src/Pure/library.ML
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     1 (*  Title: 	library
       
     2     ID:         $Id$
       
     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
       
     4     Copyright   1992  University of Cambridge
       
     5 
       
     6 Basic library: booleans, lists, pairs, input/output, etc.
       
     7 *)
       
     8 
       
     9 
       
    10 (**** Booleans: operators for combining predicates ****)
       
    11 
       
    12 infix orf; 
       
    13 fun p orf q = fn x => p x orelse q x ;
       
    14 
       
    15 infix andf; 
       
    16 fun p andf q = fn x => p x andalso q x ;
       
    17 
       
    18 fun notf p x = not (p x) ;
       
    19 
       
    20 fun orl [] = false
       
    21   | orl (x::l) =  x  orelse  orl l;
       
    22 
       
    23 fun andl [] = true
       
    24   | andl (x::l) =  x  andalso  andl l;
       
    25 
       
    26 (*exists pred [x1,...,xn] ======>  pred(x1)  orelse  ...  orelse  pred(xn)*)
       
    27 fun exists (pred: 'a -> bool) : 'a list -> bool = 
       
    28   let fun boolf [] = false
       
    29         | boolf (x::l) = (pred x) orelse boolf l
       
    30   in boolf end;
       
    31 
       
    32 (*forall pred [x1,...,xn] ======>  pred(x1)  andalso  ...  andalso  pred(xn)*)
       
    33 fun forall (pred: 'a -> bool) : 'a list -> bool = 
       
    34   let fun boolf [] = true
       
    35         | boolf (x::l) = (pred x) andalso (boolf l)
       
    36   in boolf end;
       
    37 
       
    38 
       
    39 (*** Lists ***)
       
    40 
       
    41 exception LIST of string;
       
    42 
       
    43 (*discriminator and selectors for lists. *)
       
    44 fun null   []   = true
       
    45   | null (_::_) = false;
       
    46 
       
    47 fun hd   []   = raise LIST "hd"
       
    48   | hd (a::_) = a;
       
    49 
       
    50 fun tl   []   = raise LIST "tl"
       
    51   | tl (_::l) = l;
       
    52 
       
    53 
       
    54 (*curried functions for pairing and reversed pairing*)
       
    55 fun pair x y = (x,y);
       
    56 fun rpair x y = (y,x);
       
    57 
       
    58 fun fst(x,y) = x and snd(x,y) = y;
       
    59 
       
    60 (*Handy combinators*)
       
    61 fun curry f x y = f(x,y);
       
    62 fun uncurry f(x,y) = f x y;
       
    63 fun I x = x  and  K x y = x;
       
    64 
       
    65 (*Combine two functions forming the union of their domains*)
       
    66 infix orelf;
       
    67 fun f orelf g = fn x => f x  handle Match=> g x;
       
    68 
       
    69 
       
    70 (*Application of (infix) operator to its left or right argument*)
       
    71 fun apl (x,f) y = f(x,y);
       
    72 fun apr (f,y) x = f(x,y);
       
    73 
       
    74 
       
    75 (*functional for pairs*)
       
    76 fun pairself f (x,y) = (f x, f y);
       
    77 
       
    78 (*Apply the function to a component of a pair*)
       
    79 fun apfst f (x, y) = (f x, y);
       
    80 fun apsnd f (x, y) = (x, f y);
       
    81 
       
    82 fun square (n: int) = n*n;
       
    83 
       
    84 fun fact 0 = 1
       
    85   | fact n = n * fact(n-1);
       
    86 
       
    87 
       
    88 (*The following versions of fold are designed to fit nicely with infixes.*)
       
    89 
       
    90 (*  (op @) (e, [x1,...,xn])  ======>   ((e @ x1) @ x2) ... @ xn
       
    91     for operators that associate to the left.  TAIL RECURSIVE*)
       
    92 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
       
    93   let fun itl (e, [])  = e
       
    94         | itl (e, a::l) = itl (f(e,a), l)
       
