Read
and modify
are programming-language terms.
Mathematically, saying that an ab1b step reads t
means that the value of some variable allowed by ab1b in
the step's ending state can depend on the value of t in
the step's starting state.
Saying that an ab1b step modifies t means
that ab1b allows the value of t in the
step's ending state to be different from its value in the starting
state.