doc-src/Functions/intro.tex

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+\section{Introduction}
+
+Starting from Isabelle 2007, new facilities for recursive
+function definitions~\cite{krauss2006} are available. They provide
+better support for general recursive definitions than previous
+packages.  But despite all tool support, function definitions can
+sometimes be a difficult thing. 
+
+This tutorial is an example-guided introduction to the practical use
+of the package and related tools. It should help you get started with
+defining functions quickly. For the more difficult definitions we will
+discuss what problems can arise, and how they can be solved.
+
+We assume that you have mastered the fundamentals of Isabelle/HOL
+and are able to write basic specifications and proofs. To start out
+with Isabelle in general, consult the Isabelle/HOL tutorial
+\cite{isa-tutorial}.
+
+
+
+\paragraph{Structure of this tutorial.}
+Section 2 introduces the syntax and basic operation of the \cmd{fun}
+command, which provides full automation with reasonable default
+behavior.  The impatient reader can stop after that
+section, and consult the remaining sections only when needed.
+Section 3 introduces the more verbose \cmd{function} command which
+gives fine-grained control. This form should be used
+whenever the short form fails.
+After that we discuss more specialized issues:
+termination, mutual, nested and higher-order recursion, partiality, pattern matching
+and others.
+
+
+\paragraph{Some background.}
+Following the LCF tradition, the package is realized as a definitional
+extension: Recursive definitions are internally transformed into a
+non-recursive form, such that the function can be defined using
+standard definition facilities. Then the recursive specification is
+derived from the primitive definition.  This is a complex task, but it
+is fully automated and mostly transparent to the user. Definitional
+extensions are valuable because they are conservative by construction:
+The \qt{new} concept of general wellfounded recursion is completely reduced
+to existing principles.
+
+
+
+
+The new \cmd{function} command, and its short form \cmd{fun} have mostly
+replaced the traditional \cmd{recdef} command \cite{slind-tfl}. They solve
+a few of technical issues around \cmd{recdef}, and allow definitions
+which were not previously possible.
+
+
+
+