Le Wed, 04 Jan 2012 17:49:15 +0000, Steve Horne <[email protected]> a écrit :
> On 04/01/2012 16:47, Steve Horne wrote: > > > > (a == a) > > reflexivity : (a == b) => (b == a) > > transitivity : (a == b) && (b == c) => (a == c) > > > Oops - that's... > > reflexivity : (a == a) > symmetry : (a == b) => (b == a) > transitivity : (a == b) && (b == c) => (a == c) > > An equivalence relation is a relation that meets all these conditions. > > I prefer to use "transymmetry" (although I guess it is not a regular word): reflexivity: a ≃ a transymmetry: ∀ a b. b≃a ⇒ ∀ c. c≃a ⇒ b≃c so I only have 2 rules. transymmetry is trivially derived from transitivity and symmetry. symmetry is trivially derived from reflexivity and transymmetry. transitivity is trivially derived from symmetry and transymmetry (and thus from transymmetry and reflexivity) > _______________________________________________ > Haskell-Cafe mailing list > [email protected] > http://www.haskell.org/mailman/listinfo/haskell-cafe _______________________________________________ Haskell-Cafe mailing list [email protected] http://www.haskell.org/mailman/listinfo/haskell-cafe
