After reading "The Reasoned Schemer" I had to try to write a version of minikanren myself. The implementation is basically the last section "Connecting the wires", translated to java. It is not complete or perfect, but you can run (simple) goals including conde. The test classes show examples from chapter 1 and 9 in the book.
The object Thing is holding an inner object, and if that inner object is null the Thing is a fresh variable.
Thing x = new Thing(); // fresh variable Thing x = new Thing("apple");
A Substitution is a list of pair of things. The left hand side of each pair is a variable, and it is associated with the value on the right hand side. A substitution can be walked for a variable by finding the pair with that variable on the left hand side, and if the value on the right also is a variable then see if that variable is on the left of another pair and so on, util a non-variable is reached or the value on the right does not exist in on the left of another pair. If a substitution contains the following pairs
(z, "plum") (x, y) (y, z)
then the substitution walked with x would give plum.
A Goal is a lambda expression which takes a substitution and returns a stream of substitutions.