=C2=ABAs for the suggestions you listed, I've pretty much been doing
exactly that prior to my current approach (albiet more focused on SE).
I've had plenty of univeristy coursework in those topics and have been
a software developer on "large scale" systems for some time now. The
reason I'm studying this stuff on my own with a more fundamental
approach is precisely because having done all the things you listed
didn't really produce the results I'm after.=C2=BB
Because, there is no such thing.
You are, basically seeking, there's perhaps some ultimate model of
computer language foundation, such that, once you study this in depth,
it'll help you design better computer languages. My thesis is, there
is no such thing.
There are, of course, as facts, certain studies that will help
computer language design in some formal basis, such as lambda
calculus, or the so-called so-and-so theory of types, all are just
specialized branches mathematical logic. This is a undenyable fact.
What i'm saying, is that seeking a foundation for computer language
design is a attitudinal problem. Because, however you define or
philosophize about it, there is no such unified, or even coherent
subject. What the average computer scientist lang desiners do, is
actually just to grab parts of the mathematical foundation that
happens to be what they have studied or like, and base their lang on
it. Even the notion of basing a language on some specialized
mathematical logic, is very fuzzy and can be diced in many ways. In a
sense, all languages, from assembler to C to Java to Haskell to Lisp
all are based on some mathematical foundations.
Also, i'm saying, that studing particular branch of mathematical logic
such as lambda calculus, will NOT help you design computer languages
or write compilers. (they of course do help in some way, but it's like
saying studying arithemics and set theory and group theory and number
theory and numerical analysis and each dealthy and exercise regularly
will also help you too)
In general, i'm saying, seeking to study some mathematical foundation
for designing computer language is a misleading, attitudinal problem.
It is a fruitless search. If infatuated, results frustration.
Also, you are perhaps seeking, some clear, coherent relation among
branches of mathematical logic. My thesis is, that there is no such
thing. The relations will be more like spaghetti and noodle mixed
graph that is beyond a human animal's conception. One could, have a
over all, approximate idea of the whole studies of mathematical logic
(counting or not counting modern algebra as part of it) To achieve
this understanding in some elementary way, is perhaps a decade study
by itself and without depth. And again, without any sensible relations
to existing actual computer languages or its design.
I may be all wrong here... since the topic of this thread is
reasonably fuzzy. What you mean by designing a computer language? What
do you actually want to do? What field of language? practical?
theoretical? theorem proving? domain specific? for language research?
Functional or OOP or some yet-nameless-paradim or so-called multi-
paradigm? Any particular aspect of language you are interested more?
The syntax and notation? Theory of semantics?
If given a specific language and aspect you are interested, then a
helpful math foundation can be more easily found. For example, if you
want to write theorem provers or computer algebra, certainly you'll
need to know algebra well, and in fact set theory. If you want a
notational system or knowledge presentation language (such as MathML,
TeX), then understading in depth of the theories of logic notations is
necessary (don't think there's even a proper, recognized term for this
study). ...
(Execuse me for my megalomaniac style of writing. That is just my
style. I'm not expert in any branch of mathematical logic. Also, i
don't know how to write compilers... I just have life long interest in
logic and am expert at a few computer languages)
Xah
xah@[EMAIL PROTECTED]
http://xahlee.org/
=E2=98=84
On Jan 23, 12:21 pm, "Bruce C. Miller" <bm3...@[EMAIL PROTECTED]
> wrote:
> On Jan 23, 2:24 pm,XahLee<x...@[EMAIL PROTECTED]
> wrote:
>
> > Bruce C. Miller wrote:
>
> > <<As a long-time functional programming adherent, I'm interested in
the
> > mathematical foundations of programming language theory.>>
>
> > My advice is, forget all the type theory and lambda calculus, or so-
> > called "mathematical foundation of programing languages". There is no
> > such thing. (as in your try to graph a relation, or from the few
> > replies, you probably already see this.)
>
> > Studying such will gets you no where, and the more you study these,
> > the more you gets inane and stupid in your thinking.
>
> Can you elaborate on this?
>
>
>
> > But, what to do if you are interesting in serious mathematics and
> > computer language design?
>
> > My recommendations is, to just study math. Namely, discrete
> > mathematics, concrete mathematics, or finite mathematics, with brances
> > including graph theory, set theory, category theory, algebra,
> > mathematical logic and so on. While you study these subjects deeply,
> > keep in mind that you should not do it while thinking towards computer
> > language design what-so-ever.
>
> > On the other hand, for your interest in computer language design,
> > study how to write a compiler, algorithms, and spend a lot time to
> > implement computer languages, and also spend perhaps equal amount of
> > time to actually write large scale software. Of the language you use,
> > haskell and other functional lang such as erlang, OCmal are good
> > too... but depending your interest, you might also go into so-called
> > computer algebra languages or theorem proving languages.
>
> This pretty much goes against what I've heard so far from most
> language theory types. I'd also say that the progress I've made so far
> into PLT has in fact been a result of studying the underlying
> mathematical concepts (mostly just lambda calculus so far). I'm not
> saying this is the only way to approach the topic, but it seems to be
> the "official" way.
> As for the suggestions you listed, I've pretty much been doing exactly
> that prior to my current approach (albiet more focused on SE). I've
> had plenty of univeristy coursework in those topics and have been a
> software developer on "large scale" systems for some time now. The
> reason I'm studying this stuff on my own with a more fundamental
> approach is precisely because having done all the things you listed
> didn't really produce the results I'm after.
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