src/Pure/library.ML
 author wenzelm Mon Nov 18 17:28:19 1996 +0100 (1996-11-18) changeset 2196 1b36ebc70487 parent 2182 29e56f003599 child 2243 3ebeaaacfbd1 permissions -rw-r--r--
added is_printable: string -> bool;
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 / 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 (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
116 fun exists (pred: 'a -> bool) : 'a list -> bool =
117   let fun boolf [] = false
118         | boolf (x :: xs) = pred x orelse boolf xs
119   in boolf end;
121 (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
122 fun forall (pred: 'a -> bool) : 'a list -> bool =
123   let fun boolf [] = true
124         | boolf (x :: xs) = pred x andalso boolf xs
125   in boolf end;
128 (* flags *)
130 fun set flag = (flag := true; true);
131 fun reset flag = (flag := false; false);
132 fun toggle flag = (flag := not (! flag); ! flag);
136 (** lists **)
138 exception LIST of string;
140 fun null [] = true
141   | null (_ :: _) = false;
143 fun hd [] = raise LIST "hd"
144   | hd (x :: _) = x;
146 fun tl [] = raise LIST "tl"
147   | tl (_ :: xs) = xs;
149 fun cons x xs = x :: xs;
152 (* fold *)
154 (*the following versions of fold are designed to fit nicely with infixes*)
156 (*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
157     for operators that associate to the left (TAIL RECURSIVE)*)
158 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
159   let fun itl (e, [])  = e
160         | itl (e, a::l) = itl (f(e, a), l)
161   in  itl end;
163 (*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
164     for operators that associate to the right (not tail recursive)*)
165 fun foldr f (l, e) =
166   let fun itr [] = e
167         | itr (a::l) = f(a, itr l)
168   in  itr l  end;
170 (*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
171     for n > 0, operators that associate to the right (not tail recursive)*)
172 fun foldr1 f l =
173   let fun itr [x] = x                       (* FIXME [] case: elim warn (?) *)
174         | itr (x::l) = f(x, itr l)
175   in  itr l  end;
178 (* basic list functions *)
180 (*length of a list, should unquestionably be a standard function*)
181 local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
182         | length1 (n, x :: xs) = length1 (n + 1, xs)
183 in  fun length l = length1 (0, l) end;
185 (*take the first n elements from a list*)
186 fun take (n, []) = []
187   | take (n, x :: xs) =
188       if n > 0 then x :: take (n - 1, xs) else [];
190 (*drop the first n elements from a list*)
191 fun drop (n, []) = []
192   | drop (n, x :: xs) =
193       if n > 0 then drop (n - 1, xs) else x :: xs;
195 (*return nth element of a list, where 0 designates the first element;
196   raise EXCEPTION if list too short*)
197 fun nth_elem NL =
198   (case drop NL of
199     [] => raise LIST "nth_elem"
200   | x :: _ => x);
202 (*last element of a list*)
203 fun last_elem [] = raise LIST "last_elem"
204   | last_elem [x] = x
205   | last_elem (_ :: xs) = last_elem xs;
207 (*find the position of an element in a list*)
208 fun find (x, ys) =
209   let fun f (y :: ys, i) = if x = y then i else f (ys, i + 1)
210         | f (_, _) = raise LIST "find"
211   in f (ys, 0) end;
213 (*flatten a list of lists to a list*)
214 fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
217 (*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
218   (proc x1; ...; proc xn) for side effects*)
219 fun seq (proc: 'a -> unit) : 'a list -> unit =
220   let fun seqf [] = ()
221         | seqf (x :: xs) = (proc x; seqf xs)
222   in seqf end;
225 (*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
226 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
227   | separate _ xs = xs;
229 (*make the list [x, x, ..., x] of length n*)
230 fun replicate n (x: 'a) : 'a list =
231   let fun rep (0, xs) = xs
