(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_util.ML

    Author:     Jasmin Blanchette, TU Muenchen

General-purpose functions used by the Sledgehammer modules.

*)

signature SLEDGEHAMMER_UTIL =

sig

  val plural_s : int -> string

  val serial_commas : string -> string list -> string list

  val simplify_spaces : string -> string

  val parse_bool_option : bool -> string -> string -> bool option

  val parse_time_option : string -> string -> Time.time option

  val string_from_time : Time.time -> string

  val nat_subscript : int -> string

  val unyxml : string -> string

  val maybe_quote : string -> string

  val typ_of_dtyp :

    Datatype_Aux.descr -> (Datatype_Aux.dtyp * typ) list -> Datatype_Aux.dtyp

    -> typ

  val varify_type : Proof.context -> typ -> typ

  val instantiate_type : theory -> typ -> typ -> typ -> typ

  val varify_and_instantiate_type : Proof.context -> typ -> typ -> typ -> typ

  val is_type_surely_finite : Proof.context -> typ -> bool

  val is_type_surely_infinite : Proof.context -> typ list -> typ -> bool

  val monomorphic_term : Type.tyenv -> term -> term

  val eta_expand : typ list -> term -> int -> term

  val transform_elim_prop : term -> term

  val specialize_type : theory -> (string * typ) -> term -> term

  val subgoal_count : Proof.state -> int

  val strip_subgoal :

    Proof.context -> thm -> int -> (string * typ) list * term list * term

  val reserved_isar_keyword_table : unit -> unit Symtab.table

end;

structure Sledgehammer_Util : SLEDGEHAMMER_UTIL =

struct

fun plural_s n = if n = 1 then "" else "s"

val serial_commas = Try.serial_commas

val simplify_spaces = ATP_Proof.strip_spaces false (K true)

fun parse_bool_option option name s =

  (case s of

     "smart" => if option then NONE else raise Option

   | "false" => SOME false

   | "true" => SOME true

   | "" => SOME true

   | _ => raise Option)

  handle Option.Option =>

         let val ss = map quote ((option ? cons "smart") ["true", "false"]) in

           error ("Parameter " ^ quote name ^ " must be assigned " ^

                  space_implode " " (serial_commas "or" ss) ^ ".")

         end

val has_junk =

  exists (fn s => not (Symbol.is_digit s) andalso s <> ".") o raw_explode (* FIXME Symbol.explode (?) *)

fun parse_time_option _ "none" = NONE

  | parse_time_option name s =

    let val secs = if has_junk s then NONE else Real.fromString s in

      if is_none secs orelse Real.<= (the secs, 0.0) then

        error ("Parameter " ^ quote name ^ " must be assigned a positive \

               \number of seconds (e.g., \"60\", \"0.5\") or \"none\".")

      else

        SOME (seconds (the secs))

    end

fun string_from_time t =

  string_of_real (0.01 * Real.fromInt (Time.toMilliseconds t div 10)) ^ " s"

val subscript = implode o map (prefix "\<^isub>") o raw_explode  (* FIXME Symbol.explode (?) *)

fun nat_subscript n =

  n |> string_of_int |> print_mode_active Symbol.xsymbolsN ? subscript

val unyxml = XML.content_of o YXML.parse_body

val is_long_identifier = forall Lexicon.is_identifier o space_explode "."

fun maybe_quote y =

  let val s = unyxml y in

    y |> ((not (is_long_identifier (perhaps (try (unprefix "'")) s)) andalso

           not (is_long_identifier (perhaps (try (unprefix "?")) s))) orelse

           Keyword.is_keyword s) ? quote

  end

fun typ_of_dtyp _ typ_assoc (Datatype_Aux.DtTFree a) =

    the (AList.lookup (op =) typ_assoc (Datatype_Aux.DtTFree a))

  | typ_of_dtyp descr typ_assoc (Datatype_Aux.DtType (s, Us)) =

    Type (s, map (typ_of_dtyp descr typ_assoc) Us)

  | typ_of_dtyp descr typ_assoc (Datatype_Aux.DtRec i) =

    let val (s, ds, _) = the (AList.lookup (op =) descr i) in

      Type (s, map (typ_of_dtyp descr typ_assoc) ds)

    end

fun varify_type ctxt T =

  Variable.polymorphic_types ctxt [Const (@{const_name undefined}, T)]

  |> snd |> the_single |> dest_Const |> snd

(* TODO: use "Term_Subst.instantiateT" instead? *)

fun instantiate_type thy T1 T1' T2 =

  Same.commit (Envir.subst_type_same

                   (Sign.typ_match thy (T1, T1') Vartab.empty)) T2

  handle Type.TYPE_MATCH => raise TYPE ("instantiate_type", [T1, T1'], [])

fun varify_and_instantiate_type ctxt T1 T1' T2 =

  let val thy = Proof_Context.theory_of ctxt in

    instantiate_type thy (varify_type ctxt T1) T1' (varify_type ctxt T2)

  end

fun datatype_constrs thy (T as Type (s, Ts)) =

    (case Datatype.get_info thy s of

       SOME {index, descr, ...} =>

       let val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the in

         map (apsnd (fn Us => map (typ_of_dtyp descr (dtyps ~~ Ts)) Us ---> T))

             constrs

       end

     | NONE => [])

  | datatype_constrs _ _ = []

(* Similar to "Nitpick_HOL.bounded_exact_card_of_type".

