I would think Yegge's term "mini-language" refers to the fact that it is often useful to use a language for specific problems where the language doesn't require turing-completeness to accomplish the task, and this goes to the heart of how non-turing complete languages can be useful. https://sites.google.com/site/steveyegge2/language-grubbing
Wikipedia answers this very well, right in line with what my gut said. First I was thinking pure math then I remembered regexp, and Wikipedia lists Epigram which I believe would be in the 'pure math' vein.
Many computational languages exist which are not Turing complete. One
such example is the set of regular languages, most commonly regular
expressions, which are generated by finite automata. A more powerful
but still not Turing-complete extension of finite automata is the
category of pushdown automata and context-free grammars, which are
commonly used to generate parse trees in an initial stage of program
compiling. Further examples include some of the early versions of the
pixel shader languages embedded in Direct3D and OpenGL
extensions, or a series of mathematical formulae in a
spreadsheet with no cycles. In total functional
programming languages, all functions are total, and must terminate,
such as Charity and Epigram. Charity uses a type system and control
constructs based on category theory, whereas Epigram uses dependent
The notion of Turing-completeness does not
apply to languages such as XML, JSON, YAML and S-expressions, because
they are typically used to represent structured data, not describe
computation. These are sometimes referred to as markup languages, or
more properly as "data description languages".
It also mentions data structure representations are not languages, but I would think XSLT should count as a representation of computation, XPath perhaps not based on what Yannis said above about SQL being a query language and not a computation language. Perhaps T-SQL or PL/SQL count as computation languages though since you can do a great deal of computations using their aggregates, where the generalized form of SQL doesn't specify aggregates perhaps.