exp, function simplify(backend = false), function simplifyBinaryOp(op = op));
end simplifyReduction2;

function simplifySize
  input output Expression sizeExp;
algorithm
  sizeExp := match sizeExp
    local
      Expression exp, index;
      Dimension dim;
      list<Dimension> dims;

    case Expression.SIZE(exp, SOME(index))
      algorithm
        index := simplify(index);

        if Expression.isLiteral(index) then
          dim := listGet(Type.arrayDims(Expression.typeOf(exp)), Expression.toInteger(index));

          if Dimension.isKnown(dim) then
            exp := Expression.INTEGER(Dimension.size(dim));
          else
            exp := Expression.SIZE(exp, SOME(index));
          end if;
        else
          exp := Expression.SIZE(exp, SOME(index));
        end if;
      then
        exp;

    case Expression.SIZE()
      algorithm
        dims := Type.arrayDims(Expression.typeOf(sizeExp.exp));

        if List.all(dims, function Dimension.isKnown(allowExp = true)) then
          exp := Expression.makeArray(Type.ARRAY(Type.INTEGER(), {Dimension.fromInteger(listLength(dims))}),
                                      listArray(list(Dimension.sizeExp(d) for d in dims)));
        else
          exp := sizeExp;
        end if;
      then
        exp;

  end match;
end simplifySize;

function simplifyMultary
  input output Expression exp;
algorithm
  exp := match exp
    local
      Operator operator;
      list<Expression> arguments, inv_arguments, const_args, inv_const_args;
      Expression new_const, tmp, result;
      Operator.MathClassification mcl;
      Boolean useConst, isNegative;

    // empty multary with addition -> 0
    case Expression.MULTARY(arguments = {}, inv_arguments = {}, operator = operator)
      guard(Operator.isDashClassification(Operator.getMathClassification(operator)))
    then Expression.makeZero(operator.ty);

    // empty multary with multiplication -> 1
    case Expression.MULTARY(arguments = {}, inv_arguments = {}, operator = operator)
    then Expression.makeOne(operator.ty);

    // multary with only one argument
    case Expression.MULTARY(arguments = {tmp}, inv_arguments = {})
    then tmp;

    // non-empty multaries
    case Expression.MULTARY(arguments = arguments, inv_arguments = inv_arguments, operator = operator) algorithm
      // get math classification
      mcl := Operator.getMathClassification(operator);

      // simplify arguments first
      arguments := list(simplify(arg) for arg in arguments);
      inv_arguments := list(simplify(arg) for arg in inv_arguments);
      (arguments, inv_arguments, isNegative) := simplifyMultarySigns(arguments, inv_arguments, mcl);

      // split them into constant and non constant arguments
      (const_args, arguments) := List.splitOnTrue(arguments, Expression.isConstNumber);
      (inv_const_args, inv_arguments) := List.splitOnTrue(inv_arguments, Expression.isConstNumber);

      // combine the constants
      new_const := combineConstantNumbers(const_args, inv_const_args, mcl, Operator.typeOf(operator));

      // return combined multary expression and check for trivial replacements

      // check if the constant is used
      useConst := match mcl
        case NFOperator.MathClassification.ADDITION guard(Expression.isZero(new_const)) then false;
        case NFOperator.MathClassification.MULTIPLICATION guard(Expression.isOne(new_const)) then false;
        else true;
      end match;

      result := match (mcl, arguments, inv_arguments)
        // const + {} - {} = const
        // const * {} / {} = const
        case (_, {}, {}) then new_const;

        // 0 + {cr} - {} = cr
        // 1 * {cr} / {} = cr
        case (_, {tmp}, {}) guard(not useConst) then tmp;

        // 0 + {} - {cr} = - cr
        case (NFOperator.MathClassification.ADDITION, {}, {tmp}) guard(not useConst)
        then Expression.negate(tmp);

        // 0 * {...} / {...} = 0
        case (NFOperator.MathClassification.MULTIPLICATION, _, _) guard(Expression.isZero(new_const)) then new_const;

        // THIS SEEMS LIKE A BAD IDEA STRUCTURALLY
        // apply negative constant to inverse list for addition
        //case (NFOperator.MathClassification.ADDITION, _, _) guard(Expression.isNegative(new_const) and useConst)
        //then Expression.MULTARY(
        //    arguments     = arguments,
        //    inv_arguments = Expression.negate(new_const) :: inv_arguments,
        //    operator      = operator
        //  );

        else Expression.MULTARY(
            arguments     = if useConst then new_const :: arguments else arguments,
            inv_arguments = inv_arguments,
            operator      = operator
          );
      end match;

