\frametitle{Functional Dependencies are Keys}

    \emph{Functional dependencies are partial keys.}
    The functional dependency
    A_1, \dots A_n \to B_1, \dots B_m
    holds for a relation $R$ if $\{\;A_1, \dots A_n\;\}$
    is a key for the relation obtained by restricting $R$ 
    to the columns $\{A_1, \dots A_n, B_1, \dots B_m\}$.
    The restriction of the table \sql{COURSES} to $\{\;\sql{INAME},\sql{PHONE}\;\}$ is:
        \multicolumn{2}{c}{COURSES} \\ \hline
        \hd{INAME} & \hd{PHONE} \\
        Grust & 7111 \\
        Klotz & 2418 \\
    The attribute $\sql{INAME}$ is a key of this table.

    The \emph{goal of database normalization is to turn FDs into keys}.\\
    \remark{The DBMS is then able to enforce the FDs for the user.}