src/Pure/library.ML
author wenzelm
Thu Oct 30 16:59:56 1997 +0100 (1997-10-30)
changeset 4046 f89dbf002604
parent 3973 1be726ef6813
child 4063 0b19014b9155
permissions -rw-r--r--
added merge_opts: ('a * 'a -> 'a) -> 'a option * 'a option -> 'a option;
     1 (*  Title:      Pure/library.ML
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1992  University of Cambridge
     5 
     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 *)
    10 
    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;
    14 
    15 
    16 structure Library =
    17 struct
    18 
    19 (** functions **)
    20 
    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;
    26 
    27 (*reverse apply*)
    28 fun (x |> f) = f x;
    29 
    30 (*combine two functions forming the union of their domains*)
    31 fun (f orelf g) = fn x => f x handle Match => g x;
    32 
    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);
    36 
    37 (*functional for pairs*)
    38 fun pairself f (x, y) = (f x, f y);
    39 
    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;
    45 
    46 
    47 
    48 (** stamps **)
    49 
    50 type stamp = unit ref;
    51 val stamp: unit -> stamp = ref;
    52 
    53 
    54 
    55 (** options **)
    56 
    57 datatype 'a option = None | Some of 'a;
    58 
    59 exception OPTION of string;
    60 
    61 fun the (Some x) = x
    62   | the None = raise OPTION "the";
    63 
    64 fun if_none None y = y
    65   | if_none (Some x) _ = x;
    66 
    67 fun is_some (Some _) = true
    68   | is_some None = false;
    69 
    70 fun is_none (Some _) = false
    71   | is_none None = true;
    72 
    73 fun apsome f (Some x) = Some (f x)
    74   | apsome _ None = None;
    75 
    76 fun merge_opts _ (None, None) = None
    77   | merge_opts _ (some as Some _, None) = some
    78   | merge_opts _ (None, some as Some _) = some
    79   | merge_opts merge (Some x, Some y) = Some (merge (x, y));
    80 
    81 
    82 
    83 (** pairs **)
    84 
    85 fun pair x y = (x, y);
    86 fun rpair x y = (y, x);
    87 
    88 fun fst (x, y) = x;
    89 fun snd (x, y) = y;
    90 
    91 fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
    92 fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
    93 
    94 fun swap (x, y) = (y, x);
    95 
    96 (*apply the function to a component of a pair*)
    97 fun apfst f (x, y) = (f x, y);
    98 fun apsnd f (x, y) = (x, f y);
    99 
   100 
   101 
   102 (** booleans **)
   103 
   104 (* equality *)
   105 
   106 fun equal x y = x = y;
   107 fun not_equal x y = x <> y;
   108 
   109 
   110 (* operators for combining predicates *)
   111 
   112 fun (p orf q) = fn x => p x orelse q x;
   113 
   114 fun (p andf q) = fn x => p x andalso q x;
   115 
   116 fun notf p x = not (p x);
   117 
   118 
   119 (* predicates on lists *)
   120 
   121 fun orl [] = false
   122   | orl (x :: xs) = x orelse orl xs;
   123 
   124 fun andl [] = true
   125   | andl (x :: xs) = x andalso andl xs;
   126 
   127 (*Several object-logics declare theories named List or Option, hiding the
   128   eponymous basis library structures.*)
   129 structure List_ = List
   130 and       Option_ = Option;
   131 
   132 (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
   133 fun exists (pred: 'a -> bool) : 'a list -> bool =
   134   let fun boolf [] = false
   135         | boolf (x :: xs) = pred x orelse boolf xs
   136   in boolf end;
   137 
   138 (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
   139 fun forall (pred: 'a -> bool) : 'a list -> bool =
   140   let fun boolf [] = true
   141         | boolf (x :: xs) = pred x andalso boolf xs
   142   in boolf end;
   143 
   144 
   145 (* flags *)
   146 
   147 fun set flag = (flag := true; true);
   148 fun reset flag = (flag := false; false);
   149 fun toggle flag = (flag := not (! flag); ! flag);
   150 
   151 fun setmp flag value f x =
   152   let
   153     val orig_value = ! flag;
   154     fun return y = (flag := orig_value; y);
   155   in
   156     flag := value;
   157     return (f x handle exn => (return (); raise exn))
   158   end;
   159 
   160 
   161 
   162 (** lists **)
   163 
   164 exception LIST of string;
   165 
   166 fun null [] = true
   167   | null (_ :: _) = false;
   168 
   169 fun hd [] = raise LIST "hd"
   170   | hd (x :: _) = x;
   171 
   172 fun tl [] = raise LIST "tl"
   173   | tl (_ :: xs) = xs;
   174 
   175 fun cons x xs = x :: xs;
   176 
   177 
   178 (* fold *)
   179 
   180 (*the following versions of fold are designed to fit nicely with infixes*)
