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