# The Quantomatic GUI may be useful for chemlambda (NTC vs TC, III)

Since I discovered Quantomatic (mentioned in NTC vs TC I), I continued to look and it seems that it already has, or almost, the GUI which is the step 0  in the Distributed GLC project.

This is a very good news for me, because I tend to consider that possibly complex tasks are simple, therefore as any lazy mathematician will tell you, it is always good if some piece of work has been  done before.

In the post A user interface for GLC I describe what we would need and this corresponds, apparently, to a part of what the Quantomatic GUI can do.

See Aleks Kissinger Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing, DPhil thesis, [arXiv:1203.0202] , Chapter 9.

Without much ado, I shall comment on the differences, with the hope that the similarities are clear.

Differences.  I shall use as an anchor for explaining the differences the homepage of Aleks Kissinger, because is well written and straightforward to read. Of course, this will not mean much if you don’t know what I am talking about concerning NTC vs TC, chemlambda or distributed GLC.

1. Aleks explains

“But “box-and-wire” diagrams aren’t just for physics and multilinear algebra. In fact, they make sense whenever there is a notion a “map”, a procedure for composing maps (i.e. vertical composition), and a procedure for putting two maps “side-by-side” (horizontal composition). That is, this notation makes sense in any monoidal category.”

Here is a first difference from chemlambda, because the chemlambda graphs are open graphs (in the sense that they also have arrows with one or both ends free, as well as loops), but otherwise a chemlambda graph has not any preferred external order of examination. The arrows of the graph are not “wires” and the nodes are not “boxes”. There is no meaning of the vertical or horizontal composition, because there is no vertical and no horizontal.

2. Another quote from Aleks page:

“In Open Graphs and Monoidal Theories, Lucas Dixon and I defined the category of open-graphs and described how double-pushout graph rewriting, as defined in e.g. Ehrig et al5, can be applied to open-graphs.”

This marks the second basic difference, which consists into the effort we make to NOT go global. It is a very delicate boundary between staying local and taking a God’s pov, and algebra is very quickly passing that boundary. Not that it breaks a law, but it adds extra baggage to the formalism, only for the needs to explain things in the algebraic way.

Mind that it is very interesting to algebraize from God’s pov, but it might be also interesting to see how far can one go without taking the global pov.

3.  Maybe as an effect of 1. they think in terms of processes, we think in terms of Actors. This is not the same, but OMG how hard is to effect, only via words exchanges,  the brain rewiring which is needed to understand this!

But this is not directly related to the GUI, which is only step 0 for the distributed GLC.

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Putting these differences aside, it is still clear that:

• chemlambda graphs are what they call “open graphs”
• there are some basic tools in the Quantomatic gui which we need
• mixing our minimal, purely local constraint on reasoning with their much more developed global point of view can be only fruitful, even if the goals and applications are different.

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What do you think about this?

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