--- a/src/HOL/Data_Structures/AA_Map.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/AA_Map.thy Thu Jun 14 14:23:48 2018 +0100
@@ -207,10 +207,10 @@
post_split_max post_delete split_maxD split: prod.splits)
interpretation I: Map_by_Ordered
-where empty = Leaf and lookup = lookup and update = update and delete = delete
+where empty = empty and lookup = lookup and update = update and delete = delete
and inorder = inorder and inv = invar
proof (standard, goal_cases)
- case 1 show ?case by simp
+ case 1 show ?case by (simp add: empty_def)
next
case 2 thus ?case by(simp add: lookup_map_of)
next
@@ -218,7 +218,7 @@
next
case 4 thus ?case by(simp add: inorder_delete)
next
- case 5 thus ?case by(simp)
+ case 5 thus ?case by(simp add: empty_def)
next
case 6 thus ?case by(simp add: invar_update)
next
--- a/src/HOL/Data_Structures/AA_Set.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/AA_Set.thy Thu Jun 14 14:23:48 2018 +0100
@@ -12,6 +12,9 @@
type_synonym 'a aa_tree = "('a,nat) tree"
+definition empty :: "'a aa_tree" where
+"empty = Leaf"
+
fun lvl :: "'a aa_tree \<Rightarrow> nat" where
"lvl Leaf = 0" |
"lvl (Node _ _ lv _) = lv"
@@ -482,11 +485,11 @@
(auto simp: del_list_simps inorder_adjust pre_adj_if_postL pre_adj_if_postR
post_split_max post_delete split_maxD split: prod.splits)
-interpretation I: Set_by_Ordered
-where empty = Leaf and isin = isin and insert = insert and delete = delete
+interpretation S: Set_by_Ordered
+where empty = empty and isin = isin and insert = insert and delete = delete
and inorder = inorder and inv = invar
proof (standard, goal_cases)
- case 1 show ?case by simp
+ case 1 show ?case by (simp add: empty_def)
next
case 2 thus ?case by(simp add: isin_set_inorder)
next
@@ -494,7 +497,7 @@
next
case 4 thus ?case by(simp add: inorder_delete)
next
- case 5 thus ?case by(simp)
+ case 5 thus ?case by(simp add: empty_def)
next
case 6 thus ?case by(simp add: invar_insert)
next
--- a/src/HOL/Data_Structures/AVL_Map.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/AVL_Map.thy Thu Jun 14 14:23:48 2018 +0100
@@ -180,11 +180,11 @@
qed simp_all
-interpretation Map_by_Ordered
-where empty = Leaf and lookup = lookup and update = update and delete = delete
+interpretation M: Map_by_Ordered
+where empty = empty and lookup = lookup and update = update and delete = delete
and inorder = inorder and inv = avl
proof (standard, goal_cases)
- case 1 show ?case by simp
+ case 1 show ?case by (simp add: empty_def)
next
case 2 thus ?case by(simp add: lookup_map_of)
next
@@ -192,7 +192,7 @@
next
case 4 thus ?case by(simp add: inorder_delete)
next
- case 5 show ?case by simp
+ case 5 show ?case by (simp add: empty_def)
next
case 6 thus ?case by(simp add: avl_update(1))
next
--- a/src/HOL/Data_Structures/AVL_Set.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/AVL_Set.thy Thu Jun 14 14:23:48 2018 +0100
@@ -14,6 +14,9 @@
type_synonym 'a avl_tree = "('a,nat) tree"
+definition empty :: "'a avl_tree" where
+"empty = Leaf"
+
text \<open>Invariant:\<close>
fun avl :: "'a avl_tree \<Rightarrow> bool" where
@@ -420,11 +423,11 @@
subsection "Overall correctness"
-interpretation Set_by_Ordered
-where empty = Leaf and isin = isin and insert = insert and delete = delete
+interpretation S: Set_by_Ordered
+where empty = empty and isin = isin and insert = insert and delete = delete
and inorder = inorder and inv = avl
proof (standard, goal_cases)
- case 1 show ?case by simp
