1 (* Title: Pure/library.ML
3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory
4 Author: Markus Wenzel, TU Muenchen
6 Basic library: functions, pairs, booleans, lists, integers,
7 strings, lists as sets, orders, current directory, misc.
9 See also General/basics.ML for the most fundamental concepts.
14 infix 4 ~~ upto downto
15 infix orf andf \ \\ mem mem_int mem_string union union_int
16 union_string inter inter_int inter_string subset subset_int subset_string
18 signature BASIC_LIBRARY =
21 val undefined: 'a -> 'b
24 val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
25 val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
26 val ? : bool * ('a -> 'a) -> 'a -> 'a
27 val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
28 val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
29 val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
30 val funpow: int -> ('a -> 'a) -> 'a -> 'a
33 exception SYS_ERROR of string
34 val sys_error: string -> 'a
35 exception ERROR of string
36 val error: string -> 'a
37 val cat_error: string -> string -> 'a
38 val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
41 val pair: 'a -> 'b -> 'a * 'b
42 val rpair: 'a -> 'b -> 'b * 'a
43 val fst: 'a * 'b -> 'a
44 val snd: 'a * 'b -> 'b
45 val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
46 val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
47 val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
48 val swap: 'a * 'b -> 'b * 'a
49 val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
50 val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
51 val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
54 val equal: ''a -> ''a -> bool
55 val not_equal: ''a -> ''a -> bool
56 val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
57 val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
58 val exists: ('a -> bool) -> 'a list -> bool
59 val forall: ('a -> bool) -> 'a list -> bool
60 val set: bool ref -> bool
61 val reset: bool ref -> bool
62 val toggle: bool ref -> bool
63 val change: 'a ref -> ('a -> 'a) -> unit
64 val change_result: 'a ref -> ('a -> 'b * 'a) -> 'b
65 val setmp_noncritical: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
66 val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
67 val setmp_thread_data: 'a Universal.tag -> 'a -> 'a -> ('b -> 'c) -> 'b -> 'c
70 exception UnequalLengths
71 val single: 'a -> 'a list
72 val the_single: 'a list -> 'a
73 val singleton: ('a list -> 'b list) -> 'a -> 'b
74 val yield_singleton: ('a list -> 'c -> 'b list * 'c) -> 'a -> 'c -> 'b * 'c
75 val apply: ('a -> 'a) list -> 'a -> 'a
76 val perhaps_apply: ('a -> 'a option) list -> 'a -> 'a option
77 val perhaps_loop: ('a -> 'a option) -> 'a -> 'a option
78 val foldl1: ('a * 'a -> 'a) -> 'a list -> 'a
79 val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
80 val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
81 val flat: 'a list list -> 'a list
82 val unflat: 'a list list -> 'b list -> 'b list list
83 val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
84 val burrow_options: ('a list -> 'b list) -> 'a option list -> 'b option list
85 val burrow_fst: ('a list -> 'b list) -> ('a * 'c) list -> ('b * 'c) list
86 val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
87 val maps: ('a -> 'b list) -> 'a list -> 'b list
88 val filter: ('a -> bool) -> 'a list -> 'a list
89 val filter_out: ('a -> bool) -> 'a list -> 'a list
90 val map_filter: ('a -> 'b option) -> 'a list -> 'b list
91 val chop: int -> 'a list -> 'a list * 'a list
92 val dropwhile: ('a -> bool) -> 'a list -> 'a list
93 val nth: 'a list -> int -> 'a
94 val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
95 val nth_drop: int -> 'a list -> 'a list
96 val nth_list: 'a list list -> int -> 'a list
97 val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
98 val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
99 val split_last: 'a list -> 'a list * 'a
100 val find_index: ('a -> bool) -> 'a list -> int
101 val find_index_eq: ''a -> ''a list -> int
102 val find_first: ('a -> bool) -> 'a list -> 'a option
103 val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
104 val get_first: ('a -> 'b option) -> 'a list -> 'b option
105 val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
106 val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
107 val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
108 val zip_options: 'a list -> 'b option list -> ('a * 'b) list
109 val ~~ : 'a list * 'b list -> ('a * 'b) list
