--- a/src/HOL/Record.thy Mon Dec 21 08:32:03 2009 +0100
+++ b/src/HOL/Record.thy Mon Dec 21 08:32:04 2009 +0100
@@ -59,8 +59,8 @@
time as the intermediate terms are @{text "O(log(n))"} in size and
the types needed have size bounded by K. To enable this analagous
traversal, we define the functions seen below: @{text
- "istuple_fst"}, @{text "istuple_snd"}, @{text "istuple_fst_update"}
- and @{text "istuple_snd_update"}. These functions generalise tuple
+ "iso_tuple_fst"}, @{text "iso_tuple_snd"}, @{text "iso_tuple_fst_update"}
+ and @{text "iso_tuple_snd_update"}. These functions generalise tuple
operations by taking a parameter that encapsulates a tuple
isomorphism. The rewrites needed on these functions now need an
additional assumption which is that the isomorphism works.
@@ -79,278 +79,259 @@
subsection {* Operators and lemmas for types isomorphic to tuples *}
-datatype ('a, 'b, 'c) tuple_isomorphism = TupleIsomorphism "'a \<Rightarrow> 'b \<times> 'c" "'b \<times> 'c \<Rightarrow> 'a"
+datatype ('a, 'b, 'c) tuple_isomorphism = Tuple_Isomorphism "'a \<Rightarrow> 'b \<times> 'c" "'b \<times> 'c \<Rightarrow> 'a"
primrec repr :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> 'a \<Rightarrow> 'b \<times> 'c" where
- "repr (TupleIsomorphism r a) = r"
+ "repr (Tuple_Isomorphism r a) = r"
primrec abst :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> 'b \<times> 'c \<Rightarrow> 'a" where
- "abst (TupleIsomorphism r a) = a"
+ "abst (Tuple_Isomorphism r a) = a"
-definition istuple_fst :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> 'a \<Rightarrow> 'b" where
- "istuple_fst isom = fst \<circ> repr isom"
+definition iso_tuple_fst :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> 'a \<Rightarrow> 'b" where
+ "iso_tuple_fst isom = fst \<circ> repr isom"
-definition istuple_snd :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> 'a \<Rightarrow> 'c" where
- "istuple_snd isom = snd \<circ> repr isom"
+definition iso_tuple_snd :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> 'a \<Rightarrow> 'c" where
+ "iso_tuple_snd isom = snd \<circ> repr isom"
-definition istuple_fst_update :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> ('b \<Rightarrow> 'b) \<Rightarrow> ('a \<Rightarrow> 'a)" where
- "istuple_fst_update isom f = abst isom \<circ> apfst f \<circ> repr isom"
+definition iso_tuple_fst_update :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> ('b \<Rightarrow> 'b) \<Rightarrow> ('a \<Rightarrow> 'a)" where
+ "iso_tuple_fst_update isom f = abst isom \<circ> apfst f \<circ> repr isom"
-definition istuple_snd_update :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> ('c \<Rightarrow> 'c) \<Rightarrow> ('a \<Rightarrow> 'a)" where
- "istuple_snd_update isom f = abst isom \<circ> apsnd f \<circ> repr isom"
+definition iso_tuple_snd_update :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> ('c \<Rightarrow> 'c) \<Rightarrow> ('a \<Rightarrow> 'a)" where
+ "iso_tuple_snd_update isom f = abst isom \<circ> apsnd f \<circ> repr isom"
-definition istuple_cons :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> 'b \<Rightarrow> 'c \<Rightarrow> 'a" where
- "istuple_cons isom = curry (abst isom)"
+definition iso_tuple_cons :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> 'b \<Rightarrow> 'c \<Rightarrow> 'a" where
+ "iso_tuple_cons isom = curry (abst isom)"
subsection {* Logical infrastructure for records *}
-definition istuple_surjective_proof_assist :: "'a \<Rightarrow> 'b \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> bool" where
- "istuple_surjective_proof_assist x y f \<longleftrightarrow> f x = y"
+definition iso_tuple_surjective_proof_assist :: "'a \<Rightarrow> 'b \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> bool" where
+ "iso_tuple_surjective_proof_assist x y f \<longleftrightarrow> f x = y"
-definition istuple_update_accessor_cong_assist :: "(('b \<Rightarrow> 'b) \<Rightarrow> ('a \<Rightarrow> 'a)) \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> bool" where
- "istuple_update_accessor_cong_assist upd acc \<longleftrightarrow>
+definition iso_tuple_update_accessor_cong_assist :: "(('b \<Rightarrow> 'b) \<Rightarrow> ('a \<Rightarrow> 'a)) \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> bool" where
+ "iso_tuple_update_accessor_cong_assist upd acc \<longleftrightarrow>
(\<forall>f v. upd (\<lambda>x. f (acc v)) v = upd f v) \<and> (\<forall>v. upd id v = v)"