   181 
   182 (*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
   183     for operators that associate to the left (TAIL RECURSIVE)*)
   184 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
   185   let fun itl (e, [])  = e
   186         | itl (e, a::l) = itl (f(e, a), l)
   187   in  itl end;
   188 
   189 (*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
   190     for operators that associate to the right (not tail recursive)*)
   191 fun foldr f (l, e) =
   192   let fun itr [] = e
   193         | itr (a::l) = f(a, itr l)
   194   in  itr l  end;
   195 
   196 (*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
   197     for n > 0, operators that associate to the right (not tail recursive)*)
   198 fun foldr1 f l =
   199   let fun itr [x] = x                       (* FIXME [] case: elim warn (?) *)
   200         | itr (x::l) = f(x, itr l)
   201   in  itr l  end;
   202 
   203 
   204 (* basic list functions *)
   205 
   206 (*length of a list, should unquestionably be a standard function*)
   207 local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
   208         | length1 (n, x :: xs) = length1 (n + 1, xs)
   209 in  fun length l = length1 (0, l) end;
   210 
   211 (*take the first n elements from a list*)
   212 fun take (n, []) = []
   213   | take (n, x :: xs) =
   214       if n > 0 then x :: take (n - 1, xs) else [];
   215 
   216 (*drop the first n elements from a list*)
   217 fun drop (n, []) = []
   218   | drop (n, x :: xs) =
   219       if n > 0 then drop (n - 1, xs) else x :: xs;
   220 
   221 (*return nth element of a list, where 0 designates the first element;
   222   raise EXCEPTION if list too short*)
   223 fun nth_elem NL =
   224   (case drop NL of
   225     [] => raise LIST "nth_elem"
   226   | x :: _ => x);
   227 
   228 (*last element of a list*)
   229 fun last_elem [] = raise LIST "last_elem"
   230   | last_elem [x] = x
   231   | last_elem (_ :: xs) = last_elem xs;
   232 
   233 (*rear decomposition*)
   234 fun split_last [] = raise LIST "split_last"
   235   | split_last [x] = ([], x)
   236   | split_last (x :: xs) = apfst (cons x) (split_last xs);
   237 
   238 
   239 (*find the position of an element in a list*)
   240 fun find (x, ys) =
   241   let fun f (y :: ys, i) = if x = y then i else f (ys, i + 1)
   242         | f (_, _) = raise LIST "find"
   243   in f (ys, 0) end;
   244 
   245 (*flatten a list of lists to a list*)
   246 fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
   247 
   248 
   249 (*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
   250   (proc x1; ...; proc xn) for side effects*)
   251 fun seq (proc: 'a -> unit) : 'a list -> unit =
   252   let fun seqf [] = ()
   253         | seqf (x :: xs) = (proc x; seqf xs)
   254   in seqf end;
   255 
   256 
   257 (*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
   258 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
   259   | separate _ xs = xs;
   260 
   261 (*make the list [x, x, ..., x] of length n*)
   262 fun replicate n (x: 'a) : 'a list =
   263   let fun rep (0, xs) = xs
   264         | rep (n, xs) = rep (n - 1, x :: xs)
   265   in
   266     if n < 0 then raise LIST "replicate"
   267     else rep (n, [])
   268   end;
   269 
   270 
   271 (* filter *)
   272 
   273 (*copy the list preserving elements that satisfy the predicate*)
   274 fun filter (pred: 'a->bool) : 'a list -> 'a list =
   275   let fun filt [] = []
   276         | filt (x :: xs) = if pred x then x :: filt xs else filt xs
   277   in filt end;
   278 
   279 fun filter_out f = filter (not o f);
   280 
   281 
   282 fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
   283   | mapfilter f (x :: xs) =
   284       (case f x of
   285         None => mapfilter f xs
   286       | Some y => y :: mapfilter f xs);
   287 
   288 
   289 fun find_first _ [] = None
   290   | find_first pred (x :: xs) =
   291       if pred x then Some x else find_first pred xs;
   292 
   293 
   294 (* lists of pairs *)
   295 
   296 fun map2 _ ([], []) = []
   297   | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
   298   | map2 _ _ = raise LIST "map2";
   299 
   300 fun exists2 _ ([], []) = false
   301   | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
   302   | exists2 _ _ = raise LIST "exists2";
   303 
   304 fun forall2 _ ([], []) = true
   305   | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
   306   | forall2 _ _ = raise LIST "forall2";
   307 
   308 (*combine two lists forming a list of pairs:
   309   [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
