--- a/src/HOL/indrule.ML Tue Jul 25 17:00:15 1995 +0200
+++ b/src/HOL/indrule.ML Tue Jul 25 17:00:53 1995 +0200
@@ -26,11 +26,10 @@
val (Const(_,recT),rec_params) = strip_comb (hd rec_tms);
val elem_type = dest_setT (body_type recT);
-val domTs = summands(elem_type);
val big_rec_name = space_implode "_" rec_names;
val big_rec_tm = list_comb(Const(big_rec_name,recT), rec_params);
-val _ = writeln " Proving the induction rules...";
+val _ = writeln " Proving the induction rule...";
(*** Prove the main induction rule ***)
@@ -76,29 +75,34 @@
val ind_prems = map (induct_prem (map (rpair pred) rec_tms)) intr_tms;
+(*Debugging code...
+val _ = writeln "ind_prems = ";
+val _ = seq (writeln o Sign.string_of_term sign) ind_prems;
+*)
+
val quant_induct =
prove_goalw_cterm part_rec_defs
(cterm_of sign (list_implies (ind_prems,
- mk_Trueprop (mk_all_imp(big_rec_tm,pred)))))
+ mk_Trueprop (mk_all_imp (big_rec_tm,pred)))))
(fn prems =>
[rtac (impI RS allI) 1,
- etac raw_induct 1,
+ DETERM (etac raw_induct 1),
+ asm_full_simp_tac (HOL_ss addsimps [Part_Collect]) 1,
REPEAT (FIRSTGOAL (eresolve_tac [IntE, CollectE, exE, conjE, disjE]
ORELSE' hyp_subst_tac)),
- REPEAT (FIRSTGOAL (eresolve_tac [PartE, CollectE])),
ind_tac (rev prems) (length prems)])
handle e => print_sign_exn sign e;
(*** Prove the simultaneous induction rule ***)
(*Make distinct predicates for each inductive set.
- Splits cartesian products in domT, IF nested to the right! *)
+ Splits cartesian products in elem_type, IF nested to the right! *)
-(*Given a recursive set and its domain, return the "split" predicate
+(*Given a recursive set, return the "split" predicate
and a conclusion for the simultaneous induction rule*)
-fun mk_predpair (rec_tm,domT) =
+fun mk_predpair rec_tm =
let val rec_name = (#1 o dest_Const o head_of) rec_tm
- val T = factors domT ---> boolT
+ val T = factors elem_type ---> boolT
val pfree = Free(pred_name ^ "_" ^ rec_name, T)
val frees = mk_frees "za" (binder_types T)
val qconcl =
@@ -109,7 +113,7 @@
qconcl)
end;
-val (preds,qconcls) = split_list (map mk_predpair (rec_tms~~domTs));
+val (preds,qconcls) = split_list (map mk_predpair rec_tms);
(*Used to form simultaneous induction lemma*)
fun mk_rec_imp (rec_tm,pred) =
@@ -135,6 +139,12 @@
(*Mutual induction follows by freeness of Inl/Inr.*)
+(*Simplification largely reduces the mutual induction rule to the
+ standard rule*)
+val mut_ss = set_ss addsimps [Inl_Inr_eq, Inr_Inl_eq, Inl_eq, Inr_eq];
+
+val all_defs = con_defs@part_rec_defs;
+
(*Removes Collects caused by M-operators in the intro rules*)
val cmonos = [subset_refl RS Int_Collect_mono] RL monos RLN (2,[rev_subsetD]);
@@ -143,20 +153,25 @@
| mutual_ind_tac(prem::prems) i =
DETERM
(SELECT_GOAL
- ((*unpackage and use "prem" in the corresponding place*)
- REPEAT (FIRSTGOAL
- (etac conjE ORELSE' eq_mp_tac ORELSE'
- ares_tac [impI, conjI]))
- (*prem is not allowed in the REPEAT, lest it loop!*)
- THEN TRYALL (rtac prem)
- THEN REPEAT
- (FIRSTGOAL (ares_tac [impI] ORELSE'
- eresolve_tac (mp::cmonos)))
- (*prove remaining goals by contradiction*)
- THEN rewrite_goals_tac (con_defs@part_rec_defs)
- THEN DEPTH_SOLVE (eresolve_tac (PartE :: sumprod_free_SEs) 1))
- i)
- THEN mutual_ind_tac prems (i-1);
+ (
+ (*Simplify the assumptions and goal by unfolding Part and
+ using freeness of the Sum constructors; proves all but one
+ conjunct by contradiction*)
+ rewrite_goals_tac all_defs THEN
+ simp_tac (mut_ss addsimps [Part_def]) 1 THEN
+ IF_UNSOLVED (*simp_tac may have finished it off!*)
+ ((*simplify assumptions, but don't accept new rewrite rules!*)
+ asm_full_simp_tac (mut_ss setmksimps K[]) 1 THEN
+ (*unpackage and use "prem" in the corresponding place*)
+ REPEAT (rtac impI 1) THEN
+ rtac (rewrite_rule all_defs prem) 1 THEN
+ (*prem must not be REPEATed below: could loop!*)
+ DEPTH_SOLVE (FIRSTGOAL (ares_tac [impI] ORELSE'
+ eresolve_tac (conjE::mp::cmonos))))
+ ) i)
+ THEN mutual_ind_tac prems (i-1);
+
+val _ = writeln " Proving the mutual induction rule...";
val mutual_induct_split =
prove_goalw_cterm []