Time is more like a function variable or implicit parameter, not a piece of mutable state in the imperative programming sense. Such implicit parameters are also part of Haskell, by the way...
E (between the sheets) = sigma/epsilon0
E (outside) = 0
assigning two different values to the variable E.
In applied math, there are many expressions in which a variable y is treated as a value (depending on implicit parameters) or as a function y(t) depending on explicit independent variables. This is a matter of convenience, not principle.
If Feynman had used something like imperative programming in the Lectures, I wouldn't have been as baffled as (most of?) the rest of a class of physics undergraduates confronted with "LET I=I+1" in the introductory programming class. So I have some empirical evidence from the time when your first computer might be a PDP-10 down the road from Tony Hoare, that imperative programming is really unnatural for physicists.