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 foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
79 val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
80 val flat: 'a list list -> 'a list
81 val unflat: 'a list list -> 'b list -> 'b list list
82 val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
83 val burrow_options: ('a list -> 'b list) -> 'a option list -> 'b option list
84 val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
85 val maps: ('a -> 'b list) -> 'a list -> 'b list
86 val chop: int -> 'a list -> 'a list * 'a list
87 val dropwhile: ('a -> bool) -> 'a list -> 'a list
88 val nth: 'a list -> int -> 'a
89 val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
90 val nth_drop: int -> 'a list -> 'a list
91 val nth_list: 'a list list -> int -> 'a list
92 val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
93 val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
94 val split_last: 'a list -> 'a list * 'a
95 val find_index: ('a -> bool) -> 'a list -> int
96 val find_index_eq: ''a -> ''a list -> int
97 val find_first: ('a -> bool) -> 'a list -> 'a option
98 val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
99 val get_first: ('a -> 'b option) -> 'a list -> 'b option
100 val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
101 val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
102 val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
103 val map_product: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
104 val fold_product: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
105 val zip_options: 'a list -> 'b option list -> ('a * 'b) list
106 val ~~ : 'a list * 'b list -> ('a * 'b) list
107 val split_list: ('a * 'b) list -> 'a list * 'b list
108 val separate: 'a -> 'a list -> 'a list
109 val replicate: int -> 'a -> 'a list
110 val multiply: 'a list -> 'a list list -> 'a list list
111 val filter: ('a -> bool) -> 'a list -> 'a list
112 val filter_out: ('a -> bool) -> 'a list -> 'a list
113 val map_filter: ('a -> 'b option) -> 'a list -> 'b list
114 val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
115 val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
116 val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
117 val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
118 val prefixes1: 'a list -> 'a list list
119 val prefixes: 'a list -> 'a list list
120 val suffixes1: 'a list -> 'a list list
121 val suffixes: 'a list -> 'a list list
124 val inc: int ref -> int
125 val dec: int ref -> int
126 val upto: int * int -> int list
127 val downto: int * int -> int list
128 val radixpand: int * int -> int list
129 val radixstring: int * string * int -> string
130 val string_of_int: int -> string
131 val signed_string_of_int: int -> string
132 val string_of_indexname: string * int -> string
133 val read_radix_int: int -> string list -> int * string list
134 val read_int: string list -> int * string list
135 val oct_char: string -> string
138 val nth_string: string -> int -> string
139 val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
140 val exists_string: (string -> bool) -> string -> bool
141 val forall_string: (string -> bool) -> string -> bool
142 val enclose: string -> string -> string -> string
143 val unenclose: string -> string
144 val quote: string -> string
145 val space_implode: string -> string list -> string
146 val commas: string list -> string
147 val commas_quote: string list -> string
148 val cat_lines: string list -> string
149 val space_explode: string -> string -> string list
150 val split_lines: string -> string list
151 val prefix_lines: string -> string -> string
152 val untabify: string list -> string list
153 val prefix: string -> string -> string
154 val suffix: string -> string -> string
155 val unprefix: string -> string -> string
156 val unsuffix: string -> string -> string
157 val replicate_string: int -> string -> string
158 val translate_string: (string -> string) -> string -> string
160 (*lists as sets -- see also Pure/General/ord_list.ML*)
161 val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
162 val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
163 val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
164 val update: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
165 val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
166 val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
167 val mem: ''a * ''a list -> bool
168 val mem_int: int * int list -> bool
169 val mem_string: string * string list -> bool
170 val union: ''a list * ''a list -> ''a list
171 val union_int: int list * int list -> int list
172 val union_string: string list * string list -> string list
173 val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