    95   in  itl end;
       
    96 
       
    97 (*  (op @) ([x1,...,xn], e)  ======>   x1 @ (x2 ... @ (xn @ e))
       
    98     for operators that associate to the right.  Not tail recursive.*)
       
    99 fun foldr f (l,e) =
       
   100   let fun itr [] = e
       
   101         | itr (a::l) = f(a, itr l)
       
   102   in  itr l  end;
       
   103 
       
   104 (*  (op @) [x1,...,xn]  ======>   x1 @ (x2 ..(x[n-1]. @ xn))
       
   105     for n>0, operators that associate to the right.  Not tail recursive.*)
       
   106 fun foldr1 f l =
       
   107   let fun itr [x] = x
       
   108         | itr (x::l) = f(x, itr l)
       
   109   in  itr l  end;
       
   110 
       
   111 
       
   112 (*Length of a list.  Should unquestionably be a standard function*)
       
   113 local fun length1 (n, [ ])  = n   (*TAIL RECURSIVE*)
       
   114         | length1 (n, x::l) = length1 (n+1, l)   
       
   115 in  fun length l = length1 (0,l) end;
       
   116 
       
   117 
       
   118 (*Take the first n elements from l.*)
       
   119 fun take (n, []) = []
       
   120   | take (n, x::xs) = if n>0 then x::take(n-1,xs)  
       
   121                       else  [];
       
   122 
       
   123 (*Drop the first n elements from l.*)
       
   124 fun drop (_, [])    = []
       
   125   | drop (n, x::xs) = if n>0 then drop (n-1, xs) 
       
   126                              else x::xs;
       
   127 
       
   128 (*Return nth element of l, where 0 designates the first element;
       
   129   raise EXCEPTION if list too short.*)
       
   130 fun nth_elem NL = case (drop NL) of
       
   131     []   => raise LIST "nth_elem" 
       
   132   | x::l => x;
       
   133 
       
   134 
       
   135 (*make the list [from, from+1, ..., to]*)
       
   136 infix upto;
       
   137 fun from upto to =
       
   138     if from>to then []  else  from :: ((from+1) upto to);
       
   139 
       
   140 (*make the list [from, from-1, ..., to]*)
       
   141 infix downto;
       
   142 fun from downto to =
       
   143     if from<to then []  else  from :: ((from-1) downto to);
       
   144 
       
   145 (* predicate: downto0(is,n) <=> is = [n,n-1,...,0] *)
       
   146 fun downto0(i::is,n) = i=n andalso downto0(is,n-1)
       
   147   | downto0([],n)    = n = ~1;
       
   148 
       
   149 (*Like Lisp's MAPC -- seq proc [x1,...,xn] evaluates 
       
   150   proc(x1); ... ; proc(xn) for side effects.*)
       
   151 fun seq (proc: 'a -> unit) : 'a list -> unit = 
       
   152   let fun seqf []     = ()
       
   153         | seqf (x::l) = (proc x;  seqf l)
       
   154   in  seqf end;
       
   155 
       
   156 
       
   157 (*** Balanced folding; access to balanced trees ***)
       
   158 
       
   159 exception Balance;	(*indicates non-positive argument to balancing fun*)
       
   160 
       
   161 (*Balanced folding; avoids deep nesting*)
       
   162 fun fold_bal f [x] = x
       
   163   | fold_bal f [] = raise Balance
       
   164   | fold_bal f xs =
       
   165       let val k = length xs div 2
       
   166       in  f (fold_bal f (take(k,xs)),
       
   167 	     fold_bal f (drop(k,xs)))  
       
   168       end;
       
   169 
       
   170 (*Construct something of the form f(...g(...(x)...)) for balanced access*)
       
   171 fun access_bal (f,g,x) n i =
       
   172   let fun acc n i = 	(* 1<=i<=n*)
       
   173           if n=1 then x else
       
   174 	  let val n2 = n div 2
       
   175 	  in  if i<=n2 then f (acc n2 i) 
       
