src/Pure/library.ML
 author wenzelm Wed Apr 16 18:16:02 1997 +0200 (1997-04-16) changeset 2958 7837471d2f27 parent 2806 772f6bba48a1 child 2978 83a4c4f79dcd permissions -rw-r--r--
improved inc, dec;
1 (*  Title:      Pure/library.ML
2     ID:         \$Id\$
3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
4     Copyright   1992  University of Cambridge
6 Basic library: functions, options, pairs, booleans, lists, integers,
7 strings, lists as sets, association lists, generic tables, balanced trees,
8 orders, input / output, timing, filenames, misc functions.
9 *)
11 infix |> ~~ \ \\ orelf ins ins_string ins_int orf andf prefix upto downto
12       mem mem_int mem_string union union_int union_string
13       inter inter_int inter_string subset subset_int subset_string subdir_of;
16 structure Library =
17 struct
19 (** functions **)
21 (*handy combinators*)
22 fun curry f x y = f (x, y);
23 fun uncurry f (x, y) = f x y;
24 fun I x = x;
25 fun K x y = x;
27 (*reverse apply*)
28 fun (x |> f) = f x;
30 (*combine two functions forming the union of their domains*)
31 fun (f orelf g) = fn x => f x handle Match => g x;
33 (*application of (infix) operator to its left or right argument*)
34 fun apl (x, f) y = f (x, y);
35 fun apr (f, y) x = f (x, y);
37 (*functional for pairs*)
38 fun pairself f (x, y) = (f x, f y);
40 (*function exponentiation: f(...(f x)...) with n applications of f*)
41 fun funpow n f x =
42   let fun rep (0, x) = x
43         | rep (n, x) = rep (n - 1, f x)
44   in rep (n, x) end;
48 (** stamps **)
50 type stamp = unit ref;
51 val stamp: unit -> stamp = ref;
55 (** options **)
57 datatype 'a option = None | Some of 'a;
59 exception OPTION of string;
61 fun the (Some x) = x
62   | the None = raise OPTION "the";
64 fun if_none None y = y
65   | if_none (Some x) _ = x;
67 fun is_some (Some _) = true
68   | is_some None = false;
70 fun is_none (Some _) = false
71   | is_none None = true;
73 fun apsome f (Some x) = Some (f x)
74   | apsome _ None = None;
78 (** pairs **)
80 fun pair x y = (x, y);
81 fun rpair x y = (y, x);
83 fun fst (x, y) = x;
84 fun snd (x, y) = y;
86 fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
87 fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
89 fun swap (x, y) = (y, x);
91 (*apply the function to a component of a pair*)
92 fun apfst f (x, y) = (f x, y);
93 fun apsnd f (x, y) = (x, f y);
97 (** booleans **)
99 (* equality *)
101 fun equal x y = x = y;
102 fun not_equal x y = x <> y;
105 (* operators for combining predicates *)
107 fun (p orf q) = fn x => p x orelse q x;
109 fun (p andf q) = fn x => p x andalso q x;
111 fun notf p x = not (p x);
114 (* predicates on lists *)
116 fun orl [] = false
117   | orl (x :: xs) = x orelse orl xs;
119 fun andl [] = true
120   | andl (x :: xs) = x andalso andl xs;
122 (*Needed because several object-logics declare the theory, therefore structure,
123   List.*)
124 structure List_ = List;
126 (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
127 fun exists (pred: 'a -> bool) : 'a list -> bool =
128   let fun boolf [] = false
129         | boolf (x :: xs) = pred x orelse boolf xs
130   in boolf end;
132 (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
133 fun forall (pred: 'a -> bool) : 'a list -> bool =
134   let fun boolf [] = true
135         | boolf (x :: xs) = pred x andalso boolf xs
136   in boolf end;
139 (* flags *)
141 fun set flag = (flag := true; true);
142 fun reset flag = (flag := false; false);
143 fun toggle flag = (flag := not (! flag); ! flag);
145 fun set_ap flag value f x =
146   let
147     val orig_value = ! flag;
148     fun return y = (flag := orig_value; y);
149   in
150     flag := value;
151     return (f x handle exn => (return (); raise exn))
152   end;
156 (** lists **)
158 exception LIST of string;
160 fun null [] = true
