diff -r 02c51ca9c531 -r d17c0b34d5c8 doc-src/TutorialI/Misc/pairs.thy --- a/doc-src/TutorialI/Misc/pairs.thy Fri Aug 04 23:02:11 2000 +0200 +++ b/doc-src/TutorialI/Misc/pairs.thy Sun Aug 06 15:26:53 2000 +0200 @@ -1,8 +1,26 @@ (*<*) theory pairs = Main:; -term(*>*) "let (x,y) = f z in (y,x)"; +(*>*) +text{* +HOL also has pairs: \isa{($a@1$,$a@2$)} is of type \isa{$\tau@1$ * + $\tau@2$} provided each $a@i$ is of type $\tau@i$. The components of a pair +are extracted by \isa{fst} and \isa{snd}: \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 +\isa{$\tau@1$ * $\tau@2$ * $\tau@3$} for \isa{$\tau@1$ * ($\tau@2$ * + $\tau@3$)}. Therefore we have \isa{fst(snd($a@1$,$a@2$,$a@3$)) = $a@2$}. + +It is possible to use (nested) tuples as patterns in abstractions, for +example \isa{\isasymlambda(x,y,z).x+y+z} and +\isa{\isasymlambda((x,y),z).x+y+z}. +In addition to explicit $\lambda$-abstractions, tuple patterns can be used in +most variable binding constructs. Typical examples are +\begin{quote} +@{term"let (x,y) = f z in (y,x)"}\\ +@{term"case xs of [] => 0 | (x,y)#zs => x+y"} +\end{quote} +Further important examples are quantifiers and sets (see~\S\ref{quant-pats}). +*} (*<*) -term(*>*) "case xs of [] \\ 0 | (x,y)#zs \\ x+y" -(**)(*<*) end (*>*)