174 val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
175 val inter: ''a list * ''a list -> ''a list
176 val inter_int: int list * int list -> int list
177 val inter_string: string list * string list -> string list
178 val subset: ''a list * ''a list -> bool
179 val subset_int: int list * int list -> bool
180 val subset_string: string list * string list -> bool
181 val eq_set: ''a list * ''a list -> bool
182 val eq_set_string: string list * string list -> bool
183 val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
184 val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
185 val \ : ''a list * ''a -> ''a list
186 val \\ : ''a list * ''a list -> ''a list
187 val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
188 val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
189 val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
191 (*lists as multisets*)
192 val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
193 val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
196 val is_equal: order -> bool
197 val rev_order: order -> order
198 val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
199 val bool_ord: bool * bool -> order
200 val int_ord: int * int -> order
201 val string_ord: string * string -> order
202 val fast_string_ord: string * string -> order
203 val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
204 val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
205 val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
206 val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
207 val sort: ('a * 'a -> order) -> 'a list -> 'a list
208 val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
209 val sort_strings: string list -> string list
210 val sort_wrt: ('a -> string) -> 'a list -> 'a list
214 val random: unit -> real
215 val random_range: int -> int -> int
216 val one_of: 'a list -> 'a
217 val frequency: (int * 'a) list -> 'a
220 val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
221 val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
222 val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
223 val gensym: string -> string
225 val stamp: unit -> stamp
227 val serial: unit -> serial
228 val serial_string: unit -> string
229 structure Object: sig type T end
234 include BASIC_LIBRARY
235 val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
236 val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
237 val take: int * 'a list -> 'a list
238 val drop: int * 'a list -> 'a list
239 val last_elem: 'a list -> 'a
242 structure Library: LIBRARY =
247 fun undefined _ = raise Match;
251 fun curry f x y = f (x, y);
252 fun uncurry f (x, y) = f x y;
254 (*application and structured results -- old version*)
255 fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
257 (*conditional application*)
258 fun b ? f = fn x => if b then f x else x;
260 (*composition with multiple args*)
261 fun (f oo g) x y = f (g x y);
262 fun (f ooo g) x y z = f (g x y z);
263 fun (f oooo g) x y z w = f (g x y z w);
265 (*function exponentiation: f(...(f x)...) with n applications of f*)
266 fun funpow (0: int) _ x = x
267 | funpow n f x = funpow (n - 1) f (f x);
272 exception SYS_ERROR of string;
273 fun sys_error msg = raise SYS_ERROR msg;
275 exception ERROR of string;
276 fun error msg = raise ERROR msg;
278 fun cat_error "" msg = error msg
279 | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
281 fun assert_all pred list msg =
284 | ass (x :: xs) = if pred x then ass xs else error (msg x);
290 fun pair x y = (x, y);
291 fun rpair x y = (y, x);
296 fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
297 fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
298 fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
300 fun swap (x, y) = (y, x);
302 fun apfst f (x, y) = (f x, y);
303 fun apsnd f (x, y) = (x, f y);
304 fun pairself f (x, y) = (f x, f y);
309 (*polymorphic equality*)
310 fun equal x y = x = y;
311 fun not_equal x y = x <> y;
313 (*combining predicates*)
314 fun p orf q = fn x => p x orelse q x;
315 fun p andf q = fn x => p x andalso q x;
317 (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
318 fun exists (pred: 'a -> bool) : 'a list -> bool =
319 let fun boolf [] = false
320 | boolf (x :: xs) = pred x orelse boolf xs
323 (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
324 fun forall (pred: 'a -> bool) : 'a list -> bool =
325 let fun boolf [] = true
326 | boolf (x :: xs) = pred x andalso boolf xs
332 fun set flag = (flag := true; true);
333 fun reset flag = (flag := false; false);
334 fun toggle flag = (flag := not (! flag); ! flag);
336 fun change r f = r := f (! r);
338 (*temporarily set flag during execution*)
339 fun setmp_noncritical flag value f x =
341 val orig_value = ! flag;
342 val _ = flag := value;
