A similarity criterion for sequential programs using truth-preserving partial functions

The execution of sequential programs allows them to be represented using mathematical functions formed by the composition of statements following one after the other. Each such statement is in itself a partial function, which allows only inputs satisfying a particular Boolean condition to carry forward the execution and hence, the composition of such functions (as a result of sequential execution of the statements) strengthens the valid set of input state variables for the program to complete its execution and halt succesfully. With this thought in mind, this paper tries to study a particular class of partial functions, which tend to preserve the truth of two given Boolean conditions whenever the state variables satisfying one are mapped through such functions into a domain of state variables satisfying the other. The existence of such maps allows us to study isomorphism between different programs, based not only on their structural characteristics (e.g. the kind of programming constructs used and the overall inputoutput transformation), but also the nature of computation performed on seemingly different inputs. Consequently, we can now relate programs which perform a given type of computation, like a loop counting down indefinitely, without caring about the input sets they work on individually or the set of statements each program contains.