   310 fun [] ~~ [] = []
   311   | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
   312   | _ ~~ _ = raise LIST "~~";
   313 
   314 
   315 (*inverse of ~~; the old 'split':
   316   [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
   317 fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
   318 
   319 
   320 (* prefixes, suffixes *)
   321 
   322 fun [] prefix _ = true
   323   | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
   324   | _ prefix _ = false;
   325 
   326 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
   327    where xi is the first element that does not satisfy the predicate*)
   328 fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
   329   let fun take (rxs, []) = (rev rxs, [])
   330         | take (rxs, x :: xs) =
   331             if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
   332   in  take([], xs)  end;
   333 
   334 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
   335    where xi is the last element that does not satisfy the predicate*)
   336 fun take_suffix _ [] = ([], [])
   337   | take_suffix pred (x :: xs) =
   338       (case take_suffix pred xs of
   339         ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
   340       | (prfx, sffx) => (x :: prfx, sffx));
   341 
   342 
   343 
   344 (** integers **)
   345 
   346 fun inc i = (i := ! i + 1; ! i);
   347 fun dec i = (i := ! i - 1; ! i);
   348 
   349 
   350 (* lists of integers *)
   351 
   352 (*make the list [from, from + 1, ..., to]*)
   353 fun (from upto to) =
   354   if from > to then [] else from :: ((from + 1) upto to);
   355 
   356 (*make the list [from, from - 1, ..., to]*)
   357 fun (from downto to) =
   358   if from < to then [] else from :: ((from - 1) downto to);
   359 
   360 (*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
   361 fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
   362   | downto0 ([], n) = n = ~1;
   363 
   364 
   365 (* convert integers to strings *)
   366 
   367 (*expand the number in the given base;
   368   example: radixpand (2, 8) gives [1, 0, 0, 0]*)
   369 fun radixpand (base, num) : int list =
   370   let
   371     fun radix (n, tail) =
   372       if n < base then n :: tail
   373       else radix (n div base, (n mod base) :: tail)
   374   in radix (num, []) end;
   375 
   376 (*expands a number into a string of characters starting from "zerochar";
   377   example: radixstring (2, "0", 8) gives "1000"*)
   378 fun radixstring (base, zerochar, num) =
   379   let val offset = ord zerochar;
   380       fun chrof n = chr (offset + n)
   381   in implode (map chrof (radixpand (base, num))) end;
   382 
   383 
   384 val string_of_int = Int.toString;
   385 
   386 fun string_of_indexname (a,0) = a
   387   | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
   388 
   389 
   390 (** strings **)
   391 
   392 fun is_letter ch =
   393   ord "A" <= ord ch andalso ord ch <= ord "Z" orelse
   394   ord "a" <= ord ch andalso ord ch <= ord "z";
   395 
   396 fun is_digit ch =
   397   ord "0" <= ord ch andalso ord ch <= ord "9";
   398 
   399 (*letter or _ or prime (')*)
   400 fun is_quasi_letter "_" = true
   401   | is_quasi_letter "'" = true
   402   | is_quasi_letter ch = is_letter ch;
   403 
   404 (*white space: blanks, tabs, newlines, formfeeds*)
   405 val is_blank : string -> bool =
   406   fn " " => true | "\t" => true | "\n" => true | "\^L" => true | "\160" => true
   407     | _ => false;
   408 
   409 val is_letdig = is_quasi_letter orf is_digit;
   410 
   411 (*printable chars*)
   412 fun is_printable c = ord c > ord " " andalso ord c <= ord "~";
   413 
   414 
   415 (*lower all chars of string*)
   416 val to_lower =
   417   let
   418     fun lower ch =
   419       if ch >= "A" andalso ch <= "Z" then
   420         chr (ord ch - ord "A" + ord "a")
   421       else ch;
   422   in implode o (map lower) o explode end;
   423 
   424 
   425 (*enclose in brackets*)
   426 fun enclose lpar rpar str = lpar ^ str ^ rpar;
   427 
   428 (*simple quoting (does not escape special chars)*)
   429 val quote = enclose "\"" "\"";
   430 
   431 (*space_implode "..." (explode "hello"); gives "h...e...l...l...o"*)
   432 fun space_implode a bs = implode (separate a bs);
   433 
   434 val commas = space_implode ", ";
   435 val commas_quote = commas o map quote;
   436 
   437 (*concatenate messages, one per line, into a string*)
   438 val cat_lines = space_implode "\n";
   439 
   440 (*BAD_space_explode "." "h.e..l.lo"; gives ["h", "e", "l", "lo"]*)
   441 fun BAD_space_explode sep s =
