(*  Title:      HOL/Tools/Lifting/lifting_setup.ML

    Author:     Ondrej Kuncar

Setting up the lifting infrastructure.

*)

signature LIFTING_SETUP =

sig

  exception SETUP_LIFTING_INFR of string

  val setup_lifting_infr: thm -> thm -> local_theory -> local_theory

  val setup_by_typedef_thm: thm -> local_theory -> local_theory

end;

structure Lifting_Setup: LIFTING_SETUP =

struct

infix 0 MRSL

fun ants MRSL thm = fold (fn rl => fn thm => rl RS thm) ants thm

exception SETUP_LIFTING_INFR of string

fun define_cr_rel equiv_thm abs_fun lthy =

  let

    fun force_type_of_rel rel forced_ty =

      let

        val thy = Proof_Context.theory_of lthy

        val rel_ty = (domain_type o fastype_of) rel

        val ty_inst = Sign.typ_match thy (rel_ty, forced_ty) Vartab.empty

      in

        Envir.subst_term_types ty_inst rel

      end

    val (rty, qty) = (dest_funT o fastype_of) abs_fun

    val abs_fun_graph = HOLogic.mk_eq(abs_fun $ Bound 1, Bound 0)

    val Abs_body = (case (HOLogic.dest_Trueprop o prop_of) equiv_thm of

      Const (@{const_name equivp}, _) $ _ => abs_fun_graph

      | Const (@{const_name part_equivp}, _) $ rel => 

        HOLogic.mk_conj (force_type_of_rel rel rty $ Bound 1 $ Bound 1, abs_fun_graph)

      | _ => raise SETUP_LIFTING_INFR "unsupported equivalence theorem"

      )

    val def_term = Abs ("x", rty, Abs ("y", qty, Abs_body));

    val qty_name = (fst o dest_Type) qty

    val cr_rel_name = Binding.prefix_name "cr_" (Binding.qualified_name qty_name)  

    val (fixed_def_term, lthy') = yield_singleton (Variable.importT_terms) def_term lthy

    val ((_, (_ , def_thm)), lthy'') =

      Local_Theory.define ((cr_rel_name, NoSyn), ((Thm.def_binding cr_rel_name, []), fixed_def_term)) lthy'

  in

    (def_thm, lthy'')

  end

fun define_abs_type quot_thm lthy =

  if Lifting_Def.can_generate_code_cert quot_thm then

    let

      val abs_type_thm = quot_thm RS @{thm Quotient_abs_rep}

      val add_abstype_attribute = 

          Thm.declaration_attribute (fn thm => Context.mapping (Code.add_abstype thm) I)

        val add_abstype_attrib = Attrib.internal (K add_abstype_attribute);

    in

      lthy

        |> (snd oo Local_Theory.note) ((Binding.empty, [add_abstype_attrib]), [abs_type_thm])

    end

  else

    lthy

fun setup_lifting_infr quot_thm equiv_thm lthy =

  let

    val (_, qtyp) = Lifting_Term.quot_thm_rty_qty quot_thm

    val qty_full_name = (fst o dest_Type) qtyp

    val quotients = { quot_thm = quot_thm }

    fun quot_info phi = Lifting_Info.transform_quotients phi quotients

  in

    lthy

      |> Local_Theory.declaration {syntax = false, pervasive = true}

        (fn phi => Lifting_Info.update_quotients qty_full_name (quot_info phi))

      |> define_abs_type quot_thm

  end

fun setup_by_typedef_thm typedef_thm lthy =

  let

    fun derive_quot_and_equiv_thm to_quot_thm to_equiv_thm typedef_thm lthy =

      let

        val (_ $ _ $ abs_fun $ _) = (HOLogic.dest_Trueprop o prop_of) typedef_thm

        val equiv_thm = typedef_thm RS to_equiv_thm

        val (T_def, lthy') = define_cr_rel equiv_thm abs_fun lthy

        val quot_thm =  [typedef_thm, T_def] MRSL to_quot_thm

      in

        (quot_thm, equiv_thm, lthy')

      end

    val typedef_set = (snd o dest_comb o HOLogic.dest_Trueprop o prop_of) typedef_thm

    val (quot_thm, equiv_thm, lthy') = (case typedef_set of

      Const ("Orderings.top_class.top", _) => 

        derive_quot_and_equiv_thm @{thm copy_type_to_Quotient} @{thm copy_type_to_equivp} 

          typedef_thm lthy

      | Const (@{const_name "Collect"}, _) $ Abs (_, _, _) => 

        derive_quot_and_equiv_thm @{thm invariant_type_to_Quotient} @{thm invariant_type_to_part_equivp} 

          typedef_thm lthy

      | _ => raise SETUP_LIFTING_INFR "unsupported typedef theorem")

  in

    setup_lifting_infr quot_thm equiv_thm lthy'

  end

fun setup_by_typedef_thm_aux xthm lthy = setup_by_typedef_thm (singleton (Attrib.eval_thms lthy) xthm) lthy

val _ = 

  Outer_Syntax.local_theory @{command_spec "setup_lifting"}

    "Setup lifting infrastructure" 

      (Parse_Spec.xthm >> (fn xthm => setup_by_typedef_thm_aux xthm))

end;