232         | rep (n, xs) = rep (n - 1, x :: xs)
233   in
234     if n < 0 then raise LIST "replicate"
235     else rep (n, [])
236   end;
239 (* filter *)
241 (*copy the list preserving elements that satisfy the predicate*)
242 fun filter (pred: 'a->bool) : 'a list -> 'a list =
243   let fun filt [] = []
244         | filt (x :: xs) = if pred x then x :: filt xs else filt xs
245   in filt end;
247 fun filter_out f = filter (not o f);
250 fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
251   | mapfilter f (x :: xs) =
252       (case f x of
253         None => mapfilter f xs
254       | Some y => y :: mapfilter f xs);
257 fun find_first _ [] = None
258   | find_first pred (x :: xs) =
259       if pred x then Some x else find_first pred xs;
262 (* lists of pairs *)
264 fun map2 _ ([], []) = []
265   | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
266   | map2 _ _ = raise LIST "map2";
268 fun exists2 _ ([], []) = false
269   | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
270   | exists2 _ _ = raise LIST "exists2";
272 fun forall2 _ ([], []) = true
273   | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
274   | forall2 _ _ = raise LIST "forall2";
276 (*combine two lists forming a list of pairs:
277   [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
278 fun [] ~~ [] = []
279   | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
280   | _ ~~ _ = raise LIST "~~";
283 (*inverse of ~~; the old 'split':
284   [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
285 fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
288 (* prefixes, suffixes *)
290 fun [] prefix _ = true
291   | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
292   | _ prefix _ = false;
294 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
295    where xi is the first element that does not satisfy the predicate*)
296 fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
297   let fun take (rxs, []) = (rev rxs, [])
298         | take (rxs, x :: xs) =
299             if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
300   in  take([], xs)  end;
302 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
303    where xi is the last element that does not satisfy the predicate*)
304 fun take_suffix _ [] = ([], [])
305   | take_suffix pred (x :: xs) =
306       (case take_suffix pred xs of
307         ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
308       | (prfx, sffx) => (x :: prfx, sffx));
312 (** integers **)
314 fun inc i = i := ! i + 1;
315 fun dec i = i := ! i - 1;
318 (* lists of integers *)
320 (*make the list [from, from + 1, ..., to]*)
321 fun (from upto to) =
322   if from > to then [] else from :: ((from + 1) upto to);
324 (*make the list [from, from - 1, ..., to]*)
325 fun (from downto to) =
326   if from < to then [] else from :: ((from - 1) downto to);
328 (*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
329 fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
330   | downto0 ([], n) = n = ~1;
333 (* convert integers to strings *)
335 (*expand the number in the given base;
336   example: radixpand (2, 8) gives [1, 0, 0, 0]*)
337 fun radixpand (base, num) : int list =
338   let
339     fun radix (n, tail) =
340       if n < base then n :: tail
341       else radix (n div base, (n mod base) :: tail)
342   in radix (num, []) end;
344 (*expands a number into a string of characters starting from "zerochar";
345   example: radixstring (2, "0", 8) gives "1000"*)
346 fun radixstring (base, zerochar, num) =
347   let val offset = ord zerochar;
348       fun chrof n = chr (offset + n)
349   in implode (map chrof (radixpand (base, num))) end;
352 fun string_of_int n =
353   if n < 0 then "~" ^ radixstring (10, "0", ~n) else radixstring (10, "0", n);
357 (** strings **)
359 fun is_letter ch =
360   ord "A" <= ord ch andalso ord ch <= ord "Z" orelse
