src/ZF/indrule.ML
 changeset 1461 6bcb44e4d6e5 parent 1418 f5f97ee67cbb child 1736 fe0b459273f2
```--- a/src/ZF/indrule.ML	Mon Jan 29 14:16:13 1996 +0100
+++ b/src/ZF/indrule.ML	Tue Jan 30 13:42:57 1996 +0100
@@ -1,6 +1,6 @@
-(*  Title: 	ZF/indrule.ML
+(*  Title:      ZF/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
@@ -10,8 +10,8 @@

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;

@@ -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;

@@ -40,20 +40,20 @@
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_tprop (pred \$ t) :: iprems
-	| None => (*possibly membership in M(rec_tm), for M monotone*)
-	    let fun mk_sb (rec_tm,pred) =
-			(rec_tm, Ind_Syntax.Collect_const\$rec_tm\$pred)
-	    in  subst_free (map mk_sb ind_alist) prem :: iprems  end)
+          Some pred => prem :: Ind_Syntax.mk_tprop (pred \$ t) :: iprems
+        | None => (*possibly membership in M(rec_tm), for M monotone*)
+            let fun mk_sb (rec_tm,pred) =
+                        (rec_tm, Ind_Syntax.Collect_const\$rec_tm\$pred)
+            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_tprop (pred \$ t)
@@ -64,8 +64,8 @@
Intro rules with extra Vars in premises still cause some backtracking *)
fun ind_tac [] 0 = all_tac
| ind_tac(prem::prems) i =
-    	DEPTH_SOLVE_1 (ares_tac [prem, refl] i) THEN
-	ind_tac prems (i-1);
+        DEPTH_SOLVE_1 (ares_tac [prem, refl] i) THEN
+        ind_tac prems (i-1);

val pred = Free(pred_name, Ind_Syntax.iT --> Ind_Syntax.oT);

@@ -76,15 +76,15 @@
prove_goalw_cterm part_rec_defs
(cterm_of sign
(Logic.list_implies (ind_prems,
-		Ind_Syntax.mk_tprop (Ind_Syntax.mk_all_imp(big_rec_tm,pred)))))
+                Ind_Syntax.mk_tprop (Ind_Syntax.mk_all_imp(big_rec_tm,pred)))))
(fn prems =>
[rtac (impI RS allI) 1,
-	DETERM (etac Intr_elim.raw_induct 1),
-	(*Push Part inside Collect*)
-	asm_full_simp_tac (FOL_ss addsimps [Part_Collect]) 1,
-	REPEAT (FIRSTGOAL (eresolve_tac [CollectE, exE, conjE, disjE] ORELSE'
-			   hyp_subst_tac)),
-	ind_tac (rev prems) (length prems) ]);
+        DETERM (etac Intr_elim.raw_induct 1),
+        (*Push Part inside Collect*)
+        asm_full_simp_tac (FOL_ss addsimps [Part_Collect]) 1,
+        REPEAT (FIRSTGOAL (eresolve_tac [CollectE, exE, conjE, disjE] ORELSE'
+                           hyp_subst_tac)),
+        ind_tac (rev prems) (length prems) ]);

(*** Prove the simultaneous induction rule ***)

@@ -111,11 +111,11 @@
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.mem_const \$ foldr1 (app Pr.pair) frees \$
-			   rec_tm)
-			  \$ (list_comb (pfree,frees)))
+        foldr Ind_Syntax.mk_all (frees,
+                        Ind_Syntax.imp \$
+                          (Ind_Syntax.mem_const \$ foldr1 (app Pr.pair) frees \$
+                           rec_tm)
+                          \$ (list_comb (pfree,frees)))
in  (Ind_Syntax.ap_split Pr.fsplit_const pfree (binder_types T),
qconcl)
end;
@@ -130,20 +130,20 @@
(*To instantiate the main induction rule*)
val induct_concl =
Ind_Syntax.mk_tprop(Ind_Syntax.mk_all_imp(big_rec_tm,
-	     Abs("z", Ind_Syntax.iT,
-		 fold_bal (app Ind_Syntax.conj)
-		 (map mk_rec_imp (Inductive.rec_tms~~preds)))))
+             Abs("z", Ind_Syntax.iT,
+                 fold_bal (app Ind_Syntax.conj)
+                 (map mk_rec_imp (Inductive.rec_tms~~preds)))))
and mutual_induct_concl =
Ind_Syntax.mk_tprop(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] 1
-	     ORELSE dresolve_tac [spec, mp, Pr.fsplitD] 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] 1
+             ORELSE dresolve_tac [spec, mp, Pr.fsplitD] 1)]);

(*Mutual induction follows by freeness of Inl/Inr.*)

@@ -167,42 +167,42 @@
| 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_iff]) 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 (fn _=>[])) 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_iff]) 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 (fn _=>[])) 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_fsplit =
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)]);

(*Attempts to remove all occurrences of fsplit*)
val fsplit_tac =
REPEAT (SOMEGOAL (FIRST' [rtac Pr.fsplitI,
-			      dtac Pr.fsplitD,
-			      etac Pr.fsplitE,	(*apparently never used!*)
-			      bound_hyp_subst_tac]))
+                              dtac Pr.fsplitD,
+                              etac Pr.fsplitE,  (*apparently never used!*)
+                              bound_hyp_subst_tac]))
THEN prune_params_tac

in
@@ -214,7 +214,7 @@
recursion or because it involves tuples.  This saves storage.*)
val mutual_induct =
if length Intr_elim.rec_names > 1 orelse
-	 is_sigma Inductive.dom_sum
+         is_sigma Inductive.dom_sum
then rule_by_tactic fsplit_tac mutual_induct_fsplit
else TrueI;
end```