The thing with Turing completeness is that it says something about the
capabilities of a computational model (e.g., a programming language), not
the
practicality with which computations can be done.
Literally, Turing equivalence is saying: hey, instead of using that fancy
programming language, you could accomplish the same thing by using a long
strip
of paper and taking turns either writing a mark on a specific spot of the
paper, reading from a spot, or moving around to a different spot.
Thus, since Algol and Factor (and any other programming language we've been
able to think of) aren't doing anything that couldn't be done by using this
strip of paper, in principle they can express exactly the same computations.
However, in practice, it's not worth using the strip of paper---or even a
particular language, depending on your preferences. :)
> Wondering why the core Factor language was implemented with a compiler
> written in C.
>
> Why not implement Factor on top of an existing Forth?
It's entirely possible, sure. Heck, Factor used to be written atop the JVM.
The reason to use C++ is really more social than technical. C++ is much
more
ubiquitous than Forth, so people won't need to install a dependency they
don't
already have. And despite Factor being stack-based, the representation
you're
working with by the time it gets to the *compiler* is fairly far removed
from
what Factor code actually looks like to the programmer. So, using another
stack-based language to write the compiler doesn't really confer as many
benefits as you'd think. In fact, a relatively small part of Factor is
written
in C++ anyway. The optimizing compiler is written in Factor itself (which
is
interesting for its own reasons). See
http://concatenative.org/wiki/view/Factor/FAQ/Implementation for more.
Regards,
--Alex Vondrak
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