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

Gleb Peregud gleber.p at gmail.com
Tue Apr 21 09:18:30 UTC 2015

```Thanks for answers and sorry for goofy definitions and laws. I didn't think
it thoroughly enough.

In general I think I was looking for something slightly less powerful than
this CRDTs:
https://en.wikipedia.org/wiki/Conflict-free_replicated_data_type

Basically I would like to find an algebraic structure which corresponds to
a versioned shared data-structure which can be synchronized using log
replication between multiple actors/applications/devices. Think if a
structure which can be used to synchronize chat room with messages or
friends list or notification panel content, etc. It should work over
intermittent connection, with a single source of truth (a server), can be
incrementally updated to the latest version based on some cached stale
version, etc. I think I need to think a bit more about this to find a
proper definitions and laws.

Cheers,
Gleb

On Tue, Apr 21, 2015 at 4:51 AM, Richard A. O'Keefe <ok at cs.otago.ac.nz>
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".
>
> I'm a little confused by "a" being lower case.
>
> There's a little wrinkle that tells me this isn't going to
> be simple.
>
> type A = Bool
> newtype S = S [A]
>
> empty :: S
>
> empty = S []
>
> update :: S -> A -> S
>
> update o@(S (x:xs)) y | x == y = o
> update   (S xs) y              = S (y:xs)
>
> reconstruct :: S -> [A]
>
> reconstruct (S xs) = xs
>
> Here update is *locally* idempotent:
> update (update s a) a == update s a
> But it's not *globally* idempotent:
> you can build up a list of any desired length,
> such as S [False,True,False,True,False],
> as long as the elements alternate.
>
> Perhaps I have misunderstood your specification.
>
>
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