(*  Title:      nominal_dt_alpha.ML

    Author:     Christian Urban

    Author:     Cezary Kaliszyk

  Performing quotient constructions and lifting theorems

*)

signature NOMINAL_DT_QUOT =

sig

  val define_qtypes: (string list * binding * mixfix) list -> typ list -> term list -> 

    thm list -> local_theory -> Quotient_Info.quotdata_info list * local_theory

  val define_qconsts: typ list -> (string  * term * mixfix) list -> local_theory -> 

    Quotient_Info.qconsts_info list * local_theory

  val define_qperms: typ list -> string list -> (string * sort) list -> 

    (string * term * mixfix) list -> thm list -> local_theory -> local_theory

  val define_qsizes: typ list -> string list -> (string * sort) list -> 

    (string * term * mixfix) list -> local_theory -> local_theory

  val lift_thms: typ list -> thm list -> thm list -> Proof.context -> thm list * Proof.context

end

structure Nominal_Dt_Quot: NOMINAL_DT_QUOT =

struct

(* defines the quotient types *)

fun define_qtypes qtys_descr alpha_tys alpha_trms alpha_equivp_thms lthy =

  let

    val qty_args1 = map2 (fn ty => fn trm => (ty, trm, false)) alpha_tys alpha_trms

    val qty_args2 = (qtys_descr ~~ qty_args1) ~~ alpha_equivp_thms

  in

    fold_map Quotient_Type.add_quotient_type qty_args2 lthy

  end 

(* defines quotient constants *)

fun define_qconsts qtys consts_specs lthy =

  let

    val (qconst_infos, lthy') = 

      fold_map (Quotient_Def.lift_raw_const qtys) consts_specs lthy

    val phi = ProofContext.export_morphism lthy' lthy

  in

    (map (Quotient_Info.transform_qconsts phi) qconst_infos, lthy')

  end

(* defines the quotient permutations and proves pt-class *)

fun define_qperms qtys qfull_ty_names tvs perm_specs raw_perm_laws lthy =

  let

    val lthy1 = 

      lthy

      |> Local_Theory.exit_global

      |> Class.instantiation (qfull_ty_names, tvs, @{sort pt}) 

    val (qs, lthy2) = define_qconsts qtys perm_specs lthy1

    val ((_, raw_perm_laws'), lthy3) = Variable.importT raw_perm_laws lthy2

    val lifted_perm_laws = 

      map (Quotient_Tacs.lifted lthy3 qtys []) raw_perm_laws'

      |> Variable.exportT lthy3 lthy2

    fun tac _ =

      Class.intro_classes_tac [] THEN

        (ALLGOALS (resolve_tac lifted_perm_laws))

  in

    lthy2

    |> Class.prove_instantiation_exit tac 

    |> Named_Target.theory_init

  end

(* defines the size functions and proves size-class *)

fun define_qsizes qtys qfull_ty_names tvs size_specs lthy =

  let

    val tac = K (Class.intro_classes_tac [])

  in

    lthy

    |> Local_Theory.exit_global

    |> Class.instantiation (qfull_ty_names, tvs, @{sort size})

    |> snd o (define_qconsts qtys size_specs)

    |> Class.prove_instantiation_exit tac

    |> Named_Target.theory_init

  end

(* lifts a theorem and cleans all "_raw" parts

   from variable names *)

local

  val any = Scan.one (Symbol.not_eof)

  val raw = Scan.this_string "_raw"

  val exclude =

    Scan.repeat (Scan.unless raw any) --| raw >> implode

  val parser = Scan.repeat (exclude || any)

in

  fun unraw_str s =

    s |> explode

      |> Scan.finite Symbol.stopper parser >> implode 

      |> fst

end

fun unraw_vars_thm thm =

  let

    fun unraw_var_str ((s, i), T) = ((unraw_str s, i), T)

    val vars = Term.add_vars (prop_of thm) []

    val vars' = map (Var o unraw_var_str) vars

  in

    Thm.certify_instantiate ([], (vars ~~ vars')) thm

  end

fun unraw_bounds_thm th =

  let

    val trm = Thm.prop_of th

    val trm' = Term.map_abs_vars unraw_str trm

  in

    Thm.rename_boundvars trm trm' th

  end

fun lift_thms qtys simps thms ctxt =

  (map (Quotient_Tacs.lifted ctxt qtys simps

        #> unraw_bounds_thm

        #> unraw_vars_thm

        #> Drule.zero_var_indexes) thms, ctxt)

end (* structure *)