(*  Title:      Pure/Isar/overloading.ML

     Author:     Florian Haftmann, TU Muenchen

 Overloaded definitions without any discipline.

 *)

 signature OVERLOADING =

 sig

   type improvable_syntax

   val activate_improvable_syntax: Proof.context -> Proof.context

   val map_improvable_syntax: (improvable_syntax -> improvable_syntax)

     -> Proof.context -> Proof.context

   val set_primary_constraints: Proof.context -> Proof.context

   val overloading: (string * (string * typ) * bool) list -> theory -> local_theory

   val overloading_cmd: (string * string * bool) list -> theory -> local_theory

 end;

 structure Overloading: OVERLOADING =

 struct

 (* generic check/uncheck combinators for improvable constants *)

 type improvable_syntax = ((((string * typ) list * (string * typ) list) *

   ((((string * typ -> (typ * typ) option) * (string * typ -> (typ * term) option)) * bool) *

     (term * term) list)) * bool);

 structure Improvable_Syntax = Proof_Data

 (

   type T = {

     primary_constraints: (string * typ) list,

     secondary_constraints: (string * typ) list,

     improve: string * typ -> (typ * typ) option,

     subst: string * typ -> (typ * term) option,

     consider_abbrevs: bool,

     unchecks: (term * term) list,

     passed: bool

   };

   fun init _ = {

     primary_constraints = [],

     secondary_constraints = [],

     improve = K NONE,

     subst = K NONE,

     consider_abbrevs = false,

     unchecks = [],

     passed = true

   };

 );

 fun map_improvable_syntax f = Improvable_Syntax.map (fn {primary_constraints,

     secondary_constraints, improve, subst, consider_abbrevs, unchecks, passed} =>

   let

     val (((primary_constraints', secondary_constraints'),

       (((improve', subst'), consider_abbrevs'), unchecks')), passed')

         = f (((primary_constraints, secondary_constraints),

             (((improve, subst), consider_abbrevs), unchecks)), passed)

   in

    {primary_constraints = primary_constraints', secondary_constraints = secondary_constraints',

     improve = improve', subst = subst', consider_abbrevs = consider_abbrevs',

     unchecks = unchecks', passed = passed'}

   end);

 val mark_passed = (map_improvable_syntax o apsnd) (K true);

 fun improve_term_check ts ctxt =

   let

     val thy = Proof_Context.theory_of ctxt;

     val {secondary_constraints, improve, subst, consider_abbrevs, passed, ...} =

       Improvable_Syntax.get ctxt;

     val is_abbrev = consider_abbrevs andalso Proof_Context.abbrev_mode ctxt;

     val passed_or_abbrev = passed orelse is_abbrev;

     fun accumulate_improvements (Const (c, ty)) =

           (case improve (c, ty) of

             SOME ty_ty' => Sign.typ_match thy ty_ty'

           | _ => I)

       | accumulate_improvements _ = I;

     val improvements = (fold o fold_aterms) accumulate_improvements ts Vartab.empty;

     val ts' = (map o map_types) (Envir.subst_type improvements) ts;

     fun apply_subst t =

       Envir.expand_term

         (fn Const (c, ty) =>

           (case subst (c, ty) of

             SOME (ty', t') =>

               if Sign.typ_instance thy (ty, ty')

               then SOME (ty', apply_subst t') else NONE

           | NONE => NONE)

         | _ => NONE) t;

     val ts'' = if is_abbrev then ts' else map apply_subst ts';

   in

     if eq_list (op aconv) (ts, ts'') andalso passed_or_abbrev then NONE

     else if passed_or_abbrev then SOME (ts'', ctxt)

     else

       SOME (ts'', ctxt

         |> fold (Proof_Context.add_const_constraint o apsnd SOME) secondary_constraints

         |> mark_passed)

   end;

 fun rewrite_liberal thy unchecks t =

   (case try (Pattern.rewrite_term thy unchecks []) t of

     NONE => NONE

   | SOME t' => if t aconv t' then NONE else SOME t');

 fun improve_term_uncheck ts ctxt =

   let

     val thy = Proof_Context.theory_of ctxt;

     val {unchecks, ...} = Improvable_Syntax.get ctxt;

     val ts' = map (rewrite_liberal thy unchecks) ts;

   in if exists is_some ts' then SOME (map2 the_default ts ts', ctxt) else NONE end;

 fun set_primary_constraints ctxt =

   let val {primary_constraints, ...} = Improvable_Syntax.get ctxt;

   in fold (Proof_Context.add_const_constraint o apsnd SOME) primary_constraints ctxt end;

 val activate_improvable_syntax =

   Context.proof_map

     (Syntax.context_term_check 0 "improvement" improve_term_check

     #> Syntax.context_term_uncheck 0 "improvement" improve_term_uncheck)

