(*  Title:      Pure/Isar/ML

    Author:     Florian Haftmann, TU Muenchen

Type classes derived from primitive axclasses and locales - interfaces.

*)

signature CLASS =

sig

  include CLASS_TARGET

    (*FIXME the split into class_target.ML, theory_target.ML and

      class.ML is artificial*)

  val class: binding -> class list -> Element.context_i list

    -> theory -> string * local_theory

  val class_cmd: binding -> xstring list -> Element.context list

    -> theory -> string * local_theory

  val prove_subclass: tactic -> class -> local_theory -> local_theory

  val subclass: class -> local_theory -> Proof.state

  val subclass_cmd: xstring -> local_theory -> Proof.state

end;

structure Class : CLASS =

struct

open Class_Target;

(** class definitions **)

local

(* calculating class-related rules including canonical interpretation *)

fun calculate thy class sups base_sort param_map assm_axiom =

  let

    val empty_ctxt = ProofContext.init thy;

    (* instantiation of canonical interpretation *)

    val aT = TFree (Name.aT, base_sort);

    val param_map_const = (map o apsnd) Const param_map;

    val param_map_inst = (map o apsnd)

      (Const o apsnd (map_atyps (K aT))) param_map;

    val const_morph = Element.inst_morphism thy

      (Symtab.empty, Symtab.make param_map_inst);

    val typ_morph = Element.inst_morphism thy

      (Symtab.empty |> Symtab.update (Name.aT, TFree (Name.aT, [class])), Symtab.empty);

    val (([raw_props], [(_, raw_inst_morph)], export_morph), _) = empty_ctxt

      |> Expression.cert_goal_expression ([(class, (("", false),

           Expression.Named param_map_const))], []);

    val (props, inst_morph) = if null param_map

      then (raw_props |> map (Morphism.term typ_morph),

        raw_inst_morph $> typ_morph)

      else (raw_props, raw_inst_morph); (*FIXME proper handling in

        locale.ML / expression.ML would be desirable*)

    (* witness for canonical interpretation *)

    val prop = try the_single props;

    val wit = Option.map (fn prop => let

        val sup_axioms = map_filter (fst o rules thy) sups;

        val loc_intro_tac = case Locale.intros_of thy class

          of (_, NONE) => all_tac

           | (_, SOME intro) => ALLGOALS (Tactic.rtac intro);

        val tac = loc_intro_tac

          THEN ALLGOALS (ProofContext.fact_tac (sup_axioms @ the_list assm_axiom))

      in Element.prove_witness empty_ctxt prop tac end) prop;

    val axiom = Option.map Element.conclude_witness wit;

    (* canonical interpretation *)

    val base_morph = inst_morph

      $> Morphism.binding_morphism (Binding.prefix false (class_prefix class))

      $> Element.satisfy_morphism (the_list wit);

    val defs = these_defs thy sups;

    val eq_morph = Element.eq_morphism thy defs;

    val morph = base_morph $> eq_morph;

    (* assm_intro *)

    fun prove_assm_intro thm =

      let

        val ((_, [thm']), _) = Variable.import true [thm] empty_ctxt;

        val thm'' = Morphism.thm (const_morph $> eq_morph) thm';

        val tac = ALLGOALS (ProofContext.fact_tac [thm'']);

      in SkipProof.prove_global thy [] [] (Thm.prop_of thm'') (K tac) end;

    val assm_intro = Option.map prove_assm_intro

      (fst (Locale.intros_of thy class));

    (* of_class *)

    val of_class_prop_concl = Logic.mk_inclass (aT, class);

    val of_class_prop = case prop of NONE => of_class_prop_concl

      | SOME prop => Logic.mk_implies (Morphism.term const_morph

          ((map_types o map_atyps) (K aT) prop), of_class_prop_concl);

    val sup_of_classes = map (snd o rules thy) sups;

    val loc_axiom_intros = map Drule.standard' (Locale.axioms_of thy class);

    val axclass_intro = #intro (AxClass.get_info thy class);

    val base_sort_trivs = Drule.sort_triv thy (aT, base_sort);

    val tac = REPEAT (SOMEGOAL

      (Tactic.match_tac (axclass_intro :: sup_of_classes

         @ loc_axiom_intros @ base_sort_trivs)

