(*  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 monomorphic_term : Type.tyenv -> term -> term

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

  val transform_elim_term : term -> term

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

  val subgoal_count : Proof.state -> int

  val strip_subgoal : 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"

fun serial_commas _ [] = ["??"]

  | serial_commas _ [s] = [s]

  | serial_commas conj [s1, s2] = [s1, conj, s2]

  | serial_commas conj [s1, s2, s3] = [s1 ^ ",", s2 ^ ",", conj, s3]

  | serial_commas conj (s :: ss) = s ^ "," :: serial_commas conj ss

val simplify_spaces = ATP_Proof.strip_spaces (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 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_term 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 = Logic.count_prems o prop_of o #goal o Proof.goal

fun strip_subgoal goal i =

  let

    val (t, frees) = Logic.goal_params (prop_of goal) i

    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 (map dest_Free frees), hyp_ts, concl_t) end

fun reserved_isar_keyword_table () =

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

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

end;