src/Pure/library.ML
 changeset 0 a5a9c433f639 child 24 f3d4ff75d9f2
```     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/Pure/library.ML	Thu Sep 16 12:20:38 1993 +0200
1.3 @@ -0,0 +1,585 @@
1.4 +(*  Title: 	library
1.5 +    ID:         \$Id\$
1.6 +    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
1.7 +    Copyright   1992  University of Cambridge
1.8 +
1.9 +Basic library: booleans, lists, pairs, input/output, etc.
1.10 +*)
1.11 +
1.12 +
1.13 +(**** Booleans: operators for combining predicates ****)
1.14 +
1.15 +infix orf;
1.16 +fun p orf q = fn x => p x orelse q x ;
1.17 +
1.18 +infix andf;
1.19 +fun p andf q = fn x => p x andalso q x ;
1.20 +
1.21 +fun notf p x = not (p x) ;
1.22 +
1.23 +fun orl [] = false
1.24 +  | orl (x::l) =  x  orelse  orl l;
1.25 +
1.26 +fun andl [] = true
1.27 +  | andl (x::l) =  x  andalso  andl l;
1.28 +
1.29 +(*exists pred [x1,...,xn] ======>  pred(x1)  orelse  ...  orelse  pred(xn)*)
1.30 +fun exists (pred: 'a -> bool) : 'a list -> bool =
1.31 +  let fun boolf [] = false
1.32 +        | boolf (x::l) = (pred x) orelse boolf l
1.33 +  in boolf end;
1.34 +
1.35 +(*forall pred [x1,...,xn] ======>  pred(x1)  andalso  ...  andalso  pred(xn)*)
1.36 +fun forall (pred: 'a -> bool) : 'a list -> bool =
1.37 +  let fun boolf [] = true
1.38 +        | boolf (x::l) = (pred x) andalso (boolf l)
1.39 +  in boolf end;
1.40 +
1.41 +
1.42 +(*** Lists ***)
1.43 +
1.44 +exception LIST of string;
1.45 +
1.46 +(*discriminator and selectors for lists. *)
1.47 +fun null   []   = true
1.48 +  | null (_::_) = false;
1.49 +
1.50 +fun hd   []   = raise LIST "hd"
1.51 +  | hd (a::_) = a;
1.52 +
1.53 +fun tl   []   = raise LIST "tl"
1.54 +  | tl (_::l) = l;
1.55 +
1.56 +
1.57 +(*curried functions for pairing and reversed pairing*)
1.58 +fun pair x y = (x,y);
1.59 +fun rpair x y = (y,x);
1.60 +
1.61 +fun fst(x,y) = x and snd(x,y) = y;
1.62 +
1.63 +(*Handy combinators*)
1.64 +fun curry f x y = f(x,y);
1.65 +fun uncurry f(x,y) = f x y;
1.66 +fun I x = x  and  K x y = x;
1.67 +
1.68 +(*Combine two functions forming the union of their domains*)
1.69 +infix orelf;
1.70 +fun f orelf g = fn x => f x  handle Match=> g x;
1.71 +
1.72 +
1.73 +(*Application of (infix) operator to its left or right argument*)
1.74 +fun apl (x,f) y = f(x,y);
1.75 +fun apr (f,y) x = f(x,y);
1.76 +
1.77 +
1.78 +(*functional for pairs*)
1.79 +fun pairself f (x,y) = (f x, f y);
1.80 +
1.81 +(*Apply the function to a component of a pair*)
1.82 +fun apfst f (x, y) = (f x, y);
1.83 +fun apsnd f (x, y) = (x, f y);
1.84 +
1.85 +fun square (n: int) = n*n;
1.86 +
1.87 +fun fact 0 = 1
1.88 +  | fact n = n * fact(n-1);
1.89 +
1.90 +
1.91 +(*The following versions of fold are designed to fit nicely with infixes.*)
1.92 +
1.93 +(*  (op @) (e, [x1,...,xn])  ======>   ((e @ x1) @ x2) ... @ xn
1.94 +    for operators that associate to the left.  TAIL RECURSIVE*)
1.95 +fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
1.96 +  let fun itl (e, [])  = e
1.97 +        | itl (e, a::l) = itl (f(e,a), l)
1.98 +  in  itl end;
1.99 +
1.100 +(*  (op @) ([x1,...,xn], e)  ======>   x1 @ (x2 ... @ (xn @ e))
1.101 +    for operators that associate to the right.  Not tail recursive.*)