361   ord "a" <= ord ch andalso ord ch <= ord "z";
363 fun is_digit ch =
364   ord "0" <= ord ch andalso ord ch <= ord "9";
366 (*letter or _ or prime (')*)
367 fun is_quasi_letter "_" = true
368   | is_quasi_letter "'" = true
369   | is_quasi_letter ch = is_letter ch;
371 (*white space: blanks, tabs, newlines, formfeeds*)
372 val is_blank : string -> bool =
373   fn " " => true | "\t" => true | "\n" => true | "\^L" => true | _ => false;
375 val is_letdig = is_quasi_letter orf is_digit;
377 (*printable chars*)
378 fun is_printable c = ord c > ord " " andalso ord c <= ord "~";
381 (*lower all chars of string*)
382 val to_lower =
383   let
384     fun lower ch =
385       if ch >= "A" andalso ch <= "Z" then
386         chr (ord ch - ord "A" + ord "a")
387       else ch;
388   in implode o (map lower) o explode end;
391 (*enclose in brackets*)
392 fun enclose lpar rpar str = lpar ^ str ^ rpar;
394 (*simple quoting (does not escape special chars)*)
395 val quote = enclose "\"" "\"";
397 (*space_implode "..." (explode "hello"); gives "h...e...l...l...o"*)
398 fun space_implode a bs = implode (separate a bs);
400 val commas = space_implode ", ";
401 val commas_quote = commas o map quote;
403 (*concatenate messages, one per line, into a string*)
404 val cat_lines = space_implode "\n";
406 (*space_explode "." "h.e..l.lo"; gives ["h", "e", "l", "lo"]*)
407 fun space_explode sep s =
408   let fun divide [] "" = []
409         | divide [] part = [part]
410         | divide (c::s) part =
411             if c = sep then
412               (if part = "" then divide s "" else part :: divide s "")
413             else divide s (part ^ c)
414   in divide (explode s) "" end;
417 (** lists as sets **)
419 (*membership in a list*)
420 fun x mem [] = false
421   | x mem (y :: ys) = x = y orelse x mem ys;
423 (*membership in a list, optimized version for ints*)
424 fun (x:int) mem_int [] = false
425   | x mem_int (y :: ys) = x = y orelse x mem_int ys;
427 (*membership in a list, optimized version for strings*)
428 fun (x:string) mem_string [] = false
429   | x mem_string (y :: ys) = x = y orelse x mem_string ys;
431 (*generalized membership test*)
432 fun gen_mem eq (x, []) = false
433   | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
436 (*insertion into list if not already there*)
437 fun (x ins xs) = if x mem xs then xs else x :: xs;
439 (*insertion into list, optimized version for ints*)
440 fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
442 (*insertion into list, optimized version for strings*)
443 fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
445 (*generalized insertion*)
446 fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
449 (*union of sets represented as lists: no repetitions*)
450 fun xs union [] = xs
451   | [] union ys = ys
452   | (x :: xs) union ys = xs union (x ins ys);
454 (*union of sets, optimized version for ints*)
455 fun (xs:int list) union_int [] = xs
456   | [] union_int ys = ys
457   | (x :: xs) union_int ys = xs union_int (x ins_int ys);
459 (*union of sets, optimized version for strings*)
460 fun (xs:string list) union_string [] = xs
461   | [] union_string ys = ys
462   | (x :: xs) union_string ys = xs union_string (x ins_string ys);
464 (*generalized union*)
465 fun gen_union eq (xs, []) = xs
466   | gen_union eq ([], ys) = ys
467   | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
470 (*intersection*)
471 fun [] inter ys = []
472   | (x :: xs) inter ys =
473       if x mem ys then x :: (xs inter ys) else xs inter ys;
475 (*intersection, optimized version for ints*)
476 fun ([]:int list) inter_int ys = []
477   | (x :: xs) inter_int ys =
478       if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
480 (*intersection, optimized version for strings *)
481 fun ([]:string list) inter_string ys = []
482   | (x :: xs) inter_string ys =