161   | null (_ :: _) = false;
163 fun hd [] = raise LIST "hd"
164   | hd (x :: _) = x;
166 fun tl [] = raise LIST "tl"
167   | tl (_ :: xs) = xs;
169 fun cons x xs = x :: xs;
172 (* fold *)
174 (*the following versions of fold are designed to fit nicely with infixes*)
176 (*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
177     for operators that associate to the left (TAIL RECURSIVE)*)
178 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
179   let fun itl (e, [])  = e
180         | itl (e, a::l) = itl (f(e, a), l)
181   in  itl end;
183 (*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
184     for operators that associate to the right (not tail recursive)*)
185 fun foldr f (l, e) =
186   let fun itr [] = e
187         | itr (a::l) = f(a, itr l)
188   in  itr l  end;
190 (*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
191     for n > 0, operators that associate to the right (not tail recursive)*)
192 fun foldr1 f l =
193   let fun itr [x] = x                       (* FIXME [] case: elim warn (?) *)
194         | itr (x::l) = f(x, itr l)
195   in  itr l  end;
198 (* basic list functions *)
200 (*length of a list, should unquestionably be a standard function*)
201 local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
202         | length1 (n, x :: xs) = length1 (n + 1, xs)
203 in  fun length l = length1 (0, l) end;
205 (*take the first n elements from a list*)
206 fun take (n, []) = []
207   | take (n, x :: xs) =
208       if n > 0 then x :: take (n - 1, xs) else [];
210 (*drop the first n elements from a list*)
211 fun drop (n, []) = []
212   | drop (n, x :: xs) =
213       if n > 0 then drop (n - 1, xs) else x :: xs;
215 (*return nth element of a list, where 0 designates the first element;
216   raise EXCEPTION if list too short*)
217 fun nth_elem NL =
218   (case drop NL of
219     [] => raise LIST "nth_elem"
220   | x :: _ => x);
222 (*last element of a list*)
223 fun last_elem [] = raise LIST "last_elem"
224   | last_elem [x] = x
225   | last_elem (_ :: xs) = last_elem xs;
227 (*find the position of an element in a list*)
228 fun find (x, ys) =
229   let fun f (y :: ys, i) = if x = y then i else f (ys, i + 1)
230         | f (_, _) = raise LIST "find"
231   in f (ys, 0) end;
233 (*flatten a list of lists to a list*)
234 fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
237 (*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
238   (proc x1; ...; proc xn) for side effects*)
239 fun seq (proc: 'a -> unit) : 'a list -> unit =
240   let fun seqf [] = ()
241         | seqf (x :: xs) = (proc x; seqf xs)
242   in seqf end;
245 (*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
246 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
247   | separate _ xs = xs;
249 (*make the list [x, x, ..., x] of length n*)
250 fun replicate n (x: 'a) : 'a list =
251   let fun rep (0, xs) = xs
252         | rep (n, xs) = rep (n - 1, x :: xs)
253   in
254     if n < 0 then raise LIST "replicate"
255     else rep (n, [])
256   end;
259 (* filter *)
261 (*copy the list preserving elements that satisfy the predicate*)
262 fun filter (pred: 'a->bool) : 'a list -> 'a list =
263   let fun filt [] = []
264         | filt (x :: xs) = if pred x then x :: filt xs else filt xs
265   in filt end;
267 fun filter_out f = filter (not o f);
270 fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
271   | mapfilter f (x :: xs) =
272       (case f x of
273         None => mapfilter f xs
274       | Some y => y :: mapfilter f xs);
277 fun find_first _ [] = None
278   | find_first pred (x :: xs) =
279       if pred x then Some x else find_first pred xs;
282 (* lists of pairs *)
284 fun map2 _ ([], []) = []
285   | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
286   | map2 _ _ = raise LIST "map2";
