Comments on: Debut with a Catamorphism

By: Tony Morris

Tony Morris — Fri, 11 Dec 2009 22:20:45 +0000

Hi Channing,
My sixth operation was for decompression of a trapped nerve (superficial peroneal 10cm proximal to lateral malleolus as it exits the deep fascia). It took 19 doctors two years to not find it and it took me about a year. Then it took a 15 page essay, citing several text books and medical journals, to convince 1 of 3 doctors, who upon performing the surgery, found that the site of entrapment was precisely where I’d said (I drew a dot with a marker).

Thank medical science I found it in the end. Still recovering from the nerve damage (it was extremely compressed and caused a myriad of symptoms).

By: Steven Shaw

Steven Shaw — Wed, 09 Dec 2009 15:01:06 +0000

Hi Tony, on the meaning of catamorphism - no need to repeat the literature. A link would be good :). Perhaps a book recommendation.

For instance, I get nothing from http://en.wikipedia.org/wiki/Catamorphism though I am reading the blog articles linked at the bottom.

By: Arnaud Bailly

Arnaud Bailly — Mon, 07 Dec 2009 21:24:13 +0000

Hello,

@Steven not sure this will really help you, but the first mention I read on such strange beasts was in the classical artical “Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire” (http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125). As far as I understand it, a catamorphism is pure functional way to express behavior of instances of a type, something like an interface in OO, I guess, by encapsulating in a single HOF the “constructors” of the type.

HTH
Arnaud

By: Channing Walton

Channing Walton — Mon, 07 Dec 2009 19:45:31 +0000

Hi Tony,
glad to know your health problems are being resolved. I’ve been through something similar: 4 years of (at times extreme) pain from trapped nerves. A dozen doctors, two surgeons and physios didn’t find it. A pain specialist found it in 10 mins and his physio made significant improvements in 1/2 hour!!!

Thanks for this example, its taught me a lot.

Channing

By: admin

admin — Sat, 05 Dec 2009 23:20:37 +0000

G’day Steven,
I don’t see much benefit in repeating much of the literature about what is a catamorphism, though I understand it may be difficult to digest. However, I could point out that:

option.cata(Some, None) == option.

In other words, plonking the constructors into cata gives you an identity function.

Yes, once-inhabited means there is only one solution. Finding inhabitants for a type is equivalent to proving a logical theorem (see Curry-Howard Isomorphism), however, some languages allow you to “tell lies” in your proof e.g. bottom values, non-termination, side-effects. This does not negate the fact of the matter.

The Scala mailing list has all sorts but education is paramount!

By: Steven Shaw

Steven Shaw — Sat, 05 Dec 2009 16:34:04 +0000

Haskell was a bit harder for me.

Tony, question - what *is* a catamorphism?

I saw that thread on the Scala mailing list about “once-inhabited type”. Google gives me nothing except the Scala thread on nabble :). Does once-inhabited mean that there’s only one solution for the function implementation?

By: Steven Shaw

Steven Shaw — Sat, 05 Dec 2009 15:03:20 +0000

Hi Tony, enjoyed the Scala version of this exercise. Learned some lessons from your Scala implementation too (won’t spoil for others). Cheers! On to try the Haskell version

By: Lachlan O'Dea

Lachlan O'Dea — Fri, 04 Dec 2009 05:15:35 +0000

Glad to hear things are looking up for you on the medical front.

By: Eric

Eric — Thu, 03 Dec 2009 03:53:50 +0000

Excellent exercise, that made my day!

Now there is a trait defining the behavior of an Option[A], I’m wondering. In which design situation would that be useful to have “class A extends MyOption[A]“? (excepted to create some and none of course).

Eric.

By: Tony Morris

Tony Morris — Wed, 02 Dec 2009 11:49:51 +0000

Thanks Jason.