(*  Title:      Pure/type_infer_context.ML

    Author:     Stefan Berghofer and Markus Wenzel, TU Muenchen

Type-inference preparation and standard type inference.

*)

signature TYPE_INFER_CONTEXT =

sig

  val const_sorts: bool Config.T

  val prepare_positions: Proof.context -> term list -> term list * (Position.T * typ) list

  val prepare: Proof.context -> term list -> int * term list

  val infer_types: Proof.context -> term list -> term list

end;

structure Type_Infer_Context: TYPE_INFER_CONTEXT =

struct

(** prepare types/terms: create inference parameters **)

(* constraints *)

val const_sorts = Config.bool (Config.declare "const_sorts" (K (Config.Bool true)));

fun const_type ctxt =

  try ((not (Config.get ctxt const_sorts) ? Type.strip_sorts) o

    Consts.the_constraint (Proof_Context.consts_of ctxt));

fun var_type ctxt = the_default dummyT o Proof_Context.def_type ctxt;

(* prepare_typ *)

fun prepare_typ typ params_idx =

  let

    val (params', idx) = fold_atyps

      (fn TVar (xi, S) =>

          (fn ps_idx as (ps, idx) =>

            if Type_Infer.is_param xi andalso not (Vartab.defined ps xi)

            then (Vartab.update (xi, Type_Infer.mk_param idx S) ps, idx + 1) else ps_idx)

        | _ => I) typ params_idx;

    fun prepare (T as Type (a, Ts)) idx =

          if T = dummyT then (Type_Infer.mk_param idx [], idx + 1)

          else

            let val (Ts', idx') = fold_map prepare Ts idx

            in (Type (a, Ts'), idx') end

      | prepare (T as TVar (xi, _)) idx =

          (case Vartab.lookup params' xi of

            NONE => T

          | SOME p => p, idx)

      | prepare (TFree ("'_dummy_", S)) idx = (Type_Infer.mk_param idx S, idx + 1)

      | prepare (T as TFree _) idx = (T, idx);

    val (typ', idx') = prepare typ idx;

  in (typ', (params', idx')) end;

(* prepare_term *)

fun prepare_term ctxt tm (vparams, params, idx) =

  let

    fun add_vparm xi (ps_idx as (ps, idx)) =

      if not (Vartab.defined ps xi) then

        (Vartab.update (xi, Type_Infer.mk_param idx []) ps, idx + 1)

      else ps_idx;

    val (vparams', idx') = fold_aterms

      (fn Var (_, Type ("_polymorphic_", _)) => I

        | Var (xi, _) => add_vparm xi

        | Free (x, _) => add_vparm (x, ~1)

        | _ => I)

      tm (vparams, idx);

    fun var_param xi = the (Vartab.lookup vparams' xi);

    fun polyT_of T idx =

      apsnd snd (prepare_typ (Type_Infer.paramify_vars T) (Vartab.empty, idx));

    fun constraint T t ps =

      if T = dummyT then (t, ps)

      else

        let val (T', ps') = prepare_typ T ps

        in (Type.constraint T' t, ps') end;

    fun prepare (Const ("_type_constraint_", T) $ t) ps_idx =

          let

            val A = Type.constraint_type ctxt T;

            val (A', ps_idx') = prepare_typ A ps_idx;

            val (t', ps_idx'') = prepare t ps_idx';

          in (Const ("_type_constraint_", A' --> A') $ t', ps_idx'') end

      | prepare (Const (c, T)) (ps, idx) =

          (case const_type ctxt c of

            SOME U =>

              let val (U', idx') = polyT_of U idx

              in constraint T (Const (c, U')) (ps, idx') end

          | NONE => error ("Undeclared constant: " ^ quote c))

      | prepare (Var (xi, Type ("_polymorphic_", [T]))) (ps, idx) =

          let val (T', idx') = polyT_of T idx

          in (Var (xi, T'), (ps, idx')) end

      | prepare (Var (xi, T)) ps_idx = constraint T (Var (xi, var_param xi)) ps_idx

      | prepare (Free (x, T)) ps_idx = constraint T (Free (x, var_param (x, ~1))) ps_idx

      | prepare (Bound i) ps_idx = (Bound i, ps_idx)

      | prepare (Abs (x, T, t)) ps_idx =

          let

            val (T', ps_idx') = prepare_typ T ps_idx;

            val (t', ps_idx'') = prepare t ps_idx';

          in (Abs (x, T', t'), ps_idx'') end

      | prepare (t $ u) ps_idx =

          let

            val (t', ps_idx') = prepare t ps_idx;

            val (u', ps_idx'') = prepare u ps_idx';

          in (t' $ u', ps_idx'') end;

    val (tm', (params', idx'')) = prepare tm (params, idx');

  in (tm', (vparams', params', idx'')) end;

