theory Rsp

imports Abs

begin

ML {*

fun define_quotient_type args tac ctxt =

let

  val mthd = Method.SIMPLE_METHOD tac

  val mthdt = Method.Basic (fn _ => mthd)

  val bymt = Proof.global_terminal_proof (mthdt, NONE)

in

  bymt (Quotient_Type.quotient_type args ctxt)

end

*}

ML {*

fun const_rsp lthy const =

let

  val nty = fastype_of (Quotient_Term.quotient_lift_const ("", const) lthy)

  val rel = Quotient_Term.equiv_relation_chk lthy (fastype_of const, nty);

in

  HOLogic.mk_Trueprop (rel $ const $ const)

end

*}

(* Replaces bounds by frees and meta implications by implications *)

ML {*

fun prepare_goal trm =

let

  val vars = strip_all_vars trm

  val fs = rev (map Free vars)

  val (fixes, no_alls) = ((map fst vars), subst_bounds (fs, (strip_all_body trm)))

  val prems = map HOLogic.dest_Trueprop (Logic.strip_imp_prems no_alls)

  val concl = HOLogic.dest_Trueprop (Logic.strip_imp_concl no_alls)

in

  (fixes, fold (curry HOLogic.mk_imp) prems concl)

end

*}

ML {*

fun get_rsp_goal thy trm =

let

  val goalstate = Goal.init (cterm_of thy trm);

  val tac = REPEAT o rtac @{thm fun_rel_id};

in

  case (SINGLE (tac 1) goalstate) of

    NONE => error "rsp_goal failed"

  | SOME th => prepare_goal (term_of (cprem_of th 1))

end

*}

ML {*

fun repeat_mp thm = repeat_mp (mp OF [thm]) handle THM _ => thm

*}

ML {*

fun prove_const_rsp bind consts tac ctxt =

let

  val rsp_goals = map (const_rsp ctxt) consts

  val thy = ProofContext.theory_of ctxt

  val (fixed, user_goals) = split_list (map (get_rsp_goal thy) rsp_goals)

  val fixed' = distinct (op =) (flat fixed)

  val user_goal = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj user_goals)

  val user_thm = Goal.prove ctxt fixed' [] user_goal tac

  val user_thms = map repeat_mp (HOLogic.conj_elims user_thm)

  fun tac _ = (REPEAT o rtac @{thm fun_rel_id} THEN' resolve_tac user_thms THEN_ALL_NEW atac) 1

  val rsp_thms = map (fn gl => Goal.prove ctxt [] [] gl tac) rsp_goals

in

   ctxt

|> snd o Local_Theory.note 

  ((Binding.empty, [Attrib.internal (fn _ => Quotient_Info.rsp_rules_add)]), rsp_thms)

|> snd o Local_Theory.note ((bind, []), user_thms)

end

*}

ML {*

fun fvbv_rsp_tac induct fvbv_simps =

  ((((rtac impI THEN' etac induct) ORELSE' rtac induct) THEN_ALL_NEW

  (TRY o rtac @{thm TrueI})) THEN_ALL_NEW asm_full_simp_tac

  (HOL_ss addsimps (@{thm alpha_gen} :: fvbv_simps)))

*}

ML {*

fun constr_rsp_tac inj rsp equivps =

let

  val reflps = map (fn x => @{thm equivp_reflp} OF [x]) equivps

in

  REPEAT o rtac impI THEN'

  simp_tac (HOL_ss addsimps inj) THEN'

  (TRY o REPEAT_ALL_NEW (CHANGED o rtac conjI)) THEN_ALL_NEW

  (asm_simp_tac HOL_ss THEN_ALL_NEW (

   rtac @{thm exI[of _ "0 :: perm"]} THEN'

   asm_full_simp_tac (HOL_ss addsimps (rsp @ reflps @

     @{thms alpha_gen fresh_star_def fresh_zero_perm permute_zero ball_triv}))

  ))

end

*}

(* Testing code

local_setup {* prove_const_rsp @{binding fv_rtrm2_rsp} [@{term rbv2}]

  (fn _ => fv_rsp_tac @{thm alpha_rtrm2_alpha_rassign.inducts(2)} @{thms fv_rtrm2_fv_rassign.simps} 1) *}*)

(*ML {*

  val rsp_goals = map (const_rsp @{context}) [@{term rbv2}]

  val (fixed, user_goals) = split_list (map (get_rsp_goal @{theory}) rsp_goals)

  val fixed' = distinct (op =) (flat fixed)

  val user_goal = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj user_goals)

*}

prove ug: {* user_goal *}

ML_prf {*

val induct = @{thm alpha_rtrm2_alpha_rassign.inducts(2)}

val fv_simps = @{thms rbv2.simps}

*} 

*)

end