--- a/src/HOL/indrule.ML Tue Jan 30 15:19:20 1996 +0100
+++ b/src/HOL/indrule.ML Tue Jan 30 15:24:36 1996 +0100
@@ -1,6 +1,6 @@
-(* Title: HOL/indrule.ML
+(* Title: HOL/indrule.ML
ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1994 University of Cambridge
Induction rule module -- for Inductive/Coinductive Definitions
@@ -10,14 +10,14 @@
signature INDRULE =
sig
- val induct : thm (*main induction rule*)
- val mutual_induct : thm (*mutual induction rule*)
+ val induct : thm (*main induction rule*)
+ val mutual_induct : thm (*mutual induction rule*)
end;
functor Indrule_Fun
(structure Inductive: sig include INDUCTIVE_ARG INDUCTIVE_I end and
- Intr_elim: sig include INTR_ELIM INTR_ELIM_AUX end) : INDRULE =
+ Intr_elim: sig include INTR_ELIM INTR_ELIM_AUX end) : INDRULE =
let
val sign = sign_of Inductive.thy;
@@ -32,7 +32,7 @@
(*** Prove the main induction rule ***)
-val pred_name = "P"; (*name for predicate variables*)
+val pred_name = "P"; (*name for predicate variables*)
val big_rec_def::part_rec_defs = Intr_elim.defs;
@@ -40,25 +40,25 @@
ind_alist = [(rec_tm1,pred1),...] -- associates predicates with rec ops
prem is a premise of an intr rule*)
fun add_induct_prem ind_alist (prem as Const("Trueprop",_) $
- (Const("op :",_)$t$X), iprems) =
+ (Const("op :",_)$t$X), iprems) =
(case gen_assoc (op aconv) (ind_alist, X) of
- Some pred => prem :: Ind_Syntax.mk_Trueprop (pred $ t) :: iprems
- | None => (*possibly membership in M(rec_tm), for M monotone*)
- let fun mk_sb (rec_tm,pred) =
- (case binder_types (fastype_of pred) of
- [T] => (rec_tm,
- Ind_Syntax.Int_const T $ rec_tm $
- (Ind_Syntax.Collect_const T $ pred))
- | _ => error
- "Bug: add_induct_prem called with non-unary predicate")
- in subst_free (map mk_sb ind_alist) prem :: iprems end)
+ Some pred => prem :: Ind_Syntax.mk_Trueprop (pred $ t) :: iprems
+ | None => (*possibly membership in M(rec_tm), for M monotone*)
+ let fun mk_sb (rec_tm,pred) =
+ (case binder_types (fastype_of pred) of
+ [T] => (rec_tm,
+ Ind_Syntax.Int_const T $ rec_tm $
+ (Ind_Syntax.Collect_const T $ pred))
+ | _ => error
+ "Bug: add_induct_prem called with non-unary predicate")
+ in subst_free (map mk_sb ind_alist) prem :: iprems end)
| add_induct_prem ind_alist (prem,iprems) = prem :: iprems;
(*Make a premise of the induction rule.*)
fun induct_prem ind_alist intr =
let val quantfrees = map dest_Free (term_frees intr \\ rec_params)
val iprems = foldr (add_induct_prem ind_alist)
- (Logic.strip_imp_prems intr,[])
+ (Logic.strip_imp_prems intr,[])
val (t,X) = Ind_Syntax.rule_concl intr
val (Some pred) = gen_assoc (op aconv) (ind_alist, X)
val concl = Ind_Syntax.mk_Trueprop (pred $ t)
@@ -68,8 +68,8 @@
(*Avoids backtracking by delivering the correct premise to each goal*)
fun ind_tac [] 0 = all_tac
| ind_tac(prem::prems) i =
- DEPTH_SOLVE_1 (ares_tac [Part_eqI, prem, refl] i) THEN
- ind_tac prems (i-1);
+ DEPTH_SOLVE_1 (ares_tac [Part_eqI, prem, refl] i) THEN
+ ind_tac prems (i-1);
val pred = Free(pred_name, elem_type --> Ind_Syntax.boolT);
@@ -85,15 +85,15 @@
prove_goalw_cterm part_rec_defs
(cterm_of sign
(Logic.list_implies (ind_prems,
- Ind_Syntax.mk_Trueprop (Ind_Syntax.mk_all_imp
- (big_rec_tm,pred)))))
+ Ind_Syntax.mk_Trueprop (Ind_Syntax.mk_all_imp
+ (big_rec_tm,pred)))))
(fn prems =>
[rtac (impI RS allI) 1,
- DETERM (etac Intr_elim.raw_induct 1),
- asm_full_simp_tac (!simpset addsimps [Part_Collect]) 1,