(* prepare_positions *)

fun prepare_positions ctxt tms =

  let

    val visible = Context_Position.is_visible ctxt;

    fun prepareT (Type (a, Ts)) ps_idx =

          let val (Ts', ps_idx') = fold_map prepareT Ts ps_idx

          in (Type (a, Ts'), ps_idx') end

      | prepareT T (ps, idx) =

          (case Term_Position.decode_positionT T of

            SOME pos =>

              if visible then

                let val U = Type_Infer.mk_param idx []

                in (U, ((pos, U) :: ps, idx + 1)) end

              else (dummyT, (ps, idx))

          | NONE => (T, (ps, idx)));

    fun prepare (Const ("_type_constraint_", T)) ps_idx =

          let

            val A = Type.constraint_type ctxt T;

            val (A', ps_idx') = prepareT A ps_idx;

          in (Const ("_type_constraint_", A' --> A'), ps_idx') end

      | prepare (Const (c, T)) ps_idx =

          let val (T', ps_idx') = prepareT T ps_idx

          in (Const (c, T'), ps_idx') end

      | prepare (Free (x, T)) ps_idx =

          let val (T', ps_idx') = prepareT T ps_idx

          in (Free (x, T'), ps_idx') end

      | prepare (Var (xi, T)) ps_idx =

          let val (T', ps_idx') = prepareT T ps_idx

          in (Var (xi, T'), ps_idx') end

      | prepare (t as Bound _) ps_idx = (t, ps_idx)

      | prepare (Abs (x, T, t)) ps_idx =

          let

            val (T', ps_idx') = prepareT T ps_idx;

            val (t', ps_idx'') = prepare t ps_idx';

          in (Abs (x, T', t'), ps_idx'') end

      | prepare (t $ u) ps_idx =

          let

            val (t', ps_idx') = prepare t ps_idx;

            val (u', ps_idx'') = prepare u ps_idx';

          in (t' $ u', ps_idx'') end;

    val idx = Type_Infer.param_maxidx_of tms + 1;

    val (tms', (ps, _)) = fold_map prepare tms ([], idx);

  in (tms', ps) end;

(** order-sorted unification of types **)

exception NO_UNIFIER of string * typ Vartab.table;

fun unify ctxt =

  let

    val thy = Proof_Context.theory_of ctxt;

    val arity_sorts = Type.arity_sorts (Context.pretty ctxt) (Sign.tsig_of thy);

    (* adjust sorts of parameters *)

    fun not_of_sort x S' S =

      "Variable " ^ x ^ "::" ^ Syntax.string_of_sort ctxt S' ^ " not of sort " ^

        Syntax.string_of_sort ctxt S;

    fun meet (_, []) tye_idx = tye_idx

      | meet (Type (a, Ts), S) (tye_idx as (tye, _)) =

          meets (Ts, arity_sorts a S handle ERROR msg => raise NO_UNIFIER (msg, tye)) tye_idx

      | meet (TFree (x, S'), S) (tye_idx as (tye, _)) =

          if Sign.subsort thy (S', S) then tye_idx

          else raise NO_UNIFIER (not_of_sort x S' S, tye)

      | meet (TVar (xi, S'), S) (tye_idx as (tye, idx)) =

          if Sign.subsort thy (S', S) then tye_idx

          else if Type_Infer.is_param xi then

            (Vartab.update_new

              (xi, Type_Infer.mk_param idx (Sign.inter_sort thy (S', S))) tye, idx + 1)

          else raise NO_UNIFIER (not_of_sort (Term.string_of_vname xi) S' S, tye)

    and meets (T :: Ts, S :: Ss) (tye_idx as (tye, _)) =

          meets (Ts, Ss) (meet (Type_Infer.deref tye T, S) tye_idx)

      | meets _ tye_idx = tye_idx;

