re-organized signature of AtpWrapper structure: records instead of unnamed parameters and return values,
eliminated unused provers,
turned references into configuration values
--- a/src/HOL/ATP_Linkup.thy Fri Oct 02 04:44:56 2009 +0200
+++ b/src/HOL/ATP_Linkup.thy Sat Oct 03 12:05:40 2009 +0200
@@ -96,29 +96,26 @@
use "Tools/res_reconstruct.ML" setup ResReconstruct.setup
use "Tools/res_atp.ML"
+use "Tools/ATP_Manager/atp_wrapper.ML" setup AtpWrapper.setup
use "Tools/ATP_Manager/atp_manager.ML"
-use "Tools/ATP_Manager/atp_wrapper.ML"
use "Tools/ATP_Manager/atp_minimal.ML"
text {* basic provers *}
-setup {* AtpManager.add_prover "spass" AtpWrapper.spass *}
-setup {* AtpManager.add_prover "vampire" AtpWrapper.vampire *}
-setup {* AtpManager.add_prover "e" AtpWrapper.eprover *}
+setup {* AtpManager.add_prover AtpWrapper.spass *}
+setup {* AtpManager.add_prover AtpWrapper.vampire *}
+setup {* AtpManager.add_prover AtpWrapper.eprover *}
text {* provers with stuctured output *}
-setup {* AtpManager.add_prover "vampire_full" AtpWrapper.vampire_full *}
-setup {* AtpManager.add_prover "e_full" AtpWrapper.eprover_full *}
+setup {* AtpManager.add_prover AtpWrapper.vampire_full *}
+setup {* AtpManager.add_prover AtpWrapper.eprover_full *}
text {* on some problems better results *}
-setup {* AtpManager.add_prover "spass_no_tc" (AtpWrapper.spass_opts 40 false) *}
+setup {* AtpManager.add_prover AtpWrapper.spass_no_tc *}
text {* remote provers via SystemOnTPTP *}
-setup {* AtpManager.add_prover "remote_vampire"
- (AtpWrapper.remote_prover_opts 60 false "" "Vampire---9") *}
-setup {* AtpManager.add_prover "remote_spass"
- (AtpWrapper.remote_prover_opts 40 true "-x" "SPASS---") *}
-setup {* AtpManager.add_prover "remote_e"
- (AtpWrapper.remote_prover_opts 100 false "" "EP---") *}
+setup {* AtpManager.add_prover AtpWrapper.remote_vampire *}
+setup {* AtpManager.add_prover AtpWrapper.remote_spass *}
+setup {* AtpManager.add_prover AtpWrapper.remote_eprover *}
--- a/src/HOL/MetisExamples/Abstraction.thy Fri Oct 02 04:44:56 2009 +0200
+++ b/src/HOL/MetisExamples/Abstraction.thy Sat Oct 03 12:05:40 2009 +0200
@@ -22,7 +22,7 @@
pset :: "'a set => 'a set"
order :: "'a set => ('a * 'a) set"
-ML{*AtpWrapper.problem_name := "Abstraction__Collect_triv"*}
+declare [[ atp_problem_prefix = "Abstraction__Collect_triv" ]]
lemma (*Collect_triv:*) "a \<in> {x. P x} ==> P a"
proof (neg_clausify)
assume 0: "(a\<Colon>'a\<Colon>type) \<in> Collect (P\<Colon>'a\<Colon>type \<Rightarrow> bool)"
@@ -37,12 +37,12 @@
by (metis mem_Collect_eq)
-ML{*AtpWrapper.problem_name := "Abstraction__Collect_mp"*}
+declare [[ atp_problem_prefix = "Abstraction__Collect_mp" ]]
lemma "a \<in> {x. P x --> Q x} ==> a \<in> {x. P x} ==> a \<in> {x. Q x}"
by (metis CollectI Collect_imp_eq ComplD UnE mem_Collect_eq);
--{*34 secs*}
-ML{*AtpWrapper.problem_name := "Abstraction__Sigma_triv"*}
+declare [[ atp_problem_prefix = "Abstraction__Sigma_triv" ]]
lemma "(a,b) \<in> Sigma A B ==> a \<in> A & b \<in> B a"
proof (neg_clausify)
assume 0: "(a\<Colon>'a\<Colon>type, b\<Colon>'b\<Colon>type) \<in> Sigma (A\<Colon>'a\<Colon>type set) (B\<Colon>'a\<Colon>type \<Rightarrow> 'b\<Colon>type set)"
@@ -60,7 +60,7 @@
lemma Sigma_triv: "(a,b) \<in> Sigma A B ==> a \<in> A & b \<in> B a"
by (metis SigmaD1 SigmaD2)
-ML{*AtpWrapper.problem_name := "Abstraction__Sigma_Collect"*}
+declare [[ atp_problem_prefix = "Abstraction__Sigma_Collect" ]]
lemma "(a,b) \<in> (SIGMA x: A. {y. x = f y}) ==> a \<in> A & a = f b"
(*???metis says this is satisfiable!
by (metis CollectD SigmaD1 SigmaD2)
@@ -112,7 +112,7 @@
qed
-ML{*AtpWrapper.problem_name := "Abstraction__CLF_eq_in_pp"*}
+declare [[ atp_problem_prefix = "Abstraction__CLF_eq_in_pp" ]]
lemma "(cl,f) \<in> CLF ==> CLF = (SIGMA cl: CL.{f. f \<in> pset cl}) ==> f \<in> pset cl"
by (metis Collect_mem_eq SigmaD2)
@@ -131,7 +131,7 @@
by (metis 5 0)
qed
-ML{*AtpWrapper.problem_name := "Abstraction__Sigma_Collect_Pi"*}
+declare [[ atp_problem_prefix = "Abstraction__Sigma_Collect_Pi" ]]
lemma
"(cl,f) \<in> (SIGMA cl: CL. {f. f \<in> pset cl \<rightarrow> pset cl}) ==>
f \<in> pset cl \<rightarrow> pset cl"
@@ -147,7 +147,7 @@
qed
-ML{*AtpWrapper.problem_name := "Abstraction__Sigma_Collect_Int"*}
+declare [[ atp_problem_prefix = "Abstraction__Sigma_Collect_Int" ]]
lemma
"(cl,f) \<in> (SIGMA cl: CL. {f. f \<in> pset cl \<inter> cl}) ==>
f \<in> pset cl \<inter> cl"
@@ -170,13 +170,13 @@
qed
-ML{*AtpWrapper.problem_name := "Abstraction__Sigma_Collect_Pi_mono"*}
+declare [[ atp_problem_prefix = "Abstraction__Sigma_Collect_Pi_mono" ]]
lemma
"(cl,f) \<in> (SIGMA cl: CL. {f. f \<in> pset cl \<rightarrow> pset cl & monotone f (pset cl) (order cl)}) ==>
(f \<in> pset cl \<rightarrow> pset cl) & (monotone f (pset cl) (order cl))"
by auto
-ML{*AtpWrapper.problem_name := "Abstraction__CLF_subset_Collect_Int"*}
+declare [[ atp_problem_prefix = "Abstraction__CLF_subset_Collect_Int" ]]
lemma "(cl,f) \<in> CLF ==>
CLF \<subseteq> (SIGMA cl: CL. {f. f \<in> pset cl \<inter> cl}) ==>
f \<in> pset cl \<inter> cl"
@@ -187,7 +187,7 @@
--{*@{text Int_def} is redundant*}
*)
-ML{*AtpWrapper.problem_name := "Abstraction__CLF_eq_Collect_Int"*}
+declare [[ atp_problem_prefix = "Abstraction__CLF_eq_Collect_Int" ]]
lemma "(cl,f) \<in> CLF ==>
CLF = (SIGMA cl: CL. {f. f \<in> pset cl \<inter> cl}) ==>
f \<in> pset cl \<inter> cl"
@@ -196,7 +196,7 @@
by (metis Collect_mem_eq Int_commute SigmaD2)
*)
-ML{*AtpWrapper.problem_name := "Abstraction__CLF_subset_Collect_Pi"*}
+declare [[ atp_problem_prefix = "Abstraction__CLF_subset_Collect_Pi" ]]
lemma
"(cl,f) \<in> CLF ==>
CLF \<subseteq> (SIGMA cl': CL. {f. f \<in> pset cl' \<rightarrow> pset cl'}) ==>
@@ -206,7 +206,7 @@
by (metis Collect_mem_eq SigmaD2 subsetD)
*)
-ML{*AtpWrapper.problem_name := "Abstraction__CLF_eq_Collect_Pi"*}
+declare [[ atp_problem_prefix = "Abstraction__CLF_eq_Collect_Pi" ]]
lemma
"(cl,f) \<in> CLF ==>
CLF = (SIGMA cl: CL. {f. f \<in> pset cl \<rightarrow> pset cl}) ==>
@@ -216,21 +216,21 @@
by (metis Collect_mem_eq SigmaD2 contra_subsetD equalityE)
*)
-ML{*AtpWrapper.problem_name := "Abstraction__CLF_eq_Collect_Pi_mono"*}
+declare [[ atp_problem_prefix = "Abstraction__CLF_eq_Collect_Pi_mono" ]]
lemma
"(cl,f) \<in> CLF ==>
CLF = (SIGMA cl: CL. {f. f \<in> pset cl \<rightarrow> pset cl & monotone f (pset cl) (order cl)}) ==>
(f \<in> pset cl \<rightarrow> pset cl) & (monotone f (pset cl) (order cl))"
by auto
-ML{*AtpWrapper.problem_name := "Abstraction__map_eq_zipA"*}
+declare [[ atp_problem_prefix = "Abstraction__map_eq_zipA" ]]
lemma "map (%x. (f x, g x)) xs = zip (map f xs) (map g xs)"
apply (induct xs)
(*sledgehammer*)
apply auto
done
-ML{*AtpWrapper.problem_name := "Abstraction__map_eq_zipB"*}
+declare [[ atp_problem_prefix = "Abstraction__map_eq_zipB" ]]
lemma "map (%w. (w -> w, w \<times> w)) xs =
zip (map (%w. w -> w) xs) (map (%w. w \<times> w) xs)"
apply (induct xs)
@@ -238,28 +238,28 @@
apply auto
done
-ML{*AtpWrapper.problem_name := "Abstraction__image_evenA"*}
+declare [[ atp_problem_prefix = "Abstraction__image_evenA" ]]
lemma "(%x. Suc(f x)) ` {x. even x} <= A ==> (\<forall>x. even x --> Suc(f x) \<in> A)";
(*sledgehammer*)
by auto
-ML{*AtpWrapper.problem_name := "Abstraction__image_evenB"*}
+declare [[ atp_problem_prefix = "Abstraction__image_evenB" ]]
lemma "(%x. f (f x)) ` ((%x. Suc(f x)) ` {x. even x}) <= A
==> (\<forall>x. even x --> f (f (Suc(f x))) \<in> A)";
(*sledgehammer*)
by auto
-ML{*AtpWrapper.problem_name := "Abstraction__image_curry"*}
+declare [[ atp_problem_prefix = "Abstraction__image_curry" ]]
lemma "f \<in> (%u v. b \<times> u \<times> v) ` A ==> \<forall>u v. P (b \<times> u \<times> v) ==> P(f y)"
(*sledgehammer*)
by auto
-ML{*AtpWrapper.problem_name := "Abstraction__image_TimesA"*}
+declare [[ atp_problem_prefix = "Abstraction__image_TimesA" ]]
lemma image_TimesA: "(%(x,y). (f x, g y)) ` (A \<times> B) = (f`A) \<times> (g`B)"
(*sledgehammer*)
apply (rule equalityI)
(***Even the two inclusions are far too difficult
-ML{*AtpWrapper.problem_name := "Abstraction__image_TimesA_simpler"*}
+using [[ atp_problem_prefix = "Abstraction__image_TimesA_simpler"]]
***)
apply (rule subsetI)
apply (erule imageE)
@@ -282,13 +282,13 @@
(*Given the difficulty of the previous problem, these two are probably
impossible*)
-ML{*AtpWrapper.problem_name := "Abstraction__image_TimesB"*}
+declare [[ atp_problem_prefix = "Abstraction__image_TimesB" ]]
lemma image_TimesB:
"(%(x,y,z). (f x, g y, h z)) ` (A \<times> B \<times> C) = (f`A) \<times> (g`B) \<times> (h`C)"
(*sledgehammer*)
by force
-ML{*AtpWrapper.problem_name := "Abstraction__image_TimesC"*}
+declare [[ atp_problem_prefix = "Abstraction__image_TimesC" ]]
lemma image_TimesC:
"(%(x,y). (x \<rightarrow> x, y \<times> y)) ` (A \<times> B) =
((%x. x \<rightarrow> x) ` A) \<times> ((%y. y \<times> y) ` B)"
--- a/src/HOL/MetisExamples/BT.thy Fri Oct 02 04:44:56 2009 +0200
+++ b/src/HOL/MetisExamples/BT.thy Sat Oct 03 12:05:40 2009 +0200
@@ -65,21 +65,21 @@
text {* \medskip BT simplification *}
-ML {*AtpWrapper.problem_name := "BT__n_leaves_reflect"*}
+declare [[ atp_problem_prefix = "BT__n_leaves_reflect" ]]
lemma n_leaves_reflect: "n_leaves (reflect t) = n_leaves t"
apply (induct t)
apply (metis add_right_cancel n_leaves.simps(1) reflect.simps(1))
apply (metis add_commute n_leaves.simps(2) reflect.simps(2))
done
-ML {*AtpWrapper.problem_name := "BT__n_nodes_reflect"*}
+declare [[ atp_problem_prefix = "BT__n_nodes_reflect" ]]
lemma n_nodes_reflect: "n_nodes (reflect t) = n_nodes t"
apply (induct t)
apply (metis reflect.simps(1))
apply (metis n_nodes.simps(2) nat_add_commute reflect.simps(2))
done
-ML {*AtpWrapper.problem_name := "BT__depth_reflect"*}
+declare [[ atp_problem_prefix = "BT__depth_reflect" ]]
lemma depth_reflect: "depth (reflect t) = depth t"
apply (induct t)
apply (metis depth.simps(1) reflect.simps(1))
@@ -90,21 +90,21 @@
The famous relationship between the numbers of leaves and nodes.