1.102 +fun foldr f (l,e) =
1.103 +  let fun itr [] = e
1.104 +        | itr (a::l) = f(a, itr l)
1.105 +  in  itr l  end;
1.106 +
1.107 +(*  (op @) [x1,...,xn]  ======>   x1 @ (x2 ..(x[n-1]. @ xn))
1.108 +    for n>0, operators that associate to the right.  Not tail recursive.*)
1.109 +fun foldr1 f l =
1.110 +  let fun itr [x] = x
1.111 +        | itr (x::l) = f(x, itr l)
1.112 +  in  itr l  end;
1.113 +
1.114 +
1.115 +(*Length of a list.  Should unquestionably be a standard function*)
1.116 +local fun length1 (n, [ ])  = n   (*TAIL RECURSIVE*)
1.117 +        | length1 (n, x::l) = length1 (n+1, l)
1.118 +in  fun length l = length1 (0,l) end;
1.119 +
1.120 +
1.121 +(*Take the first n elements from l.*)
1.122 +fun take (n, []) = []
1.123 +  | take (n, x::xs) = if n>0 then x::take(n-1,xs)
1.124 +                      else  [];
1.125 +
1.126 +(*Drop the first n elements from l.*)
1.127 +fun drop (_, [])    = []
1.128 +  | drop (n, x::xs) = if n>0 then drop (n-1, xs)
1.129 +                             else x::xs;
1.130 +
1.131 +(*Return nth element of l, where 0 designates the first element;
1.132 +  raise EXCEPTION if list too short.*)
1.133 +fun nth_elem NL = case (drop NL) of
1.134 +    []   => raise LIST "nth_elem"
1.135 +  | x::l => x;
1.136 +
1.137 +
1.138 +(*make the list [from, from+1, ..., to]*)
1.139 +infix upto;
1.140 +fun from upto to =
1.141 +    if from>to then []  else  from :: ((from+1) upto to);
1.142 +
1.143 +(*make the list [from, from-1, ..., to]*)
1.144 +infix downto;
1.145 +fun from downto to =
1.146 +    if from<to then []  else  from :: ((from-1) downto to);
1.147 +
1.148 +(* predicate: downto0(is,n) <=> is = [n,n-1,...,0] *)
1.149 +fun downto0(i::is,n) = i=n andalso downto0(is,n-1)
1.150 +  | downto0([],n)    = n = ~1;
1.151 +
1.152 +(*Like Lisp's MAPC -- seq proc [x1,...,xn] evaluates
1.153 +  proc(x1); ... ; proc(xn) for side effects.*)
1.154 +fun seq (proc: 'a -> unit) : 'a list -> unit =
1.155 +  let fun seqf []     = ()
1.156 +        | seqf (x::l) = (proc x;  seqf l)
1.157 +  in  seqf end;
1.158 +
1.159 +
1.161 +
1.162 +exception Balance;	(*indicates non-positive argument to balancing fun*)
1.163 +
1.164 +(*Balanced folding; avoids deep nesting*)
1.165 +fun fold_bal f [x] = x
1.166 +  | fold_bal f [] = raise Balance
1.167 +  | fold_bal f xs =
1.168 +      let val k = length xs div 2
1.169 +      in  f (fold_bal f (take(k,xs)),
1.170 +	     fold_bal f (drop(k,xs)))
1.171 +      end;
1.172 +
1.173 +(*Construct something of the form f(...g(...(x)...)) for balanced access*)
1.174 +fun access_bal (f,g,x) n i =
1.175 +  let fun acc n i = 	(* 1<=i<=n*)
1.176 +          if n=1 then x else
1.177 +	  let val n2 = n div 2
1.178 +	  in  if i<=n2 then f (acc n2 i)
1.179 +	               else g (acc (n-n2) (i-n2))
1.180 +          end
1.181 +  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
1.182 +
1.183 +(*Construct ALL such accesses; could try harder to share recursive calls!*)
1.184 +fun accesses_bal (f,g,x) n =
1.185 +  let fun acc n =
1.186 +          if n=1 then [x] else
1.187 +	  let val n2 = n div 2
1.188 +	      val acc2 = acc n2
1.189 +	  in  if n-n2=n2 then map f acc2 @ map g acc2
