We study the position of the AUTOMATH systems within the framework of Pure Type Systems (PTSs). In [1,15], a rough relationship has been given between AUTOMATH and PTSs. That relationship ignores three of the most important features of AUTOMATH: definitions, parameters and Pi-reduction, because at the time, PTSs did not have these features. Since, PTSs have been extended with these features and in view of this, we revisit the correspondence between AUTOMATH and PTSs. This paper gives the most accurate description of AUTOMATH as a PTS so far. ©2003 Published by Elsevier Science B. V.