      // negate the expression if there was an odd number of negative arguments (only multiplication)
    then if isNegative then Expression.negate(result) else result;

    else algorithm
      Error.addMessage(Error.INTERNAL_ERROR,{getInstanceName() + " failed for expression: " + Expression.toString(exp)});
    then fail();
  end match;

end simplifyMultary;

function simplifyMultarySigns
  input list<Expression> arguments;
  input list<Expression> inv_arguments;
  input Operator.MathClassification mcl;
  output list<Expression> new_arguments = {};
  output list<Expression> new_inv_arguments = {};
  output Boolean isNegative = false; // only relevant for multiplication
algorithm
  _ := match mcl
    case NFOperator.MathClassification.ADDITION algorithm
      // check if arguments are negative
      // negate them and swap them to the other list
      for arg in listReverse(arguments) loop
        if Expression.isNegative(arg) then
          new_inv_arguments := Expression.negate(arg) :: new_inv_arguments;
        else
          new_arguments := arg :: new_arguments;
        end if;
      end for;
      for arg in listReverse(inv_arguments) loop
        if Expression.isNegative(arg) then
          new_arguments := Expression.negate(arg) :: new_arguments;
        else
          new_inv_arguments := arg :: new_inv_arguments;
        end if;
      end for;
    then ();

    case NFOperator.MathClassification.MULTIPLICATION algorithm
      // check if arguments are negative and negate them.
      // track if there is an even or odd number of negative arguments
      for arg in listReverse(arguments) loop
        if Expression.isNegative(arg) then
          new_arguments := Expression.negate(arg) :: new_arguments;
          isNegative := not isNegative;
        else
          new_arguments := arg :: new_arguments;
        end if;
      end for;
      for arg in listReverse(inv_arguments) loop
        if Expression.isNegative(arg) then
          new_inv_arguments := Expression.negate(arg) :: new_inv_arguments;
          isNegative := not isNegative;
        else
          new_inv_arguments := arg :: new_inv_arguments;
        end if;
      end for;
    then ();

    else algorithm
      Error.addMessage(Error.INTERNAL_ERROR,{getInstanceName() + " failed."});
    then fail();
  end match;
end simplifyMultarySigns;

function simplifyBinary
  input output Expression binaryExp;
protected
  Expression e1, e2, se1, se2;
  Operator op;
algorithm
  Expression.BINARY(e1, op, e2) := binaryExp;
  se1 := simplify(e1);
  se2 := simplify(e2);

  binaryExp := simplifyBinaryOp(se1, op, se2);

  if Flags.isSet(Flags.NF_EXPAND_OPERATIONS) and not Expression.hasArrayCall(binaryExp) then
    binaryExp := ExpandExp.expand(binaryExp);
  end if;
end simplifyBinary;

function simplifyBinaryOp
  input Expression exp1;
  input Operator op;
  input Expression exp2;
  output Expression outExp;

  import NFOperator.Op;
algorithm
  if Expression.isLiteral(exp1) and Expression.isLiteral(exp2) then
    outExp := Ceval.evalBinaryOp(ExpandExp.expand(exp1), op, ExpandExp.expand(exp2));
  else
    outExp := match op.op
      case Op.ADD then simplifyBinaryAdd(exp1, op, exp2);
      case Op.SUB then simplifyBinarySub(exp1, op, exp2);
      case Op.MUL then simplifyBinaryMul(exp1, op, exp2);
      case Op.DIV then simplifyBinaryDiv(exp1, op, exp2);
      case Op.POW then simplifyBinaryPow(exp1, op, exp2);
      else Expression.BINARY(exp1, op, exp2);
    end match;
  end if;
end simplifyBinaryOp;

function simplifyBinaryAdd
  input Expression exp1;
  input Operator op;
  input Expression exp2;
  output Expression outExp;
algorithm
  if Expression.isZero(exp1) then
    // 0 + e = e
    outExp := exp2;
  elseif Expression.isZero(exp2) then
    // e + 0 = e
    outExp := exp1;
  elseif Expression.isNegated(exp2) then
    // e1 + -(e2) = e1 - e2
    outExp := Expression.BINARY(exp1, Operator.invert(op), Expression.negate(exp2));
  else
    outExp := Expression.BINARY(exp1, op, exp2);
  end if;
end simplifyBinaryAdd;