   176 	               else g (acc (n-n2) (i-n2))
       
   177           end
       
   178   in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
       
   179 
       
   180 (*Construct ALL such accesses; could try harder to share recursive calls!*)
       
   181 fun accesses_bal (f,g,x) n =
       
   182   let fun acc n =  
       
   183           if n=1 then [x] else 
       
   184 	  let val n2 = n div 2
       
   185 	      val acc2 = acc n2
       
   186 	  in  if n-n2=n2 then map f acc2 @ map g acc2
       
   187 	                 else map f acc2 @ map g (acc (n-n2)) end
       
   188   in  if 1<=n then acc n else raise Balance  end;
       
   189 
       
   190 
       
   191 (*** Input/Output ***)
       
   192 
       
   193 fun prs s = output(std_out,s);
       
   194 fun writeln s = prs (s ^ "\n");
       
   195 
       
   196 (*Print error message and abort to top level*)
       
   197 exception ERROR;
       
   198 fun error (msg) = (writeln msg;  raise ERROR);
       
   199 
       
   200 fun assert p msg = if p then () else error msg;
       
   201 fun deny p msg = if p then error msg else ();
       
   202 
       
   203 (*For the "test" target in Makefiles -- signifies successful termination*)
       
   204 fun maketest msg = 
       
   205     (writeln msg;
       
   206      output(open_out "test", "Test examples ran successfully\n"));
       
   207 
       
   208 (*print a list surrounded by the brackets lpar and rpar, with comma separator
       
   209   print nothing for empty list*)
       
   210 fun print_list (lpar, rpar, pre: 'a -> unit)  (l : 'a list) = 
       
   211     let fun prec(x) = (prs",";  pre(x)) 
       
   212     in  case l of
       
   213 	    [] => () 
       
   214 	  | x::l =>  (prs lpar;  pre x;  seq prec l;  prs rpar)
       
   215     end;
       
   216 
       
   217 (*print a list of items separated by newlines*)
       
   218 fun print_list_ln (pre: 'a -> unit)  : 'a list -> unit = 
       
   219     seq (fn x => (pre x;  writeln""));
       
   220 
       
   221 fun is_letter ch =
       
   222   (ord"A" <= ord ch)  andalso  (ord ch <= ord"Z")   orelse
       
   223   (ord"a" <= ord ch)  andalso  (ord ch <= ord"z");
       
   224 
       
   225 fun is_digit ch =
       
   226   (ord"0" <= ord ch)  andalso  (ord ch <= ord"9");
       
   227 
       
   228 (*letter or _ or prime (') *)
       
   229 fun is_quasi_letter "_" = true
       
   230   | is_quasi_letter "'" = true
       
   231   | is_quasi_letter ch  = is_letter ch;
       
   232 
       
   233 (*white space: blanks, tabs, newlines*)
       
   234 val is_blank : string -> bool = fn
       
   235      " " => true  |  "\t" => true  |  "\n" => true  |  _ => false;
       
   236 
       
   237 val is_letdig = is_quasi_letter orf is_digit;
       
   238 
       
   239 val to_lower =
       
   240   let
       
   241     fun lower ch =
       
   242       if ch >= "A" andalso ch <= "Z" then
       
   243         chr (ord ch - ord "A" + ord "a")
       
   244       else ch;
       
   245   in
       
   246     implode o (map lower) o explode
       
   247   end;
       
   248 
       
   249 
       
   250 (*** Timing ***)
       
   251 
       
   252 (*Unconditional timing function*)
       
   253 val timeit = cond_timeit true;
       
   254 
       
   255 (*Timed application function*)
       
   256 fun timeap f x = timeit(fn()=> f x);
       
   257 
       
   258 (*Timed "use" function, printing filenames*)
       
   259 fun time_use fname = timeit(fn()=> 
       
   260    (writeln("\n**** Starting " ^ fname ^ " ****");  use fname;  
       
