--- Join dependencies ---

 (taken from [Abiteboul \& Hull \& Vianu, 1995], using their Figure 8.2)

 Consider the relation R, with an instance given by

          Snack    Distributor    Price   Theater
         -----------------------------------------
          coffee      Smart       2.35      Rex
          coffee      Smart       2.35      Le Champo
          coffee      Smart       2.35      Cinoche
          coffee     Leclerc      2.60      Cinoche
          wine        Smart       0.80      Rex
          wine        Smart       0.80      Cinoche
          popcorn    Leclerc      5.60      Cinoche

We can assume the functional dependency
    Snack,Distributor -> Price
but other non-trivial dependencies are hard to spot.
In particular, a multi-valued dependency like
    Snack ->-> Theater  does NOT hold.
To see this, observe that R contains the tuples
          coffee      Smart       2.35      Rex
          coffee     Leclerc      2.60      Cinoche
so the dependency proposed above would imply that R also has the tuples
          coffee      Smart       2.35      Cinoche
          coffee     Leclerc      2.60      Rex
but only the first belongs to R.

We might decompose R as follows:
  Snack,Distributor,Price     Distributor,Theater     Snack,Theater
  coffee   Smart    2.35          Smart    Rex       coffee  Rex
  coffee  Leclerc   2.60          Smart  LeChampo    coffee  LeChampo
  wine     Smart    0.80          Smart   Cinoche    coffee  Cinoche
  popcorn Leclerc   5.60         Leclerc  Cinoche    wine    Rex
                                                     wine    Cinoche
                                                     popcorn Cinoche

It is easy to check that this decomposition is lossless
  for our specific instance.
If that also holds in the general case, we say that there is a
  *join dependency* between the attribute sets
 {Snack,Distributor,Price} and  {Distributor,Theater} and {Snack,Theater}

A multi-valued dependency can be viewed as a special case of a join dependency,
 where there are only two attribute sets.