partially revert 0dac0158b8d4 as it too aggressively spreads card_UNIV type class whose dictionary constructions can slow down generated code;
provide better error messages instead for card and subseteq
--- a/src/HOL/Codegenerator_Test/RBT_Set_Test.thy Thu Feb 14 17:58:28 2013 +0100
+++ b/src/HOL/Codegenerator_Test/RBT_Set_Test.thy Fri Feb 15 09:41:25 2013 +0100
@@ -25,9 +25,17 @@
lemma [code, code del]:
"acc = acc" ..
-lemmas [code del] =
- finite_set_code finite_coset_code
- equal_set_code
+lemma [code, code del]:
+ "Cardinality.card' = Cardinality.card'" ..
+
+lemma [code, code del]:
+ "Cardinality.finite' = Cardinality.finite'" ..
+
+lemma [code, code del]:
+ "Cardinality.subset' = Cardinality.subset'" ..
+
+lemma [code, code del]:
+ "Cardinality.eq_set = Cardinality.eq_set" ..
(*
If the code generation ends with an exception with the following message:
--- a/src/HOL/Library/Cardinality.thy Thu Feb 14 17:58:28 2013 +0100
+++ b/src/HOL/Library/Cardinality.thy Fri Feb 15 09:41:25 2013 +0100
@@ -388,65 +388,133 @@
subsection {* Code setup for sets *}
text {*
- Implement operations @{term "finite"}, @{term "card"}, @{term "op \<subseteq>"}, and @{term "op ="}
- for sets using @{term "finite_UNIV"} and @{term "card_UNIV"}.
+ Implement @{term "CARD('a)"} via @{term card_UNIV} and provide
+ implementations for @{term "finite"}, @{term "card"}, @{term "op \<subseteq>"},
+ and @{term "op ="}if the calling context already provides @{class finite_UNIV}
+ and @{class card_UNIV} instances. If we implemented the latter
+ always via @{term card_UNIV}, we would require instances of essentially all
+ element types, i.e., a lot of instantiation proofs and -- at run time --
+ possibly slow dictionary constructions.
*}
+definition card_UNIV' :: "'a card_UNIV"
+where [code del]: "card_UNIV' = Phantom('a) CARD('a)"
+
+lemma CARD_code [code_unfold]:
+ "CARD('a) = of_phantom (card_UNIV' :: 'a card_UNIV)"
+by(simp add: card_UNIV'_def)
+
+lemma card_UNIV'_code [code]:
+ "card_UNIV' = card_UNIV"
+by(simp add: card_UNIV card_UNIV'_def)
+
+hide_const (open) card_UNIV'
+
lemma card_Compl:
"finite A \<Longrightarrow> card (- A) = card (UNIV :: 'a set) - card (A :: 'a set)"
by (metis Compl_eq_Diff_UNIV card_Diff_subset top_greatest)
-lemma card_coset_code [code]:
- fixes xs :: "'a :: card_UNIV list"
- shows "card (List.coset xs) = of_phantom (card_UNIV :: 'a card_UNIV) - length (remdups xs)"
-by(simp add: List.card_set card_Compl card_UNIV)
-
-lemma [code, code del]: "finite = finite" ..
+context fixes xs :: "'a :: finite_UNIV list"
+begin
-lemma [code]:
- fixes xs :: "'a :: card_UNIV list"
- shows finite_set_code:
- "finite (set xs) = True"
- and finite_coset_code:
- "finite (List.coset xs) \<longleftrightarrow> of_phantom (finite_UNIV :: 'a finite_UNIV)"
+definition finite' :: "'a set \<Rightarrow> bool"
+where [simp, code del, code_abbrev]: "finite' = finite"
+
+lemma finite'_code [code]:
+ "finite' (set xs) \<longleftrightarrow> True"
+ "finite' (List.coset xs) \<longleftrightarrow> of_phantom (finite_UNIV :: 'a finite_UNIV)"
by(simp_all add: card_gt_0_iff finite_UNIV)
-lemma coset_subset_code [code]:
- fixes xs :: "'a list" shows
- "List.coset xs \<subseteq> set ys \<longleftrightarrow> (let n = CARD('a) in n > 0 \<and> card (set (xs @ ys)) = n)"
+end
+
+context fixes xs :: "'a :: card_UNIV list"
+begin
+
+definition card' :: "'a set \<Rightarrow> nat"
+where [simp, code del, code_abbrev]: "card' = card"
+
+lemma card'_code [code]:
+ "card' (set xs) = length (remdups xs)"
+ "card' (List.coset xs) = of_phantom (card_UNIV :: 'a card_UNIV) - length (remdups xs)"
+by(simp_all add: List.card_set card_Compl card_UNIV)
+
+
+definition subset' :: "'a set \<Rightarrow> 'a set \<Rightarrow> bool"
+where [simp, code del, code_abbrev]: "subset' = op \<subseteq>"
+
+lemma subset'_code [code]:
+ "subset' A (List.coset ys) \<longleftrightarrow> (\<forall>y \<in> set ys. y \<notin> A)"
+ "subset' (set ys) B \<longleftrightarrow> (\<forall>y \<in> set ys. y \<in> B)"
+ "subset' (List.coset xs) (set ys) \<longleftrightarrow> (let n = CARD('a) in n > 0 \<and> card(set (xs @ ys)) = n)"
by(auto simp add: Let_def card_gt_0_iff dest: card_eq_UNIV_imp_eq_UNIV intro: arg_cong[where f=card])
(metis finite_compl finite_set rev_finite_subset)
-lemma equal_set_code [code]:
- fixes xs ys :: "'a :: equal list"