1.190 +	                 else map f acc2 @ map g (acc (n-n2)) end
1.191 +  in  if 1<=n then acc n else raise Balance  end;
1.192 +
1.193 +
1.194 +(*** Input/Output ***)
1.195 +
1.196 +fun prs s = output(std_out,s);
1.197 +fun writeln s = prs (s ^ "\n");
1.198 +
1.199 +(*Print error message and abort to top level*)
1.200 +exception ERROR;
1.201 +fun error (msg) = (writeln msg;  raise ERROR);
1.202 +
1.203 +fun assert p msg = if p then () else error msg;
1.204 +fun deny p msg = if p then error msg else ();
1.205 +
1.206 +(*For the "test" target in Makefiles -- signifies successful termination*)
1.207 +fun maketest msg =
1.208 +    (writeln msg;
1.209 +     output(open_out "test", "Test examples ran successfully\n"));
1.210 +
1.211 +(*print a list surrounded by the brackets lpar and rpar, with comma separator
1.212 +  print nothing for empty list*)
1.213 +fun print_list (lpar, rpar, pre: 'a -> unit)  (l : 'a list) =
1.214 +    let fun prec(x) = (prs",";  pre(x))
1.215 +    in  case l of
1.216 +	    [] => ()
1.217 +	  | x::l =>  (prs lpar;  pre x;  seq prec l;  prs rpar)
1.218 +    end;
1.219 +
1.220 +(*print a list of items separated by newlines*)
1.221 +fun print_list_ln (pre: 'a -> unit)  : 'a list -> unit =
1.222 +    seq (fn x => (pre x;  writeln""));
1.223 +
1.224 +fun is_letter ch =
1.225 +  (ord"A" <= ord ch)  andalso  (ord ch <= ord"Z")   orelse
1.226 +  (ord"a" <= ord ch)  andalso  (ord ch <= ord"z");
1.227 +
1.228 +fun is_digit ch =
1.229 +  (ord"0" <= ord ch)  andalso  (ord ch <= ord"9");
1.230 +
1.231 +(*letter or _ or prime (') *)
1.232 +fun is_quasi_letter "_" = true
1.233 +  | is_quasi_letter "'" = true
1.234 +  | is_quasi_letter ch  = is_letter ch;
1.235 +
1.236 +(*white space: blanks, tabs, newlines*)
1.237 +val is_blank : string -> bool = fn
1.238 +     " " => true  |  "\t" => true  |  "\n" => true  |  _ => false;
1.239 +
1.240 +val is_letdig = is_quasi_letter orf is_digit;
1.241 +
1.242 +val to_lower =
1.243 +  let
1.244 +    fun lower ch =
1.245 +      if ch >= "A" andalso ch <= "Z" then
1.246 +        chr (ord ch - ord "A" + ord "a")
1.247 +      else ch;
1.248 +  in
1.249 +    implode o (map lower) o explode
1.250 +  end;
1.251 +
1.252 +
1.253 +(*** Timing ***)
1.254 +
1.255 +(*Unconditional timing function*)
1.256 +val timeit = cond_timeit true;
1.257 +
1.258 +(*Timed application function*)
1.259 +fun timeap f x = timeit(fn()=> f x);
1.260 +
1.261 +(*Timed "use" function, printing filenames*)
1.262 +fun time_use fname = timeit(fn()=>
1.263 +   (writeln("\n**** Starting " ^ fname ^ " ****");  use fname;
1.264 +    writeln("\n**** Finished " ^ fname ^ " ****")));
1.265 +
1.266 +
1.267 +(*** Misc functions ***)
1.268 +
1.269 +(*Function exponentiation: f(...(f x)...) with n applications of f *)
1.270 +fun funpow n f x =
1.271 +  let fun rep (0,x) = x
1.272 +        | rep (n,x) = rep (n-1, f x)
1.273 +  in  rep (n,x)  end;
1.274 +
1.275 +(*Combine two lists forming a list of pairs:
1.276 +  [x1,...,xn] ~~ [y1,...,yn]  ======>   [(x1,y1), ..., (xn,yn)] *)
1.277 +infix ~~;
1.278 +fun []   ~~  []   = []
1.279 +  | (x::xs) ~~ (y::ys) = (x,y) :: (xs ~~ ys)
1.280 +  |  _   ~~   _   = raise LIST "~~";
1.281 +
1.282 +(*Inverse of ~~;  the old 'split'.