483       if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
486 (*subset*)
487 fun [] subset ys = true
488   | (x :: xs) subset ys = x mem ys andalso xs subset ys;
490 (*subset, optimized version for ints*)
491 fun ([]:int list) subset_int ys = true
492   | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
494 (*subset, optimized version for strings*)
495 fun ([]:string list) subset_string ys = true
496   | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
498 (*set equality for strings*)
499 fun eq_set_string ((xs:string list), ys) =
500   xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
502 fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
505 (*removing an element from a list WITHOUT duplicates*)
506 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
507   | [] \ x = [];
509 val op \\ = foldl (op \);
511 (*removing an element from a list -- possibly WITH duplicates*)
512 fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
514 val gen_rems = foldl o gen_rem;
517 (*makes a list of the distinct members of the input; preserves order, takes
518   first of equal elements*)
519 fun gen_distinct eq lst =
520   let
521     val memb = gen_mem eq;
523     fun dist (rev_seen, []) = rev rev_seen
524       | dist (rev_seen, x :: xs) =
525           if memb (x, rev_seen) then dist (rev_seen, xs)
526           else dist (x :: rev_seen, xs);
527   in
528     dist ([], lst)
529   end;
531 val distinct = gen_distinct (op =);
534 (*returns the tail beginning with the first repeated element, or []*)
535 fun findrep [] = []
536   | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
539 (*returns a list containing all repeated elements exactly once; preserves
540   order, takes first of equal elements*)
541 fun gen_duplicates eq lst =
542   let
543     val memb = gen_mem eq;
545     fun dups (rev_dups, []) = rev rev_dups
546       | dups (rev_dups, x :: xs) =
547           if memb (x, rev_dups) orelse not (memb (x, xs)) then
548             dups (rev_dups, xs)
549           else dups (x :: rev_dups, xs);
550   in
551     dups ([], lst)
552   end;
554 val duplicates = gen_duplicates (op =);
558 (** association lists **)
560 (*association list lookup*)
561 fun assoc ([], key) = None
562   | assoc ((keyi, xi) :: pairs, key) =
563       if key = keyi then Some xi else assoc (pairs, key);
565 (*association list lookup, optimized version for ints*)
566 fun assoc_int ([], (key:int)) = None
567   | assoc_int ((keyi, xi) :: pairs, key) =
568       if key = keyi then Some xi else assoc_int (pairs, key);
570 (*association list lookup, optimized version for strings*)
571 fun assoc_string ([], (key:string)) = None
572   | assoc_string ((keyi, xi) :: pairs, key) =
573       if key = keyi then Some xi else assoc_string (pairs, key);
575 (*association list lookup, optimized version for string*ints*)
576 fun assoc_string_int ([], (key:string*int)) = None
577   | assoc_string_int ((keyi, xi) :: pairs, key) =
578       if key = keyi then Some xi else assoc_string_int (pairs, key);
580 fun assocs ps x =
581   (case assoc (ps, x) of
582     None => []
583   | Some ys => ys);
585 (*two-fold association list lookup*)
586 fun assoc2 (aal, (key1, key2)) =
587   (case assoc (aal, key1) of
588     Some al => assoc (al, key2)
589   | None => None);
591 (*generalized association list lookup*)
592 fun gen_assoc eq ([], key) = None
593   | gen_assoc eq ((keyi, xi) :: pairs, key) =
594       if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
596 (*association list update*)
597 fun overwrite (al, p as (key, _)) =
598   let fun over ((q as (keyi, _)) :: pairs) =
599             if keyi = key then p :: pairs else q :: (over pairs)
600         | over [] = [p]
601   in over al end;
605 (** generic tables **)
607 (*Tables are supposed to be 'efficient' encodings of lists of elements distinct
