src/Pure/library.ML
 author wenzelm Thu Dec 05 13:31:32 1996 +0100 (1996-12-05) changeset 2317 672015b535d7 parent 2303 84ed9e0d7c50 child 2403 8115988ccc22 permissions -rw-r--r--
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 input / TextIO.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 (** options **)
50 datatype 'a option = None | Some of 'a;
52 exception OPTION of string;
54 fun the (Some x) = x
55   | the None = raise OPTION "the";
57 fun if_none None y = y
58   | if_none (Some x) _ = x;
60 fun is_some (Some _) = true
61   | is_some None = false;
63 fun is_none (Some _) = false
64   | is_none None = true;
66 fun apsome f (Some x) = Some (f x)
67   | apsome _ None = None;
71 (** pairs **)
73 fun pair x y = (x, y);
74 fun rpair x y = (y, x);
76 fun fst (x, y) = x;
77 fun snd (x, y) = y;
79 fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
80 fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
82 fun swap (x, y) = (y, x);
84 (*apply the function to a component of a pair*)
85 fun apfst f (x, y) = (f x, y);
86 fun apsnd f (x, y) = (x, f y);
90 (** booleans **)
92 (* equality *)
94 fun equal x y = x = y;
95 fun not_equal x y = x <> y;
98 (* operators for combining predicates *)
100 fun (p orf q) = fn x => p x orelse q x;
102 fun (p andf q) = fn x => p x andalso q x;
104 fun notf p x = not (p x);
107 (* predicates on lists *)
109 fun orl [] = false
110   | orl (x :: xs) = x orelse orl xs;
112 fun andl [] = true
113   | andl (x :: xs) = x andalso andl xs;
115 (*Needed because several object-logics declare the theory, therefore structure,
116   List.*)
117 structure List_ = List;
119 (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
120 fun exists (pred: 'a -> bool) : 'a list -> bool =
121   let fun boolf [] = false
122         | boolf (x :: xs) = pred x orelse boolf xs
123   in boolf end;
125 (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
126 fun forall (pred: 'a -> bool) : 'a list -> bool =
127   let fun boolf [] = true
128         | boolf (x :: xs) = pred x andalso boolf xs
129   in boolf end;
132 (* flags *)
134 fun set flag = (flag := true; true);
135 fun reset flag = (flag := false; false);
136 fun toggle flag = (flag := not (! flag); ! flag);
140 (** lists **)
142 exception LIST of string;
144 fun null [] = true
145   | null (_ :: _) = false;
147 fun hd [] = raise LIST "hd"
148   | hd (x :: _) = x;
150 fun tl [] = raise LIST "tl"
151   | tl (_ :: xs) = xs;
153 fun cons x xs = x :: xs;
156 (* fold *)
158 (*the following versions of fold are designed to fit nicely with infixes*)
160 (*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
161     for operators that associate to the left (TAIL RECURSIVE)*)
162 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
163   let fun itl (e, [])  = e
164         | itl (e, a::l) = itl (f(e, a), l)
165   in  itl end;
167 (*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
168     for operators that associate to the right (not tail recursive)*)
169 fun foldr f (l, e) =
170   let fun itr [] = e
171         | itr (a::l) = f(a, itr l)
172   in  itr l  end;
174 (*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
175     for n > 0, operators that associate to the right (not tail recursive)*)
176 fun foldr1 f l =
177   let fun itr [x] = x                       (* FIXME [] case: elim warn (?) *)
178         | itr (x::l) = f(x, itr l)
179   in  itr l  end;
182 (* basic list functions *)
184 (*length of a list, should unquestionably be a standard function*)
185 local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
186         | length1 (n, x :: xs) = length1 (n + 1, xs)
187 in  fun length l = length1 (0, l) end;
189 (*take the first n elements from a list*)
190 fun take (n, []) = []
191   | take (n, x :: xs) =
192       if n > 0 then x :: take (n - 1, xs) else [];
194 (*drop the first n elements from a list*)
195 fun drop (n, []) = []
196   | drop (n, x :: xs) =
197       if n > 0 then drop (n - 1, xs) else x :: xs;
199 (*return nth element of a list, where 0 designates the first element;
200   raise EXCEPTION if list too short*)
201 fun nth_elem NL =