288 fun exists2 _ ([], []) = false
289   | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
290   | exists2 _ _ = raise LIST "exists2";
292 fun forall2 _ ([], []) = true
293   | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
294   | forall2 _ _ = raise LIST "forall2";
296 (*combine two lists forming a list of pairs:
297   [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
298 fun [] ~~ [] = []
299   | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
300   | _ ~~ _ = raise LIST "~~";
303 (*inverse of ~~; the old 'split':
304   [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
305 fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
308 (* prefixes, suffixes *)
310 fun [] prefix _ = true
311   | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
312   | _ prefix _ = false;
314 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
315    where xi is the first element that does not satisfy the predicate*)
316 fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
317   let fun take (rxs, []) = (rev rxs, [])
318         | take (rxs, x :: xs) =
319             if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
320   in  take([], xs)  end;
322 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
323    where xi is the last element that does not satisfy the predicate*)
324 fun take_suffix _ [] = ([], [])
325   | take_suffix pred (x :: xs) =
326       (case take_suffix pred xs of
327         ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
328       | (prfx, sffx) => (x :: prfx, sffx));
332 (** integers **)
334 fun inc i = (i := ! i + 1; ! i);
335 fun dec i = (i := ! i - 1; ! i);
338 (* lists of integers *)
340 (*make the list [from, from + 1, ..., to]*)
341 fun (from upto to) =
342   if from > to then [] else from :: ((from + 1) upto to);
344 (*make the list [from, from - 1, ..., to]*)
345 fun (from downto to) =
346   if from < to then [] else from :: ((from - 1) downto to);
348 (*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
349 fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
350   | downto0 ([], n) = n = ~1;
353 (* convert integers to strings *)
355 (*expand the number in the given base;
356   example: radixpand (2, 8) gives [1, 0, 0, 0]*)
357 fun radixpand (base, num) : int list =
358   let
359     fun radix (n, tail) =
360       if n < base then n :: tail
361       else radix (n div base, (n mod base) :: tail)
362   in radix (num, []) end;
364 (*expands a number into a string of characters starting from "zerochar";
365   example: radixstring (2, "0", 8) gives "1000"*)
366 fun radixstring (base, zerochar, num) =
367   let val offset = ord zerochar;
368       fun chrof n = chr (offset + n)
369   in implode (map chrof (radixpand (base, num))) end;
372 fun string_of_int n =
373   if n < 0 then "~" ^ radixstring (10, "0", ~n) else radixstring (10, "0", n);
377 (** strings **)
379 fun is_letter ch =
380   ord "A" <= ord ch andalso ord ch <= ord "Z" orelse
381   ord "a" <= ord ch andalso ord ch <= ord "z";
383 fun is_digit ch =
384   ord "0" <= ord ch andalso ord ch <= ord "9";
386 (*letter or _ or prime (')*)
387 fun is_quasi_letter "_" = true
388   | is_quasi_letter "'" = true
389   | is_quasi_letter ch = is_letter ch;
391 (*white space: blanks, tabs, newlines, formfeeds*)
392 val is_blank : string -> bool =
393   fn " " => true | "\t" => true | "\n" => true | "\^L" => true | _ => false;
395 val is_letdig = is_quasi_letter orf is_digit;
397 (*printable chars*)
398 fun is_printable c = ord c > ord " " andalso ord c <= ord "~";
401 (*lower all chars of string*)
402 val to_lower =
403   let
404     fun lower ch =
405       if ch >= "A" andalso ch <= "Z" then
406         chr (ord ch - ord "A" + ord "a")
407       else ch;
408   in implode o (map lower) o explode end;
411 (*enclose in brackets*)
