text‹\noindent
the definition of @{term trev} below is quite natural, we will have
overcome a minor difficulty in convincing Isabelle of its termination.
is precisely this difficulty that is the \textit{raison d'\^etre} of
subsection.
@{term trev} by \isacommand{recdef} rather than \isacommand{primrec}
matters because we are now free to use the recursion equation
at the end of \S\ref{sec:nested-datatype}: ›
recdef(*<*)(permissive)(*>*)trev "measure size" "trev (Var x) = Var x" "trev (App f ts) = App f (rev(map trev ts))"
text‹\noindent
that function @{term size} is defined for each \isacommand{datatype}.
, the definition does not succeed. Isabelle complains about an
termination condition
{prop[display]"t : set ts --> size t < Suc (size_term_list ts)"}
@{term set} returns the set of elements of a list ‹size_term_list :: term list → nat› is an auxiliary
automatically defined by Isabelle
while processing the declaration of ‹term›). Why does the
call of @{const trev} lead to this
? Because \isacommand{recdef} knows that @{term map}
apply @{const trev} only to elements of @{term ts}. Thus the
expresses that the size of the argument @{prop"t : set ts"} of any
call of @{const trev} is strictly less than @{term"size(App f ts)"},
equals @{term"Suc(size_term_list ts)"}. We will now prove the termination condition and
with our definition. Below we return to the question of how
isacommand{recdef} knows about @{term map}.
termination condition is easily proved by induction: ›
(*<*) end (*>*)
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