cdsmith / cfrac

This is the code that goes along with my blog post at https://cdsmithus.medium.com/continued-fractions-haskell-equational-reasoning-property-testing-and-rewrite-rules-in-action-77a16d750e3f

There are some small revisions since the blog post. Contributions are appreciated.

This is not yet released to Hackage. If someone is interested in depending on it, please ask and I'll revise and release it. But it was intended as just playing around, so I don't yet see value in publishing and taking up Hackage namespace and resources.

There are several previous Hackage packages related to continued fractions:

• https://hackage.haskell.org/package/cf looks similar to this one and claims to offer even more operations, including portions of the Floating class. However, I wasn't able to get it to work. Most operations just hang.
• https://hackage.haskell.org/package/continued-fraction implements only a couple operations, such as conversion to and from rationals, and convergents. In particular, it does not define a new type, nor offer any classes in the Num hierarchy.
• https://hackage.haskell.org/package/continued-fractions also implements only a few operations, though there are several variations on them. Again, there are no standard arithmetic classes or operations.

cfrac's Issues

Floating operations

There is an implementation of floating point operations in https://hackage.haskell.org/package/cf, but it doesn't seem to work in my tests. Where computationally feasible, it would be nice to implement these operations on CFrac, as well.

Signed numbers

The existing implementation assumes that all numbers are non-negative.

Smart constructor

Instead of allowing the user to build invalid continued fractions and exporting isCanonical to detect them, we ought to have a smart constructor that automatically corrects these infelicities on the fly.

Then a good question is whether to export the underlying constructor. Maybe :+/ itself should be turned into a pattern synonym that does this conversion but can still be matched on to access the underlying terms.