function simplifyBinarySub
  input Expression exp1;
  input Operator op;
  input Expression exp2;
  output Expression outExp;
algorithm
  if Expression.isZero(exp1) then
    // 0 - e = -e
    outExp := Expression.UNARY(Operator.makeUMinus(Operator.typeOf(op)), exp2);
  elseif Expression.isZero(exp2) then
    // e - 0 = e
    outExp := exp1;
  elseif Expression.isNegated(exp2) then
    // e1 - -(e2) = e1 + e2
    outExp := Expression.BINARY(exp1, Operator.invert(op), Expression.negate(exp2));
  else
    outExp := Expression.BINARY(exp1, op, exp2);
  end if;
end simplifyBinarySub;

function simplifyBinaryMul
  input Expression exp1;
  input Operator op;
  input Expression exp2;
  input Boolean switched = false;
  output Expression outExp;
algorithm
  outExp := match exp1
    // 0 * e = 0
    case Expression.INTEGER(value = 0) then exp1;
    case Expression.REAL(value = 0.0) then exp1;

    // 1 * e = e
    case Expression.INTEGER(value = 1) then exp2;
    case Expression.REAL(value = 1.0) then exp2;

    else
      if switched then
        Expression.BINARY(exp2, op, exp1)
      else
        simplifyBinaryMul(exp2, op, exp1, true);
  end match;
end simplifyBinaryMul;

function simplifyBinaryDiv
  input Expression exp1;
  input Operator op;
  input Expression exp2;
  output Expression outExp;
algorithm
  // fix constants
  // e / 1 = e
  // e / (-1) = -e
  // 0 / e = 0 (e <> 0)
  outExp :=
    if Expression.isOne(exp2) then exp1
    elseif Expression.isMinusOne(exp2) then Expression.negate(exp1)
    elseif Expression.isZero(exp1) and not Expression.isZero(exp2) then exp1
    // fix minus signs
    // (-e1)/(-e2) = e1/e2
    // e1/(-e2) = -(e1/e2)
    // (-e1)/e2 = -(e1/e2)
    // e1/e2 = e1/e2
    else match (Expression.isNegative(exp1), Expression.isNegative(exp1))
      case (true, true)     then Expression.BINARY(Expression.negate(exp1), op, Expression.negate(exp2));
      case (false, true)    then Expression.negate(Expression.BINARY(exp1, op, Expression.negate(exp2)));
      case (true, false)    then Expression.negate(Expression.BINARY(Expression.negate(exp1), op, exp2));
      case (false, false)   then Expression.BINARY(exp1, op, exp2);
    end match;
end simplifyBinaryDiv;

function simplifyBinaryPow
  input Expression exp1;
  input Operator op;
  input Expression exp2;
  output Expression outExp;
algorithm
  if Expression.isZero(exp2) then
    outExp := Expression.makeOne(Operator.typeOf(op));
  elseif Expression.isOne(exp2) then
    outExp := exp1;
  else
    outExp := Expression.BINARY(exp1, op, exp2);
  end if;
end simplifyBinaryPow;

function simplifyUnary
  input output Expression unaryExp;
protected
  Expression e, se;
  Operator op;
algorithm
  unaryExp := match unaryExp
    case Expression.UNARY(_, Expression.UNARY(_, e))
    then simplify(e);

    case Expression.UNARY(op, e) algorithm
      se := simplify(e);
    then simplifyUnaryOp(se, op);

    else algorithm
      Error.addMessage(Error.INTERNAL_ERROR,{getInstanceName() + " failed."});
    then fail();
  end match;

  if Flags.isSet(Flags.NF_EXPAND_OPERATIONS) and not Expression.hasArrayCall(unaryExp) then
    unaryExp := ExpandExp.expand(unaryExp);
  end if;
end simplifyUnary;

function simplifyUnaryOp
  input Expression exp;
  input Operator op;
  output Expression outExp;
algorithm
  if Expression.isLiteral(exp) then
    outExp := Ceval.evalUnaryOp(exp, op);
  else
    outExp := simplifyUnarySign(exp, true);
  end if;
end simplifyUnaryOp;

function simplifyUnarySign
  input output Expression unaryExp;
  input Boolean isNegative = false;
algorithm
  unaryExp := match unaryExp
    case Expression.UNARY() then simplifyUnarySign(unaryExp.exp, not isNegative);
    else if isNegative then Expression.negate(unaryExp) else unaryExp;
  end match;
end simplifyUnarySign;