343 val result = Exn.capture f x;
344 val _ = flag := orig_value;
345 in Exn.release result end;
347 fun setmp flag value f x = NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x);
353 exception UnequalLengths;
357 fun the_single [x] = x
358 | the_single _ = raise Empty;
360 fun singleton f x = the_single (f [x]);
362 fun yield_singleton f x = f [x] #>> the_single;
365 | apply (f :: fs) x = apply fs (f x);
367 fun perhaps_apply funs arg =
370 | app (f :: fs) (changed, x) =
372 NONE => app fs (changed, x)
373 | SOME x' => app fs (true, x'));
374 in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
376 fun perhaps_loop f arg =
378 fun loop (changed, x) =
381 | SOME x' => loop (true, x'));
382 in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
385 (* fold -- old versions *)
387 (*the following versions of fold are designed to fit nicely with infixes*)
389 (* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn
390 for operators that associate to the left (TAIL RECURSIVE)*)
391 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
392 let fun itl (e, []) = e
393 | itl (e, a::l) = itl (f(e, a), l)
396 (* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e))
397 for operators that associate to the right (not tail recursive)*)
400 | itr (a::l) = f(a, itr l)
403 (* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n-1] @ xn))
404 for n > 0, operators that associate to the right (not tail recursive)*)
405 fun foldr1 f [] = raise Empty
408 | itr (x::l) = f(x, itr l)
413 fun fold_aux (x, []) = (x, [])
414 | fold_aux (x, y :: ys) =
416 val (x', y') = f (x, y);
417 val (x'', ys') = fold_aux (x', ys);
418 in (x'', y' :: ys') end;
422 (* basic list functions *)
424 fun eq_list eq (list1, list2) =
426 fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
428 in length list1 = length list2 andalso eq_lst (list1, list2) end;
431 | maps f (x :: xs) = f x @ maps f xs;
433 (*copy the list preserving elements that satisfy the predicate*)
434 val filter = List.filter;
435 fun filter_out f = filter (not o f);
436 val map_filter = List.mapPartial;
438 fun chop (0: int) xs = ([], xs)
439 | chop _ [] = ([], [])
440 | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
442 (*take the first n elements from a list*)
443 fun take (n: int, []) = []
444 | take (n, x :: xs) =
445 if n > 0 then x :: take (n - 1, xs) else [];
447 (*drop the first n elements from a list*)
448 fun drop (n: int, []) = []
449 | drop (n, x :: xs) =
450 if n > 0 then drop (n - 1, xs) else x :: xs;
452 fun dropwhile P [] = []
453 | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
455 (*return nth element of a list, where 0 designates the first element;
456 raise Subscript if list too short*)
457 fun nth xs i = List.nth (xs, i);
459 fun nth_list xss i = nth xss i handle Subscript => [];
461 fun nth_map 0 f (x :: xs) = f x :: xs
462 | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
463 | nth_map (_: int) _ [] = raise Subscript;
466 List.take (xs, n) @ List.drop (xs, n + 1);
470 fun mapp (_: int) [] = []
471 | mapp i (x :: xs) = f (i, x) :: mapp (i + 1) xs
476 fun fold_aux (_: int) [] y = y
477 | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y);
480 val last_elem = List.last;
482 (*rear decomposition*)
483 fun split_last [] = raise Empty
484 | split_last [x] = ([], x)
485 | split_last (x :: xs) = apfst (cons x) (split_last xs);
487 (*find the position of an element in a list*)
488 fun find_index pred =
489 let fun find (_: int) [] = ~1
490 | find n (x :: xs) = if pred x then n else find (n + 1) xs;
493 fun find_index_eq x = find_index (equal x);
495 (*find first element satisfying predicate*)
496 val find_first = List.find;
498 (*get first element by lookup function*)
499 fun get_first _ [] = NONE
500 | get_first f (x :: xs) =
502 NONE => get_first f xs
507 fun get (_: int) [] = NONE
510 of NONE => get (i + 1) xs
511 | SOME y => SOME (i, y)
514 val flat = List.concat;
516 fun unflat (xs :: xss) ys =
517 let val (ps, qs) = chop (length xs) ys
518 in ps :: unflat xss qs end
520 | unflat _ _ = raise UnequalLengths;
522 fun burrow f xss = unflat xss (f (flat xss));
524 fun burrow_options f os = map (try hd) (burrow f (map the_list os));
526 fun fold_burrow f xss s =
527 apfst (unflat xss) (f (flat xss) s);
529 (*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*)
530 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
531 | separate _ xs = xs;
533 (*make the list [x, x, ..., x] of length n*)
534 fun replicate (n: int) x =
535 let fun rep (0, xs) = xs
536 | rep (n, xs) = rep (n - 1, x :: xs)
538 if n < 0 then raise Subscript
542 fun translate_string f = String.translate (f o String.str);
544 (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
545 fun multiply [] _ = []