*}
-ML {*AtpWrapper.problem_name := "BT__n_leaves_nodes"*}
+declare [[ atp_problem_prefix = "BT__n_leaves_nodes" ]]
lemma n_leaves_nodes: "n_leaves t = Suc (n_nodes t)"
apply (induct t)
apply (metis n_leaves.simps(1) n_nodes.simps(1))
apply auto
done
-ML {*AtpWrapper.problem_name := "BT__reflect_reflect_ident"*}
+declare [[ atp_problem_prefix = "BT__reflect_reflect_ident" ]]
lemma reflect_reflect_ident: "reflect (reflect t) = t"
apply (induct t)
apply (metis add_right_cancel reflect.simps(1));
apply (metis reflect.simps(2))
done
-ML {*AtpWrapper.problem_name := "BT__bt_map_ident"*}
+declare [[ atp_problem_prefix = "BT__bt_map_ident" ]]
lemma bt_map_ident: "bt_map (%x. x) = (%y. y)"
apply (rule ext)
apply (induct_tac y)
@@ -115,7 +115,7 @@
done
-ML {*AtpWrapper.problem_name := "BT__bt_map_appnd"*}
+declare [[ atp_problem_prefix = "BT__bt_map_appnd" ]]
lemma bt_map_appnd: "bt_map f (appnd t u) = appnd (bt_map f t) (bt_map f u)"
apply (induct t)
apply (metis appnd.simps(1) bt_map.simps(1))
@@ -123,7 +123,7 @@
done
-ML {*AtpWrapper.problem_name := "BT__bt_map_compose"*}
+declare [[ atp_problem_prefix = "BT__bt_map_compose" ]]
lemma bt_map_compose: "bt_map (f o g) t = bt_map f (bt_map g t)"
apply (induct t)
apply (metis bt_map.simps(1))
@@ -133,42 +133,42 @@
done
-ML {*AtpWrapper.problem_name := "BT__bt_map_reflect"*}
+declare [[ atp_problem_prefix = "BT__bt_map_reflect" ]]
lemma bt_map_reflect: "bt_map f (reflect t) = reflect (bt_map f t)"
apply (induct t)
apply (metis add_right_cancel bt_map.simps(1) reflect.simps(1))
apply (metis add_right_cancel bt_map.simps(2) reflect.simps(2))
done
-ML {*AtpWrapper.problem_name := "BT__preorder_bt_map"*}
+declare [[ atp_problem_prefix = "BT__preorder_bt_map" ]]
lemma preorder_bt_map: "preorder (bt_map f t) = map f (preorder t)"
apply (induct t)
apply (metis bt_map.simps(1) map.simps(1) preorder.simps(1))
apply simp
done
-ML {*AtpWrapper.problem_name := "BT__inorder_bt_map"*}
+declare [[ atp_problem_prefix = "BT__inorder_bt_map" ]]
lemma inorder_bt_map: "inorder (bt_map f t) = map f (inorder t)"
apply (induct t)
apply (metis bt_map.simps(1) inorder.simps(1) map.simps(1))
apply simp
done
-ML {*AtpWrapper.problem_name := "BT__postorder_bt_map"*}
+declare [[ atp_problem_prefix = "BT__postorder_bt_map" ]]
lemma postorder_bt_map: "postorder (bt_map f t) = map f (postorder t)"
apply (induct t)
apply (metis bt_map.simps(1) map.simps(1) postorder.simps(1))
apply simp
done
-ML {*AtpWrapper.problem_name := "BT__depth_bt_map"*}
+declare [[ atp_problem_prefix = "BT__depth_bt_map" ]]
lemma depth_bt_map [simp]: "depth (bt_map f t) = depth t"
apply (induct t)
apply (metis bt_map.simps(1) depth.simps(1))
apply simp
done
-ML {*AtpWrapper.problem_name := "BT__n_leaves_bt_map"*}
+declare [[ atp_problem_prefix = "BT__n_leaves_bt_map" ]]
lemma n_leaves_bt_map [simp]: "n_leaves (bt_map f t) = n_leaves t"
apply (induct t)
apply (metis One_nat_def Suc_eq_plus1 bt_map.simps(1) less_add_one less_antisym linorder_neq_iff n_leaves.simps(1))
@@ -176,21 +176,21 @@
done
-ML {*AtpWrapper.problem_name := "BT__preorder_reflect"*}
+declare [[ atp_problem_prefix = "BT__preorder_reflect" ]]
lemma preorder_reflect: "preorder (reflect t) = rev (postorder t)"
apply (induct t)
apply (metis postorder.simps(1) preorder.simps(1) reflect.simps(1) rev_is_Nil_conv)
apply (metis append_Nil Cons_eq_append_conv postorder.simps(2) preorder.simps(2) reflect.simps(2) rev.simps(2) rev_append rev_rev_ident)
done
-ML {*AtpWrapper.problem_name := "BT__inorder_reflect"*}
+declare [[ atp_problem_prefix = "BT__inorder_reflect" ]]
lemma inorder_reflect: "inorder (reflect t) = rev (inorder t)"
apply (induct t)
apply (metis inorder.simps(1) reflect.simps(1) rev.simps(1))
apply simp
done
-ML {*AtpWrapper.problem_name := "BT__postorder_reflect"*}
+declare [[ atp_problem_prefix = "BT__postorder_reflect" ]]
lemma postorder_reflect: "postorder (reflect t) = rev (preorder t)"
apply (induct t)
apply (metis postorder.simps(1) preorder.simps(1) reflect.simps(1) rev.simps(1))
@@ -201,7 +201,7 @@
Analogues of the standard properties of the append function for lists.
*}
-ML {*AtpWrapper.problem_name := "BT__appnd_assoc"*}
+declare [[ atp_problem_prefix = "BT__appnd_assoc" ]]
lemma appnd_assoc [simp]:
"appnd (appnd t1 t2) t3 = appnd t1 (appnd t2 t3)"
apply (induct t1)
@@ -209,14 +209,14 @@
apply (metis appnd.simps(2))
done
-ML {*AtpWrapper.problem_name := "BT__appnd_Lf2"*}
+declare [[ atp_problem_prefix = "BT__appnd_Lf2" ]]
lemma appnd_Lf2 [simp]: "appnd t Lf = t"
apply (induct t)
apply (metis appnd.simps(1))
apply (metis appnd.simps(2))
done
-ML {*AtpWrapper.problem_name := "BT__depth_appnd"*}
+declare [[ atp_problem_prefix = "BT__depth_appnd" ]]
declare max_add_distrib_left [simp]
lemma depth_appnd [simp]: "depth (appnd t1 t2) = depth t1 + depth t2"
apply (induct t1)
@@ -224,7 +224,7 @@
apply (simp add: );
done
-ML {*AtpWrapper.problem_name := "BT__n_leaves_appnd"*}
+declare [[ atp_problem_prefix = "BT__n_leaves_appnd" ]]
lemma n_leaves_appnd [simp]:
"n_leaves (appnd t1 t2) = n_leaves t1 * n_leaves t2"
apply (induct t1)
@@ -232,7 +232,7 @@
apply (simp add: left_distrib)
done
-ML {*AtpWrapper.problem_name := "BT__bt_map_appnd"*}
+declare [[ atp_problem_prefix = "BT__bt_map_appnd" ]]
lemma (*bt_map_appnd:*)
"bt_map f (appnd t1 t2) = appnd (bt_map f t1) (bt_map f t2)"
apply (induct t1)
--- a/src/HOL/MetisExamples/BigO.thy Fri Oct 02 04:44:56 2009 +0200
+++ b/src/HOL/MetisExamples/BigO.thy Sat Oct 03 12:05:40 2009 +0200
@@ -15,7 +15,7 @@
definition bigo :: "('a => 'b::ordered_idom) => ('a => 'b) set" ("(1O'(_'))") where
"O(f::('a => 'b)) == {h. EX c. ALL x. abs (h x) <= c * abs (f x)}"
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_pos_const"*}
+declare [[ atp_problem_prefix = "BigO__bigo_pos_const" ]]
lemma bigo_pos_const: "(EX (c::'a::ordered_idom).
