src/Doc/Tutorial/Misc/pairs2.thy
 author wenzelm Sat Nov 01 14:20:38 2014 +0100 (2014-11-01) changeset 58860 fee7cfa69c50 parent 48985 5386df44a037 child 67406 23307fd33906 permissions -rw-r--r--
eliminated spurious semicolons;
     1 (*<*)

     2 theory pairs2 imports Main begin

     3 (*>*)

     4 text{*\label{sec:pairs}\index{pairs and tuples}

     5 HOL also has ordered pairs: \isa{($a@1$,$a@2$)} is of type $\tau@1$

     6 \indexboldpos{\isasymtimes}{$Isatype}$\tau@2$provided each$a@i$is of type   7$\tau@i$. The functions \cdx{fst} and   8 \cdx{snd} extract the components of a pair:   9 \isa{fst($x$,$y$) =$x$} and \isa{snd($x$,$y$) =$y$}. Tuples   10 are simulated by pairs nested to the right: \isa{($a@1$,$a@2$,$a@3$)} stands   11 for \isa{($a@1$,($a@2$,$a@3$))} and$\tau@1 \times \tau@2 \times \tau@3$for   12$\tau@1 \times (\tau@2 \times \tau@3)$. Therefore we have   13 \isa{fst(snd($a@1$,$a@2$,$a@3$)) =$a@2\$}.

    14

    15 Remarks:

    16 \begin{itemize}

    17 \item

    18 There is also the type \tydx{unit}, which contains exactly one

    19 element denoted by~\cdx{()}.  This type can be viewed

    20 as a degenerate product with 0 components.

    21 \item

    22 Products, like type @{typ nat}, are datatypes, which means

    23 in particular that @{text induct_tac} and @{text case_tac} are applicable to

    24 terms of product type.

    25 Both split the term into a number of variables corresponding to the tuple structure

    26 (up to 7 components).

    27 \item

    28 Tuples with more than two or three components become unwieldy;

    29 records are preferable.

    30 \end{itemize}

    31 For more information on pairs and records see Chapter~\ref{ch:more-types}.

    32 *}

    33 (*<*)

    34 end

    35 (*>*)