+ case 1 show ?case by (simp add: empty_def)
next
case 2 thus ?case by(simp add: isin_set_inorder)
next
@@ -432,7 +435,7 @@
next
case 4 thus ?case by(simp add: inorder_delete)
next
- case 5 thus ?case by simp
+ case 5 thus ?case by (simp add: empty_def)
next
case 6 thus ?case by (simp add: avl_insert(1))
next
--- a/src/HOL/Data_Structures/Brother12_Map.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/Brother12_Map.thy Thu Jun 14 14:23:48 2018 +0100
@@ -192,7 +192,7 @@
subsection "Overall correctness"
interpretation Map_by_Ordered
-where empty = N0 and lookup = lookup and update = update.update
+where empty = empty and lookup = lookup and update = update.update
and delete = delete.delete and inorder = inorder and inv = "\<lambda>t. \<exists>h. t \<in> B h"
proof (standard, goal_cases)
case 2 thus ?case by(auto intro!: lookup_map_of)
@@ -204,6 +204,6 @@
case 6 thus ?case using update.update_type by (metis Un_iff)
next
case 7 thus ?case using delete.delete_type by blast
-qed auto
+qed (auto simp: empty_def)
end
--- a/src/HOL/Data_Structures/Brother12_Set.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/Brother12_Set.thy Thu Jun 14 14:23:48 2018 +0100
@@ -19,6 +19,9 @@
L2 'a |
N3 "'a bro" 'a "'a bro" 'a "'a bro"
+definition empty :: "'a bro" where
+"empty = N0"
+
fun inorder :: "'a bro \<Rightarrow> 'a list" where
"inorder N0 = []" |
"inorder (N1 t) = inorder t" |
@@ -465,7 +468,7 @@
subsection "Overall correctness"
interpretation Set_by_Ordered
-where empty = N0 and isin = isin and insert = insert.insert
+where empty = empty and isin = isin and insert = insert.insert
and delete = delete.delete and inorder = inorder and inv = "\<lambda>t. \<exists>h. t \<in> B h"
proof (standard, goal_cases)
case 2 thus ?case by(auto intro!: isin_set)
@@ -477,7 +480,7 @@
case 6 thus ?case using insert.insert_type by blast
next
case 7 thus ?case using delete.delete_type by blast
-qed auto
+qed (auto simp: empty_def)
subsection \<open>Height-Size Relation\<close>
--- a/src/HOL/Data_Structures/Map_Specs.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/Map_Specs.thy Thu Jun 14 14:23:48 2018 +0100
@@ -31,36 +31,41 @@
fixes lookup :: "'t \<Rightarrow> 'a \<Rightarrow> 'b option"
fixes inorder :: "'t \<Rightarrow> ('a * 'b) list"
fixes inv :: "'t \<Rightarrow> bool"
-assumes empty: "inorder empty = []"
-and lookup: "inv t \<and> sorted1 (inorder t) \<Longrightarrow>
+assumes inorder_empty: "inorder empty = []"
+and inorder_lookup: "inv t \<and> sorted1 (inorder t) \<Longrightarrow>
lookup t a = map_of (inorder t) a"
-and update: "inv t \<and> sorted1 (inorder t) \<Longrightarrow>
+and inorder_update: "inv t \<and> sorted1 (inorder t) \<Longrightarrow>
inorder(update a b t) = upd_list a b (inorder t)"
-and delete: "inv t \<and> sorted1 (inorder t) \<Longrightarrow>
+and inorder_delete: "inv t \<and> sorted1 (inorder t) \<Longrightarrow>
inorder(delete a t) = del_list a (inorder t)"
-and inv_empty: "inv empty"
-and inv_update: "inv t \<and> sorted1 (inorder t) \<Longrightarrow> inv(update a b t)"
-and inv_delete: "inv t \<and> sorted1 (inorder t) \<Longrightarrow> inv(delete a t)"
+and inorder_inv_empty: "inv empty"
+and inorder_inv_update: "inv t \<and> sorted1 (inorder t) \<Longrightarrow> inv(update a b t)"
+and inorder_inv_delete: "inv t \<and> sorted1 (inorder t) \<Longrightarrow> inv(delete a t)"
begin
text \<open>It implements the traditional specification:\<close>
+definition invar :: "'t \<Rightarrow> bool" where