   261     writeln("\n**** Finished " ^ fname ^ " ****")));  
       
   262 
       
   263 
       
   264 (*** Misc functions ***)
       
   265 
       
   266 (*Function exponentiation: f(...(f x)...) with n applications of f *)
       
   267 fun funpow n f x =
       
   268   let fun rep (0,x) = x
       
   269         | rep (n,x) = rep (n-1, f x)
       
   270   in  rep (n,x)  end;
       
   271 
       
   272 (*Combine two lists forming a list of pairs:
       
   273   [x1,...,xn] ~~ [y1,...,yn]  ======>   [(x1,y1), ..., (xn,yn)] *)
       
   274 infix ~~;
       
   275 fun []   ~~  []   = []
       
   276   | (x::xs) ~~ (y::ys) = (x,y) :: (xs ~~ ys)
       
   277   |  _   ~~   _   = raise LIST "~~";
       
   278 
       
   279 (*Inverse of ~~;  the old 'split'.
       
   280    [(x1,y1), ..., (xn,yn)]  ======>  ( [x1,...,xn] , [y1,...,yn] ) *)
       
   281 fun split_list (l: ('a*'b)list) = (map #1 l, map #2 l);
       
   282 
       
   283 (*make the list [x; x; ...; x] of length n*)
       
   284 fun replicate n (x: 'a) : 'a list =
       
   285   let fun rep (0,xs) = xs
       
   286         | rep (n,xs) = rep(n-1, x::xs) 
       
   287   in   if n<0 then raise LIST "replicate"
       
   288        else rep (n,[])
       
   289   end;
       
   290 
       
   291 (*Flatten a list of lists to a list.*)
       
   292 fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls,[]);
       
   293 
       
   294 
       
   295 (*** polymorphic set operations ***)
       
   296 
       
   297 (*membership in a list*)
       
   298 infix mem;
       
   299 fun x mem []  =  false
       
   300   | x mem (y::l)  =  (x=y) orelse (x mem l);
       
   301 
       
   302 (*insertion into list if not already there*)
       
   303 infix ins;
       
   304 fun x ins xs = if x mem xs then  xs   else  x::xs;
       
   305 
       
   306 (*union of sets represented as lists: no repetitions*)
       
   307 infix union;
       
   308 fun   xs    union [] = xs
       
   309   |   []    union ys = ys
       
   310   | (x::xs) union ys = xs union (x ins ys);
       
   311 
       
   312 infix inter;
       
   313 fun   []    inter ys = []
       
   314   | (x::xs) inter ys = if x mem ys then x::(xs inter ys)
       
   315                                    else     xs inter ys;
       
   316 
       
   317 infix subset;
       
   318 fun   []    subset ys = true
       
   319   | (x::xs) subset ys = x mem ys   andalso  xs subset ys;
       
   320 
       
   321 (*removing an element from a list WITHOUT duplicates*)
       
   322 infix \;
       
   323 fun (y::ys) \ x = if x=y then ys else y::(ys \ x)
       
   324   |   []    \ x = [];
       
   325 
       
   326 infix \\;
       
   327 val op \\ = foldl (op \);
       
   328 
       
   329 (*** option stuff ***)
       
   330 
       
   331 datatype 'a option = None | Some of 'a;
       
   332 
       
   333 exception OPTION of string;
       
   334 
       
   335 fun the (Some x) = x
       
   336   | the None = raise OPTION "the";
       
   337 
       
   338 fun is_some (Some _) = true
       
   339   | is_some None = false;
       
   340 
       
   341 fun is_none (Some _) = false
       
   342   | is_none None = true;
       
   343 
       
   344 
       
   345 (*** Association lists ***)
       
   346 
       
   347 (*Association list lookup*)
       
   348 fun assoc ([], key) = None
       
   349   | assoc ((keyi,xi)::pairs, key) =
       
   350       if key=keyi then Some xi  else assoc (pairs,key);
       
   351 
       
   352 fun assocs ps x = case assoc(ps,x) of None => [] | Some(ys) => ys;
       