1.283 +   [(x1,y1), ..., (xn,yn)]  ======>  ( [x1,...,xn] , [y1,...,yn] ) *)
1.284 +fun split_list (l: ('a*'b)list) = (map #1 l, map #2 l);
1.285 +
1.286 +(*make the list [x; x; ...; x] of length n*)
1.287 +fun replicate n (x: 'a) : 'a list =
1.288 +  let fun rep (0,xs) = xs
1.289 +        | rep (n,xs) = rep(n-1, x::xs)
1.290 +  in   if n<0 then raise LIST "replicate"
1.291 +       else rep (n,[])
1.292 +  end;
1.293 +
1.294 +(*Flatten a list of lists to a list.*)
1.295 +fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls,[]);
1.296 +
1.297 +
1.298 +(*** polymorphic set operations ***)
1.299 +
1.300 +(*membership in a list*)
1.301 +infix mem;
1.302 +fun x mem []  =  false
1.303 +  | x mem (y::l)  =  (x=y) orelse (x mem l);
1.304 +
1.305 +(*insertion into list if not already there*)
1.306 +infix ins;
1.307 +fun x ins xs = if x mem xs then  xs   else  x::xs;
1.308 +
1.309 +(*union of sets represented as lists: no repetitions*)
1.310 +infix union;
1.311 +fun   xs    union [] = xs
1.312 +  |   []    union ys = ys
1.313 +  | (x::xs) union ys = xs union (x ins ys);
1.314 +
1.315 +infix inter;
1.316 +fun   []    inter ys = []
1.317 +  | (x::xs) inter ys = if x mem ys then x::(xs inter ys)
1.318 +                                   else     xs inter ys;
1.319 +
1.320 +infix subset;
1.321 +fun   []    subset ys = true
1.322 +  | (x::xs) subset ys = x mem ys   andalso  xs subset ys;
1.323 +
1.324 +(*removing an element from a list WITHOUT duplicates*)
1.325 +infix \;
1.326 +fun (y::ys) \ x = if x=y then ys else y::(ys \ x)
1.327 +  |   []    \ x = [];
1.328 +
1.329 +infix \\;
1.330 +val op \\ = foldl (op \);
1.331 +
1.332 +(*** option stuff ***)
1.333 +
1.334 +datatype 'a option = None | Some of 'a;
1.335 +
1.336 +exception OPTION of string;
1.337 +
1.338 +fun the (Some x) = x
1.339 +  | the None = raise OPTION "the";
1.340 +
1.341 +fun is_some (Some _) = true
1.342 +  | is_some None = false;
1.343 +
1.344 +fun is_none (Some _) = false
1.345 +  | is_none None = true;
1.346 +
1.347 +
1.348 +(*** Association lists ***)
1.349 +
1.350 +(*Association list lookup*)
1.351 +fun assoc ([], key) = None
1.352 +  | assoc ((keyi,xi)::pairs, key) =
1.353 +      if key=keyi then Some xi  else assoc (pairs,key);
1.354 +
1.355 +fun assocs ps x = case assoc(ps,x) of None => [] | Some(ys) => ys;
1.356 +
1.357 +(*Association list update*)
1.358 +fun overwrite(al,p as (key,_)) =
1.359 +  let fun over((q as (keyi,_))::pairs) =
1.360 +	    if keyi=key then p::pairs else q::(over pairs)
1.361 +	| over[] = [p]
1.362 +  in over al end;
1.363 +
1.364 +(*Copy the list preserving elements that satisfy the predicate*)
1.365 +fun filter (pred: 'a->bool) : 'a list -> 'a list =
1.366 +  let fun filt [] = []