-definition istuple_update_accessor_eq_assist :: "(('b \<Rightarrow> 'b) \<Rightarrow> ('a \<Rightarrow> 'a)) \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> ('b \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b \<Rightarrow> bool" where
- "istuple_update_accessor_eq_assist upd acc v f v' x \<longleftrightarrow>
- upd f v = v' \<and> acc v = x \<and> istuple_update_accessor_cong_assist upd acc"
+definition iso_tuple_update_accessor_eq_assist :: "(('b \<Rightarrow> 'b) \<Rightarrow> ('a \<Rightarrow> 'a)) \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> ('b \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b \<Rightarrow> bool" where
+ "iso_tuple_update_accessor_eq_assist upd acc v f v' x \<longleftrightarrow>
+ upd f v = v' \<and> acc v = x \<and> iso_tuple_update_accessor_cong_assist upd acc"
lemma update_accessor_congruence_foldE:
- assumes uac: "istuple_update_accessor_cong_assist upd acc"
+ assumes uac: "iso_tuple_update_accessor_cong_assist upd acc"
and r: "r = r'" and v: "acc r' = v'"
and f: "\<And>v. v' = v \<Longrightarrow> f v = f' v"
shows "upd f r = upd f' r'"
using uac r v [symmetric]
apply (subgoal_tac "upd (\<lambda>x. f (acc r')) r' = upd (\<lambda>x. f' (acc r')) r'")
- apply (simp add: istuple_update_accessor_cong_assist_def)
+ apply (simp add: iso_tuple_update_accessor_cong_assist_def)
apply (simp add: f)
done
lemma update_accessor_congruence_unfoldE:
- "istuple_update_accessor_cong_assist upd acc \<Longrightarrow> r = r' \<Longrightarrow> acc r' = v' \<Longrightarrow> (\<And>v. v = v' \<Longrightarrow> f v = f' v)
+ "iso_tuple_update_accessor_cong_assist upd acc \<Longrightarrow> r = r' \<Longrightarrow> acc r' = v' \<Longrightarrow> (\<And>v. v = v' \<Longrightarrow> f v = f' v)
\<Longrightarrow> upd f r = upd f' r'"
apply (erule(2) update_accessor_congruence_foldE)
apply simp
done
-lemma istuple_update_accessor_cong_assist_id:
- "istuple_update_accessor_cong_assist upd acc \<Longrightarrow> upd id = id"
- by rule (simp add: istuple_update_accessor_cong_assist_def)
+lemma iso_tuple_update_accessor_cong_assist_id:
+ "iso_tuple_update_accessor_cong_assist upd acc \<Longrightarrow> upd id = id"
+ by rule (simp add: iso_tuple_update_accessor_cong_assist_def)
lemma update_accessor_noopE:
- assumes uac: "istuple_update_accessor_cong_assist upd acc"
+ assumes uac: "iso_tuple_update_accessor_cong_assist upd acc"
and acc: "f (acc x) = acc x"
shows "upd f x = x"
-using uac by (simp add: acc istuple_update_accessor_cong_assist_id [OF uac, unfolded id_def]
+using uac by (simp add: acc iso_tuple_update_accessor_cong_assist_id [OF uac, unfolded id_def]
cong: update_accessor_congruence_unfoldE [OF uac])
lemma update_accessor_noop_compE:
- assumes uac: "istuple_update_accessor_cong_assist upd acc"
+ assumes uac: "iso_tuple_update_accessor_cong_assist upd acc"
assumes acc: "f (acc x) = acc x"
shows "upd (g \<circ> f) x = upd g x"
by (simp add: acc cong: update_accessor_congruence_unfoldE[OF uac])
lemma update_accessor_cong_assist_idI:
- "istuple_update_accessor_cong_assist id id"
- by (simp add: istuple_update_accessor_cong_assist_def)
+ "iso_tuple_update_accessor_cong_assist id id"
+ by (simp add: iso_tuple_update_accessor_cong_assist_def)
lemma update_accessor_cong_assist_triv:
- "istuple_update_accessor_cong_assist upd acc \<Longrightarrow> istuple_update_accessor_cong_assist upd acc"
+ "iso_tuple_update_accessor_cong_assist upd acc \<Longrightarrow> iso_tuple_update_accessor_cong_assist upd acc"
by assumption
lemma update_accessor_accessor_eqE:
- "istuple_update_accessor_eq_assist upd acc v f v' x \<Longrightarrow> acc v = x"
- by (simp add: istuple_update_accessor_eq_assist_def)
+ "iso_tuple_update_accessor_eq_assist upd acc v f v' x \<Longrightarrow> acc v = x"
+ by (simp add: iso_tuple_update_accessor_eq_assist_def)
lemma update_accessor_updator_eqE:
- "istuple_update_accessor_eq_assist upd acc v f v' x \<Longrightarrow> upd f v = v'"
- by (simp add: istuple_update_accessor_eq_assist_def)
+ "iso_tuple_update_accessor_eq_assist upd acc v f v' x \<Longrightarrow> upd f v = v'"
+ by (simp add: iso_tuple_update_accessor_eq_assist_def)
-lemma istuple_update_accessor_eq_assist_idI:
- "v' = f v \<Longrightarrow> istuple_update_accessor_eq_assist id id v f v' v"
- by (simp add: istuple_update_accessor_eq_assist_def update_accessor_cong_assist_idI)
+lemma iso_tuple_update_accessor_eq_assist_idI:
+ "v' = f v \<Longrightarrow> iso_tuple_update_accessor_eq_assist id id v f v' v"
+ by (simp add: iso_tuple_update_accessor_eq_assist_def update_accessor_cong_assist_idI)
-lemma istuple_update_accessor_eq_assist_triv:
- "istuple_update_accessor_eq_assist upd acc v f v' x \<Longrightarrow> istuple_update_accessor_eq_assist upd acc v f v' x"
+lemma iso_tuple_update_accessor_eq_assist_triv:
+ "iso_tuple_update_accessor_eq_assist upd acc v f v' x \<Longrightarrow> iso_tuple_update_accessor_eq_assist upd acc v f v' x"
by assumption
-lemma istuple_update_accessor_cong_from_eq:
- "istuple_update_accessor_eq_assist upd acc v f v' x \<Longrightarrow> istuple_update_accessor_cong_assist upd acc"
- by (simp add: istuple_update_accessor_eq_assist_def)
-
-lemma o_eq_dest:
- "a o b = c o d \<Longrightarrow> a (b v) = c (d v)"
- apply (clarsimp simp: o_def)
- apply (erule fun_cong)
- done
+lemma iso_tuple_update_accessor_cong_from_eq:
+ "iso_tuple_update_accessor_eq_assist upd acc v f v' x \<Longrightarrow> iso_tuple_update_accessor_cong_assist upd acc"
+ by (simp add: iso_tuple_update_accessor_eq_assist_def)
-lemma o_eq_elim:
- "a o b = c o d \<Longrightarrow> ((\<And>v. a (b v) = c (d v)) \<Longrightarrow> R) \<Longrightarrow> R"
- apply (erule meta_mp)
- apply (erule o_eq_dest)
- done
+lemma iso_tuple_surjective_proof_assistI:
+ "f x = y \<Longrightarrow> iso_tuple_surjective_proof_assist x y f"
+ by (simp add: iso_tuple_surjective_proof_assist_def)
-lemma istuple_surjective_proof_assistI:
- "f x = y \<Longrightarrow> istuple_surjective_proof_assist x y f"
- by (simp add: istuple_surjective_proof_assist_def)
-
-lemma istuple_surjective_proof_assist_idE:
- "istuple_surjective_proof_assist x y id \<Longrightarrow> x = y"
- by (simp add: istuple_surjective_proof_assist_def)
+lemma iso_tuple_surjective_proof_assist_idE:
+ "iso_tuple_surjective_proof_assist x y id \<Longrightarrow> x = y"
+ by (simp add: iso_tuple_surjective_proof_assist_def)
locale isomorphic_tuple =
fixes isom :: "('a, 'b, 'c) tuple_isomorphism"
- and repr and abst
- defines "repr \<equiv> Record.repr isom"
- defines "abst \<equiv> Record.abst isom"
- assumes repr_inv: "\<And>x. abst (repr x) = x"
- assumes abst_inv: "\<And>y. repr (abst y) = y"
+ assumes repr_inv: "\<And>x. abst isom (repr isom x) = x"
+ assumes abst_inv: "\<And>y. repr isom (abst isom y) = y"
begin
lemma repr_inj:
- "repr x = repr y \<longleftrightarrow> x = y"
- apply (rule iffI, simp_all)
- apply (drule_tac f=abst in arg_cong, simp add: repr_inv)
- done
+ "repr isom x = repr isom y \<longleftrightarrow> x = y"
+ by (auto dest: arg_cong [of "repr isom x" "repr isom y" "abst isom"] simp add: repr_inv)
lemma abst_inj:
- "abst x = abst y \<longleftrightarrow> x = y"
- apply (rule iffI, simp_all)
- apply (drule_tac f=repr in arg_cong, simp add: abst_inv)
- done
+ "abst isom x = abst isom y \<longleftrightarrow> x = y"
+ by (auto dest: arg_cong [of "abst isom x" "abst isom y" "repr isom"] simp add: abst_inv)
+
+lemmas simps = Let_def repr_inv abst_inv repr_inj abst_inj
-lemmas simps = Let_def repr_inv abst_inv repr_inj abst_inj repr_def [symmetric] abst_def [symmetric]
-
-lemma istuple_access_update_fst_fst:
+lemma iso_tuple_access_update_fst_fst:
"f o h g = j o f \<Longrightarrow>
- (f o istuple_fst isom) o (istuple_fst_update isom o h) g
- = j o (f o istuple_fst isom)"
- by (clarsimp simp: istuple_fst_update_def istuple_fst_def simps
+ (f o iso_tuple_fst isom) o (iso_tuple_fst_update isom o h) g
+ = j o (f o iso_tuple_fst isom)"
+ by (clarsimp simp: iso_tuple_fst_update_def iso_tuple_fst_def simps
intro!: ext elim!: o_eq_elim)
-lemma istuple_access_update_snd_snd:
+lemma iso_tuple_access_update_snd_snd:
"f o h g = j o f \<Longrightarrow>
- (f o istuple_snd isom) o (istuple_snd_update isom o h) g
- = j o (f o istuple_snd isom)"
- by (clarsimp simp: istuple_snd_update_def istuple_snd_def simps
+ (f o iso_tuple_snd isom) o (iso_tuple_snd_update isom o h) g
+ = j o (f o iso_tuple_snd isom)"
+ by (clarsimp simp: iso_tuple_snd_update_def iso_tuple_snd_def simps
intro!: ext elim!: o_eq_elim)
-lemma istuple_access_update_fst_snd:
- "(f o istuple_fst isom) o (istuple_snd_update isom o h) g
- = id o (f o istuple_fst isom)"
- by (clarsimp simp: istuple_snd_update_def istuple_fst_def simps
+lemma iso_tuple_access_update_fst_snd:
+ "(f o iso_tuple_fst isom) o (iso_tuple_snd_update isom o h) g
+ = id o (f o iso_tuple_fst isom)"
+ by (clarsimp simp: iso_tuple_snd_update_def iso_tuple_fst_def simps
intro!: ext elim!: o_eq_elim)
-lemma istuple_access_update_snd_fst:
- "(f o istuple_snd isom) o (istuple_fst_update isom o h) g
- = id o (f o istuple_snd isom)"
- by (clarsimp simp: istuple_fst_update_def istuple_snd_def simps
+lemma iso_tuple_access_update_snd_fst:
+ "(f o iso_tuple_snd isom) o (iso_tuple_fst_update isom o h) g