546 | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
549 fun map_product f _ [] = []
550 | map_product f [] _ = []
551 | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
553 fun fold_product f _ [] z = z
554 | fold_product f [] _ z = z
555 | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
559 exception UnequalLengths;
561 fun map2 _ [] [] = []
562 | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
563 | map2 _ _ _ = raise UnequalLengths;
565 fun fold2 f [] [] z = z
566 | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
567 | fold2 f _ _ _ = raise UnequalLengths;
569 fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
570 | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
571 | zip_options _ [] = []
572 | zip_options [] _ = raise UnequalLengths;
574 (*combine two lists forming a list of pairs:
575 [x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*)
577 | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
578 | _ ~~ _ = raise UnequalLengths;
580 (*inverse of ~~; the old 'split':
581 [(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*)
582 val split_list = ListPair.unzip;
585 (* prefixes, suffixes *)
587 fun is_prefix _ [] _ = true
588 | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
589 | is_prefix eq _ _ = false;
591 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., x(i-1)], [xi, ..., xn])
592 where xi is the first element that does not satisfy the predicate*)
593 fun take_prefix (pred : 'a -> bool) (xs: 'a list) : 'a list * 'a list =
594 let fun take (rxs, []) = (rev rxs, [])
595 | take (rxs, x :: xs) =
596 if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs)
599 fun chop_prefix eq ([], ys) = ([], ([], ys))
600 | chop_prefix eq (xs, []) = ([], (xs, []))
601 | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
603 let val (ps', xys'') = chop_prefix eq (xs', ys')
604 in (x :: ps', xys'') end
607 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., xi], [x(i+1), ..., xn])
608 where xi is the last element that does not satisfy the predicate*)
609 fun take_suffix _ [] = ([], [])
610 | take_suffix pred (x :: xs) =
611 (case take_suffix pred xs of
612 ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
613 | (prfx, sffx) => (x :: prfx, sffx));
615 fun prefixes1 [] = []
616 | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
618 fun prefixes xs = [] :: prefixes1 xs;
620 fun suffixes1 xs = map rev (prefixes1 (rev xs));
621 fun suffixes xs = [] :: suffixes1 xs;
627 fun inc i = (i := ! i + (1: int); ! i);
628 fun dec i = (i := ! i - (1: int); ! i);
631 (* lists of integers *)
633 (*make the list [from, from + 1, ..., to]*)
634 fun ((i: int) upto j) =
635 if i > j then [] else i :: (i + 1 upto j);
637 (*make the list [from, from - 1, ..., to]*)
638 fun ((i: int) downto j) =
639 if i < j then [] else i :: (i - 1 downto j);
642 (* convert integers to strings *)
644 (*expand the number in the given base;
645 example: radixpand (2, 8) gives [1, 0, 0, 0]*)
646 fun radixpand (base, num) : int list =
648 fun radix (n, tail) =
649 if n < base then n :: tail
650 else radix (n div base, (n mod base) :: tail)
651 in radix (num, []) end;
653 (*expands a number into a string of characters starting from "zerochar";
654 example: radixstring (2, "0", 8) gives "1000"*)
655 fun radixstring (base, zerochar, num) =
656 let val offset = ord zerochar;
657 fun chrof n = chr (offset + n)
658 in implode (map chrof (radixpand (base, num))) end;
661 val string_of_int = Int.toString;
663 fun signed_string_of_int i =
664 if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
666 fun string_of_indexname (a, 0) = a
667 | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
672 fun read_radix_int radix cs =
675 val limit = zero + radix;
676 fun scan (num, []) = (num, [])
677 | scan (num, c :: cs) =
678 if zero <= ord c andalso ord c < limit then
679 scan (radix * num + (ord c - zero), cs)
683 val read_int = read_radix_int 10;
685 fun oct_char s = chr (#1 (read_radix_int 8 (explode s)));
691 (* functions tuned for strings, avoiding explode *)
693 fun nth_string str i =
694 (case try String.substring (str, i, 1) of
696 | NONE => raise Subscript);
698 fun fold_string f str x0 =
702 if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
705 fun exists_string pred str =
708 fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
711 fun forall_string pred = not o exists_string (not o pred);
713 (*enclose in brackets*)
714 fun enclose lpar rpar str = lpar ^ str ^ rpar;
715 fun unenclose str = String.substring (str, 1, size str - 2);
717 (*simple quoting (does not escape special chars)*)
718 val quote = enclose "\"" "\"";
720 (*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
721 fun space_implode a bs = implode (separate a bs);
723 val commas = space_implode ", ";
