MiniKanren is a logic programming language embedded in Scheme, originally. The most popular port is probably Clojure's core.logic.
You can learn much more about it at minikanren.org.
This port aims to be philosophically close to the original implementation of MiniKanren, that is, it should be simple to read and understand, perhaps in favor of doing optimizations like convert everything to continuation passing style. That said, hopefully it will remain fast enough to be used for real applications.
The main difference with original MiniKanren is that because F# is typed, the embedded logic programming language is also typed. For example, it isn't statically possible to unify
a list<int> with an int or even a list<bool> (whhich would not unify at runtime anyway).
In time I'd like to take some of the extensions on board, like alpha-kanren and I'm especially interested in cKanren.
For now, have a look at the tests for examples.