110 val map_split: ('a -> 'b * 'c) -> 'a list -> 'b list * 'c list
111 val split_list: ('a * 'b) list -> 'a list * 'b list
112 val map_product: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
113 val fold_product: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
114 val separate: 'a -> 'a list -> 'a list
115 val surround: 'a -> 'a list -> 'a list
116 val replicate: int -> 'a -> 'a list
117 val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
118 val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
119 val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
120 val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
121 val prefixes1: 'a list -> 'a list list
122 val prefixes: 'a list -> 'a list list
123 val suffixes1: 'a list -> 'a list list
124 val suffixes: 'a list -> 'a list list
127 val inc: int ref -> int
128 val dec: int ref -> int
129 val upto: int * int -> int list
130 val downto: int * int -> int list
131 val radixpand: int * int -> int list
132 val radixstring: int * string * int -> string
133 val string_of_int: int -> string
134 val signed_string_of_int: int -> string
135 val string_of_indexname: string * int -> string
136 val read_radix_int: int -> string list -> int * string list
137 val read_int: string list -> int * string list
138 val oct_char: string -> string
141 val nth_string: string -> int -> string
142 val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
143 val exists_string: (string -> bool) -> string -> bool
144 val forall_string: (string -> bool) -> string -> bool
145 val first_field: string -> string -> (string * string) option
146 val enclose: string -> string -> string -> string
147 val unenclose: string -> string
148 val quote: string -> string
149 val space_implode: string -> string list -> string
150 val commas: string list -> string
151 val commas_quote: string list -> string
152 val cat_lines: string list -> string
153 val space_explode: string -> string -> string list
154 val split_lines: string -> string list
155 val prefix_lines: string -> string -> string
156 val prefix: string -> string -> string
157 val suffix: string -> string -> string
158 val unprefix: string -> string -> string
159 val unsuffix: string -> string -> string
160 val replicate_string: int -> string -> string
161 val translate_string: (string -> string) -> string -> string
162 val multiply: 'a list -> 'a list list -> 'a list list
164 (*lists as sets -- see also Pure/General/ord_list.ML*)
165 val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
166 val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
167 val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
168 val update: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
169 val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
170 val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
171 val mem: ''a * ''a list -> bool
172 val mem_int: int * int list -> bool
173 val mem_string: string * string list -> bool
174 val union: ''a list * ''a list -> ''a list
175 val union_int: int list * int list -> int list
176 val union_string: string list * string list -> string list
177 val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
178 val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
179 val inter: ''a list * ''a list -> ''a list
180 val inter_int: int list * int list -> int list
181 val inter_string: string list * string list -> string list
182 val subset: ''a list * ''a list -> bool
183 val subset_int: int list * int list -> bool
184 val subset_string: string list * string list -> bool
185 val eq_set: ''a list * ''a list -> bool
186 val eq_set_string: string list * string list -> bool
187 val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
188 val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
189 val \ : ''a list * ''a -> ''a list
190 val \\ : ''a list * ''a list -> ''a list
191 val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
192 val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
193 val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
195 (*lists as multisets*)
196 val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
197 val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
200 val is_equal: order -> bool
201 val rev_order: order -> order
202 val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
203 val bool_ord: bool * bool -> order
204 val int_ord: int * int -> order
205 val string_ord: string * string -> order
206 val fast_string_ord: string * string -> order
207 val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
