(* Title: HOL/Sledgehammer.thy
Author: Lawrence C. Paulson, Cambridge University Computer Laboratory
Author: Jia Meng, Cambridge University Computer Laboratory and NICTA
Author: Fabian Immler, TU Muenchen
Author: Jasmin Blanchette, TU Muenchen
*)
header {* Sledgehammer: Isabelle--ATP Linkup *}
theory Sledgehammer
imports Plain Hilbert_Choice
uses
("Tools/ATP/async_manager.ML")
("Tools/ATP/atp_problem.ML")
("Tools/ATP/atp_systems.ML")
("~~/src/Tools/Metis/metis.ML")
("Tools/Sledgehammer/clausifier.ML")
("Tools/Sledgehammer/meson_tactic.ML")
("Tools/Sledgehammer/metis_clauses.ML")
("Tools/Sledgehammer/metis_tactics.ML")
("Tools/Sledgehammer/sledgehammer_util.ML")
("Tools/Sledgehammer/sledgehammer_filter.ML")
("Tools/Sledgehammer/sledgehammer_translate.ML")
("Tools/Sledgehammer/sledgehammer_reconstruct.ML")
("Tools/Sledgehammer/sledgehammer.ML")
("Tools/Sledgehammer/sledgehammer_minimize.ML")
("Tools/Sledgehammer/sledgehammer_isar.ML")
begin
definition skolem_id :: "'a \<Rightarrow> 'a" where
[no_atp]: "skolem_id = (\<lambda>x. x)"
definition COMBI :: "'a \<Rightarrow> 'a" where
[no_atp]: "COMBI P = P"
definition COMBK :: "'a \<Rightarrow> 'b \<Rightarrow> 'a" where
[no_atp]: "COMBK P Q = P"
definition COMBB :: "('b => 'c) \<Rightarrow> ('a => 'b) \<Rightarrow> 'a \<Rightarrow> 'c" where [no_atp]:
"COMBB P Q R = P (Q R)"
definition COMBC :: "('a \<Rightarrow> 'b \<Rightarrow> 'c) \<Rightarrow> 'b \<Rightarrow> 'a \<Rightarrow> 'c" where
[no_atp]: "COMBC P Q R = P R Q"
definition COMBS :: "('a \<Rightarrow> 'b \<Rightarrow> 'c) \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'c" where
[no_atp]: "COMBS P Q R = P R (Q R)"
definition fequal :: "'a \<Rightarrow> 'a \<Rightarrow> bool" where [no_atp]:
"fequal X Y \<longleftrightarrow> (X = Y)"
lemma fequal_imp_equal [no_atp]: "\<not> fequal X Y \<or> X = Y"
by (simp add: fequal_def)
lemma equal_imp_fequal [no_atp]: "\<not> X = Y \<or> fequal X Y"
by (simp add: fequal_def)
lemma equal_imp_equal [no_atp]: "X = Y ==> X = Y"
by auto
text{*Theorems for translation to combinators*}
lemma abs_S [no_atp]: "\<lambda>x. (f x) (g x) \<equiv> COMBS f g"
apply (rule eq_reflection)
apply (rule ext)
apply (simp add: COMBS_def)
done
lemma abs_I [no_atp]: "\<lambda>x. x \<equiv> COMBI"
apply (rule eq_reflection)
apply (rule ext)
apply (simp add: COMBI_def)
done
lemma abs_K [no_atp]: "\<lambda>x. y \<equiv> COMBK y"
apply (rule eq_reflection)
apply (rule ext)
apply (simp add: COMBK_def)
done
lemma abs_B [no_atp]: "\<lambda>x. a (g x) \<equiv> COMBB a g"
apply (rule eq_reflection)
apply (rule ext)
apply (simp add: COMBB_def)
done
lemma abs_C [no_atp]: "\<lambda>x. (f x) b \<equiv> COMBC f b"
apply (rule eq_reflection)
apply (rule ext)
apply (simp add: COMBC_def)
done
use "Tools/ATP/async_manager.ML"
use "Tools/ATP/atp_problem.ML"
use "Tools/ATP/atp_systems.ML"
setup ATP_Systems.setup
use "~~/src/Tools/Metis/metis.ML"
use "Tools/Sledgehammer/clausifier.ML"
use "Tools/Sledgehammer/meson_tactic.ML"
setup Meson_Tactic.setup
use "Tools/Sledgehammer/metis_clauses.ML"
use "Tools/Sledgehammer/metis_tactics.ML"
use "Tools/Sledgehammer/sledgehammer_util.ML"
use "Tools/Sledgehammer/sledgehammer_filter.ML"
use "Tools/Sledgehammer/sledgehammer_translate.ML"
use "Tools/Sledgehammer/sledgehammer_reconstruct.ML"
use "Tools/Sledgehammer/sledgehammer.ML"
setup Sledgehammer.setup
use "Tools/Sledgehammer/sledgehammer_minimize.ML"
use "Tools/Sledgehammer/sledgehammer_isar.ML"
setup Metis_Tactics.setup
end