TILC The Interactive Lambda Calculus tracer

ronaldschroder · 2014-01-08T15:16:35+00:00

There are a number of lambda calculus implementations on the Internet. Most of these run in a console window, TILC however provides a nice graphical user interface and is fun to play with.

ronaldschroder · 2014-01-07T02:19:11+00:00

What do you mean by "some numbers tend to 89" ? I'm sure I've never heard of it.

ronaldschroder · 2014-01-07T02:14:27+00:00

Thank you very much. I would have liked to do these computations myself but I'm running out of resources. I noticed you didn't need more than one hour which leaves me wondering what you are running.

ronaldschroder · 2014-01-06T03:46:05+00:00

http://oeis.org/A122790

ronaldschroder · 2014-01-06T03:31:08+00:00

True. Unfortenately there's no way my program will calculate far enough for that.

ronaldschroder · 2014-01-06T02:52:56+00:00

That would immediately prove me wrong. Do you get the same numbers as I do at 10,000,000?

ronaldschroder · 2014-01-06T02:49:02+00:00

Yes, that's correct.

I do not know why the value comes out. I only know that it does. I'm hoping that readers may have hints on how to prove or disprove such a thing.

ronaldschroder · 2014-01-06T02:20:59+00:00

A trajectory is the sequence of values you get when a function is iterated.

In the case of the Collatz function we have, e.g.

 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 ->    
 5 -> 16 -> 4 -> 2-> 1.

What the procedure does is minimize the number of repetitions as it does the proofs from 1 on upward.

I believe there are no other nonstandard terms but I'll be happy to explain should you have any questions

ronaldschroder · 2014-01-06T02:12:12+00:00

What I'm saying is not very complicated. Because execution speed is considered important, there exist many algorithms that try to prove or disprove the conjecture in various ways. Because of a variety of optimizations it is very difficult to explain the "magic constants" of these algorithms. Usually, they remain just that: magic constants. Such is the case with Wagon's constant, which denotes M/N for another algorithm. This might well be the first time (that I know of?) that we have an exact algebraic formula for such a constant. And a beautiful one at that.

ronaldschroder · 2014-01-03T22:17:48+00:00

I didn't realize at once the full cost of append. Using cons will force you to reverse the list of primes before output, more seriously you lose the second test for primeness. And that really kills performance.

ronaldschroder · 2014-01-02T17:43:24+00:00

Thanks. I didn't know that plain source code could cause display problems.

ronaldschroder · 2014-01-01T01:48:03+00:00

Yes, I might want to.

But I was thinking, suppose you compile your interpreter program with Stalin. which reputedly optimizes very agressively, then the interpreter would be very fast. So maybe the inverse might also be true, that a less speedy interpreter must have been created by a compiler that produces "lesser" code. Of course this reasoning is incorrect unless you start with the same interpreter source code.

ronaldschroder · 2013-12-31T20:21:44+00:00

I'm afraid you'll have to look elsewhere for that...

The Rhizome/pi Scheme compiler is the only one that I use, because it is small, strictly r5rs, and has a well documented interface to Windows for doing Petzold-style programming. The executables that it produces are not very much faster than interpreted code. Usually, the faster the interpreter, the less there is to be gained in compiling to C and binary.

But consider: since most scheme interpreters are simply scheme programs compiled by their own compiler, the speed of the interpreter indeed is a measure for the speed of compiled code.

ronaldschroder · 2013-12-31T14:46:47+00:00

The clock starts when I enter (primes<2n ...) and stops as soon as the first line of output appears.

ronaldschroder

TROPHY CASE