'cases' / 'induct' method: ?case binding, 'of:' spec;
Sat, 06 Jan 2001 21:22:35 +0100
changeset 10802 7fa042e28c43
parent 10801 c00ac928fc6f
child 10803 bdc3aa1c193b
'cases' / 'induct' method: ?case binding, 'of:' spec;
--- a/doc-src/IsarRef/hol.tex	Sat Jan 06 12:39:05 2001 +0100
+++ b/doc-src/IsarRef/hol.tex	Sat Jan 06 21:22:35 2001 +0100
@@ -278,14 +278,12 @@
 about large specifications.
-  'cases' simplified? open? args rule?
+  'cases' ('(' 'simplified' ')')? spec
-  'induct' stripped? open? args rule?
+  'induct' ('(' 'stripped' ')')? spec
-  simplified: '(' 'simplified' ')'
-  ;
-  stripped: '(' 'stripped' ')'
+  spec: open? args rule? params?
   open: '(' 'open' ')'
@@ -293,10 +291,12 @@
   rule: ('type' | 'set') ':' nameref | 'rule' ':' thmref
+  params: 'of' ':' insts
+  ;
-\item [$cases~insts~R$] applies method $rule$ with an appropriate case
+\item [$cases~insts~R~ps$] applies method $rule$ with an appropriate case
   distinction theorem, instantiated to the subjects $insts$.  Symbolic case
   names are bound according to the rule's local contexts.
@@ -315,6 +315,13 @@
   variables is instantiated.  In most situations, only a single term needs to
   be specified; this refers to the first variable of the last premise (it is
   usually the same for all cases).
+  Additional parameters may be specified as $ps$; these are applied after the
+  primary instantiation in the same manner as by the $of$ attribute (cf.\ 
+  \S\ref{sec:pure-meth-att}).  This feature is rarely needed in practice; a
+  typical application would be to specify additional arguments for rules
+  stemming from parameterized inductive definitions (see also
+  \S\ref{sec:inductive}).
   The $simplified$ option causes ``obvious cases'' of the rule to be solved
   beforehand, while the others are left unscathed.
@@ -325,8 +332,8 @@
   manner, which can be quite confusing to the reader.  Furthermore, this
   option may cause unwanted hiding of existing local variables, resulting in
   less robust proof texts.
-\item [$induct~insts~R$] is analogous to the $cases$ method, but refers to
+\item [$induct~insts~R~ps$] is analogous to the $cases$ method, but refers to
   induction rules, which are determined as follows:
     \Text{facts}    &        & \Text{arguments} & \Text{rule} \\\hline
@@ -342,6 +349,8 @@
   This enables the writer to specify only induction variables, or both
   predicates and variables, for example.
+  Additional parameters may be given in the same way as for $cases$.
   The $stripped$ option causes implications and (bounded) universal
   quantifiers to be removed from each new subgoal emerging from the
   application of the induction rule.  This accommodates special applications
@@ -359,7 +368,9 @@
 emerging local contexts and subgoals are concerned.  In particular, for
 induction both the predicates and variables have to be specified.  Otherwise
 the $\CASENAME$ command would refuse to invoke cases containing schematic
+variables.  Furthermore the resulting local goal statement is bound to the
+term variable $\Var{case}$\indexisarvar{case} --- for each case where it is
+fully specified.
 The $\isarkeyword{print_cases}$ command (\S\ref{sec:cases}) prints all named
 cases present in the current proof state.
@@ -421,7 +432,7 @@
 declared by HOL definitional packages.  For special applications, these may be
 replaced manually by variant versions.
-Refer to the $case_names$ and $params$ attributes (see \S\ref{sec:cases}) to
+Refer to the $case_names$ and $ps$ attributes (see \S\ref{sec:cases}) to
 adjust names of cases and parameters of a rule.
 The $consumes$ declaration (cf.\ \S\ref{sec:cases}) is taken care of