(*<*) theory pairs2 imports Main begin (*>*) text‹\label{sec:pairs}\index{pairs and tuples} HOL 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 are simulated by pairs nested to the right: \isa{($a@1$,$a@2$,$a@3$)} stands for \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($a@1$,$a@2$,$a@3$)) = $a@2$}. Remarks: \begin{itemize} \item There is also the type \tydx{unit}, which contains exactly one element denoted by~\cdx{()}. This type can be viewed as a degenerate product with 0 components. \item Products, like type 🍋‹nat›, in particular that ‹induct_tac›and‹case_tac› are applicable to
terms of product type.
Both split the term into a number of variables corresponding to the tuple structure
(up to 7 components). \item
Tuples with more than two or three components become unwieldy;
records are preferable. \end{itemize} For more information on pairs and records see Chapter~\ref{ch:more-types}. › (*<*) end (*>*)
Messung V0.5 in Prozent
¤ Dauer der Verarbeitung: 0.12 Sekunden
(vorverarbeitet am 2026-05-03)
¤
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung und die Messung sind noch experimentell.
