[vii]

Enumerating what we want from notation helps us understand how far we are from the ideal. The whimsical introduction of Notation to talk about notation makes it practical. Given a domain in mathematics, adding notation (e.g. modulo arithmetic) can make complex notions pretty to express and quick to prove. I used to really enjoy this and tried to redefine notation for each exposition. It's shorter and prettier, but just pushes complexity into the notation :) and teaching people new notations is expensive, actually unless repeatedly used, more expensive than laying out details in a less concise notation.

Programming languages are notations within this framework - and domain specific languages, while much more efficient are unpopular as the costs of changing notation, in terms of training people, are too high.

The cost of communicating the notation is captured in a few of the desiderata (e.g. 1,7) but practically it is most important. If we want to be easily understood we should speak a common language!

[dragonwriter]

> domain specific languages, while much more efficient are unpopular

JSX seems pretty popular, and when XML was popular similar XML embeddings were, as well. Templating languages are popular. Heck, the relative popularity of “general purpose” programming languages is not consistent across domains, with domain fit being a factor even for general purpose languages.

[Transfinity]

I would say that JSX is popular precisely because the cost of teaching it is low, which in turn is because of its similarity to other commonly used notation (HTML / XML).

Of course it's got its fair share of dumb gotchas, but I found it far easier to learn than, say, any of the myriad Rails DSLs.

[lmm]

> JSX seems pretty popular, and when XML was popular similar XML embeddings were, as well. Templating languages are popular.

I don't think any of these things are popular; in my experience people using them mostly hate them, or at best grudgingly accept that they're the least-bad option.