[Categoricaldata_announce] newbie to FQL

[Koksa, Vit]

Hi David,

Thank you a lot for the explanation and the piece of the FQL code which helped me to proceed with my exercise.

Btw., the compilation of my code with a pi-ed instance with just a small amount of data seemed to last forever, before the SQL Engine was changed from Naïve to H2 in the Options (or before I reduced the small amount of data to really just a few items). Unchecking Elements and Observables and the other options of the viewer brought no significant speed-up there. As the long waiting periods might deter some new users I suggest to consider automatic switching from Naïve to H2 engine if the compilation doesn’t finish after some time-out.

With best regards.
Vit

From: David Spivak [mailto:dspivak at gmail.com]
Sent: Tuesday, July 01, 2014 7:33 PM
To: Koksa, Vit
Cc: categoricaldata_announce at categoricaldata.net
Subject: Re: [Categoricaldata_announce] newbie to FQL

Hi Vit,

Thanks for the email; I'm glad you're using this tool and finding it a nice way to get acquainted with category theory.

Your first question is a bit easier. The high-level answer is that "the limit of an empty diagram is the terminal object". Basically since nothing is hitting a3 or a4, the sets that Pi puts there are empty products, i.e. terminal objects in Set. The terminal object in Set is the set with one element. You can see this issue as a kind of generalization of the fact that 5^0=1 because 5^0 is an empty product (multiply 5*5*5...&5, but do it 0 times) and the answer is 1.

Your second question is more involved. To answer your first question we will try to write an FQL file that does this example and send it to you (and the list) soon. As to your second question, given a schema S=[A   B] consisting of just two nodes, A and B, one can make a new schema T=[A <--X --->B] with an additional object and two additional arrows. Then one can create a functor F: S-->T. The query pi F will put the product into X with the foreign keys you want. See the attached FQL file.

Best regards,
David

On Tue, Jul 1, 2014 at 5:28 AM, Koksa, Vit <Vit.Koksa at honeywell.com<mailto:Vit.Koksa at honeywell.com>> wrote:
Hello,

Is there any discussion forum on FQL available, please? I didn’t find any, so I resort to send my e-mail to this mailing list. The FQL IDE is a very interesting and user-friendly tool, it enables even people without a deep mathematical background like me to play with categories. But I don’t see things, which would be obvious to the more knowledgeable people.

The questions which I have currently in mind are:

1.  The FQL sample code “Query Composition” contains the query q1: S -> T . To see how the data migration proceeds inside this query I added these two instances:

instance Delta_sm = delta sm I
instance Pi_fm = pi fm Delta_sm

What I don’t understand is why both tables a3 and a4 in Pi_fm contain a record, when there is no mapping to these tables of the schema A from the tables of the schema B in the schema mapping fm.

2. How would the example given on the slide 45 of http://categoricaldata.net/fql/introSlides.pdf be encoded in FQL?
(SELECT title, isbn FROM book WHERE price > 100)
In particular and more generally I don’t know how to migrate data from nodes {a, b} to nodes {a, b, aXb} where aXb is the product/join of a and b, while “preserving” the foreign keys from aXb elements to their constituent parts in a and b.

With regards.
Vit

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