- REPEAT (FIRSTGOAL (eresolve_tac [IntE, CollectE, exE, conjE, disjE]
- ORELSE' hyp_subst_tac)),
- ind_tac (rev prems) (length prems)])
+ DETERM (etac Intr_elim.raw_induct 1),
+ asm_full_simp_tac (!simpset addsimps [Part_Collect]) 1,
+ REPEAT (FIRSTGOAL (eresolve_tac [IntE, CollectE, exE, conjE, disjE]
+ ORELSE' hyp_subst_tac)),
+ ind_tac (rev prems) (length prems)])
handle e => print_sign_exn sign e;
(*** Prove the simultaneous induction rule ***)
@@ -109,11 +109,11 @@
val pfree = Free(pred_name ^ "_" ^ rec_name, T)
val frees = mk_frees "za" (binder_types T)
val qconcl =
- foldr Ind_Syntax.mk_all
- (frees,
- Ind_Syntax.imp $ (Ind_Syntax.mk_mem
- (foldr1 Ind_Syntax.mk_Pair frees, rec_tm))
- $ (list_comb (pfree,frees)))
+ foldr Ind_Syntax.mk_all
+ (frees,
+ Ind_Syntax.imp $ (Ind_Syntax.mk_mem
+ (foldr1 Ind_Syntax.mk_Pair frees, rec_tm))
+ $ (list_comb (pfree,frees)))
in (Ind_Syntax.ap_split Ind_Syntax.boolT pfree (binder_types T),
qconcl)
end;
@@ -129,21 +129,21 @@
Ind_Syntax.mk_Trueprop
(Ind_Syntax.mk_all_imp
(big_rec_tm,
- Abs("z", elem_type,
- fold_bal (app Ind_Syntax.conj)
- (map mk_rec_imp (Inductive.rec_tms~~preds)))))
+ Abs("z", elem_type,
+ fold_bal (app Ind_Syntax.conj)
+ (map mk_rec_imp (Inductive.rec_tms~~preds)))))
and mutual_induct_concl =
Ind_Syntax.mk_Trueprop (fold_bal (app Ind_Syntax.conj) qconcls);
val lemma = (*makes the link between the two induction rules*)
prove_goalw_cterm part_rec_defs
- (cterm_of sign (Logic.mk_implies (induct_concl,
- mutual_induct_concl)))
- (fn prems =>
- [cut_facts_tac prems 1,
- REPEAT (eresolve_tac [asm_rl, conjE, PartE, mp] 1
- ORELSE resolve_tac [allI, impI, conjI, Part_eqI, refl] 1
- ORELSE dresolve_tac [spec, mp, splitD] 1)])
+ (cterm_of sign (Logic.mk_implies (induct_concl,
+ mutual_induct_concl)))
+ (fn prems =>
+ [cut_facts_tac prems 1,
+ REPEAT (eresolve_tac [asm_rl, conjE, PartE, mp] 1
+ ORELSE resolve_tac [allI, impI, conjI, Part_eqI, refl] 1
+ ORELSE dresolve_tac [spec, mp, splitD] 1)])
handle e => print_sign_exn sign e;
(*Mutual induction follows by freeness of Inl/Inr.*)
@@ -164,43 +164,43 @@
| mutual_ind_tac(prem::prems) i =
DETERM
(SELECT_GOAL
- (
- (*Simplify the assumptions and goal by unfolding Part and
- using freeness of the Sum constructors; proves all but one
+ (
+ (*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)
+ 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 []
- (cterm_of sign
- (Logic.list_implies (map (induct_prem (Inductive.rec_tms ~~ preds))
- Inductive.intr_tms,
- mutual_induct_concl)))
- (fn prems =>
- [rtac (quant_induct RS lemma) 1,
- mutual_ind_tac (rev prems) (length prems)])
+ (cterm_of sign
+ (Logic.list_implies (map (induct_prem (Inductive.rec_tms ~~ preds))
+ Inductive.intr_tms,
+ mutual_induct_concl)))
+ (fn prems =>
+ [rtac (quant_induct RS lemma) 1,
+ mutual_ind_tac (rev prems) (length prems)])
handle e => print_sign_exn sign e;
(*Attempts to remove all occurrences of split*)
val split_tac =
REPEAT (SOMEGOAL (FIRST' [rtac splitI,
- dtac splitD,
- etac splitE,
- bound_hyp_subst_tac]))
+ dtac splitD,
+ etac splitE,
+ bound_hyp_subst_tac]))
THEN prune_params_tac;
in
@@ -210,7 +210,7 @@
val mutual_induct =
if length Intr_elim.rec_names > 1 orelse
- length (Ind_Syntax.factors elem_type) > 1
+ length (Ind_Syntax.factors elem_type) > 1
then rule_by_tactic split_tac mutual_induct_split
else TrueI;
end