+ = id o (f o iso_tuple_snd isom)"
+ by (clarsimp simp: iso_tuple_fst_update_def iso_tuple_snd_def simps
intro!: ext elim!: o_eq_elim)
-lemma istuple_update_swap_fst_fst:
+lemma iso_tuple_update_swap_fst_fst:
"h f o j g = j g o h f \<Longrightarrow>
- (istuple_fst_update isom o h) f o (istuple_fst_update isom o j) g
- = (istuple_fst_update isom o j) g o (istuple_fst_update isom o h) f"
- by (clarsimp simp: istuple_fst_update_def simps apfst_compose intro!: ext)
+ (iso_tuple_fst_update isom o h) f o (iso_tuple_fst_update isom o j) g
+ = (iso_tuple_fst_update isom o j) g o (iso_tuple_fst_update isom o h) f"
+ by (clarsimp simp: iso_tuple_fst_update_def simps apfst_compose intro!: ext)
-lemma istuple_update_swap_snd_snd:
+lemma iso_tuple_update_swap_snd_snd:
"h f o j g = j g o h f \<Longrightarrow>
- (istuple_snd_update isom o h) f o (istuple_snd_update isom o j) g
- = (istuple_snd_update isom o j) g o (istuple_snd_update isom o h) f"
- by (clarsimp simp: istuple_snd_update_def simps apsnd_compose intro!: ext)
+ (iso_tuple_snd_update isom o h) f o (iso_tuple_snd_update isom o j) g
+ = (iso_tuple_snd_update isom o j) g o (iso_tuple_snd_update isom o h) f"
+ by (clarsimp simp: iso_tuple_snd_update_def simps apsnd_compose intro!: ext)
-lemma istuple_update_swap_fst_snd:
- "(istuple_snd_update isom o h) f o (istuple_fst_update isom o j) g
- = (istuple_fst_update isom o j) g o (istuple_snd_update isom o h) f"
- by (clarsimp simp: istuple_fst_update_def istuple_snd_update_def simps intro!: ext)
+lemma iso_tuple_update_swap_fst_snd:
+ "(iso_tuple_snd_update isom o h) f o (iso_tuple_fst_update isom o j) g
+ = (iso_tuple_fst_update isom o j) g o (iso_tuple_snd_update isom o h) f"
+ by (clarsimp simp: iso_tuple_fst_update_def iso_tuple_snd_update_def simps intro!: ext)
-lemma istuple_update_swap_snd_fst:
- "(istuple_fst_update isom o h) f o (istuple_snd_update isom o j) g
- = (istuple_snd_update isom o j) g o (istuple_fst_update isom o h) f"
- by (clarsimp simp: istuple_fst_update_def istuple_snd_update_def simps intro!: ext)
+lemma iso_tuple_update_swap_snd_fst:
+ "(iso_tuple_fst_update isom o h) f o (iso_tuple_snd_update isom o j) g
+ = (iso_tuple_snd_update isom o j) g o (iso_tuple_fst_update isom o h) f"
+ by (clarsimp simp: iso_tuple_fst_update_def iso_tuple_snd_update_def simps intro!: ext)
-lemma istuple_update_compose_fst_fst:
+lemma iso_tuple_update_compose_fst_fst:
"h f o j g = k (f o g) \<Longrightarrow>
- (istuple_fst_update isom o h) f o (istuple_fst_update isom o j) g
- = (istuple_fst_update isom o k) (f o g)"
- by (clarsimp simp: istuple_fst_update_def simps apfst_compose intro!: ext)
+ (iso_tuple_fst_update isom o h) f o (iso_tuple_fst_update isom o j) g
+ = (iso_tuple_fst_update isom o k) (f o g)"
+ by (clarsimp simp: iso_tuple_fst_update_def simps apfst_compose intro!: ext)
-lemma istuple_update_compose_snd_snd:
+lemma iso_tuple_update_compose_snd_snd:
"h f o j g = k (f o g) \<Longrightarrow>
- (istuple_snd_update isom o h) f o (istuple_snd_update isom o j) g
- = (istuple_snd_update isom o k) (f o g)"
- by (clarsimp simp: istuple_snd_update_def simps apsnd_compose intro!: ext)
+ (iso_tuple_snd_update isom o h) f o (iso_tuple_snd_update isom o j) g
+ = (iso_tuple_snd_update isom o k) (f o g)"
+ by (clarsimp simp: iso_tuple_snd_update_def simps apsnd_compose intro!: ext)
-lemma istuple_surjective_proof_assist_step:
- "istuple_surjective_proof_assist v a (istuple_fst isom o f) \<Longrightarrow>
- istuple_surjective_proof_assist v b (istuple_snd isom o f)
- \<Longrightarrow> istuple_surjective_proof_assist v (istuple_cons isom a b) f"
- by (clarsimp simp: istuple_surjective_proof_assist_def simps
- istuple_fst_def istuple_snd_def istuple_cons_def)
+lemma iso_tuple_surjective_proof_assist_step:
+ "iso_tuple_surjective_proof_assist v a (iso_tuple_fst isom o f) \<Longrightarrow>
+ iso_tuple_surjective_proof_assist v b (iso_tuple_snd isom o f)
+ \<Longrightarrow> iso_tuple_surjective_proof_assist v (iso_tuple_cons isom a b) f"
+ by (clarsimp simp: iso_tuple_surjective_proof_assist_def simps
+ iso_tuple_fst_def iso_tuple_snd_def iso_tuple_cons_def)
-lemma istuple_fst_update_accessor_cong_assist:
- assumes "istuple_update_accessor_cong_assist f g"
- shows "istuple_update_accessor_cong_assist (istuple_fst_update isom o f) (g o istuple_fst isom)"
+lemma iso_tuple_fst_update_accessor_cong_assist:
+ assumes "iso_tuple_update_accessor_cong_assist f g"
+ shows "iso_tuple_update_accessor_cong_assist (iso_tuple_fst_update isom o f) (g o iso_tuple_fst isom)"
proof -
