kanren

Logic/relational programming in Python with miniKanren.

Motivation

Logic programming is a general programming paradigm. This implementation however came about specifically to serve as an algorithmic core for Computer Algebra Systems in Python and for the automated generation and optimization of numeric software. Domain specific languages, code generation, and compilers have recently been a hot topic in the Scientific Python community. kanren aims to be a low-level core for these projects.

Examples

kanren enables one to express sophisticated relations—in the form of goals—and generate values that satisfy the relations. The following code is the "Hello, world!" of logic programming; it asks for values of the logic variable x such that x == 5:

>>> from kanren import run, eq, membero, var, lall
>>> x = var()
>>> run(1, x, eq(x, 5))
(5,)

Multiple logic variables and goals can be used simultaneously. The following code asks for one list containing the values of x and z such that x == z and z == 3:

>>> z = var()
>>> run(1, [x, z], eq(x, z),
                   eq(z, 3))
([3, 4],)

kanren uses unification to match forms within expression trees. The following code asks for values of x such that (1, 2) == (1, x):

>>> run(1, x, eq((1, 2), (1, x)))
(2,)

The above examples use eq: a goal constructor that creates a goal for unification between two objects. Other goal constructors, such as membero(item, coll), express more sophisticated relations and are often constructed from simpler ones like eq. More specifically, membero states that item is a member of the collection coll.

The following example uses membero to ask for all values of x, such that x is a member of (1, 2, 3) and x is a member of (2, 3, 4).

>>> run(0, x, membero(x, (1, 2, 3)),  # x is a member of (1, 2, 3)
              membero(x, (2, 3, 4)))  # x is a member of (2, 3, 4)
(2, 3)

The examples above made implicit use of the goal constructors lall and lany, which represent goal conjunction and disjunction, respectively. Many useful relations can be expressed with lall, lany, and eq alone, but in kanren it's also easy to leverage the host language and explicitly create any relation expressible in Python.

Representing Knowledge

kanren stores data as facts that state relationships between terms. The following code creates a parent relationship and uses it to state facts about who is a parent of whom within the Simpsons family:

>>> from kanren import Relation, facts
>>> parent = Relation()
>>> facts(parent, ("Homer", "Bart"),
...               ("Homer", "Lisa"),
...               ("Abe",  "Homer"))

>>> run(1, x, parent(x, "Bart"))
('Homer',)

>>> run(2, x, parent("Homer", x))
('Lisa', 'Bart')

We can use intermediate variables for more complex queries. For instance, who is Bart's grandfather?

>>> grandparent_lv, parent_lv = var(), var()
>>> run(1, grandparent_lv, parent(grandparent_lv, parent_lv),
                           parent(parent_lv, 'Bart'))
('Abe',)

We can express the grandfather relationship as a distinct relation by creating a goal constructor:

>>> def grandparent(x, z):
...     y = var()
...     return lall(parent(x, y), parent(y, z))

>>> run(1, x, grandparent(x, 'Bart'))
('Abe,')

Constraints

kanren provides a fully functional constraint system that allows one to restrict unification and object types:

>>> from kanren.constraints import neq, isinstanceo

>>> run(0, x,
...     neq(x, 1),  # Not "equal" to 1
...     neq(x, 3),  # Not "equal" to 3
...     membero(x, (1, 2, 3)))
(2,)

>>> from numbers import Integral
>>> run(0, x,
...     isinstanceo(x, Integral),  # `x` must be of type `Integral`
...     membero(x, (1.1, 2, 3.2, 4)))
(2, 4)

Graph Relations

kanren comes with support for relational graph operations suitable for basic symbolic algebra operations. See the examples in doc/graphs.md.

Extending kanren

kanren uses multipledispatch and the logical-unification library to support pattern matching on user defined types. Essentially, types that can be unified can be used with most kanren goals. See the logical-unification project's examples for demonstrations of how arbitrary types can be made unifiable.

Installation

Using pip:

pip install miniKanren

To install from source:

git clone git@github.com:pythological/kanren.git
cd kanren
pip install -r requirements.txt

Tests can be run with the provided Makefile:

make check

About

This project is a fork of logpy.

References

• Logic Programming on wikipedia
• miniKanren, a Scheme library for relational programming on which this library is based. More information can be found in the thesis of William Byrd.