[Haskell-cafe] Re: Improved documentation for Bool

[ajb at spamcop.net]

G'day all.

Quoting David Menendez <dave at zednenem.com>:

> Are there any instances of Boolean that aren't isomorphic to Bool?

Sure.  Two obvious examples:

- The lattice of subsets of a "universe" set, where "or" is union
"and" is intersection and "not" is complement with respect to the
universe.

- Many-valued logic systems.

- Intuitionistic logic systems.

- The "truth values" of an arbitrary topos (i.e. the points of the
subobject classifier).

Look up "Heyting algebra" for examples.

Cheers,
Andrew Bromage