           ORELSE' Tactic.assume_tac));

    val of_class = SkipProof.prove_global thy [] [] of_class_prop (K tac);

  in (base_morph, morph, export_morph, axiom, assm_intro, of_class) end;

(* reading and processing class specifications *)

fun prep_class_elems prep_decl thy supexpr sups proto_base_sort raw_elems =

  let

    (* user space type system: only permits 'a type variable, improves towards 'a *)

    val base_constraints = (map o apsnd)

      (map_type_tfree (K (TVar ((Name.aT, 0), proto_base_sort))) o fst o snd)

        (these_operations thy sups);

    val reject_bcd_etc = (map o map_atyps) (fn T as TFree (v, sort) =>

          if v = Name.aT then T

          else error ("No type variable other than " ^ Name.aT ^ " allowed in class specification")

      | T => T);

    fun singleton_fixate thy algebra Ts =

      let

        fun extract f = (fold o fold_atyps) f Ts [];

        val tfrees = extract

          (fn TFree (v, sort) => insert (op =) (v, sort) | _ => I);

        val inferred_sort = extract

          (fn TVar (_, sort) => curry (Sorts.inter_sort algebra) sort | _ => I);

        val fixate_sort = if null tfrees then inferred_sort

          else case tfrees

           of [(_, a_sort)] => if Sorts.sort_le algebra (a_sort, inferred_sort)

                then Sorts.inter_sort algebra (a_sort, inferred_sort)

                else error ("Type inference imposes additional sort constraint "

                  ^ Syntax.string_of_sort_global thy inferred_sort

                  ^ " of type parameter " ^ Name.aT ^ " of sort "

                  ^ Syntax.string_of_sort_global thy a_sort ^ ".")

            | _ => error "Multiple type variables in class specification.";

      in (map o map_atyps) (K (TFree (Name.aT, fixate_sort))) Ts end;

    fun add_typ_check level name f = Context.proof_map (Syntax.add_typ_check level name (fn xs => fn ctxt =>

      let val xs' = f xs in if eq_list (op =) (xs, xs') then NONE else SOME (xs', ctxt) end));

    (* preprocessing elements, retrieving base sort from type-checked elements *)

    val init_class_body = fold (ProofContext.add_const_constraint o apsnd SOME) base_constraints

      #> redeclare_operations thy sups

      #> add_typ_check 10 "reject_bcd_etc" reject_bcd_etc

      #> add_typ_check ~10 "singleton_fixate" (singleton_fixate thy (Sign.classes_of thy));

    val ((_, _, inferred_elems), _) = ProofContext.init thy

      |> prep_decl supexpr init_class_body raw_elems;

    fun fold_element_types f (Element.Fixes fxs) = fold (fn (_, SOME T, _) => f T) fxs

      | fold_element_types f (Element.Constrains cnstrs) = fold (f o snd) cnstrs

      | fold_element_types f (Element.Assumes assms) = fold (fold (fn (t, ts) =>

          fold_types f t #> (fold o fold_types) f ts) o snd) assms

      | fold_element_types f (Element.Defines _) =

          error ("\"defines\" element not allowed in class specification.")

