Barliman is written in miniKanren[0], a logic/relational programming system built by Daniel Friedman[1], Will Byrd[2] & Oleg Kiselyov[3]. There are implementations of miniKanren in languages other than Scheme, one of the prominent being Clojure[4].

To oversimplify, in the miniKanren world programs are written using relational logic, wherein there are "variables" and then certain "relationships" between the variables. That is the program specification. Now we can run the specification and allow miniKanren to generate one or more variables that satisfy the relations. Thus a miniKanren program can have more than one answers. One interesting side-effect of this kind of an abstraction is that programs can also be run backwards to generate more programs that satisfy certain relations. That's pretty much what's happening with Barliman.

[0] http://minikanren.org/ [1] https://en.wikipedia.org/wiki/Daniel_P._Friedman [2] http://webyrd.net/ [3] http://okmij.org/ftp/ [4] https://github.com/clojure/core.logic