(*  Title:      HOL/ATP_Linkup.thy

     Author:     Lawrence C Paulson

     Author:     Jia Meng, NICTA

     Author:     Fabian Immler, TUM

 *)

 header {* The Isabelle-ATP Linkup *}

 theory ATP_Linkup

 imports Record Hilbert_Choice

 uses

   "Tools/polyhash.ML"

   "Tools/res_clause.ML"

   ("Tools/res_axioms.ML")

   ("Tools/res_hol_clause.ML")

   ("Tools/res_reconstruct.ML")

   ("Tools/res_atp.ML")

   ("Tools/atp_manager.ML")

   ("Tools/atp_wrapper.ML")

   "~~/src/Tools/Metis/metis.ML"

   ("Tools/metis_tools.ML")

 begin

 definition COMBI :: "'a => 'a"

   where "COMBI P == P"

 definition COMBK :: "'a => 'b => 'a"

   where "COMBK P Q == P"

 definition COMBB :: "('b => 'c) => ('a => 'b) => 'a => 'c"

   where "COMBB P Q R == P (Q R)"

 definition COMBC :: "('a => 'b => 'c) => 'b => 'a => 'c"

   where "COMBC P Q R == P R Q"

 definition COMBS :: "('a => 'b => 'c) => ('a => 'b) => 'a => 'c"

   where "COMBS P Q R == P R (Q R)"

 definition fequal :: "'a => 'a => bool"

   where "fequal X Y == (X=Y)"

 lemma fequal_imp_equal: "fequal X Y ==> X=Y"

   by (simp add: fequal_def)

 lemma equal_imp_fequal: "X=Y ==> fequal X Y"

   by (simp add: fequal_def)

 text{*These two represent the equivalence between Boolean equality and iff.

 They can't be converted to clauses automatically, as the iff would be

 expanded...*}

 lemma iff_positive: "P | Q | P=Q"

 by blast

 lemma iff_negative: "~P | ~Q | P=Q"

 by blast

 text{*Theorems for translation to combinators*}

 lemma abs_S: "(%x. (f x) (g x)) == COMBS f g"

 apply (rule eq_reflection)

 apply (rule ext) 

 apply (simp add: COMBS_def) 

 done

 lemma abs_I: "(%x. x) == COMBI"

 apply (rule eq_reflection)

 apply (rule ext) 

 apply (simp add: COMBI_def) 

 done

 lemma abs_K: "(%x. y) == COMBK y"

 apply (rule eq_reflection)

 apply (rule ext) 

 apply (simp add: COMBK_def) 

 done

 lemma abs_B: "(%x. a (g x)) == COMBB a g"

 apply (rule eq_reflection)

 apply (rule ext) 

 apply (simp add: COMBB_def) 

 done

 lemma abs_C: "(%x. (f x) b) == COMBC f b"

 apply (rule eq_reflection)

 apply (rule ext) 

 apply (simp add: COMBC_def) 

 done

 subsection {* Setup of external ATPs *}

 use "Tools/res_axioms.ML" setup ResAxioms.setup

 use "Tools/res_hol_clause.ML"

 use "Tools/res_reconstruct.ML" setup ResReconstruct.setup

 use "Tools/res_atp.ML"

 use "Tools/atp_manager.ML"

 use "Tools/atp_wrapper.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 *}

 text {* provers with stuctured output *}

 setup {* AtpManager.add_prover "vampire_full" AtpWrapper.vampire_full *}

 setup {* AtpManager.add_prover "e_full" AtpWrapper.eprover_full *}

 text {* on some problems better results *}

 setup {* AtpManager.add_prover "spass_no_tc" (AtpWrapper.spass_opts 40 false) *}

 text {* remote provers via SystemOnTPTP *}

 setup {* AtpManager.add_prover "remote_vampire"

   (AtpWrapper.remote_prover "-s Vampire---9.0") *}

 setup {* AtpManager.add_prover "remote_spass"

   (AtpWrapper.remote_prover "-s SPASS---3.01") *}

 setup {* AtpManager.add_prover "remote_e"

   (AtpWrapper.remote_prover "-s EP---1.0") *}

 subsection {* The Metis prover *}

 use "Tools/metis_tools.ML"

 setup MetisTools.setup

 end