theory NewFv

begin

ML {*

datatype bmodes =

   BEmy of int

|  BLst of ((term option * int) list) * (int list)

|  BSet of ((term option * int) list) * (int list)

|  BRes of ((term option * int) list) * (int list)

*}

ML {*

fun mk_singleton_atom x = HOLogic.mk_set @{typ atom} [mk_atom x];

val noatoms = @{term "{} :: atom set"};

fun mk_union sets =

  fold (fn a => fn b =>

  if a = noatoms then b else

  if b = noatoms then a else

  if a = b then a else

  HOLogic.mk_binop @{const_name sup} (a, b)) (rev sets) noatoms;

*}

ML {*

fun is_atom thy ty =

  Sign.of_sort thy (ty, @{sort at_base})

fun is_atom_set thy (Type ("fun", [t, @{typ bool}])) = is_atom thy t

  | is_atom_set _ _ = false;

fun is_atom_fset thy (Type ("FSet.fset", [t])) = is_atom thy t

  | is_atom_fset _ _ = false;

fun mk_atom_set t =

let

  val ty = fastype_of t;

  val atom_ty = HOLogic.dest_setT ty --> @{typ atom};

  val img_ty = atom_ty --> ty --> @{typ "atom set"};

in

  (Const (@{const_name image}, img_ty) $ mk_atom_ty atom_ty t)

end;

fun mk_atom_fset t =

let

  val ty = fastype_of t;

  val atom_ty = dest_fsetT ty --> @{typ atom};

  val fmap_ty = atom_ty --> ty --> @{typ "atom fset"};

  val fset_to_set = @{term "fset_to_set :: atom fset \<Rightarrow> atom set"}

in

  fset_to_set $ (Const (@{const_name fmap}, fmap_ty) $ mk_atom_ty atom_ty t)

end;

fun mk_diff a b =

  if b = noatoms then a else

  if b = a then noatoms else

  HOLogic.mk_binop @{const_name minus} (a, b);

*}

ML {*

fun atoms thy t =

let

  val ty = fastype_of t;

in

  if is_atom thy ty 

    then mk_singleton_atom t 

  else if is_atom_set thy ty 

    then mk_atom_set t 

  else if is_atom_fset thy ty 

    then mk_atom_fset t 

  else noatoms

end

*}

ML {*

fun setify x =

  if fastype_of x = @{typ "atom list"} 

  then @{term "set::atom list \<Rightarrow> atom set"} $ x 

  else x

*}

ML {*

fun fv_bm_lsts thy dts args fv_frees bn_fvbn binds bodys =

let

  fun fv_body i =

    let

      val x = nth args i;

      val dt = nth dts i;

    in

    end

  val fv_bodys = mk_union (map fv_body bodys)

  val bound_vars =

    case binds of

      [(SOME bn, i)] => setify (bn $ nth args i)

    | _ => mk_union (map fv_body (map snd binds));

  val non_rec_vars =

    case binds of

      [(SOME bn, i)] =>

        if i mem bodys

        then ((the (AList.lookup (op=) bn_fvbn bn)) $ nth args i)

        else noatoms

    | _ => noatoms

in

  mk_union [mk_diff fv_bodys bound_vars, non_rec_vars]

end

*}

ML {*

fun fv_bn_bm thy dts args fv_frees bn_fvbn args_in_bn bm =

case bm of

  BEmy i =>

    let

      val x = nth args i;

      val dt = nth dts i;

    in

      case AList.lookup (op=) args_in_bn i of

      | SOME (SOME (f : term)) => (the (AList.lookup (op=) bn_fvbn f)) $ x

      | SOME NONE => noatoms

    end

| BLst (x, y) => fv_bm_lsts thy dts args fv_frees bn_fvbn x y

| BSet (x, y) => fv_bm_lsts thy dts args fv_frees bn_fvbn x y

| BRes (x, y) => fv_bm_lsts thy dts args fv_frees bn_fvbn x y

*}

ML {*

let

  let

    val Ts = map (Datatype_Aux.typ_of_dtyp dt_descr sorts) dts;

    val names = Datatype_Prop.make_tnames Ts;

    val args = map Free (names ~~ Ts);

    val c = Const (cname, Ts ---> (nth_dtyp dt_descr sorts ith_dtyp));

    val fv_bn_bm = fv_bn_bm thy dts args fv_frees bn_fvbn args_in_bn

  in

    HOLogic.mk_Trueprop (HOLogic.mk_eq

  end;

  val (_, (_, _, constrs)) = nth dt_descr ith_dtyp;

in

end

*}

ML {*

let

  fun mk_fvbn_free (bn, ith, _) =

    let

      val fvbn_name = "fv_" ^ (Long_Name.base_name (fst (dest_Const bn)));

    in

      (fvbn_name, Free (fvbn_name, fastype_of (nth fv_frees ith)))

    end;

  val (fvbn_names, fvbn_frees) = split_list (map mk_fvbn_free bn_funs);

  val bn_fvbn = (map (fn (bn, _, _) => bn) bn_funs) ~~ fvbn_frees

in

  (bn_fvbn, fvbn_names, eqs)

end

*}

ML {*

fun fv_bm thy dts args fv_frees bn_fvbn bm =

case bm of

  BEmy i =>

    let

      val x = nth args i;

      val dt = nth dts i;

    in

    end

| BLst (x, y) => fv_bm_lsts thy dts args fv_frees bn_fvbn x y

| BSet (x, y) => fv_bm_lsts thy dts args fv_frees bn_fvbn x y

| BRes (x, y) => fv_bm_lsts thy dts args fv_frees bn_fvbn x y

*}

ML {*

let

  let

    val Ts = map (Datatype_Aux.typ_of_dtyp dt_descr sorts) dts;

    val names = Datatype_Prop.make_tnames Ts;

    val args = map Free (names ~~ Ts);

    val c = Const (cname, Ts ---> (nth_dtyp dt_descr sorts ith_dtyp));

    val fv_bn_bm = fv_bm thy dts args fv_frees bn_fvbn

  in

    HOLogic.mk_Trueprop (HOLogic.mk_eq

  end;

  val (_, (_, _, constrs)) = nth dt_descr ith_dtyp;

in

end

*}

ML {*

*}

ML {*

fun define_raw_fv (dt_info : Datatype_Aux.info) bn_funs bclauses lthy =

let

  val thy = ProofContext.theory_of lthy;

  val {descr as dt_descr, sorts, ...} = dt_info;

  val fv_names = prefix_dt_names dt_descr sorts "fv_"

  val fv_types = map (fn (i, _) => nth_dtyp descr sorts i --> @{typ "atom set"}) dt_descr;

  val fv_frees = map Free (fv_names ~~ fv_types);

    fv_bns thy dt_descr sorts fv_frees bn_funs bclauses;

  val fvbns = map snd bn_fvbn;

  val fv_nums = 0 upto (length fv_frees - 1)

  val fv_eqs = map2 (fv thy dt_descr sorts fv_frees bn_fvbn) bclauses (fv_frees ~~ fv_nums);

  val all_fv_names = map (fn s => (Binding.name s, NONE, NoSyn)) (fv_names @ fv_bn_names)

  val all_fv_eqs = map (pair Attrib.empty_binding) (flat fv_eqs @ flat fv_bn_eqs)

in

end

*}

end