(*  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 rep_fun lthy =

   let

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

     val rep_fun_graph = (HOLogic.eq_const rty) $ Bound 1 $ (rep_fun $ Bound 0)

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

     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 (_ $ rep_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 rep_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 UNIV_typedef_to_Quotient} @{thm UNIV_typedef_to_equivp} 

           typedef_thm lthy

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

         derive_quot_and_equiv_thm @{thm open_typedef_to_Quotient} @{thm open_typedef_to_part_equivp} 

           typedef_thm lthy

       | _ => derive_quot_and_equiv_thm @{thm typedef_to_Quotient} @{thm typedef_to_part_equivp} 

           typedef_thm lthy)

   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;