608   wrt. an equality "eq". The extend and merge operations below are optimized
609   for long-term space efficiency.*)
611 (*append (new) elements to a table*)
612 fun generic_extend _ _ _ tab [] = tab
613   | generic_extend eq dest_tab mk_tab tab1 lst2 =
614       let
615         val lst1 = dest_tab tab1;
616         val new_lst2 = gen_rems eq (lst2, lst1);
617       in
618         if null new_lst2 then tab1
619         else mk_tab (lst1 @ new_lst2)
620       end;
622 (*append (new) elements of 2nd table to 1st table*)
623 fun generic_merge eq dest_tab mk_tab tab1 tab2 =
624   let
625     val lst1 = dest_tab tab1;
626     val lst2 = dest_tab tab2;
627     val new_lst2 = gen_rems eq (lst2, lst1);
628   in
629     if null new_lst2 then tab1
630     else if gen_subset eq (lst1, lst2) then tab2
631     else mk_tab (lst1 @ new_lst2)
632   end;
635 (*lists as tables*)
636 val extend_list = generic_extend (op =) I I;
637 val merge_lists = generic_merge (op =) I I;
639 fun merge_rev_lists xs [] = xs
640   | merge_rev_lists [] ys = ys
641   | merge_rev_lists xs (y :: ys) =
642       (if y mem xs then I else cons y) (merge_rev_lists xs ys);
646 (** balanced trees **)
648 exception Balance;      (*indicates non-positive argument to balancing fun*)
650 (*balanced folding; avoids deep nesting*)
651 fun fold_bal f [x] = x
652   | fold_bal f [] = raise Balance
653   | fold_bal f xs =
654       let val k = length xs div 2
655       in  f (fold_bal f (take(k, xs)),
656              fold_bal f (drop(k, xs)))
657       end;
659 (*construct something of the form f(...g(...(x)...)) for balanced access*)
660 fun access_bal (f, g, x) n i =
661   let fun acc n i =     (*1<=i<=n*)
662           if n=1 then x else
663           let val n2 = n div 2
664           in  if i<=n2 then f (acc n2 i)
665                        else g (acc (n-n2) (i-n2))
666           end
667   in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
669 (*construct ALL such accesses; could try harder to share recursive calls!*)
670 fun accesses_bal (f, g, x) n =
671   let fun acc n =
672           if n=1 then [x] else
673           let val n2 = n div 2
674               val acc2 = acc n2
675           in  if n-n2=n2 then map f acc2 @ map g acc2
676                          else map f acc2 @ map g (acc (n-n2)) end
677   in  if 1<=n then acc n else raise Balance  end;
681 (** input / output **)
683 val prs_fn = ref(fn s => output (std_out, s));
685 fun prs s = !prs_fn s;
686 fun writeln s = prs (s ^ "\n");
688 (* output to LaTeX / xdvi *)
689 fun latex s =
690 	execute ( "( cd /tmp ; echo \"" ^ s ^
691 	"\" | isa2latex -s > \$\$.tex ; latex \$\$.tex ; xdvi \$\$.dvi ; rm \$\$.* ) > /dev/null &" ) ;
693 (*print warning*)
694 val warning_fn = ref(fn s => output (std_out, s ^ "\n"));
695 fun warning s = !warning_fn ("Warning: " ^ s);
697 (*print error message and abort to top level*)
699 val error_fn = ref(fn s => output (std_out, s ^ "\n"));
701 exception ERROR;
702 fun error msg = (!error_fn msg; raise ERROR);
703 fun sys_error msg = (!error_fn "*** SYSTEM ERROR ***"; error msg);
705 fun assert p msg = if p then () else error msg;
706 fun deny p msg = if p then error msg else ();
708 (*Assert pred for every member of l, generating a message if pred fails*)
709 fun assert_all pred l msg_fn =
710   let fun asl [] = ()
711 	| asl (x::xs) = if pred x then asl xs
712 	                else error (msg_fn x)
713   in  asl l  end;
715 (*for the "test" target in Makefiles -- signifies successful termination*)
716 fun maketest msg =
717   (writeln msg;
718    let val os = open_out "test"
719    in  output (os, "Test examples ran successfully\n");
720        close_out os
721    end);
724 (*print a list surrounded by the brackets lpar and rpar, with comma separator
725   print nothing for empty list*)
726 fun print_list (lpar, rpar, pre: 'a -> unit) (l : 'a list) =
