[Haskell-cafe] Is there a name for this algebraic structure?

[Tom Ellis]

On Tue, Apr 21, 2015 at 02:51:16PM +1200, Richard A. O'Keefe wrote:
> You said in words that
> 
> > Every S can be reconstructed from a sequence of updates:
> 
> but your formula
> 
> >     forall s. exists [a]. s == foldl update empty [a]
> 
> says that a (not necessarily unique) sequence of updates
> can be reconstructed from every S.  I think you meant
> something like "there are no elements of S but those
> that can be constructed by a sequence of updates".

Those sound like the same thing to me!