202   (case drop NL of
203     [] => raise LIST "nth_elem"
204   | x :: _ => x);
206 (*last element of a list*)
207 fun last_elem [] = raise LIST "last_elem"
208   | last_elem [x] = x
209   | last_elem (_ :: xs) = last_elem xs;
211 (*find the position of an element in a list*)
212 fun find (x, ys) =
213   let fun f (y :: ys, i) = if x = y then i else f (ys, i + 1)
214         | f (_, _) = raise LIST "find"
215   in f (ys, 0) end;
217 (*flatten a list of lists to a list*)
218 fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
221 (*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
222   (proc x1; ...; proc xn) for side effects*)
223 fun seq (proc: 'a -> unit) : 'a list -> unit =
224   let fun seqf [] = ()
225         | seqf (x :: xs) = (proc x; seqf xs)
226   in seqf end;
229 (*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
230 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
231   | separate _ xs = xs;
233 (*make the list [x, x, ..., x] of length n*)
234 fun replicate n (x: 'a) : 'a list =
235   let fun rep (0, xs) = xs
236         | rep (n, xs) = rep (n - 1, x :: xs)
237   in
238     if n < 0 then raise LIST "replicate"
239     else rep (n, [])
240   end;
243 (* filter *)
245 (*copy the list preserving elements that satisfy the predicate*)
246 fun filter (pred: 'a->bool) : 'a list -> 'a list =
247   let fun filt [] = []
248         | filt (x :: xs) = if pred x then x :: filt xs else filt xs
249   in filt end;
251 fun filter_out f = filter (not o f);
254 fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
255   | mapfilter f (x :: xs) =
256       (case f x of
257         None => mapfilter f xs
258       | Some y => y :: mapfilter f xs);
261 fun find_first _ [] = None
262   | find_first pred (x :: xs) =
263       if pred x then Some x else find_first pred xs;
266 (* lists of pairs *)
268 fun map2 _ ([], []) = []
269   | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
270   | map2 _ _ = raise LIST "map2";
272 fun exists2 _ ([], []) = false
273   | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
274   | exists2 _ _ = raise LIST "exists2";
276 fun forall2 _ ([], []) = true
277   | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
278   | forall2 _ _ = raise LIST "forall2";
280 (*combine two lists forming a list of pairs:
281   [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
282 fun [] ~~ [] = []
283   | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
284   | _ ~~ _ = raise LIST "~~";
287 (*inverse of ~~; the old 'split':
288   [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
289 fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
292 (* prefixes, suffixes *)
294 fun [] prefix _ = true
295   | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
296   | _ prefix _ = false;
298 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
299    where xi is the first element that does not satisfy the predicate*)
300 fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
301   let fun take (rxs, []) = (rev rxs, [])
302         | take (rxs, x :: xs) =
303             if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
304   in  take([], xs)  end;
306 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
307    where xi is the last element that does not satisfy the predicate*)
308 fun take_suffix _ [] = ([], [])
309   | take_suffix pred (x :: xs) =
310       (case take_suffix pred xs of
311         ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
312       | (prfx, sffx) => (x :: prfx, sffx));
316 (** integers **)
318 fun inc i = i := ! i + 1;
319 fun dec i = i := ! i - 1;
322 (* lists of integers *)
324 (*make the list [from, from + 1, ..., to]*)
325 fun (from upto to) =
326   if from > to then [] else from :: ((from + 1) upto to);
328 (*make the list [from, from - 1, ..., to]*)
329 fun (from downto to) =
330   if from < to then [] else from :: ((from - 1) downto to);
332 (*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
333 fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
334   | downto0 ([], n) = n = ~1;
337 (* convert integers to strings *)