- from assms have "f id = id" by (rule istuple_update_accessor_cong_assist_id)
- with assms show ?thesis by (clarsimp simp: istuple_update_accessor_cong_assist_def simps
- istuple_fst_update_def istuple_fst_def)
+ from assms have "f id = id" by (rule iso_tuple_update_accessor_cong_assist_id)
+ with assms show ?thesis by (clarsimp simp: iso_tuple_update_accessor_cong_assist_def simps
+ iso_tuple_fst_update_def iso_tuple_fst_def)
qed
-lemma istuple_snd_update_accessor_cong_assist:
- assumes "istuple_update_accessor_cong_assist f g"
- shows "istuple_update_accessor_cong_assist (istuple_snd_update isom o f) (g o istuple_snd isom)"
+lemma iso_tuple_snd_update_accessor_cong_assist:
+ assumes "iso_tuple_update_accessor_cong_assist f g"
+ shows "iso_tuple_update_accessor_cong_assist (iso_tuple_snd_update isom o f) (g o iso_tuple_snd isom)"
proof -
- from assms have "f id = id" by (rule istuple_update_accessor_cong_assist_id)
- with assms show ?thesis by (clarsimp simp: istuple_update_accessor_cong_assist_def simps
- istuple_snd_update_def istuple_snd_def)
+ from assms have "f id = id" by (rule iso_tuple_update_accessor_cong_assist_id)
+ with assms show ?thesis by (clarsimp simp: iso_tuple_update_accessor_cong_assist_def simps
+ iso_tuple_snd_update_def iso_tuple_snd_def)
qed
-lemma istuple_fst_update_accessor_eq_assist:
- assumes "istuple_update_accessor_eq_assist f g a u a' v"
- shows "istuple_update_accessor_eq_assist (istuple_fst_update isom o f) (g o istuple_fst isom)
- (istuple_cons isom a b) u (istuple_cons isom a' b) v"
+lemma iso_tuple_fst_update_accessor_eq_assist:
+ assumes "iso_tuple_update_accessor_eq_assist f g a u a' v"
+ shows "iso_tuple_update_accessor_eq_assist (iso_tuple_fst_update isom o f) (g o iso_tuple_fst isom)
+ (iso_tuple_cons isom a b) u (iso_tuple_cons isom a' b) v"
proof -
from assms have "f id = id"
- by (auto simp add: istuple_update_accessor_eq_assist_def intro: istuple_update_accessor_cong_assist_id)
- with assms show ?thesis by (clarsimp simp: istuple_update_accessor_eq_assist_def
- istuple_fst_update_def istuple_fst_def istuple_update_accessor_cong_assist_def istuple_cons_def simps)
+ by (auto simp add: iso_tuple_update_accessor_eq_assist_def intro: iso_tuple_update_accessor_cong_assist_id)
+ with assms show ?thesis by (clarsimp simp: iso_tuple_update_accessor_eq_assist_def
+ iso_tuple_fst_update_def iso_tuple_fst_def iso_tuple_update_accessor_cong_assist_def iso_tuple_cons_def simps)
qed
-lemma istuple_snd_update_accessor_eq_assist:
- assumes "istuple_update_accessor_eq_assist f g b u b' v"
- shows "istuple_update_accessor_eq_assist (istuple_snd_update isom o f) (g o istuple_snd isom)
- (istuple_cons isom a b) u (istuple_cons isom a b') v"
+lemma iso_tuple_snd_update_accessor_eq_assist:
+ assumes "iso_tuple_update_accessor_eq_assist f g b u b' v"
+ shows "iso_tuple_update_accessor_eq_assist (iso_tuple_snd_update isom o f) (g o iso_tuple_snd isom)
+ (iso_tuple_cons isom a b) u (iso_tuple_cons isom a b') v"
proof -
from assms have "f id = id"
- by (auto simp add: istuple_update_accessor_eq_assist_def intro: istuple_update_accessor_cong_assist_id)
- with assms show ?thesis by (clarsimp simp: istuple_update_accessor_eq_assist_def
- istuple_snd_update_def istuple_snd_def istuple_update_accessor_cong_assist_def istuple_cons_def simps)
+ by (auto simp add: iso_tuple_update_accessor_eq_assist_def intro: iso_tuple_update_accessor_cong_assist_id)
+ with assms show ?thesis by (clarsimp simp: iso_tuple_update_accessor_eq_assist_def
+ iso_tuple_snd_update_def iso_tuple_snd_def iso_tuple_update_accessor_cong_assist_def iso_tuple_cons_def simps)
qed
-lemma istuple_cons_conj_eqI:
+lemma iso_tuple_cons_conj_eqI:
"a = c \<and> b = d \<and> P \<longleftrightarrow> Q \<Longrightarrow>
- istuple_cons isom a b = istuple_cons isom c d \<and> P \<longleftrightarrow> Q"
- by (clarsimp simp: istuple_cons_def simps)
+ iso_tuple_cons isom a b = iso_tuple_cons isom c d \<and> P \<longleftrightarrow> Q"
+ by (clarsimp simp: iso_tuple_cons_def simps)
lemmas intros =
- istuple_access_update_fst_fst
- istuple_access_update_snd_snd
- istuple_access_update_fst_snd
- istuple_access_update_snd_fst
- istuple_update_swap_fst_fst
- istuple_update_swap_snd_snd
- istuple_update_swap_fst_snd
- istuple_update_swap_snd_fst
- istuple_update_compose_fst_fst
- istuple_update_compose_snd_snd
- istuple_surjective_proof_assist_step
- istuple_fst_update_accessor_eq_assist
- istuple_snd_update_accessor_eq_assist
- istuple_fst_update_accessor_cong_assist
- istuple_snd_update_accessor_cong_assist