1.367 +        | filt (x::xs) =  if pred(x) then x :: filt xs  else  filt xs
1.368 +  in  filt   end;
1.369 +
1.370 +fun filter_out f = filter (not o f);
1.371 +
1.372 +
1.373 +(*** List operations, generalized to an arbitrary equality function "eq"
1.374 +     -- so what good are equality types?? ***)
1.375 +
1.376 +(*removing an element from a list -- possibly WITH duplicates*)
1.377 +fun gen_rem eq (xs,y) = filter_out (fn x => eq(x,y)) xs;
1.378 +
1.379 +(*generalized membership test*)
1.380 +fun gen_mem eq (x, [])     =  false
1.381 +  | gen_mem eq (x, y::ys)  =  eq(x,y) orelse gen_mem eq (x,ys);
1.382 +
1.383 +(*generalized insertion*)
1.384 +fun gen_ins eq (x,xs) = if gen_mem eq (x,xs) then  xs   else  x::xs;
1.385 +
1.386 +(*generalized union*)
1.387 +fun gen_union eq (xs,[]) = xs
1.388 +  | gen_union eq ([],ys) = ys
1.389 +  | gen_union eq (x::xs,ys) = gen_union eq (xs, gen_ins eq (x,ys));
1.390 +
1.391 +(*Generalized association list lookup*)
1.392 +fun gen_assoc eq ([], key) = None
1.393 +  | gen_assoc eq ((keyi,xi)::pairs, key) =
1.394 +      if eq(key,keyi) then Some xi  else gen_assoc eq (pairs,key);
1.395 +
1.396 +(** Finding list elements and duplicates **)
1.397 +
1.398 +(* find the position of an element in a list *)
1.399 +fun find(x,ys) =
1.400 +    let fun f(y::ys,i) = if x=y then i else f(ys,i+1)
1.401 +          | f(_,_) = raise LIST "find"
1.402 +    in f(ys,0) end;
1.403 +
1.404 +(*Returns the tail beginning with the first repeated element, or []. *)
1.405 +fun findrep [] = []
1.406 +  | findrep (x::xs) = if  x mem xs  then  x::xs   else   findrep xs;
1.407 +
1.408 +fun distinct1 (seen, []) = rev seen
1.409 +  | distinct1 (seen, x::xs) =
1.410 +      if x mem seen then distinct1 (seen, xs)
1.411 +    		    else distinct1 (x::seen, xs);
1.412 +
1.413 +(*Makes a list of the distinct members of the input*)
1.414 +fun distinct xs = distinct1([],xs);
1.415 +
1.416 +
1.417 +(*Use the keyfun to make a list of (x,key) pairs.*)
1.418 +fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
1.419 +  let fun keypair x = (x, keyfun x)
1.420 +  in   map keypair  end;
1.421 +
1.422 +(*Given a list of (x,key) pairs and a searchkey
1.423 +  return the list of xs from each pair whose key equals searchkey*)
1.424 +fun keyfilter [] searchkey = []
1.425 +  | keyfilter ((x,key)::pairs) searchkey =
1.426 +	if key=searchkey then x :: keyfilter pairs searchkey
1.427 +	else keyfilter pairs searchkey;
1.428 +
1.429 +fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
1.430 +  | mapfilter f (x::xs) =
1.431 +      case (f x) of
1.432 +	  None => mapfilter f xs
1.433 +	| Some y => y :: mapfilter f xs;
1.434 +
1.435 +
1.436 +(*Partition list into elements that satisfy predicate and those that don't.