   353 
       
   354 (*Association list update*)
       
   355 fun overwrite(al,p as (key,_)) =
       
   356   let fun over((q as (keyi,_))::pairs) =
       
   357 	    if keyi=key then p::pairs else q::(over pairs)
       
   358 	| over[] = [p]
       
   359   in over al end;
       
   360 
       
   361 (*Copy the list preserving elements that satisfy the predicate*)
       
   362 fun filter (pred: 'a->bool) : 'a list -> 'a list = 
       
   363   let fun filt [] = []
       
   364         | filt (x::xs) =  if pred(x) then x :: filt xs  else  filt xs
       
   365   in  filt   end;
       
   366 
       
   367 fun filter_out f = filter (not o f);
       
   368 
       
   369 
       
   370 (*** List operations, generalized to an arbitrary equality function "eq"
       
   371      -- so what good are equality types?? ***)
       
   372 
       
   373 (*removing an element from a list -- possibly WITH duplicates*)
       
   374 fun gen_rem eq (xs,y) = filter_out (fn x => eq(x,y)) xs;
       
   375 
       
   376 (*generalized membership test*)
       
   377 fun gen_mem eq (x, [])     =  false
       
   378   | gen_mem eq (x, y::ys)  =  eq(x,y) orelse gen_mem eq (x,ys);
       
   379 
       
   380 (*generalized insertion*)
       
   381 fun gen_ins eq (x,xs) = if gen_mem eq (x,xs) then  xs   else  x::xs;
       
   382 
       
   383 (*generalized union*)
       
   384 fun gen_union eq (xs,[]) = xs
       
   385   | gen_union eq ([],ys) = ys
       
   386   | gen_union eq (x::xs,ys) = gen_union eq (xs, gen_ins eq (x,ys));
       
   387 
       
   388 (*Generalized association list lookup*)
       
   389 fun gen_assoc eq ([], key) = None
       
   390   | gen_assoc eq ((keyi,xi)::pairs, key) =
       
   391       if eq(key,keyi) then Some xi  else gen_assoc eq (pairs,key);
       
   392 
       
   393 (** Finding list elements and duplicates **)
       
   394 
       
   395 (* find the position of an element in a list *)
       
   396 fun find(x,ys) =
       
   397     let fun f(y::ys,i) = if x=y then i else f(ys,i+1)
       
   398           | f(_,_) = raise LIST "find"
       
   399     in f(ys,0) end;
       
   400 
       
   401 (*Returns the tail beginning with the first repeated element, or []. *)
       
   402 fun findrep [] = []
       
   403   | findrep (x::xs) = if  x mem xs  then  x::xs   else   findrep xs;
       
   404 
       
   405 fun distinct1 (seen, []) = rev seen
       
   406   | distinct1 (seen, x::xs) =
       
   407       if x mem seen then distinct1 (seen, xs)
       
   408     		    else distinct1 (x::seen, xs);
       
   409 
       
   410 (*Makes a list of the distinct members of the input*)
       
   411 fun distinct xs = distinct1([],xs);
       
   412 
       
   413 
       
   414 (*Use the keyfun to make a list of (x,key) pairs.*)
       
   415 fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
       
   416   let fun keypair x = (x, keyfun x) 
       
   417   in   map keypair  end;
       
   418 
       
   419 (*Given a list of (x,key) pairs and a searchkey
       
   420   return the list of xs from each pair whose key equals searchkey*)
       
   421 fun keyfilter [] searchkey = []
       
   422   | keyfilter ((x,key)::pairs) searchkey = 
       
   423 	if key=searchkey then x :: keyfilter pairs searchkey
       
   424 	else keyfilter pairs searchkey;
       
   425 
       
   426 fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
       
   427   | mapfilter f (x::xs) =
       
   428       case (f x) of
       
   429 	  None => mapfilter f xs
       
   430 	| Some y => y :: mapfilter f xs;
       
   431 
       
   432 
       
   433 (*Partition list into elements that satisfy predicate and those that don't.
       
