miniKanren.lua

Description

miniKanren is a minimalist logic programming language. This project is an implemention of miniKanren in Lua.

Usage

Core miniKanren.lua extends Lua with four operations: eq(), not_eq(), all(), and conde()(also alli() and condi(), where i means interleaves).

eq() unifies two terms, which return false when failed to unify, or return a pair called substitution.

not_eq() and eq() works in opposite ways, which return false when the two terms can unified.

There is also two function run() and fresh_vars().

run() serves as an interface between Lua and miniKanren.lua, and whose value is a list.

fresh_vars() introduces a certain number of fresh variables, which takes an argument to specify the number of fresh variables.

For example:

a = fresh_vars(1)
run(1, a, conde(
       eq(a, 1),
       eq(a, 2)))
-- {1}

The first argument of run() specify the number of answer, where false means all the answers.

a = fresh_vars(1)
run(2, a, conde(
       eq(a, 1),
       eq(a, 2)))
-- {1, 2}

a = fresh_vars(1)
run(false, a, conde(
       eq(a, 1),
       eq(a, 2),
       eq(a, 3)))
-- {1, 2, 3}

There is a shortcut for false:

a = fresh_vars(1)
run_all(a, conde(
       eq(a, 1),
       eq(a, 2),
       eq(a, 3)))
-- {1, 2, 3}

conde() and all() can be nested within each other.

a, b = fresh_vars(2)
run(false, {a, b}, conde(
    all(eq(a, 1), eq(b, 1)),
    all(eq(a, 2), eq(b, 2))))
-- { { 1, 1 }, { 2, 2 } }

If there is no answer, return an empty table.

a = fresh_vars(1)
run(false, a, all(
       eq(a, 1),
       eq(a, 2)))
-- {}

A string like "_.0" will be returned when a variable remains unbound. And it represents any value.

a, b, c = fresh_vars(3)
run(false, a, all(
    eq(a, b),
    eq(1, c)))
-- { "_.0" }

not_eq():

a, b = fresh_vars(2)
run(false, a, all(
    eq(a, b),
    not_eq(b, 2),
    eq(a, 2)))
-- {}

a, b, c = fresh_vars(3)
run(false, a, all(
    eq(a, b),
    eq(b, c),
    not_eq(a, 1),
    not_eq(b, 2),
    not_eq(c, 3)))
-- { "_.0 not eq: 3,2,1" }

See miniKanren: an interactive Tutorial for detail of miniKanren.