1 (* Title: Pure/library.ML
3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory
4 Author: Markus Wenzel, TU Muenchen
6 Basic library: functions, options, pairs, booleans, lists, integers,
7 strings, lists as sets, orders, current directory, misc.
9 See also General/basics.ML for the most fundamental concepts.
15 infix 4 ~~ upto downto
16 infix orf andf \ \\ mem mem_int mem_string union union_int
17 union_string inter inter_int inter_string subset subset_int subset_string
19 signature BASIC_LIBRARY =
22 val undefined: 'a -> 'b
25 val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
26 val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
27 val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
28 val ? : bool * ('a -> 'a) -> 'a -> 'a
29 val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
30 val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
31 val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
32 val funpow: int -> ('a -> 'a) -> 'a -> 'a
35 exception SYS_ERROR of string
36 val sys_error: string -> 'a
37 exception ERROR of string
38 val error: string -> 'a
39 val cat_error: string -> string -> 'a
40 val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
43 val pair: 'a -> 'b -> 'a * 'b
44 val rpair: 'a -> 'b -> 'b * 'a
45 val fst: 'a * 'b -> 'a
46 val snd: 'a * 'b -> 'b
47 val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
48 val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
49 val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
50 val swap: 'a * 'b -> 'b * 'a
51 val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
52 val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
53 val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
56 val equal: ''a -> ''a -> bool
57 val not_equal: ''a -> ''a -> bool
58 val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
59 val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
60 val exists: ('a -> bool) -> 'a list -> bool
61 val forall: ('a -> bool) -> 'a list -> bool
62 val set: bool ref -> bool
63 val reset: bool ref -> bool
64 val toggle: bool ref -> bool
65 val change: 'a ref -> ('a -> 'a) -> unit
66 val setmp_noncritical: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
67 val setmp: 'a ref -> '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 fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
86 val maps: ('a -> 'b list) -> 'a list -> 'b list
87 val filter: ('a -> bool) -> 'a list -> 'a list
88 val filter_out: ('a -> bool) -> 'a list -> 'a list
89 val map_filter: ('a -> 'b option) -> 'a list -> 'b list
90 val chop: int -> 'a list -> 'a list * 'a list
91 val dropwhile: ('a -> bool) -> 'a list -> 'a list
92 val nth: 'a list -> int -> 'a
93 val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
94 val nth_drop: int -> 'a list -> 'a list
95 val nth_list: 'a list list -> int -> 'a list
96 val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
97 val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
98 val split_last: 'a list -> 'a list * 'a
99 val find_index: ('a -> bool) -> 'a list -> int
100 val find_index_eq: ''a -> ''a list -> int
101 val find_first: ('a -> bool) -> 'a list -> 'a option
102 val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
103 val get_first: ('a -> 'b option) -> 'a list -> 'b option
104 val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
105 val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
106 val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
107 val zip_options: 'a list -> 'b option list -> ('a * 'b) list
108 val ~~ : 'a list * 'b list -> ('a * 'b) list
109 val split_list: ('a * 'b) list -> 'a list * 'b list
110 val separate: 'a -> 'a list -> 'a list
111 val replicate: int -> 'a -> 'a list
112 val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
113 val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
114 val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
115 val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
116 val prefixes1: 'a list -> 'a list list
117 val prefixes: 'a list -> 'a list list
118 val suffixes1: 'a list -> 'a list list
119 val suffixes: 'a list -> 'a list list
122 val inc: int ref -> int