   434   Preserves order of elements in both lists. *)
       
   435 fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
       
   436     let fun part ([], answer) = answer
       
   437 	  | part (x::xs, (ys, ns)) = if pred(x)
       
   438 	    then  part (xs, (x::ys, ns))
       
   439 	    else  part (xs, (ys, x::ns))
       
   440     in  part (rev ys, ([],[]))  end;
       
   441 
       
   442 
       
   443 fun partition_eq (eq:'a * 'a -> bool) =
       
   444     let fun part [] = []
       
   445 	  | part (x::ys) = let val (xs,xs') = partition (apl(x,eq)) ys
       
   446 			   in (x::xs)::(part xs') end
       
   447     in part end;
       
   448 
       
   449 
       
   450 (*Partition a list into buckets  [ bi, b(i+1),...,bj ]
       
   451    putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
       
   452 fun partition_list p i j =
       
   453   let fun part k xs = 
       
   454             if k>j then 
       
   455               (case xs of [] => []
       
   456                          | _ => raise LIST "partition_list")
       
   457             else
       
   458 	    let val (ns,rest) = partition (p k) xs;
       
   459 	    in  ns :: part(k+1)rest  end
       
   460   in  part i end;
       
   461 
       
   462 
       
   463 (*Insertion sort.  Stable (does not reorder equal elements)
       
   464   'less' is less-than test on type 'a. *)
       
   465 fun sort (less: 'a*'a -> bool) = 
       
   466   let fun insert (x, []) = [x]
       
   467         | insert (x, y::ys) = 
       
   468               if less(y,x) then y :: insert (x,ys) else x::y::ys;
       
   469       fun sort1 [] = []
       
   470         | sort1 (x::xs) = insert (x, sort1 xs)
       
   471   in  sort1  end;
       
   472 
       
   473 (*Transitive Closure. Not Warshall's algorithm*)
       
   474 fun transitive_closure [] = []
       
   475   | transitive_closure ((x,ys)::ps) =
       
   476       let val qs = transitive_closure ps
       
   477           val zs = foldl (fn (zs,y) => assocs qs y union zs) (ys,ys)
       
   478           fun step(u,us) = (u, if x mem us then zs union us else us)
       
   479       in (x,zs) :: map step qs end;
       
   480 
       
   481 (*** Converting integers to strings, generating identifiers, etc. ***)
       
   482 
       
   483 (*Expand the number in the given base 
       
   484  example: radixpand(2, 8)  gives   [1, 0, 0, 0] *)
       
   485 fun radixpand (base,num) : int list =
       
   486   let fun radix (n,tail) =
       
   487   	if n<base then n :: tail
       
   488 	else radix (n div base, (n mod base) :: tail)
       
   489   in  radix (num,[])  end;
       
   490 
       
   491 (*Expands a number into a string of characters starting from "zerochar"
       
   492  example: radixstring(2,"0", 8)  gives  "1000" *)
       
   493 fun radixstring (base,zerochar,num) =
       
   494   let val offset = ord(zerochar); 
       
   495       fun chrof n = chr(offset+n)
       
   496   in  implode (map chrof (radixpand (base,num)))  end;
       
   497 
       
   498 fun string_of_int n = 
       
   499   if n < 0 then "~" ^ radixstring(10,"0",~n)  else radixstring(10,"0",n);
       
   500 
       
   501 val print_int = prs o string_of_int;
       
   502 
       
   503 local
       
   504 val a = ord("a") and z = ord("z") and A = ord("A") and Z = ord("Z")
       
   505 and k0 = ord("0") and k9 = ord("9")
       
   506 in
       
   507 
       
   508 (*Increment a list of letters like a reversed base 26 number.
       
   509   If head is "z",  bumps chars in tail.
       
   510   Digits are incremented as if they were integers.
       
   511   "_" and "'" are not changed.
       