+"invar t == inv t \<and> sorted1 (inorder t)"
+
sublocale Map
- empty update delete lookup "\<lambda>t. inv t \<and> sorted1 (inorder t)"
+ empty update delete lookup invar
proof(standard, goal_cases)
- case 1 show ?case by (auto simp: lookup empty inv_empty)
+ case 1 show ?case by (auto simp: inorder_lookup inorder_empty inorder_inv_empty)
next
case 2 thus ?case
- by(simp add: fun_eq_iff update inv_update map_of_ins_list lookup sorted_upd_list)
+ by(simp add: fun_eq_iff inorder_update inorder_inv_update map_of_ins_list inorder_lookup
+ sorted_upd_list invar_def)
next
case 3 thus ?case
- by(simp add: fun_eq_iff delete inv_delete map_of_del_list lookup sorted_del_list)
-next
- case 4 thus ?case by(simp add: empty inv_empty)
+ by(simp add: fun_eq_iff inorder_delete inorder_inv_delete map_of_del_list inorder_lookup
+ sorted_del_list invar_def)
next
- case 5 thus ?case by(simp add: update inv_update sorted_upd_list)
+ case 4 thus ?case by(simp add: inorder_empty inorder_inv_empty invar_def)
next
- case 6 thus ?case by (auto simp: delete inv_delete sorted_del_list)
+ case 5 thus ?case by(simp add: inorder_update inorder_inv_update sorted_upd_list invar_def)
+next
+ case 6 thus ?case by (auto simp: inorder_delete inorder_inv_delete sorted_del_list invar_def)
qed
end
--- a/src/HOL/Data_Structures/RBT_Map.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/RBT_Map.thy Thu Jun 14 14:23:48 2018 +0100
@@ -104,11 +104,11 @@
theorem rbt_delete: "rbt t \<Longrightarrow> rbt (delete k t)"
by (metis delete_def rbt_def color_paint_Black del_invc_invh invc_paint_Black invc2I invh_paint)
-interpretation Map_by_Ordered
-where empty = Leaf and lookup = lookup and update = update and delete = delete
+interpretation M: Map_by_Ordered
+where empty = empty and lookup = lookup and update = update and delete = delete
and inorder = inorder and inv = rbt
proof (standard, goal_cases)
- case 1 show ?case by simp
+ case 1 show ?case by (simp add: empty_def)
next
case 2 thus ?case by(simp add: lookup_map_of)
next
@@ -116,7 +116,7 @@
next
case 4 thus ?case by(simp add: inorder_delete)
next
- case 5 thus ?case by (simp add: rbt_Leaf)
+ case 5 thus ?case by (simp add: rbt_def empty_def)
next
case 6 thus ?case by (simp add: rbt_update)
next
--- a/src/HOL/Data_Structures/RBT_Set.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/RBT_Set.thy Thu Jun 14 14:23:48 2018 +0100
@@ -10,6 +10,9 @@
Isin2
begin
+definition empty :: "'a rbt" where
+"empty = Leaf"
+
fun ins :: "'a::linorder \<Rightarrow> 'a rbt \<Rightarrow> 'a rbt" where
"ins x Leaf = R Leaf x Leaf" |
"ins x (B l a r) =
@@ -121,9 +124,6 @@
lemma color_paint_Black: "color (paint Black t) = Black"
by (cases t) auto
-theorem rbt_Leaf: "rbt Leaf"
-by (simp add: rbt_def)
-
lemma paint_invc2: "invc2 t \<Longrightarrow> invc2 (paint c t)"
by (cases t) auto
@@ -256,11 +256,11 @@
text \<open>Overall correctness:\<close>
-interpretation Set_by_Ordered
-where empty = Leaf and isin = isin and insert = insert and delete = delete
+interpretation S: Set_by_Ordered
+where empty = empty and isin = isin and insert = insert and delete = delete
and inorder = inorder and inv = rbt
proof (standard, goal_cases)
- case 1 show ?case by simp
+ case 1 show ?case by (simp add: empty_def)
next
case 2 thus ?case by(simp add: isin_set_inorder)
next
@@ -268,7 +268,7 @@
next
case 4 thus ?case by(simp add: inorder_delete)
next
- case 5 thus ?case by (simp add: rbt_Leaf)