- istuple_cons_conj_eqI
+ iso_tuple_access_update_fst_fst
+ iso_tuple_access_update_snd_snd
+ iso_tuple_access_update_fst_snd
+ iso_tuple_access_update_snd_fst
+ iso_tuple_update_swap_fst_fst
+ iso_tuple_update_swap_snd_snd
+ iso_tuple_update_swap_fst_snd
+ iso_tuple_update_swap_snd_fst
+ iso_tuple_update_compose_fst_fst
+ iso_tuple_update_compose_snd_snd
+ iso_tuple_surjective_proof_assist_step
+ iso_tuple_fst_update_accessor_eq_assist
+ iso_tuple_snd_update_accessor_eq_assist
+ iso_tuple_fst_update_accessor_cong_assist
+ iso_tuple_snd_update_accessor_cong_assist
+ iso_tuple_cons_conj_eqI
end
@@ -358,29 +339,32 @@
fixes repr abst
assumes repr_inj: "\<And>x y. repr x = repr y \<longleftrightarrow> x = y"
and abst_inv: "\<And>z. repr (abst z) = z"
- assumes v: "v \<equiv> TupleIsomorphism repr abst"
+ assumes v: "v \<equiv> Tuple_Isomorphism repr abst"
shows "isomorphic_tuple v"
- apply (rule isomorphic_tuple.intro)
- apply (simp_all add: abst_inv v)
- apply (cut_tac x="abst (repr x)" and y="x" in repr_inj)
- apply (simp add: abst_inv)
- done
+proof
+ have "\<And>x. repr (abst (repr x)) = repr x"
+ by (simp add: abst_inv)
+ then show "\<And>x. Record.abst v (Record.repr v x) = x"
+ by (simp add: v repr_inj)
+ show P: "\<And>y. Record.repr v (Record.abst v y) = y"
+ by (simp add: v) (fact abst_inv)
+qed
definition
- "tuple_istuple \<equiv> TupleIsomorphism id id"
+ "tuple_iso_tuple \<equiv> Tuple_Isomorphism id id"
-lemma tuple_istuple:
- "isomorphic_tuple tuple_istuple"
- by (simp add: isomorphic_tuple_intro [OF _ _ reflexive] tuple_istuple_def)
+lemma tuple_iso_tuple:
+ "isomorphic_tuple tuple_iso_tuple"
+ by (simp add: isomorphic_tuple_intro [OF _ _ reflexive] tuple_iso_tuple_def)
lemma refl_conj_eq:
"Q = R \<Longrightarrow> P \<and> Q \<longleftrightarrow> P \<and> R"
by simp
-lemma istuple_UNIV_I: "x \<in> UNIV \<equiv> True"
+lemma iso_tuple_UNIV_I: "x \<in> UNIV \<equiv> True"
by simp
-lemma istuple_True_simp: "(True \<Longrightarrow> PROP P) \<equiv> PROP P"
+lemma iso_tuple_True_simp: "(True \<Longrightarrow> PROP P) \<equiv> PROP P"
by simp
lemma prop_subst: "s = t \<Longrightarrow> PROP P t \<Longrightarrow> PROP P s"
@@ -437,9 +421,9 @@
use "Tools/record.ML"
setup Record.setup
-hide (open) const TupleIsomorphism repr abst istuple_fst istuple_snd
- istuple_fst_update istuple_snd_update istuple_cons
- istuple_surjective_proof_assist istuple_update_accessor_cong_assist
- istuple_update_accessor_eq_assist tuple_istuple
+hide (open) const Tuple_Isomorphism repr abst iso_tuple_fst iso_tuple_snd
+ iso_tuple_fst_update iso_tuple_snd_update iso_tuple_cons
+ iso_tuple_surjective_proof_assist iso_tuple_update_accessor_cong_assist
+ iso_tuple_update_accessor_eq_assist tuple_iso_tuple
end
--- a/src/HOL/Tools/record.ML Mon Dec 21 08:32:03 2009 +0100
+++ b/src/HOL/Tools/record.ML Mon Dec 21 08:32:04 2009 +0100
@@ -50,24 +50,24 @@
end;
-signature ISTUPLE_SUPPORT =
+signature ISO_TUPLE_SUPPORT =
sig
- val add_istuple_type: bstring * string list -> typ * typ -> theory -> (term * term) * theory
+ val add_iso_tuple_type: bstring * string list -> typ * typ -> theory -> (term * term) * theory
val mk_cons_tuple: term * term -> term
val dest_cons_tuple: term -> term * term
- val istuple_intros_tac: int -> tactic
+ val iso_tuple_intros_tac: int -> tactic
val named_cterm_instantiate: (string * cterm) list -> thm -> thm
end;
-structure IsTupleSupport: ISTUPLE_SUPPORT =
+structure Iso_Tuple_Support: ISO_TUPLE_SUPPORT =
struct
-val isomN = "_TupleIsom";
-
-val istuple_intro = @{thm isomorphic_tuple_intro};
-val istuple_intros = Tactic.build_net @{thms isomorphic_tuple.intros};
-
-val tuple_istuple = (@{const_name tuple_istuple}, @{thm tuple_istuple});
+val isoN = "_Tuple_Iso";
+
+val iso_tuple_intro = @{thm isomorphic_tuple_intro};
+val iso_tuple_intros = Tactic.build_net @{thms isomorphic_tuple.intros};
+
+val tuple_iso_tuple = (@{const_name tuple_iso_tuple}, @{thm tuple_iso_tuple});
fun named_cterm_instantiate values thm =
let
@@ -81,10 +81,10 @@
cterm_instantiate (map (apfst getvar) values) thm
end;
-structure IsTupleThms = Theory_Data
+structure Iso_Tuple_Thms = Theory_Data
(
type T = thm Symtab.table;
- val empty = Symtab.make [tuple_istuple];
+ val empty = Symtab.make [tuple_iso_tuple];
val extend = I;
fun merge data = Symtab.merge Thm.eq_thm_prop data; (* FIXME handle Symtab.DUP ?? *)
);
@@ -96,7 +96,7 @@
val SOME {Rep_inject = rep_inject, Abs_name = absN, abs_type = absT,
Abs_inverse = abs_inverse, ...} = Typedef.get_info thy name;
val rewrite_rule =