   442   let fun divide [] "" = []
   443         | divide [] part = [part]
   444         | divide (c::s) part =
   445             if c = sep then
   446               (if part = "" then divide s "" else part :: divide s "")
   447             else divide s (part ^ c)
   448   in divide (explode s) "" end;
   449 
   450 (*space_explode "." "h.e..l.lo"; gives ["h", "e", "", "l", "lo"]*)
   451 fun space_explode _ "" = []
   452   | space_explode sep str =
   453       let
   454         fun expl chs =
   455           (case take_prefix (not_equal sep) chs of
   456             (cs, []) => [implode cs]
   457           | (cs, _ :: cs') => implode cs :: expl cs');
   458       in expl (explode str) end;
   459 
   460 val split_lines = space_explode "\n";
   461 
   462 
   463 
   464 (** lists as sets **)
   465 
   466 (*membership in a list*)
   467 fun x mem [] = false
   468   | x mem (y :: ys) = x = y orelse x mem ys;
   469 
   470 (*membership in a list, optimized version for ints*)
   471 fun (x:int) mem_int [] = false
   472   | x mem_int (y :: ys) = x = y orelse x mem_int ys;
   473 
   474 (*membership in a list, optimized version for strings*)
   475 fun (x:string) mem_string [] = false
   476   | x mem_string (y :: ys) = x = y orelse x mem_string ys;
   477 
   478 (*generalized membership test*)
   479 fun gen_mem eq (x, []) = false
   480   | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
   481 
   482 
   483 (*insertion into list if not already there*)
   484 fun (x ins xs) = if x mem xs then xs else x :: xs;
   485 
   486 (*insertion into list, optimized version for ints*)
   487 fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
   488 
   489 (*insertion into list, optimized version for strings*)
   490 fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
   491 
   492 (*generalized insertion*)
   493 fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
   494 
   495 
   496 (*union of sets represented as lists: no repetitions*)
   497 fun xs union [] = xs
   498   | [] union ys = ys
   499   | (x :: xs) union ys = xs union (x ins ys);
   500 
   501 (*union of sets, optimized version for ints*)
   502 fun (xs:int list) union_int [] = xs
   503   | [] union_int ys = ys
   504   | (x :: xs) union_int ys = xs union_int (x ins_int ys);
   505 
   506 (*union of sets, optimized version for strings*)
   507 fun (xs:string list) union_string [] = xs
   508   | [] union_string ys = ys
   509   | (x :: xs) union_string ys = xs union_string (x ins_string ys);
   510 
   511 (*generalized union*)
   512 fun gen_union eq (xs, []) = xs
   513   | gen_union eq ([], ys) = ys
   514   | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
   515 
   516 
   517 (*intersection*)
   518 fun [] inter ys = []
   519   | (x :: xs) inter ys =
   520       if x mem ys then x :: (xs inter ys) else xs inter ys;
   521 
   522 (*intersection, optimized version for ints*)
   523 fun ([]:int list) inter_int ys = []
   524   | (x :: xs) inter_int ys =
   525       if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
   526 
   527 (*intersection, optimized version for strings *)
   528 fun ([]:string list) inter_string ys = []
   529   | (x :: xs) inter_string ys =
   530       if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
   531 
   532 
   533 (*subset*)
   534 fun [] subset ys = true
   535   | (x :: xs) subset ys = x mem ys andalso xs subset ys;
   536 
   537 (*subset, optimized version for ints*)
   538 fun ([]:int list) subset_int ys = true
   539   | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
   540 
   541 (*subset, optimized version for strings*)
   542 fun ([]:string list) subset_string ys = true
   543   | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
   544 
   545 (*set equality for strings*)
   546 fun eq_set_string ((xs:string list), ys) =
   547   xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
   548 
   549 fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
   550 
   551 
   552 (*removing an element from a list WITHOUT duplicates*)
   553 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
   554   | [] \ x = [];
   555 
   556 fun ys \\ xs = foldl (op \) (ys,xs);
   557 
   558 (*removing an element from a list -- possibly WITH duplicates*)
   559 fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
   560 
   561 fun gen_rems eq = foldl (gen_rem eq);
   562 
   563 
   564 (*makes a list of the distinct members of the input; preserves order, takes
   565   first of equal elements*)
   566 fun gen_distinct eq lst =
   567   let
   568     val memb = gen_mem eq;