123 val dec: int ref -> int
124 val upto: int * int -> int list
125 val downto: int * int -> int list
126 val radixpand: int * int -> int list
127 val radixstring: int * string * int -> string
128 val string_of_int: int -> string
129 val signed_string_of_int: int -> string
130 val string_of_indexname: string * int -> string
131 val read_radix_int: int -> string list -> int * string list
132 val read_int: string list -> int * string list
133 val oct_char: string -> string
136 val nth_string: string -> int -> string
137 val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
138 val exists_string: (string -> bool) -> string -> bool
139 val forall_string: (string -> bool) -> string -> bool
140 val enclose: string -> string -> string -> string
141 val unenclose: string -> string
142 val quote: string -> string
143 val space_implode: string -> string list -> string
144 val commas: string list -> string
145 val commas_quote: string list -> string
146 val cat_lines: string list -> string
147 val space_explode: string -> string -> string list
148 val split_lines: string -> string list
149 val prefix_lines: string -> string -> string
150 val untabify: string list -> string list
151 val prefix: string -> string -> string
152 val suffix: string -> string -> string
153 val unprefix: string -> string -> string
154 val unsuffix: string -> string -> string
155 val replicate_string: int -> string -> string
156 val translate_string: (string -> string) -> string -> string
157 val multiply: 'a list -> 'a list list -> 'a list list
158 val map_product: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
159 val fold_product: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
161 (*lists as sets -- see also Pure/General/ord_list.ML*)
162 val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
163 val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
164 val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
165 val update: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
166 val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
167 val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
168 val mem: ''a * ''a list -> bool
169 val mem_int: int * int list -> bool
170 val mem_string: string * string list -> bool
171 val union: ''a list * ''a list -> ''a list
172 val union_int: int list * int list -> int list
173 val union_string: string list * string list -> string list
174 val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
175 val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
176 val inter: ''a list * ''a list -> ''a list
177 val inter_int: int list * int list -> int list
178 val inter_string: string list * string list -> string list
179 val subset: ''a list * ''a list -> bool
180 val subset_int: int list * int list -> bool
181 val subset_string: string list * string list -> bool
182 val eq_set: ''a list * ''a list -> bool
183 val eq_set_string: string list * string list -> bool
184 val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
185 val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
186 val \ : ''a list * ''a -> ''a list
187 val \\ : ''a list * ''a list -> ''a list
188 val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
189 val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
190 val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
192 (*lists as multisets*)
193 val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
194 val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
197 val is_equal: order -> bool
198 val rev_order: order -> order
199 val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
200 val bool_ord: bool * bool -> order
201 val int_ord: int * int -> order
202 val string_ord: string * string -> order
203 val fast_string_ord: string * string -> order
204 val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
205 val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
206 val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
207 val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
208 val sort: ('a * 'a -> order) -> 'a list -> 'a list
209 val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
210 val sort_strings: string list -> string list
