[isabelle] (v2007) Strange lemmas generated by inductive_set package



Hi all,

I was porting some code from v2005 to v2007. I encountered just few
problems, I'll describe one of them here, perhaps someone knows if this
behaviour is intended:

I have the following inductive set definitions:

text {* Transitive reflexive closure of labelled transition system *}
inductive_set
  trcl :: "('c*'a*'c) set \<Rightarrow> ('c*'a list*'c) set"
  for t
  where
  empty[simp]: "(c,[],c) \<in> trcl t"
  | cons[simp]: "\<lbrakk> (c,a,c') \<in> t; (c',w,c'') \<in> trcl t
\<rbrakk> \<Longrightarrow> (c,a#w,c'') \<in> trcl t"

inductive_set
  foo :: "(('c*'c)*'a*('c*'c)) set"
where
  "((s,c),a,(s,c'))\<in>foo"

consts P :: "'a \<Rightarrow> bool"

inductive_set
  bar :: "('c*'a list list*'c) set"
  where
  "\<lbrakk>((s,c),a,(s',c'))\<in>trcl foo; (s,w,s')\<in>bar\<rbrakk>
\<Longrightarrow> (c,a#w,c')\<in>bar"

foo and bar are just some artifical definitions, the point seems to be,
that the definition of bar contains trcl applied to an LTS over *pairs*,
while trcl is defined over arbitrary states, not just pairs. The last
definition of bar creates strange induction, intro and elim theorems:
thm bar.intros
(* \<lbrakk>((?s, ?c), ?a, ?s', ?c') \<in> trcl {((xa, x), xd, xc, xb).
((xa, x), xd, xc, xb) \<in> foo}; (?s, ?w, ?s') \<in> bar\<rbrakk>
\<Longrightarrow> (?c, ?a # ?w, ?c') \<in> bar*)

The expression "{((xa, x), xd, xc, xb). ((xa, x), xd, xc, xb) \<in>
foo}" is obviously the same as just "foo", the simplifier knows that, too:

thm bar.intros[simplified]
(* \<lbrakk>((?s, ?c), ?a, ?s', ?c') \<in> trcl foo; (?s, ?w, ?s') \<in>
bar\<rbrakk> \<Longrightarrow> (?c, ?a # ?w, ?c') \<in> bar *)

I would have expected the latter version of the theorems being generated
(as the old inductive package of v2005 did). My current workaround is to
use the simplified attribute or some
    (simp)-steps where the altered definitions cause problems.

My question is: Is this the intended behaviour ? If yes: Why? And can I
get it to generate the simplified lemmas?

regards and thanks in advance for any hints
    Peter



-- 
Peter Lammich, Institut für Informatik
Raum 715, Einsteinstrasse 62, 48149 Münster
Mail: peter.lammich at uni-muenster.de
Tel: 0251-83-32749
Mobil: 0163-5310380







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