339 (*expand the number in the given base;
340   example: radixpand (2, 8) gives [1, 0, 0, 0]*)
341 fun radixpand (base, num) : int list =
342   let
343     fun radix (n, tail) =
344       if n < base then n :: tail
345       else radix (n div base, (n mod base) :: tail)
346   in radix (num, []) end;
348 (*expands a number into a string of characters starting from "zerochar";
349   example: radixstring (2, "0", 8) gives "1000"*)
350 fun radixstring (base, zerochar, num) =
351   let val offset = ord zerochar;
352       fun chrof n = chr (offset + n)
353   in implode (map chrof (radixpand (base, num))) end;
356 fun string_of_int n =
357   if n < 0 then "~" ^ radixstring (10, "0", ~n) else radixstring (10, "0", n);
361 (** strings **)
363 fun is_letter ch =
364   ord "A" <= ord ch andalso ord ch <= ord "Z" orelse
365   ord "a" <= ord ch andalso ord ch <= ord "z";
367 fun is_digit ch =
368   ord "0" <= ord ch andalso ord ch <= ord "9";
370 (*letter or _ or prime (')*)
371 fun is_quasi_letter "_" = true
372   | is_quasi_letter "'" = true
373   | is_quasi_letter ch = is_letter ch;
375 (*white space: blanks, tabs, newlines, formfeeds*)
376 val is_blank : string -> bool =
377   fn " " => true | "\t" => true | "\n" => true | "\^L" => true | _ => false;
379 val is_letdig = is_quasi_letter orf is_digit;
381 (*printable chars*)
382 fun is_printable c = ord c > ord " " andalso ord c <= ord "~";
385 (*lower all chars of string*)
386 val to_lower =
387   let
388     fun lower ch =
389       if ch >= "A" andalso ch <= "Z" then
390         chr (ord ch - ord "A" + ord "a")
391       else ch;
392   in implode o (map lower) o explode end;
395 (*enclose in brackets*)
396 fun enclose lpar rpar str = lpar ^ str ^ rpar;
398 (*simple quoting (does not escape special chars)*)
399 val quote = enclose "\"" "\"";
401 (*space_implode "..." (explode "hello"); gives "h...e...l...l...o"*)
402 fun space_implode a bs = implode (separate a bs);
404 val commas = space_implode ", ";
405 val commas_quote = commas o map quote;
407 (*concatenate messages, one per line, into a string*)
408 val cat_lines = space_implode "\n";
410 (*space_explode "." "h.e..l.lo"; gives ["h", "e", "l", "lo"]*)
411 fun space_explode sep s =
412   let fun divide [] "" = []
413         | divide [] part = [part]
414         | divide (c::s) part =
415             if c = sep then
416               (if part = "" then divide s "" else part :: divide s "")
417             else divide s (part ^ c)
418   in divide (explode s) "" end;
421 (** lists as sets **)
423 (*membership in a list*)
424 fun x mem [] = false
425   | x mem (y :: ys) = x = y orelse x mem ys;
427 (*membership in a list, optimized version for ints*)
428 fun (x:int) mem_int [] = false
429   | x mem_int (y :: ys) = x = y orelse x mem_int ys;
431 (*membership in a list, optimized version for strings*)
432 fun (x:string) mem_string [] = false
433   | x mem_string (y :: ys) = x = y orelse x mem_string ys;
435 (*generalized membership test*)
436 fun gen_mem eq (x, []) = false
437   | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
440 (*insertion into list if not already there*)
441 fun (x ins xs) = if x mem xs then xs else x :: xs;
443 (*insertion into list, optimized version for ints*)
444 fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
446 (*insertion into list, optimized version for strings*)
447 fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
449 (*generalized insertion*)
450 fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
453 (*union of sets represented as lists: no repetitions*)
454 fun xs union [] = xs
455   | [] union ys = ys
456   | (x :: xs) union ys = xs union (x ins ys);
458 (*union of sets, optimized version for ints*)
459 fun (xs:int list) union_int [] = xs
460   | [] union_int ys = ys
461   | (x :: xs) union_int ys = xs union_int (x ins_int ys);
463 (*union of sets, optimized version for strings*)
464 fun (xs:string list) union_string [] = xs
465   | [] union_string ys = ys
466   | (x :: xs) union_string ys = xs union_string (x ins_string ys);
468 (*generalized union*)
469 fun gen_union eq (xs, []) = xs