208 val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
209 val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
210 val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
211 val sort: ('a * 'a -> order) -> 'a list -> 'a list
212 val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
213 val sort_strings: string list -> string list
214 val sort_wrt: ('a -> string) -> 'a list -> 'a list
218 val random: unit -> real
219 val random_range: int -> int -> int
220 val one_of: 'a list -> 'a
221 val frequency: (int * 'a) list -> 'a
224 val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
225 val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
226 val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
227 val gensym: string -> string
229 val stamp: unit -> stamp
231 val serial: unit -> serial
232 val serial_string: unit -> string
233 structure Object: sig type T end
238 include BASIC_LIBRARY
239 val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
240 val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
241 val take: int * 'a list -> 'a list
242 val drop: int * 'a list -> 'a list
243 val last_elem: 'a list -> 'a
246 structure Library: LIBRARY =
251 fun undefined _ = raise Match;
255 fun curry f x y = f (x, y);
256 fun uncurry f (x, y) = f x y;
258 (*conditional application*)
259 fun b ? f = fn x => if b then f x else x;
261 (*composition with multiple args*)
262 fun (f oo g) x y = f (g x y);
263 fun (f ooo g) x y z = f (g x y z);
264 fun (f oooo g) x y z w = f (g x y z w);
266 (*function exponentiation: f(...(f x)...) with n applications of f*)
267 fun funpow (0: int) _ x = x
268 | funpow n f x = funpow (n - 1) f (f x);
273 exception SYS_ERROR of string;
274 fun sys_error msg = raise SYS_ERROR msg;
276 exception ERROR of string;
277 fun error msg = raise ERROR msg;
279 fun cat_error "" msg = error msg
280 | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
282 fun assert_all pred list msg =
285 | ass (x :: xs) = if pred x then ass xs else error (msg x);
291 fun pair x y = (x, y);
292 fun rpair x y = (y, x);
297 fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
298 fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
299 fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
301 fun swap (x, y) = (y, x);
303 fun apfst f (x, y) = (f x, y);
304 fun apsnd f (x, y) = (x, f y);
305 fun pairself f (x, y) = (f x, f y);
310 (*polymorphic equality*)
311 fun equal x y = x = y;
312 fun not_equal x y = x <> y;
314 (*combining predicates*)
315 fun p orf q = fn x => p x orelse q x;
316 fun p andf q = fn x => p x andalso q x;
318 val exists = List.exists;
319 val forall = List.all;
324 fun set flag = (flag := true; true);
325 fun reset flag = (flag := false; false);
326 fun toggle flag = (flag := not (! flag); ! flag);
328 fun change r f = r := f (! r);
329 fun change_result r f = let val (x, y) = f (! r) in r := y; x end;
331 (*temporarily set flag during execution*)
332 fun setmp_noncritical flag value f x =
333 uninterruptible (fn restore_attributes => fn () =>
335 val orig_value = ! flag;
336 val _ = flag := value;
337 val result = Exn.capture (restore_attributes f) x;
338 val _ = flag := orig_value;
339 in Exn.release result end) ();
341 fun setmp flag value f x =
342 NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x);
344 fun setmp_thread_data tag orig_data data f x =
345 uninterruptible (fn restore_attributes => fn () =>
347 val _ = Thread.setLocal (tag, data);
348 val result = Exn.capture (restore_attributes f) x;
349 val _ = Thread.setLocal (tag, orig_data);
350 in Exn.release result end) ();
356 exception UnequalLengths;
360 fun the_single [x] = x
361 | the_single _ = raise Empty;
363 fun singleton f x = the_single (f [x]);
365 fun yield_singleton f x = f [x] #>> the_single;
368 | apply (f :: fs) x = apply fs (f x);
370 fun perhaps_apply funs arg =
373 | app (f :: fs) (changed, x) =
375 NONE => app fs (changed, x)
376 | SOME x' => app fs (true, x'));
377 in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
379 fun perhaps_loop f arg =
381 fun loop (changed, x) =
384 | SOME x' => loop (true, x'));
385 in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
388 (* fold -- old versions *)
390 (*the following versions of fold are designed to fit nicely with infixes*)
392 (* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn
393 for operators that associate to the left (TAIL RECURSIVE)*)
394 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
395 let fun itl (e, []) = e
396 | itl (e, a::l) = itl (f(e, a), l)
