Tom Schrijvers, Peter Stuckey and Philip Wadler Abstract: A constraint programming system combines two essential components: a constraint solver and a search engine. The constraint solver reasons about satisfiability of conjunctions of constraints, and the search engine controls the search for solutions by iteratively exploring a disjunctive search tree defined by the constraint program. In this paper we give a monadic definition of constraint programming where the solver is defined as a monad threaded through the monadic search tree. We are then able to define search and search strategies as first class objects that can themselves be built or extended by composable search transformers. Search transformers give a powerful and unifying approach to viewing search in constraint programming, and the resulting constraint programming system is first class and extremely flexible. Let's briefly look at the n queens example from the paper. First, there is the nqueens model:
Once you start thinking about structuring your code to use Option in languages which have built-in support for it, you’ll find yourself dreaming about such patterns in other, less fortunate languages. It’s really sort of bizarre how much this little device can open your mind to new possibilities. Take my code, and give it a try in your project. Better yet, implement something on your own which solves the problem more elegantly! The stodgy old Java “best practices” could use a little fresh air. P.S. Yes, I know that the original implementation of this was actually the Maybe monad in Haskell. I picked Option instead mainly because a) I like the name better, and b) it’s Scala, so it’s far more approachable than Haskell.