The Lattices of Plato

Published 2012-10-13

The Complaint

There are four (ish) ways of looking at 'type theory stuff' in most standard OO languages: the class-instance relation, the exemplar-mimic relation, the metaclass-class relation, and the supertype-subtype relation. I dislike these ways of looking at things, as they seem to be hopelessly muddled.

The Resolution

So, I have thought of a different way of looking at this kind of thing. 'Type stuff' forms a lattice, as the union of two partial orderings. The first partial ordering is 'meta-whatever'1 - an instance of an Integer is 'meta-whatever' 'Integer', and 'Integer' is 'meta-whatever' 'Class'. The second partial ordering is 'mimic', which is kind of like prototypal inheritance. 'Integer' mimics 'Comparable', 'Class' mimics 'Module', 'four_but_truthy' mimics '4'2. The upshot is no more brittle and specific koans like "the superclass of the metaclass is the metaclass of the superclass".

The End?

I am not certain how this will work in practice; the confusing legacy terminology still infests my thinking, and will probably continue to do so at least until I have found some better names for things3.

  1. Better name much desired.
  2. It may also mimic 'true' or 'false', or may 'meta-whatever' 'Truthy', in addition to the mimicing and 'meta-whatever' relations it picks up from mimicing '4'.
  3. … and also have written a programming language that actually uses this kind of object model fully without the arbitrary limitations that secondarily necessitate brittle and specific koans.

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