In order to fire a given program at a given state, we may not need to know all about the state. Only some values of external functions may be needed for firing. We may not care about or even know the values of external functions which are not needed for the execution. Some of those values may even be ill-defined. There is also an issue of influencing the environment by requiring an extra value, e.g., by requiring a user-provided datum.
It is natural to set all irrelevant values of external functions to undef. However, caution should be exercised in the distributed situation (see ) where other agents may have different views of those values.
Sometimes it may be simpler to use partial states. A partial -state
S with carrier C can be defined as a partial function from
to C . See examples in [BGR, GM]. For simplicity, we will
not use partial states here.