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This is my attempt at implementing μKanren in Hy.

All credit for μKanren to Jason Hemann and Daniel P. Friedman (clearly explained in their paper), and for miniKanren to Daniel P. Friedman, William E. Byrd and Oleg Kiselyov (see their book The Reasoned Schemer).

Much appreciation to Bodil Stokke for explaining things clearly in her talk: μKanren: Running the Little Things Backwards, EuroClojure, Barcelona, Spain, 25 June 2015.

μKanren Relational Programming Basics, with Hy

With Hy, a fun Lisp powered by—and bi-directionally interoperable with—Python, we'll explore the μKanren relational logic system without leaving Python's comfy surroundings.

Why Lisp?

The Lisp family of languages has inspired features which have found their way into Python and many other languages. Are you interested in Lisp, but unwilling to give up your investment in Python’s vast ecosystem? With Hy, and the magical Python AST, you can have it all: call Hy from Python, and Python from Hy, learn some Lisp, and keep the Python tools you’ve come to love. Hy extends your reach into Lisp’s five-decade long heritage, while remaining interoperable with Python.

Why μKanren?

Relational programming is an interesting and declarative way to do logic programming. miniKanren offers a fuller feature set, and a nicer user API for solving logic problems. So, if you're really interested in building a significant system, you'll probably want to check out a miniKanren system. Adderall is a miniKanren that is implemented in Hy.

But, if you'd like to understand how all this works, μKanren is for you. It's a simplified version of miniKanren with fewer user-space bells and whistles. It's small enough that you can implement in yourself, and read through other implementations simply (the original paper has a ~70 line implementation, whereas miniKanren is ~1000 lines).

What is this?

This is an implementation of a relational logic programming system, μKanren, a minimalist version of miniKanren.

I’m not an expert on any of these things, just interested in hacking on fun tools and learning about new things. I’ve found Hy to be a unique opportunity to explore Python internals and data science libraries, while also playing to the strengths of Python.

This μKanren implementation in Hy is heavily inspired by Bodil Stokke’s Clojure implementation and talk at EuroClojure and reading "μKanren: A Minimal Functional Core for Relational Programming," by Jason Hemann and Daniel P. Friedman.


  • python 3.5
  • pyrsistent
  • pytest


Check out the tests for some examples. Run them with $ py.test tests/

I don't understand how any of this works.

It's kind of tough to understand what relational programming is just by reading someone's website. But there are a lot of good online resources for learning about how to use μKanren. Once you understand what it's for, you can dive into how it's built.

Generally useful:

Helped me understand how to use relational programming:

Helped me understand how it works:

Specific parts:

Other notes

This style of programming has evolved over many years (about a decade just for Kanren). For this reason, some of the names have changed. You'll see names which are different in older papers. Here's a few things of note:

  • condi is the same as conde
  • exist is the same as fresh

Thanks to folks who've helped with ideas, comments and questions:

  • Kevin McCarthy (@kevin1024) - Knows everything about Python
  • @olasb on #hy - For the idea to change var into a subclass of pset, rather than a literal pset, thus allowing control of how it's printed, and use of instance? to check for vars (and not confuse them with literal psets)


GNU GENERAL PUBLIC LICENSE, see LICENSE file (Due to use of code from Hydiomatic)


Hy on μKanren







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