kanren

• kanren
• Introduction
• Getting Started
• Work in Progress
• Contributing

Introduction

Kanren is a port of microKanren to TypeScript. I'll defer to miniKanren.org for an explanation of what types of problems the kanren family of languages solve.

The initial goal with this particular port is to provide an API that can easily be extended to include additional term types and constraints.

Getting Started

First things first, install kanren: npm install --save kanren

Import kanren.

// es6
import { kanren }  from "kanren";

// commonjs
const { kanren } = require("kanren");

const { unify, callWithFresh, disj, conj, runAll } = kanren();

Real quick aside - kanren operates over Terms. No other values are supported within kanren. Note that symbol Terms are reserved for internal use within kanren; please don't use them.

type Term = boolean | undefined | null | number | string | symbol | Array<any>;

Anyway... Now that we have kanren, use runAll to determine if 1 unifies with 1.

> runAll( unify(1, 1) ).size
1

As you can see, there's one state in which the unify(1, 1) goal succeeds. So yes, 1 unifies with 1. Does 1 unify with 2?

> runAll( unify(1, 2) ).size
0

It sure doesn't. There are 0 states in which the unify(1, 2) goal succeeds. What happens when we unify other Terms?

> runAll( unify([1], 1) ).size
0
> runAll( unify([1], [1]) ).size
1
> runAll( unify([1], [1,2]) ).size
0
> runAll( unify(true, true) ).size
1
> runAll( unify(true, false) ).size
0
> runAll( unify(false, false) ).size
1

So, in general, Terms with equivalent structures and values tend to unify. What about wildcards? The callWithFresh goal wraps a goals and introduces a variable that can be used within the internal goal.

> // Wrap a goal with a hole (`unify(_,5)`) with a function of one argument.
> // Use the single parameter to fill in the hole
> const goalWithVariable = (joker) => unify(joker, 5);
> // Pass `goalWithVariable` to `callWithFresh` to create a goal that creates a logic variable
> runAll( callWithFresh(goalWithVariable) ).size
1
> runAll( callWithFresh((joker) => unify(joker, 5)) ).get(0).substitution.get(0)
{ left: Symbol(0), right: 5 }
> runAll( callWithFresh((joker) => unify(5, joker)) ).get(0).substitution.get(0)
{ left: Symbol(0), right: 5 }

We've just created what's known as a logic variable. Like normal variables in the javascript world, this can be used to represent values. As you can see within the subsitution above, you can assign a logic variable by unifying it with another term. You can also assign logic variables to values within non-primitive terms, such as Arrays.

> runAll( callWithFresh((a) => unify([a], [5])) ).get(0).substitution.get(0)
{ left: Symbol(0), right: 5 }

You might want to make multiple calls to unify. Using conj (conjunction a.k.a logical "and") we can create an aggregate goal that encompasses two smaller goals. Both goals must succeed for the aggregate to succeed.

> runAll( conj(unify(1,1), unify(1,1)) ).size
1
> runAll( conj(unify(1,1), unify(1,2)) ).size
0
> runAll( conj(unify(1,2), unify(1,2)) ).size
0
> runAll( callWithFresh((a) => conj(unify(a,5), unify([a],[5]))) ).size
1
> runAll( callWithFresh((a) => conj(unify(a,5), unify(a,[]))) ).size
0

Like conj, you could also use disj (disjunction a.k.a logical "or") to create an aggregate goal that encompasses two smaller goals. Unlike conj, only one of disj's sub-goal need succeed for the aggregate to succeed.

> runAll( disj(unify(1,1), unify(1,1)) ).size
2
> runAll( disj(unify(1,1), unify(1,2)) ).size
1
> runAll( disj(unify(1,2), unify(1,2)) ).size
0
> runAll( callWithFresh((a) => disj(unify(a,5), unify(a,6))) ).size
2
> runAll( callWithFresh((a) => disj(unify(a,5), unify([a],[]))) ).size
1

Note that disj has the power to create new states; it creates a branch. conj is used to compound new information to existing states.

Work in Progress

• Benchmarking
• Constraint Extensions - Extend kanren with custom constraints
• Term type Extensions - Extend kanren with custom term types
  • [ ] Hook new terms into unification algorithm via a predicate and a unifier
• Standard Libraries
  • [ ] Array
  • [ ] Object

Contributing

kanren is welcoming contributions. If you have something to say, I'd like to hear it. If you have something to code, I'd like to see it. Read more about how to contribute and how to get set up with development here.