- MetaSimplifier.rewrite_rule [@{thm istuple_UNIV_I}, @{thm istuple_True_simp}];
+ MetaSimplifier.rewrite_rule [@{thm iso_tuple_UNIV_I}, @{thm iso_tuple_True_simp}];
in
(map rewrite_rule [rep_inject, abs_inverse], Const (absN, repT --> absT), absT)
end;
@@ -112,14 +112,14 @@
val prodT = HOLogic.mk_prodT (leftT, rightT);
val isomT = Type (@{type_name tuple_isomorphism}, [prodT, leftT, rightT]);
in
- Const (@{const_name istuple_cons}, isomT --> leftT --> rightT --> prodT) $
- Const (fst tuple_istuple, isomT) $ left $ right
+ Const (@{const_name iso_tuple_cons}, isomT --> leftT --> rightT --> prodT) $
+ Const (fst tuple_iso_tuple, isomT) $ left $ right
end;
-fun dest_cons_tuple (Const (@{const_name istuple_cons}, _) $ Const _ $ t $ u) = (t, u)
+fun dest_cons_tuple (Const (@{const_name iso_tuple_cons}, _) $ Const _ $ t $ u) = (t, u)
| dest_cons_tuple t = raise TERM ("dest_cons_tuple", [t]);
-fun add_istuple_type (name, alphas) (leftT, rightT) thy =
+fun add_iso_tuple_type (name, alphas) (leftT, rightT) thy =
let
val repT = HOLogic.mk_prodT (leftT, rightT);
@@ -131,39 +131,39 @@
(*construct a type and body for the isomorphism constant by
instantiating the theorem to which the definition will be applied*)
val intro_inst =
- rep_inject RS named_cterm_instantiate [("abst", cterm_of typ_thy absC)] istuple_intro;
+ rep_inject RS named_cterm_instantiate [("abst", cterm_of typ_thy absC)] iso_tuple_intro;
val (_, body) = Logic.dest_equals (List.last (prems_of intro_inst));
val isomT = fastype_of body;
- val isom_bind = Binding.name (name ^ isomN);
+ val isom_bind = Binding.name (name ^ isoN);
val isom_name = Sign.full_name typ_thy isom_bind;
val isom = Const (isom_name, isomT);
- val isom_spec = (Thm.def_name (name ^ isomN), Logic.mk_equals (isom, body));
+ val isom_spec = (Thm.def_name (name ^ isoN), Logic.mk_equals (isom, body));
val ([isom_def], cdef_thy) =
typ_thy
|> Sign.add_consts_i [Syntax.no_syn (isom_bind, isomT)]
|> PureThy.add_defs false [Thm.no_attributes (apfst Binding.name isom_spec)];
- val istuple = isom_def RS (abs_inverse RS (rep_inject RS istuple_intro));
- val cons = Const (@{const_name istuple_cons}, isomT --> leftT --> rightT --> absT);
+ val iso_tuple = isom_def RS (abs_inverse RS (rep_inject RS iso_tuple_intro));
+ val cons = Const (@{const_name iso_tuple_cons}, isomT --> leftT --> rightT --> absT);
val thm_thy =
cdef_thy
- |> IsTupleThms.map (Symtab.insert Thm.eq_thm_prop (isom_name, istuple))
+ |> Iso_Tuple_Thms.map (Symtab.insert Thm.eq_thm_prop (isom_name, iso_tuple))
|> Sign.parent_path
|> Code.add_default_eqn isom_def;
in
((isom, cons $ isom), thm_thy)
end;
-val istuple_intros_tac = resolve_from_net_tac istuple_intros THEN'
+val iso_tuple_intros_tac = resolve_from_net_tac iso_tuple_intros THEN'
CSUBGOAL (fn (cgoal, i) =>
let
val thy = Thm.theory_of_cterm cgoal;
val goal = Thm.term_of cgoal;
- val isthms = IsTupleThms.get thy;
- fun err s t = raise TERM ("istuple_intros_tac: " ^ s, [t]);
+ val isthms = Iso_Tuple_Thms.get thy;
+ fun err s t = raise TERM ("iso_tuple_intros_tac: " ^ s, [t]);
val goal' = Envir.beta_eta_contract goal;
val is =
@@ -197,13 +197,13 @@
val refl_conj_eq = @{thm refl_conj_eq};
-val surject_assistI = @{thm "istuple_surjective_proof_assistI"};
-val surject_assist_idE = @{thm "istuple_surjective_proof_assist_idE"};
+val surject_assistI = @{thm "iso_tuple_surjective_proof_assistI"};
+val surject_assist_idE = @{thm "iso_tuple_surjective_proof_assist_idE"};
val updacc_accessor_eqE = @{thm "update_accessor_accessor_eqE"};
val updacc_updator_eqE = @{thm "update_accessor_updator_eqE"};
-val updacc_eq_idI = @{thm "istuple_update_accessor_eq_assist_idI"};
-val updacc_eq_triv = @{thm "istuple_update_accessor_eq_assist_triv"};
+val updacc_eq_idI = @{thm "iso_tuple_update_accessor_eq_assist_idI"};
+val updacc_eq_triv = @{thm "iso_tuple_update_accessor_eq_assist_triv"};
val updacc_foldE = @{thm "update_accessor_congruence_foldE"};
val updacc_unfoldE = @{thm "update_accessor_congruence_unfoldE"};
@@ -211,7 +211,7 @@
val updacc_noop_compE = @{thm "update_accessor_noop_compE"};
val updacc_cong_idI = @{thm "update_accessor_cong_assist_idI"};
val updacc_cong_triv = @{thm "update_accessor_cong_assist_triv"};
-val updacc_cong_from_eq = @{thm "istuple_update_accessor_cong_from_eq"};
+val updacc_cong_from_eq = @{thm "iso_tuple_update_accessor_cong_from_eq"};
val o_eq_dest = @{thm o_eq_dest};
val o_eq_id_dest = @{thm o_eq_id_dest};
@@ -1066,7 +1066,7 @@
Goal.prove (ProofContext.init thy) [] [] prop
(fn _ =>
simp_tac defset 1 THEN
- REPEAT_DETERM (IsTupleSupport.istuple_intros_tac 1) THEN
