identicalsnowflake/cantor-pairing

Convert data to and from a natural number representation

cantor-pairing's Issues

Missing instances for Word

Is it intentional that there is no instance for Word? there are instances for the fixed width word varieties and Int so it surprises me that the instance is missing.

Need to choose the correct diagonal, not just a diagonal

This tree completely breaks because the zero case is not in the expected corner:

data Tree a = Branch (Tree a) a (Tree a) | Node

Cardinality on type level

Is it possible to promote cardinality to the type level? Like,

data Cardinality = Finite Nat | Countable

class Cantor a where 
  type Measure a :: Cardinality
  ...

instead of

data Cardinality = Finite Integer | Countable 

class Cantor where 
  cardinality :: Cardinality
  ...

This would allow to distinguish between finite and countable on type level, eliminating the need in deriving an additional Finite typeclass. Constraint Finite a would be simply Measure a ~ Finite n.

Cardinality for mutually-recursive types

Current HEAD fails to detect cardinality of mutually-recursive types as Countable. Here is an example:

{-# LANGUAGE DeriveGeneric, TypeApplications #-}

import Cantor
import GHC.Generics

data Foo = FooNil | Foo Bool Bar deriving (Generic)
data Bar = BarNil | Bar Bool Foo deriving (Generic)

instance Cantor Foo
instance Cantor Bar

main = print $ cardinality @Foo

$ ghc MutualRec.hs && ./MutualRec
MutualRec: <<loop>>

I believe that this can be improved by keepind track of all encountered types (instead of only the last one) in the first argument of GCantor class, as a type-level list. Does it look worse pursuing?