# Title

One-Day Tutorial on miniKanren

One-Day Tutorial on miniKanren

Overview

miniKanren is a family of embedded Domain Specific Languages (DSLs) for logic programming. It allows for writing declarative code and is often used for tasks like constraint solving, relational programming, and more. In this tutorial, we'll introduce miniKanren using Scheme, which is one of the languages it was originally developed in.

Prerequisites

Basic understanding of Scheme.
Installation of Scheme (e.g., Racket, Chicken Scheme).
miniKanren library installed.

Schedule

Introduction to miniKanren (1 hour)
Basic Concepts and Operators (1 hour)
Advanced Techniques (1 hour)
Practical Examples (1 hour)
Exercises and Practice (2 hours)

1. Introduction to miniKanren

What is miniKanren?

miniKanren is a logic programming language that enables the expression of relations and constraints directly within your code.

Installation

Install miniKanren by following the instructions for your Scheme interpreter. For example, using Racket:

#lang racket
(require (planet weinholt/schemeunit))
(require (planet weinholt/schemeunit/text-ui))

2. Basic Concepts and Operators

Core Concepts

Goals: Statements that can be true or false.
Relations: Connections between different variables or values.
Unification: The process of making two terms identical.

Key Operators

==: Asserts that two terms are equal.
fresh: Introduces new logical variables.
conde: Represents logical disjunction (OR).

Basic Examples

Equality (==)

#lang racket
(require minikanren)

(run* (q)
  (== q 5))

Introducing Variables (fresh)

#lang racket
(require minikanren)

(run* (q)
  (fresh (x y)
    (== x 5)
    (== y 6)
    (== q (list x y))))

Logical OR (conde)

#lang racket
(require minikanren)

(run* (q)
  (conde
    [(== q 5)]
    [(== q 6)]))

3. Advanced Techniques

Recursive Relations

miniKanren supports defining recursive relations. For example, a simple relation to check if a list is empty:

#lang racket
(require minikanren)

(define emptyo
  (lambda (l)
    (== l '())))

Defining More Complex Relations

Define a relation that checks if an element is in a list:

#lang racket
(require minikanren)

(define membero
  (lambda (x l)
    (conde
      [(== (cons x (fresh (rest))) l)]
      [(fresh (y rest)
         (== (cons y rest) l)
         (membero x rest))])))

4. Practical Examples

Example 1: Simple Arithmetic

Using miniKanren to solve simple arithmetic constraints:

#lang racket
(require minikanren)

(run* (q)
  (fresh (x y)
    (== x 3)
    (== y 4)
    (== q (+ x y))))

Example 2: Family Relations

Define and query family relationships:

#lang racket
(require minikanren)

(define parento
  (lambda (parent child)
    (conde
      [(== parent 'alice) (== child 'bob)]
      [(== parent 'bob) (== child 'charlie)])))

(run* (q)
  (parento 'alice q))

5. Exercises and Practice

Basic Relations: Define a relation grandparento that relates grandparents to their grandchildren.
List Processing: Create a relation reverso that relates a list to its reverse.
Constraint Solving: Use miniKanren to solve a Sudoku puzzle.

Exercise Solutions

grandparento Relation

#lang racket
(require minikanren)

(define grandparento
  (lambda (gp gc)
    (fresh (p)
      (parento gp p)
      (parento p gc))))

reverso Relation

#lang racket
(require minikanren)

(define reverso
  (lambda (l r)
    (conde
      [(== l '()) (== r '())]
      [(fresh (a d rd)
         (== (cons a d) l)
         (reverso d rd)
         (append rd (list a) r))])))

Solving Sudoku

(Implement a simple Sudoku solver using miniKanren constraints.)

Conclusion

This tutorial provided an introduction to miniKanren, its basic concepts, and some practical applications. By working through these examples and exercises, you should have a foundational understanding of how to use miniKanren for logic programming in Scheme.