[Haskell-cafe] type metaphysics
gtener at gmail.com
Mon Feb 2 11:30:01 EST 2009
Do they? Haskell is a programing language. Therefore legal Haskell types has
to be represented by some string. And there are countably many strings (of
which only a subset is legal type representation, but that's not
On Mon, Feb 2, 2009 at 17:09, Gregg Reynolds <dev at mobileink.com> wrote:
> On Mon, Feb 2, 2009 at 10:05 AM, Andrew Butterfield
> <Andrew.Butterfield at cs.tcd.ie> wrote:
> > Martijn van Steenbergen wrote:
> >>> To my naive mind this sounds
> >>> suspiciously like the set of all sets, so it's too big to be a set.
> >> Here you're probably thinking about the distinction between countable
> >> uncountable sets. See also:
> >> http://en.wikipedia.org/wiki/Countable_set
> > No - it's even bigger than those !
> > He is thinking of proper classes, not sets.
> > http://en.wikipedia.org/wiki/Class_(set_theory)
> Yes, that's my hypothesis: type constructors take us outside of set
> theory (ZF set theory, at least). I just can't prove it.
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