--- a/src/HOL/List.ML Fri Feb 06 11:18:29 1998 +0100
+++ b/src/HOL/List.ML Fri Feb 06 18:55:18 1998 +0100
@@ -350,6 +350,19 @@
qed "set_map";
Addsimps [set_map];
+goal thy "set(map f xs) = f``(set xs)";
+by (induct_tac "xs" 1);
+by (ALLGOALS Asm_simp_tac);
+qed "set_map";
+Addsimps [set_map];
+
+goal thy "(x : set(filter P xs)) = (x : set xs & P x)";
+by (induct_tac "xs" 1);
+by (ALLGOALS (asm_simp_tac (simpset() addsplits [expand_if])));
+by(Blast_tac 1);
+qed "in_set_filter";
+Addsimps [in_set_filter];
+
(** list_all **)
@@ -384,10 +397,22 @@
qed "filter_append";
Addsimps [filter_append];
-goal thy "size (filter P xs) <= size xs";
+goal thy "filter (%x. True) xs = xs";
+by (induct_tac "xs" 1);
+by (ALLGOALS Asm_simp_tac);
+qed "filter_True";
+Addsimps [filter_True];
+
+goal thy "filter (%x. False) xs = []";
+by (induct_tac "xs" 1);
+by (ALLGOALS Asm_simp_tac);
+qed "filter_False";
+Addsimps [filter_False];
+
+goal thy "length (filter P xs) <= length xs";
by (induct_tac "xs" 1);
by (ALLGOALS (asm_simp_tac (simpset() addsplits [expand_if])));
-qed "filter_size";
+qed "length_filter";
(** concat **)
@@ -715,6 +740,30 @@
qed_goal "zip_Nil_Nil" thy "zip [] [] = []" (K [Simp_tac 1]);
qed_goal "zip_Cons_Cons" thy "zip (x#xs) (y#ys) = (x,y)#zip xs ys"
(K [Simp_tac 1]);
+
+(** nodups & remdups **)
+section "nodups & remdups";
+
+goal thy "set(remdups xs) = set xs";
+by (induct_tac "xs" 1);
+ by (Simp_tac 1);
+by (asm_full_simp_tac (simpset() addsimps [insert_absorb]
+ addsplits [expand_if]) 1);
+qed "set_remdups";
+Addsimps [set_remdups];
+
+goal thy "nodups(remdups xs)";
+by (induct_tac "xs" 1);
+ by (Simp_tac 1);
+by (asm_full_simp_tac (simpset() addsplits [expand_if]) 1);
+qed "nodups_remdups";
+
+goal thy "nodups xs --> nodups (filter P xs)";
+by (induct_tac "xs" 1);
+ by (Simp_tac 1);
+by (asm_full_simp_tac (simpset() addsplits [expand_if]) 1);
+qed_spec_mp "nodups_filter";
+
(** replicate **)
section "replicate";
--- a/src/HOL/List.thy Fri Feb 06 11:18:29 1998 +0100
+++ b/src/HOL/List.thy Fri Feb 06 18:55:18 1998 +0100
@@ -27,7 +27,8 @@
tl, butlast :: 'a list => 'a list
rev :: 'a list => 'a list
zip :: "'a list => 'b list => ('a * 'b) list"
- nodup :: "'a list => bool"
+ remdups :: 'a list => 'a list
+ nodups :: "'a list => bool"
replicate :: nat => 'a => 'a list
syntax
@@ -117,9 +118,12 @@
primrec zip list
"zip xs [] = []"
"zip xs (y#ys) = (hd xs,y)#zip (tl xs) ys"
-primrec nodup list
- "nodup [] = True"
- "nodup (x#xs) = (x ~: set xs & nodup xs)"
+primrec nodups list
+ "nodups [] = True"
+ "nodups (x#xs) = (x ~: set xs & nodups xs)"
+primrec remdups list
+ "remdups [] = []"
+ "remdups (x#xs) = (if x : set xs then remdups xs else x # remdups xs)"
primrec replicate nat
replicate_0 "replicate 0 x = []"
replicate_Suc "replicate (Suc n) x = x # replicate n x"
--- a/src/HOL/equalities.ML Fri Feb 06 11:18:29 1998 +0100
+++ b/src/HOL/equalities.ML Fri Feb 06 18:55:18 1998 +0100
@@ -45,6 +45,9 @@
goal thy "!!a. a:A ==> insert a A = A";
by (Blast_tac 1);
qed "insert_absorb";
+(* Addsimps [insert_absorb] causes recursive (ie quadtratic) calls
+ in case of nested inserts!
+*)
goal thy "insert x (insert x A) = insert x A";
by (Blast_tac 1);