BinaryOperator

A practice of abstract algebra on C# with a convenient way on C# .NET platform. Great thanks to

https://antimatroid.wordpress.com/2012/04/01/abstract-algebra-in-c/ who inspired me on this repository.

Introduction

Imagine you have to implement a new class called Even, which should behave always the same functionality of int: adding, substracting. But only with the even numbers. It should not receive any odd number in its calculation. Then it can be written using implicit approach:

public static implicit operator Even(int a)
{
  if (a % 2 == 0)
    return new Even(a);
  else
    throw new ArgumentOutOfRangeException();
}

However, there is still many behaviour that does not get from integer it self. Then we try using inherit approach:

public class Even: int
{  
}

But wait... int is sealed so it cannot be inherited by any class! Even though it is a homomorphism between int and even but we still cannot find a simple way to use them. This repository is aim for solving these problems!

Usage

To clearify, G here represent for any of Groupoid / Semigroup / Monoid / Group / AbelianGroup

Create

var addingIntegerGroupoid = Groupoid.From((int a, int b) => a + b);

Represent a Groupoid with + as binary operator, closed inside integer.

var addingIntegerSemigroup = Semigroup.From((int a, int b) => a + b);

Same as above, but should be associable.

var addingIntegerMonoid = Monoid.From((int a, int b) => a + b, 0);

Same as above, but with an identity 0.

var addingIntegerGroup = Group.From((int a, int b) => a + b, 0, (int a) => -a);

Same as above, but assign with an inverse function f(a) = -a so such that a + f(a) = identity.

var addingIntegerAbelianGroup = AbelianGroup.From((int a, int b) => a + b, 0, (int a) => -a);

Same as above, but should be commutable.

Mapping

addingIntegerGroup.Map(integer => integer * 2);

G(+) is multiplied by 2. It is no longer closable in N but 2N.

Upgrade

Every G is extending the basis G class. Eg. A group should already be considered as a groupoid. To upgrade, you can use:

var addingIntegerAbelianGroup = 
  Groupoid.From((int a, int b) => a + b)
    .ToSemigroup()
    .ToMonoid(0)
    .ToGroup((int a) => -a)
    .ToAbelianGroup();
// valid

Fluent form

All G support fluent form so you can understand flow by flow easily.

Groupoid.From((int a, int b) => a + b)
  .Map(inta => inta * 2)
  .Map(even => even as double)
  .Map(decimal =>decimal.ToString());
// will create an integer groupoid with Functor that double, set as decimal number and set as string.

Future plan / TODO

1. Validation of a groupoid / semi-group / monoid / group / abelian group
2. Group Element type
3. No plan on maintaining this repository. Just for fun.

Contact

Create issue at this repository