470   | gen_union eq ([], ys) = ys
471   | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
474 (*intersection*)
475 fun [] inter ys = []
476   | (x :: xs) inter ys =
477       if x mem ys then x :: (xs inter ys) else xs inter ys;
479 (*intersection, optimized version for ints*)
480 fun ([]:int list) inter_int ys = []
481   | (x :: xs) inter_int ys =
482       if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
484 (*intersection, optimized version for strings *)
485 fun ([]:string list) inter_string ys = []
486   | (x :: xs) inter_string ys =
487       if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
490 (*subset*)
491 fun [] subset ys = true
492   | (x :: xs) subset ys = x mem ys andalso xs subset ys;
494 (*subset, optimized version for ints*)
495 fun ([]:int list) subset_int ys = true
496   | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
498 (*subset, optimized version for strings*)
499 fun ([]:string list) subset_string ys = true
500   | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
502 (*set equality for strings*)
503 fun eq_set_string ((xs:string list), ys) =
504   xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
506 fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
509 (*removing an element from a list WITHOUT duplicates*)
510 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
511   | [] \ x = [];
513 fun ys \\ xs = foldl (op \) (ys,xs);
515 (*removing an element from a list -- possibly WITH duplicates*)
516 fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
518 fun gen_rems eq = foldl (gen_rem eq);
521 (*makes a list of the distinct members of the input; preserves order, takes
522   first of equal elements*)
523 fun gen_distinct eq lst =
524   let
525     val memb = gen_mem eq;
527     fun dist (rev_seen, []) = rev rev_seen
528       | dist (rev_seen, x :: xs) =
529           if memb (x, rev_seen) then dist (rev_seen, xs)
530           else dist (x :: rev_seen, xs);
531   in
532     dist ([], lst)
533   end;
535 fun distinct l = gen_distinct (op =) l;
538 (*returns the tail beginning with the first repeated element, or []*)
539 fun findrep [] = []
540   | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
543 (*returns a list containing all repeated elements exactly once; preserves
544   order, takes first of equal elements*)
545 fun gen_duplicates eq lst =
546   let
547     val memb = gen_mem eq;
549     fun dups (rev_dups, []) = rev rev_dups
550       | dups (rev_dups, x :: xs) =
551           if memb (x, rev_dups) orelse not (memb (x, xs)) then
552             dups (rev_dups, xs)
553           else dups (x :: rev_dups, xs);
554   in
555     dups ([], lst)
556   end;
558 fun duplicates l = gen_duplicates (op =) l;
562 (** association lists **)
564 (*association list lookup*)
565 fun assoc ([], key) = None
566   | assoc ((keyi, xi) :: pairs, key) =
567       if key = keyi then Some xi else assoc (pairs, key);
569 (*association list lookup, optimized version for ints*)
570 fun assoc_int ([], (key:int)) = None
571   | assoc_int ((keyi, xi) :: pairs, key) =
572       if key = keyi then Some xi else assoc_int (pairs, key);
574 (*association list lookup, optimized version for strings*)
575 fun assoc_string ([], (key:string)) = None
576   | assoc_string ((keyi, xi) :: pairs, key) =
577       if key = keyi then Some xi else assoc_string (pairs, key);
579 (*association list lookup, optimized version for string*ints*)
580 fun assoc_string_int ([], (key:string*int)) = None
581   | assoc_string_int ((keyi, xi) :: pairs, key) =
582       if key = keyi then Some xi else assoc_string_int (pairs, key);
584 fun assocs ps x =
585   (case assoc (ps, x) of
586     None => []
587   | Some ys => ys);
589 (*two-fold association list lookup*)
590 fun assoc2 (aal, (key1, key2)) =
591   (case assoc (aal, key1) of
592     Some al => assoc (al, key2)
593   | None => None);
595 (*generalized association list lookup*)
596 fun gen_assoc eq ([], key) = None
597   | gen_assoc eq ((keyi, xi) :: pairs, key) =
598       if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
600 (*association list update*)
