Characterizing minimal semantics-preserving slices of function-linear, free, liberal program schemas

A program schema defines a class of programs, all of which have identical statement structure, but whose functions and predicates may differ. A schema thus defines an entire class of programs according to how its symbols are interpreted. As defined in this paper, a slice of a schema is obtained from a schema by deleting some of its statements. We prove that given a schema S which is function-linear, free and liberal, and a slicing criterion defined by the final value of a given variable after execution of any program defined by S, the minimal slice of S which respects this slicing criterion contains only the symbols ‘needed’ by the variable according to the data dependence and control dependence relations used in program slicing, which is the symbol set given by Weiser’s static slicing algorithm. Thus this algorithm gives minimal slices for programs representable by function-linear, free, liberal schemas. We also prove a similar result with termination behaviour used as a slicing criterion. This strengthens a recent result, in which S was required to be linear, free and liberal, and termination behaviour as a slicing criterion was not considered.