[DMDB] relational model, relational algebra, SQL very basics

semester4/dmdb/parts/00_relational-model_logic/00_model/00_intro.tex

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+In the relational model, relations are sets of tuples (similar to \glspl{record}). They are denoted $R(f_1: D_1, \ldots, f_n: D_n)$,
+or sometimes simply $R(D_1, \ldots, D_n)$.
+An \bi{instance} is a \bi{set} of tuples $I_R \subseteq D_1 \times \ldots \times D_n$.
+
+\inlineintuition You can think of the instance to be the rows in the table.
+
+\shade{orange}{Important} We define relations as \bi{mathematical sets}. This means that they cannot contain duplicates and the order does not matter.
+Database engines may elect to do this differently, but this course assumes set semantics for the relational model.

semester4/dmdb/parts/00_relational-model_logic/00_model/01_keys.tex

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+\subsubsection{Keys}
+\inlinedefinition[Candidate Key] The minimal set of fields that identify each tuple uniquely
+
+\inlinedefinition[Primary Key] A single candidate key, i.e. just a single field.
+We mark the primary key using \underline{underlining} in visual \glspl{schema}.
+Formally, we write $R(\underline{k : D_k}, a:D_a, b:D_b)$ for a given relation, with all valid instances fulfilling
+\[
+	I \subseteq D_k \times D_a \times D_b \land \forall (k, a, b), (k', a', b') \in I : k = k' \rightarrow (a, b) = (a', b')
+\]
+i.e. if the key is equal, so is the rest of the tuple (thus they are one and the same\footnote{\hlhref{https://www.youtube.com/watch?v=tGeSEbYzhBU}{Heidrun is her name}}).
+

semester4/dmdb/parts/00_relational-model_logic/00_model/02_queries.tex

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+\subsubsection{Queries}
+We write queries in a relational model using the following set notation (using \acrshort{sql} for an actual DB):
+\[
+    \{ (r, p) \divider r \in \texttt{Supplies} \land p \in \texttt{Parts} \land \texttt{r.pid = p.pid} \land \texttt{p.name = "A"} \}
+\]
+The query language thus processes an entire set at a time and applies set operations over the relations.