My first thought was that while this was really cool, it does seem to have only a finite tape; I would be quite prepared to believe it was possible to have an unbounded tape, but my mind would be blown. The author admits that the tape is indeed finite.
Logically infinite if not practically infinite. Python specifies a language which has access to logically infinite amounts of memory: it's an implementation detail that there's an upper bound on the size of tape it can simulate on a computer. PPTXTM is by design unable to simulate unbounded tapes.
When talking about Turing completeness I use an alternate definition of infinity that I call practically infinite: for a given a program that halts on an arbitrary Turing machine it also halts on this specific on. I call this practical Turing completeness (though I suspect the literature has already considered this idea and has a different term)
I mean that the technical limits are a not an issue for the program you want to run. Hello World will run on an AppleII computer, but it doesn't have enough memory to run Libre Office (Assume an unlimited budget to create/port the compiler, POSIX layer, X server ...)
If the conversation is concerned with running Hello world it doesn't matter that an AppleII can't do everything, for our purposes it can do anything. If we expand the conversation a little but though we realize this machine is unable to run many things we find useful today.
I'm happy with that. It's an explicit design decision of C that there is a bound on the number of pointers. If I want to consider a Turing-complete variant, all I need to do is let pointers be of arbitrary size somehow, or let it have an "integer" type which really does hold any size of integer.
For example skip to page 114, "Automated Distributed Execution of LLVM code using SQL JIT Compilation" with such gems as:
"The resulting PL/pgSQL code can then be executed
on any database system, as long as that database system
is PostgreSQL"
"Another solution to distributed programming has been
proposed by Microsoft with their innovative Excel system. In large companies, distributed execution can be achieved using Microsoft Excel by having hundreds of people all sitting on their own machine working with Excel spreadsheets. These hundreds of people combined can easily do the work of a single database server"
"For easy reproducibility, we have included a SHA-3 hash
of the complete source code [2]. If you want to reproduce the experiments, simply reverse this hash and run the provided source code. "
I'm not putting more quotes because they would be spoilers.
"Any sufficiently complicated C or Fortran program contains an ad-hoc, informally-specified, bug-ridden, slow implementation of half of Common Lisp."
You can, of course, safely drop the "C or Fortran" part.
Every program I've ever written, if it keeps getting used, maintained and expanded after ~2 years it gets it's own programming language, and therefore usually becomes turing-complete.
The most powerful abstraction one can make in an application is the ability to quickly combine large parts of the application into new functionalities, effectively implementing a programming language. Usually this starts with "macros": the ability to specify sequences to be executed in series with either fully implicit data-passing (e.g. we're always acting on this global state), and then someone points out that variables would be really good, and then you do that : local, named variables in macros. And there's your programming language.
Well, users need to extend our programs or automate repetitive mechanical tasks, at the end of the day, that's a big part of why computation is so useful. We need to customise how certain actions happen, say how a blur effect is applied to a photo, and presets don't always work. Actually I can't see how tuning some sliders to adjust a certain variable is fundamentally different from setting it via an extension language. This process of adjusting a program or extending it is as natural as cutting a pair of jeans and making it into a pair of shorts.
And this is why I like emacs so much: within it customisability and extendableness is a product of the programming paradigm, and you don't even need to allow the user explicitly. The online docs, the debugger that automatically comes up when needed, the lisp mechanisms like advices and live editing of the running program furnish a great environment where one is not confined to the application designer's decisions, and where making customisations and extensions are really approachable.
Would it be cheating to mention PowerPoint's Visual Basic support? I think your assertion could be even stronger -- every sufficiently advanced program embeds a full programming language.
No, but speaking of functional, there is a FixedPoint. It's that point in the presentation when your bleary eyes have seen fifty slides and now all subsequent slides look the same.
My first thought was that while this was really cool, it does seem to have only a finite tape; I would be quite prepared to believe it was possible to have an unbounded tape, but my mind would be blown. The author admits that the tape is indeed finite.