ALL x. (abs (h x)) <= (c * (abs (f x))))
= (EX c. 0 < c & (ALL x. (abs(h x)) <= (c * (abs (f x)))))"
@@ -212,7 +212,7 @@
{h. EX c. (0 < c & (ALL x. abs (h x) <= c * abs (f x)))}"
by (auto simp add: bigo_def bigo_pos_const)
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_elt_subset"*}
+declare [[ atp_problem_prefix = "BigO__bigo_elt_subset" ]]
lemma bigo_elt_subset [intro]: "f : O(g) ==> O(f) <= O(g)"
apply (auto simp add: bigo_alt_def)
apply (rule_tac x = "ca * c" in exI)
@@ -230,7 +230,7 @@
done
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_refl"*}
+declare [[ atp_problem_prefix = "BigO__bigo_refl" ]]
lemma bigo_refl [intro]: "f : O(f)"
apply(auto simp add: bigo_def)
proof (neg_clausify)
@@ -244,7 +244,7 @@
by (metis 0 2)
qed
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_zero"*}
+declare [[ atp_problem_prefix = "BigO__bigo_zero" ]]
lemma bigo_zero: "0 : O(g)"
apply (auto simp add: bigo_def func_zero)
proof (neg_clausify)
@@ -334,7 +334,7 @@
apply (auto del: subsetI simp del: bigo_plus_idemp)
done
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_plus_eq"*}
+declare [[ atp_problem_prefix = "BigO__bigo_plus_eq" ]]
lemma bigo_plus_eq: "ALL x. 0 <= f x ==> ALL x. 0 <= g x ==>
O(f + g) = O(f) \<oplus> O(g)"
apply (rule equalityI)
@@ -357,13 +357,13 @@
apply (rule abs_triangle_ineq)
apply (metis add_nonneg_nonneg)
apply (rule add_mono)
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_plus_eq_simpler"*}
+using [[ atp_problem_prefix = "BigO__bigo_plus_eq_simpler" ]]
(*Found by SPASS; SLOW*)
apply (metis le_maxI2 linorder_linear linorder_not_le min_max.sup_absorb1 mult_le_cancel_right order_trans)
apply (metis le_maxI2 linorder_not_le mult_le_cancel_right order_trans)
done
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_bounded_alt"*}
+declare [[ atp_problem_prefix = "BigO__bigo_bounded_alt" ]]
lemma bigo_bounded_alt: "ALL x. 0 <= f x ==> ALL x. f x <= c * g x ==>
f : O(g)"
apply (auto simp add: bigo_def)
@@ -423,7 +423,7 @@
text{*So here is the easier (and more natural) problem using transitivity*}
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_bounded_alt_trans"*}
+declare [[ atp_problem_prefix = "BigO__bigo_bounded_alt_trans" ]]
lemma "ALL x. 0 <= f x ==> ALL x. f x <= c * g x ==> f : O(g)"
apply (auto simp add: bigo_def)
(*Version 1: one-shot proof*)
@@ -431,7 +431,7 @@
done
text{*So here is the easier (and more natural) problem using transitivity*}
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_bounded_alt_trans"*}
+declare [[ atp_problem_prefix = "BigO__bigo_bounded_alt_trans" ]]
lemma "ALL x. 0 <= f x ==> ALL x. f x <= c * g x ==> f : O(g)"
apply (auto simp add: bigo_def)
(*Version 2: single-step proof*)
@@ -470,7 +470,7 @@
apply simp
done
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_bounded2"*}
+declare [[ atp_problem_prefix = "BigO__bigo_bounded2" ]]
lemma bigo_bounded2: "ALL x. lb x <= f x ==> ALL x. f x <= lb x + g x ==>
f : lb +o O(g)"
apply (rule set_minus_imp_plus)
@@ -493,7 +493,7 @@
by (metis 4 2 0)
qed
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_abs"*}
+declare [[ atp_problem_prefix = "BigO__bigo_abs" ]]
lemma bigo_abs: "(%x. abs(f x)) =o O(f)"
apply (unfold bigo_def)
apply auto
@@ -508,7 +508,7 @@
by (metis 0 2)
qed
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_abs2"*}
+declare [[ atp_problem_prefix = "BigO__bigo_abs2" ]]
lemma bigo_abs2: "f =o O(%x. abs(f x))"
apply (unfold bigo_def)
apply auto
@@ -580,7 +580,7 @@
by (simp add: bigo_abs3 [symmetric])
qed
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_mult"*}
+declare [[ atp_problem_prefix = "BigO__bigo_mult" ]]
lemma bigo_mult [intro]: "O(f)\<otimes>O(g) <= O(f * g)"
apply (rule subsetI)
apply (subst bigo_def)
@@ -592,7 +592,7 @@
apply(erule_tac x = x in allE)+
apply(subgoal_tac "c * ca * abs(f x * g x) =
(c * abs(f x)) * (ca * abs(g x))")
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_mult_simpler"*}
+using [[ atp_problem_prefix = "BigO__bigo_mult_simpler" ]]
prefer 2
apply (metis mult_assoc mult_left_commute
OrderedGroup.abs_of_pos OrderedGroup.mult_left_commute
@@ -657,14 +657,14 @@
qed
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_mult2"*}
+declare [[ atp_problem_prefix = "BigO__bigo_mult2" ]]
lemma bigo_mult2 [intro]: "f *o O(g) <= O(f * g)"
apply (auto simp add: bigo_def elt_set_times_def func_times abs_mult)
(*sledgehammer*);
apply (rule_tac x = c in exI)
apply clarify
apply (drule_tac x = x in spec)
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_mult2_simpler"*}
+using [[ atp_problem_prefix = "BigO__bigo_mult2_simpler" ]]
(*sledgehammer [no luck]*);
apply (subgoal_tac "abs(f x) * abs(b x) <= abs(f x) * (c * abs(g x))")
apply (simp add: mult_ac)
@@ -672,11 +672,11 @@
apply (rule abs_ge_zero)
done
-ML_command{*AtpWrapper.problem_name:="BigO__bigo_mult3"*}
+declare [[ atp_problem_prefix = "BigO__bigo_mult3" ]]
lemma bigo_mult3: "f : O(h) ==> g : O(j) ==> f * g : O(h * j)"
by (metis bigo_mult set_times_intro subset_iff)
-ML_command{*AtpWrapper.problem_name:="BigO__bigo_mult4"*}
+declare [[ atp_problem_prefix = "BigO__bigo_mult4" ]]
lemma bigo_mult4 [intro]:"f : k +o O(h) ==> g * f : (g * k) +o O(g * h)"
by (metis bigo_mult2 set_plus_mono_b set_times_intro2 set_times_plus_distrib)
@@ -710,13 +710,13 @@
qed
qed
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_mult6"*}
+declare [[ atp_problem_prefix = "BigO__bigo_mult6" ]]
lemma bigo_mult6: "ALL x. f x ~= 0 ==>
O(f * g) = (f::'a => ('b::ordered_field)) *o O(g)"
by (metis bigo_mult2 bigo_mult5 order_antisym)
(*proof requires relaxing relevance: 2007-01-25*)
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_mult7"*}
+declare [[ atp_problem_prefix = "BigO__bigo_mult7" ]]
declare bigo_mult6 [simp]
lemma bigo_mult7: "ALL x. f x ~= 0 ==>
O(f * g) <= O(f::'a => ('b::ordered_field)) \<otimes> O(g)"
@@ -728,7 +728,7 @@
done
declare bigo_mult6 [simp del]
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_mult8"*}
+declare [[ atp_problem_prefix = "BigO__bigo_mult8" ]]
declare bigo_mult7[intro!]
lemma bigo_mult8: "ALL x. f x ~= 0 ==>
O(f * g) = O(f::'a => ('b::ordered_field)) \<otimes> O(g)"
@@ -779,7 +779,7 @@
qed
qed
-ML_command{*AtpWrapper.problem_name:="BigO__bigo_plus_absorb"*}
+declare [[ atp_problem_prefix = "BigO__bigo_plus_absorb" ]]
lemma bigo_plus_absorb [simp]: "f : O(g) ==> f +o O(g) = O(g)"
by (metis bigo_plus_absorb_lemma1 bigo_plus_absorb_lemma2 order_eq_iff);
@@ -806,7 +806,7 @@
lemma bigo_const1: "(%x. c) : O(%x. 1)"
by (auto simp add: bigo_def mult_ac)
-ML_command{*AtpWrapper.problem_name:="BigO__bigo_const2"*}
+declare [[ atp_problem_prefix = "BigO__bigo_const2" ]]
lemma (*bigo_const2 [intro]:*) "O(%x. c) <= O(%x. 1)"
by (metis bigo_const1 bigo_elt_subset);
@@ -829,7 +829,7 @@
apply (rule bigo_const1)
done
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_const3"*}
+declare [[ atp_problem_prefix = "BigO__bigo_const3" ]]
lemma bigo_const3: "(c::'a::ordered_field) ~= 0 ==> (%x. 1) : O(%x. c)"
apply (simp add: bigo_def)
proof (neg_clausify)
@@ -853,7 +853,7 @@
O(%x. c) = O(%x. 1)"
by (rule equalityI, rule bigo_const2, rule bigo_const4, assumption)
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_const_mult1"*}
+declare [[ atp_problem_prefix = "BigO__bigo_const_mult1" ]]
lemma bigo_const_mult1: "(%x. c * f x) : O(f)"
apply (simp add: bigo_def abs_mult)
proof (neg_clausify)
@@ -869,7 +869,7 @@
lemma bigo_const_mult2: "O(%x. c * f x) <= O(f)"
by (rule bigo_elt_subset, rule bigo_const_mult1)
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_const_mult3"*}
+declare [[ atp_problem_prefix = "BigO__bigo_const_mult3" ]]
lemma bigo_const_mult3: "(c::'a::ordered_field) ~= 0 ==> f : O(%x. c * f x)"
apply (simp add: bigo_def)
(*sledgehammer [no luck]*);
@@ -887,7 +887,7 @@
O(%x. c * f x) = O(f)"
by (rule equalityI, rule bigo_const_mult2, erule bigo_const_mult4)
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_const_mult5"*}
+declare [[ atp_problem_prefix = "BigO__bigo_const_mult5" ]]
lemma bigo_const_mult5 [simp]: "(c::'a::ordered_field) ~= 0 ==>
(%x. c) *o O(f) = O(f)"
apply (auto del: subsetI)
@@ -907,7 +907,7 @@
done
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_const_mult6"*}
+declare [[ atp_problem_prefix = "BigO__bigo_const_mult6" ]]
lemma bigo_const_mult6 [intro]: "(%x. c) *o O(f) <= O(f)"
apply (auto intro!: subsetI
simp add: bigo_def elt_set_times_def func_times
@@ -964,7 +964,7 @@
apply (blast intro: order_trans mult_right_mono abs_ge_self)
done
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_setsum1"*}
+declare [[ atp_problem_prefix = "BigO__bigo_setsum1" ]]
lemma bigo_setsum1: "ALL x y. 0 <= h x y ==>
EX c. ALL x y. abs(f x y) <= c * (h x y) ==>
(%x. SUM y : A x. f x y) =o O(%x. SUM y : A x. h x y)"
@@ -981,7 +981,7 @@
(%x. SUM y : A x. f y) =o O(%x. SUM y : A x. h y)"
by (rule bigo_setsum1, auto)
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_setsum3"*}
+declare [[ atp_problem_prefix = "BigO__bigo_setsum3" ]]
lemma bigo_setsum3: "f =o O(h) ==>
(%x. SUM y : A x. (l x y) * f(k x y)) =o
O(%x. SUM y : A x. abs(l x y * h(k x y)))"
@@ -1012,7 +1012,7 @@
apply (erule set_plus_imp_minus)
done
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_setsum5"*}
+declare [[ atp_problem_prefix = "BigO__bigo_setsum5" ]]
lemma bigo_setsum5: "f =o O(h) ==> ALL x y. 0 <= l x y ==>
ALL x. 0 <= h x ==>
