[rekenaut]

Where does this idea that a programming language has to be Turing complete come from? As far as I can tell from cursory searches, the most broadly understood understanding of a programming language is a formal language for directing computations on a computer. HTML does this, CSS does this, and SQL does this. Frankly even configuration languages like YAML or the spare INI file do this in the proper context.

Can these languages do everything or even most computations you would be interested in doing in a computer? Of course not. But why should the definition be restricted to languages that can do everything?

[ctenb]

Your definition is overly broad and makes everything a programming language, at which point the term isn't useful anymore.

[ngruhn]

But Turing completeness is also too broad. Otherwise Power point animations and Conways game of life are programming languages.