   512   For making variants of identifiers. *)
       
   513 
       
   514 fun bump_int_list(c::cs) = if c="9" then "0" :: bump_int_list cs else
       
   515 	if k0 <= ord(c) andalso ord(c) < k9 then chr(ord(c)+1) :: cs
       
   516 	else "1" :: c :: cs
       
   517   | bump_int_list([]) = error("bump_int_list: not an identifier");
       
   518 
       
   519 fun bump_list([],d) = [d]
       
   520   | bump_list(["'"],d) = [d,"'"]
       
   521   | bump_list("z"::cs,_) = "a" :: bump_list(cs,"a")
       
   522   | bump_list("Z"::cs,_) = "A" :: bump_list(cs,"A")
       
   523   | bump_list("9"::cs,_) = "0" :: bump_int_list cs
       
   524   | bump_list(c::cs,_) = let val k = ord(c)
       
   525 	in if (a <= k andalso k < z) orelse (A <= k andalso k < Z) orelse
       
   526 	      (k0 <= k andalso k < k9) then chr(k+1) :: cs else
       
   527 	   if c="'" orelse c="_" then c :: bump_list(cs,"") else
       
   528 		error("bump_list: not legal in identifier: " ^
       
   529 			implode(rev(c::cs)))
       
   530 	end;
       
   531 
       
   532 end;
       
   533 
       
   534 fun bump_string s : string = implode (rev (bump_list(rev(explode s),"")));
       
   535 
       
   536 
       
   537 (*** Operations on integer lists ***)
       
   538 
       
   539 fun sum [] = 0
       
   540   | sum (n::ns) = n + sum ns;
       
   541 
       
   542 fun max[m : int]  = m
       
   543   | max(m::n::ns) = if m>n  then  max(m::ns)  else  max(n::ns)
       
   544   | max []        = raise LIST "max";
       
   545 
       
   546 fun min[m : int]  = m
       
   547   | min(m::n::ns) = if m<n  then  min(m::ns)  else  min(n::ns)
       
   548   | min []        = raise LIST "min";
       
   549 
       
   550 
       
   551 (*** Lexical scanning ***)
       
   552 
       
   553 (* [x1,...,xi,...,xn]  --->  ([x1,...,x(i-1)], [xi,..., xn])
       
   554    where xi is the first element that does not satisfy the predicate*)
       
   555 fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
       
   556   let fun take (rxs, []) = (rev rxs, [])
       
   557 	| take (rxs, x::xs) =
       
   558 	    if  pred x  then  take(x::rxs, xs)  else  (rev rxs, x::xs)
       
   559   in  take([],xs)  end;
       
   560 
       
   561 infix prefix;
       
   562 fun [] prefix _ = true
       
   563   | (x::xs) prefix (y::ys) = (x=y) andalso (xs prefix ys)
       
   564   | _ prefix _ = false;
       
   565 
       
   566 (* [x1, x2, ..., xn] ---> [x1, s, x2, s, ..., s, xn] *)
       
   567 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
       
   568   | separate _ xs = xs;
       
   569 
       
   570 (*space_implode "..." (explode "hello");  gives  "h...e...l...l...o" *)
       
   571 fun space_implode a bs = implode (separate a bs); 
       
   572 
       
   573 fun quote s = "\"" ^ s ^ "\"";
       
   574 
       
   575 (*Concatenate messages, one per line, into a string*)
       
   576 val cat_lines = implode o (map (apr(op^,"\n")));
       
   577 
       
   578 (*Scan a list of characters into "words" composed of "letters" (recognized
       
   579   by is_let) and separated by any number of non-"letters".*)
       
   580 fun scanwords is_let cs = 
       
   581   let fun scan1 [] = []
       
   582 	| scan1 cs =
       
   583 	    let val (lets, rest) = take_prefix is_let cs
       
   584 	    in  implode lets :: scanwords is_let rest  end;
       
   585   in  scan1 (#2 (take_prefix (not o is_let) cs))  end;