   569 
   570     fun dist (rev_seen, []) = rev rev_seen
   571       | dist (rev_seen, x :: xs) =
   572           if memb (x, rev_seen) then dist (rev_seen, xs)
   573           else dist (x :: rev_seen, xs);
   574   in
   575     dist ([], lst)
   576   end;
   577 
   578 fun distinct l = gen_distinct (op =) l;
   579 
   580 
   581 (*returns the tail beginning with the first repeated element, or []*)
   582 fun findrep [] = []
   583   | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
   584 
   585 
   586 (*returns a list containing all repeated elements exactly once; preserves
   587   order, takes first of equal elements*)
   588 fun gen_duplicates eq lst =
   589   let
   590     val memb = gen_mem eq;
   591 
   592     fun dups (rev_dups, []) = rev rev_dups
   593       | dups (rev_dups, x :: xs) =
   594           if memb (x, rev_dups) orelse not (memb (x, xs)) then
   595             dups (rev_dups, xs)
   596           else dups (x :: rev_dups, xs);
   597   in
   598     dups ([], lst)
   599   end;
   600 
   601 fun duplicates l = gen_duplicates (op =) l;
   602 
   603 
   604 
   605 (** association lists **)
   606 
   607 (*association list lookup*)
   608 fun assoc ([], key) = None
   609   | assoc ((keyi, xi) :: pairs, key) =
   610       if key = keyi then Some xi else assoc (pairs, key);
   611 
   612 (*association list lookup, optimized version for ints*)
   613 fun assoc_int ([], (key:int)) = None
   614   | assoc_int ((keyi, xi) :: pairs, key) =
   615       if key = keyi then Some xi else assoc_int (pairs, key);
   616 
   617 (*association list lookup, optimized version for strings*)
   618 fun assoc_string ([], (key:string)) = None
   619   | assoc_string ((keyi, xi) :: pairs, key) =
   620       if key = keyi then Some xi else assoc_string (pairs, key);
   621 
   622 (*association list lookup, optimized version for string*ints*)
   623 fun assoc_string_int ([], (key:string*int)) = None
   624   | assoc_string_int ((keyi, xi) :: pairs, key) =
   625       if key = keyi then Some xi else assoc_string_int (pairs, key);
   626 
   627 fun assocs ps x =
   628   (case assoc (ps, x) of
   629     None => []
   630   | Some ys => ys);
   631 
   632 (*two-fold association list lookup*)
   633 fun assoc2 (aal, (key1, key2)) =
   634   (case assoc (aal, key1) of
   635     Some al => assoc (al, key2)
   636   | None => None);
   637 
   638 (*generalized association list lookup*)
   639 fun gen_assoc eq ([], key) = None
   640   | gen_assoc eq ((keyi, xi) :: pairs, key) =
   641       if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
   642 
   643 (*association list update*)
   644 fun overwrite (al, p as (key, _)) =
   645   let fun over ((q as (keyi, _)) :: pairs) =
   646             if keyi = key then p :: pairs else q :: (over pairs)
   647         | over [] = [p]
   648   in over al end;
   649 
   650 fun gen_overwrite eq (al, p as (key, _)) =
   651   let fun over ((q as (keyi, _)) :: pairs) =
   652             if eq (keyi, key) then p :: pairs else q :: (over pairs)
   653         | over [] = [p]
   654   in over al end;
   655 
   656 
   657 
   658 (** generic tables **)
   659 
   660 (*Tables are supposed to be 'efficient' encodings of lists of elements distinct
   661   wrt. an equality "eq". The extend and merge operations below are optimized
   662   for long-term space efficiency.*)
   663 
   664 (*append (new) elements to a table*)
   665 fun generic_extend _ _ _ tab [] = tab
   666   | generic_extend eq dest_tab mk_tab tab1 lst2 =
   667       let
   668         val lst1 = dest_tab tab1;
   669         val new_lst2 = gen_rems eq (lst2, lst1);
   670       in
   671         if null new_lst2 then tab1
   672         else mk_tab (lst1 @ new_lst2)
   673       end;
   674 
   675 (*append (new) elements of 2nd table to 1st table*)
   676 fun generic_merge eq dest_tab mk_tab tab1 tab2 =
   677   let
   678     val lst1 = dest_tab tab1;
   679     val lst2 = dest_tab tab2;
   680     val new_lst2 = gen_rems eq (lst2, lst1);
   681   in
   682     if null new_lst2 then tab1
   683     else if gen_subset eq (lst1, lst2) then tab2
   684     else mk_tab (lst1 @ new_lst2)
   685   end;
   686 
   687 
   688 (*lists as tables*)
   689 fun extend_list tab = generic_extend (op =) I I tab;
   690 fun merge_lists tab = generic_merge (op =) I I tab;
   691 
   692 fun merge_rev_lists xs [] = xs
   693   | merge_rev_lists [] ys = ys
   694   | merge_rev_lists xs (y :: ys) =
   695       (if y mem xs then I else cons y) (merge_rev_lists xs ys);
   696 
   697 
   698 
   699 (** balanced trees **)