412 fun enclose lpar rpar str = lpar ^ str ^ rpar;
414 (*simple quoting (does not escape special chars)*)
415 val quote = enclose "\"" "\"";
417 (*space_implode "..." (explode "hello"); gives "h...e...l...l...o"*)
418 fun space_implode a bs = implode (separate a bs);
420 val commas = space_implode ", ";
421 val commas_quote = commas o map quote;
423 (*concatenate messages, one per line, into a string*)
424 val cat_lines = space_implode "\n";
426 (*space_explode "." "h.e..l.lo"; gives ["h", "e", "l", "lo"]*)
427 fun space_explode sep s =
428   let fun divide [] "" = []
429         | divide [] part = [part]
430         | divide (c::s) part =
431             if c = sep then
432               (if part = "" then divide s "" else part :: divide s "")
433             else divide s (part ^ c)
434   in divide (explode s) "" end;
437 (** lists as sets **)
439 (*membership in a list*)
440 fun x mem [] = false
441   | x mem (y :: ys) = x = y orelse x mem ys;
443 (*membership in a list, optimized version for ints*)
444 fun (x:int) mem_int [] = false
445   | x mem_int (y :: ys) = x = y orelse x mem_int ys;
447 (*membership in a list, optimized version for strings*)
448 fun (x:string) mem_string [] = false
449   | x mem_string (y :: ys) = x = y orelse x mem_string ys;
451 (*generalized membership test*)
452 fun gen_mem eq (x, []) = false
453   | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
456 (*insertion into list if not already there*)
457 fun (x ins xs) = if x mem xs then xs else x :: xs;
459 (*insertion into list, optimized version for ints*)
460 fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
462 (*insertion into list, optimized version for strings*)
463 fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
465 (*generalized insertion*)
466 fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
469 (*union of sets represented as lists: no repetitions*)
470 fun xs union [] = xs
471   | [] union ys = ys
472   | (x :: xs) union ys = xs union (x ins ys);
474 (*union of sets, optimized version for ints*)
475 fun (xs:int list) union_int [] = xs
476   | [] union_int ys = ys
477   | (x :: xs) union_int ys = xs union_int (x ins_int ys);
479 (*union of sets, optimized version for strings*)
480 fun (xs:string list) union_string [] = xs
481   | [] union_string ys = ys
482   | (x :: xs) union_string ys = xs union_string (x ins_string ys);
484 (*generalized union*)
485 fun gen_union eq (xs, []) = xs
486   | gen_union eq ([], ys) = ys
487   | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
490 (*intersection*)
491 fun [] inter ys = []
492   | (x :: xs) inter ys =
493       if x mem ys then x :: (xs inter ys) else xs inter ys;
495 (*intersection, optimized version for ints*)
496 fun ([]:int list) inter_int ys = []
497   | (x :: xs) inter_int ys =
498       if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
500 (*intersection, optimized version for strings *)
501 fun ([]:string list) inter_string ys = []
502   | (x :: xs) inter_string ys =
503       if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
506 (*subset*)
507 fun [] subset ys = true
508   | (x :: xs) subset ys = x mem ys andalso xs subset ys;
510 (*subset, optimized version for ints*)
511 fun ([]:int list) subset_int ys = true
512   | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
514 (*subset, optimized version for strings*)
515 fun ([]:string list) subset_string ys = true
516   | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
518 (*set equality for strings*)
519 fun eq_set_string ((xs:string list), ys) =
520   xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
522 fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
525 (*removing an element from a list WITHOUT duplicates*)
526 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
527   | [] \ x = [];
529 fun ys \\ xs = foldl (op \) (ys,xs);
