Functor, applicative and monad interfaces

interfaces.cs

// In C# we can't enforce generic classes in interfaces, so we can't use interfaces to define the contract.
// I can only give examples of the minimal code it needs to implement.

class FunctorImpl<T> {
    FunctorImpl<T> Pure(T val);
    FunctorImpl<S> Apply<S>(Func<T, S> fn);
    // Requirement: Pure(val).Apply(x=>x) == Pure(val)
}

class ApplicativeImpl<T> where  {
  ApplicativeImpl<T> Pure(T val);
  ApplicativeImpl<S> Apply<S>(Func<ApplicativeImpl<T>, ApplicativeImpl<S>> fn) 
  static Func<ApplicativeImpl<T>, ApplicativeImpl<S>> Lift<S>(Func<T, S> fn);
  // Requirement: Pure(val).Apply(Lift(x => x)) == Pure(val)
}

class MonadImpl<T> {
  MonadImpl<T> Pure(T val);
  MonadImpl<S> Apply<S>(Func<T, MonadImpl<S>> fn);
  static Func<S, MonadImpl<T>> Lift<S>(Func<T, MonadImpl<S>> fn);
  // Requirement: Pure(val).Apply(Lift(x => x)) == Pure(val)
}