   700 
   701 exception Balance;      (*indicates non-positive argument to balancing fun*)
   702 
   703 (*balanced folding; avoids deep nesting*)
   704 fun fold_bal f [x] = x
   705   | fold_bal f [] = raise Balance
   706   | fold_bal f xs =
   707       let val k = length xs div 2
   708       in  f (fold_bal f (take(k, xs)),
   709              fold_bal f (drop(k, xs)))
   710       end;
   711 
   712 (*construct something of the form f(...g(...(x)...)) for balanced access*)
   713 fun access_bal (f, g, x) n i =
   714   let fun acc n i =     (*1<=i<=n*)
   715           if n=1 then x else
   716           let val n2 = n div 2
   717           in  if i<=n2 then f (acc n2 i)
   718                        else g (acc (n-n2) (i-n2))
   719           end
   720   in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
   721 
   722 (*construct ALL such accesses; could try harder to share recursive calls!*)
   723 fun accesses_bal (f, g, x) n =
   724   let fun acc n =
   725           if n=1 then [x] else
   726           let val n2 = n div 2
   727               val acc2 = acc n2
   728           in  if n-n2=n2 then map f acc2 @ map g acc2
   729                          else map f acc2 @ map g (acc (n-n2)) end
   730   in  if 1<=n then acc n else raise Balance  end;
   731 
   732 
   733 
   734 (** orders **)
   735 
   736 datatype order = LESS | EQUAL | GREATER;
   737 
   738 fun intord (i, j: int) =
   739   if i < j then LESS
   740   else if i = j then EQUAL
   741   else GREATER;
   742 
   743 fun stringord (a, b: string) =
   744   if a < b then LESS
   745   else if a = b then EQUAL
   746   else GREATER;
   747 
   748 
   749 
   750 (** input / output and diagnostics **)
   751 
   752 val cd = OS.FileSys.chDir;
   753 val pwd = OS.FileSys.getDir;
   754 
   755 
   756 local
   757   fun out s =
   758     (TextIO.output (TextIO.stdOut, s); TextIO.flushOut TextIO.stdOut);
   759 
   760   fun prefix_lines prfx txt =
   761     txt |> split_lines |> map (fn s => prfx ^ s ^ "\n") |> implode;
   762 in
   763 
   764 (*hooks for output channels: normal, warning, error*)
   765 val prs_fn = ref (fn s => out s);
   766 val warning_fn = ref (fn s => out (prefix_lines "### " s));
   767 val error_fn = ref (fn s => out (prefix_lines "*** " s));
   768 
   769 end;
   770 
   771 fun prs s = !prs_fn s;
   772 fun writeln s = prs (s ^ "\n");
   773 
   774 fun warning s = !warning_fn s;
   775 
   776 (*print error message and abort to top level*)
   777 exception ERROR;
   778 fun error_msg s = !error_fn s;			(*promise to raise ERROR later!*)
   779 fun error s = (error_msg s; raise ERROR);
   780 fun sys_error msg = (error_msg " !! SYSTEM ERROR !!\n"; error msg);
   781 
   782 fun assert p msg = if p then () else error msg;
   783 fun deny p msg = if p then error msg else ();
   784 
   785 (*Assert pred for every member of l, generating a message if pred fails*)
   786 fun assert_all pred l msg_fn = 
   787   let fun asl [] = ()
   788         | asl (x::xs) = if pred x then asl xs
   789                         else error (msg_fn x)
   790   in  asl l  end;
   791 
   792 
   793 (* handle errors (capturing messages) *)
   794 
   795 datatype 'a error =
   796   Error of string |
   797   OK of 'a;
   798 
   799 fun handle_error f x =
   800   let
   801     val buffer = ref "";
   802     fun capture s = buffer := ! buffer ^ s ^ "\n";
   803     val result = Some (setmp error_fn capture f x) handle ERROR => None;
   804   in
   805     case result of
   806       None => Error (! buffer)
   807     | Some y => OK y
   808   end;
   809 
   810 
   811 (* read / write files *)
   812 
   813 fun read_file name =
   814   let
   815     val instream  = TextIO.openIn name;
   816     val intext = TextIO.inputAll instream;
   817   in
   818     TextIO.closeIn instream;
   819     intext
   820   end;
   821 
   822 fun write_file name txt =
   823   let val outstream = TextIO.openOut name in
   824     TextIO.output (outstream, txt);
   825     TextIO.closeOut outstream
   826   end;
   827 
   828 fun append_file name txt =
   829   let val outstream = TextIO.openAppend name in
   830     TextIO.output (outstream, txt);
   831     TextIO.closeOut outstream
   832   end;
   833 
   834 
   835 (*for the "test" target in IsaMakefiles -- signifies successful termination*)
   836 fun maketest msg =
   837   (writeln msg; write_file "test" "Test examples ran successfully\n");
   838 
   839 
   840 (*print a list surrounded by the brackets lpar and rpar, with comma separator
   841   print nothing for empty list*)