399 (* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e))
400 for operators that associate to the right (not tail recursive)*)
403 | itr (a::l) = f(a, itr l)
406 (* (op @) [x1, ..., xn] ===> ((x1 @ x2) @ x3) ... @ xn
407 for operators that associate to the left (TAIL RECURSIVE)*)
408 fun foldl1 f [] = raise Empty
409 | foldl1 f (x :: xs) = foldl f (x, xs);
411 (* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n-1] @ xn))
412 for n > 0, operators that associate to the right (not tail recursive)*)
413 fun foldr1 f [] = raise Empty
416 | itr (x::l) = f(x, itr l)
421 fun fold_aux (x, []) = (x, [])
422 | fold_aux (x, y :: ys) =
424 val (x', y') = f (x, y);
425 val (x'', ys') = fold_aux (x', ys);
426 in (x'', y' :: ys') end;
430 (* basic list functions *)
432 fun eq_list eq (list1, list2) =
434 fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
436 in length list1 = length list2 andalso eq_lst (list1, list2) end;
439 | maps f (x :: xs) = f x @ maps f xs;
441 val filter = List.filter;
442 fun filter_out f = filter (not o f);
443 val map_filter = List.mapPartial;
445 fun chop (0: int) xs = ([], xs)
446 | chop _ [] = ([], [])
447 | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
449 (*take the first n elements from a list*)
450 fun take (n: int, []) = []
451 | take (n, x :: xs) =
452 if n > 0 then x :: take (n - 1, xs) else [];
454 (*drop the first n elements from a list*)
455 fun drop (n: int, []) = []
456 | drop (n, x :: xs) =
457 if n > 0 then drop (n - 1, xs) else x :: xs;
459 fun dropwhile P [] = []
460 | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
462 (*return nth element of a list, where 0 designates the first element;
463 raise Subscript if list too short*)
464 fun nth xs i = List.nth (xs, i);
466 fun nth_list xss i = nth xss i handle Subscript => [];
468 fun nth_map 0 f (x :: xs) = f x :: xs
469 | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
470 | nth_map (_: int) _ [] = raise Subscript;
473 List.take (xs, n) @ List.drop (xs, n + 1);
477 fun mapp (_: int) [] = []
478 | mapp i (x :: xs) = f (i, x) :: mapp (i + 1) xs
483 fun fold_aux (_: int) [] y = y
484 | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y);
487 val last_elem = List.last;
489 (*rear decomposition*)
490 fun split_last [] = raise Empty
491 | split_last [x] = ([], x)
492 | split_last (x :: xs) = apfst (cons x) (split_last xs);
494 (*find the position of an element in a list*)
495 fun find_index pred =
496 let fun find (_: int) [] = ~1
497 | find n (x :: xs) = if pred x then n else find (n + 1) xs;
500 fun find_index_eq x = find_index (equal x);
502 (*find first element satisfying predicate*)
503 val find_first = List.find;
505 (*get first element by lookup function*)
506 fun get_first _ [] = NONE
507 | get_first f (x :: xs) =
509 NONE => get_first f xs
514 fun get (_: int) [] = NONE
517 of NONE => get (i + 1) xs
518 | SOME y => SOME (i, y)
521 val flat = List.concat;
523 fun unflat (xs :: xss) ys =
524 let val (ps, qs) = chop (length xs) ys
525 in ps :: unflat xss qs end
527 | unflat _ _ = raise UnequalLengths;
529 fun burrow f xss = unflat xss (f (flat xss));
531 fun burrow_options f os = map (try hd) (burrow f (map the_list os));
533 fun fold_burrow f xss s =
534 apfst (unflat xss) (f (flat xss) s);
536 (*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*)
537 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
538 | separate _ xs = xs;
540 fun surround s (x :: xs) = s :: x :: surround s xs
541 | surround s [] = [s];
543 (*make the list [x, x, ..., x] of length n*)
544 fun replicate (n: int) x =
545 let fun rep (0, xs) = xs
546 | rep (n, xs) = rep (n - 1, x :: xs)
548 if n < 0 then raise Subscript
552 fun translate_string f = String.translate (f o String.str);
554 (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
555 fun multiply [] _ = []
556 | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
561 fun map_product f _ [] = []
562 | map_product f [] _ = []
563 | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
565 fun fold_product f _ [] z = z
566 | fold_product f [] _ z = z
567 | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
572 exception UnequalLengths;
574 fun map2 _ [] [] = []
575 | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
576 | map2 _ _ _ = raise UnequalLengths;
578 fun fold2 f [] [] z = z
579 | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
580 | fold2 f _ _ _ = raise UnequalLengths;
582 fun map_split f [] = ([], [])
583 | map_split f (x :: xs) =
586 val (ys, ws) = map_split f xs;