531 (*removing an element from a list -- possibly WITH duplicates*)
532 fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
534 fun gen_rems eq = foldl (gen_rem eq);
537 (*makes a list of the distinct members of the input; preserves order, takes
538   first of equal elements*)
539 fun gen_distinct eq lst =
540   let
541     val memb = gen_mem eq;
543     fun dist (rev_seen, []) = rev rev_seen
544       | dist (rev_seen, x :: xs) =
545           if memb (x, rev_seen) then dist (rev_seen, xs)
546           else dist (x :: rev_seen, xs);
547   in
548     dist ([], lst)
549   end;
551 fun distinct l = gen_distinct (op =) l;
554 (*returns the tail beginning with the first repeated element, or []*)
555 fun findrep [] = []
556   | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
559 (*returns a list containing all repeated elements exactly once; preserves
560   order, takes first of equal elements*)
561 fun gen_duplicates eq lst =
562   let
563     val memb = gen_mem eq;
565     fun dups (rev_dups, []) = rev rev_dups
566       | dups (rev_dups, x :: xs) =
567           if memb (x, rev_dups) orelse not (memb (x, xs)) then
568             dups (rev_dups, xs)
569           else dups (x :: rev_dups, xs);
570   in
571     dups ([], lst)
572   end;
574 fun duplicates l = gen_duplicates (op =) l;
578 (** association lists **)
580 (*association list lookup*)
581 fun assoc ([], key) = None
582   | assoc ((keyi, xi) :: pairs, key) =
583       if key = keyi then Some xi else assoc (pairs, key);
585 (*association list lookup, optimized version for ints*)
586 fun assoc_int ([], (key:int)) = None
587   | assoc_int ((keyi, xi) :: pairs, key) =
588       if key = keyi then Some xi else assoc_int (pairs, key);
590 (*association list lookup, optimized version for strings*)
591 fun assoc_string ([], (key:string)) = None
592   | assoc_string ((keyi, xi) :: pairs, key) =
593       if key = keyi then Some xi else assoc_string (pairs, key);
595 (*association list lookup, optimized version for string*ints*)
596 fun assoc_string_int ([], (key:string*int)) = None
597   | assoc_string_int ((keyi, xi) :: pairs, key) =
598       if key = keyi then Some xi else assoc_string_int (pairs, key);
600 fun assocs ps x =
601   (case assoc (ps, x) of
602     None => []
603   | Some ys => ys);
605 (*two-fold association list lookup*)
606 fun assoc2 (aal, (key1, key2)) =
607   (case assoc (aal, key1) of
608     Some al => assoc (al, key2)
609   | None => None);
611 (*generalized association list lookup*)
612 fun gen_assoc eq ([], key) = None
613   | gen_assoc eq ((keyi, xi) :: pairs, key) =
614       if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
616 (*association list update*)
617 fun overwrite (al, p as (key, _)) =
618   let fun over ((q as (keyi, _)) :: pairs) =
619             if keyi = key then p :: pairs else q :: (over pairs)
620         | over [] = [p]
621   in over al end;
623 fun gen_overwrite eq (al, p as (key, _)) =
624   let fun over ((q as (keyi, _)) :: pairs) =
625             if eq (keyi, key) then p :: pairs else q :: (over pairs)
626         | over [] = [p]
627   in over al end;
631 (** generic tables **)
633 (*Tables are supposed to be 'efficient' encodings of lists of elements distinct
634   wrt. an equality "eq". The extend and merge operations below are optimized
635   for long-term space efficiency.*)
637 (*append (new) elements to a table*)
638 fun generic_extend _ _ _ tab [] = tab
639   | generic_extend eq dest_tab mk_tab tab1 lst2 =
640       let
641         val lst1 = dest_tab tab1;
642         val new_lst2 = gen_rems eq (lst2, lst1);
643       in
644         if null new_lst2 then tab1
645         else mk_tab (lst1 @ new_lst2)
646       end;
648 (*append (new) elements of 2nd table to 1st table*)
649 fun generic_merge eq dest_tab mk_tab tab1 tab2 =