+ case 5 thus ?case by (simp add: rbt_def empty_def)
next
case 6 thus ?case by (simp add: rbt_insert)
next
--- a/src/HOL/Data_Structures/Set_Specs.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/Set_Specs.thy Thu Jun 14 14:23:48 2018 +0100
@@ -33,37 +33,43 @@
fixes isin :: "'t \<Rightarrow> 'a \<Rightarrow> bool"
fixes inorder :: "'t \<Rightarrow> 'a list"
fixes inv :: "'t \<Rightarrow> bool"
-assumes empty: "inorder empty = []"
+assumes inorder_empty: "inorder empty = []"
assumes isin: "inv t \<and> sorted(inorder t) \<Longrightarrow>
isin t x = (x \<in> set (inorder t))"
-assumes insert: "inv t \<and> sorted(inorder t) \<Longrightarrow>
+assumes inorder_insert: "inv t \<and> sorted(inorder t) \<Longrightarrow>
inorder(insert x t) = ins_list x (inorder t)"
-assumes delete: "inv t \<and> sorted(inorder t) \<Longrightarrow>
+assumes inorder_delete: "inv t \<and> sorted(inorder t) \<Longrightarrow>
inorder(delete x t) = del_list x (inorder t)"
-assumes inv_empty: "inv empty"
-assumes inv_insert: "inv t \<and> sorted(inorder t) \<Longrightarrow> inv(insert x t)"
-assumes inv_delete: "inv t \<and> sorted(inorder t) \<Longrightarrow> inv(delete x t)"
+assumes inorder_inv_empty: "inv empty"
+assumes inorder_inv_insert: "inv t \<and> sorted(inorder t) \<Longrightarrow> inv(insert x t)"
+assumes inorder_inv_delete: "inv t \<and> sorted(inorder t) \<Longrightarrow> inv(delete x t)"
begin
text \<open>It implements the traditional specification:\<close>
+definition set :: "'t \<Rightarrow> 'a set" where
+"set == List.set o inorder"
+
+definition invar :: "'t \<Rightarrow> bool" where
+"invar t == inv t \<and> sorted (inorder t)"
+
sublocale Set
- empty insert delete isin "set o inorder" "\<lambda>t. inv t \<and> sorted(inorder t)"
+ empty insert delete isin set invar
proof(standard, goal_cases)
- case 1 show ?case by (auto simp: empty)
+ case 1 show ?case by (auto simp: inorder_empty set_def)
next
- case 2 thus ?case by(simp add: isin)
+ case 2 thus ?case by(simp add: isin invar_def set_def)
next
- case 3 thus ?case by(simp add: insert set_ins_list)
+ case 3 thus ?case by(simp add: inorder_insert set_ins_list set_def invar_def)
next
case (4 s x) thus ?case
- using delete[OF 4, of x] by (auto simp: distinct_if_sorted set_del_list_eq)
+ by (auto simp: inorder_delete distinct_if_sorted set_del_list_eq invar_def set_def)
next
- case 5 thus ?case by(simp add: empty inv_empty)
+ case 5 thus ?case by(simp add: inorder_empty inorder_inv_empty invar_def)
next
- case 6 thus ?case by(simp add: insert inv_insert sorted_ins_list)
+ case 6 thus ?case by(simp add: inorder_insert inorder_inv_insert sorted_ins_list invar_def)
next
- case 7 thus ?case by (auto simp: delete inv_delete sorted_del_list)
+ case 7 thus ?case by (auto simp: inorder_delete inorder_inv_delete sorted_del_list invar_def)
qed
end
--- a/src/HOL/Data_Structures/Tree234_Map.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/Tree234_Map.thy Thu Jun 14 14:23:48 2018 +0100
@@ -160,8 +160,8 @@
subsection \<open>Overall Correctness\<close>
-interpretation Map_by_Ordered
-where empty = Leaf and lookup = lookup and update = update and delete = delete
+interpretation M: Map_by_Ordered
+where empty = empty and lookup = lookup and update = update and delete = delete
and inorder = inorder and inv = bal
proof (standard, goal_cases)
case 2 thus ?case by(simp add: lookup_map_of)
@@ -173,6 +173,6 @@
case 6 thus ?case by(simp add: bal_update)
next
case 7 thus ?case by(simp add: bal_delete)