function simplifyLogicBinary
  input output Expression binaryExp;
protected
  Expression e1, e2, se1, se2;
  Operator op;
algorithm
  Expression.LBINARY(e1, op, e2) := binaryExp;
  se1 := simplify(e1);
  se2 := simplify(e2);

  binaryExp := match op.op
    case Op.AND then simplifyLogicBinaryAnd(se1, op, se2);
    case Op.OR then simplifyLogicBinaryOr(se1, op, se2);
  end match;
end simplifyLogicBinary;

function simplifyLogicBinaryAnd
  input Expression exp1;
  input Operator op;
  input Expression exp2;
  output Expression exp;
algorithm
  exp := match (exp1, exp2)
    local
      list<Expression> expl;
      Operator o;
      array<Expression> arr;

    // false and e => false
    case (Expression.BOOLEAN(false), _) then exp1;
    // e and false => false
    case (_, Expression.BOOLEAN(false)) then exp2;
    // true and e => e
    case (Expression.BOOLEAN(true), _)  then exp2;
    // e and true => e
    case (_, Expression.BOOLEAN(true))  then exp1;

    case (Expression.ARRAY(), Expression.ARRAY())
      algorithm
        o := Operator.unlift(op);
        arr := Array.threadMap(exp1.elements, exp2.elements,
          function simplifyLogicBinaryAnd(op = o));
      then
        Expression.makeArray(Operator.typeOf(op), arr);

    else Expression.LBINARY(exp1, op, exp2);
  end match;
end simplifyLogicBinaryAnd;

function simplifyLogicBinaryOr
  input Expression exp1;
  input Operator op;
  input Expression exp2;
  output Expression exp;
algorithm
  exp := match (exp1, exp2)
    local
      list<Expression> expl;
      Operator o;
      array<Expression> arr;

    // true or e => true
    case (Expression.BOOLEAN(true), _) then exp1;
    // e or true => true
    case (_, Expression.BOOLEAN(true)) then exp2;
    // false or e => e
    case (Expression.BOOLEAN(false), _) then exp2;
    // e or false => e
    case (_, Expression.BOOLEAN(false)) then exp1;

    case (Expression.ARRAY(), Expression.ARRAY())
      algorithm
        o := Operator.unlift(op);
        arr := Array.threadMap(exp1.elements, exp2.elements,
          function simplifyLogicBinaryOr(op = o));
      then
        Expression.makeArray(Operator.typeOf(op), arr);

    else Expression.LBINARY(exp1, op, exp2);
  end match;
end simplifyLogicBinaryOr;

function simplifyLogicUnary
  input output Expression unaryExp;
protected
  Expression e, se;
  Operator op;
algorithm
  Expression.LUNARY(op, e) := unaryExp;
  se := simplify(e);

  if Expression.isLiteral(se) then
    unaryExp := Ceval.evalLogicUnaryOp(se, op);
  elseif not referenceEq(e, se) then
    unaryExp := Expression.LUNARY(op, se);
  end if;
end simplifyLogicUnary;

function simplifyRelation
  input output Expression relationExp;
protected
  Expression e1, e2, se1, se2;
  Operator op;
algorithm
  Expression.RELATION(e1, op, e2) := relationExp;
  se1 := simplify(e1);
  se2 := simplify(e2);

  if Expression.isLiteral(se1) and Expression.isLiteral(se2) then
    relationExp := Ceval.evalRelationOp(se1, op, se2);
  elseif not (referenceEq(e1, se1) and referenceEq(e2, se2)) then
    relationExp := Expression.RELATION(se1, op, se2);
  end if;
end simplifyRelation;

function simplifyIf
  input output Expression ifExp;
protected
  Type ty;
  Expression cond, tb, fb;
  Boolean tb_val;
algorithm
  Expression.IF(ty, cond, tb, fb) := ifExp;
  cond := simplify(cond);

  ifExp := match cond
    case Expression.BOOLEAN()
      then simplify(if cond.value then tb else fb);

    else
      algorithm
        tb := simplify(tb);
        fb := simplify(fb);

        if Expression.isEqual(tb, fb) then
          // if cond then x else x => x
          ifExp := tb;
        elseif Expression.isBoolean(tb) and Expression.isBoolean(fb) then
          // if cond then true else false => cond
          // if cond then false else true => not cond
          Expression.BOOLEAN(value = tb_val) := tb;
          ifExp := if tb_val then cond else Expression.logicNegate(cond);
        else
          ifExp := Expression.IF(ty, cond, tb, fb);
        end if;
      then
        ifExp;

