The Roles of Witness-Finding in Software Synthesis

In the 1970’s and early 80’s most program derivations were special cases of divide-and-conquer (unfortunately, this is still too often true), probably because they are some of the easiest induction arguments to push through a prover. So it seemed interesting to try to capture divide-and-conquer more abstractly, rather than repeatedly discovering instances of it. From this effort came the notion of constructing a program by instantiating a program scheme and using deductive techniques to synthesize the definitions or specifications for the free operators in program schemes (Smith 1985; 1987; Lowry 1991).