-qed simp+
+qed (simp add: empty_def)+
end
--- a/src/HOL/Data_Structures/Tree234_Set.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/Tree234_Set.thy Thu Jun 14 14:23:48 2018 +0100
@@ -13,6 +13,9 @@
subsection \<open>Set operations on 2-3-4 trees\<close>
+definition empty :: "'a tree234" where
+"empty = Leaf"
+
fun isin :: "'a::linorder tree234 \<Rightarrow> 'a \<Rightarrow> bool" where
"isin Leaf x = False" |
"isin (Node2 l a r) x =
@@ -501,8 +504,8 @@
subsection \<open>Overall Correctness\<close>
-interpretation Set_by_Ordered
-where empty = Leaf and isin = isin and insert = insert and delete = delete
+interpretation S: Set_by_Ordered
+where empty = empty and isin = isin and insert = insert and delete = delete
and inorder = inorder and inv = bal
proof (standard, goal_cases)
case 2 thus ?case by(simp add: isin_set)
@@ -514,6 +517,6 @@
case 6 thus ?case by(simp add: bal_insert)
next
case 7 thus ?case by(simp add: bal_delete)
-qed simp+
+qed (simp add: empty_def)+
end
--- a/src/HOL/Data_Structures/Tree23_Map.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/Tree23_Map.thy Thu Jun 14 14:23:48 2018 +0100
@@ -119,19 +119,23 @@
subsection \<open>Overall Correctness\<close>
-interpretation Map_by_Ordered
-where empty = Leaf and lookup = lookup and update = update and delete = delete
+interpretation M: Map_by_Ordered
+where empty = empty and lookup = lookup and update = update and delete = delete
and inorder = inorder and inv = bal
proof (standard, goal_cases)
+ case 1 thus ?case by(simp add: empty_def)
+next
case 2 thus ?case by(simp add: lookup_map_of)
next
case 3 thus ?case by(simp add: inorder_update)
next
case 4 thus ?case by(simp add: inorder_delete)
next
+ case 5 thus ?case by(simp add: empty_def)
+next
case 6 thus ?case by(simp add: bal_update)
next
case 7 thus ?case by(simp add: bal_delete)
-qed simp+
+qed
end
--- a/src/HOL/Data_Structures/Tree23_Set.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/Tree23_Set.thy Thu Jun 14 14:23:48 2018 +0100
@@ -11,6 +11,9 @@
declare sorted_wrt.simps(2)[simp del]
+definition empty :: "'a tree23" where
+"empty = Leaf"
+
fun isin :: "'a::linorder tree23 \<Rightarrow> 'a \<Rightarrow> bool" where
"isin Leaf x = False" |
"isin (Node2 l a r) x =
@@ -376,8 +379,8 @@
subsection \<open>Overall Correctness\<close>
-interpretation Set_by_Ordered
-where empty = Leaf and isin = isin and insert = insert and delete = delete
+interpretation S: Set_by_Ordered
+where empty = empty and isin = isin and insert = insert and delete = delete
and inorder = inorder and inv = bal
proof (standard, goal_cases)
case 2 thus ?case by(simp add: isin_set)
@@ -389,6 +392,6 @@
case 6 thus ?case by(simp add: bal_insert)
next
case 7 thus ?case by(simp add: bal_delete)
-qed simp+
+qed (simp add: empty_def)+
end
--- a/src/HOL/Data_Structures/Tree_Map.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/Tree_Map.thy Thu Jun 14 14:23:48 2018 +0100
@@ -42,11 +42,11 @@
"sorted1(inorder t) \<Longrightarrow> inorder(delete x t) = del_list x (inorder t)"
by(induction t) (auto simp: del_list_simps split_minD split: prod.splits)
-interpretation Map_by_Ordered
-where empty = Leaf and lookup = lookup and update = update and delete = delete
+interpretation M: Map_by_Ordered
+where empty = empty and lookup = lookup and update = update and delete = delete
and inorder = inorder and inv = "\<lambda>_. True"
proof (standard, goal_cases)
- case 1 show ?case by simp