  end match;
end simplifyIf;

function simplifyCast
  input Expression exp;
  input Type ty;
  output Expression castExp;
algorithm
  castExp := match (ty, exp)
    local
      Type ety;

    case (Type.REAL(), Expression.INTEGER())
      then Expression.REAL(intReal(exp.value));

    case (Type.ARRAY(elementType = Type.REAL()), Expression.ARRAY())
      algorithm
        ety := Type.unliftArray(ty);
        exp.elements := Array.map(exp.elements, function simplifyCast(ty = ety));
        exp.ty := Type.setArrayElementType(exp.ty, Type.arrayElementType(ty));
      then
        exp;

    else Expression.CAST(ty, exp);
  end match;
end simplifyCast;

function simplifySubscriptedExp
  input output Expression subscriptedExp;
protected
  Expression e;
  list<Subscript> subs;
  Type ty;
  Boolean split;
algorithm
  Expression.SUBSCRIPTED_EXP(e, subs, ty, split) := subscriptedExp;
  subscriptedExp := simplify(e);
  subs := Subscript.simplifyList(subs, Type.arrayDims(Expression.typeOf(e)));

  if not split and not List.all(subs, Subscript.isLiteral) then
    // Select the first element as long as the subscripted expression is an
    // array where all elements are equal, unless all the subscripts are literal
    // in which case it's cheaper to just apply them.
    while not listEmpty(subs) and Expression.isArray(subscriptedExp) and not Expression.isEmptyArray(subscriptedExp) and
          Array.allEqual(Expression.arrayElements(subscriptedExp), Expression.isEqual) loop
      subs := listRest(subs);
      subscriptedExp := arrayGet(Expression.arrayElements(subscriptedExp), 1);
    end while;

    if listEmpty(subs) then
      return;
    end if;
  end if;


  if split then
    subscriptedExp := Expression.SUBSCRIPTED_EXP(subscriptedExp, subs, ty, split);
  else
    subscriptedExp := Expression.applySubscripts(subs, subscriptedExp);
  end if;
end simplifySubscriptedExp;

function simplifyTupleElement
  input output Expression tupleExp;
protected
  Expression e;
  Integer index;
  Type ty;
algorithm
  Expression.TUPLE_ELEMENT(e, index, ty) := tupleExp;
  e := simplify(e);
  tupleExp := Expression.tupleElement(e, ty, index);
end simplifyTupleElement;

function simplifyRecordElement
  input output Expression exp;
protected
  Expression e, e2;
  Integer idx;
  Type ty;
algorithm
  Expression.RECORD_ELEMENT(e, idx, _, ty) := exp;
  e2 := simplify(e);

  if not referenceEq(e, e2) then
    exp := Expression.nthRecordElement(idx, e2);
  end if;
end simplifyRecordElement;

public function combineConstantNumbers
  input list<Expression> const      "has to be a list of REAL(), INTEGER() and/or CAST()";
  input list<Expression> inv_const  "has to be a list of REAL(), INTEGER() and/or CAST()";
  input Operator.MathClassification mcl;
  input Type ty;
  output Expression res;
protected
  Real tmp, result;
algorithm
  result := match mcl

    case NFOperator.MathClassification.ADDITION algorithm
      result := 0.0;
      // sum all constants
      for exp in const loop
        tmp := getConstantValue(exp);
        result := result + tmp;
      end for;
      // subtract all inverse constants
      for exp in inv_const loop
        tmp := getConstantValue(exp);
        result := result - tmp;
      end for;
    then result;

    case NFOperator.MathClassification.MULTIPLICATION algorithm
      result := 1.0;
      // multiply all constants
      for exp in const loop
        tmp := getConstantValue(exp);
        result := result * tmp;
      end for;
      // devide all inverse constants
      for exp in inv_const loop
        tmp := getConstantValue(exp);
        result := result / tmp;
      end for;
    then result;

    else algorithm
      Error.assertion(false, getInstanceName() + " detected non-commutative operator in MULTARY(): [" + Operator.mathSymbol(mcl) +
       "]\n with following arguments: " + stringDelimitList(list(Expression.toString(e) for e in const), ", ") +
       "\n and following inverse arguments: " + stringDelimitList(list(Expression.toString(e) for e in inv_const), ", "),
       sourceInfo());
    then fail();

  end match;

  res := if Type.isInteger(ty) then Expression.INTEGER(realInt(result)) else Expression.REAL(result);
end combineConstantNumbers;

