The logic of search algorithms: Theory and applications

Search algorithms in type theory

“…In particular, just as assignments can be generalized to cache computations (as described in Section 7), so information about impossible values and con ict sets for future variables could be stored in generalized assignments. Indeed, in an earlier paper the second and third authors reported on the implementation of the equivalent of FC+CBJ for propositional satisÿability [21] in a framework similar to that of this paper. However, our framework is not the best for implementation of lookahead techniques in general.…”

“…Indeed, call=cc in Scheme is so suitable for implementing backtracking algorithms that code based on it is likely to be faster than Scheme code implemented di erently. In a previous study, code developed formally was marginally faster than the original implementation of CBJ in Scheme for constraint satisfaction problems [21]. In the case of Hamiltonian Circuit, no such comparison is possible since CBJ has not previously been implemented for it.…”

“…One approach to solving these problems is to base application code on an informal proof such as the one presented above in Section 5. This is the approach taken by Gent and Underwood in [21]. However, the process of translation leaves considerable room for errors.…”

“…Finally, the Nuprl proof could be generalized to more abstract types for sets and assignments. In earlier work [21], two of the authors formalized the core of this work in Lego [30,38], an implementation of type theory based on an extension of the calculus of constructions [15]. Lego does not have Nuprl's sophisticated program extraction mechanisms, so the result was not so closely connected to Scheme code.…”