The List Trifecta, Part 1

// ISetImm and its component interfaces, ISetTests and ISetOperations
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Loyc.Collections
{
	/// <summary>Set testing operations.</summary>
	/// <typeparam name="SetT">Type of set that this set can be tested against.</typeparam>
	public interface ISetTests<SetT>
	{
		bool IsProperSubsetOf(SetT other);
		bool IsProperSupersetOf(SetT other);
		bool IsSubsetOf(SetT other);
		bool IsSupersetOf(SetT other);
		bool Overlaps(SetT other);
		bool SetEquals(SetT other);
	}

	/// <summary>Set-combining operations: With, Without, Union, Intersect, Except, Xor.</summary>
	/// <typeparam name="T">Type of items in the set.</typeparam>
	/// <typeparam name="SetT">Type of the set itself.</typeparam>
	#if CSharp4
	public interface ISetOperations<in T, SetT> : ISetOperations<T, SetT, SetT> { }
	public interface ISetOperations<in T, in InSetT, out OutSetT>
	#else
	public interface ISetOperations<T, SetT> : ISetOperations<T, SetT, SetT> { }
	public interface ISetOperations<T, InSetT, OutSetT>
	#endif
	{
		OutSetT With(T item);
		OutSetT Without(T item);
		OutSetT Union(InSetT other);
		OutSetT Intersect(InSetT other);
		OutSetT Except(InSetT other);
		OutSetT Xor(InSetT other);
	}


	/// <summary>Immutable set operations.</summary>
	/// <typeparam name="SetT">Type of this set.</typeparam>
	/// <typeparam name="T">Type of items in the set</typeparam>
	public interface ISetImm<T, SetT> : ISetOperations<T, SetT>, ISetTests<SetT>, IReadOnlyCollection<T> //ICount
	{
		/// <summary>Returns true if the set is inverted, which means that the
		/// enumerator returns all the items that are <i>not</i> in the set, 
		/// and the <see cref="Count"/> returns the number of items that are
		/// not in the set.</summary>
		/// <remarks><see cref="InvertibleSet{T}"/> is an example of a set that 
		/// can be inverted. In most set implementations, this property always 
		/// returns false.</remarks>
		bool IsInverted { get; }
	}
}