   #> set_primary_constraints;

 (* overloading target *)

 structure Data = Proof_Data

 (

   type T = ((string * typ) * (string * bool)) list;

   fun init _ = [];

 );

 val get_overloading = Data.get o Local_Theory.target_of;

 val map_overloading = Local_Theory.target o Data.map;

 fun operation lthy b =

   get_overloading lthy

   |> get_first (fn ((c, _), (v, checked)) =>

       if Binding.name_of b = v then SOME (c, (v, checked)) else NONE);

 fun synchronize_syntax ctxt =

   let

     val overloading = Data.get ctxt;

     fun subst (c, ty) =

       (case AList.lookup (op =) overloading (c, ty) of

         SOME (v, _) => SOME (ty, Free (v, ty))

       | NONE => NONE);

     val unchecks =

       map (fn (c_ty as (_, ty), (v, _)) => (Free (v, ty), Const c_ty)) overloading;

   in 

     ctxt

     |> map_improvable_syntax (K ((([], []), (((K NONE, subst), false), unchecks)), false))

   end

 fun define_overloaded (c, U) (v, checked) (b_def, rhs) =

   Local_Theory.background_theory_result

     (Thm.add_def_global (not checked) true

       (b_def, Logic.mk_equals (Const (c, Term.fastype_of rhs), rhs)))

   ##> map_overloading (filter_out (fn (_, (v', _)) => v' = v))

   ##> Local_Theory.target synchronize_syntax

   #-> (fn (_, def) => pair (Const (c, U), def))

 fun foundation (((b, U), mx), (b_def, rhs)) (type_params, term_params) lthy =

   (case operation lthy b of

     SOME (c, (v, checked)) =>

       if mx <> NoSyn

       then error ("Illegal mixfix syntax for overloaded constant " ^ quote c)

       else lthy |> define_overloaded (c, U) (v, checked) (b_def, rhs)

   | NONE => lthy

       |> Generic_Target.theory_foundation (((b, U), mx), (b_def, rhs)) (type_params, term_params));

 fun pretty lthy =

   let

     val overloading = get_overloading lthy;

     fun pr_operation ((c, ty), (v, _)) =

       Pretty.block (Pretty.breaks

         [Pretty.str v, Pretty.str "==", Pretty.str (Proof_Context.extern_const lthy c),

           Pretty.str "::", Syntax.pretty_typ lthy ty]);

   in Pretty.str "overloading" :: map pr_operation overloading end;

 fun conclude lthy =

   let

     val overloading = get_overloading lthy;

     val _ =

       if null overloading then ()

       else

         error ("Missing definition(s) for parameter(s) " ^

           commas_quote (map (Syntax.string_of_term lthy o Const o fst) overloading));

   in lthy end;

 fun gen_overloading prep_const raw_overloading thy =

   let

     val ctxt = Proof_Context.init_global thy;

     val _ = if null raw_overloading then error "At least one parameter must be given" else ();

     val overloading = raw_overloading |> map (fn (v, const, checked) =>

       (Term.dest_Const (prep_const ctxt const), (v, checked)));

   in

     thy

     |> Theory.checkpoint

     |> Proof_Context.init_global

     |> Data.put overloading

     |> fold (fn ((_, ty), (v, _)) => Variable.declare_names (Free (v, ty))) overloading

     |> activate_improvable_syntax

     |> synchronize_syntax

     |> Local_Theory.init NONE ""

        {define = Generic_Target.define foundation,

         notes = Generic_Target.notes

           (fn kind => fn global_facts => fn _ => Generic_Target.theory_notes kind global_facts),

         abbrev = Generic_Target.abbrev

           (fn prmode => fn (b, mx) => fn (t, _) => fn _ =>

             Generic_Target.theory_abbrev prmode ((b, mx), t)),

         declaration = Generic_Target.theory_declaration o #syntax,

         pretty = pretty,

         exit = Local_Theory.target_of o conclude}

   end;

 val overloading = gen_overloading (fn ctxt => Syntax.check_term ctxt o Const);

 val overloading_cmd = gen_overloading Syntax.read_term;

 end;