Legal notion of proceeding's relationship

In French law, there arise controversies about legal notion of proceedings’ relationship (lien d’instance). Some authors addressing on proceedings’ connection as real riddle. Some other qualified this relationship as contractual or quasi-contractual and refer to it as judicial contract- as formerly described in reference to, especially during the classical period in Rome. Some authors believe that best leave the contractual qualification of the proceedings’ relationship unto Roman Law, because the litigants’ obligations have only the legal origin. Despite the aforementioned criticisms, very principles of civil procedure law may authorize qualifying as contractual, the concept of civil proceedings.