Use C3 linearization for multimethod dispatch

[Gattag]

Procedure: Method Dispatch

1. Compute the call signature:

   • Let M be the set of all methods.
   • Let m_cs be the method referenced at the call-site.
   • Let s_cs be the signature of m_cs.
   • Let s_a be the type signature of the arguments at runtime.
   • The call signature s is obtained by substituting null arguments in s_a with the corresponding parameter types from s_cs.

2. Collect methods that match the call-site method’s name and number of arguments and have a supertype signiture of the :

   • Let M′ = {m ∈ M ∣ name(m) = name(m_cs) ∧ numArgs(m) = numArgs(m_cs) ∧ signature(m) :≥ s}.

3. If M′ is empty, throw an exception as there are no dispatchable
   methods.

   • This condition may occur only when the method is called reflectively.

4. Reduce the set to methods that are not supertypes of any other method in the set, these are the most specific signatures:

   • Let M″ = {m ∈ M′ ∣ ∀n ∈ M′ ∣ ¬(signature(m):>signature(n))}.

5. At this point, M″ will have at least one member.

   • If |M″| = 1, dispatch to the single method in M″.

6. If |M″| > 1, resolve ambiguity using a modified C3 linearization (the MPS variant) with precedence for arguments left to right.

   • Apply the modified C3 linearization algorithm to order the methods in M″ and determine the most preferred method for dispatch.

7. At this point, the algorithm will always produce one most preferred method to dispatch to.

TODO formalize C3 and left to right precedence