(*  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 pair_from_fun : (bool -> 'a) -> 'a * 'a

   val fun_from_pair : 'a * 'a -> bool -> 'a

   val int_from_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 plural_s : int -> string

   val plural_s_for_list : 'a list -> string

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

   val pretty_serial_commas : string -> Pretty.T list -> Pretty.T list

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

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

   val nat_subscript : int -> string

   val flip_polarity : polarity -> polarity

   val prop_T : typ

   val bool_T : typ

   val nat_T : typ

   val int_T : typ

   val simple_string_of_typ : typ -> string

   val is_real_constr : theory -> string * typ -> bool

   val typ_of_dtyp :

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

     -> typ

   val is_of_class_const : theory -> string * typ -> bool

   val get_class_def : theory -> string -> (string * term) option

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

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

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

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

   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 pretty_maybe_quote : Pretty.T -> Pretty.T

   val hashw : word * word -> word

   val hashw_string : string * word -> word

 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."

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

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

 fun pair_from_fun f = (f false, f true)

 fun fun_from_pair (f, t) b = if b then t else f

 fun int_from_bool b = if b then 1 else 0

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

 val max_exponent = 16384

 fun reasonable_power _ 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

 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

 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

 fun fold1 f = foldl1 (uncurry f)

 fun replicate_list 0 _ = []

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

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

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

 fun filter_indices js xs =

   let

     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

     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

 fun cartesian_product [] _ = []

   | cartesian_product (x :: xs) yss =

     map (cons x) yss @ cartesian_product xs yss

 fun n_fold_cartesian_product xss = fold_rev cartesian_product xss [[]]

 fun all_distinct_unordered_pairs_of [] = []

   | all_distinct_unordered_pairs_of (x :: xs) =

     map (pair x) xs @ all_distinct_unordered_pairs_of xs

 val nth_combination =

   let

     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

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

 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))

 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))

 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

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

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

   | map3 _ _ _ _ = raise UnequalLengths

 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

 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

 fun is_substring_of needle stack =

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

                                                   (Substring.full stack))))

 val plural_s = Sledgehammer_Util.plural_s

 fun plural_s_for_list xs = plural_s (length xs)

 val serial_commas = Sledgehammer_Util.serial_commas

 fun pretty_serial_commas _ [] = []

   | pretty_serial_commas _ [p] = [p]

   | pretty_serial_commas conj [p1, p2] =

     [p1, Pretty.brk 1, Pretty.str conj, Pretty.brk 1, p2]

   | pretty_serial_commas conj [p1, p2, p3] =

     [p1, Pretty.str ",", Pretty.brk 1, p2, Pretty.str ",", Pretty.brk 1,

      Pretty.str conj, Pretty.brk 1, p3]

   | pretty_serial_commas conj (p :: ps) =

     p :: Pretty.str "," :: Pretty.brk 1 :: pretty_serial_commas conj ps

 val parse_bool_option = Sledgehammer_Util.parse_bool_option

 val parse_time_option = Sledgehammer_Util.parse_time_option

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

 fun be_subscript s = "\<^bsub>" ^ s ^ "\<^esub>"

 fun nat_subscript n =

   let val s = signed_string_of_int n in

     if print_mode_active Symbol.xsymbolsN then

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

          two-digit numbers *)

       (if n <= 9 then be_subscript else i_subscript) s

     else

       s

   end

 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}

 val simple_string_of_typ = Refute.string_of_typ

 val is_real_constr = Refute.is_IDT_constructor

 val typ_of_dtyp = Refute.typ_of_dtyp

 val is_of_class_const = Refute.is_const_of_class

 val get_class_def = Refute.get_classdef

 val monomorphic_term = Sledgehammer_Util.monomorphic_term

 val specialize_type = Sledgehammer_Util.specialize_type

 fun varify_type ctxt T =

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

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

 val eta_expand = Sledgehammer_Util.eta_expand

 fun time_limit NONE = I

   | time_limit (SOME delay) = TimeLimit.timeLimit delay

 fun DETERM_TIMEOUT delay tac st =

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

 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

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

 val unyxml = Sledgehammer_Util.unyxml

 val maybe_quote = Sledgehammer_Util.maybe_quote

 fun pretty_maybe_quote pretty =

   let val s = Pretty.str_of pretty in

     if maybe_quote s = s then pretty else Pretty.enum "" "\"" "\"" [pretty]

   end

 (* This hash function is recommended in Compilers: Principles, Techniques, and

    Tools, by Aho, Sethi, and Ullman. The "hashpjw" function, which they

    particularly recommend, triggers a bug in versions of Poly/ML up to 4.2.0. *)

 fun hashw (u, w) = Word.+ (u, Word.* (0w65599, w))

 fun hashw_char (c, w) = hashw (Word.fromInt (Char.ord c), w)

 fun hashw_string (s:string, w) = CharVector.foldl hashw_char w s

 end;