Prior to version 10 of Mathematica, there was a menu option Evaluation / Interrupt Evaluation... with the hot-key ALT-, (comma). This would temporarily suspend the current evaluation in progress.
The bad news is that this menu item is gone. The good news is that the hot-key still works in versions 10 and 11.
The sequence of events is as follows:
- Start a long-running evaluation.
- At some point, press ALT-,
- A dialog appears that allows us to abort or continue -- or to "enter a subsession". This last will suspend the evaluation and return control to the front-end interface.
- We can evaluate expressions within the subsession as we see fit to examine the current kernel state.
- When we are ready to continue, we evaluate the expression
Return (with no brackets).
This screenshot shows the process:
I can only imagine that WRI has a reason for hiding the Interrupt Evaluation menu item. Perhaps the feature is being deprecated -- maybe there are issues trying to interrupt evaluations in recent versions due to increased parallelization. Before you start a great big evaluation, it might be prudent to experiment with this feature a few times with your actual code in order to see whether it will suspend properly.