/// <summary>
/// Returns a composition of the two morphisms.
/// </summary>
public static IMorphism <A, C> Compose <A, B, C>(IMorphism <A, B> m1, IMorphism <B, C> m2)
{
var mappings = m1.Domain.Select(a =>
{
var bo = m1.Apply(a);
var co = bo.FlatMap(b => m2.Apply(b));
return(co.Map(c => Product2.Create(a, c)));
});
return(Create(mappings.Flatten()));
}
public IsoMorphism(IEnumerable <IProduct2 <A, B> > mappings)
: base(mappings)
{
Inverse = Morphism.Create(mappings.Select(m => Product2.Create(m.ProductValue2, m.ProductValue1)));
}
/// <summary>
/// Returns an identity morphism of the specified values.
/// </summary>
public static IMorphism <A, A> Identity <A>(IEnumerable <A> values)
{
return(Create(values.Select(v => Product2.Create(v, v))));
}
/// <summary>
/// Converts the specified normalized function back to a standard function used in .NET.
/// </summary>
public static Func <T1, T2, TResult> Denormalized <T1, T2, TResult>(this Func <IProduct2 <T1, T2>, TResult> f)
{
return((t1, t2) => f(Product2.Create(t1, t2)));
}