601 fun overwrite (al, p as (key, _)) =
602   let fun over ((q as (keyi, _)) :: pairs) =
603             if keyi = key then p :: pairs else q :: (over pairs)
604         | over [] = [p]
605   in over al end;
609 (** generic tables **)
611 (*Tables are supposed to be 'efficient' encodings of lists of elements distinct
612   wrt. an equality "eq". The extend and merge operations below are optimized
613   for long-term space efficiency.*)
615 (*append (new) elements to a table*)
616 fun generic_extend _ _ _ tab [] = tab
617   | generic_extend eq dest_tab mk_tab tab1 lst2 =
618       let
619         val lst1 = dest_tab tab1;
620         val new_lst2 = gen_rems eq (lst2, lst1);
621       in
622         if null new_lst2 then tab1
623         else mk_tab (lst1 @ new_lst2)
624       end;
626 (*append (new) elements of 2nd table to 1st table*)
627 fun generic_merge eq dest_tab mk_tab tab1 tab2 =
628   let
629     val lst1 = dest_tab tab1;
630     val lst2 = dest_tab tab2;
631     val new_lst2 = gen_rems eq (lst2, lst1);
632   in
633     if null new_lst2 then tab1
634     else if gen_subset eq (lst1, lst2) then tab2
635     else mk_tab (lst1 @ new_lst2)
636   end;
639 (*lists as tables*)
640 fun extend_list tab = generic_extend (op =) I I tab;
641 fun merge_lists tab = generic_merge (op =) I I tab;
643 fun merge_rev_lists xs [] = xs
644   | merge_rev_lists [] ys = ys
645   | merge_rev_lists xs (y :: ys) =
646       (if y mem xs then I else cons y) (merge_rev_lists xs ys);
650 (** balanced trees **)
652 exception Balance;      (*indicates non-positive argument to balancing fun*)
654 (*balanced folding; avoids deep nesting*)
655 fun fold_bal f [x] = x
656   | fold_bal f [] = raise Balance
657   | fold_bal f xs =
658       let val k = length xs div 2
659       in  f (fold_bal f (take(k, xs)),
660              fold_bal f (drop(k, xs)))
661       end;
663 (*construct something of the form f(...g(...(x)...)) for balanced access*)
664 fun access_bal (f, g, x) n i =
665   let fun acc n i =     (*1<=i<=n*)
666           if n=1 then x else
667           let val n2 = n div 2
668           in  if i<=n2 then f (acc n2 i)
669                        else g (acc (n-n2) (i-n2))
670           end
671   in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
673 (*construct ALL such accesses; could try harder to share recursive calls!*)
674 fun accesses_bal (f, g, x) n =
675   let fun acc n =
676           if n=1 then [x] else
677           let val n2 = n div 2
678               val acc2 = acc n2
679           in  if n-n2=n2 then map f acc2 @ map g acc2
680                          else map f acc2 @ map g (acc (n-n2)) end
681   in  if 1<=n then acc n else raise Balance  end;
685 (** input / output **)
687 val cd = OS.FileSys.chDir;
688 val pwd = OS.FileSys.getDir;
690 val prs_fn = ref(fn s => TextIO.output (TextIO.stdOut, s));
692 fun prs s = !prs_fn s;
693 fun writeln s = prs (s ^ "\n");
695 (* TextIO.output to LaTeX / xdvi *)
696 fun latex s =
697         execute ( "( cd /tmp ; echo \"" ^ s ^
698         "\" | isa2latex -s > \$\$.tex ; latex \$\$.tex ; xdvi \$\$.dvi ; rm \$\$.* ) > /dev/null &" ) ;
700 (*print warning*)
701 val warning_fn = ref(fn s => TextIO.output (TextIO.stdOut, s ^ "\n"));
702 fun warning s = !warning_fn ("Warning: " ^ s);
704 (*print error message and abort to top level*)
706 val error_fn = ref(fn s => TextIO.output (TextIO.stdOut, s ^ "\n"));
708 exception ERROR;
709 fun error msg = (!error_fn msg; raise ERROR);
710 fun sys_error msg = (!error_fn "*** SYSTEM ERROR ***"; error msg);
712 fun assert p msg = if p then () else error msg;
713 fun deny p msg = if p then error msg else ();
715 (*Assert pred for every member of l, generating a message if pred fails*)
716 fun assert_all pred l msg_fn =
717   let fun asl [] = ()
718         | asl (x::xs) = if pred x then asl xs
719                         else error (msg_fn x)
720   in  asl l  end;
722 (*for the "test" target in Makefiles -- signifies successful termination*)
723 fun maketest msg =
724   (writeln msg;
725    let val os = TextIO.openOut "test"
726    in  TextIO.output (os, "Test examples ran successfully\n");
