changed importing introduction rules to fix the same type variables in all introduction rules; improved mode analysis for partially applied relations; added test case; tuned
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theory Nested0 imports Main begin
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text{*
\index{datatypes!nested}%
In \S\ref{sec:nested-datatype} we defined the datatype of terms
*}
datatype ('a,'b)"term" = Var 'a | App 'b "('a,'b)term list"
text{*\noindent
and closed with the observation that the associated schema for the definition
of primitive recursive functions leads to overly verbose definitions. Moreover,
if you have worked exercise~\ref{ex:trev-trev} you will have noticed that
you needed to declare essentially the same function as @{term"rev"}
and prove many standard properties of list reversal all over again.
We will now show you how \isacommand{recdef} can simplify
definitions and proofs about nested recursive datatypes. As an example we
choose exercise~\ref{ex:trev-trev}:
*}
consts trev :: "('a,'b)term \<Rightarrow> ('a,'b)term"
(*<*)end(*>*)