727   let fun prec x = (prs ","; pre x)
728   in
729     (case l of
730       [] => ()
731     | x::l => (prs lpar; pre x; seq prec l; prs rpar))
732   end;
734 (*print a list of items separated by newlines*)
735 fun print_list_ln (pre: 'a -> unit) : 'a list -> unit =
736   seq (fn x => (pre x; writeln ""));
739 val print_int = prs o string_of_int;
743 (** timing **)
745 (*unconditional timing function*)
746 val timeit = cond_timeit true;
748 (*timed application function*)
749 fun timeap f x = timeit (fn () => f x);
751 (*timed "use" function, printing filenames*)
752 fun time_use fname = timeit (fn () =>
753   (writeln ("\n**** Starting " ^ fname ^ " ****"); use fname;
754    writeln ("\n**** Finished " ^ fname ^ " ****")));
756 (*For Makefiles: use the file, but exit with error code if errors found.*)
757 fun exit_use fname = use fname handle _ => exit 1;
760 (** filenames and paths **)
762 (*Convert UNIX filename of the form "path/file" to "path/" and "file";
763   if filename contains no slash, then it returns "" and "file"*)
764 val split_filename =
765   (pairself implode) o take_suffix (not_equal "/") o explode;
767 val base_name = #2 o split_filename;
769 (*Merge splitted filename (path and file);
770   if path does not end with one a slash is appended*)
771 fun tack_on "" name = name
772   | tack_on path name =
773       if last_elem (explode path) = "/" then path ^ name
774       else path ^ "/" ^ name;
776 (*Remove the extension of a filename, i.e. the part after the last '.'*)
777 val remove_ext = implode o #1 o take_suffix (not_equal ".") o explode;
779 (*Make relative path to reach an absolute location from a different one*)
780 fun relative_path cur_path dest_path =
781   let (*Remove common beginning of both paths and make relative path*)
782       fun mk_relative [] [] = []
783         | mk_relative [] ds = ds
784         | mk_relative cs [] = map (fn _ => "..") cs
785         | mk_relative (c::cs) (d::ds) =
786             if c = d then mk_relative cs ds
787             else ".." :: map (fn _ => "..") cs @ (d::ds);
788   in if cur_path = "" orelse hd (explode cur_path) <> "/" orelse
789         dest_path = "" orelse hd (explode dest_path) <> "/" then
790        error "Relative or empty path passed to relative_path"
791      else ();
792      space_implode "/" (mk_relative (space_explode "/" cur_path)
793                                     (space_explode "/" dest_path))
794   end;
796 (*Determine if absolute path1 is a subdirectory of absolute path2*)
797 fun path1 subdir_of path2 =
798   if hd (explode path1) <> "/" orelse hd (explode path2) <> "/" then
799     error "Relative or empty path passed to subdir_of"
800   else (space_explode "/" path2) prefix (space_explode "/" path1);
802 fun absolute_path cwd file =
803   let fun rm_points [] result = rev result
804         | rm_points (".."::ds) result = rm_points ds (tl result)
805         | rm_points ("."::ds) result = rm_points ds result
806         | rm_points (d::ds) result = rm_points ds (d::result);
807   in if file = "" then ""
808      else if hd (explode file) = "/" then file
809      else "/" ^ space_implode "/"
810                   (rm_points (space_explode "/" (tack_on cwd file)) [])
811   end;
814 (** misc functions **)
816 (*use the keyfun to make a list of (x, key) pairs*)
817 fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
818   let fun keypair x = (x, keyfun x)
819   in map keypair end;
821 (*given a list of (x, key) pairs and a searchkey
822   return the list of xs from each pair whose key equals searchkey*)
823 fun keyfilter [] searchkey = []
824   | keyfilter ((x, key) :: pairs) searchkey =
825       if key = searchkey then x :: keyfilter pairs searchkey
826       else keyfilter pairs searchkey;
829 (*Partition list into elements that satisfy predicate and those that don't.
