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 const lthy =
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
*}

ML {*
fun remove_alls trm =
let
  val vars = strip_all_vars trm
  val fs = rev (map Free vars)
in
  ((map fst vars), subst_bounds (fs, (strip_all_body trm)))
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 => remove_alls (term_of (cprem_of th 1))
end
*}

ML {*
fun prove_const_rsp bind const tac ctxt =
let
  val rsp_goal = const_rsp const ctxt
  val thy = ProofContext.theory_of ctxt
  val (fixed, user_goal) = get_rsp_goal thy rsp_goal
  val user_thm = Goal.prove ctxt fixed [] user_goal tac
  fun tac _ = (REPEAT o rtac @{thm fun_rel_id} THEN' rtac user_thm THEN_ALL_NEW atac) 1
  val rsp_thm = Goal.prove ctxt [] [] rsp_goal tac
in
   ctxt
|> snd o Local_Theory.note 
  ((Binding.empty, [Attrib.internal (fn _ => Quotient_Info.rsp_rules_add)]), [rsp_thm])
|> snd o Local_Theory.note ((bind, []), [user_thm])
end
*}

ML {*
fun fv_rsp_tac induct fv_simps =
  eresolve_tac induct THEN_ALL_NEW
  asm_full_simp_tac (HOL_ss addsimps (@{thm alpha_gen} :: fv_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 @{thm fun_rel_id} 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
*}


end