211 val sort_wrt: ('a -> string) -> 'a list -> 'a list
215 val random: unit -> real
216 val random_range: int -> int -> int
217 val one_of: 'a list -> 'a
218 val frequency: (int * 'a) list -> 'a
221 val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
222 val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
223 val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
224 val gensym: string -> string
226 val stamp: unit -> stamp
228 val serial: unit -> serial
229 val serial_string: unit -> string
230 structure Object: sig type T end
235 include BASIC_LIBRARY
236 val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
237 val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
238 val take: int * 'a list -> 'a list
239 val drop: int * 'a list -> 'a list
240 val last_elem: 'a list -> 'a
243 structure Library: LIBRARY =
248 fun undefined _ = raise Match;
252 fun curry f x y = f (x, y);
253 fun uncurry f (x, y) = f x y;
255 (*application and structured results -- old version*)
256 fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
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 (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
319 fun exists (pred: 'a -> bool) : 'a list -> bool =
320 let fun boolf [] = false
321 | boolf (x :: xs) = pred x orelse boolf xs
324 (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
325 fun forall (pred: 'a -> bool) : 'a list -> bool =
326 let fun boolf [] = true
327 | boolf (x :: xs) = pred x andalso boolf xs
333 fun set flag = (flag := true; true);
334 fun reset flag = (flag := false; false);
335 fun toggle flag = (flag := not (! flag); ! flag);
337 fun change r f = r := f (! r);
339 (*temporarily set flag during execution*)
340 fun setmp_noncritical flag value f x =
342 val orig_value = ! flag;
343 val _ = flag := value;
344 val result = Exn.capture f x;
345 val _ = flag := orig_value;
346 in Exn.release result end;
348 fun setmp flag value f x = NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x);
354 exception UnequalLengths;
358 fun the_single [x] = x
359 | the_single _ = raise Empty;
361 fun singleton f x = the_single (f [x]);
363 fun yield_singleton f x = f [x] #>> the_single;
366 | apply (f :: fs) x = apply fs (f x);
368 fun perhaps_apply funs arg =
371 | app (f :: fs) (changed, x) =
373 NONE => app fs (changed, x)
374 | SOME x' => app fs (true, x'));
375 in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
377 fun perhaps_loop f arg =
379 fun loop (changed, x) =
382 | SOME x' => loop (true, x'));
383 in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
386 (* fold -- old versions *)
388 (*the following versions of fold are designed to fit nicely with infixes*)
390 (* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn
391 for operators that associate to the left (TAIL RECURSIVE)*)
392 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
393 let fun itl (e, []) = e
394 | itl (e, a::l) = itl (f(e, a), l)
397 (* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e))
398 for operators that associate to the right (not tail recursive)*)
401 | itr (a::l) = f(a, itr l)
404 (* (op @) [x1, ..., xn] ===> ((x1 @ x2) @ x3) ... @ xn
405 for operators that associate to the left (TAIL RECURSIVE)*)
406 fun foldl1 f [] = raise Empty
407 | foldl1 f (x :: xs) = foldl f (x, xs);
409 (* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n-1] @ xn))
410 for n > 0, operators that associate to the right (not tail recursive)*)
411 fun foldr1 f [] = raise Empty
414 | itr (x::l) = f(x, itr l)
419 fun fold_aux (x, []) = (x, [])
420 | fold_aux (x, y :: ys) =
422 val (x', y') = f (x, y);
423 val (x'', ys') = fold_aux (x', ys);
424 in (x'', y' :: ys') end;
428 (* basic list functions *)
430 fun eq_list eq (list1, list2) =
432 fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
434 in length list1 = length list2 andalso eq_lst (list1, list2) end;
437 | maps f (x :: xs) = f x @ maps f xs;
439 val filter = List.filter;
440 fun filter_out f = filter (not o f);
441 val map_filter = List.mapPartial;
443 fun chop (0: int) xs = ([], xs)
444 | chop _ [] = ([], [])
445 | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
447 (*take the first n elements from a list*)