    (* occurs check and assignment *)

    fun occurs_check tye xi (TVar (xi', _)) =

          if xi = xi' then raise NO_UNIFIER ("Occurs check!", tye)

          else

            (case Vartab.lookup tye xi' of

              NONE => ()

            | SOME T => occurs_check tye xi T)

      | occurs_check tye xi (Type (_, Ts)) = List.app (occurs_check tye xi) Ts

      | occurs_check _ _ _ = ();

    fun assign xi (T as TVar (xi', _)) S env =

          if xi = xi' then env

          else env |> meet (T, S) |>> Vartab.update_new (xi, T)

      | assign xi T S (env as (tye, _)) =

          (occurs_check tye xi T; env |> meet (T, S) |>> Vartab.update_new (xi, T));

    (* unification *)

    fun show_tycon (a, Ts) =

      quote (Syntax.string_of_typ ctxt (Type (a, replicate (length Ts) dummyT)));

    fun unif (T1, T2) (env as (tye, _)) =

      (case pairself (`Type_Infer.is_paramT o Type_Infer.deref tye) (T1, T2) of

        ((true, TVar (xi, S)), (_, T)) => assign xi T S env

      | ((_, T), (true, TVar (xi, S))) => assign xi T S env

      | ((_, Type (a, Ts)), (_, Type (b, Us))) =>

          if a <> b then

            raise NO_UNIFIER

              ("Clash of types " ^ show_tycon (a, Ts) ^ " and " ^ show_tycon (b, Us), tye)

          else fold unif (Ts ~~ Us) env

      | ((_, T), (_, U)) => if T = U then env else raise NO_UNIFIER ("", tye));

  in unif end;

(** simple type inference **)

(* infer *)

fun infer ctxt =

  let

    (* errors *)

    fun prep_output tye bs ts Ts =

      let

        val (Ts_bTs', ts') = Type_Infer.finish ctxt tye (Ts @ map snd bs, ts);

        val (Ts', Ts'') = chop (length Ts) Ts_bTs';

        fun prep t =

          let val xs = rev (Term.variant_frees t (rev (map fst bs ~~ Ts'')))

          in Term.subst_bounds (map Syntax_Trans.mark_boundT xs, t) end;

      in (map prep ts', Ts') end;

    fun err_loose i = error ("Loose bound variable: B." ^ string_of_int i);

    fun unif_failed msg =

      "Type unification failed" ^ (if msg = "" then "" else ": " ^ msg) ^ "\n\n";

    fun err_appl msg tye bs t T u U =

      let val ([t', u'], [T', U']) = prep_output tye bs [t, u] [T, U]

      in error (unif_failed msg ^ Type.appl_error ctxt t' T' u' U' ^ "\n") end;

    (* main *)

    fun inf _ (Const (_, T)) tye_idx = (T, tye_idx)

      | inf _ (Free (_, T)) tye_idx = (T, tye_idx)

      | inf _ (Var (_, T)) tye_idx = (T, tye_idx)

      | inf bs (Bound i) tye_idx =

          (snd (nth bs i handle General.Subscript => err_loose i), tye_idx)

      | inf bs (Abs (x, T, t)) tye_idx =

          let val (U, tye_idx') = inf ((x, T) :: bs) t tye_idx

          in (T --> U, tye_idx') end

      | inf bs (t $ u) tye_idx =

          let

            val (T, tye_idx') = inf bs t tye_idx;

            val (U, (tye, idx)) = inf bs u tye_idx';

            val V = Type_Infer.mk_param idx [];

            val tye_idx'' = unify ctxt (U --> V, T) (tye, idx + 1)

              handle NO_UNIFIER (msg, tye') => err_appl msg tye' bs t T u U;

          in (V, tye_idx'') end;

  in inf [] end;

(* main interfaces *)

fun prepare ctxt raw_ts =

  let

    val constrain_vars = Term.map_aterms

      (fn Free (x, T) => Type.constraint T (Free (x, var_type ctxt (x, ~1)))

        | Var (xi, T) => Type.constraint T (Var (xi, var_type ctxt xi))

        | t => t);

    val ts = burrow_types (Syntax.check_typs ctxt) raw_ts;

    val idx = Type_Infer.param_maxidx_of ts + 1;

    val (ts', (_, _, idx')) =

      fold_map (prepare_term ctxt o constrain_vars) ts

        (Vartab.empty, Vartab.empty, idx);

  in (idx', ts') end;

fun infer_types ctxt raw_ts =

  let

    val (idx, ts) = prepare ctxt raw_ts;

    val (tye, _) = fold (snd oo infer ctxt) ts (Vartab.empty, idx);

    val (_, ts') = Type_Infer.finish ctxt tye ([], ts);

  in ts' end;

end;