Regarding “le compte est bon” you can implement that fairly directly as a hylomorphism. You need an algebra for an anamorphism that generates a list of all trees, and a coalgebra for a catamorphism that searches the list for the answers.

With more thought there is probably some kind of dynamorphic variation that evaluations the subtrees, figures out their valuation, and then proceeds as above, saving some effort in computing valuations of the subtrees in the catamorphism. For that matter, there is the code elsewhere on this blog for incremental folds which might be an easier way to integrate that incremental result.

The Rubik’s cube is probably most easily solved in the same manner. The choice of catamorphism will determine if you search breadth-first, depth-first, or using some other strategy.

I have toyed with the Charity language hence some basic schemes (catamorphism,paramorphism,anamorphism) are already familiar to me.

Plus histomorphism/futumorphism are well documented by Varmo Vene.

Others are not so well documented and quite difficult to grasp for mere mortal fonctional programmers like me.

One corecursion scheme that i face again and again is exploration. I mean i have an arithmetic expression type and i want to solve some “le compte est bon” problem. Or i have this move type (front|back|left|right|up|down) list, and i want to solve my Rubik’s cube. What corecursion scheme is that ?

> newtype RanT f g c m m’ = (c -> K m) -> T m’

Should be:

> newtype RanT k t c m m’ = (c -> k m) -> t m’

right?

That said, Ravi did bring a video camera today, so when we finally get a chance to do the talk, we should be able to have some semblance of video. ;)

Thanks for the references! The TREC IR Measures overview seems to be exactly what I was looking for.

The big web search engines, in particular, are concerned with precision “above the fold” (in the newspaper sense). That is, if you take a default install of IE or Firefox and do a search on Bing, Yahoo, or Google, what’s the precision for the number of results you can see on the screen. The chance to continue browsing is not continuous. Basically, that would induce a kink in your probability of keeping going to the next items.

There are also applications which are highly recall oriented, like curating databases of protein interactions from the literature or intelligence analysis over the news. It’d still fit your model, it’d just give you a different likelihood of looking at another item. We’re particularly interested in precision at 99% recall or 99.9% recall for these situations.

The other major issue to consider is diversity of results. If I send you ten different versions of the same information, it’s not very useful even if they’re all “relevant” in the binary relevant/not relevant sense. The problem is that to measure this idea, you need a notion of relative information contribution of a new result given a set of other results.

What the IR folks call precision is what the epidemiologists call “positive predictive accuracy”. It’s basically the likelihood that you have a condition if you test positive for it, and it’s very useful exactly as stated in that context.

You might want to consult the section of the Wikipedia entry Information Retrieval about performance measures, or the TREC IR Measures overview.

What he ended up with was a similar idea, but base on the information theoretic entropy. He called it relevance information.

If we assume R relevant documents in a corpus of D documents, the probability of any given document being relevant is uniformly R/D. If we score and then rank them by some procedure we can then assume the probability is no longer uniform, but decreasing (hopefully) sharply over the rankings. The effectiveness of the scoring scheme is measured by the decrease in entropy over the whole distribution.

He examined some of the properties of this measure and felt that it captured the best of both precision and recall in one number and was reasonably robust, but AFAIK it never caught on in the literature.

I can’t find the original paper, and he seems to have moved away from it in any of his more recent papers.

(Disclosure — I used to work for him)

Wait — I found it:

An Information Measure of Retrieval Performance (1992)
by W J Wilbur

http://citeseerx.ist.psu.edu/showciting?cid=1837654