587 in (y :: ys, w :: ws) end;
589 fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
590 | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
591 | zip_options _ [] = []
592 | zip_options [] _ = raise UnequalLengths;
594 (*combine two lists forming a list of pairs:
595 [x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*)
597 | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
598 | _ ~~ _ = raise UnequalLengths;
600 (*inverse of ~~; the old 'split':
601 [(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*)
602 val split_list = ListPair.unzip;
604 fun burrow_fst f xs = split_list xs |>> f |> op ~~;
607 (* prefixes, suffixes *)
609 fun is_prefix _ [] _ = true
610 | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
611 | is_prefix eq _ _ = false;
613 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., x(i-1)], [xi, ..., xn])
614 where xi is the first element that does not satisfy the predicate*)
615 fun take_prefix (pred : 'a -> bool) (xs: 'a list) : 'a list * 'a list =
616 let fun take (rxs, []) = (rev rxs, [])
617 | take (rxs, x :: xs) =
618 if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs)
621 fun chop_prefix eq ([], ys) = ([], ([], ys))
622 | chop_prefix eq (xs, []) = ([], (xs, []))
623 | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
625 let val (ps', xys'') = chop_prefix eq (xs', ys')
626 in (x :: ps', xys'') end
629 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., xi], [x(i+1), ..., xn])
630 where xi is the last element that does not satisfy the predicate*)
631 fun take_suffix _ [] = ([], [])
632 | take_suffix pred (x :: xs) =
633 (case take_suffix pred xs of
634 ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
635 | (prfx, sffx) => (x :: prfx, sffx));
637 fun prefixes1 [] = []
638 | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
640 fun prefixes xs = [] :: prefixes1 xs;
642 fun suffixes1 xs = map rev (prefixes1 (rev xs));
643 fun suffixes xs = [] :: suffixes1 xs;
649 fun inc i = (i := ! i + (1: int); ! i);
650 fun dec i = (i := ! i - (1: int); ! i);
653 (* lists of integers *)
655 (*make the list [from, from + 1, ..., to]*)
656 fun ((i: int) upto j) =
657 if i > j then [] else i :: (i + 1 upto j);
659 (*make the list [from, from - 1, ..., to]*)
660 fun ((i: int) downto j) =
661 if i < j then [] else i :: (i - 1 downto j);
664 (* convert integers to strings *)
666 (*expand the number in the given base;
667 example: radixpand (2, 8) gives [1, 0, 0, 0]*)
668 fun radixpand (base, num) : int list =
670 fun radix (n, tail) =
671 if n < base then n :: tail
672 else radix (n div base, (n mod base) :: tail)
673 in radix (num, []) end;
675 (*expands a number into a string of characters starting from "zerochar";
676 example: radixstring (2, "0", 8) gives "1000"*)
677 fun radixstring (base, zerochar, num) =
678 let val offset = ord zerochar;
679 fun chrof n = chr (offset + n)
680 in implode (map chrof (radixpand (base, num))) end;
683 val string_of_int = Int.toString;
685 fun signed_string_of_int i =
686 if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
688 fun string_of_indexname (a, 0) = a
689 | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
694 fun read_radix_int radix cs =
697 val limit = zero + radix;
698 fun scan (num, []) = (num, [])
699 | scan (num, c :: cs) =
700 if zero <= ord c andalso ord c < limit then
701 scan (radix * num + (ord c - zero), cs)
705 val read_int = read_radix_int 10;
707 fun oct_char s = chr (#1 (read_radix_int 8 (explode s)));
713 (* functions tuned for strings, avoiding explode *)
715 fun nth_string str i =
716 (case try String.substring (str, i, 1) of
718 | NONE => raise Subscript);
720 fun fold_string f str x0 =
724 if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
727 fun exists_string pred str =
730 fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
733 fun forall_string pred = not o exists_string (not o pred);
735 fun first_field sep str =
740 if i + n > len then NONE
741 else if String.substring (str, i, n) = sep then SOME i
746 | SOME i => SOME (String.substring (str, 0, i), String.extract (str, i + n, NONE)))
749 (*enclose in brackets*)
750 fun enclose lpar rpar str = lpar ^ str ^ rpar;
751 fun unenclose str = String.substring (str, 1, size str - 2);
753 (*simple quoting (does not escape special chars)*)
754 val quote = enclose "\"" "\"";
756 (*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
757 fun space_implode a bs = implode (separate a bs);
759 val commas = space_implode ", ";
760 val commas_quote = commas o map quote;
