isomorphism / typewriter

ridiculous, utterly inexcusable type hackery

What is this?

A dumping ground for all my senseless acts of wonton type hackery. Not for the faint of heart. In fact, you should probably stop reading right now.

Why?

Why not?

What were you thinking?

Good question! If you ever find out, let me know.

Ok. I'd love to gaze into the abyss with you. What've you got?

This is still a work in progress, as I make a half-hearted effort to organize the bits and pieces of type hackery I had lying around. As of last time I bothered to update the README, it has:

• Type classes for working with term proxies for type values, and for kicking type-level values downstairs to go slumming amongst the value-level commoners.
• A rehash of Oleg's TypeEq, modernized slightly by replacing TypeCast with the new ~.
• Simple type-level lists
• Type-level unsigned binary numbers, i.e., natural numbers as lists of bits instead of grossly inefficient Peano numbers
• Grossly-inefficient Peano numbers, used for setting recusion depth for some other stuff:
  • N-fold replication for type constructors (basically a "type-level fold" on the Peano numbers)
  • Variadic function application, with type-level lists or regular lists
  • Nat-indexed argument rotation (generalizing flip, roughly) and function composition (generalizing (.), (.).(.), &c.)
• Generic algebraic data constructors, used for:
  • A class for cardinality of a type, with conversions to and from Integer based on assigning ordinals to the values of the type. Sort of an enhanced version of Enum, where enhanced mostly means more ability to do really dumb things.

Coming soon(er than never):

• Expanding the features of some of the above, e.g. implement better math on the binary nats.

• More silliness with the generic algebraic constructors. Probably stuff involving partial derivatives, or algebraic refactoring, or isomorphisms between types with compatible structure, or something absurd like that. I don't even know.

• Some decent generic recursion operators, once I make them work in a way that's a bit less terrible. Don't hold your breath.

• A type-level expression evaluator with some "type" checking and such, which is riduclously convoluted and arcane already and it's not even working yet. You could say that the whole thing is kind of horrible.

  Ha, ha. Ha.

• Some Template Haskell rubbish to derive boilerplate-heavy instances like all those TermProxy and Demote instances all over the place and ughhhh.

Also:

• Suggestions welcome! No idea is too ridiculous to consider!

This is completely inexcusable. What do you have to say for yourself?

I regret nothing.