724 val commas_quote = commas o map quote;
726 (*concatenate messages, one per line, into a string*)
727 val cat_lines = space_implode "\n";
729 (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
730 fun space_explode _ "" = []
731 | space_explode sep s = String.fields (fn c => str c = sep) s;
733 val split_lines = space_explode "\n";
735 fun prefix_lines "" txt = txt
736 | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
742 fun untab pos [] ys = rev ys
743 | untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys)
744 | untab pos ("\t" :: xs) ys =
745 let val d = tab_width - (pos mod tab_width)
746 in untab (pos + d) xs (funpow d (cons " ") ys) end
747 | untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys);
749 if not (exists (fn c => c = "\t") chs) then chs
753 fun prefix prfx s = prfx ^ s;
754 fun suffix sffx s = s ^ sffx;
756 fun unprefix prfx s =
757 if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
758 else raise Fail "unprefix";
760 fun unsuffix sffx s =
761 if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
762 else raise Fail "unsuffix";
764 fun replicate_string (0: int) _ = ""
765 | replicate_string 1 a = a
766 | replicate_string k a =
767 if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
768 else replicate_string (k div 2) (a ^ a) ^ a;
772 (** lists as sets -- see also Pure/General/ord_list.ML **)
774 (*canonical member, insert, remove*)
775 fun member eq list x =
778 | memb (y :: ys) = eq (x, y) orelse memb ys;
781 fun insert eq x xs = if member eq xs x then xs else x :: xs;
782 fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
783 fun update eq x xs = cons x (remove eq x xs);
785 fun subtract eq = fold (remove eq);
787 fun merge _ ([], ys) = ys
788 | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
790 (*old-style infixes*)
791 fun x mem xs = member (op =) xs x;
792 fun (x: int) mem_int xs = member (op =) xs x;
793 fun (x: string) mem_string xs = member (op =) xs x;
796 (*union of sets represented as lists: no repetitions*)
799 | (x :: xs) union ys = xs union (insert (op =) x ys);
801 (*union of sets, optimized version for ints*)
802 fun (xs:int list) union_int [] = xs
803 | [] union_int ys = ys
804 | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
806 (*union of sets, optimized version for strings*)
807 fun (xs:string list) union_string [] = xs
808 | [] union_string ys = ys
809 | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
811 (*generalized union*)
812 fun gen_union eq (xs, []) = xs
813 | gen_union eq ([], ys) = ys
814 | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
819 | (x :: xs) inter ys =
820 if x mem ys then x :: (xs inter ys) else xs inter ys;
822 (*intersection, optimized version for ints*)
823 fun ([]:int list) inter_int ys = []
824 | (x :: xs) inter_int ys =
825 if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
827 (*intersection, optimized version for strings *)
828 fun ([]:string list) inter_string ys = []
829 | (x :: xs) inter_string ys =
830 if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
832 (*generalized intersection*)
833 fun gen_inter eq ([], ys) = []
834 | gen_inter eq (x::xs, ys) =
835 if member eq ys x then x :: gen_inter eq (xs, ys)
836 else gen_inter eq (xs, ys);
840 fun [] subset ys = true
841 | (x :: xs) subset ys = x mem ys andalso xs subset ys;
843 (*subset, optimized version for ints*)
844 fun ([]: int list) subset_int ys = true
845 | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
847 (*subset, optimized version for strings*)
848 fun ([]: string list) subset_string ys = true
849 | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
852 fun eq_set (xs, ys) =
853 xs = ys orelse (xs subset ys andalso ys subset xs);
855 (*set equality for strings*)
856 fun eq_set_string ((xs: string list), ys) =
857 xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
859 fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
861 fun gen_eq_set eq (xs, ys) =
862 eq_list eq (xs, ys) orelse
863 (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
866 (*removing an element from a list WITHOUT duplicates*)
867 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
869 fun ys \\ xs = foldl (op \) (ys,xs);
872 (*makes a list of the distinct members of the input; preserves order, takes
873 first of equal elements*)
874 fun distinct eq lst =
876 fun dist (rev_seen, []) = rev rev_seen
877 | dist (rev_seen, x :: xs) =
878 if member eq rev_seen x then dist (rev_seen, xs)
879 else dist (x :: rev_seen, xs);
880 in dist ([], lst) end;
882 (*returns a list containing all repeated elements exactly once; preserves
883 order, takes first of equal elements*)
884 fun duplicates eq lst =
886 fun dups (rev_dups, []) = rev rev_dups
887 | dups (rev_dups, x :: xs) =