+ case 1 show ?case by (simp add: empty_def)
next
case 2 thus ?case by(simp add: lookup_map_of)
next
--- a/src/HOL/Data_Structures/Tree_Set.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Data_Structures/Tree_Set.thy Thu Jun 14 14:23:48 2018 +0100
@@ -9,6 +9,9 @@
Set_Specs
begin
+definition empty :: "'a tree" where
+"empty == Leaf"
+
fun isin :: "'a::linorder tree \<Rightarrow> 'a \<Rightarrow> bool" where
"isin Leaf x = False" |
"isin (Node l a r) x =
@@ -59,11 +62,11 @@
"sorted(inorder t) \<Longrightarrow> inorder(delete x t) = del_list x (inorder t)"
by(induction t) (auto simp: del_list_simps split_minD split: prod.splits)
-interpretation Set_by_Ordered
-where empty = Leaf and isin = isin and insert = insert and delete = delete
+interpretation S: Set_by_Ordered
+where empty = empty and isin = isin and insert = insert and delete = delete
and inorder = inorder and inv = "\<lambda>_. True"
proof (standard, goal_cases)
- case 1 show ?case by simp
+ case 1 show ?case by (simp add: empty_def)
next
case 2 thus ?case by(simp add: isin_set)
next
--- a/src/HOL/Rat.thy Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Rat.thy Thu Jun 14 14:23:48 2018 +0100
@@ -710,13 +710,13 @@
lemma nonzero_of_rat_inverse: "a \<noteq> 0 \<Longrightarrow> of_rat (inverse a) = inverse (of_rat a)"
by (rule inverse_unique [symmetric]) (simp add: of_rat_mult [symmetric])
-lemma of_rat_inverse: "(of_rat (inverse a) :: 'a::{field_char_0,field}) = inverse (of_rat a)"
+lemma of_rat_inverse: "(of_rat (inverse a) :: 'a::field_char_0) = inverse (of_rat a)"
by (cases "a = 0") (simp_all add: nonzero_of_rat_inverse)
lemma nonzero_of_rat_divide: "b \<noteq> 0 \<Longrightarrow> of_rat (a / b) = of_rat a / of_rat b"
by (simp add: divide_inverse of_rat_mult nonzero_of_rat_inverse)
-lemma of_rat_divide: "(of_rat (a / b) :: 'a::{field_char_0,field}) = of_rat a / of_rat b"
+lemma of_rat_divide: "(of_rat (a / b) :: 'a::field_char_0) = of_rat a / of_rat b"
by (cases "b = 0") (simp_all add: nonzero_of_rat_divide)
lemma of_rat_power: "(of_rat (a ^ n) :: 'a::field_char_0) = of_rat a ^ n"
@@ -869,31 +869,17 @@
apply (rule of_rat_mult [symmetric])
done
-lemma nonzero_Rats_inverse: "a \<in> \<rat> \<Longrightarrow> a \<noteq> 0 \<Longrightarrow> inverse a \<in> \<rat>"
+lemma Rats_inverse [simp]: "a \<in> \<rat> \<Longrightarrow> inverse a \<in> \<rat>"
for a :: "'a::field_char_0"
apply (auto simp add: Rats_def)
apply (rule range_eqI)
- apply (erule nonzero_of_rat_inverse [symmetric])
- done
-
-lemma Rats_inverse [simp]: "a \<in> \<rat> \<Longrightarrow> inverse a \<in> \<rat>"
- for a :: "'a::{field_char_0,field}"
- apply (auto simp add: Rats_def)
- apply (rule range_eqI)
apply (rule of_rat_inverse [symmetric])
done
-lemma nonzero_Rats_divide: "a \<in> \<rat> \<Longrightarrow> b \<in> \<rat> \<Longrightarrow> b \<noteq> 0 \<Longrightarrow> a / b \<in> \<rat>"
+lemma Rats_divide [simp]: "a \<in> \<rat> \<Longrightarrow> b \<in> \<rat> \<Longrightarrow> a / b \<in> \<rat>"
for a b :: "'a::field_char_0"
apply (auto simp add: Rats_def)
apply (rule range_eqI)
- apply (erule nonzero_of_rat_divide [symmetric])
- done
-
-lemma Rats_divide [simp]: "a \<in> \<rat> \<Longrightarrow> b \<in> \<rat> \<Longrightarrow> a / b \<in> \<rat>"
- for a b :: "'a::{field_char_0, field}"
- apply (auto simp add: Rats_def)
- apply (rule range_eqI)
apply (rule of_rat_divide [symmetric])
done
--- a/src/HOL/Types_To_Sets/unoverload_type.ML Thu Jun 14 14:23:38 2018 +0100