830   Preserves order of elements in both lists.*)
831 fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
832     let fun part ([], answer) = answer
833           | part (x::xs, (ys, ns)) = if pred(x)
834             then  part (xs, (x::ys, ns))
835             else  part (xs, (ys, x::ns))
836     in  part (rev ys, ([], []))  end;
839 fun partition_eq (eq:'a * 'a -> bool) =
840     let fun part [] = []
841           | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
842                            in (x::xs)::(part xs') end
843     in part end;
846 (*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
847    putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
848 fun partition_list p i j =
849   let fun part k xs =
850             if k>j then
851               (case xs of [] => []
852                          | _ => raise LIST "partition_list")
853             else
854             let val (ns, rest) = partition (p k) xs;
855             in  ns :: part(k+1)rest  end
856   in  part i end;
859 (* sorting *)
861 (*insertion sort; stable (does not reorder equal elements)
862   'less' is less-than test on type 'a*)
863 fun sort (less: 'a*'a -> bool) =
864   let fun insert (x, []) = [x]
865         | insert (x, y::ys) =
866               if less(y, x) then y :: insert (x, ys) else x::y::ys;
867       fun sort1 [] = []
868         | sort1 (x::xs) = insert (x, sort1 xs)
869   in  sort1  end;
871 (*sort strings*)
872 val sort_strings = sort (op <= : string * string -> bool);
875 (* transitive closure (not Warshall's algorithm) *)
877 fun transitive_closure [] = []
878   | transitive_closure ((x, ys)::ps) =
879       let val qs = transitive_closure ps
880           val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
881           fun step(u, us) = (u, if x mem_string us then zs union_string us
882 				else us)
883       in (x, zs) :: map step qs end;
886 (** Recommended by Stephen K. Park and Keith W. Miller,
887       Random number generators: good ones are hard to find,
888       CACM 31 (1988), 1192-1201.
889     Real number version for systems with 46-bit mantissae
890     Computes  (a*seed) mod m ;  should be applied to integers only! **)
891 local val a = 16807.0  and  m = 2147483647.0  (* 2^31 - 1 *)
892 in  fun nextrandom seed =
893           let val t = a*seed
894           in  t - m * real(floor(t/m))  end
895 end;
897 (* generating identifiers *)
899 local
900   val a = ord "a" and z = ord "z" and A = ord "A" and Z = ord "Z"
901   and k0 = ord "0" and k9 = ord "9"
903   val seedr = ref 10000.0;
904 in
906 (*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
907 fun newid n =
908   let fun char i =
909                if i<26 then chr (A+i)
910           else if i<52 then chr (a+i-26)
911           else if i<62 then chr (k0+i-52)
912           else if i=62 then "_"
913           else  (*i=63*)    "'"
914   in  implode (map char (radixpand (64,n)))  end;
916 (*Randomly generated identifiers with given prefix; MUST start with a letter
917     [division by two avoids overflow for ML systems whose maxint is 2^30 - 1 *)
918 fun gensym pre = pre ^
919                  (#1(newid (floor (!seedr/2.0)),
920 		     seedr := nextrandom (!seedr)))
922 (*Increment a list of letters like a reversed base 26 number.
923   If head is "z", bumps chars in tail.
924   Digits are incremented as if they were integers.
925   "_" and "'" are not changed.
926   For making variants of identifiers.*)
928 fun bump_int_list(c::cs) = if c="9" then "0" :: bump_int_list cs else
929         if k0 <= ord(c) andalso ord(c) < k9 then chr(ord(c)+1) :: cs
930         else "1" :: c :: cs
931   | bump_int_list([]) = error("bump_int_list: not an identifier");
933 fun bump_list([], d) = [d]
934   | bump_list(["'"], d) = [d, "'"]
935   | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
936   | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
937   | bump_list("9"::cs, _) = "0" :: bump_int_list cs
938   | bump_list(c::cs, _) = let val k = ord(c)
939         in if (a <= k andalso k < z) orelse (A <= k andalso k < Z) orelse
940               (k0 <= k andalso k < k9) then chr(k+1) :: cs else
941            if c="'" orelse c="_" then c :: bump_list(cs, "") else
942                 error("bump_list: not legal in identifier: " ^
943                         implode(rev(c::cs)))
944         end;
946 end;
948 fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
951 (* lexical scanning *)
953 (*scan a list of characters into "words" composed of "letters" (recognized by
954   is_let) and separated by any number of non-"letters"*)
955 fun scanwords is_let cs =
956   let fun scan1 [] = []
957         | scan1 cs =
958             let val (lets, rest) = take_prefix is_let cs
959             in implode lets :: scanwords is_let rest end;
960   in scan1 (#2 (take_prefix (not o is_let) cs)) end;
962 end;
964 (*Variable-branching trees: for proof terms*)
965 datatype 'a mtree = Join of 'a * 'a mtree list;
967 open Library;