1.437 +  Preserves order of elements in both lists. *)
1.438 +fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
1.440 +	  | part (x::xs, (ys, ns)) = if pred(x)
1.441 +	    then  part (xs, (x::ys, ns))
1.442 +	    else  part (xs, (ys, x::ns))
1.443 +    in  part (rev ys, ([],[]))  end;
1.444 +
1.445 +
1.446 +fun partition_eq (eq:'a * 'a -> bool) =
1.447 +    let fun part [] = []
1.448 +	  | part (x::ys) = let val (xs,xs') = partition (apl(x,eq)) ys
1.449 +			   in (x::xs)::(part xs') end
1.450 +    in part end;
1.451 +
1.452 +
1.453 +(*Partition a list into buckets  [ bi, b(i+1),...,bj ]
1.454 +   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
1.455 +fun partition_list p i j =
1.456 +  let fun part k xs =
1.457 +            if k>j then
1.458 +              (case xs of [] => []
1.459 +                         | _ => raise LIST "partition_list")
1.460 +            else
1.461 +	    let val (ns,rest) = partition (p k) xs;
1.462 +	    in  ns :: part(k+1)rest  end
1.463 +  in  part i end;
1.464 +
1.465 +
1.466 +(*Insertion sort.  Stable (does not reorder equal elements)
1.467 +  'less' is less-than test on type 'a. *)
1.468 +fun sort (less: 'a*'a -> bool) =
1.469 +  let fun insert (x, []) = [x]
1.470 +        | insert (x, y::ys) =
1.471 +              if less(y,x) then y :: insert (x,ys) else x::y::ys;
1.472 +      fun sort1 [] = []
1.473 +        | sort1 (x::xs) = insert (x, sort1 xs)
1.474 +  in  sort1  end;
1.475 +
1.476 +(*Transitive Closure. Not Warshall's algorithm*)
1.477 +fun transitive_closure [] = []
1.478 +  | transitive_closure ((x,ys)::ps) =
1.479 +      let val qs = transitive_closure ps
1.480 +          val zs = foldl (fn (zs,y) => assocs qs y union zs) (ys,ys)
1.481 +          fun step(u,us) = (u, if x mem us then zs union us else us)
1.482 +      in (x,zs) :: map step qs end;
1.483 +
1.484 +(*** Converting integers to strings, generating identifiers, etc. ***)
1.485 +
1.486 +(*Expand the number in the given base
1.487 + example: radixpand(2, 8)  gives   [1, 0, 0, 0] *)
1.488 +fun radixpand (base,num) : int list =
1.489 +  let fun radix (n,tail) =
1.490 +  	if n<base then n :: tail
1.491 +	else radix (n div base, (n mod base) :: tail)
1.492 +  in  radix (num,[])  end;
1.493 +
1.494 +(*Expands a number into a string of characters starting from "zerochar"
1.495 + example: radixstring(2,"0", 8)  gives  "1000" *)
1.497 +  let val offset = ord(zerochar);
1.498 +      fun chrof n = chr(offset+n)
1.499 +  in  implode (map chrof (radixpand (base,num)))  end;
1.500 +
1.501 +fun string_of_int n =
1.502 +  if n < 0 then "~" ^ radixstring(10,"0",~n)  else radixstring(10,"0",n);
1.503 +
1.504 +val print_int = prs o string_of_int;
1.505 +
1.506 +local
1.507 +val a = ord("a") and z = ord("z") and A = ord("A") and Z = ord("Z")
1.508 +and k0 = ord("0") and k9 = ord("9")
1.509 +in
1.510 +
1.511 +(*Increment a list of letters like a reversed base 26 number.