762 (*concatenate messages, one per line, into a string*)
763 val cat_lines = space_implode "\n";
765 (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
766 fun space_explode _ "" = []
767 | space_explode sep s = String.fields (fn c => str c = sep) s;
769 val split_lines = space_explode "\n";
771 fun prefix_lines "" txt = txt
772 | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
774 fun prefix prfx s = prfx ^ s;
775 fun suffix sffx s = s ^ sffx;
777 fun unprefix prfx s =
778 if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
779 else raise Fail "unprefix";
781 fun unsuffix sffx s =
782 if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
783 else raise Fail "unsuffix";
785 fun replicate_string (0: int) _ = ""
786 | replicate_string 1 a = a
787 | replicate_string k a =
788 if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
789 else replicate_string (k div 2) (a ^ a) ^ a;
793 (** lists as sets -- see also Pure/General/ord_list.ML **)
795 (* canonical operations *)
797 fun member eq list x =
800 | memb (y :: ys) = eq (x, y) orelse memb ys;
803 fun insert eq x xs = if member eq xs x then xs else x :: xs;
804 fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
805 fun update eq x xs = cons x (remove eq x xs);
807 fun subtract eq = fold (remove eq);
809 fun merge _ ([], ys) = ys
810 | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
813 (* old-style infixes *)
815 fun x mem xs = member (op =) xs x;
816 fun (x: int) mem_int xs = member (op =) xs x;
817 fun (x: string) mem_string xs = member (op =) xs x;
819 (*union of sets represented as lists: no repetitions*)
822 | (x :: xs) union ys = xs union (insert (op =) x ys);
824 (*union of sets, optimized version for ints*)
825 fun (xs:int list) union_int [] = xs
826 | [] union_int ys = ys
827 | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
829 (*union of sets, optimized version for strings*)
830 fun (xs:string list) union_string [] = xs
831 | [] union_string ys = ys
832 | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
834 (*generalized union*)
835 fun gen_union eq (xs, []) = xs
836 | gen_union eq ([], ys) = ys
837 | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
842 | (x :: xs) inter ys =
843 if x mem ys then x :: (xs inter ys) else xs inter ys;
845 (*intersection, optimized version for ints*)
846 fun ([]:int list) inter_int ys = []
847 | (x :: xs) inter_int ys =
848 if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
850 (*intersection, optimized version for strings *)
851 fun ([]:string list) inter_string ys = []
852 | (x :: xs) inter_string ys =
853 if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
855 (*generalized intersection*)
856 fun gen_inter eq ([], ys) = []
857 | gen_inter eq (x::xs, ys) =
858 if member eq ys x then x :: gen_inter eq (xs, ys)
859 else gen_inter eq (xs, ys);
863 fun [] subset ys = true
864 | (x :: xs) subset ys = x mem ys andalso xs subset ys;
866 (*subset, optimized version for ints*)
867 fun ([]: int list) subset_int ys = true
868 | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
870 (*subset, optimized version for strings*)
871 fun ([]: string list) subset_string ys = true
872 | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
875 fun eq_set (xs, ys) =
876 xs = ys orelse (xs subset ys andalso ys subset xs);
878 (*set equality for strings*)
879 fun eq_set_string ((xs: string list), ys) =
880 xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
882 fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
884 fun gen_eq_set eq (xs, ys) =
885 eq_list eq (xs, ys) orelse
886 (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
889 (*removing an element from a list WITHOUT duplicates*)
890 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
892 fun ys \\ xs = foldl (op \) (ys,xs);
895 (*makes a list of the distinct members of the input; preserves order, takes
896 first of equal elements*)
897 fun distinct eq lst =
899 fun dist (rev_seen, []) = rev rev_seen
900 | dist (rev_seen, x :: xs) =
901 if member eq rev_seen x then dist (rev_seen, xs)
902 else dist (x :: rev_seen, xs);
903 in dist ([], lst) end;
905 (*returns a list containing all repeated elements exactly once; preserves
906 order, takes first of equal elements*)
907 fun duplicates eq lst =
909 fun dups (rev_dups, []) = rev rev_dups
910 | dups (rev_dups, x :: xs) =
911 if member eq rev_dups x orelse not (member eq xs x) then
913 else dups (x :: rev_dups, xs);
914 in dups ([], lst) end;
916 fun has_duplicates eq =
919 | dups (x :: xs) = member eq xs x orelse dups xs;