(%x. SUM y : A x. (l x y) * f(k x y)) =o
@@ -1069,7 +1069,7 @@
apply (simp add: func_times)
done
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_fix"*}
+declare [[ atp_problem_prefix = "BigO__bigo_fix" ]]
lemma bigo_fix: "(%x. f ((x::nat) + 1)) =o O(%x. h(x + 1)) ==> f 0 = 0 ==>
f =o O(h)"
apply (simp add: bigo_alt_def)
@@ -1134,7 +1134,7 @@
apply (erule spec)+
done
-ML_command{*AtpWrapper.problem_name:="BigO__bigo_lesso1"*}
+declare [[ atp_problem_prefix = "BigO__bigo_lesso1" ]]
lemma bigo_lesso1: "ALL x. f x <= g x ==> f <o g =o O(h)"
apply (unfold lesso_def)
apply (subgoal_tac "(%x. max (f x - g x) 0) = 0")
@@ -1146,7 +1146,7 @@
done
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_lesso2"*}
+declare [[ atp_problem_prefix = "BigO__bigo_lesso2" ]]
lemma bigo_lesso2: "f =o g +o O(h) ==>
ALL x. 0 <= k x ==> ALL x. k x <= f x ==>
k <o g =o O(h)"
@@ -1183,7 +1183,7 @@
by (metis min_max.sup_commute min_max.inf_commute min_max.sup_inf_absorb min_max.le_iff_inf 0 max_diff_distrib_left 1 linorder_not_le 8)
qed
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_lesso3"*}
+declare [[ atp_problem_prefix = "BigO__bigo_lesso3" ]]
lemma bigo_lesso3: "f =o g +o O(h) ==>
ALL x. 0 <= k x ==> ALL x. g x <= k x ==>
f <o k =o O(h)"
@@ -1200,7 +1200,7 @@
apply (simp)
apply (subst abs_of_nonneg)
apply (drule_tac x = x in spec) back
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_lesso3_simpler"*}
+using [[ atp_problem_prefix = "BigO__bigo_lesso3_simpler" ]]
apply (metis diff_less_0_iff_less linorder_not_le not_leE uminus_add_conv_diff xt1(12) xt1(6))
apply (metis add_minus_cancel diff_le_eq le_diff_eq uminus_add_conv_diff)
apply (metis abs_ge_zero linorder_linear min_max.sup_absorb1 min_max.sup_commute)
@@ -1220,7 +1220,7 @@
split: split_max abs_split)
done
-ML_command{*AtpWrapper.problem_name := "BigO__bigo_lesso5"*}
+declare [[ atp_problem_prefix = "BigO__bigo_lesso5" ]]
lemma bigo_lesso5: "f <o g =o O(h) ==>
EX C. ALL x. f x <= g x + C * abs(h x)"
apply (simp only: lesso_def bigo_alt_def)
--- a/src/HOL/MetisExamples/Message.thy Fri Oct 02 04:44:56 2009 +0200
+++ b/src/HOL/MetisExamples/Message.thy Sat Oct 03 12:05:40 2009 +0200
@@ -77,7 +77,7 @@
| Body: "Crypt K X \<in> parts H ==> X \<in> parts H"
-ML{*AtpWrapper.problem_name := "Message__parts_mono"*}
+declare [[ atp_problem_prefix = "Message__parts_mono" ]]
lemma parts_mono: "G \<subseteq> H ==> parts(G) \<subseteq> parts(H)"
apply auto
apply (erule parts.induct)
@@ -101,7 +101,7 @@
subsubsection{*Inverse of keys *}
-ML{*AtpWrapper.problem_name := "Message__invKey_eq"*}
+declare [[ atp_problem_prefix = "Message__invKey_eq" ]]
lemma invKey_eq [simp]: "(invKey K = invKey K') = (K=K')"
by (metis invKey)
@@ -202,7 +202,7 @@
apply (simp only: parts_Un)
done
-ML{*AtpWrapper.problem_name := "Message__parts_insert_two"*}
+declare [[ atp_problem_prefix = "Message__parts_insert_two" ]]
lemma parts_insert2:
"parts (insert X (insert Y H)) = parts {X} \<union> parts {Y} \<union> parts H"
by (metis Un_commute Un_empty_left Un_empty_right Un_insert_left Un_insert_right parts_Un)
@@ -239,7 +239,7 @@
lemma parts_idem [simp]: "parts (parts H) = parts H"
by blast
-ML{*AtpWrapper.problem_name := "Message__parts_subset_iff"*}
+declare [[ atp_problem_prefix = "Message__parts_subset_iff" ]]
lemma parts_subset_iff [simp]: "(parts G \<subseteq> parts H) = (G \<subseteq> parts H)"
apply (rule iffI)
apply (metis Un_absorb1 Un_subset_iff parts_Un parts_increasing)
@@ -250,7 +250,7 @@
by (blast dest: parts_mono);
-ML{*AtpWrapper.problem_name := "Message__parts_cut"*}
+declare [[ atp_problem_prefix = "Message__parts_cut" ]]
lemma parts_cut: "[|Y\<in> parts(insert X G); X\<in> parts H|] ==> Y\<in> parts(G \<union> H)"
by (metis Un_subset_iff insert_subset parts_increasing parts_trans)
@@ -315,7 +315,7 @@
done
-ML{*AtpWrapper.problem_name := "Message__msg_Nonce_supply"*}
+declare [[ atp_problem_prefix = "Message__msg_Nonce_supply" ]]
lemma msg_Nonce_supply: "\<exists>N. \<forall>n. N\<le>n --> Nonce n \<notin> parts {msg}"
apply (induct_tac "msg")
apply (simp_all add: parts_insert2)
@@ -367,7 +367,7 @@
lemmas not_parts_not_analz = analz_subset_parts [THEN contra_subsetD, standard]
-ML{*AtpWrapper.problem_name := "Message__parts_analz"*}
+declare [[ atp_problem_prefix = "Message__parts_analz" ]]
lemma parts_analz [simp]: "parts (analz H) = parts H"
apply (rule equalityI)
apply (metis analz_subset_parts parts_subset_iff)
@@ -519,7 +519,7 @@
by (drule analz_mono, blast)
-ML{*AtpWrapper.problem_name := "Message__analz_cut"*}
+declare [[ atp_problem_prefix = "Message__analz_cut" ]]
declare analz_trans[intro]
lemma analz_cut: "[| Y\<in> analz (insert X H); X\<in> analz H |] ==> Y\<in> analz H"
(*TOO SLOW
@@ -537,7 +537,7 @@
text{*A congruence rule for "analz" *}
-ML{*AtpWrapper.problem_name := "Message__analz_subset_cong"*}
+declare [[ atp_problem_prefix = "Message__analz_subset_cong" ]]
lemma analz_subset_cong:
"[| analz G \<subseteq> analz G'; analz H \<subseteq> analz H' |]
==> analz (G \<union> H) \<subseteq> analz (G' \<union> H')"
@@ -615,7 +615,7 @@
by (intro Un_least synth_mono Un_upper1 Un_upper2)
-ML{*AtpWrapper.problem_name := "Message__synth_insert"*}
+declare [[ atp_problem_prefix = "Message__synth_insert" ]]
lemma synth_insert: "insert X (synth H) \<subseteq> synth(insert X H)"
by (metis insert_iff insert_subset subset_insertI synth.Inj synth_mono)
@@ -637,7 +637,7 @@
lemma synth_trans: "[| X\<in> synth G; G \<subseteq> synth H |] ==> X\<in> synth H"
by (drule synth_mono, blast)
-ML{*AtpWrapper.problem_name := "Message__synth_cut"*}
+declare [[ atp_problem_prefix = "Message__synth_cut" ]]
lemma synth_cut: "[| Y\<in> synth (insert X H); X\<in> synth H |] ==> Y\<in> synth H"
(*TOO SLOW
by (metis insert_absorb insert_mono insert_subset synth_idem synth_increasing synth_mono)
@@ -669,7 +669,7 @@
subsubsection{*Combinations of parts, analz and synth *}
-ML{*AtpWrapper.problem_name := "Message__parts_synth"*}
+declare [[ atp_problem_prefix = "Message__parts_synth" ]]
lemma parts_synth [simp]: "parts (synth H) = parts H \<union> synth H"
apply (rule equalityI)
apply (rule subsetI)
@@ -684,14 +684,14 @@
-ML{*AtpWrapper.problem_name := "Message__analz_analz_Un"*}
+declare [[ atp_problem_prefix = "Message__analz_analz_Un" ]]
lemma analz_analz_Un [simp]: "analz (analz G \<union> H) = analz (G \<union> H)"
apply (rule equalityI);
apply (metis analz_idem analz_subset_cong order_eq_refl)
apply (metis analz_increasing analz_subset_cong order_eq_refl)
done
-ML{*AtpWrapper.problem_name := "Message__analz_synth_Un"*}
+declare [[ atp_problem_prefix = "Message__analz_synth_Un" ]]
declare analz_mono [intro] analz.Fst [intro] analz.Snd [intro] Un_least [intro]
lemma analz_synth_Un [simp]: "analz (synth G \<union> H) = analz (G \<union> H) \<union> synth G"
apply (rule equalityI)
@@ -705,7 +705,7 @@
done
-ML{*AtpWrapper.problem_name := "Message__analz_synth"*}
+declare [[ atp_problem_prefix = "Message__analz_synth" ]]
lemma analz_synth [simp]: "analz (synth H) = analz H \<union> synth H"
proof (neg_clausify)
assume 0: "analz (synth H) \<noteq> analz H \<union> synth H"
@@ -728,7 +728,7 @@
subsubsection{*For reasoning about the Fake rule in traces *}
-ML{*AtpWrapper.problem_name := "Message__parts_insert_subset_Un"*}
+declare [[ atp_problem_prefix = "Message__parts_insert_subset_Un" ]]
lemma parts_insert_subset_Un: "X\<in> G ==> parts(insert X H) \<subseteq> parts G \<union> parts H"
proof (neg_clausify)
assume 0: "X \<in> G"
@@ -747,7 +747,7 @@
by (metis 6 0)
qed
-ML{*AtpWrapper.problem_name := "Message__Fake_parts_insert"*}
+declare [[ atp_problem_prefix = "Message__Fake_parts_insert" ]]
lemma Fake_parts_insert:
"X \<in> synth (analz H) ==>
parts (insert X H) \<subseteq> synth (analz H) \<union> parts H"
@@ -790,14 +790,14 @@
==> Z \<in> synth (analz H) \<union> parts H";
by (blast dest: Fake_parts_insert [THEN subsetD, dest])
-ML{*AtpWrapper.problem_name := "Message__Fake_analz_insert"*}
+declare [[ atp_problem_prefix = "Message__Fake_analz_insert" ]]
declare analz_mono [intro] synth_mono [intro]
lemma Fake_analz_insert:
"X\<in> synth (analz G) ==>
analz (insert X H) \<subseteq> synth (analz G) \<union> analz (G \<union> H)"
by (metis Un_commute Un_insert_left Un_insert_right Un_upper1 analz_analz_Un analz_mono analz_synth_Un equalityE insert_absorb order_le_less xt1(12))
-ML{*AtpWrapper.problem_name := "Message__Fake_analz_insert_simpler"*}
+declare [[ atp_problem_prefix = "Message__Fake_analz_insert_simpler" ]]
(*simpler problems? BUT METIS CAN'T PROVE
lemma Fake_analz_insert_simpler:
"X\<in> synth (analz G) ==>
--- a/src/HOL/MetisExamples/Tarski.thy Fri Oct 02 04:44:56 2009 +0200
+++ b/src/HOL/MetisExamples/Tarski.thy Sat Oct 03 12:05:40 2009 +0200
@@ -416,7 +416,7 @@
(*never proved, 2007-01-22: Tarski__CLF_unnamed_lemma
NOT PROVABLE because of the conjunction used in the definition: we don't
allow reasoning with rules like conjE, which is essential here.*)
-ML_command{*AtpWrapper.problem_name:="Tarski__CLF_unnamed_lemma"*}
+declare [[ atp_problem_prefix = "Tarski__CLF_unnamed_lemma" ]]
lemma (in CLF) [simp]:
"f: pset cl -> pset cl & monotone f (pset cl) (order cl)"
apply (insert f_cl)
@@ -433,7 +433,7 @@
by (simp add: A_def r_def)
(*never proved, 2007-01-22*)
-ML_command{*AtpWrapper.problem_name:="Tarski__CLF_CLF_dual"*}
+declare [[ atp_problem_prefix = "Tarski__CLF_CLF_dual" ]]
