(*  Title:      HOL/Tools/Nitpick/nitpick_util.ML

    Author:     Jasmin Blanchette, TU Muenchen

    Copyright   2008, 2009, 2010

General-purpose functions used by the Nitpick modules.

*)

signature NITPICK_UTIL =

sig

  type styp = string * typ

  datatype polarity = Pos | Neg | Neut

  exception ARG of string * string

  exception BAD of string * string

  exception TOO_SMALL of string * string

  exception TOO_LARGE of string * string

  exception NOT_SUPPORTED of string

  exception SAME of unit

  val nitpick_prefix : string

  val curry3 : ('a * 'b * 'c -> 'd) -> 'a -> 'b -> 'c -> 'd

  val pairf : ('a -> 'b) -> ('a -> 'c) -> 'a -> 'b * 'c

  val int_for_bool : bool -> int

  val nat_minus : int -> int -> int

  val reasonable_power : int -> int -> int

  val exact_log : int -> int -> int

  val exact_root : int -> int -> int

  val offset_list : int list -> int list

  val index_seq : int -> int -> int list

  val filter_indices : int list -> 'a list -> 'a list

  val filter_out_indices : int list -> 'a list -> 'a list

  val fold1 : ('a -> 'a -> 'a) -> 'a list -> 'a

  val replicate_list : int -> 'a list -> 'a list

  val n_fold_cartesian_product : 'a list list -> 'a list list

  val all_distinct_unordered_pairs_of : ''a list -> (''a * ''a) list

  val nth_combination : (int * int) list -> int -> int list

  val all_combinations : (int * int) list -> int list list

  val all_permutations : 'a list -> 'a list list

  val batch_list : int -> 'a list -> 'a list list

  val chunk_list_unevenly : int list -> 'a list -> 'a list list

  val map3 : ('a -> 'b -> 'c -> 'd) -> 'a list -> 'b list -> 'c list -> 'd list

  val double_lookup :

    ('a * 'a -> bool) -> ('a option * 'b) list -> 'a -> 'b option

  val triple_lookup :

    (''a * ''a -> bool) -> (''a option * 'b) list -> ''a -> 'b option

  val is_substring_of : string -> string -> bool

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

  val plural_s : int -> string

  val plural_s_for_list : 'a list -> string

  val flip_polarity : polarity -> polarity

  val prop_T : typ

  val bool_T : typ

  val nat_T : typ

  val int_T : typ

  val nat_subscript : int -> string

  val time_limit : Time.time option -> ('a -> 'b) -> 'a -> 'b

  val DETERM_TIMEOUT : Time.time option -> tactic -> tactic

  val setmp_show_all_types : ('a -> 'b) -> 'a -> 'b

  val indent_size : int

  val pstrs : string -> Pretty.T list

  val unyxml : string -> string

  val maybe_quote : string -> string

end

structure Nitpick_Util : NITPICK_UTIL =

struct

type styp = string * typ

datatype polarity = Pos | Neg | Neut

exception ARG of string * string

exception BAD of string * string

exception TOO_SMALL of string * string

exception TOO_LARGE of string * string

exception NOT_SUPPORTED of string

exception SAME of unit

val nitpick_prefix = "Nitpick."

(* ('a * 'b * 'c -> 'd) -> 'a -> 'b -> 'c -> 'd *)

fun curry3 f = fn x => fn y => fn z => f (x, y, z)

(* ('a -> 'b) -> ('a -> 'c) -> 'a -> 'b * 'c *)

fun pairf f g x = (f x, g x)

(* bool -> int *)

fun int_for_bool b = if b then 1 else 0

(* int -> int -> int *)

fun nat_minus i j = if i > j then i - j else 0

val max_exponent = 16384

(* int -> int -> int *)

fun reasonable_power a 0 = 1

  | reasonable_power a 1 = a

  | reasonable_power 0 _ = 0

  | reasonable_power 1 _ = 1

  | reasonable_power a b =

    if b < 0 then

      raise ARG ("Nitpick_Util.reasonable_power",

                 "negative exponent (" ^ signed_string_of_int b ^ ")")

    else if b > max_exponent then

      raise TOO_LARGE ("Nitpick_Util.reasonable_power",

                       "too large exponent (" ^ signed_string_of_int b ^ ")")

    else

      let val c = reasonable_power a (b div 2) in

        c * c * reasonable_power a (b mod 2)

      end

(* int -> int -> int *)

fun exact_log m n =

  let

    val r = Math.ln (Real.fromInt n) / Math.ln (Real.fromInt m) |> Real.round

  in

    if reasonable_power m r = n then

      r

    else

      raise ARG ("Nitpick_Util.exact_log",

                 commas (map signed_string_of_int [m, n]))

  end

(* int -> int -> int *)

fun exact_root m n =

  let val r = Math.pow (Real.fromInt n, 1.0 / (Real.fromInt m)) |> Real.round in

    if reasonable_power r m = n then

      r

    else

      raise ARG ("Nitpick_Util.exact_root",

                 commas (map signed_string_of_int [m, n]))

  end

(* ('a -> 'a -> 'a) -> 'a list -> 'a *)

fun fold1 f = foldl1 (uncurry f)

(* int -> 'a list -> 'a list *)

fun replicate_list 0 _ = []

  | replicate_list n xs = xs @ replicate_list (n - 1) xs

(* int list -> int list *)

fun offset_list ns = rev (tl (fold (fn x => fn xs => (x + hd xs) :: xs) ns [0]))

