$use Access Arithm Box Compare Convert List StdIO;

$func Main = e;
Main = <WriteLn <GEN ('xaby') ('ybax')>>;

$func GEN (e.left) (e.right) = (e.consts) (e.vars) s.BDnum e.GEs;
GEN (e.left) (e.right) = 
  <Split &Gt ('p') (<Paren <Nub e.left e.right>>)> :: (e.consts) (e.vars),
  <ToQuadratic <Concat e.vars> (e.left) (e.right)> :: (e.left) (e.right) e.EQs,
  (<Concat e.consts>) (e.vars <Concat <MapIn &R 0 (e.EQs)>>) 0 (e.left) (e.right);

$func ToQuadratic e.vars (e.left) (e.right) = (e.left) (e.right) e.EQs;
ToQuadratic {
  e1 sx e2 (e.left) (e.right), e.left e.right : ea sx eb sx ec sx ed =
    <NewVar sx> :: sx1,
    {
      e.right : ef sx ed = <ToQuadratic sx e2 (e.left) (ef sx1 ed)> (sx sx1);
      e.d : ef e.right = <ToQuadratic sx e2 (ea sx eb sx ec sx1 ef) (e.right)> (sx sx1);
    };
  e (e.left) (e.right) = (e.left) (e.right);
};

$box FreeIdx;

$func NewVar s.var = s.new_var;
NewVar s.var =
  {
    <Get &FreeIdx> : s.idx,
      <Store &FreeIdx <Add s.idx 1>>, s.idx;
    <Store &FreeIdx 1>, 0;
  } :: s.idx,
  <ToWord s.var s.idx>;