public static T MonoidOp <T>(this IEnumerable <T> summables, Monoid <T> mon)
{
return(summables.Aggregate(mon.Unit, mon.Op));
}
public static T InnerProduct <T>(this IEnumerable <T> left, IEnumerable <T> right
, Monoid <T> sum, Monoid <T> product)
{
return(left.Zip(right, (x, y) => product.Op(x, y)).MonoidOp(sum));
}
public SemiRing(Monoid <T> add, Monoid <T> product)
{
Add = add;
Product = product;
}
public Group(Monoid <T> monoid, Func <T, T> inverse)
{
Monoid = monoid;
Inverse = inverse;
}
/// <summary>
/// Repeatedly apply a monoid operation to the consecutive elements of a container
/// </summary>
/// <typeparam name="T">A type that has monoid properties
/// (a zero element and an associative binary operation)</typeparam>
/// <param name="summables">An enumerable container of objects of type T</param>
/// <param name="mon">A monoid object that defines a zero element and
/// an associative binary operation on T</param>
/// <returns>An object of type T formed by applying the monoid's
/// associative operations over each consecutive pair in the source.
/// This is just an aggregation of an IEnumerable of the monoid operation.</returns>
public static T MonoidOp <T>(this IEnumerable <T> source, Monoid <T> mon)
{
return(source.Aggregate(mon.Unit, mon.Op));
}