448 fun take (n: int, []) = []
449 | take (n, x :: xs) =
450 if n > 0 then x :: take (n - 1, xs) else [];
452 (*drop the first n elements from a list*)
453 fun drop (n: int, []) = []
454 | drop (n, x :: xs) =
455 if n > 0 then drop (n - 1, xs) else x :: xs;
457 fun dropwhile P [] = []
458 | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
460 (*return nth element of a list, where 0 designates the first element;
461 raise Subscript if list too short*)
462 fun nth xs i = List.nth (xs, i);
464 fun nth_list xss i = nth xss i handle Subscript => [];
466 fun nth_map 0 f (x :: xs) = f x :: xs
467 | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
468 | nth_map (_: int) _ [] = raise Subscript;
471 List.take (xs, n) @ List.drop (xs, n + 1);
475 fun mapp (_: int) [] = []
476 | mapp i (x :: xs) = f (i, x) :: mapp (i + 1) xs
481 fun fold_aux (_: int) [] y = y
482 | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y);
485 val last_elem = List.last;
487 (*rear decomposition*)
488 fun split_last [] = raise Empty
489 | split_last [x] = ([], x)
490 | split_last (x :: xs) = apfst (cons x) (split_last xs);
492 (*find the position of an element in a list*)
493 fun find_index pred =
494 let fun find (_: int) [] = ~1
495 | find n (x :: xs) = if pred x then n else find (n + 1) xs;
498 fun find_index_eq x = find_index (equal x);
500 (*find first element satisfying predicate*)
501 val find_first = List.find;
503 (*get first element by lookup function*)
504 fun get_first _ [] = NONE
505 | get_first f (x :: xs) =
507 NONE => get_first f xs
512 fun get (_: int) [] = NONE
515 of NONE => get (i + 1) xs
516 | SOME y => SOME (i, y)
519 val flat = List.concat;
521 fun unflat (xs :: xss) ys =
522 let val (ps, qs) = chop (length xs) ys
523 in ps :: unflat xss qs end
525 | unflat _ _ = raise UnequalLengths;
527 fun burrow f xss = unflat xss (f (flat xss));
529 fun burrow_options f os = map (try hd) (burrow f (map the_list os));
531 fun fold_burrow f xss s =
532 apfst (unflat xss) (f (flat xss) s);
534 (*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*)
535 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
536 | separate _ xs = xs;
538 (*make the list [x, x, ..., x] of length n*)
539 fun replicate (n: int) x =
540 let fun rep (0, xs) = xs
541 | rep (n, xs) = rep (n - 1, x :: xs)
543 if n < 0 then raise Subscript
547 fun translate_string f = String.translate (f o String.str);
549 (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
550 fun multiply [] _ = []
551 | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
556 fun map_product f _ [] = []
557 | map_product f [] _ = []
558 | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
560 fun fold_product f _ [] z = z
561 | fold_product f [] _ z = z
562 | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
567 exception UnequalLengths;
569 fun map2 _ [] [] = []
570 | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
571 | map2 _ _ _ = raise UnequalLengths;
573 fun fold2 f [] [] z = z
574 | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
575 | fold2 f _ _ _ = raise UnequalLengths;
577 fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
578 | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
579 | zip_options _ [] = []
580 | zip_options [] _ = raise UnequalLengths;
582 (*combine two lists forming a list of pairs:
583 [x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*)
585 | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
586 | _ ~~ _ = raise UnequalLengths;
588 (*inverse of ~~; the old 'split':
589 [(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*)
590 val split_list = ListPair.unzip;
593 (* prefixes, suffixes *)
595 fun is_prefix _ [] _ = true
596 | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
597 | is_prefix eq _ _ = false;
599 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., x(i-1)], [xi, ..., xn])
600 where xi is the first element that does not satisfy the predicate*)
601 fun take_prefix (pred : 'a -> bool) (xs: 'a list) : 'a list * 'a list =
602 let fun take (rxs, []) = (rev rxs, [])
603 | take (rxs, x :: xs) =
604 if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs)
607 fun chop_prefix eq ([], ys) = ([], ([], ys))
