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seen May 27 '13 at 20:21

My main interest is in the design of pathological programming languages. While this subject is not entirely (perhaps not even primarily) mathematical, it does rely significantly on results from computability, computational complexity, and formal languages. Results from pretty much any field are welcome additions if they can be applied to the design of a programming language to make it (more) pathological. Currently I am somewhat interested in the possibilities of abstract algebra in this regard.


Dec
14
awarded  Custodian
Dec
14
reviewed Reviewed cyclic vector exists for symmetric operator iff there no repeated eigenvalues
Dec
14
awarded  Scholar
Dec
14
accepted Has this algebraic structure been named or studied?
Dec
12
comment The G.C.D of two numbers is $23$. The other two factors of the L.C.M are $13$ and $14$.
I find the statement "The other two factors of the LCM are 13 and 14" somewhat confusing, as 14 is not prime. Why does it not say "The other factor is 182" or "The other prime factors are 13, 7, and 2"? I'm concerned that there might have been an error in transcription.
Dec
11
comment Has this algebraic structure been named or studied?
True, Joy's quote does not work like that, but it's fairly easy to make a variation which does, and I was hoping that adding another property (however slight) might bring it closer to something algebraically conventional. Joy's quote is also intensional, whereas what I'm working with is extensional. I just realized that that means, in Joy, a=b does not imply [a]=[b]; but [a]=[b] still does imply a=b, and at any rate, extensionality is pretty important for my current purposes.
Dec
11
awarded  Commentator
Dec
11
comment Has this algebraic structure been named or studied?
That would work better, assuming I can find a suitable $c$. It is possible to transform programs in these languages in a way that removes brackets and adds a symbol which basically says "bracket this other thing"; that operator is a good candidate for this $c$. But there are issues with associativity that I don't know if I can get around, with that approach; it'll take some time for me to look into it.
Dec
11
comment Has this algebraic structure been named or studied?
@Thomas, if you want to post that as an answer, I'll vote it up. Even knowing that it's not an endomorphism is helpful. In a sense, ^ imposes a hierarchical structure on the elements of S, which I think suggests that I should look into things like lattices instead.
Dec
10
revised Has this algebraic structure been named or studied?
explicitly state non-idempotency of ^
Dec
10
comment Has this algebraic structure been named or studied?
The commutativity of + is not a good fit, but the idea of fixing a c like that is intriguing. Do you happen to know if there's a good example of using that technique in some other context?
Dec
10
revised Has this algebraic structure been named or studied?
included the cancellative property of ^ and reformatted properties into bulleted lists
Dec
10
comment Has this algebraic structure been named or studied?
@Thomas: a concrete example of the structure is: strings of symbols with brackets, with a semantics which gives the substrings inside brackets a different meaning. Joy is one such programming language based on this framework. The underlying monoid for Joy is well-described in that paper, but the bracketing operator (Joy's [...], my ^) is much less well-described algebraically, and I'm trying to find out more about where it might fit in (or be made to fit in.)
Dec
10
comment Has this algebraic structure been named or studied?
@Thomas: Yes, ^a=^b implies a=b. But no, ^1≠1. I take it that, if ^1=1 held, it would be an endomorphism? Thanks to you and ineff for pointing this out -- it may be possible to reformulate things (in a contrived way) to get a special restricted case where ^1=1 and see where that leads me.
Dec
10
awarded  Student
Dec
10
asked Has this algebraic structure been named or studied?
Dec
9
awarded  Analytical
Dec
9
comment How can Busy beaver($10 \uparrow \uparrow 10$) have no provable upper bound?
This makes sense, thanks. But I'm still a bit mystified about why $10\uparrow\uparrow 10$ was chosen as the stated bound -- you seem to agree that it is much larger than you would actually need. Is it just a case of being extremely conservative? (Is this worth asking in a separate question?)
Dec
8
comment Proving that the halting problem is undecidable without reductions or diagonalization?
I should note that when I say the reasoning is not absolutely watertight, I mainly mean that I don't see a way to work this into an proper proof; but at the same time, I can't say that it's impossible to do so. It does seem likely that such a proof would be somewhat more "informative" than one based outright on diagonalization.
Dec
8
answered Proving that the halting problem is undecidable without reductions or diagonalization?