declare (in CLF) CLF_set_def [simp] CL_dualCL [simp] monotone_dual [simp] dualA_iff [simp]
lemma (in CLF) CLF_dual: "(dual cl, f) \<in> CLF_set"
@@ -461,7 +461,7 @@
subsection {* lemmas for Tarski, lub *}
(*never proved, 2007-01-22*)
-ML{*AtpWrapper.problem_name:="Tarski__CLF_lubH_le_flubH"*}
+declare [[ atp_problem_prefix = "Tarski__CLF_lubH_le_flubH" ]]
declare CL.lub_least[intro] CLF.f_in_funcset[intro] funcset_mem[intro] CL.lub_in_lattice[intro] PO.transE[intro] PO.monotoneE[intro] CLF.monotone_f[intro] CL.lub_upper[intro]
lemma (in CLF) lubH_le_flubH:
"H = {x. (x, f x) \<in> r & x \<in> A} ==> (lub H cl, f (lub H cl)) \<in> r"
@@ -471,7 +471,7 @@
-- {* @{text "\<forall>x:H. (x, f (lub H r)) \<in> r"} *}
apply (rule ballI)
(*never proved, 2007-01-22*)
-ML_command{*AtpWrapper.problem_name:="Tarski__CLF_lubH_le_flubH_simpler"*}
+using [[ atp_problem_prefix = "Tarski__CLF_lubH_le_flubH_simpler" ]]
apply (rule transE)
-- {* instantiates @{text "(x, ?z) \<in> order cl to (x, f x)"}, *}
-- {* because of the def of @{text H} *}
@@ -489,7 +489,7 @@
CLF.monotone_f[rule del] CL.lub_upper[rule del]
(*never proved, 2007-01-22*)
-ML{*AtpWrapper.problem_name:="Tarski__CLF_flubH_le_lubH"*}
+declare [[ atp_problem_prefix = "Tarski__CLF_flubH_le_lubH" ]]
declare CLF.f_in_funcset[intro] funcset_mem[intro] CL.lub_in_lattice[intro]
PO.monotoneE[intro] CLF.monotone_f[intro] CL.lub_upper[intro]
CLF.lubH_le_flubH[simp]
@@ -499,7 +499,7 @@
apply (rule_tac t = "H" in ssubst, assumption)
apply (rule CollectI)
apply (rule conjI)
-ML_command{*AtpWrapper.problem_name:="Tarski__CLF_flubH_le_lubH_simpler"*}
+using [[ atp_problem_prefix = "Tarski__CLF_flubH_le_lubH_simpler" ]]
(*??no longer terminates, with combinators
apply (metis CO_refl_on lubH_le_flubH monotone_def monotone_f reflD1 reflD2)
*)
@@ -513,7 +513,7 @@
(*never proved, 2007-01-22*)
-ML{*AtpWrapper.problem_name:="Tarski__CLF_lubH_is_fixp"*}
+declare [[ atp_problem_prefix = "Tarski__CLF_lubH_is_fixp" ]]
(*Single-step version fails. The conjecture clauses refer to local abstraction
functions (Frees), which prevents expand_defs_tac from removing those
"definitions" at the end of the proof. *)
@@ -588,7 +588,7 @@
"H = {x. (x, f x) \<in> r & x \<in> A} ==> lub H cl \<in> fix f A"
apply (simp add: fix_def)
apply (rule conjI)
-ML_command{*AtpWrapper.problem_name:="Tarski__CLF_lubH_is_fixp_simpler"*}
+using [[ atp_problem_prefix = "Tarski__CLF_lubH_is_fixp_simpler" ]]
apply (metis CO_refl_on lubH_le_flubH refl_onD1)
apply (metis antisymE flubH_le_lubH lubH_le_flubH)
done
@@ -607,7 +607,7 @@
apply (simp_all add: P_def)
done
-ML{*AtpWrapper.problem_name:="Tarski__CLF_lubH_least_fixf"*}
+declare [[ atp_problem_prefix = "Tarski__CLF_lubH_least_fixf" ]]
lemma (in CLF) lubH_least_fixf:
"H = {x. (x, f x) \<in> r & x \<in> A}
==> \<forall>L. (\<forall>y \<in> fix f A. (y,L) \<in> r) --> (lub H cl, L) \<in> r"
@@ -615,7 +615,7 @@
done
subsection {* Tarski fixpoint theorem 1, first part *}
-ML{*AtpWrapper.problem_name:="Tarski__CLF_T_thm_1_lub"*}
+declare [[ atp_problem_prefix = "Tarski__CLF_T_thm_1_lub" ]]
declare CL.lubI[intro] fix_subset[intro] CL.lub_in_lattice[intro]
CLF.fixf_le_lubH[simp] CLF.lubH_least_fixf[simp]
lemma (in CLF) T_thm_1_lub: "lub P cl = lub {x. (x, f x) \<in> r & x \<in> A} cl"
@@ -623,7 +623,7 @@
apply (rule sym)
apply (simp add: P_def)
apply (rule lubI)
-ML_command{*AtpWrapper.problem_name:="Tarski__CLF_T_thm_1_lub_simpler"*}
+using [[ atp_problem_prefix = "Tarski__CLF_T_thm_1_lub_simpler" ]]
apply (metis P_def fix_subset)
apply (metis Collect_conj_eq Collect_mem_eq Int_commute Int_lower1 lub_in_lattice vimage_def)
(*??no longer terminates, with combinators
@@ -638,7 +638,7 @@
(*never proved, 2007-01-22*)
-ML{*AtpWrapper.problem_name:="Tarski__CLF_glbH_is_fixp"*}
+declare [[ atp_problem_prefix = "Tarski__CLF_glbH_is_fixp" ]]
declare glb_dual_lub[simp] PO.dualA_iff[intro] CLF.lubH_is_fixp[intro]
PO.dualPO[intro] CL.CL_dualCL[intro] PO.dualr_iff[simp]
lemma (in CLF) glbH_is_fixp: "H = {x. (f x, x) \<in> r & x \<in> A} ==> glb H cl \<in> P"
@@ -662,13 +662,13 @@
(*never proved, 2007-01-22*)
-ML{*AtpWrapper.problem_name:="Tarski__T_thm_1_glb"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__T_thm_1_glb" ]] (*ALL THEOREMS*)
lemma (in CLF) T_thm_1_glb: "glb P cl = glb {x. (f x, x) \<in> r & x \<in> A} cl"
(*sledgehammer;*)
apply (simp add: glb_dual_lub P_def A_def r_def)
apply (rule dualA_iff [THEN subst])
(*never proved, 2007-01-22*)
-ML_command{*AtpWrapper.problem_name:="Tarski__T_thm_1_glb_simpler"*} (*ALL THEOREMS*)
+using [[ atp_problem_prefix = "Tarski__T_thm_1_glb_simpler" ]] (*ALL THEOREMS*)
(*sledgehammer;*)
apply (simp add: CLF.T_thm_1_lub [of _ f, OF CLF.intro, OF CL.intro CLF_axioms.intro, OF PO.intro CL_axioms.intro,
OF dualPO CL_dualCL] dualPO CL_dualCL CLF_dual dualr_iff)
@@ -677,13 +677,13 @@
subsection {* interval *}
-ML{*AtpWrapper.problem_name:="Tarski__rel_imp_elem"*}
+declare [[ atp_problem_prefix = "Tarski__rel_imp_elem" ]]
declare (in CLF) CO_refl_on[simp] refl_on_def [simp]
lemma (in CLF) rel_imp_elem: "(x, y) \<in> r ==> x \<in> A"
by (metis CO_refl_on refl_onD1)
declare (in CLF) CO_refl_on[simp del] refl_on_def [simp del]
-ML{*AtpWrapper.problem_name:="Tarski__interval_subset"*}
+declare [[ atp_problem_prefix = "Tarski__interval_subset" ]]
declare (in CLF) rel_imp_elem[intro]
declare interval_def [simp]
lemma (in CLF) interval_subset: "[| a \<in> A; b \<in> A |] ==> interval r a b \<subseteq> A"
@@ -718,7 +718,7 @@
"[| a \<in> A; b \<in> A; S \<subseteq> interval r a b |]==> S \<subseteq> A"
by (simp add: subset_trans [OF _ interval_subset])
-ML{*AtpWrapper.problem_name:="Tarski__L_in_interval"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__L_in_interval" ]] (*ALL THEOREMS*)
lemma (in CLF) L_in_interval:
"[| a \<in> A; b \<in> A; S \<subseteq> interval r a b;
S \<noteq> {}; isLub S cl L; interval r a b \<noteq> {} |] ==> L \<in> interval r a b"
@@ -737,7 +737,7 @@
done
(*never proved, 2007-01-22*)
-ML{*AtpWrapper.problem_name:="Tarski__G_in_interval"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__G_in_interval" ]] (*ALL THEOREMS*)
lemma (in CLF) G_in_interval:
"[| a \<in> A; b \<in> A; interval r a b \<noteq> {}; S \<subseteq> interval r a b; isGlb S cl G;
S \<noteq> {} |] ==> G \<in> interval r a b"
@@ -746,7 +746,7 @@
dualA_iff A_def dualPO CL_dualCL CLF_dual isGlb_dual_isLub)
done
-ML{*AtpWrapper.problem_name:="Tarski__intervalPO"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__intervalPO" ]] (*ALL THEOREMS*)
lemma (in CLF) intervalPO:
"[| a \<in> A; b \<in> A; interval r a b \<noteq> {} |]
==> (| pset = interval r a b, order = induced (interval r a b) r |)
@@ -819,7 +819,7 @@
lemmas (in CLF) intv_CL_glb = intv_CL_lub [THEN Rdual]
(*never proved, 2007-01-22*)
-ML{*AtpWrapper.problem_name:="Tarski__interval_is_sublattice"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__interval_is_sublattice" ]] (*ALL THEOREMS*)
lemma (in CLF) interval_is_sublattice:
"[| a \<in> A; b \<in> A; interval r a b \<noteq> {} |]
==> interval r a b <<= cl"
@@ -827,7 +827,7 @@
apply (rule sublatticeI)
apply (simp add: interval_subset)
(*never proved, 2007-01-22*)
-ML_command{*AtpWrapper.problem_name:="Tarski__interval_is_sublattice_simpler"*}
+using [[ atp_problem_prefix = "Tarski__interval_is_sublattice_simpler" ]]
(*sledgehammer *)
apply (rule CompleteLatticeI)
apply (simp add: intervalPO)
@@ -846,7 +846,7 @@
lemma (in CLF) Bot_dual_Top: "Bot cl = Top (dual cl)"
by (simp add: Top_def Bot_def least_def greatest_def dualA_iff dualr_iff)
-ML_command{*AtpWrapper.problem_name:="Tarski__Bot_in_lattice"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__Bot_in_lattice" ]] (*ALL THEOREMS*)
lemma (in CLF) Bot_in_lattice: "Bot cl \<in> A"
(*sledgehammer; *)
apply (simp add: Bot_def least_def)
@@ -856,12 +856,12 @@
done
(*first proved 2007-01-25 after relaxing relevance*)
-ML_command{*AtpWrapper.problem_name:="Tarski__Top_in_lattice"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__Top_in_lattice" ]] (*ALL THEOREMS*)
lemma (in CLF) Top_in_lattice: "Top cl \<in> A"
(*sledgehammer;*)
apply (simp add: Top_dual_Bot A_def)
(*first proved 2007-01-25 after relaxing relevance*)
-ML_command{*AtpWrapper.problem_name:="Tarski__Top_in_lattice_simpler"*} (*ALL THEOREMS*)
+using [[ atp_problem_prefix = "Tarski__Top_in_lattice_simpler" ]] (*ALL THEOREMS*)
(*sledgehammer*)
apply (rule dualA_iff [THEN subst])
apply (blast intro!: CLF.Bot_in_lattice [OF CLF.intro, OF CL.intro CLF_axioms.intro, OF PO.intro CL_axioms.intro] dualPO CL_dualCL CLF_dual)
@@ -876,7 +876,7 @@
done
(*never proved, 2007-01-22*)
-ML_command{*AtpWrapper.problem_name:="Tarski__Bot_prop"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__Bot_prop" ]] (*ALL THEOREMS*)
lemma (in CLF) Bot_prop: "x \<in> A ==> (Bot cl, x) \<in> r"
(*sledgehammer*)
apply (simp add: Bot_dual_Top r_def)
@@ -885,12 +885,12 @@
dualA_iff A_def dualPO CL_dualCL CLF_dual)
done
-ML_command{*AtpWrapper.problem_name:="Tarski__Bot_in_lattice"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__Bot_in_lattice" ]] (*ALL THEOREMS*)
lemma (in CLF) Top_intv_not_empty: "x \<in> A ==> interval r x (Top cl) \<noteq> {}"
apply (metis Top_in_lattice Top_prop empty_iff intervalI reflE)
done
-ML_command{*AtpWrapper.problem_name:="Tarski__Bot_intv_not_empty"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__Bot_intv_not_empty" ]] (*ALL THEOREMS*)
