--- a/doc-src/TutorialI/fp.tex Wed Aug 02 11:30:38 2000 +0200
+++ b/doc-src/TutorialI/fp.tex Wed Aug 02 13:17:11 2000 +0200
@@ -125,7 +125,8 @@
\isa{\isacommand{use\_thy}\indexbold{*use_thy}~"T"}.
If you suddenly discover that you need to modify a parent theory of your
- current theory you must first abandon your current theory (at the shell
+ current theory you must first abandon your current theory\indexbold{abandon
+ theory}\indexbold{theory!abandon} (at the shell
level type \isacommand{kill}\indexbold{*kill}). After the parent theory has
been modified you go back to your original theory. When its first line
\isacommand{theory}\texttt{~T~=}~\dots~\texttt{:} is processed, the
@@ -316,21 +317,22 @@
see~\S\ref{nat-numerals}.
\begin{warn}
- The operations \ttindexboldpos{+}{$HOL2arithfun},
- \ttindexboldpos{-}{$HOL2arithfun}, \ttindexboldpos{*}{$HOL2arithfun},
- \isaindexbold{min}, \isaindexbold{max},
+ The constant \ttindexbold{0} and the operations
+ \ttindexboldpos{+}{$HOL2arithfun}, \ttindexboldpos{-}{$HOL2arithfun},
+ \ttindexboldpos{*}{$HOL2arithfun}, \isaindexbold{min}, \isaindexbold{max},
\indexboldpos{\isasymle}{$HOL2arithrel} and
\ttindexboldpos{<}{$HOL2arithrel} are overloaded, i.e.\ they are available
not just for natural numbers but at other types as well (see
- \S\ref{sec:TypeClasses}). For example, given the goal \isa{x+y = y+x},
- there is nothing to indicate that you are talking about natural numbers.
- Hence Isabelle can only infer that \isa{x} and \isa{y} are of some
- arbitrary type where \isa{+} is declared. As a consequence, you will be
- unable to prove the goal (although it may take you some time to realize
- what has happened if \texttt{show_types} is not set). In this particular
- example, you need to include an explicit type constraint, for example
- \isa{x+y = y+(x::nat)}. If there is enough contextual information this may
- not be necessary: \isa{x+0 = x} automatically implies \isa{x::nat}.
+ \S\ref{sec:TypeClasses}). For example, given the goal \isa{x+0 = x}, there
+ is nothing to indicate that you are talking about natural numbers. Hence
+ Isabelle can only infer that \isa{x} is of some arbitrary type where
+ \isa{0} and \isa{+} are declared. As a consequence, you will be unable to
+ prove the goal (although it may take you some time to realize what has
+ happened if \texttt{show_types} is not set). In this particular example,
+ you need to include an explicit type constraint, for example \isa{x+0 =
+ (x::nat)}. If there is enough contextual information this may not be
+ necessary: \isa{Suc x = x} automatically implies \isa{x::nat} because
+ \isa{Suc} is not overloaded.
\end{warn}
Simple arithmetic goals are proved automatically by both \isa{auto}