--- a/doc-src/Logics/HOL.tex Thu Apr 09 12:29:39 1998 +0200
+++ b/doc-src/Logics/HOL.tex Thu Apr 09 12:31:35 1998 +0200
@@ -1963,15 +1963,16 @@
\index{*primrec|)}
-\subsection{Well-founded recursive functions}
+\subsection{General recursive functions}
\label{sec:HOL:recdef}
\index{recursion!general|(}
\index{*recdef|(}
-Well-founded recursion can express any function whose termination can be
-proved by showing that each recursive call makes the argument smaller in a
-suitable sense. The recursion need not involve datatypes and there are few
-syntactic restrictions. Nested recursion and pattern-matching are allowed.
+Using \texttt{recdef}, you can declare functions involving nested recursion
+and pattern-matching. Recursion need not involve datatypes and there are few
+syntactic restrictions. Termination is proved by showing that each recursive
+call makes the argument smaller in a suitable sense, which you specify by
+supplying a well-founded relation.
Here is a simple example, the Fibonacci function. The first line declares
\texttt{fib} to be a constant. The well-founded relation is simply~$<$ (on
@@ -1989,6 +1990,14 @@
overlap, as in functional programming. The \texttt{recdef} package
disambiguates overlapping patterns by taking the order of rules into account.
For missing patterns, the function is defined to return an arbitrary value.
+For example, here is a declaration of the list function \cdx{hd}:
+\begin{ttbox}
+consts hd :: 'a list => 'a
+recdef hd "\{\}"
+ "hd (x#l) = x"
+\end{ttbox}
+Because this function is not recursive, we may supply the empty well-founded
+relation, $\{\}$.
The well-founded relation defines a notion of ``smaller'' for the function's
argument type. The relation $\prec$ is \textbf{well-founded} provided it