lemma (in CLF) Bot_intv_not_empty: "x \<in> A ==> interval r (Bot cl) x \<noteq> {}"
apply (metis Bot_prop ex_in_conv intervalI reflE rel_imp_elem)
done
@@ -902,7 +902,7 @@
by (simp add: P_def fix_subset po_subset_po)
(*first proved 2007-01-25 after relaxing relevance*)
-ML_command{*AtpWrapper.problem_name:="Tarski__Y_subset_A"*}
+declare [[ atp_problem_prefix = "Tarski__Y_subset_A" ]]
declare (in Tarski) P_def[simp] Y_ss [simp]
declare fix_subset [intro] subset_trans [intro]
lemma (in Tarski) Y_subset_A: "Y \<subseteq> A"
@@ -918,7 +918,7 @@
by (rule Y_subset_A [THEN lub_in_lattice])
(*never proved, 2007-01-22*)
-ML_command{*AtpWrapper.problem_name:="Tarski__lubY_le_flubY"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__lubY_le_flubY" ]] (*ALL THEOREMS*)
lemma (in Tarski) lubY_le_flubY: "(lub Y cl, f (lub Y cl)) \<in> r"
(*sledgehammer*)
apply (rule lub_least)
@@ -927,12 +927,12 @@
apply (rule lubY_in_A)
-- {* @{text "Y \<subseteq> P ==> f x = x"} *}
apply (rule ballI)
-ML_command{*AtpWrapper.problem_name:="Tarski__lubY_le_flubY_simpler"*} (*ALL THEOREMS*)
+using [[ atp_problem_prefix = "Tarski__lubY_le_flubY_simpler" ]] (*ALL THEOREMS*)
(*sledgehammer *)
apply (rule_tac t = "x" in fix_imp_eq [THEN subst])
apply (erule Y_ss [simplified P_def, THEN subsetD])
-- {* @{text "reduce (f x, f (lub Y cl)) \<in> r to (x, lub Y cl) \<in> r"} by monotonicity *}
-ML_command{*AtpWrapper.problem_name:="Tarski__lubY_le_flubY_simplest"*} (*ALL THEOREMS*)
+using [[ atp_problem_prefix = "Tarski__lubY_le_flubY_simplest" ]] (*ALL THEOREMS*)
(*sledgehammer*)
apply (rule_tac f = "f" in monotoneE)
apply (rule monotone_f)
@@ -942,7 +942,7 @@
done
(*first proved 2007-01-25 after relaxing relevance*)
-ML_command{*AtpWrapper.problem_name:="Tarski__intY1_subset"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__intY1_subset" ]] (*ALL THEOREMS*)
lemma (in Tarski) intY1_subset: "intY1 \<subseteq> A"
(*sledgehammer*)
apply (unfold intY1_def)
@@ -954,7 +954,7 @@
lemmas (in Tarski) intY1_elem = intY1_subset [THEN subsetD]
(*never proved, 2007-01-22*)
-ML_command{*AtpWrapper.problem_name:="Tarski__intY1_f_closed"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__intY1_f_closed" ]] (*ALL THEOREMS*)
lemma (in Tarski) intY1_f_closed: "x \<in> intY1 \<Longrightarrow> f x \<in> intY1"
(*sledgehammer*)
apply (simp add: intY1_def interval_def)
@@ -962,7 +962,7 @@
apply (rule transE)
apply (rule lubY_le_flubY)
-- {* @{text "(f (lub Y cl), f x) \<in> r"} *}
-ML_command{*AtpWrapper.problem_name:="Tarski__intY1_f_closed_simpler"*} (*ALL THEOREMS*)
+using [[ atp_problem_prefix = "Tarski__intY1_f_closed_simpler" ]] (*ALL THEOREMS*)
(*sledgehammer [has been proved before now...]*)
apply (rule_tac f=f in monotoneE)
apply (rule monotone_f)
@@ -975,13 +975,13 @@
apply (simp add: intY1_def interval_def intY1_elem)
done
-ML_command{*AtpWrapper.problem_name:="Tarski__intY1_func"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__intY1_func" ]] (*ALL THEOREMS*)
lemma (in Tarski) intY1_func: "(%x: intY1. f x) \<in> intY1 -> intY1"
apply (rule restrict_in_funcset)
apply (metis intY1_f_closed restrict_in_funcset)
done
-ML_command{*AtpWrapper.problem_name:="Tarski__intY1_mono"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__intY1_mono" ]] (*ALL THEOREMS*)
lemma (in Tarski) intY1_mono:
"monotone (%x: intY1. f x) intY1 (induced intY1 r)"
(*sledgehammer *)
@@ -990,7 +990,7 @@
done
(*proof requires relaxing relevance: 2007-01-25*)
-ML_command{*AtpWrapper.problem_name:="Tarski__intY1_is_cl"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__intY1_is_cl" ]] (*ALL THEOREMS*)
lemma (in Tarski) intY1_is_cl:
"(| pset = intY1, order = induced intY1 r |) \<in> CompleteLattice"
(*sledgehammer*)
@@ -1003,7 +1003,7 @@
done
(*never proved, 2007-01-22*)
-ML_command{*AtpWrapper.problem_name:="Tarski__v_in_P"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__v_in_P" ]] (*ALL THEOREMS*)
lemma (in Tarski) v_in_P: "v \<in> P"
(*sledgehammer*)
apply (unfold P_def)
@@ -1013,7 +1013,7 @@
v_def CL_imp_PO intY1_is_cl CLF_set_def intY1_func intY1_mono)
done
-ML_command{*AtpWrapper.problem_name:="Tarski__z_in_interval"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__z_in_interval" ]] (*ALL THEOREMS*)
lemma (in Tarski) z_in_interval:
"[| z \<in> P; \<forall>y\<in>Y. (y, z) \<in> induced P r |] ==> z \<in> intY1"
(*sledgehammer *)
@@ -1027,14 +1027,14 @@
apply (simp add: induced_def)
done
-ML_command{*AtpWrapper.problem_name:="Tarski__fz_in_int_rel"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__fz_in_int_rel" ]] (*ALL THEOREMS*)
lemma (in Tarski) f'z_in_int_rel: "[| z \<in> P; \<forall>y\<in>Y. (y, z) \<in> induced P r |]
==> ((%x: intY1. f x) z, z) \<in> induced intY1 r"
apply (metis P_def acc_def fix_imp_eq fix_subset indI reflE restrict_apply subset_eq z_in_interval)
done
(*never proved, 2007-01-22*)
-ML_command{*AtpWrapper.problem_name:="Tarski__tarski_full_lemma"*} (*ALL THEOREMS*)
+declare [[ atp_problem_prefix = "Tarski__tarski_full_lemma" ]] (*ALL THEOREMS*)
lemma (in Tarski) tarski_full_lemma:
"\<exists>L. isLub Y (| pset = P, order = induced P r |) L"
apply (rule_tac x = "v" in exI)
@@ -1064,12 +1064,12 @@
prefer 2 apply (simp add: v_in_P)
apply (unfold v_def)
(*never proved, 2007-01-22*)
-ML_command{*AtpWrapper.problem_name:="Tarski__tarski_full_lemma_simpler"*}
+using [[ atp_problem_prefix = "Tarski__tarski_full_lemma_simpler" ]]
(*sledgehammer*)
apply (rule indE)
apply (rule_tac [2] intY1_subset)
(*never proved, 2007-01-22*)
-ML_command{*AtpWrapper.problem_name:="Tarski__tarski_full_lemma_simplest"*}
+using [[ atp_problem_prefix = "Tarski__tarski_full_lemma_simplest" ]]
(*sledgehammer*)
apply (rule CL.glb_lower [OF CL.intro, OF PO.intro CL_axioms.intro, OF _ intY1_is_cl, simplified])
apply (simp add: CL_imp_PO intY1_is_cl)
@@ -1087,7 +1087,7 @@
(*never proved, 2007-01-22*)
-ML_command{*AtpWrapper.problem_name:="Tarski__Tarski_full"*}
+declare [[ atp_problem_prefix = "Tarski__Tarski_full" ]]
declare (in CLF) fixf_po[intro] P_def [simp] A_def [simp] r_def [simp]
Tarski.tarski_full_lemma [intro] cl_po [intro] cl_co [intro]
CompleteLatticeI_simp [intro]
@@ -1097,7 +1097,7 @@
apply (rule CompleteLatticeI_simp)
apply (rule fixf_po, clarify)
(*never proved, 2007-01-22*)
-ML_command{*AtpWrapper.problem_name:="Tarski__Tarski_full_simpler"*}
+using [[ atp_problem_prefix = "Tarski__Tarski_full_simpler" ]]
(*sledgehammer*)
apply (simp add: P_def A_def r_def)
apply (blast intro!: Tarski.tarski_full_lemma [OF Tarski.intro, OF CLF.intro Tarski_axioms.intro,
--- a/src/HOL/MetisExamples/TransClosure.thy Fri Oct 02 04:44:56 2009 +0200
+++ b/src/HOL/MetisExamples/TransClosure.thy Sat Oct 03 12:05:40 2009 +0200
@@ -22,7 +22,7 @@
consts f:: "addr \<Rightarrow> val"
-ML {*AtpWrapper.problem_name := "TransClosure__test"*}
+declare [[ atp_problem_prefix = "TransClosure__test" ]]
lemma "\<lbrakk> f c = Intg x; \<forall> y. f b = Intg y \<longrightarrow> y \<noteq> x; (a,b) \<in> R\<^sup>*; (b,c) \<in> R\<^sup>* \<rbrakk>
\<Longrightarrow> \<exists> c. (b,c) \<in> R \<and> (a,c) \<in> R\<^sup>*"
by (metis Transitive_Closure.rtrancl_into_rtrancl converse_rtranclE trancl_reflcl)
@@ -51,7 +51,7 @@
by (metis 10 3)
qed
-ML {*AtpWrapper.problem_name := "TransClosure__test_simpler"*}
+declare [[ atp_problem_prefix = "TransClosure__test_simpler" ]]
lemma "\<lbrakk> f c = Intg x; \<forall> y. f b = Intg y \<longrightarrow> y \<noteq> x; (a,b) \<in> R\<^sup>*; (b,c) \<in> R\<^sup>* \<rbrakk>
\<Longrightarrow> \<exists> c. (b,c) \<in> R \<and> (a,c) \<in> R\<^sup>*"
apply (erule_tac x="b" in converse_rtranclE)
--- a/src/HOL/MetisExamples/set.thy Fri Oct 02 04:44:56 2009 +0200
+++ b/src/HOL/MetisExamples/set.thy Sat Oct 03 12:05:40 2009 +0200
@@ -197,7 +197,7 @@
by (metis 11 6 Un_upper2 1 Un_upper1 0 9 Un_upper2 1 Un_upper1 0)
qed
-ML {*AtpWrapper.problem_name := "set__equal_union"*}
+declare [[ atp_problem_prefix = "set__equal_union" ]]
lemma (*equal_union: *)
"(X = Y \<union> Z) =
(Y \<subseteq> X \<and> Z \<subseteq> X \<and> (\<forall>V. Y \<subseteq> V \<and> Z \<subseteq> V \<longrightarrow> X \<subseteq> V))"
@@ -205,12 +205,12 @@
by (metis Un_least Un_upper1 Un_upper2 set_eq_subset)
-ML {*AtpWrapper.problem_name := "set__equal_inter"*}
+declare [[ atp_problem_prefix = "set__equal_inter" ]]
lemma "(X = Y \<inter> Z) =
(X \<subseteq> Y \<and> X \<subseteq> Z \<and> (\<forall>V. V \<subseteq> Y \<and> V \<subseteq> Z \<longrightarrow> V \<subseteq> X))"
by (metis Int_greatest Int_lower1 Int_lower2 set_eq_subset)
-ML {*AtpWrapper.problem_name := "set__fixedpoint"*}
+declare [[ atp_problem_prefix = "set__fixedpoint" ]]
lemma fixedpoint:
"\<exists>!x. f (g x) = x \<Longrightarrow> \<exists>!y. g (f y) = y"
by metis
@@ -229,7 +229,7 @@
by (metis 4 0)
qed
-ML {*AtpWrapper.problem_name := "set__singleton_example"*}
+declare [[ atp_problem_prefix = "set__singleton_example" ]]
lemma (*singleton_example_2:*)
"\<forall>x \<in> S. \<Union>S \<subseteq> x \<Longrightarrow> \<exists>z. S \<subseteq> {z}"
by (metis Set.subsetI Union_upper insertCI set_eq_subset)
@@ -259,7 +259,7 @@
293-314.
*}
-ML {*AtpWrapper.problem_name := "set__Bledsoe_Fung"*}
+declare [[ atp_problem_prefix = "set__Bledsoe_Fung" ]]
(*Notes: 1, the numbering doesn't completely agree with the paper.