924 (** lists as multisets **)
926 fun remove1 _ _ [] = raise Empty
927 | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs;
929 fun submultiset _ ([], _) = true
930 | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
936 fun is_equal EQUAL = true
937 | is_equal _ = false;
939 fun rev_order LESS = GREATER
940 | rev_order EQUAL = EQUAL
941 | rev_order GREATER = LESS;
943 (*assume rel is a linear strict order*)
944 fun make_ord rel (x, y) =
945 if rel (x, y) then LESS
946 else if rel (y, x) then GREATER
949 fun bool_ord (false, true) = LESS
950 | bool_ord (true, false) = GREATER
951 | bool_ord _ = EQUAL;
953 val int_ord = Int.compare;
954 val string_ord = String.compare;
956 fun fast_string_ord (s1, s2) =
957 (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
959 fun option_ord ord (SOME x, SOME y) = ord (x, y)
960 | option_ord _ (NONE, NONE) = EQUAL
961 | option_ord _ (NONE, SOME _) = LESS
962 | option_ord _ (SOME _, NONE) = GREATER;
964 (*lexicographic product*)
965 fun prod_ord a_ord b_ord ((x, y), (x', y')) =
966 (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
968 (*dictionary order -- in general NOT well-founded!*)
969 fun dict_ord elem_ord (x :: xs, y :: ys) =
970 (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
971 | dict_ord _ ([], []) = EQUAL
972 | dict_ord _ ([], _ :: _) = LESS
973 | dict_ord _ (_ :: _, []) = GREATER;
975 (*lexicographic product of lists*)
976 fun list_ord elem_ord (xs, ys) =
977 (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
982 (*quicksort -- stable, i.e. does not reorder equal elements*)
983 fun quicksort unique ord =
986 | qsort (xs as [_]) = xs
987 | qsort (xs as [x, y]) =
990 | EQUAL => if unique then [x] else xs
993 let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
994 in qsort lts @ eqs @ qsort gts end
995 and part _ [] = ([], [], [])
996 | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
997 and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
998 | add EQUAL x (lts, [], gts) = (lts, [x], gts)
999 | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
1000 | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
1003 fun sort ord = quicksort false ord;
1004 fun sort_distinct ord = quicksort true ord;
1006 val sort_strings = sort string_ord;
1007 fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
1011 (** random numbers **)
1015 fun rmod x y = x - y * Real.realFloor (x / y);
1019 val m = 2147483647.0;
1020 val random_seed = ref 1.0;
1023 fun random () = CRITICAL (fn () =>
1024 let val r = rmod (a * ! random_seed) m
1025 in (random_seed := r; r) end);
1029 fun random_range l h =
1030 if h < l orelse l < 0 then raise RANDOM
1031 else l + Real.floor (rmod (random ()) (real (h - l + 1)));
1033 fun one_of xs = nth xs (random_range 0 (length xs - 1));
1037 val sum = foldl op + (0, map fst xs);
1038 fun pick n ((k: int, x) :: xs) =
1039 if n <= k then x else pick (n - k) xs
1040 in pick (random_range 1 sum) xs end;
1046 fun divide_and_conquer decomp x =
1047 let val (ys, recomb) = decomp x
1048 in recomb (map (divide_and_conquer decomp) ys) end;
1051 (*Partition a list into buckets [ bi, b(i+1), ..., bj ]
1052 putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*)
1053 fun partition_list p i j =
1056 (case xs of [] => []
1057 | _ => raise Fail "partition_list")
1059 let val (ns, rest) = List.partition (p k) xs;
1060 in ns :: part(k+1)rest end
1061 in part (i: int) end;
1063 fun partition_eq (eq:'a * 'a -> bool) =
1067 let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
1068 in (x::xs)::(part xs') end
1073 (* generating identifiers *)
1075 (** Freshly generated identifiers; supplied prefix MUST start with a letter **)
1077 (*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
1079 if i<26 then chr (ord "A" + i)
1080 else if i<52 then chr (ord "a" + i - 26)
1081 else chr (ord "0" + i - 52);
1083 val char_vec = Vector.tabulate (62, gensym_char);
1084 fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
1086 val gensym_seed = ref (0: int);
1089 fun gensym pre = pre ^ newid (NAMED_CRITICAL "gensym" (fn () => inc gensym_seed));
1093 (* stamps and serial numbers *)
1095 type stamp = unit ref;
1096 val stamp: unit -> stamp = ref;
1099 val serial = Multithreading.serial;
1100 val serial_string = string_of_int o serial;
1103 (* generic objects *)
1105 (*note that the builtin exception datatype may be extended by new
1106 constructors at any time*)
1107 structure Object = struct type T = exn end;
1111 structure BasicLibrary: BASIC_LIBRARY = Library;