Am Donnerstag 18 Februar 2010 21:47:02 schrieb Hans Aberg: > On 18 Feb 2010, at 20:20, Daniel Fischer wrote: > >> + definition backtracking: «A closure operation c is defined by the > >> property c(c(x)) = c(x). > > > > Actually, that's incomplete, ... > > That's right, it is just the idempotency relation. > > > ...missing are > > - c(x) contains x > > - c(x) is minimal among the sets containing x with y = c(y). > > It suffices*) with a lattice L with relation <= (inclusion in the case > of sets) satifying > i. x <= y implies c(x) <= c(y) > ii. x <= c(x) for all x in L. > iii. c(c(x)) = x.
Typo, iii. c(c(x)) = c(x), of course. If we replace "set" by "lattice element" and "contains" by ">=", the definitions are equivalent. The one you quoted is better, though. > > Hans > > *) The definition in a book on lattice theory by Balbes & Dwinger. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