2, we must rename set variables to avoid type clashes.*)
lemma "\<exists>B. (\<forall>x \<in> B. x \<le> (0::int))"
--- a/src/HOL/Mirabelle/Tools/mirabelle_sledgehammer.ML Fri Oct 02 04:44:56 2009 +0200
+++ b/src/HOL/Mirabelle/Tools/mirabelle_sledgehammer.ML Sat Oct 03 12:05:40 2009 +0200
@@ -291,39 +291,27 @@
local
-fun safe init done f x =
- let
- val y = init x
- val z = Exn.capture f y
- val _ = done y
- in Exn.release z end
-
-fun init_sh NONE = !AtpWrapper.destdir
- | init_sh (SOME path) =
- let
- (* Warning: we implicitly assume single-threaded execution here! *)
- val old = !AtpWrapper.destdir
- val _ = AtpWrapper.destdir := path
- in old end
-
-fun done_sh path = AtpWrapper.destdir := path
-
datatype sh_result =
SH_OK of int * int * string list |
SH_FAIL of int * int |
SH_ERROR
-fun run_sh (prover_name, prover) hard_timeout timeout st _ =
+fun run_sh prover hard_timeout timeout dir st =
let
- val atp = prover timeout NONE NONE prover_name 1
+ val (ctxt, goal) = Proof.get_goal st
+ val ctxt' = ctxt |> is_some dir ? Config.put AtpWrapper.destdir (the dir)
+ val atp = prover (AtpWrapper.atp_problem_of_goal
+ (AtpManager.get_full_types ()) 1 (ctxt', goal))
+
val time_limit =
(case hard_timeout of
NONE => I
| SOME secs => TimeLimit.timeLimit (Time.fromSeconds secs))
- val ((success, (message, thm_names), time_atp, _, _, _), time_isa) =
- time_limit (Mirabelle.cpu_time atp) (Proof.get_goal st)
+ val (AtpWrapper.Prover_Result {success, message, theorem_names,
+ runtime=time_atp, ...}, time_isa) =
+ time_limit (Mirabelle.cpu_time atp) timeout
in
- if success then (message, SH_OK (time_isa, time_atp, thm_names))
+ if success then (message, SH_OK (time_isa, time_atp, theorem_names))
else (message, SH_FAIL(time_isa, time_atp))
end
handle ResHolClause.TOO_TRIVIAL => ("trivial", SH_OK (0, 0, []))
@@ -348,13 +336,12 @@
fun run_sledgehammer args named_thms id ({pre=st, log, ...}: Mirabelle.run_args) =
let
val _ = change_data id inc_sh_calls
- val atp as (prover_name, _) = get_atp (Proof.theory_of st) args
+ val (prover_name, prover) = get_atp (Proof.theory_of st) args
val dir = AList.lookup (op =) args keepK
val timeout = Mirabelle.get_int_setting args (prover_timeoutK, 30)
val hard_timeout = AList.lookup (op =) args prover_hard_timeoutK
|> Option.map (fst o read_int o explode)
- val (msg, result) = safe init_sh done_sh
- (run_sh atp hard_timeout timeout st) dir
+ val (msg, result) = run_sh prover hard_timeout timeout dir st
in
case result of
SH_OK (time_isa, time_atp, names) =>
--- a/src/HOL/Tools/ATP_Manager/atp_manager.ML Fri Oct 02 04:44:56 2009 +0200
+++ b/src/HOL/Tools/ATP_Manager/atp_manager.ML Sat Oct 03 12:05:40 2009 +0200
@@ -21,13 +21,9 @@
val kill: unit -> unit
val info: unit -> unit
val messages: int option -> unit
- type prover = int -> (thm * (string * int)) list option ->
- (thm * (string * int)) list option -> string -> int ->
- Proof.context * (thm list * thm) ->
- bool * (string * string list) * int * string * string vector * (thm * (string * int)) list
- val add_prover: string -> prover -> theory -> theory
+ val add_prover: string * AtpWrapper.prover -> theory -> theory
val print_provers: theory -> unit
- val get_prover: string -> theory -> prover option
+ val get_prover: string -> theory -> AtpWrapper.prover option
val sledgehammer: string list -> Proof.state -> unit
end;
@@ -302,16 +298,11 @@
(* named provers *)
-type prover = int -> (thm * (string * int)) list option ->
- (thm * (string * int)) list option -> string -> int ->
- Proof.context * (thm list * thm) ->
- bool * (string * string list) * int * string * string vector * (thm * (string * int)) list
-
fun err_dup_prover name = error ("Duplicate prover: " ^ quote name);
structure Provers = TheoryDataFun
(
- type T = (prover * stamp) Symtab.table
+ type T = (AtpWrapper.prover * stamp) Symtab.table
val empty = Symtab.empty
val copy = I
val extend = I
@@ -319,7 +310,7 @@
handle Symtab.DUP dup => err_dup_prover dup
);
-fun add_prover name prover thy =
+fun add_prover (name, prover) thy =
Provers.map (Symtab.update_new (name, (prover, stamp ()))) thy
handle Symtab.DUP dup => err_dup_prover dup;
@@ -344,9 +335,11 @@
val _ = SimpleThread.fork true (fn () =>
let
val _ = register birthtime deadtime (Thread.self (), desc)
+ val problem = AtpWrapper.atp_problem_of_goal (get_full_types ()) i
+ (Proof.get_goal proof_state)
val result =
- let val (success, (message, _), _, _, _, _) =
- prover (get_timeout ()) NONE NONE name i (Proof.get_goal proof_state)
+ let val AtpWrapper.Prover_Result {success, message, ...} =
+ prover problem (get_timeout ())
in (success, message) end
handle ResHolClause.TOO_TRIVIAL
=> (true, "Empty clause: Try this command: " ^ Markup.markup Markup.sendback "apply metis")
--- a/src/HOL/Tools/ATP_Manager/atp_minimal.ML Fri Oct 02 04:44:56 2009 +0200
+++ b/src/HOL/Tools/ATP_Manager/atp_minimal.ML Sat Oct 03 12:05:40 2009 +0200
@@ -6,7 +6,7 @@
signature ATP_MINIMAL =
sig
- val minimalize: AtpManager.prover -> string -> int -> Proof.state ->
+ val minimalize: AtpWrapper.prover -> string -> int -> Proof.state ->
(string * thm list) list -> ((string * thm list) list * int) option * string
end
@@ -97,7 +97,11 @@
("# Cannot determine problem status within resource limit", Timeout),
("Error", Error)]
-fun produce_answer (success, message, _, result_string, thm_name_vec, filtered) =
+fun produce_answer result =
+ let
+ val AtpWrapper.Prover_Result {success, message, proof=result_string,
+ internal_thm_names=thm_name_vec, filtered_clauses=filtered, ...} = result
+ in
if success then
(Success (Vector.foldr op:: [] thm_name_vec, filtered), result_string)
else
@@ -110,19 +114,23 @@
else
(Failure, result_string)
end
-
+ end
(* wrapper for calling external prover *)
-fun sh_test_thms prover prover_name time_limit subgoalno state filtered name_thms_pairs =
+fun sh_test_thms prover time_limit subgoalno state filtered name_thms_pairs =
let
val _ = println ("Testing " ^ (length_string name_thms_pairs) ^ " theorems... ")
val name_thm_pairs = maps (fn (n, ths) => map (pair n) ths) name_thms_pairs
val _ = debug_fn (fn () => print_names name_thm_pairs)
val axclauses = ResAxioms.cnf_rules_pairs (Proof.theory_of state) name_thm_pairs
- val (result, proof) =
- produce_answer
- (prover time_limit (SOME axclauses) filtered prover_name subgoalno (Proof.get_goal state))
+ val problem = AtpWrapper.ATP_Problem {
+ with_full_types = AtpManager.get_full_types (),
+ subgoal = subgoalno,
+ goal = Proof.get_goal state,
+ axiom_clauses = SOME axclauses,
+ filtered_clauses = filtered }
+ val (result, proof) = produce_answer (prover problem time_limit)
val _ = println (string_of_result result)
val _ = debug proof
in
@@ -140,7 +148,7 @@
val _ = debug_fn (fn () => app (fn (n, tl) =>
(debug n; app (fn t =>
debug (" " ^ Display.string_of_thm (Proof.context_of state) t)) tl)) name_thms_pairs)
- val test_thms_fun = sh_test_thms prover prover_name time_limit 1 state
+ val test_thms_fun = sh_test_thms prover time_limit 1 state
fun test_thms filtered thms =
case test_thms_fun filtered thms of (Success _, _) => true | _ => false
val answer' = pair and answer'' = pair NONE
--- a/src/HOL/Tools/ATP_Manager/atp_wrapper.ML Fri Oct 02 04:44:56 2009 +0200
+++ b/src/HOL/Tools/ATP_Manager/atp_wrapper.ML Sat Oct 03 12:05:40 2009 +0200
@@ -6,25 +6,46 @@
signature ATP_WRAPPER =
sig
- val destdir: string Unsynchronized.ref
- val problem_name: string Unsynchronized.ref
- val tptp_prover_opts_full: int -> bool -> bool -> Path.T * string -> AtpManager.prover
- val tptp_prover_opts: int -> bool -> Path.T * string -> AtpManager.prover
- val tptp_prover: Path.T * string -> AtpManager.prover
- val full_prover_opts: int -> bool -> Path.T * string -> AtpManager.prover
- val full_prover: Path.T * string -> AtpManager.prover
- val vampire_opts: int -> bool -> AtpManager.prover
- val vampire: AtpManager.prover
- val vampire_opts_full: int -> bool -> AtpManager.prover
- val vampire_full: AtpManager.prover
- val eprover_opts: int -> bool -> AtpManager.prover
- val eprover: AtpManager.prover
- val eprover_opts_full: int -> bool -> AtpManager.prover
- val eprover_full: AtpManager.prover
- val spass_opts: int -> bool -> AtpManager.prover
- val spass: AtpManager.prover
- val remote_prover_opts: int -> bool -> string -> string -> AtpManager.prover
- val remote_prover: string -> string -> AtpManager.prover
+ (*hooks for problem files*)
+ val destdir: string Config.T
+ val problem_prefix: string Config.T
+ val setup: theory -> theory
+
+ (*prover configuration, problem format, and prover result*)
+ datatype prover_config = Prover_Config of {
+ command: Path.T,
+ arguments: int -> string,
+ max_new_clauses: int,
+ insert_theory_const: bool,
+ emit_structured_proof: bool }
+ datatype atp_problem = ATP_Problem of {
+ with_full_types: bool,
+ subgoal: int,
+ goal: Proof.context * (thm list * thm),
+ axiom_clauses: (thm * (string * int)) list option,
+ filtered_clauses: (thm * (string * int)) list option }
+ val atp_problem_of_goal: bool -> int -> Proof.context * (thm list * thm) ->
+ atp_problem
+ datatype prover_result = Prover_Result of {
+ success: bool,
+ message: string,
+ theorem_names: string list,
+ runtime: int,
+ proof: string,
+ internal_thm_names: string Vector.vector,
+ filtered_clauses: (thm * (string * int)) list }
+ type prover = atp_problem -> int -> prover_result
+
+ (*common provers*)
+ val vampire: string * prover
+ val vampire_full: string * prover
+ val eprover: string * prover
+ val eprover_full: string * prover
+ val spass: string * prover
+ val spass_no_tc: string * prover
+ val remote_vampire: string * prover
+ val remote_eprover: string * prover
+ val remote_spass: string * prover
val refresh_systems: unit -> unit
end;
@@ -33,10 +54,50 @@
(** generic ATP wrapper **)
-(* global hooks for writing problemfiles *)
+(* hooks for writing problem files *)
+
+val (destdir, destdir_setup) = Attrib.config_string "atp_destdir" "";
+ (*Empty string means create files in Isabelle's temporary files directory.*)
+
+val (problem_prefix, problem_prefix_setup) =
+ Attrib.config_string "atp_problem_prefix" "prob";
+
+val setup = destdir_setup #> problem_prefix_setup;
+
+
+(* prover configuration, problem format, and prover result *)
+
+datatype prover_config = Prover_Config of {
+ command: Path.T,
+ arguments: int -> string,
