(* Title: HOL/Metis.thy
Author: Lawrence C. Paulson, Cambridge University Computer Laboratory
Author: Jia Meng, Cambridge University Computer Laboratory and NICTA
Author: Jasmin Blanchette, TU Muenchen
*)
header {* Metis Proof Method *}
theory Metis
imports Meson
uses "~~/src/Tools/Metis/metis.ML"
("Tools/Metis/metis_translate.ML")
("Tools/Metis/metis_reconstruct.ML")
("Tools/Metis/metis_tactics.ML")
("Tools/try_methods.ML")
begin
subsection {* Higher-order reasoning helpers *}
definition fFalse :: bool where [no_atp]:
"fFalse \<longleftrightarrow> False"
definition fTrue :: bool where [no_atp]:
"fTrue \<longleftrightarrow> True"
definition fNot :: "bool \<Rightarrow> bool" where [no_atp]:
"fNot P \<longleftrightarrow> \<not> P"
definition fconj :: "bool \<Rightarrow> bool \<Rightarrow> bool" where [no_atp]:
"fconj P Q \<longleftrightarrow> P \<and> Q"
definition fdisj :: "bool \<Rightarrow> bool \<Rightarrow> bool" where [no_atp]:
"fdisj P Q \<longleftrightarrow> P \<or> Q"
definition fimplies :: "bool \<Rightarrow> bool \<Rightarrow> bool" where [no_atp]:
"fimplies P Q \<longleftrightarrow> (P \<longrightarrow> Q)"
definition fequal :: "'a \<Rightarrow> 'a \<Rightarrow> bool" where [no_atp]:
"fequal x y \<longleftrightarrow> (x = y)"
subsection {* Literal selection helpers *}
definition select :: "'a \<Rightarrow> 'a" where
[no_atp]: "select = (\<lambda>x. x)"
lemma not_atomize: "(\<not> A \<Longrightarrow> False) \<equiv> Trueprop A"
by (cut_tac atomize_not [of "\<not> A"]) simp
lemma atomize_not_select: "(A \<Longrightarrow> select False) \<equiv> Trueprop (\<not> A)"
unfolding select_def by (rule atomize_not)
lemma not_atomize_select: "(\<not> A \<Longrightarrow> select False) \<equiv> Trueprop A"
unfolding select_def by (rule not_atomize)
lemma select_FalseI: "False \<Longrightarrow> select False" by simp
subsection {* Metis package *}
use "Tools/Metis/metis_translate.ML"
use "Tools/Metis/metis_reconstruct.ML"
use "Tools/Metis/metis_tactics.ML"
setup {* Metis_Tactics.setup *}
hide_const (open) fFalse fTrue fNot fconj fdisj fimplies fequal select
hide_fact (open) fFalse_def fTrue_def fNot_def fconj_def fdisj_def fimplies_def
fequal_def select_def not_atomize atomize_not_select not_atomize_select
select_FalseI
subsection {* Try Methods *}
use "Tools/try_methods.ML"
setup {* Try_Methods.setup *}
end