Composability

State of the art – software engineering

Composability is a system design principle that deals with the inter-relationships of components. A highly composable system provides recombinant components that can be selected and assembled in various combinations … .”For information systems, from a software engineering perspective,  the essential features are regarded as modularity and statelessness. Current inhibitors include:  

“Lack of clear composition semantics that describe the intention of the composition and allow to manage change propagation.”

Broader context

Composability has a natural interpretation as readiness to be composed with others, and has broader applicability. For example, one suspects that if some people met their own clone, they would not be able to collaborate. Quite generally, composability would seem necessary but perhaps not sufficient to ‘good’ behaviour. Thus each culture tends to develop ways for people to work effectively together, but some sub-cultures seem parasitic, in that they couldn’t sustain themselves on their own.

Cultures tend to evolve, but technical interventions tend to be designed. How can we be sure that the resultant systems are viable under evolutionary pressure? Composability would seem to be an important element, as it allows elements to be re-used and recombined, with the aspiration of supporting change propagation.

Analysis

Composability is particularly evident, and important, in algorithms in statistics and data fusion.  If modularity and statelessness are important for the implementation of the algorithms, it is clear that there are also characteristics of the algorithms as functions (ignoring internal details) that are also important.

If we partition a given data set, apply a function to the parts and the combine the result, we want to get the same result no matter how the data is partitioned. That is, we want the result to depend on the data, not the partitioning.

In elections for example, it is not necessarily true that a party who gets a majority of the votes overall will get the most candidates elected. This lack of composability can lead to a loss of confidence in the electoral process. Similarly, media coverage is often an editor’s precis of the precis by different reporters. One would hope that a similar story would emerge if one reporter had covered the whole. 

More technically, averages over parts cannot, in general, be combined to give a true overall average, whereas counting and summing are composable. Desired functions can often be computed composably by using a preparation function, then composable function, then a projection or interpretation function. Thus an average can be computed by finding the number of terms averaged, reporting the sum and count, summing over parts to give an overall sum and count, then projecting to get the average. If a given function can be implented via two or more composable functions, then those functions must be ‘conjugate’: the same up to some change of basis. (For example, multiplication is composable, but one could prepare using logs and project using exponentiation to calculate a product using a sum.)

In any domain, then, it is natural to look for composable functions and to implement algorithms in terms of them. This seems to have been widespread practice until the late 1980s, when it became more common to implement algorithms directly and then to worry about how to distribute them.

Iterative Composability

In some cases it is not possible to determine composable functions in advance, or perhaps at all. For example, where innovation can take place, or one is otherwise ignorant of what may be. Here one may look for a form of ‘iterative composability’ in which one hopes tha the results is normally adequate, there will be signs if it is not, and that one will be able to improve the situation. What matters is that this process should converge, so that one can get as close as one likes to the results one would get from using all the data.

Elections under FPTP (first past the post) are not composable, and one cannot tell if the party who is most voter’s first preference has failed to get in. AV (alternative vote) is also not composable, but one has more information (voters give rankings) and so can sometimes tell that there cannot have been a party who was most voters first preference who failed to get in. If there can have been, one could have a second round with only the top parties’ candidates. This is a partial step towards general iterative composability, which might often be iteratively composable for the given situation, much more so than fptp.

Parametric estimation is generally composable when one has a fixed number of entities whose parameters are being estimated. Otherwise one has an ‘association’ problem, which might be tackled differently for the different parts. If so, this needs to be detected and remedied, perhaps iteratively. This is effectively a form of hypothesis testing. Here the problem is that the testing of hypotheses using likelihood ratios is not composable. But, again, if hypotheses are compared differences can be detected and remedial action taken. It is less obvious that this process will converge, but for constrained hypothesis spaces it does.

Innovation, transformation, freedom and rationality

It is common to suppose that people acting in their environment should characterise their situation within a context in enough detail to removes all but (numeric) probabilistic uncertainty, so that they can optimize. Acting sub-optimally, it is supposed, would not be rational. But if innovation is about transformation then a supposedly rational act may undermine the context of another, leading to a loss of performance and possibly crisis or chaos.

Simultaneous innovation could be managed by having an over-arching policy or plan, but this would clearly constrain freedom and hence genuine innovation. To much innovation and one has chaos, too little and there is too little progress.

A composable approach is to seek innovations that respect each other’s contexts, and to make clear to other’s what one’s essential context is. This supports only very timid innovation if the innovation is rational (in the above sense), since no true (Knightian) uncertainty can be accepted. A more composable approach is to seek to minimise dependencies and to innovate in a way that accepts – possibly embraces – true uncertainty. This necessitates a deep understanding of the situation and its potentialities.  

Conclusion

Composability is an important concept that can be applied quite generally. The structure of activity shouldn’t impact on the outcome of the activity (other than resource usage). This can mean developing core components that provide a sound infrastructure, and then adapting it to perform the desired tasks, rather than seeking to implement the desired functionality directly.

Dave Marsay

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About Dave Marsay
Mathematician with an interest in 'good' reasoning.

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