--- a/src/ZF/ex/bt_fn.ML Sat Apr 05 16:18:58 2003 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,128 +0,0 @@
-(* Title: ZF/bt.ML
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1992 University of Cambridge
-
-For bt.thy. Binary trees
-*)
-
-open BT_Fn;
-
-
-
-(** bt_rec -- by Vset recursion **)
-
-goalw BT.thy BT.con_defs "rank(l) < rank(Br(a,l,r))";
-by (simp_tac rank_ss 1);
-val rank_Br1 = result();
-
-goalw BT.thy BT.con_defs "rank(r) < rank(Br(a,l,r))";
-by (simp_tac rank_ss 1);
-val rank_Br2 = result();
-
-goal BT_Fn.thy "bt_rec(Lf,c,h) = c";
-by (rtac (bt_rec_def RS def_Vrec RS trans) 1);
-by (simp_tac (ZF_ss addsimps BT.case_eqns) 1);
-val bt_rec_Lf = result();
-
-goal BT_Fn.thy
- "bt_rec(Br(a,l,r), c, h) = h(a, l, r, bt_rec(l,c,h), bt_rec(r,c,h))";
-by (rtac (bt_rec_def RS def_Vrec RS trans) 1);
-by (simp_tac (rank_ss addsimps (BT.case_eqns @ [rank_Br1, rank_Br2])) 1);
-val bt_rec_Br = result();
-
-(*Type checking -- proved by induction, as usual*)
-val prems = goal BT_Fn.thy
- "[| t: bt(A); \
-\ c: C(Lf); \
-\ !!x y z r s. [| x:A; y:bt(A); z:bt(A); r:C(y); s:C(z) |] ==> \
-\ h(x,y,z,r,s): C(Br(x,y,z)) \
-\ |] ==> bt_rec(t,c,h) : C(t)";
-by (bt_ind_tac "t" prems 1);
-by (ALLGOALS (asm_simp_tac (ZF_ss addsimps
- (prems@[bt_rec_Lf,bt_rec_Br]))));
-val bt_rec_type = result();
-
-(** Versions for use with definitions **)
-
-val [rew] = goal BT_Fn.thy "[| !!t. j(t)==bt_rec(t, c, h) |] ==> j(Lf) = c";
-by (rewtac rew);
-by (rtac bt_rec_Lf 1);
-val def_bt_rec_Lf = result();
-
-val [rew] = goal BT_Fn.thy
- "[| !!t. j(t)==bt_rec(t, c, h) |] ==> j(Br(a,l,r)) = h(a,l,r,j(l),j(r))";
-by (rewtac rew);
-by (rtac bt_rec_Br 1);
-val def_bt_rec_Br = result();
-
-fun bt_recs def = map standard ([def] RL [def_bt_rec_Lf, def_bt_rec_Br]);
-
-(** n_nodes **)
-
-val [n_nodes_Lf,n_nodes_Br] = bt_recs n_nodes_def;
-
-val prems = goalw BT_Fn.thy [n_nodes_def]
- "xs: bt(A) ==> n_nodes(xs) : nat";
-by (REPEAT (ares_tac (prems @ [bt_rec_type, nat_0I, nat_succI, add_type]) 1));
-val n_nodes_type = result();
-
-
-(** n_leaves **)
-
-val [n_leaves_Lf,n_leaves_Br] = bt_recs n_leaves_def;
-
-val prems = goalw BT_Fn.thy [n_leaves_def]
- "xs: bt(A) ==> n_leaves(xs) : nat";
-by (REPEAT (ares_tac (prems @ [bt_rec_type, nat_0I, nat_succI, add_type]) 1));
-val n_leaves_type = result();
-
-(** bt_reflect **)
-
-val [bt_reflect_Lf, bt_reflect_Br] = bt_recs bt_reflect_def;
-
-val prems = goalw BT_Fn.thy [bt_reflect_def]
- "xs: bt(A) ==> bt_reflect(xs) : bt(A)";
-by (REPEAT (ares_tac (prems @ [bt_rec_type, LfI, BrI]) 1));
-val bt_reflect_type = result();
-
-
-(** BT_Fn simplification **)
-
-
-val bt_typechecks =
- [LfI, BrI, bt_rec_type, n_nodes_type, n_leaves_type, bt_reflect_type];
-
-val bt_ss = arith_ss
- addsimps BT.case_eqns
- addsimps bt_typechecks
- addsimps [bt_rec_Lf, bt_rec_Br,
- n_nodes_Lf, n_nodes_Br,
- n_leaves_Lf, n_leaves_Br,
- bt_reflect_Lf, bt_reflect_Br];
-
-
-(*** theorems about n_leaves ***)
-
-val prems = goal BT_Fn.thy
- "t: bt(A) ==> n_leaves(bt_reflect(t)) = n_leaves(t)";
-by (bt_ind_tac "t" prems 1);
-by (ALLGOALS (asm_simp_tac bt_ss));
-by (REPEAT (ares_tac [add_commute, n_leaves_type] 1));
-val n_leaves_reflect = result();
-
-val prems = goal BT_Fn.thy
- "t: bt(A) ==> n_leaves(t) = succ(n_nodes(t))";
-by (bt_ind_tac "t" prems 1);
-by (ALLGOALS (asm_simp_tac (bt_ss addsimps [add_succ_right])));
-val n_leaves_nodes = result();
-
-(*** theorems about bt_reflect ***)
-
-val prems = goal BT_Fn.thy
- "t: bt(A) ==> bt_reflect(bt_reflect(t))=t";
-by (bt_ind_tac "t" prems 1);
-by (ALLGOALS (asm_simp_tac bt_ss));
-val bt_reflect_bt_reflect_ident = result();
-
-