      | fold_element_types f (Element.Notes _) =

          error ("\"notes\" element not allowed in class specification.");

    val base_sort = if null inferred_elems then proto_base_sort else

      case (fold o fold_element_types) Term.add_tfreesT inferred_elems []

       of [] => error "No type variable in class specification"

        | [(_, sort)] => sort

        | _ => error "Multiple type variables in class specification"

  in (base_sort, inferred_elems) end;

val cert_class_elems = prep_class_elems Expression.cert_declaration;

val read_class_elems = prep_class_elems Expression.cert_read_declaration;

fun prep_class_spec prep_class prep_class_elems thy raw_supclasses raw_elems =

  let

    (* prepare import *)

    val inter_sort = curry (Sorts.inter_sort (Sign.classes_of thy));

    val sups = map (prep_class thy) raw_supclasses

      |> Sign.minimize_sort thy;

    val _ = case filter_out (is_class thy) sups

     of [] => ()

      | no_classes => error ("No (proper) classes: " ^ commas (map quote no_classes));

    val supparams = (map o apsnd) (snd o snd) (these_params thy sups);

    val supparam_names = map fst supparams;

    val _ = if has_duplicates (op =) supparam_names

      then error ("Duplicate parameter(s) in superclasses: "

        ^ (commas o map quote o duplicates (op =)) supparam_names)

      else ();

    val supexpr = (map (fn sup => (sup, (("", false), Expression.Positional [])))

      sups, []);

    val given_basesort = fold inter_sort (map (base_sort thy) sups) [];

    (* infer types and base sort *)

    val (base_sort, inferred_elems) = prep_class_elems thy supexpr sups

      given_basesort raw_elems;

    val sup_sort = inter_sort base_sort sups

    (* process elements as class specification *)

    val class_ctxt = begin sups base_sort (ProofContext.init thy)

    val ((_, _, syntax_elems), _) = class_ctxt

      |> Expression.cert_declaration supexpr I inferred_elems;

    fun check_vars e vs = if null vs

      then error ("No type variable in part of specification element "

        ^ (Pretty.output o Pretty.chunks) (Element.pretty_ctxt class_ctxt e))

      else ();

    fun check_element (e as Element.Fixes fxs) =

          map (fn (_, SOME T, _) => check_vars e (Term.add_tfreesT T [])) fxs

      | check_element (e as Element.Assumes assms) =

          maps (fn (_, ts_pss) => map

            (fn (t, _) => check_vars e (Term.add_tfrees t [])) ts_pss) assms

      | check_element e = [()];

    val _ = map check_element syntax_elems;

    fun fork_syn (Element.Fixes xs) =

          fold_map (fn (c, ty, syn) => cons (c, syn) #> pair (c, ty, NoSyn)) xs

          #>> Element.Fixes

      | fork_syn x = pair x;

    val (elems, global_syntax) = fold_map fork_syn syntax_elems [];

    val constrain = Element.Constrains ((map o apsnd o map_atyps)

      (K (TFree (Name.aT, base_sort))) supparams);

      (*FIXME perhaps better: control type variable by explicit

      parameter instantiation of import expression*)

  in (((sups, supparam_names), (sup_sort, base_sort, supexpr)), (constrain :: elems, global_syntax)) end;

val cert_class_spec = prep_class_spec (K I) cert_class_elems;

val read_class_spec = prep_class_spec Sign.intern_class read_class_elems;

(* class establishment *)

fun add_consts class base_sort sups supparams global_syntax thy =

  let

    (*FIXME simplify*)

    val supconsts = supparams

      |> AList.make (snd o the o AList.lookup (op =) (these_params thy sups))

      |> (map o apsnd o apsnd o map_atyps o K o TFree) (Name.aT, [class]);

    val all_params = Locale.params_of thy class;

    val raw_params = (snd o chop (length supparams)) all_params;

    fun add_const ((raw_c, raw_ty), _) thy =

      let

        val b = Binding.name raw_c;

        val c = Sign.full_name thy b;

        val ty = map_atyps (K (TFree (Name.aT, base_sort))) raw_ty;

        val ty0 = Type.strip_sorts ty;

        val ty' = map_atyps (K (TFree (Name.aT, [class]))) ty0;

        val syn = (the_default NoSyn o AList.lookup Binding.eq_name global_syntax) b;

      in

        thy

        |> Sign.declare_const [] ((b, ty0), syn)

        |> snd

        |> pair ((Name.of_binding b, ty), (c, ty'))

      end;

  in

    thy

    |> Sign.add_path (class_prefix class)

