Skip to main content

Rewriting does not work?

I am having a little trouble figuring out the details of graph rewriting semantics for BPMN. The issue is merges (pesky things - should be banned).

In communication, message receive is by far the hardest to get right. It seems that in BPM, merge has a similar role: get merges right and nothing else will be a problem.

Anyway, in traditional graph rewriting, a new 'activity' is created by reading-off a new active copy from the original graph. This corresponds to beta substitution in functional languages. The trouble is that, compared to expressions, BPM graphs are decidedly not well formed: there are loops and all sorts without being specially marked.


Snap1


Well, the issue is, when you copy off a new activity, how do you ensure that the existing activities are properly linked in to the new one. You can see this in the sequence above. (1) is the start point, and the problem shows up by (4). The (inclusive) merge has lots of connections going in, but only some of these are relevant.

You can't use special markers -- that would allow you to copy off bigger chunks of the graph, including subsequent merges from a split -- because BPMN does not have them!

Graph rewriting works in functional languages because a well defined chunk of the graph is rewritten at each stage: that chunk is defined by a particular pattern in the graph which is rewritten with a template (equation).

More thinking required I believe. It was such good idea too!

Popular posts from this blog

Existential Types are the flip side of generics

Generic types, as can now be seen in all the major programming languages have a flip side that has yet to be widely appreciated: existential types.

Variables whose types are generic may not be modified within a generic function (or class): they can be kept in variables, they can be passed to other functions (provided they too have been supplied to the generic function), but other than that they are opaque. Again, when a generic function (or class) is used, then the actual type binding for the generic must be provided – although that type may also be generic, in which case the enclosing entity must also be generic.

Existential types are often motivated by modules. A module can be seen to be equivalent to a record with its included functions: except that modules also typically encapsulate types too. Abstract data types are a closely related topic that also naturally connect to existential types (there is an old but still very relevant and readable article on the topic Abstract types have …

Concept Oriented Markup

I have long been frustrated with all the different text mark up languages and word processors that I have used. There are many reasons for this; but the biggest issue is that markups (including very powerful ones like TeX) are not targeted at the kind of stuff I write.

Nowadays, it seems archaic to still be thinking in terms of sections and chapters. The world is linked and that applies to the kind of technical writing that I do.

I believe that the issue is fundamental. A concept like "section" is inherently about the structure of a document. But, what I want to focus on are concepts like "example", "definition", and "function type".

A second problem is that, in a complex environment, the range of documentation that is available to an individual reader is actually composed of multiple sources. Javadoc exemplifies this: an individual library may be documented using Javadoc into a single HTML tree. However, most programmers require access to multiple…

Robotic Wisdom

It seems to me that one of the basic questions that haunt AI researchers is 'what have we missed?' Assuming that the goal of AI is to create intelligence with similar performance to natural intelligence; what are the key ingredients to such a capability?

There is an old saw
It takes 10,000 hours to master a skill
There is a lot of truth to that; it effectively amounts to 10 years of more-or-less full-time focus. This has been demonstrated for many fields of activity from learning an instrument, learning a language or learning to program.

But it does not take 10,000 hours to figure out if it is raining outside, and to decide to carry an umbrella. What is the difference?

One informal way of distinguishing the two forms of learning is to categorize one as `muscle memory' and the other as 'declarative memory'. Typically, skills take a lot of practice to acquire, whereas declarative learning is instant. Skills are more permanent too: you tend not to forget a skill; but it is…