+ max_new_clauses: int,
+ insert_theory_const: bool,
+ emit_structured_proof: bool }
-val destdir = Unsynchronized.ref ""; (*Empty means write files to /tmp*)
-val problem_name = Unsynchronized.ref "prob";
+datatype atp_problem = ATP_Problem of {
+ with_full_types: bool,
+ subgoal: int,
+ goal: Proof.context * (thm list * thm),
+ axiom_clauses: (thm * (string * int)) list option,
+ filtered_clauses: (thm * (string * int)) list option }
+
+fun atp_problem_of_goal with_full_types subgoal goal = ATP_Problem {
+ with_full_types = with_full_types,
+ subgoal = subgoal,
+ goal = goal,
+ axiom_clauses = NONE,
+ filtered_clauses = NONE }
+
+datatype prover_result = Prover_Result of {
+ success: bool,
+ message: string,
+ theorem_names: string list, (* relevant theorems *)
+ runtime: int, (* user time of the ATP, in milliseconds *)
+ proof: string,
+ internal_thm_names: string Vector.vector,
+ filtered_clauses: (thm * (string * int)) list }
+
+type prover = atp_problem -> int -> prover_result
(* basic template *)
@@ -47,20 +108,9 @@
|> Exn.release
|> tap (after path)
-fun external_prover relevance_filter preparer writer (cmd, args) find_failure produce_answer
- timeout axiom_clauses filtered_clauses name subgoalno goal =
+fun external_prover relevance_filter preparer writer cmd args find_failure produce_answer
+ axiom_clauses filtered_clauses name subgoalno goal =
let
- (* path to unique problem file *)
- val destdir' = ! destdir
- val problem_name' = ! problem_name
- fun prob_pathname nr =
- let val probfile = Path.basic (problem_name' ^ serial_string () ^ "_" ^ string_of_int nr)
- in if destdir' = "" then File.tmp_path probfile
- else if File.exists (Path.explode (destdir'))
- then Path.append (Path.explode (destdir')) probfile
- else error ("No such directory: " ^ destdir')
- end
-
(* get clauses and prepare them for writing *)
val (ctxt, (chain_ths, th)) = goal
val thy = ProofContext.theory_of ctxt
@@ -78,6 +128,17 @@
val (thm_names, clauses) =
preparer goal_cls chain_ths the_axiom_clauses the_filtered_clauses thy
+ (* path to unique problem file *)
+ val destdir' = Config.get ctxt destdir
+ val problem_prefix' = Config.get ctxt problem_prefix
+ fun prob_pathname nr =
+ let val probfile = Path.basic (problem_prefix' ^ serial_string () ^ "_" ^ string_of_int nr)
+ in if destdir' = "" then File.tmp_path probfile
+ else if File.exists (Path.explode (destdir'))
+ then Path.append (Path.explode (destdir')) probfile
+ else error ("No such directory: " ^ destdir')
+ end
+
(* write out problem file and call prover *)
fun cmd_line probfile = "TIMEFORMAT='%3U'; { time " ^ space_implode " "
[File.shell_path cmd, args, File.platform_path probfile] ^ " ; } 2>&1"
@@ -110,97 +171,100 @@
(* check for success and print out some information on failure *)
val failure = find_failure proof
val success = rc = 0 andalso is_none failure
- val message =
+ val (message, real_thm_names) =
if is_some failure then ("External prover failed.", [])
else if rc <> 0 then ("External prover failed: " ^ proof, [])
else apfst (fn s => "Try this command: " ^ s)
(produce_answer name (proof, thm_names, conj_pos, ctxt, th, subgoalno))
val _ = Output.debug (fn () => "Sledgehammer response (rc = " ^ string_of_int rc ^ "):\n" ^ proof)
- in (success, message, time, proof, thm_names, the_filtered_clauses) end;
-
+ in
+ Prover_Result {success=success, message=message,
+ theorem_names=real_thm_names, runtime=time, proof=proof,
+ internal_thm_names = thm_names, filtered_clauses=the_filtered_clauses}
+ end
-(** common provers **)
-
(* generic TPTP-based provers *)
-fun tptp_prover_opts_full max_new theory_const full command timeout ax_clauses fcls name n goal =
- external_prover
- (ResAtp.get_relevant max_new theory_const)
- (ResAtp.prepare_clauses false)
- (ResHolClause.tptp_write_file (AtpManager.get_full_types()))
- command
- ResReconstruct.find_failure
- (if full then ResReconstruct.structured_proof else ResReconstruct.lemma_list false)
- timeout ax_clauses fcls name n goal;
+fun gen_tptp_prover (name, prover_config) problem timeout =
+ let
+ val Prover_Config {max_new_clauses, insert_theory_const,
+ emit_structured_proof, command, arguments} = prover_config
+ val ATP_Problem {with_full_types, subgoal, goal, axiom_clauses,
+ filtered_clauses} = problem
+ in
+ external_prover
+ (ResAtp.get_relevant max_new_clauses insert_theory_const)
+ (ResAtp.prepare_clauses false)
+ (ResHolClause.tptp_write_file with_full_types)
+ command
+ (arguments timeout)
+ ResReconstruct.find_failure
+ (if emit_structured_proof then ResReconstruct.structured_proof
+ else ResReconstruct.lemma_list false)
+ axiom_clauses
+ filtered_clauses
+ name
+ subgoal
+ goal
+ end
-(*arbitrary ATP with TPTP input/output and problemfile as last argument*)
-fun tptp_prover_opts max_new theory_const =
- tptp_prover_opts_full max_new theory_const false;
-
-fun tptp_prover x = tptp_prover_opts 60 true x;
+fun tptp_prover (name, config) = (name, gen_tptp_prover (name, config))
-(*for structured proofs: prover must support TSTP*)
-fun full_prover_opts max_new theory_const =
- tptp_prover_opts_full max_new theory_const true;
-fun full_prover x = full_prover_opts 60 true x;
-
+(** common provers **)
(* Vampire *)
(*NB: Vampire does not work without explicit timelimit*)
-fun vampire_opts max_new theory_const timeout = tptp_prover_opts
- max_new theory_const
- (Path.explode "$VAMPIRE_HOME/vampire",
- ("--output_syntax tptp --mode casc -t " ^ string_of_int timeout))
- timeout;
-
-val vampire = vampire_opts 60 false;
+val vampire_max_new_clauses = 60
+val vampire_insert_theory_const = false
-fun vampire_opts_full max_new theory_const timeout = full_prover_opts
- max_new theory_const
- (Path.explode "$VAMPIRE_HOME/vampire",
- ("--output_syntax tptp --mode casc -t " ^ string_of_int timeout))
- timeout;
+fun vampire_prover_config full = Prover_Config {
+ command = Path.explode "$VAMPIRE_HOME/vampire",
+ arguments = (fn timeout => "--output_syntax tptp --mode casc" ^
+ " -t " ^ string_of_int timeout),
+ max_new_clauses = vampire_max_new_clauses,
+ insert_theory_const = vampire_insert_theory_const,
+ emit_structured_proof = full }
-val vampire_full = vampire_opts_full 60 false;
+val vampire = tptp_prover ("vampire", vampire_prover_config false)
+val vampire_full = tptp_prover ("vampire_full", vampire_prover_config true)
(* E prover *)
-fun eprover_opts max_new theory_const timeout = tptp_prover_opts
- max_new theory_const
- (Path.explode "$E_HOME/eproof",
- "--tstp-in --tstp-out -l5 -xAutoDev -tAutoDev --silent --cpu-limit=" ^ string_of_int timeout)
- timeout;
-
-val eprover = eprover_opts 100 false;
+val eprover_max_new_clauses = 100
+val eprover_insert_theory_const = false
-fun eprover_opts_full max_new theory_const timeout = full_prover_opts
- max_new theory_const
- (Path.explode "$E_HOME/eproof",
- "--tstp-in --tstp-out -l5 -xAutoDev -tAutoDev --silent --cpu-limit=" ^ string_of_int timeout)
- timeout;
+fun eprover_config full = Prover_Config {
+ command = Path.explode "$E_HOME/eproof",
+ arguments = (fn timeout => "--tstp-in --tstp-out -l5 -xAutoDev -tAutoDev" ^
+ " --silent --cpu-limit=" ^ string_of_int timeout),
+ max_new_clauses = eprover_max_new_clauses,
+ insert_theory_const = eprover_insert_theory_const,
+ emit_structured_proof = full }
-val eprover_full = eprover_opts_full 100 false;
+val eprover = tptp_prover ("e", eprover_config false)
+val eprover_full = tptp_prover ("e_full", eprover_config true)
(* SPASS *)
-fun spass_opts max_new theory_const timeout ax_clauses fcls name n goal = external_prover
- (ResAtp.get_relevant max_new theory_const)
- (ResAtp.prepare_clauses true)
- (ResHolClause.dfg_write_file (AtpManager.get_full_types()))
- (Path.explode "$SPASS_HOME/SPASS",
- "-Auto -SOS=1 -PGiven=0 -PProblem=0 -Splits=0 -FullRed=0 -DocProof -TimeLimit=" ^
- string_of_int timeout)
- ResReconstruct.find_failure
- (ResReconstruct.lemma_list true)
- timeout ax_clauses fcls name n goal;
+val spass_max_new_clauses = 40
+val spass_insert_theory_const = true
-val spass = spass_opts 40 true;
+fun spass_config insert_theory_const = Prover_Config {
+ command = Path.explode "$SPASS_HOME/SPASS",
+ arguments = (fn timeout => "-Auto -SOS=1 -PGiven=0 -PProblem=0 -Splits=0" ^
+ " -FullRed=0 -DocProof -TimeLimit=" ^ string_of_int timeout),
+ max_new_clauses = spass_max_new_clauses,
+ insert_theory_const = insert_theory_const,
+ emit_structured_proof = false }
+
+val spass = tptp_prover ("spass", spass_config spass_insert_theory_const)
+val spass_no_tc = tptp_prover ("spass_no_tc", spass_config false)
(* remote prover invocation via SystemOnTPTP *)
@@ -220,20 +284,29 @@
get_systems ());
fun get_system prefix = Synchronized.change_result systems (fn systems =>
- let val systems = if null systems then get_systems() else systems
- in (find_first (String.isPrefix prefix) systems, systems) end);
+ (if null systems then get_systems () else systems)
+ |> ` (find_first (String.isPrefix prefix)));
+
+fun get_the_system prefix =
+ (case get_system prefix of
+ NONE => error ("No system like " ^ quote prefix ^ " at SystemOnTPTP")
+ | SOME sys => sys)
-fun remote_prover_opts max_new theory_const args prover_prefix timeout =
- let val sys =
- case get_system prover_prefix of
- NONE => error ("No system like " ^ quote prover_prefix ^ " at SystemOnTPTP")
- | SOME sys => sys
- in tptp_prover_opts max_new theory_const
- (Path.explode "$ISABELLE_ATP_MANAGER/SystemOnTPTP",
- args ^ " -t " ^ string_of_int timeout ^ " -s " ^ sys) timeout
- end;
+fun remote_prover_config prover_prefix args max_new insert_tc = Prover_Config {
+ command = Path.explode "$ISABELLE_ATP_MANAGER/SystemOnTPTP",
+ arguments = (fn timeout => args ^ " -t " ^ string_of_int timeout ^ " -s " ^
+ get_the_system prover_prefix),
+ max_new_clauses = max_new,
+ insert_theory_const = insert_tc,
+ emit_structured_proof = false }
-val remote_prover = remote_prover_opts 60 false;
+val remote_vampire = tptp_prover ("remote_vampire", remote_prover_config
+ "Vampire---9" "" vampire_max_new_clauses vampire_insert_theory_const)
+
+val remote_eprover = tptp_prover ("remote_e", remote_prover_config
+ "EP---" "" eprover_max_new_clauses eprover_insert_theory_const)
+
+val remote_spass = tptp_prover ("remote_spass", remote_prover_config
+ "SPASS---" "-x" spass_max_new_clauses spass_insert_theory_const)
end;
-