For more details on microKanren see the original paper, though I find the racket implementation a bit clearer

Files:

• microkanren.sml: The microKanren implementation, around 100 lines of Standard ML, and 150 lines of comments.
• sequence.sml: A simple lazy-list/stream/sequence library for Standard ML, necessary for microkanren.sml.
• microkanren_prettyprint.sml: Basic pretty-printers for terms, necessary for microkanren_examples.sml.
• microkanren_examples.sm: A couple of examples, with their corresponding Prolog implementation.

There is the branch structures which uses Standard ML's signatures and structures, and might or might not be easier to read. The benefit of that is you are able to see the types of functions side-by-side with their implementations, by looking at both the *.sig and *.sml file.

Running: To run in PolyML, run poly --use microkanren.sml, to run the examples, do poly --use microkanren.sml --use microkanren_prettyprint.sml --use microkanren_examples.sml -q (the -q makes PolyML quiet, and supresses printing of types, which makes the printed output stand on its own).

To run in SML/NJ, use sml microkanren.sml and sml microkanren.sml microkanren_prettyprint.sml microkanren_examples.sml.

Here is what the output should be (minus any types and warnings):

$ poly --use microkanren.sml --use microkanren_prettyprint.sml --use microkanren_examples.sml -q
X==x
x

X==x || X==y
x
y

X==x && Y==X
x

peano(N)
z
s(z)
s(s(z))

wait(N) || peano N
please_wait
please_wait
please_wait

wait N II peano N
please_wait
z
please_wait
s(z)

append(L,R,[1,2,3])
(nil, cons(1, cons(2, cons(3, nil))))
(cons(1, nil), cons(2, cons(3, nil)))
(cons(1, cons(2, nil)), cons(3, nil))
(cons(1, cons(2, cons(3, nil))), nil)

c(P,Q,R)
c(x, 3, R)
c(x, 3, R)

c(1,6,R)
c(1, 6, 7)

Happy hacking!