+definition eq_set :: "'a set \<Rightarrow> 'a set \<Rightarrow> bool"
+where [simp, code del, code_abbrev]: "eq_set = op ="
+
+lemma eq_set_code [code]:
+ fixes ys
defines "rhs \<equiv>
let n = CARD('a)
in if n = 0 then False else
let xs' = remdups xs; ys' = remdups ys
in length xs' + length ys' = n \<and> (\<forall>x \<in> set xs'. x \<notin> set ys') \<and> (\<forall>y \<in> set ys'. y \<notin> set xs')"
- shows "equal_class.equal (List.coset xs) (set ys) \<longleftrightarrow> rhs" (is ?thesis1)
- and "equal_class.equal (set ys) (List.coset xs) \<longleftrightarrow> rhs" (is ?thesis2)
- and "equal_class.equal (set xs) (set ys) \<longleftrightarrow> (\<forall>x \<in> set xs. x \<in> set ys) \<and> (\<forall>y \<in> set ys. y \<in> set xs)" (is ?thesis3)
- and "equal_class.equal (List.coset xs) (List.coset ys) \<longleftrightarrow> (\<forall>x \<in> set xs. x \<in> set ys) \<and> (\<forall>y \<in> set ys. y \<in> set xs)" (is ?thesis4)
+ shows "eq_set (List.coset xs) (set ys) \<longleftrightarrow> rhs" (is ?thesis1)
+ and "eq_set (set ys) (List.coset xs) \<longleftrightarrow> rhs" (is ?thesis2)
+ and "eq_set (set xs) (set ys) \<longleftrightarrow> (\<forall>x \<in> set xs. x \<in> set ys) \<and> (\<forall>y \<in> set ys. y \<in> set xs)" (is ?thesis3)
+ and "eq_set (List.coset xs) (List.coset ys) \<longleftrightarrow> (\<forall>x \<in> set xs. x \<in> set ys) \<and> (\<forall>y \<in> set ys. y \<in> set xs)" (is ?thesis4)
proof -
show ?thesis1 (is "?lhs \<longleftrightarrow> ?rhs")
proof
assume ?lhs thus ?rhs
- by(auto simp add: equal_eq rhs_def Let_def List.card_set[symmetric] card_Un_Int[where A="set xs" and B="- set xs"] card_UNIV Compl_partition card_gt_0_iff dest: sym)(metis finite_compl finite_set)
+ by(auto simp add: rhs_def Let_def List.card_set[symmetric] card_Un_Int[where A="set xs" and B="- set xs"] card_UNIV Compl_partition card_gt_0_iff dest: sym)(metis finite_compl finite_set)
next
assume ?rhs
moreover have "\<lbrakk> \<forall>y\<in>set xs. y \<notin> set ys; \<forall>x\<in>set ys. x \<notin> set xs \<rbrakk> \<Longrightarrow> set xs \<inter> set ys = {}" by blast
ultimately show ?lhs
- by(auto simp add: equal_eq rhs_def Let_def List.card_set[symmetric] card_UNIV card_gt_0_iff card_Un_Int[where A="set xs" and B="set ys"] dest: card_eq_UNIV_imp_eq_UNIV split: split_if_asm)
+ by(auto simp add: rhs_def Let_def List.card_set[symmetric] card_UNIV card_gt_0_iff card_Un_Int[where A="set xs" and B="set ys"] dest: card_eq_UNIV_imp_eq_UNIV split: split_if_asm)
qed
- thus ?thesis2 unfolding equal_eq by blast
- show ?thesis3 ?thesis4 unfolding equal_eq List.coset_def by blast+
+ thus ?thesis2 unfolding eq_set_def by blast
+ show ?thesis3 ?thesis4 unfolding eq_set_def List.coset_def by blast+
qed
-notepad begin (* test code setup *)
-have "List.coset [True] = set [False] \<and> List.coset [] \<subseteq> List.set [True, False] \<and> finite (List.coset [True])"
+end
+
+text {*
+ Provide more informative exceptions than Match for non-rewritten cases.
+ If generated code raises one these exceptions, then a code equation calls
+ the mentioned operator for an element type that is not an instance of
+ @{class card_UNIV} and is therefore not implemented via @{term card_UNIV}.
+ Constrain the element type with sort @{class card_UNIV} to change this.
+*}
+
+definition card_coset_requires_card_UNIV :: "'a list \<Rightarrow> nat"
+where [code del, simp]: "card_coset_requires_card_UNIV xs = card (List.coset xs)"
+
+code_abort card_coset_requires_card_UNIV
+
+lemma card_coset_error [code]:
+ "card (List.coset xs) = card_coset_requires_card_UNIV xs"
+by(simp)
+
+definition coset_subseteq_set_requires_card_UNIV :: "'a list \<Rightarrow> 'a list \<Rightarrow> bool"
+where [code del, simp]: "coset_subseteq_set_requires_card_UNIV xs ys \<longleftrightarrow> List.coset xs \<subseteq> set ys"
+
+code_abort coset_subseteq_set_requires_card_UNIV
+
+lemma coset_subseteq_set_code [code]:
+ "List.coset xs \<subseteq> set ys \<longleftrightarrow>
+ (if xs = [] \<and> ys = [] then False else coset_subseteq_set_requires_card_UNIV xs ys)"
+by simp
+
+notepad begin -- "test code setup"
+have "List.coset [True] = set [False] \<and>
+ List.coset [] \<subseteq> List.set [True, False] \<and>
+ finite (List.coset [True])"
by eval
end
+hide_const (open) card' finite' subset' eq_set
+
end