608 | chop_prefix eq (xs, []) = ([], (xs, []))
609 | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
611 let val (ps', xys'') = chop_prefix eq (xs', ys')
612 in (x :: ps', xys'') end
615 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., xi], [x(i+1), ..., xn])
616 where xi is the last element that does not satisfy the predicate*)
617 fun take_suffix _ [] = ([], [])
618 | take_suffix pred (x :: xs) =
619 (case take_suffix pred xs of
620 ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
621 | (prfx, sffx) => (x :: prfx, sffx));
623 fun prefixes1 [] = []
624 | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
626 fun prefixes xs = [] :: prefixes1 xs;
628 fun suffixes1 xs = map rev (prefixes1 (rev xs));
629 fun suffixes xs = [] :: suffixes1 xs;
635 fun inc i = (i := ! i + (1: int); ! i);
636 fun dec i = (i := ! i - (1: int); ! i);
639 (* lists of integers *)
641 (*make the list [from, from + 1, ..., to]*)
642 fun ((i: int) upto j) =
643 if i > j then [] else i :: (i + 1 upto j);
645 (*make the list [from, from - 1, ..., to]*)
646 fun ((i: int) downto j) =
647 if i < j then [] else i :: (i - 1 downto j);
650 (* convert integers to strings *)
652 (*expand the number in the given base;
653 example: radixpand (2, 8) gives [1, 0, 0, 0]*)
654 fun radixpand (base, num) : int list =
656 fun radix (n, tail) =
657 if n < base then n :: tail
658 else radix (n div base, (n mod base) :: tail)
659 in radix (num, []) end;
661 (*expands a number into a string of characters starting from "zerochar";
662 example: radixstring (2, "0", 8) gives "1000"*)
663 fun radixstring (base, zerochar, num) =
664 let val offset = ord zerochar;
665 fun chrof n = chr (offset + n)
666 in implode (map chrof (radixpand (base, num))) end;
669 val string_of_int = Int.toString;
671 fun signed_string_of_int i =
672 if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
674 fun string_of_indexname (a, 0) = a
675 | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
680 fun read_radix_int radix cs =
683 val limit = zero + radix;
684 fun scan (num, []) = (num, [])
685 | scan (num, c :: cs) =
686 if zero <= ord c andalso ord c < limit then
687 scan (radix * num + (ord c - zero), cs)
691 val read_int = read_radix_int 10;
693 fun oct_char s = chr (#1 (read_radix_int 8 (explode s)));
699 (* functions tuned for strings, avoiding explode *)
701 fun nth_string str i =
702 (case try String.substring (str, i, 1) of
704 | NONE => raise Subscript);
706 fun fold_string f str x0 =
710 if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
713 fun exists_string pred str =
716 fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
719 fun forall_string pred = not o exists_string (not o pred);
721 (*enclose in brackets*)
722 fun enclose lpar rpar str = lpar ^ str ^ rpar;
723 fun unenclose str = String.substring (str, 1, size str - 2);
725 (*simple quoting (does not escape special chars)*)
726 val quote = enclose "\"" "\"";
728 (*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
729 fun space_implode a bs = implode (separate a bs);
731 val commas = space_implode ", ";
732 val commas_quote = commas o map quote;
734 (*concatenate messages, one per line, into a string*)
735 val cat_lines = space_implode "\n";
737 (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
738 fun space_explode _ "" = []
739 | space_explode sep s = String.fields (fn c => str c = sep) s;
741 val split_lines = space_explode "\n";
743 fun prefix_lines "" txt = txt
744 | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
750 fun untab pos [] ys = rev ys
751 | untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys)
752 | untab pos ("\t" :: xs) ys =
753 let val d = tab_width - (pos mod tab_width)
754 in untab (pos + d) xs (funpow d (cons " ") ys) end
755 | untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys);
757 if not (exists (fn c => c = "\t") chs) then chs
761 fun prefix prfx s = prfx ^ s;
762 fun suffix sffx s = s ^ sffx;
764 fun unprefix prfx s =
765 if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
766 else raise Fail "unprefix";
768 fun unsuffix sffx s =
769 if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
770 else raise Fail "unsuffix";
