Simple Data Structuring

A simple structured type can be formed by the set product† of two or more unstructured types. The result is known as a record type. A familiar example is the type complex number, which consists of all possible ordered pairs of real numbers. Thus <math display="block"><mtable columnalign="right"><mtr><mtd><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>o</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi><mi>x</mi><mo>=</mo><mi>r</mi><mi>e</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>d</mi></mtd></mtr><mtr><mtd><mi>r</mi><mi>e</mi><mi>a</mi><mi>l</mi><mi>p</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo>:</mo><mi>r</mi><mi>e</mi><mi>a</mi><mi>l</mi></mtd></mtr><mtr><mtd><mi>i</mi><mi>m</mi><mi>a</mi><mi>g</mi><mi>p</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo>:</mo><mi>r</mi><mi>e</mi><mi>a</mi><mi>l</mi></mtd></mtr><mtr><mtd><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math> $$ \begin{gathered} \hfill type\,complex=record \\ \hfill realpart: real \\ \hfill imagpart : real \\ \hfill end \\ \end{gathered} $$ or more briefly <math display="block"><mtable columnalign="right"><mtr><mtd><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>o</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi><mi>x</mi><mo>=</mo><mi>r</mi><mi>e</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>d</mi></mtd></mtr><mtr><mtd><mi>r</mi><mi>e</mi><mi>a</mi><mi>l</mi><mi>p</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo>,</mo><mi>i</mi><mi>m</mi><mi>a</mi><mi>g</mi><mi>p</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo>:</mo><mi>r</mi><mi>e</mi><mi>a</mi><mi>l</mi></mtd></mtr><mtr><mtd><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math> $$ \begin{gathered} \hfill type\,complex = record \\ \hfill realpart, imagpart:real \\ \hfill end \\ \end{gathered} $$ define complex numbers to be records with realpart and imagpart components, and each components is of type real.