Carrot is not the first XSLT-inspired project to provide a shorter syntax than XSLT itself. Syntax shorthands have included Paul Tchistopolskii's XSLScript, Sam Wilmott's RXSLT, and another project called XSLTXT. Although none of these projects provided direct inspiration for Carrot, they all address one of the same desires that Carrot addresses: being able to program in XSLT more concisely
Since programmers often build task-specific tools, one way to make them more productive is to give them better tool-making tools. When tools take the form of program generators, this idea leads to libraries for creating languages that are directly extensible. Programmers may even be encouraged to think about a problem in terms of a language that would better support the task. This approach is sometimes called language-oriented programming
You might have read (about) the book Domain-Specific Languages written by Martin Fowler. As the name suggests it is about these little useful programming languages you can built very easily with Xtext.