772 fun replicate_string (0: int) _ = ""
773 | replicate_string 1 a = a
774 | replicate_string k a =
775 if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
776 else replicate_string (k div 2) (a ^ a) ^ a;
780 (** lists as sets -- see also Pure/General/ord_list.ML **)
782 (*canonical member, insert, remove*)
783 fun member eq list x =
786 | memb (y :: ys) = eq (x, y) orelse memb ys;
789 fun insert eq x xs = if member eq xs x then xs else x :: xs;
790 fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
791 fun update eq x xs = cons x (remove eq x xs);
793 fun subtract eq = fold (remove eq);
795 fun merge _ ([], ys) = ys
796 | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
798 (*old-style infixes*)
799 fun x mem xs = member (op =) xs x;
800 fun (x: int) mem_int xs = member (op =) xs x;
801 fun (x: string) mem_string xs = member (op =) xs x;
804 (*union of sets represented as lists: no repetitions*)
807 | (x :: xs) union ys = xs union (insert (op =) x ys);
809 (*union of sets, optimized version for ints*)
810 fun (xs:int list) union_int [] = xs
811 | [] union_int ys = ys
812 | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
814 (*union of sets, optimized version for strings*)
815 fun (xs:string list) union_string [] = xs
816 | [] union_string ys = ys
817 | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
819 (*generalized union*)
820 fun gen_union eq (xs, []) = xs
821 | gen_union eq ([], ys) = ys
822 | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
827 | (x :: xs) inter ys =
828 if x mem ys then x :: (xs inter ys) else xs inter ys;
830 (*intersection, optimized version for ints*)
831 fun ([]:int list) inter_int ys = []
832 | (x :: xs) inter_int ys =
833 if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
835 (*intersection, optimized version for strings *)
836 fun ([]:string list) inter_string ys = []
837 | (x :: xs) inter_string ys =
838 if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
840 (*generalized intersection*)
841 fun gen_inter eq ([], ys) = []
842 | gen_inter eq (x::xs, ys) =
843 if member eq ys x then x :: gen_inter eq (xs, ys)
844 else gen_inter eq (xs, ys);
848 fun [] subset ys = true
849 | (x :: xs) subset ys = x mem ys andalso xs subset ys;
851 (*subset, optimized version for ints*)
852 fun ([]: int list) subset_int ys = true
853 | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
855 (*subset, optimized version for strings*)
856 fun ([]: string list) subset_string ys = true
857 | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
860 fun eq_set (xs, ys) =
861 xs = ys orelse (xs subset ys andalso ys subset xs);
863 (*set equality for strings*)
864 fun eq_set_string ((xs: string list), ys) =
865 xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
867 fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
869 fun gen_eq_set eq (xs, ys) =
870 eq_list eq (xs, ys) orelse
871 (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
874 (*removing an element from a list WITHOUT duplicates*)
875 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
877 fun ys \\ xs = foldl (op \) (ys,xs);
880 (*makes a list of the distinct members of the input; preserves order, takes
881 first of equal elements*)
882 fun distinct eq lst =
884 fun dist (rev_seen, []) = rev rev_seen
885 | dist (rev_seen, x :: xs) =
886 if member eq rev_seen x then dist (rev_seen, xs)
887 else dist (x :: rev_seen, xs);
888 in dist ([], lst) end;
890 (*returns a list containing all repeated elements exactly once; preserves
891 order, takes first of equal elements*)
892 fun duplicates eq lst =
894 fun dups (rev_dups, []) = rev rev_dups
895 | dups (rev_dups, x :: xs) =
896 if member eq rev_dups x orelse not (member eq xs x) then
898 else dups (x :: rev_dups, xs);
899 in dups ([], lst) end;
901 fun has_duplicates eq =
904 | dups (x :: xs) = member eq xs x orelse dups xs;
909 (** lists as multisets **)
911 fun remove1 _ _ [] = raise Empty
912 | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs;
914 fun submultiset _ ([], _) = true
915 | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
921 fun is_equal EQUAL = true
922 | is_equal _ = false;
924 fun rev_order LESS = GREATER