   0 means infinite type, 1 means singleton type (e.g., "unit"), and 2 means

   cardinality 2 or more. The specified default cardinality is returned if the

   cardinality of the type can't be determined. *)

fun tiny_card_of_type ctxt default_card assigns T =

  let

    val thy = Proof_Context.theory_of ctxt

    val max = 2 (* 1 would be too small for the "fun" case *)

    fun aux slack avoid T =

      if member (op =) avoid T then

        0

      else case AList.lookup (Sign.typ_instance thy o swap) assigns T of

        SOME k => k

      | NONE =>

        case T of

          Type (@{type_name fun}, [T1, T2]) =>

          (case (aux slack avoid T1, aux slack avoid T2) of

             (k, 1) => if slack andalso k = 0 then 0 else 1

           | (0, _) => 0

           | (_, 0) => 0

           | (k1, k2) =>

             if k1 >= max orelse k2 >= max then max

             else Int.min (max, Integer.pow k2 k1))

        | @{typ prop} => 2

        | @{typ bool} => 2 (* optimization *)

        | @{typ nat} => 0 (* optimization *)

        | @{typ int} => 0 (* optimization *)

        | Type (s, _) =>

          (case datatype_constrs thy T of

             constrs as _ :: _ =>

             let

               val constr_cards =

                 map (Integer.prod o map (aux slack (T :: avoid)) o binder_types

                      o snd) constrs

             in

               if exists (curry (op =) 0) constr_cards then 0

               else Int.min (max, Integer.sum constr_cards)

             end

           | [] =>

             case Typedef.get_info ctxt s of

               ({abs_type, rep_type, ...}, _) :: _ =>

               (* We cheat here by assuming that typedef types are infinite if

                  their underlying type is infinite. This is unsound in general

                  but it's hard to think of a realistic example where this would

                  not be the case. We are also slack with representation types:

                  If a representation type has the form "sigma => tau", we

                  consider it enough to check "sigma" for infiniteness. (Look

                  for "slack" in this function.) *)

               (case varify_and_instantiate_type ctxt

                         (Logic.varifyT_global abs_type) T

                         (Logic.varifyT_global rep_type)

                     |> aux true avoid of

                  0 => 0

                | 1 => 1

                | _ => default_card)

             | [] => default_card)

          (* Very slightly unsound: Type variables are assumed not to be

             constrained to cardinality 1. (In practice, the user would most

             likely have used "unit" directly anyway.) *)

        | TFree _ => if default_card = 1 then 2 else default_card

          (* Schematic type variables that contain only unproblematic sorts

             (with no finiteness axiom) can safely be considered infinite. *)

        | TVar _ => default_card

  in Int.min (max, aux false [] T) end

fun is_type_surely_finite ctxt T = tiny_card_of_type ctxt 0 [] T <> 0

fun is_type_surely_infinite ctxt infinite_Ts T =

  tiny_card_of_type ctxt 1 (map (rpair 0) infinite_Ts) T = 0

fun monomorphic_term subst t =

  map_types (map_type_tvar (fn v =>

      case Type.lookup subst v of

        SOME typ => typ

      | NONE => raise TERM ("monomorphic_term: uninstanitated schematic type \

                            \variable", [t]))) t

fun eta_expand _ t 0 = t

  | eta_expand Ts (Abs (s, T, t')) n =

    Abs (s, T, eta_expand (T :: Ts) t' (n - 1))

  | eta_expand Ts t n =

    fold_rev (fn T => fn t' => Abs ("x" ^ nat_subscript n, T, t'))

             (List.take (binder_types (fastype_of1 (Ts, t)), n))

             (list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))

(* Converts an elim-rule into an equivalent theorem that does not have the

   predicate variable. Leaves other theorems unchanged. We simply instantiate

   the conclusion variable to False. (Cf. "transform_elim_theorem" in

   "Meson_Clausify".) *)

fun transform_elim_prop t =

  case Logic.strip_imp_concl t of

    @{const Trueprop} $ Var (z, @{typ bool}) =>

    subst_Vars [(z, @{const False})] t

  | Var (z, @{typ prop}) => subst_Vars [(z, @{prop False})] t

  | _ => t

fun specialize_type thy (s, T) t =

  let

    fun subst_for (Const (s', T')) =

      if s = s' then

        SOME (Sign.typ_match thy (T', T) Vartab.empty)

        handle Type.TYPE_MATCH => NONE

      else

        NONE

    | subst_for (t1 $ t2) =

      (case subst_for t1 of SOME x => SOME x | NONE => subst_for t2)

    | subst_for (Abs (_, _, t')) = subst_for t'

    | subst_for _ = NONE

  in

    case subst_for t of

      SOME subst => monomorphic_term subst t

    | NONE => raise Type.TYPE_MATCH

  end

val subgoal_count = Try.subgoal_count

fun strip_subgoal ctxt goal i =

  let

    val (t, (frees, params)) =

      Logic.goal_params (prop_of goal) i

      ||> (map dest_Free #> Variable.variant_frees ctxt [] #> `(map Free))

    val hyp_ts = t |> Logic.strip_assums_hyp |> map (curry subst_bounds frees)

    val concl_t = t |> Logic.strip_assums_concl |> curry subst_bounds frees

  in (rev params, hyp_ts, concl_t) end

fun reserved_isar_keyword_table () =

  union (op =) (Keyword.dest_keywords ()) (Keyword.dest_commands ())

  |> map (rpair ()) |> Symtab.make

end;