727        TextIO.closeOut os
728    end);
731 (*print a list surrounded by the brackets lpar and rpar, with comma separator
732   print nothing for empty list*)
733 fun print_list (lpar, rpar, pre: 'a -> unit) (l : 'a list) =
734   let fun prec x = (prs ","; pre x)
735   in
736     (case l of
737       [] => ()
738     | x::l => (prs lpar; pre x; seq prec l; prs rpar))
739   end;
741 (*print a list of items separated by newlines*)
742 fun print_list_ln (pre: 'a -> unit) : 'a list -> unit =
743   seq (fn x => (pre x; writeln ""));
746 val print_int = prs o string_of_int;
750 (** timing **)
752 (*unconditional timing function*)
753 fun timeit x = cond_timeit true x;
755 (*timed application function*)
756 fun timeap f x = timeit (fn () => f x);
758 (*timed "use" function, printing filenames*)
759 fun time_use fname = timeit (fn () =>
760   (writeln ("\n**** Starting " ^ fname ^ " ****"); use fname;
761    writeln ("\n**** Finished " ^ fname ^ " ****")));
763 (*For Makefiles: use the file, but exit with error code if errors found.*)
764 fun exit_use fname = use fname handle _ => exit 1;
767 (** filenames and paths **)
769 (*Convert UNIX filename of the form "path/file" to "path/" and "file";
770   if filename contains no slash, then it returns "" and "file"*)
771 val split_filename =
772   (pairself implode) o take_suffix (not_equal "/") o explode;
774 val base_name = #2 o split_filename;
776 (*Merge splitted filename (path and file);
777   if path does not end with one a slash is appended*)
778 fun tack_on "" name = name
779   | tack_on path name =
780       if last_elem (explode path) = "/" then path ^ name
781       else path ^ "/" ^ name;
783 (*Remove the extension of a filename, i.e. the part after the last '.'*)
784 val remove_ext = implode o #1 o take_suffix (not_equal ".") o explode;
786 (*Make relative path to reach an absolute location from a different one*)
787 fun relative_path cur_path dest_path =
788   let (*Remove common beginning of both paths and make relative path*)
789       fun mk_relative [] [] = []
790         | mk_relative [] ds = ds
791         | mk_relative cs [] = map (fn _ => "..") cs
792         | mk_relative (c::cs) (d::ds) =
793             if c = d then mk_relative cs ds
794             else ".." :: map (fn _ => "..") cs @ (d::ds);
795   in if cur_path = "" orelse hd (explode cur_path) <> "/" orelse
796         dest_path = "" orelse hd (explode dest_path) <> "/" then
797        error "Relative or empty path passed to relative_path"
798      else ();
799      space_implode "/" (mk_relative (space_explode "/" cur_path)
800                                     (space_explode "/" dest_path))
801   end;
803 (*Determine if absolute path1 is a subdirectory of absolute path2*)
804 fun path1 subdir_of path2 =
805   if hd (explode path1) <> "/" orelse hd (explode path2) <> "/" then
806     error "Relative or empty path passed to subdir_of"
807   else (space_explode "/" path2) prefix (space_explode "/" path1);
809 fun absolute_path cwd file =
810   let fun rm_points [] result = rev result
811         | rm_points (".."::ds) result = rm_points ds (tl result)
812         | rm_points ("."::ds) result = rm_points ds result
813         | rm_points (d::ds) result = rm_points ds (d::result);
814   in if file = "" then ""
815      else if hd (explode file) = "/" then file
816      else "/" ^ space_implode "/"
817                   (rm_points (space_explode "/" (tack_on cwd file)) [])
818   end;
821 (** misc functions **)
823 (*use the keyfun to make a list of (x, key) pairs*)
824 fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
825   let fun keypair x = (x, keyfun x)
826   in map keypair end;
828 (*given a list of (x, key) pairs and a searchkey
829   return the list of xs from each pair whose key equals searchkey*)
830 fun keyfilter [] searchkey = []
831   | keyfilter ((x, key) :: pairs) searchkey =
832       if key = searchkey then x :: keyfilter pairs searchkey
833       else keyfilter pairs searchkey;
836 (*Partition list into elements that satisfy predicate and those that don't.
