(*<*) theory pairs2 imports Main begin (*>*) text‹\label{sec:pairs}\index{pairs and tuples}
also has ordered pairs: \isa{($a@1$,$a@2$)} is of type $\tau@1$
indexboldpos{\isasymtimes}{$Isatype} $\tau@2$ provided each $a@i$ is of type \tau@i$. The functions \cdx{fst} and
cdx{snd} extract the components of a pair: \isa{fst($x$,$y$) = $x$} and \isa{snd($x$,$y$) = $y$}. Tuples
simulated by pairs nested to the right: \isa{($a@1$,$a@2$,$a@3$)} stands \isa{($a@1$,($a@2$,$a@3$))} and $\tau@1 \times\tau@2 \times\tau@3$ for \tau@1 \times (\tau@2 \times\tau@3)$. Therefore we have
isa{fst(snd($a@1$,$a@2$,$a@3$)) = $a@2$}.
:
begin{itemize}
item
is also the type \tydx{unit}, which contains exactly one
denoted by~\cdx{()}. This type can be viewed
a degenerate product with 0 components.
item
, like type 🍋‹nat›, are datatypes, which means
particular that ‹induct_tac› and ‹case_tac› are applicable to
of product type.
split the term into a number of variables corresponding to the tuple structure
up to 7 components).
item
with more than two or three components become unwieldy;
are preferable.
end{itemize}
more information on pairs and records see Chapter~\ref{ch:more-types}. › (*<*) end (*>*)
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