protected function getConstantValue
  input Expression exp "REAL(), INTEGER(), CAST(), UNARY()";
  output Real value;
algorithm
  value := match exp
    case Expression.REAL()                                                          then exp.value;
    case Expression.INTEGER()                                                       then intReal(exp.value);
    case Expression.CAST()                                                          then getConstantValue(exp.exp);
    // negate r because it has a minus sign
    case Expression.UNARY(operator = Operator.OPERATOR(op = NFOperator.Op.UMINUS))  then -getConstantValue(exp.exp);
    else algorithm
      Error.assertion(false, getInstanceName() + " expression is not known to be a constant number: " + Expression.toString(exp), sourceInfo());
    then fail();
  end match;
end getConstantValue;

public function combineBinaries
  "just a wrapper to remove the interface for traversal"
  input output Expression exp;
algorithm
  exp := combineBinariesExp(exp);
end combineBinaries;

public function splitMultary
  "inverse functionality to combineBinaries.
  returns a multary to its original binary representation."
  input output Expression exp;
algorithm
  exp := match exp
    local
      Expression new_exp;
      list<Expression> args, inv_args;
      Operator inv_op;

    case Expression.MULTARY() algorithm
      if listLength(exp.arguments) > 0 then
        // it has arguments, take the first one and start with it
        new_exp :: args := exp.arguments;
        inv_args    := exp.inv_arguments;
      elseif listLength(exp.inv_arguments) > 0 then
        // it has no arguments but inverse arguments
        if Operator.getMathClassification(exp.operator) == NFOperator.MathClassification.ADDITION then
          // take the first one out and negate it
          new_exp :: inv_args := exp.inv_arguments;
          args      := exp.arguments;
          new_exp   := Expression.negate(new_exp);
        else
          // create an artificial 1 to devide by the inverse arguments
          new_exp   := Expression.makeOne(Operator.typeOf(exp.operator));
          args      := exp.arguments;
          inv_args  := exp.inv_arguments;
        end if;
      else
        // empty, make either 0 or 1 depending on math classification
        if Operator.getMathClassification(exp.operator) == NFOperator.MathClassification.ADDITION then
          new_exp   := Expression.makeZero(Operator.typeOf(exp.operator));
        else
          new_exp   := Expression.makeOne(Operator.typeOf(exp.operator));
        end if;
        args        := exp.arguments;
        inv_args    := exp.inv_arguments;
      end if;

      inv_op := Operator.invert(exp.operator);
      // chain all arguments
      for arg in args loop
        new_exp := Expression.BINARY(new_exp, exp.operator, arg);
      end for;
      // chain all inverse arguments
      for arg in inv_args loop
        new_exp := Expression.BINARY(new_exp, inv_op, arg);
      end for;
    then new_exp;

    else exp;
  end match;
end splitMultary;

protected function combineBinariesExp
  "author: kabdelhak 09-2020
  Combines binaries for better handling in the backend.
  NOTE: 1. does not do any other simplification
        2. also combines inverse operations
  e.g. BINARY(BINARY(2, /, y^2), *, BINARY(3, *, x))
   --> MULTARY({2, 3, x}, {y^2},*)"
  input Expression exp;
  input Option<Operator> optOperator = NONE();
  input output Expression result = Expression.EMPTY(Expression.typeOf(exp));
  input Boolean inverse = false;
algorithm
  result := match (optOperator, exp)
    local
      Operator op;
      list<Expression> tmp, tmp_inv;
      list<Expression> final_stack = {};
      list<Expression> final_inverse_stack = {};
      Expression new_exp;
      ComponentRef cref;
      Call call;

    // #######################################################
    //          Building MULTARY() recursively
    // #######################################################

    // case 1.0 binary SOME(op) same operator (+, *)
    case (SOME(op), Expression.BINARY()) guard(Operator.compare(op, exp.operator) == 0) algorithm
      result := combineBinariesExp(exp.exp1, SOME(op), result, inverse);
      result := combineBinariesExp(exp.exp2, SOME(op), result, inverse);
    then result;

    // case 1.1 multary SOME(op) same operator (+, *)
    case (SOME(op), Expression.MULTARY()) guard(Operator.compare(op, exp.operator) == 0) algorithm
      for arg in exp.arguments loop
        result := combineBinariesExp(arg, SOME(exp.operator), result, inverse);
      end for;
      for arg in exp.inv_arguments loop
        result := combineBinariesExp(arg, SOME(exp.operator), result, not inverse);
      end for;
    then result;