925 | rev_order EQUAL = EQUAL
926 | rev_order GREATER = LESS;
928 (*assume rel is a linear strict order*)
929 fun make_ord rel (x, y) =
930 if rel (x, y) then LESS
931 else if rel (y, x) then GREATER
934 fun bool_ord (false, true) = LESS
935 | bool_ord (true, false) = GREATER
936 | bool_ord _ = EQUAL;
938 val int_ord = Int.compare;
939 val string_ord = String.compare;
941 fun fast_string_ord (s1, s2) =
942 (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
944 fun option_ord ord (SOME x, SOME y) = ord (x, y)
945 | option_ord _ (NONE, NONE) = EQUAL
946 | option_ord _ (NONE, SOME _) = LESS
947 | option_ord _ (SOME _, NONE) = GREATER;
949 (*lexicographic product*)
950 fun prod_ord a_ord b_ord ((x, y), (x', y')) =
951 (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
953 (*dictionary order -- in general NOT well-founded!*)
954 fun dict_ord elem_ord (x :: xs, y :: ys) =
955 (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
956 | dict_ord _ ([], []) = EQUAL
957 | dict_ord _ ([], _ :: _) = LESS
958 | dict_ord _ (_ :: _, []) = GREATER;
960 (*lexicographic product of lists*)
961 fun list_ord elem_ord (xs, ys) =
962 (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
967 (*quicksort -- stable, i.e. does not reorder equal elements*)
968 fun quicksort unique ord =
971 | qsort (xs as [_]) = xs
972 | qsort (xs as [x, y]) =
975 | EQUAL => if unique then [x] else xs
978 let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
979 in qsort lts @ eqs @ qsort gts end
980 and part _ [] = ([], [], [])
981 | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
982 and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
983 | add EQUAL x (lts, [], gts) = (lts, [x], gts)
984 | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
985 | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
988 fun sort ord = quicksort false ord;
989 fun sort_distinct ord = quicksort true ord;
991 val sort_strings = sort string_ord;
992 fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
996 (** random numbers **)
1000 fun rmod x y = x - y * Real.realFloor (x / y);
1004 val m = 2147483647.0;
1005 val random_seed = ref 1.0;
1008 fun random () = CRITICAL (fn () =>
1009 let val r = rmod (a * ! random_seed) m
1010 in (random_seed := r; r) end);
1014 fun random_range l h =
1015 if h < l orelse l < 0 then raise RANDOM
1016 else l + Real.floor (rmod (random ()) (real (h - l + 1)));
1018 fun one_of xs = nth xs (random_range 0 (length xs - 1));
1022 val sum = foldl op + (0, map fst xs);
1023 fun pick n ((k: int, x) :: xs) =
1024 if n <= k then x else pick (n - k) xs
1025 in pick (random_range 1 sum) xs end;
1031 fun divide_and_conquer decomp x =
1032 let val (ys, recomb) = decomp x
1033 in recomb (map (divide_and_conquer decomp) ys) end;
1036 (*Partition a list into buckets [ bi, b(i+1), ..., bj ]
1037 putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*)
1038 fun partition_list p i j =
1041 (case xs of [] => []
1042 | _ => raise Fail "partition_list")
1044 let val (ns, rest) = List.partition (p k) xs;
1045 in ns :: part(k+1)rest end
1046 in part (i: int) end;
1048 fun partition_eq (eq:'a * 'a -> bool) =
1052 let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
1053 in (x::xs)::(part xs') end
1058 (* generating identifiers *)
1060 (** Freshly generated identifiers; supplied prefix MUST start with a letter **)
1062 (*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
1064 if i<26 then chr (ord "A" + i)
1065 else if i<52 then chr (ord "a" + i - 26)
1066 else chr (ord "0" + i - 52);
1068 val char_vec = Vector.tabulate (62, gensym_char);
1069 fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
1071 val gensym_seed = ref (0: int);
1074 fun gensym pre = pre ^ newid (NAMED_CRITICAL "gensym" (fn () => inc gensym_seed));
1078 (* stamps and serial numbers *)
1080 type stamp = unit ref;
1081 val stamp: unit -> stamp = ref;
1084 val serial = Multithreading.serial;
1085 val serial_string = string_of_int o serial;
1088 (* generic objects *)
1090 (*note that the builtin exception datatype may be extended by new
1091 constructors at any time*)
1092 structure Object = struct type T = exn end;
1096 structure BasicLibrary: BASIC_LIBRARY = Library;