src/Tools/adhoc_overloading.ML

avoid low-level Same structure;

(* Author: Alexander Krauss, TU Muenchen
   Author: Christian Sternagel, University of Innsbruck

Adhoc overloading of constants based on their types.
*)

signature ADHOC_OVERLOADING =
sig
  val is_overloaded: Proof.context -> string -> bool
  val generic_add_overloaded: string -> Context.generic -> Context.generic
  val generic_remove_overloaded: string -> Context.generic -> Context.generic
  val generic_add_variant: string -> term -> Context.generic -> Context.generic
  (*If the list of variants is empty at the end of "generic_remove_variant", then
  "generic_remove_overloaded" is called implicitly.*)
  val generic_remove_variant: string -> term -> Context.generic -> Context.generic
  val show_variants: bool Config.T
end

structure Adhoc_Overloading: ADHOC_OVERLOADING =
struct

val show_variants = Attrib.setup_config_bool @{binding show_variants} (K false);

(* errors *)

fun duplicate_variant_error oconst =
  error ("Duplicate variant of " ^ quote oconst);

fun not_a_variant_error oconst =
  error ("Not a variant of " ^  quote oconst);

fun not_overloaded_error oconst =
  error ("Constant " ^ quote oconst ^ " is not declared as overloaded");

fun unresolved_overloading_error ctxt (c, T) t instances =
  let val ctxt' = Config.put show_variants true ctxt
  in
    cat_lines (
      "Unresolved overloading of constant" ::
      quote c ^ " :: " ^ quote (Syntax.string_of_typ ctxt' T) ::
      "in term " ::
      quote (Syntax.string_of_term ctxt' t) ::
      (if null instances then "no instances" else "multiple instances:") ::
    map (Markup.markup Markup.item o Syntax.string_of_term ctxt') instances)
    |> error
  end;

(* generic data *)

fun variants_eq ((v1, T1), (v2, T2)) =
  Term.aconv_untyped (v1, v2) andalso T1 = T2;

structure Overload_Data = Generic_Data
(
  type T =
    {variants : (term * typ) list Symtab.table,
     oconsts : string Termtab.table};
  val empty = {variants = Symtab.empty, oconsts = Termtab.empty};
  val extend = I;

  fun merge
    ({variants = vtab1, oconsts = otab1},
     {variants = vtab2, oconsts = otab2}) : T =
    let
      fun merge_oconsts _ (oconst1, oconst2) =
        if oconst1 = oconst2 then oconst1
        else duplicate_variant_error oconst1;
    in
      {variants = Symtab.merge_list variants_eq (vtab1, vtab2),
       oconsts = Termtab.join merge_oconsts (otab1, otab2)}
    end;
);

fun map_tables f g =
  Overload_Data.map (fn {variants = vtab, oconsts = otab} =>
    {variants = f vtab, oconsts = g otab});

val is_overloaded = Symtab.defined o #variants o Overload_Data.get o Context.Proof;
val get_variants = Symtab.lookup o #variants o Overload_Data.get o Context.Proof;
val get_overloaded = Termtab.lookup o #oconsts o Overload_Data.get o Context.Proof;

fun generic_add_overloaded oconst context =
  if is_overloaded (Context.proof_of context) oconst then context
  else map_tables (Symtab.update (oconst, [])) I context;

fun generic_remove_overloaded oconst context =
  let
    fun remove_oconst_and_variants context oconst =
      let
        val remove_variants =
          (case get_variants (Context.proof_of context) oconst of
            NONE => I
          | SOME vs => fold (Termtab.remove (op =) o rpair oconst o fst) vs);
      in map_tables (Symtab.delete_safe oconst) remove_variants context end;
  in
    if is_overloaded (Context.proof_of context) oconst then remove_oconst_and_variants context oconst
    else not_overloaded_error oconst
  end;

local
  fun generic_variant add oconst t context =
    let
      val ctxt = Context.proof_of context;
      val _ = if is_overloaded ctxt oconst then () else not_overloaded_error oconst;
      val T = t |> fastype_of;
      val t' = Term.map_types (K dummyT) t;
    in
      if add then
        let
          val _ =
            (case get_overloaded ctxt t' of
              NONE => ()
            | SOME oconst' => duplicate_variant_error oconst');
        in
          map_tables (Symtab.cons_list (oconst, (t', T))) (Termtab.update (t', oconst)) context
        end
      else
        let
          val _ =
            if member variants_eq (the (get_variants ctxt oconst)) (t', T) then ()
            else not_a_variant_error oconst;
        in
          map_tables (Symtab.map_entry oconst (remove1 variants_eq (t', T)))
            (Termtab.delete_safe t') context
          |> (fn context =>
            (case get_variants (Context.proof_of context) oconst of
              SOME [] => generic_remove_overloaded oconst context
            | _ => context))
        end
    end;
in
  val generic_add_variant = generic_variant true;
  val generic_remove_variant = generic_variant false;
end;