650   let
651     val lst1 = dest_tab tab1;
652     val lst2 = dest_tab tab2;
653     val new_lst2 = gen_rems eq (lst2, lst1);
654   in
655     if null new_lst2 then tab1
656     else if gen_subset eq (lst1, lst2) then tab2
657     else mk_tab (lst1 @ new_lst2)
658   end;
661 (*lists as tables*)
662 fun extend_list tab = generic_extend (op =) I I tab;
663 fun merge_lists tab = generic_merge (op =) I I tab;
665 fun merge_rev_lists xs [] = xs
666   | merge_rev_lists [] ys = ys
667   | merge_rev_lists xs (y :: ys) =
668       (if y mem xs then I else cons y) (merge_rev_lists xs ys);
672 (** balanced trees **)
674 exception Balance;      (*indicates non-positive argument to balancing fun*)
676 (*balanced folding; avoids deep nesting*)
677 fun fold_bal f [x] = x
678   | fold_bal f [] = raise Balance
679   | fold_bal f xs =
680       let val k = length xs div 2
681       in  f (fold_bal f (take(k, xs)),
682              fold_bal f (drop(k, xs)))
683       end;
685 (*construct something of the form f(...g(...(x)...)) for balanced access*)
686 fun access_bal (f, g, x) n i =
687   let fun acc n i =     (*1<=i<=n*)
688           if n=1 then x else
689           let val n2 = n div 2
690           in  if i<=n2 then f (acc n2 i)
691                        else g (acc (n-n2) (i-n2))
692           end
693   in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
695 (*construct ALL such accesses; could try harder to share recursive calls!*)
696 fun accesses_bal (f, g, x) n =
697   let fun acc n =
698           if n=1 then [x] else
699           let val n2 = n div 2
700               val acc2 = acc n2
701           in  if n-n2=n2 then map f acc2 @ map g acc2
702                          else map f acc2 @ map g (acc (n-n2)) end
703   in  if 1<=n then acc n else raise Balance  end;
707 (** orders **)
709 datatype order = LESS | EQUAL | GREATER;
711 fun intord (i, j: int) =
712   if i < j then LESS
713   else if i = j then EQUAL
714   else GREATER;
716 fun stringord (a, b: string) =
717   if a < b then LESS
718   else if a = b then EQUAL
719   else GREATER;
723 (** input / output **)
725 val cd = OS.FileSys.chDir;
726 val pwd = OS.FileSys.getDir;
728 val prs_fn = ref(fn s => TextIO.output (TextIO.stdOut, s));
730 fun prs s = !prs_fn s;
731 fun writeln s = prs (s ^ "\n");
733 (* TextIO.output to LaTeX / xdvi *)
734 fun latex s =
735         execute ( "( cd /tmp ; echo \"" ^ s ^
736         "\" | isa2latex -s > \$\$.tex ; latex \$\$.tex ; xdvi \$\$.dvi ; rm \$\$.* ) > /dev/null &" ) ;
738 (*print warning*)
739 val warning_fn = ref(fn s => TextIO.output (TextIO.stdOut, s ^ "\n"));
740 fun warning s = !warning_fn ("Warning: " ^ s);
742 (*print error message and abort to top level*)
744 val error_fn = ref(fn s => TextIO.output (TextIO.stdOut, s ^ "\n"));
746 exception ERROR;
747 fun error msg = (!error_fn msg; raise ERROR);
748 fun sys_error msg = (!error_fn "*** SYSTEM ERROR ***"; error msg);
750 fun assert p msg = if p then () else error msg;
751 fun deny p msg = if p then error msg else ();
753 (*Assert pred for every member of l, generating a message if pred fails*)
754 fun assert_all pred l msg_fn =
755   let fun asl [] = ()
756         | asl (x::xs) = if pred x then asl xs
757                         else error (msg_fn x)
758   in  asl l  end;
760 (*for the "test" target in Makefiles -- signifies successful termination*)
761 fun maketest msg =
762   (writeln msg;
763    let val os = TextIO.openOut "test"
764    in  TextIO.output (os, "Test examples ran successfully\n");
765        TextIO.closeOut os
766    end);
769 (*print a list surrounded by the brackets lpar and rpar, with comma separator
770   print nothing for empty list*)
771 fun print_list (lpar, rpar, pre: 'a -> unit) (l : 'a list) =
772   let fun prec x = (prs ","; pre x)