(* int -> int -> int list *)

fun index_seq j0 n = if j0 < 0 then j0 downto j0 - n + 1 else j0 upto j0 + n - 1

(* int list -> 'a list -> 'a list *)

fun filter_indices js xs =

  let

    (* int -> int list -> 'a list -> 'a list *)

    fun aux _ [] _ = []

      | aux i (j :: js) (x :: xs) =

        if i = j then x :: aux (i + 1) js xs else aux (i + 1) (j :: js) xs

      | aux _ _ _ = raise ARG ("Nitpick_Util.filter_indices",

                               "indices unordered or out of range")

  in aux 0 js xs end

fun filter_out_indices js xs =

  let

    (* int -> int list -> 'a list -> 'a list *)

    fun aux _ [] xs = xs

      | aux i (j :: js) (x :: xs) =

        if i = j then aux (i + 1) js xs else x :: aux (i + 1) (j :: js) xs

      | aux _ _ _ = raise ARG ("Nitpick_Util.filter_out_indices",

                               "indices unordered or out of range")

  in aux 0 js xs end

(* 'a list -> 'a list list -> 'a list list *)

fun cartesian_product [] _ = []

  | cartesian_product (x :: xs) yss =

    map (cons x) yss @ cartesian_product xs yss

(* 'a list list -> 'a list list *)

fun n_fold_cartesian_product xss = fold_rev cartesian_product xss [[]]

(* ''a list -> (''a * ''a) list *)

fun all_distinct_unordered_pairs_of [] = []

  | all_distinct_unordered_pairs_of (x :: xs) =

    map (pair x) xs @ all_distinct_unordered_pairs_of xs

(* (int * int) list -> int -> int list *)

val nth_combination =

  let

    (* (int * int) list -> int -> int list * int *)

    fun aux [] n = ([], n)

      | aux ((k, j0) :: xs) n =

        let val (js, n) = aux xs n in ((n mod k) + j0 :: js, n div k) end

  in fst oo aux end

(* (int * int) list -> int list list *)

val all_combinations = n_fold_cartesian_product o map (uncurry index_seq o swap)

(* 'a list -> 'a list list *)

fun all_permutations [] = [[]]

  | all_permutations xs =

    maps (fn j => map (cons (nth xs j)) (all_permutations (nth_drop j xs)))

         (index_seq 0 (length xs))

(* int -> 'a list -> 'a list list *)

fun batch_list _ [] = []

  | batch_list k xs =

    if length xs <= k then [xs]

    else List.take (xs, k) :: batch_list k (List.drop (xs, k))

(* int list -> 'a list -> 'a list list *)

fun chunk_list_unevenly _ [] = []

  | chunk_list_unevenly [] ys = map single ys

  | chunk_list_unevenly (k :: ks) ys =

    let val (ys1, ys2) = chop k ys in ys1 :: chunk_list_unevenly ks ys2 end

(* ('a -> 'b -> 'c -> 'd) -> 'a list -> 'b list -> 'c list -> 'd list *)

fun map3 _ [] [] [] = []

  | map3 f (x :: xs) (y :: ys) (z :: zs) = f x y z :: map3 f xs ys zs

  | map3 _ _ _ _ = raise UnequalLengths

(* ('a * 'a -> bool) -> ('a option * 'b) list -> 'a -> 'b option *)

fun double_lookup eq ps key =

  case AList.lookup (fn (SOME x, SOME y) => eq (x, y) | _ => false) ps

                    (SOME key) of

    SOME z => SOME z

  | NONE => ps |> find_first (is_none o fst) |> Option.map snd

(* (''a * ''a -> bool) -> (''a option * 'b) list -> ''a -> 'b option *)

fun triple_lookup _ [(NONE, z)] _ = SOME z

  | triple_lookup eq ps key =

    case AList.lookup (op =) ps (SOME key) of

      SOME z => SOME z

    | NONE => double_lookup eq ps key

(* string -> string -> bool *)

fun is_substring_of needle stack =

  not (Substring.isEmpty (snd (Substring.position needle

                                                  (Substring.full stack))))

(* string -> string list -> string list *)

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

(* int -> string *)

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

(* 'a list -> string *)

fun plural_s_for_list xs = plural_s (length xs)

(* polarity -> polarity *)

fun flip_polarity Pos = Neg

  | flip_polarity Neg = Pos

  | flip_polarity Neut = Neut

val prop_T = @{typ prop}

val bool_T = @{typ bool}

val nat_T = @{typ nat}

val int_T = @{typ int}

(* string -> string *)

val subscript = implode o map (prefix "\<^isub>") o explode

(* int -> string *)

fun nat_subscript n =

  (* cheap trick to ensure proper alphanumeric ordering for one- and two-digit

     numbers *)

  if n <= 9 then "\<^bsub>" ^ signed_string_of_int n ^ "\<^esub>"

  else subscript (string_of_int n)

(* Time.time option -> ('a -> 'b) -> 'a -> 'b *)

fun time_limit NONE = I

  | time_limit (SOME delay) = TimeLimit.timeLimit delay

(* Time.time option -> tactic -> tactic *)

fun DETERM_TIMEOUT delay tac st =

  Seq.of_list (the_list (time_limit delay (fn () => SINGLE tac st) ()))

(* ('a -> 'b) -> 'a -> 'b *)

fun setmp_show_all_types f =

  setmp_CRITICAL show_all_types

                 (! show_types orelse ! show_sorts orelse ! show_all_types) f

val indent_size = 2

(* string -> Pretty.T list *)

val pstrs = Pretty.breaks o map Pretty.str o space_explode " "

(* XML.tree -> string *)

fun plain_string_from_xml_tree t =

  Buffer.empty |> XML.add_content t |> Buffer.content

(* string -> string *)

val unyxml = plain_string_from_xml_tree o YXML.parse

(* string -> bool *)

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

(* string -> string *)

fun maybe_quote y =

  let val s = unyxml y in

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

          OuterKeyword.is_keyword s) ? quote

  end

end;