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 (*>*)