+ REPEAT_DETERM (Iso_Tuple_Support.iso_tuple_intros_tac 1) THEN
TRY (simp_tac (HOL_ss addsimps id_o_apps) 1));
val dest =
if is_sel_upd_pair thy acc upd
@@ -1089,7 +1089,7 @@
Goal.prove (ProofContext.init thy) [] [] prop
(fn _ =>
simp_tac defset 1 THEN
- REPEAT_DETERM (IsTupleSupport.istuple_intros_tac 1) THEN
+ REPEAT_DETERM (Iso_Tuple_Support.iso_tuple_intros_tac 1) THEN
TRY (simp_tac (HOL_ss addsimps [id_apply]) 1));
val dest = if comp then o_eq_dest_lhs else o_eq_dest;
in Drule.standard (othm RS dest) end;
@@ -1117,7 +1117,7 @@
else swaps_needed us (u :: prev) (Symtab.insert (K true) (cname u, ()) seen) swaps;
in swaps_needed upd_funs [] Symtab.empty Symreltab.empty end;
-val named_cterm_instantiate = IsTupleSupport.named_cterm_instantiate;
+val named_cterm_instantiate = Iso_Tuple_Support.named_cterm_instantiate;
fun prove_unfold_defs thy ex_simps ex_simprs prop =
let
@@ -1222,7 +1222,7 @@
Goal.prove (ProofContext.init thy) [] [] prop
(fn _ =>
simp_tac simpset 1 THEN
- REPEAT_DETERM (IsTupleSupport.istuple_intros_tac 1) THEN
+ REPEAT_DETERM (Iso_Tuple_Support.iso_tuple_intros_tac 1) THEN
TRY (resolve_tac [updacc_cong_idI] 1))
end;
@@ -1612,22 +1612,22 @@
(*before doing anything else, create the tree of new types
that will back the record extension*)
- val mktreeV = Balanced_Tree.make IsTupleSupport.mk_cons_tuple;
-
- fun mk_istuple (left, right) (thy, i) =
+ val mktreeV = Balanced_Tree.make Iso_Tuple_Support.mk_cons_tuple;
+
+ fun mk_iso_tuple (left, right) (thy, i) =
let
val suff = if i = 0 then ext_typeN else inner_typeN ^ string_of_int i;
val nm = suffix suff (Long_Name.base_name name);
val ((_, cons), thy') =
- IsTupleSupport.add_istuple_type
+ Iso_Tuple_Support.add_iso_tuple_type
(nm, alphas_zeta) (fastype_of left, fastype_of right) thy;
in
(cons $ left $ right, (thy', i + 1))
end;
- (*trying to create a 1-element istuple will fail, and is pointless anyway*)
- fun mk_even_istuple [arg] = pair arg
- | mk_even_istuple args = mk_istuple (IsTupleSupport.dest_cons_tuple (mktreeV args));
+ (*trying to create a 1-element iso_tuple will fail, and is pointless anyway*)
+ fun mk_even_iso_tuple [arg] = pair arg
+ | mk_even_iso_tuple args = mk_iso_tuple (Iso_Tuple_Support.dest_cons_tuple (mktreeV args));
fun build_meta_tree_type i thy vars more =
let val len = length vars in
@@ -1637,12 +1637,12 @@
fun group16 [] = []
| group16 xs = take 16 xs :: group16 (drop 16 xs);
val vars' = group16 vars;
- val (composites, (thy', i')) = fold_map mk_even_istuple vars' (thy, i);
+ val (composites, (thy', i')) = fold_map mk_even_iso_tuple vars' (thy, i);
in
build_meta_tree_type i' thy' composites more
end
else
- let val (term, (thy', _)) = mk_istuple (mktreeV vars, more) (thy, 0)
+ let val (term, (thy', _)) = mk_iso_tuple (mktreeV vars, more) (thy, 0)
in (term, thy') end
end;
@@ -1712,7 +1712,7 @@
simp_tac (HOL_basic_ss addsimps [ext_def]) 1 THEN
REPEAT_DETERM
(rtac refl_conj_eq 1 ORELSE
- IsTupleSupport.istuple_intros_tac 1 ORELSE
+ Iso_Tuple_Support.iso_tuple_intros_tac 1 ORELSE
rtac refl 1)));
val inject = timeit_msg "record extension inject proof:" inject_prf;
@@ -1730,7 +1730,7 @@
val start = named_cterm_instantiate [("y", cterm_ext)] surject_assist_idE;
val tactic1 =
simp_tac (HOL_basic_ss addsimps [ext_def]) 1 THEN
- REPEAT_ALL_NEW IsTupleSupport.istuple_intros_tac 1;
+ REPEAT_ALL_NEW Iso_Tuple_Support.iso_tuple_intros_tac 1;
val tactic2 = REPEAT (rtac surject_assistI 1 THEN rtac refl 1);
val [halfway] = Seq.list_of (tactic1 start);
val [surject] = Seq.list_of (tactic2 (Drule.standard halfway));
@@ -1954,7 +1954,7 @@
val ext_defs = ext_def :: map #extdef parents;
- (*Theorems from the istuple intros.
+ (*Theorems from the iso_tuple intros.
This is complex enough to deserve a full comment.
By unfolding ext_defs from r_rec0 we create a tree of constructor
calls (many of them Pair, but others as well). The introduction
@@ -1979,7 +1979,7 @@
val terminal = rtac updacc_eq_idI 1 THEN rtac refl 1;
val tactic =
simp_tac (HOL_basic_ss addsimps ext_defs) 1 THEN
- REPEAT (IsTupleSupport.istuple_intros_tac 1 ORELSE terminal);
+ REPEAT (Iso_Tuple_Support.iso_tuple_intros_tac 1 ORELSE terminal);
val updaccs = Seq.list_of (tactic init_thm);
in
(updaccs RL [updacc_accessor_eqE],
@@ -2207,7 +2207,7 @@
[rtac surject_assist_idE 1,
simp_tac init_ss 1,
REPEAT
- (IsTupleSupport.istuple_intros_tac 1 ORELSE
+ (Iso_Tuple_Support.iso_tuple_intros_tac 1 ORELSE
(rtac surject_assistI 1 THEN simp_tac leaf_ss 1))])
end;
val surjective = timeit_msg "record surjective proof:" surjective_prf;