#haskell - Sun 6 May 2007 between 00:00 and 00:14

sphynxoh, I've got it, soory for stupid questions :)
kc5tjalittledan: In fact, the language you'll end up with will look amazingly like Joy or Factor. :)
littledankc5tja, yeah, but with laziness and typeclasses; that's the gap
mutjidai think continuity is just assumed for most programming language semantics applications
sorearHaskell style is pretty much impossible to implement with anything other than a batch compiler.
kc5tjaDitto for Joy, actually.
sorearForth is the epitome of nonbatch.
kc5tjaTo get it to be interactive, you'll need to structure it more like Postscript.
monochromYes, continuity is assumed. There is also proof that continuity = bounded nondeterminism.
mutjidai think conitnuity is necessary for fix points.
littledanFactor actually has what amounts to a batch compiler (though the interpreter is used fairly often)
I think
and, of course, you could redefine : to make a batch compiler in Forth!
monochromcontinuity is sufficient, but not necessary.
kc5tja: is already a batch compiler.
It just so happens that ; terminates it. :)
mutjidahow do you prove existence of fixed points without conitnuity?
i mean continuity
monochrommonotonicity is also sufficient. tarski-knaster or something.
mutjidaoh yes you're right. monotinicity is necessary. tarski's fixpoint theorem.
kc5tjaGAWD, this is so monotonous! ;D
monochromIf f is continuous, it is a bonus, because f^omega(_|_) is the least fixed point. Without continuity, may have to replace omega by an even larger ordinal.
kc5tja(sorry, it was just begging to be said)
littledanwhere could i read about stuff like the theory behind fixed points?
monochromI recommend Davey & Priestley "introduction to lattices and order".
You can also wait for me to write it up on haskell wiki and haskell wikibook. :)
Right now I'm writing a Parsec example instead.
sorearmonochrom: even LARGER ordinals? ouch!
mutjidawikipedia has some stuff, but perhaps not introductory. many graduate level programming language texts also cover it (e.g. pierce or mitchell)
monochromI can make it sound very simple. I just don't have time to write it up.
kc5tjaOK, back to my modeling. I was hoping to have new code out by today, but I'm wasting too much time on IRC.
mutjidawith just monotinicity, you can still construct a fixed point by starting with bottom.. right?
sorearmutjida: you'll never get close enough
monochromYeah, f^(huge ordinal here)(_|_).
littledanmonochrom, thanks, Google Books apparently has that in full
monochromW H A T ??!!!
N I C E !!!111
littledanthere's no PDF, though
(which would be better)
also, I'm too stupid to understand it

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