Definition. A translation to turn partial traces into completed traces [pa-0009]
Define a syntactic transformation on CCS terms (augmented with \textbf {1}) \Upsilon as follows:
\begin {array}{lcl} \Upsilon (\textbf {0}) &=& \textbf {1} \\ \Upsilon (\textbf {1}) &=& \textbf {1} \\ \Upsilon (a.P) &=& \textbf {1} + a.\Upsilon (P) \\ \Upsilon (\sum _{i \in I} P_i) &=& \textbf {1} + \sum _{i \in I} \Upsilon (P_i) \\ \Upsilon (P | Q) &=& \Upsilon (P) | \Upsilon (Q)\\ \Upsilon (P \setminus \alpha ) &=& \Upsilon (P) \setminus \alpha \\ \Upsilon (P [ f ]) &=& \Upsilon (P) [ f ] \end {array}