773   in
774     (case l of
775       [] => ()
776     | x::l => (prs lpar; pre x; seq prec l; prs rpar))
777   end;
779 (*print a list of items separated by newlines*)
780 fun print_list_ln (pre: 'a -> unit) : 'a list -> unit =
781   seq (fn x => (pre x; writeln ""));
784 val print_int = prs o string_of_int;
788 (** timing **)
790 (*unconditional timing function*)
791 fun timeit x = cond_timeit true x;
793 (*timed application function*)
794 fun timeap f x = timeit (fn () => f x);
796 (*timed "use" function, printing filenames*)
797 fun time_use fname = timeit (fn () =>
798   (writeln ("\n**** Starting " ^ fname ^ " ****"); use fname;
799    writeln ("\n**** Finished " ^ fname ^ " ****")));
801 (*For Makefiles: use the file, but exit with error code if errors found.*)
802 fun exit_use fname = use fname handle _ => exit 1;
805 (** filenames and paths **)
807 (*Convert UNIX filename of the form "path/file" to "path/" and "file";
808   if filename contains no slash, then it returns "" and "file"*)
809 val split_filename =
810   (pairself implode) o take_suffix (not_equal "/") o explode;
812 val base_name = #2 o split_filename;
814 (*Merge splitted filename (path and file);
815   if path does not end with one a slash is appended*)
816 fun tack_on "" name = name
817   | tack_on path name =
818       if last_elem (explode path) = "/" then path ^ name
819       else path ^ "/" ^ name;
821 (*Remove the extension of a filename, i.e. the part after the last '.'*)
822 val remove_ext = implode o #1 o take_suffix (not_equal ".") o explode;
824 (*Make relative path to reach an absolute location from a different one*)
825 fun relative_path cur_path dest_path =
826   let (*Remove common beginning of both paths and make relative path*)
827       fun mk_relative [] [] = []
828         | mk_relative [] ds = ds
829         | mk_relative cs [] = map (fn _ => "..") cs
830         | mk_relative (c::cs) (d::ds) =
831             if c = d then mk_relative cs ds
832             else ".." :: map (fn _ => "..") cs @ (d::ds);
833   in if cur_path = "" orelse hd (explode cur_path) <> "/" orelse
834         dest_path = "" orelse hd (explode dest_path) <> "/" then
835        error "Relative or empty path passed to relative_path"
836      else ();
837      space_implode "/" (mk_relative (space_explode "/" cur_path)
838                                     (space_explode "/" dest_path))
839   end;
841 (*Determine if absolute path1 is a subdirectory of absolute path2*)
842 fun path1 subdir_of path2 =
843   if hd (explode path1) <> "/" orelse hd (explode path2) <> "/" then
844     error "Relative or empty path passed to subdir_of"
845   else (space_explode "/" path2) prefix (space_explode "/" path1);
847 fun absolute_path cwd file =
848   let fun rm_points [] result = rev result
849         | rm_points (".."::ds) result = rm_points ds (tl result)
850         | rm_points ("."::ds) result = rm_points ds result
851         | rm_points (d::ds) result = rm_points ds (d::result);
852   in if file = "" then ""
853      else if hd (explode file) = "/" then file
854      else "/" ^ space_implode "/"
855                   (rm_points (space_explode "/" (tack_on cwd file)) [])
856   end;
859 (** misc functions **)
861 (*use the keyfun to make a list of (x, key) pairs*)
862 fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
863   let fun keypair x = (x, keyfun x)
864   in map keypair end;
866 (*given a list of (x, key) pairs and a searchkey
867   return the list of xs from each pair whose key equals searchkey*)
868 fun keyfilter [] searchkey = []
869   | keyfilter ((x, key) :: pairs) searchkey =
870       if key = searchkey then x :: keyfilter pairs searchkey
871       else keyfilter pairs searchkey;
874 (*Partition list into elements that satisfy predicate and those that don't.