   842 fun print_list (lpar, rpar, pre: 'a -> unit) (l : 'a list) =
   843   let fun prec x = (prs ","; pre x)
   844   in
   845     (case l of
   846       [] => ()
   847     | x::l => (prs lpar; pre x; seq prec l; prs rpar))
   848   end;
   849 
   850 (*print a list of items separated by newlines*)
   851 fun print_list_ln (pre: 'a -> unit) : 'a list -> unit =
   852   seq (fn x => (pre x; writeln ""));
   853 
   854 
   855 val print_int = prs o string_of_int;
   856 
   857 
   858 (* output to LaTeX / xdvi *)
   859 fun latex s =
   860   execute ("( cd /tmp ; echo \"" ^ s ^
   861     "\" | isa2latex -s > $$.tex ; latex $$.tex ; xdvi $$.dvi ; rm $$.* ) > /dev/null &");
   862 
   863 
   864 (** timing **)
   865 
   866 (*unconditional timing function*)
   867 fun timeit x = cond_timeit true x;
   868 
   869 (*timed application function*)
   870 fun timeap f x = timeit (fn () => f x);
   871 
   872 (*timed "use" function, printing filenames*)
   873 fun time_use fname = timeit (fn () =>
   874   (writeln ("\n**** Starting " ^ fname ^ " ****"); use fname;
   875    writeln ("\n**** Finished " ^ fname ^ " ****")));
   876 
   877 (*use the file, but exit with error code if errors found.*)
   878 fun exit_use fname = use fname handle _ => exit 1;
   879 
   880 
   881 (** filenames and paths **)
   882 
   883 (*Convert UNIX filename of the form "path/file" to "path/" and "file";
   884   if filename contains no slash, then it returns "" and "file"*)
   885 val split_filename =
   886   (pairself implode) o take_suffix (not_equal "/") o explode;
   887 
   888 val base_name = #2 o split_filename;
   889 
   890 (*Merge splitted filename (path and file);
   891   if path does not end with one a slash is appended*)
   892 fun tack_on "" name = name
   893   | tack_on path name =
   894       if last_elem (explode path) = "/" then path ^ name
   895       else path ^ "/" ^ name;
   896 
   897 (*Remove the extension of a filename, i.e. the part after the last '.'*)
   898 val remove_ext = implode o #1 o take_suffix (not_equal ".") o explode;
   899 
   900 (*Make relative path to reach an absolute location from a different one*)
   901 fun relative_path cur_path dest_path =
   902   let (*Remove common beginning of both paths and make relative path*)
   903       fun mk_relative [] [] = []
   904         | mk_relative [] ds = ds
   905         | mk_relative cs [] = map (fn _ => "..") cs
   906         | mk_relative (c::cs) (d::ds) =
   907             if c = d then mk_relative cs ds
   908             else ".." :: map (fn _ => "..") cs @ (d::ds);
   909   in if cur_path = "" orelse hd (explode cur_path) <> "/" orelse
   910         dest_path = "" orelse hd (explode dest_path) <> "/" then
   911        error "Relative or empty path passed to relative_path"
   912      else ();
   913      space_implode "/" (mk_relative (BAD_space_explode "/" cur_path)
   914                                     (BAD_space_explode "/" dest_path))
   915   end;
   916 
   917 (*Determine if absolute path1 is a subdirectory of absolute path2*)
   918 fun path1 subdir_of path2 =
   919   if hd (explode path1) <> "/" orelse hd (explode path2) <> "/" then
   920     error "Relative or empty path passed to subdir_of"
   921   else (BAD_space_explode "/" path2) prefix (BAD_space_explode "/" path1);
   922 
   923 fun absolute_path cwd file =
   924   let fun rm_points [] result = rev result
   925         | rm_points (".."::ds) result = rm_points ds (tl result)
   926         | rm_points ("."::ds) result = rm_points ds result
   927         | rm_points (d::ds) result = rm_points ds (d::result);
   928   in if file = "" then ""
   929      else if hd (explode file) = "/" then file
   930      else "/" ^ space_implode "/"
   931                   (rm_points (BAD_space_explode "/" (tack_on cwd file)) [])
   932   end;
   933 
   934 fun file_exists file = (file_info file <> "");
   935 
   936 
   937 (** misc functions **)
   938 
   939 (*use the keyfun to make a list of (x, key) pairs*)
   940 fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
   941   let fun keypair x = (x, keyfun x)
   942   in map keypair end;
   943 
   944 (*given a list of (x, key) pairs and a searchkey
   945   return the list of xs from each pair whose key equals searchkey*)
   946 fun keyfilter [] searchkey = []
   947   | keyfilter ((x, key) :: pairs) searchkey =
   948       if key = searchkey then x :: keyfilter pairs searchkey
   949       else keyfilter pairs searchkey;
   950 
   951 
   952 (*Partition list into elements that satisfy predicate and those that don't.
