G'day all.
On Mon, 2009-01-19 at 19:33 +0000, Andrew Coppin wrote:
My only problem with it is that it's called Bool, while every other
programming language on Earth calls it Boolean. (Or at least, the
languages that *have* a name for it...)
Jonathan Cast commented:
Except C++?
And perhaps more to the point, "Boolean" is an adjective, not a noun.
Therefore, it would be better reserved for a typeclass.
class (PartialOrder a) => JoinSemilattice a where
(||) :: a -> a -> a
class (MeetSemilattice a) => BoundedJoinSemilattice a where
bottom :: a
class (PartialOrder a) => MeetSemilattice a where
(&&) :: a -> a -> a
class (MeetSemilattice a) => BoundedMeetSemilattice a where
top :: a
class (BoundedJoinSemilattice a, BoundedMeetSemilattice a) => Heyting a where
implies :: a -> a -> a
not :: a -> a
not x = x `implies` bottom
class (Heyting a) => Boolean a where
{- the additional axiom that x || not x == top -}
Cheers,
Andrew Bromage
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