    |> fold_map add_const raw_params

    ||> Sign.restore_naming thy

    |-> (fn params => pair (supconsts @ (map o apfst) fst params, params))

  end;

fun adjungate_axclass bname class base_sort sups supsort supparams global_syntax thy =

  let

    (*FIXME simplify*)

    fun globalize param_map = map_aterms

      (fn Free (v, ty) => Const ((fst o the o AList.lookup (op =) param_map) v, ty)

        | t => t);

    val raw_pred = Locale.intros_of thy class

      |> fst

      |> Option.map (Logic.unvarify o Logic.strip_imp_concl o Thm.prop_of);

    fun get_axiom thy = case (#axioms o AxClass.get_info thy) class

     of [] => NONE

      | [thm] => SOME thm;

  in

    thy

    |> add_consts class base_sort sups supparams global_syntax

    |-> (fn (param_map, params) => AxClass.define_class (bname, supsort)

          (map (fst o snd) params)

          [(Thm.empty_binding, Option.map (globalize param_map) raw_pred |> the_list)]

    #> snd

    #> `get_axiom

    #-> (fn assm_axiom => fold (Sign.add_const_constraint o apsnd SOME o snd) params

    #> pair (param_map, params, assm_axiom)))

  end;

fun gen_class prep_spec bname raw_supclasses raw_elems thy =

  let

    val class = Sign.full_name thy bname;

    val (((sups, supparams), (supsort, base_sort, supexpr)), (elems, global_syntax)) =

      prep_spec thy raw_supclasses raw_elems;

  in

    thy

    |> Expression.add_locale bname Binding.empty supexpr elems

    |> snd |> LocalTheory.exit_global

    |> adjungate_axclass bname class base_sort sups supsort supparams global_syntax

    ||> Theory.checkpoint

    |-> (fn (param_map, params, assm_axiom) =>

       `(fn thy => calculate thy class sups base_sort param_map assm_axiom)

    #-> (fn (base_morph, morph, export_morph, axiom, assm_intro, of_class) =>

       Locale.add_registration (class, (morph, export_morph))

    #> Context.theory_map (Locale.activate_facts (class, morph $> export_morph))

    #> register class sups params base_sort base_morph axiom assm_intro of_class))

    |> TheoryTarget.init (SOME class)

    |> pair class

  end;

in

val class = gen_class cert_class_spec;

val class_cmd = gen_class read_class_spec;

end; (*local*)

(** subclass relations **)

local

fun gen_subclass prep_class do_proof raw_sup lthy =

  let

    val thy = ProofContext.theory_of lthy;

    val proto_sup = prep_class thy raw_sup;

    val proto_sub = case TheoryTarget.peek lthy

     of {is_class = false, ...} => error "Not in a class context"

      | {target, ...} => target;

    val (sub, sup) = AxClass.cert_classrel thy (proto_sub, proto_sup)

    val expr = ([(sup, (("", false), Expression.Positional []))], []);

    val (([props], deps, export), goal_ctxt) =

      Expression.cert_goal_expression expr lthy;

    val some_prop = try the_single props;

    val some_dep_morph = try the_single (map snd deps);

    fun after_qed some_wit =

      ProofContext.theory (register_subclass (sub, sup)

        some_dep_morph some_wit export)

      #> ProofContext.theory_of #> TheoryTarget.init (SOME sub);

  in do_proof after_qed some_prop goal_ctxt end;

fun user_proof after_qed some_prop =

  Element.witness_proof (after_qed o try the_single o the_single)

    [the_list some_prop];

fun tactic_proof tac after_qed some_prop ctxt =

  after_qed (Option.map

    (fn prop => Element.prove_witness ctxt prop tac) some_prop) ctxt;

in

val subclass = gen_subclass (K I) user_proof;

fun prove_subclass tac = gen_subclass (K I) (tactic_proof tac);

val subclass_cmd = gen_subclass Sign.read_class user_proof;

end; (*local*)

end;