+++ b/src/HOL/Types_To_Sets/unoverload_type.ML Thu Jun 14 14:23:48 2018 +0100
@@ -6,51 +6,58 @@
signature UNOVERLOAD_TYPE =
sig
- val unoverload_type: Context.generic -> string -> thm -> thm
- val unoverload_type_attr: string -> attribute
+ val unoverload_type: Context.generic -> indexname list -> thm -> thm
+ val unoverload_type_attr: indexname list -> attribute
end;
structure Unoverload_Type : UNOVERLOAD_TYPE =
struct
-fun those [] = []
- | those (NONE::xs) = those xs
- | those (SOME x::xs) = x::those xs
-
-fun params_of_sort context sort =
+fun internalize_sort' ctvar thm =
let
- val algebra = Sign.classes_of (Context.theory_of context)
- val params = List.concat (map (Sorts.super_classes algebra) sort) |>
- map (try (Axclass.get_info (Context.theory_of context))) |>
- those |>
- map #params |>
- List.concat
- in params end
+ val (_, thm') = Internalize_Sort.internalize_sort ctvar thm
+ val class_premise = case Thm.prems_of thm' of t::_=> t | [] =>
+ raise THM ("internalize_sort': no premise?", 0, [thm'])
+ val class_vars = Term.add_tvars class_premise []
+ val tvar = case class_vars of [x] => TVar x | _ =>
+ raise TERM ("internalize_sort': not one type class variable.", [class_premise])
+ in
+ (tvar, thm')
+ end
-fun unoverload_type context s thm =
+fun params_of_class thy class = try (Axclass.get_info thy #> #params) class |> these
+
+fun params_of_super_classes thy class =
+ Sorts.super_classes (Sign.classes_of thy) class |> maps (params_of_class thy)
+
+fun params_of_sort thy sort = maps (params_of_super_classes thy) sort
+
+fun subst_TFree n' ty' ty = map_type_tfree (fn x as (n, _) => if n = n' then ty' else TFree x) ty
+
+fun unoverload_single_type context x thm =
let
val tvars = Term.add_tvars (Thm.prop_of thm) []
val thy = Context.theory_of context
in
- case find_first (fn ((n,_), _) => n = s) tvars of NONE =>
- raise THM ("unoverload_internalize_deps: type variable ("^s^") not in theorem", 0, [thm])
+ case find_first (fn (y, _) => x = y) tvars of NONE =>
+ raise TYPE ("unoverload_type: no such type variable in theorem", [TVar (x,[])], [])
| SOME (x as (_, sort)) =>
let
- val (tvar, thm') = Internalize_Sort.internalize_sort (Thm.global_ctyp_of thy (TVar x)) thm
- val consts = params_of_sort context sort |>
- map (apsnd (map_type_tfree (fn ("'a", _) => tvar | x => TFree x)))
+ val (tvar, thm') = internalize_sort' (Thm.global_ctyp_of thy (TVar x)) thm
+ val consts = params_of_sort thy sort
+ |> map (apsnd (subst_TFree "'a" tvar) #> Const #> Thm.global_cterm_of thy)
in
- fold (fn c => Unoverloading.unoverload (Thm.global_cterm_of thy (Const c))) consts thm'
+ fold Unoverloading.unoverload consts thm'
+ |> Raw_Simplifier.norm_hhf (Context.proof_of context)
end
end
-val tyN = (Args.context -- Args.typ) >>
- (fn (_, TFree (n, _)) => n
- | (ctxt, t) => error ("Not a type variable: " ^ Syntax.string_of_typ ctxt t))
+fun unoverload_type context xs = fold (unoverload_single_type context) xs
-fun unoverload_type_attr n = Thm.rule_attribute [] (fn context => unoverload_type context n)
+fun unoverload_type_attr xs = Thm.rule_attribute [] (fn context => unoverload_type context xs)
val _ = Context.>> (Context.map_theory (Attrib.setup @{binding unoverload_type}
- (tyN >> unoverload_type_attr) "internalize a sort"))
+ (Scan.lift (Scan.repeat Args.var) >> unoverload_type_attr)
+ "internalize and unoverload type class parameters"))
end
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