A fairly surreal and probably overly optimistic example would be, for example, to solve traveling salesman problems using chess engines. What we would need is to find right mappings: (1) from a traveling salesman problem to a chess position and, (2) from a traveling salesman route to a chess move (or move sequence)
A general solution for a "compiler" that can translate between any pair of problems feels unrealistic but I can imagine developing a mapping between, say, a tic tac toe game and simple chess positions where you could: (1) translate a tic tac toe position into a chess position (2) solve the chess position (3) translate the solution into a tic tac toe sequence
Any thoughts or pointers to relevant research would be much appreciated!