Lambda the Ultimate

Everything-is-a thread (Ï€-calcullus)?

Everything-is-a proof?

I suppose that would be Martin-Löf Type Theory.

Epigram! I suppose in reality not everything is a proof, since we don't have everything. But who knew Turing incompleteness could be so sweet...

...everything is a set :-)

I'm thinking more in terms of popularity than in terms of quality. Everyone and their momma has designed a multiparadigm programming language, so the space is crowded - just try sorting out all the different better-than-Java languages than run on the JVM. But there seem to be only a handful of languages that make an attempt to be pure, so each can have its own sphere of influence.

That some multiparadigm languages are better than others is a useful fact. That compartmentalized purity makes programming easier is an important insight. That the pure subsets of languages portrayed as pure is usually inadequate for real programming is informative. But I'm asking about popularity here! :-)

CL-USER> (defvar squaring-function '(lambda(x)(* x x)))

CL-USER> (setf (symbol-function 'cube)
               (compile nil
                        (subst '(x x x)
                               '(x x)
                               squaring-function
                               :test #'equal)))
; Compiling LAMBDA (X): 
; Compiling Top-Level Form: 

#<Function "LAMBDA (X)" {48A3A529}>

CL-USER> (cube 3)
27

Another way of putting it is that Common Lisp says 'compiler is an abbreviation for parser-compiler, just as 'cello is an abbreviation for violin-cello. Thus Common Lisp lets you write (defmacro ...) and operate on the data structures built by the parser before the compiler compiles them.

The parentheses are there to let the human reader and the parser (the Common Lisp function READ) parse data structures without having to know the arity of the keywords. Other languages use parentheses in this way for functions. You write f(x, y, z) and the C compiler uses the parentheses to parse the text. This frees you of the need to tell the compiler that the function has three arguments prior to the compiler encountering a function call. Lisp's purity lies in applying the same principle to the control constructs too (because it lets you define your own, just as other languages let you define functions).

Another perspective is to note that a computer programming language has three syntaxes.

Base Language

The syntax that you use when you are coding with the language as it comes, straight out of the box.

Meta Language

The language you use for adding source-to-source transformations in order to extend the language

Extended Language

What the language looks like after you have extended it. For example, if you extend C with macros the source acquires more parentheses and has fewer brackets and braces

Using fully parenthesised prefix notation is arguably the only choice for the Extended Language. How else are members of the programming team going to be able to parse each others code? However Lisp could have used an Algol style for the Base Language and the Meta Language. So the relevant purity is best called Tri-syntactic Identity - rejecting features that are mildly helpful or at least familiar for Base and Meta Languages because they are not appropriate to include in the Extended Language.

But, how do you form that theory, given that all languages have a lot of zealots?

Now I'm not sure what I really mean by "zealot". I was thinking of someone who not only thinks that, say, Java is the bee's knees, but also that

• Java is the solution to all problems
• Java can only be improved by making it more Java-like
• Java is the most powerful and expressive language yet to be invented

And so on. What I see as keeping a language alive is the belief among adherents that they are the only ones who get it. Yeah, it's arrogant, but sometimes it's true. And, regardles of the truth, it keeps people using the language, which is really what I'm trying to ask: what kind of language will find and keep users?

... someone who not only thinks that, say, Java is the bees knees ...

I would think the number of Java users who also use the expression "X is the bee's knees" would be pretty small (but apparently non-empty) :) .

What would kids say these days for bee's knees (or cat's pajamas)?

The first printable equivalent that comes to mind is "the bomb". (But even that is perhaps 5-10 years out of date.)

otherwise, perhaps "X is the shit".

That phrase has spawned an uncountably infinite set of alternatives such as "the shiznit" and "the shizzle", as in "Lambda is the shiznit, yo". If you find this particular mechanism for encoding sentences attractive or amusing, you can read this page using Gizoogle (yo).

And for the opposite feeling, theoretical math types have a bumper sticker:

Peano arithmetic succ(s)!

is that for all it's warts (mostly piss-poor closure syntax, and a weaker type parameterization model than necessary), Java really is best-of-breed on a fair number of axes. On portability, ease of deployment, breadth and quality of libraries, tooling, ease of integration, and depth of recruiting pool, Java is an easy order of magnitude beyond any of the current alternatives, and probably two orders of magnitude better than prior art (bar Smalltalk and Lisp). In terms of actually getting apps shipped, those sorts of thing matters.

Everything in APL is an array (well, every data structure, anyway).

Luckily, there were (are?) no APL zealots :) .

Luckily, there were (are?) no APL zealots :) .

I actually had one as a professor, once. Graphics class, back in the day, but he also swore by APL for doing computational number theory. Not quite sure how he stayed sane...

Everything is a goal, ie goal oriented programming.

What about constraint propagation.

At least that's my impression. :-)

A thought I had the other day:

If instead of taking a stack and returning a stack, a concatenative language's operators took a tuple of say (Stack, Environment, Code, Dump) and returned a transformed version of same, then the operators become the code of a Lisp virtual machine.

Similarly if in an actor language, the actors all took a message which was a tuple of (Stack, Environment, Code, Dump), and sent a transformed version along to another actor, then the chain of actors become the code of a Lisp virtual machine (capable of running concurrently any number of Lisp machines).

Reminds me of the reflective procedures in 3-Lisp (ACM link), which take 3 arguments: the environment (of the caller), the current continuation, and then a list of the actual arguments (unevaluated, IIRC). You can build up a large number of different constructs from this.

XY is a concatenative language in which everything is a word which takes and returns a pair of objects (stack queue). stack is a list which represents the evaluation of the computation so far, and queue is a list which represents the unevaluated future of the computation.

i have writeups here:

http://www.nsl.com/k/xy/xy.htm
http://www.nsl.com/k/xy/xy.txt

Everything is a sub-routine. They are called either in compile-time or execution-time. The stack is just some memory to store temporary values.