837   Preserves order of elements in both lists.*)
838 fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
839     let fun part ([], answer) = answer
840           | part (x::xs, (ys, ns)) = if pred(x)
841             then  part (xs, (x::ys, ns))
842             else  part (xs, (ys, x::ns))
843     in  part (rev ys, ([], []))  end;
846 fun partition_eq (eq:'a * 'a -> bool) =
847     let fun part [] = []
848           | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
849                            in (x::xs)::(part xs') end
850     in part end;
853 (*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
854    putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
855 fun partition_list p i j =
856   let fun part k xs =
857             if k>j then
858               (case xs of [] => []
859                          | _ => raise LIST "partition_list")
860             else
861             let val (ns, rest) = partition (p k) xs;
862             in  ns :: part(k+1)rest  end
863   in  part i end;
866 (* sorting *)
868 (*insertion sort; stable (does not reorder equal elements)
869   'less' is less-than test on type 'a*)
870 fun sort (less: 'a*'a -> bool) =
871   let fun insert (x, []) = [x]
872         | insert (x, y::ys) =
873               if less(y, x) then y :: insert (x, ys) else x::y::ys;
874       fun sort1 [] = []
875         | sort1 (x::xs) = insert (x, sort1 xs)
876   in  sort1  end;
878 (*sort strings*)
879 val sort_strings = sort (op <= : string * string -> bool);
882 (* transitive closure (not Warshall's algorithm) *)
884 fun transitive_closure [] = []
885   | transitive_closure ((x, ys)::ps) =
886       let val qs = transitive_closure ps
887           val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
888           fun step(u, us) = (u, if x mem_string us then zs union_string us
889                                 else us)
890       in (x, zs) :: map step qs end;
893 (** Simple random number generator; not guaranteed to be good, because modulus
894     has been reduced from 2^31-1 to 2^29-1 to prevent integer overflows
895 **)
896 local val a = 16807.0  and  m = 536870911.0  (* 2^29 - 1 *)
897 in  fun nextrandom seed =
898           let val t = a*seed
899           in  t - m * real(floor(t/m))  end
900 end;
902 (* generating identifiers *)
904 local
905   val a = ord "a" and z = ord "z" and A = ord "A" and Z = ord "Z"
906   and k0 = ord "0" and k9 = ord "9"
908   val seedr = ref 10000.0;
909 in
911 (*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
912 fun newid n =
913   let fun char i =
914                if i<26 then chr (A+i)
915           else if i<52 then chr (a+i-26)
916           else if i<62 then chr (k0+i-52)
917           else if i=62 then "_"
918           else  (*i=63*)    "'"
919   in  implode (map char (radixpand (64,n)))  end;
921 (*Randomly generated identifiers with given prefix; MUST start with a letter*)
922 fun gensym pre = pre ^
923                  (#1(newid (floor (!seedr)),
924                      seedr := nextrandom (!seedr)))
926 (*Increment a list of letters like a reversed base 26 number.
927   If head is "z", bumps chars in tail.
928   Digits are incremented as if they were integers.
929   "_" and "'" are not changed.
930   For making variants of identifiers.*)
932 fun bump_int_list(c::cs) = if c="9" then "0" :: bump_int_list cs else
933         if k0 <= ord(c) andalso ord(c) < k9 then chr(ord(c)+1) :: cs
934         else "1" :: c :: cs
935   | bump_int_list([]) = error("bump_int_list: not an identifier");
937 fun bump_list([], d) = [d]
938   | bump_list(["'"], d) = [d, "'"]
939   | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
940   | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
941   | bump_list("9"::cs, _) = "0" :: bump_int_list cs
942   | bump_list(c::cs, _) = let val k = ord(c)
943         in if (a <= k andalso k < z) orelse (A <= k andalso k < Z) orelse
944               (k0 <= k andalso k < k9) then chr(k+1) :: cs else
945            if c="'" orelse c="_" then c :: bump_list(cs, "") else
946                 error("bump_list: not legal in identifier: " ^
947                         implode(rev(c::cs)))
948         end;
950 end;
952 fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
955 (* lexical scanning *)
957 (*scan a list of characters into "words" composed of "letters" (recognized by
958   is_let) and separated by any number of non-"letters"*)
959 fun scanwords is_let cs =
960   let fun scan1 [] = []
961         | scan1 cs =
962             let val (lets, rest) = take_prefix is_let cs
963             in implode lets :: scanwords is_let rest end;
964   in scan1 (#2 (take_prefix (not o is_let) cs)) end;
966 end;
968 (*Variable-branching trees: for proof terms*)
969 datatype 'a mtree = Join of 'a * 'a mtree list;
971 open Library;