888 if member eq rev_dups x orelse not (member eq xs x) then
890 else dups (x :: rev_dups, xs);
891 in dups ([], lst) end;
893 fun has_duplicates eq =
896 | dups (x :: xs) = member eq xs x orelse dups xs;
901 (** lists as multisets **)
903 fun remove1 _ _ [] = raise Empty
904 | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs;
906 fun submultiset _ ([], _) = true
907 | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
913 fun is_equal EQUAL = true
914 | is_equal _ = false;
916 fun rev_order LESS = GREATER
917 | rev_order EQUAL = EQUAL
918 | rev_order GREATER = LESS;
920 (*assume rel is a linear strict order*)
921 fun make_ord rel (x, y) =
922 if rel (x, y) then LESS
923 else if rel (y, x) then GREATER
926 fun bool_ord (false, true) = LESS
927 | bool_ord (true, false) = GREATER
928 | bool_ord _ = EQUAL;
930 val int_ord = Int.compare;
931 val string_ord = String.compare;
933 fun fast_string_ord (s1, s2) =
934 (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
936 fun option_ord ord (SOME x, SOME y) = ord (x, y)
937 | option_ord _ (NONE, NONE) = EQUAL
938 | option_ord _ (NONE, SOME _) = LESS
939 | option_ord _ (SOME _, NONE) = GREATER;
941 (*lexicographic product*)
942 fun prod_ord a_ord b_ord ((x, y), (x', y')) =
943 (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
945 (*dictionary order -- in general NOT well-founded!*)
946 fun dict_ord elem_ord (x :: xs, y :: ys) =
947 (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
948 | dict_ord _ ([], []) = EQUAL
949 | dict_ord _ ([], _ :: _) = LESS
950 | dict_ord _ (_ :: _, []) = GREATER;
952 (*lexicographic product of lists*)
953 fun list_ord elem_ord (xs, ys) =
954 (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
959 (*quicksort -- stable, i.e. does not reorder equal elements*)
960 fun quicksort unique ord =
963 | qsort (xs as [_]) = xs
964 | qsort (xs as [x, y]) =
967 | EQUAL => if unique then [x] else xs
970 let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
971 in qsort lts @ eqs @ qsort gts end
972 and part _ [] = ([], [], [])
973 | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
974 and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
975 | add EQUAL x (lts, [], gts) = (lts, [x], gts)
976 | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
977 | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
980 fun sort ord = quicksort false ord;
981 fun sort_distinct ord = quicksort true ord;
983 val sort_strings = sort string_ord;
984 fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
988 (** random numbers **)
992 fun rmod x y = x - y * Real.realFloor (x / y);
996 val m = 2147483647.0;
997 val random_seed = ref 1.0;
1000 fun random () = CRITICAL (fn () =>
1001 let val r = rmod (a * ! random_seed) m
1002 in (random_seed := r; r) end);
1006 fun random_range l h =
1007 if h < l orelse l < 0 then raise RANDOM
1008 else l + Real.floor (rmod (random ()) (real (h - l + 1)));
1010 fun one_of xs = nth xs (random_range 0 (length xs - 1));
1014 val sum = foldl op + (0, map fst xs);
1015 fun pick n ((k: int, x) :: xs) =
1016 if n <= k then x else pick (n - k) xs
1017 in pick (random_range 1 sum) xs end;
1023 fun divide_and_conquer decomp x =
1024 let val (ys, recomb) = decomp x
1025 in recomb (map (divide_and_conquer decomp) ys) end;
1028 (*Partition a list into buckets [ bi, b(i+1), ..., bj ]
1029 putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*)
1030 fun partition_list p i j =
1033 (case xs of [] => []
1034 | _ => raise Fail "partition_list")
1036 let val (ns, rest) = List.partition (p k) xs;
1037 in ns :: part(k+1)rest end
1038 in part (i: int) end;
1040 fun partition_eq (eq:'a * 'a -> bool) =
1044 let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
1045 in (x::xs)::(part xs') end
1050 (* generating identifiers *)
1052 (** Freshly generated identifiers; supplied prefix MUST start with a letter **)
1054 (*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
1056 if i<26 then chr (ord "A" + i)
1057 else if i<52 then chr (ord "a" + i - 26)
1058 else chr (ord "0" + i - 52);
1060 val char_vec = Vector.tabulate (62, gensym_char);
1061 fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
1063 val gensym_seed = ref (0: int);
1066 fun gensym pre = pre ^ newid (NAMED_CRITICAL "gensym" (fn () => inc gensym_seed));
1070 (* stamps and serial numbers *)
1072 type stamp = unit ref;
1073 val stamp: unit -> stamp = ref;
1076 local val count = ref (0: int)
1077 in fun serial () = NAMED_CRITICAL "serial" (fn () => inc count) end;
1079 val serial_string = string_of_int o serial;
1082 (* generic objects *)
1084 (*note that the builtin exception datatype may be extended by new
1085 constructors at any time*)
1086 structure Object = struct type T = exn end;
1090 structure BasicLibrary: BASIC_LIBRARY = Library;