> Functions that return values must be declared as being of the same type as the value returned. [...] The arguments of mymulti() are two matrices of real numbers. They too need to be declared as such.

This is not strictly true. Stata is very forgiving in this respect, so that manually specifying return/argument types is not necessary. Doing so is a good idea---it documents the function and permits optimizations---but you could just as correctly write "function mymulti(A, B) {".

> Stata syntax is interpreted. This makes it easy to use and write code in, but slower to run than a compiled alternative would be. Mata offers such an alternative.

This is true as far as it goes, but I'm a little uncomfortable with it. Bytecode isn't machine code; it's still interpreted. I don't know how extensive the optimizations Mata does at compile time, but a priori there's a fair chance that compiling to bytecode beforehand won't make much of a difference. Java, for instance, has a relatively unsophisticated compiler, leaving real optimziations for runtime---leaving the byte-compilation step until runtime really wouldn't be that big a deal.

(Python is this way. There is no explicit compilation step; the first time a file is executed it is compiled to bytecode, which is then run.)

That isn't to say byte-compiling won't make a huge difference in Mata! I haven't done enough to notice. But there's nothing inherent in byte compilation that would make it so.