Data-flow and control-flow perspectives are the most important perspectives to workflow management. As scientific workflows often operate on large, complex, and heterogeneous data, data-flow is particularly important to them. DFL is a formal, graphical workflow language for data-flows based on Petri nets and nested relational calculus. The focus of this paper is to articulate the transition system semantics of DFL. The major flaws of the existing work in terms of the transition system semantics lie in the following aspects, containing token unnesting history management, enabling configuration and state transition, are clearly revised. The following improvements can be obtained from revising those flaws: (1)The token unnesting history management is more efficient in terms of time and space. It can be increased when unnest edges lead to output places and be decreased when nest edges lead from input places. Empty sets are dealt with in coherence with non-empty sets to identify an enabling configuration. (2)The prerequisites of enabling configurations are complemented with that tokens in all input places of the firing transition have the same history and enable the transition. (3)The transition system semantics are clarified in detail on what tokens are consumed from and produced in which places.