(* check / uncheck *)

fun unifiable_with thy T1 T2 =
  let
    val maxidx1 = Term.maxidx_of_typ T1;
    val T2' = Logic.incr_tvar (maxidx1 + 1) T2;
    val maxidx2 = Term.maxidx_typ T2' maxidx1;
  in can (Sign.typ_unify thy (T1, T2')) (Vartab.empty, maxidx2) end;

fun get_candidates ctxt (c, T) =
  get_variants ctxt c
  |> Option.map (map_filter (fn (t, T') =>
    if unifiable_with (Proof_Context.theory_of ctxt) T T' then SOME t
    else NONE));

fun insert_variants ctxt t (oconst as Const (c, T)) =
      (case get_candidates ctxt (c, T) of
        SOME [] => unresolved_overloading_error ctxt (c, T) t []
      | SOME [variant] => variant
      | _ => oconst)
  | insert_variants _ _ oconst = oconst;

fun insert_overloaded ctxt variant =
  (case try Term.type_of variant of
    NONE => variant
  | SOME T =>
    Pattern.rewrite_term (Proof_Context.theory_of ctxt) []
      [Option.map (Const o rpair T) o get_overloaded ctxt o Term.map_types (K dummyT)] variant);

fun check ctxt =
  map (fn t => Term.map_aterms (insert_variants ctxt t) t);

fun uncheck ctxt =
  if Config.get ctxt show_variants then I
  else map (insert_overloaded ctxt);

fun reject_unresolved ctxt =
  let
    val the_candidates = the o get_candidates ctxt;
    fun check_unresolved t =
      (case filter (is_overloaded ctxt o fst) (Term.add_consts t []) of
        [] => t
      | (cT :: _) => unresolved_overloading_error ctxt cT t (the_candidates cT));
  in map check_unresolved end;

(* setup *)

val _ = Context.>>
  (Syntax_Phases.term_check 0 "adhoc_overloading" check
   #> Syntax_Phases.term_check 1 "adhoc_overloading_unresolved_check" reject_unresolved
   #> Syntax_Phases.term_uncheck 0 "adhoc_overloading" uncheck);

(* commands *)

fun generic_adhoc_overloading_cmd add =
  if add then
    fold (fn (oconst, ts) =>
      generic_add_overloaded oconst
      #> fold (generic_add_variant oconst) ts)
  else
    fold (fn (oconst, ts) =>
      fold (generic_remove_variant oconst) ts);

fun adhoc_overloading_cmd' add args phi =
  let val args' = args
    |> map (apsnd (map_filter (fn t =>
         let val t' = Morphism.term phi t;
         in if Term.aconv_untyped (t, t') then SOME t' else NONE end)));
  in generic_adhoc_overloading_cmd add args' end;

fun adhoc_overloading_cmd add raw_args lthy =
  let
    fun const_name ctxt = fst o dest_Const o Proof_Context.read_const ctxt false dummyT;
    fun read_term ctxt = singleton (Variable.polymorphic ctxt) o Syntax.read_term ctxt;
    val args =
      raw_args
      |> map (apfst (const_name lthy))
      |> map (apsnd (map (read_term lthy)));
  in
    Local_Theory.declaration {syntax = true, pervasive = false}
      (adhoc_overloading_cmd' add args) lthy
  end;

val _ =
  Outer_Syntax.local_theory @{command_spec "adhoc_overloading"}
    "add adhoc overloading for constants / fixed variables"
    (Parse.and_list1 (Parse.const -- Scan.repeat Parse.term) >> adhoc_overloading_cmd true);

val _ =
  Outer_Syntax.local_theory @{command_spec "no_adhoc_overloading"}
    "add adhoc overloading for constants / fixed variables"
    (Parse.and_list1 (Parse.const -- Scan.repeat Parse.term) >> adhoc_overloading_cmd false);

end;