    // case 2.0 binary SOME(op) inverse operator (-, :)
    case (SOME(op), Expression.BINARY()) guard(Operator.isCombineable(op, exp.operator)) algorithm
      result := combineBinariesExp(exp.exp1, SOME(op), result, inverse);
      result := combineBinariesExp(exp.exp2, SOME(op), result, not inverse);
    then result;

    // case 2.1 multary SOME(op) inverse operator (-, :)
    case (SOME(op), Expression.MULTARY()) guard(Operator.isCombineable(op, exp.operator)) algorithm
      for arg in exp.arguments loop
        result := combineBinariesExp(arg, SOME(exp.operator), result, inverse);
      end for;
      for arg in exp.inv_arguments loop
        result := combineBinariesExp(arg, SOME(exp.operator), result, not inverse);
      end for;
    then result;

    // ##########################################################
    //                 Starts a new MULTARY()
    // previous not compatible or no MULTARY on the stack at all
    // ##########################################################

   // case 3.0 _ binary | commutative operator (+, *)
    case (_, Expression.BINARY()) guard(Operator.isCommutative(exp.operator)) algorithm
      new_exp := Expression.MULTARY({}, {}, exp.operator);
      new_exp := combineBinariesExp(exp.exp2, SOME(exp.operator), new_exp, false);
      new_exp := combineBinariesExp(exp.exp1, SOME(exp.operator), new_exp, false);
    then addArgument(result, new_exp, inverse);

    // case 3.1 _ multary | commutative operator (+, *)
    case (_, Expression.MULTARY()) guard(Operator.isCommutative(exp.operator)) algorithm
      new_exp := Expression.MULTARY({}, {}, exp.operator);
      for arg in exp.arguments loop
        new_exp := combineBinariesExp(arg, SOME(exp.operator), new_exp, false);
      end for;
      for arg in exp.inv_arguments loop
        new_exp := combineBinariesExp(arg, SOME(exp.operator), new_exp, true);
      end for;
    then addArgument(result, new_exp, inverse);

    // case 4.0 _ binary | soft commutative operator (-, :)
    case (_, Expression.BINARY()) guard(Operator.isSoftCommutative(exp.operator)) algorithm
      op := Operator.invert(exp.operator);
      new_exp := Expression.MULTARY({}, {}, op);
      new_exp := combineBinariesExp(exp.exp1, SOME(op), new_exp, false);
      new_exp := combineBinariesExp(exp.exp2, SOME(op), new_exp, true);
    then addArgument(result, new_exp, inverse);

    // case 4.1 _ multary soft | commutative operator (-, :)
    // THIS IS NOT ALLOWED TO EXIST!

    // #######################################################
    //      Other expressions that do not get combined
    // #######################################################

    // going deeper on the different expression types

    case (_, Expression.CREF(cref = cref as ComponentRef.CREF())) algorithm
      cref.subscripts := list(combineBinariesSubscript(sub) for sub in cref.subscripts);
      exp.cref := cref;
    then addArgument(result, exp, inverse);

    case (_, Expression.ARRAY()) algorithm
      if not exp.literal then
        exp.elements := Array.map(exp.elements,
          function combineBinariesExp(optOperator = NONE(),
            result = Expression.EMPTY(Expression.typeOf(exp)), inverse = false));
      end if;
    then addArgument(result, exp, inverse);

    case (_, Expression.RANGE()) algorithm
      exp.start := combineBinariesExp(exp.start);
      exp.stop := combineBinariesExp(exp.stop);
      if Util.isSome(exp.step) then
        exp.step := SOME(combineBinariesExp(Util.getOption(exp.step)));
      end if;
    then addArgument(result, exp, inverse);

    case (_, Expression.TUPLE()) algorithm
      exp.elements := list(combineBinariesExp(element) for element in exp.elements);
    then addArgument(result, exp, inverse);

    case (_, Expression.RECORD()) algorithm
      exp.elements := list(combineBinariesExp(element) for element in exp.elements);
    then addArgument(result, exp, inverse);

    case (_, Expression.CALL(call = call as Call.TYPED_CALL())) algorithm
      call.arguments := list(combineBinariesExp(arg) for arg in call.arguments);
      exp.call := call;
    then addArgument(result, exp, inverse);

    case (_, Expression.SIZE()) algorithm
      exp.exp := combineBinariesExp(exp.exp);
      if Util.isSome(exp.dimIndex) then
        exp.dimIndex := SOME(combineBinariesExp(Util.getOption(exp.dimIndex)));
      end if;
    then addArgument(result, exp, inverse);

    case (_, Expression.UNARY()) algorithm
      exp.exp := combineBinariesExp(exp.exp);
    then addArgument(result, exp, inverse);

