Suppose we have a class of objects that represent the state of a computer, and a function that takes one of these objects as an argument and returns another one of these objects. If we have a way to translate a program into such a function, we have established a timeless meaning for that program, as opposed to simply seeing it as a set of instructions whose meaning can be seen only by executing it at a particular time.

Suppose we have a function that combines two such functions and returns one, producing the effect of executing the program represented by the first function, followed by the program represented by the second. We have then established the meaning of sequencing in programs. We can in a similar way establish the meaning of loops and conditionals, and by using these functions, establish the meaning of more complex programs.

This is an informal description of the idea of denotational semantics. When dealing with concurrency, we need a more general function that considers the possible interleavings of threads of control.

A huge amount of work has been done in this area, and this paper is just one example. It is of interest because it was developed in Russia, somewhat in isolation and away from the main core of such work, though influenced by it. For those unfamiliar with the theory, at its center is the use of resumption monads. I would like to have seen some concrete examples in this paper to better judge the extent to which the proposed approach has general application.