875   Preserves order of elements in both lists.*)
876 fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
877     let fun part ([], answer) = answer
878           | part (x::xs, (ys, ns)) = if pred(x)
879             then  part (xs, (x::ys, ns))
880             else  part (xs, (ys, x::ns))
881     in  part (rev ys, ([], []))  end;
884 fun partition_eq (eq:'a * 'a -> bool) =
885     let fun part [] = []
886           | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
887                            in (x::xs)::(part xs') end
888     in part end;
891 (*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
892    putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
893 fun partition_list p i j =
894   let fun part k xs =
895             if k>j then
896               (case xs of [] => []
897                          | _ => raise LIST "partition_list")
898             else
899             let val (ns, rest) = partition (p k) xs;
900             in  ns :: part(k+1)rest  end
901   in  part i end;
904 (* sorting *)
906 (*insertion sort; stable (does not reorder equal elements)
907   'less' is less-than test on type 'a*)
908 fun sort (less: 'a*'a -> bool) =
909   let fun insert (x, []) = [x]
910         | insert (x, y::ys) =
911               if less(y, x) then y :: insert (x, ys) else x::y::ys;
912       fun sort1 [] = []
913         | sort1 (x::xs) = insert (x, sort1 xs)
914   in  sort1  end;
916 (*sort strings*)
917 val sort_strings = sort (op <= : string * string -> bool);
920 (* transitive closure (not Warshall's algorithm) *)
922 fun transitive_closure [] = []
923   | transitive_closure ((x, ys)::ps) =
924       let val qs = transitive_closure ps
925           val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
926           fun step(u, us) = (u, if x mem_string us then zs union_string us
927                                 else us)
928       in (x, zs) :: map step qs end;
931 (* generating identifiers *)
933 local
934   val a = ord "a" and z = ord "z" and A = ord "A" and Z = ord "Z"
935   and k0 = ord "0" and k9 = ord "9"
937   val seedr = ref 0;
938 in
940 (*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
941 fun newid n =
942   let fun char i =
943                if i<26 then chr (A+i)
944           else if i<52 then chr (a+i-26)
945           else if i<62 then chr (k0+i-52)
946           else if i=62 then "_"
947           else  (*i=63*)    "'"
948   in  implode (map char (radixpand (64,n)))  end;
950 (*Freshly generated identifiers with given prefix; MUST start with a letter*)
951 fun gensym pre = pre ^
952                  (#1(newid (!seedr),
953                      seedr := 1+ !seedr))
955 (*Increment a list of letters like a reversed base 26 number.
956   If head is "z", bumps chars in tail.
957   Digits are incremented as if they were integers.
958   "_" and "'" are not changed.
959   For making variants of identifiers.*)
961 fun bump_int_list(c::cs) = if c="9" then "0" :: bump_int_list cs else
962         if k0 <= ord(c) andalso ord(c) < k9 then chr(ord(c)+1) :: cs
963         else "1" :: c :: cs
964   | bump_int_list([]) = error("bump_int_list: not an identifier");
966 fun bump_list([], d) = [d]
967   | bump_list(["'"], d) = [d, "'"]
968   | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
969   | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
970   | bump_list("9"::cs, _) = "0" :: bump_int_list cs
971   | bump_list(c::cs, _) = let val k = ord(c)
972         in if (a <= k andalso k < z) orelse (A <= k andalso k < Z) orelse
973               (k0 <= k andalso k < k9) then chr(k+1) :: cs else
974            if c="'" orelse c="_" then c :: bump_list(cs, "") else
975                 error("bump_list: not legal in identifier: " ^
976                         implode(rev(c::cs)))
977         end;
979 end;
981 fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
984 (* lexical scanning *)
986 (*scan a list of characters into "words" composed of "letters" (recognized by
987   is_let) and separated by any number of non-"letters"*)
988 fun scanwords is_let cs =
989   let fun scan1 [] = []
990         | scan1 cs =
991             let val (lets, rest) = take_prefix is_let cs
992             in implode lets :: scanwords is_let rest end;
993   in scan1 (#2 (take_prefix (not o is_let) cs)) end;
995 end;
997 (*Variable-branching trees: for proof terms*)
998 datatype 'a mtree = Join of 'a * 'a mtree list;
1000 open Library;