make two copies (!) of Library.UnequalLengths coincide with ListPair.UnequalLengths;
(* 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 string_from_time : Time.time -> string
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 set_show_all_types : Proof.context -> Proof.context
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 ListPair.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 string_from_time = Sledgehammer_Util.string_from_time
val i_subscript = implode o map (prefix "\<^isub>") o raw_explode (* FIXME Symbol.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 set_show_all_types ctxt =
Config.put show_all_types
(Config.get ctxt show_types orelse Config.get ctxt show_sorts
orelse Config.get ctxt show_all_types) ctxt
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;