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Brendan Zabarauskas

Yeah I remember now seeing your tweet about it! Was contemplating asking if you'd got any further on it!

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· Aug 19, 2019

So the nightmare with "dependent string diagrams" is that the *topology* of a diagram can depend on values in it. I think the idea is that each possible topology goes in its own slice This often happens in game theory, when the structure of the game depends on earlier choices

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Brendan Zabarauskas

I'm cool with deferring the harder CT stuff to more experienced people - I'm more interested in experimenting with silly programming language implementations based on this kind of thing (but perhaps that's premature? 😅).

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Since then I started playing around with branching string diagrams for game theory, running mostly with my gut feeling. I think these are like sigma types. When I try to figure out what I'm actually doing here, my brain melts for 2 whole different reasons

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· Oct 18, 2019

The neo-EX form of the extended market entry game from example 9.C.2 of Mas-Colell, Whinston and Green Now I'm cooking with plutonium!

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Brendan Zabarauskas

Oooh, are the left-pointing triangles sort of splitting the diagram into slices(?) - ie. depending on what is in the first element of the sigma type?

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Brendan Zabarauskas

Oh no what is happening to me

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Brendan Zabarauskas

thinking about how disjoint union (sum) types are special cases of dependent pair (sigma) types

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Brendan Zabarauskas

Couldn’t help making a paper model!

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Coooool! You're right not to focus too much on the specifics of my diagram, because my category (of open games) is weird. In particular my forwards and backwards arrows don't behave symmetrically

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Brendan Zabarauskas

Yeah! I was wondering about those backwards diagrams 😅 I was also thinking about diagrams where the class wires affect the types of other wires, but I could be off the mark there:

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Brendan Zabarauskas

· Oct 30, 2019

Replying to @brendanzab and @typeswitch

Something weird

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This is funky. I have no clue whether you could make this precise or not, I can believe both possibilities

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Brendan Zabarauskas

Replying to

Yeah, me neither! One thing that I don't think is captured here is evaluation... not sure if that is important.

had some comments in that thread that suggested stuff along those lines.

12:17 PM · Oct 30, 2019Twitter Web App

Brendan Zabarauskas

Replying to

and

Might have to do some more complicated things that need to be reduced to see if anything starts to break down. 🤔

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