   953   Preserves order of elements in both lists.*)
   954 fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
   955     let fun part ([], answer) = answer
   956           | part (x::xs, (ys, ns)) = if pred(x)
   957             then  part (xs, (x::ys, ns))
   958             else  part (xs, (ys, x::ns))
   959     in  part (rev ys, ([], []))  end;
   960 
   961 
   962 fun partition_eq (eq:'a * 'a -> bool) =
   963     let fun part [] = []
   964           | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
   965                            in (x::xs)::(part xs') end
   966     in part end;
   967 
   968 
   969 (*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
   970    putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
   971 fun partition_list p i j =
   972   let fun part k xs =
   973             if k>j then
   974               (case xs of [] => []
   975                          | _ => raise LIST "partition_list")
   976             else
   977             let val (ns, rest) = partition (p k) xs;
   978             in  ns :: part(k+1)rest  end
   979   in  part i end;
   980 
   981 
   982 (* sorting *)
   983 
   984 (*insertion sort; stable (does not reorder equal elements)
   985   'less' is less-than test on type 'a*)
   986 fun sort (less: 'a*'a -> bool) =
   987   let fun insert (x, []) = [x]
   988         | insert (x, y::ys) =
   989               if less(y, x) then y :: insert (x, ys) else x::y::ys;
   990       fun sort1 [] = []
   991         | sort1 (x::xs) = insert (x, sort1 xs)
   992   in  sort1  end;
   993 
   994 (*sort strings*)
   995 fun sort_wrt sel xs = sort (op <= o pairself (sel: 'a -> string)) xs;
   996 val sort_strings = sort_wrt I;
   997 
   998 
   999 (* transitive closure (not Warshall's algorithm) *)
  1000 
  1001 fun transitive_closure [] = []
  1002   | transitive_closure ((x, ys)::ps) =
  1003       let val qs = transitive_closure ps
  1004           val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
  1005           fun step(u, us) = (u, if x mem_string us then zs union_string us 
  1006                                 else us)
  1007       in (x, zs) :: map step qs end;
  1008 
  1009 
  1010 (* generating identifiers *)
  1011 
  1012 local
  1013   val a = ord "a" and z = ord "z" and A = ord "A" and Z = ord "Z"
  1014   and k0 = ord "0" and k9 = ord "9"
  1015 
  1016   val seedr = ref 0;
  1017 in
  1018 
  1019 (*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
  1020 fun newid n = 
  1021   let fun char i =
  1022                if i<26 then chr (A+i)
  1023           else if i<52 then chr (a+i-26)
  1024           else if i<62 then chr (k0+i-52)
  1025           else if i=62 then "_"
  1026           else  (*i=63*)    "'"
  1027   in  implode (map char (radixpand (64,n)))  end;
  1028 
  1029 (*Freshly generated identifiers with given prefix; MUST start with a letter*)
  1030 fun gensym pre = pre ^ 
  1031                  (#1(newid (!seedr), 
  1032                      seedr := 1+ !seedr))
  1033 
  1034 (*Increment a list of letters like a reversed base 26 number.
  1035   If head is "z", bumps chars in tail.
  1036   Digits are incremented as if they were integers.
  1037   "_" and "'" are not changed.
  1038   For making variants of identifiers.*)
  1039 
  1040 fun bump_int_list(c::cs) = if c="9" then "0" :: bump_int_list cs else
  1041         if k0 <= ord(c) andalso ord(c) < k9 then chr(ord(c)+1) :: cs
  1042         else "1" :: c :: cs
  1043   | bump_int_list([]) = error("bump_int_list: not an identifier");
  1044 
  1045 fun bump_list([], d) = [d]
  1046   | bump_list(["'"], d) = [d, "'"]
  1047   | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
  1048   | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
  1049   | bump_list("9"::cs, _) = "0" :: bump_int_list cs
  1050   | bump_list(c::cs, _) = let val k = ord(c)
  1051         in if (a <= k andalso k < z) orelse (A <= k andalso k < Z) orelse
  1052               (k0 <= k andalso k < k9) then chr(k+1) :: cs else
  1053            if c="'" orelse c="_" then c :: bump_list(cs, "") else
  1054                 error("bump_list: not legal in identifier: " ^
  1055                         implode(rev(c::cs)))
  1056         end;
  1057 
  1058 end;
  1059 
  1060 fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
  1061 
  1062 
  1063 (* lexical scanning *)
  1064 
  1065 (*scan a list of characters into "words" composed of "letters" (recognized by
  1066   is_let) and separated by any number of non-"letters"*)
  1067 fun scanwords is_let cs =
  1068   let fun scan1 [] = []
  1069         | scan1 cs =
  1070             let val (lets, rest) = take_prefix is_let cs
  1071             in implode lets :: scanwords is_let rest end;
  1072   in scan1 (#2 (take_prefix (not o is_let) cs)) end;
  1073 
  1074 end;
  1075 
  1076 (*Variable-branching trees: for proof terms*)
  1077 datatype 'a mtree = Join of 'a * 'a mtree list;
  1078 
  1079 open Library;