I'm interested in different notions or aspects of execution and how they relate to each other: in particular reversible, incremental, lazy and parallel computation. These concepts are more closely related than they might seem on first inspection. For example, lazy evaluation exploits the parallel structure of a computation, i.e. the fact that some parts can be executed independently of others. Biswas first noticed this in his PhD thesis on program slicing.
A reversible computation is one where you can scrub backwards and forwards in time, as in a time-travel debugger. An incremental computation is one that responds to input changes by undoing and redoing affected parts of the computation. One can think of this as stepping sideways into an alternate universe where a different course of events took place. I call this retroactive update. Here is a blog article I wrote about what retroactive update might mean for open systems.
Since 2001 I've been interested in “transparent” programming models where where every value comes equipped with an account of how it was computed. James Cheney coined the nice phrase self-explaining computation to describe such a system. For distributed computations, being able to discover what happened after the fact is essential, since we will usually lack the authority, or even the means, to restart the computation in a debugger.
In our 2012 ICFP paper, we made a connection between self-explaining computation and reversibility: a trace of a computation explains a result v precisely when it contains enough information to execute backwards from v to a slice of the original program which preserves its capacity to execute forwards to v. In later work we extended this idea to a labelled transition semantics for reversible pi calculus.