    // ToDo: rules for logical operators (LMULTARY ?)
    // For now leave them as is and traverse branches
    case (_, Expression.LBINARY()) algorithm
      exp.exp1 := combineBinariesExp(exp.exp1);
      exp.exp2 := combineBinariesExp(exp.exp2);
    then addArgument(result, exp, inverse);

    case (_, Expression.LUNARY()) algorithm
      exp.exp := combineBinariesExp(exp.exp);
    then addArgument(result, exp, inverse);

    case (_, Expression.RELATION()) algorithm
      exp.exp1 := combineBinariesExp(exp.exp1);
      exp.exp2 := combineBinariesExp(exp.exp2);
    then addArgument(result, exp, inverse);

    case (_, Expression.IF()) algorithm
      exp.condition := combineBinariesExp(exp.condition);
      exp.trueBranch := combineBinariesExp(exp.trueBranch);
      exp.falseBranch := combineBinariesExp(exp.falseBranch);
    then addArgument(result, exp, inverse);

    case (_, Expression.CAST()) algorithm
      exp.exp := combineBinariesExp(exp.exp);
    then addArgument(result, exp, inverse);

    case (_, Expression.BOX()) algorithm
      exp.exp := combineBinariesExp(exp.exp);
    then addArgument(result, exp, inverse);

    case (_, Expression.UNBOX()) algorithm
      exp.exp := combineBinariesExp(exp.exp);
    then addArgument(result, exp, inverse);

    case (_, Expression.SUBSCRIPTED_EXP()) algorithm
      exp.exp := combineBinariesExp(exp.exp);
      exp.subscripts := list(combineBinariesSubscript(sub) for sub in exp.subscripts);
    then addArgument(result, exp, inverse);

    case (_, Expression.TUPLE_ELEMENT()) algorithm
      exp.tupleExp := combineBinariesExp(exp.tupleExp);
    then addArgument(result, exp, inverse);

    case (_, Expression.RECORD_ELEMENT()) algorithm
      exp.recordExp := combineBinariesExp(exp.recordExp);
    then addArgument(result, exp, inverse);

    case (_, Expression.MUTABLE()) algorithm
      Mutable.update(exp.exp, combineBinariesExp(Mutable.access(exp.exp)));
    then addArgument(result, exp, inverse);

    case (_, Expression.PARTIAL_FUNCTION_APPLICATION()) algorithm
      exp.args := list(combineBinariesExp(arg) for arg in exp.args);
    then addArgument(result, exp, inverse);

    // done on this branch
    else addArgument(result, exp, inverse);
  end match;
end combineBinariesExp;

protected function combineBinariesSubscript
  input output Subscript subscript;
algorithm
  subscript := match subscript
    case Subscript.UNTYPED() algorithm
      subscript.exp := combineBinariesExp(subscript.exp);
    then subscript;

    case Subscript.INDEX() algorithm
      subscript.index := combineBinariesExp(subscript.index);
    then subscript;

    case Subscript.SLICE() algorithm
      subscript.slice := combineBinariesExp(subscript.slice);
    then subscript;

    case Subscript.EXPANDED_SLICE() algorithm
      subscript.indices := list(combineBinariesSubscript(sub) for sub in subscript.indices);
    then subscript;

    else subscript;
  end match;
end combineBinariesSubscript;

protected function addArgument
  input output Expression exp;
  input Expression arg;
  input Boolean inverse;
algorithm
  exp := match exp
    // add to inverse arguments
    case Expression.MULTARY() guard(inverse) algorithm
      exp.inv_arguments := arg :: exp.inv_arguments;
    then exp;

    // add to arguments
    case Expression.MULTARY() algorithm
      exp.arguments := arg :: exp.arguments;
    then exp;

    // no multary on the stack, just return the expression
    case Expression.EMPTY() then arg;

    // cannot be parsed
    else algorithm
      Error.addMessage(Error.INTERNAL_ERROR,{getInstanceName() + " failed to add : " +
        Expression.toString(arg) + " to " + Expression.toString(exp) + ". Only works for MULTARY()!"});
    then fail();
  end match;
end addArgument;


annotation(__OpenModelica_Interface="frontend");
end NFSimplifyExp;