1.512 +  If head is "z",  bumps chars in tail.
1.513 +  Digits are incremented as if they were integers.
1.514 +  "_" and "'" are not changed.
1.515 +  For making variants of identifiers. *)
1.516 +
1.517 +fun bump_int_list(c::cs) = if c="9" then "0" :: bump_int_list cs else
1.518 +	if k0 <= ord(c) andalso ord(c) < k9 then chr(ord(c)+1) :: cs
1.519 +	else "1" :: c :: cs
1.520 +  | bump_int_list([]) = error("bump_int_list: not an identifier");
1.521 +
1.522 +fun bump_list([],d) = [d]
1.523 +  | bump_list(["'"],d) = [d,"'"]
1.524 +  | bump_list("z"::cs,_) = "a" :: bump_list(cs,"a")
1.525 +  | bump_list("Z"::cs,_) = "A" :: bump_list(cs,"A")
1.526 +  | bump_list("9"::cs,_) = "0" :: bump_int_list cs
1.527 +  | bump_list(c::cs,_) = let val k = ord(c)
1.528 +	in if (a <= k andalso k < z) orelse (A <= k andalso k < Z) orelse
1.529 +	      (k0 <= k andalso k < k9) then chr(k+1) :: cs else
1.530 +	   if c="'" orelse c="_" then c :: bump_list(cs,"") else
1.531 +		error("bump_list: not legal in identifier: " ^
1.532 +			implode(rev(c::cs)))
1.533 +	end;
1.534 +
1.535 +end;
1.536 +
1.537 +fun bump_string s : string = implode (rev (bump_list(rev(explode s),"")));
1.538 +
1.539 +
1.540 +(*** Operations on integer lists ***)
1.541 +
1.542 +fun sum [] = 0
1.543 +  | sum (n::ns) = n + sum ns;
1.544 +
1.545 +fun max[m : int]  = m
1.546 +  | max(m::n::ns) = if m>n  then  max(m::ns)  else  max(n::ns)
1.547 +  | max []        = raise LIST "max";
1.548 +
1.549 +fun min[m : int]  = m
1.550 +  | min(m::n::ns) = if m<n  then  min(m::ns)  else  min(n::ns)
1.551 +  | min []        = raise LIST "min";
1.552 +
1.553 +
1.554 +(*** Lexical scanning ***)
1.555 +
1.556 +(* [x1,...,xi,...,xn]  --->  ([x1,...,x(i-1)], [xi,..., xn])
1.557 +   where xi is the first element that does not satisfy the predicate*)
1.558 +fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
1.559 +  let fun take (rxs, []) = (rev rxs, [])
1.560 +	| take (rxs, x::xs) =
1.561 +	    if  pred x  then  take(x::rxs, xs)  else  (rev rxs, x::xs)
1.562 +  in  take([],xs)  end;
1.563 +
1.564 +infix prefix;
1.565 +fun [] prefix _ = true
1.566 +  | (x::xs) prefix (y::ys) = (x=y) andalso (xs prefix ys)
1.567 +  | _ prefix _ = false;
1.568 +
1.569 +(* [x1, x2, ..., xn] ---> [x1, s, x2, s, ..., s, xn] *)
1.570 +fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
1.571 +  | separate _ xs = xs;
1.572 +
1.573 +(*space_implode "..." (explode "hello");  gives  "h...e...l...l...o" *)
1.574 +fun space_implode a bs = implode (separate a bs);
1.575 +
1.576 +fun quote s = "\"" ^ s ^ "\"";
1.577 +
1.578 +(*Concatenate messages, one per line, into a string*)
1.579 +val cat_lines = implode o (map (apr(op^,"\n")));
1.580 +
1.581 +(*Scan a list of characters into "words" composed of "letters" (recognized
1.582 +  by is_let) and separated by any number of non-"letters".*)
1.583 +fun scanwords is_let cs =
1.584 +  let fun scan1 [] = []
1.585 +	| scan1 cs =
1.586 +	    let val (lets, rest) = take_prefix is_let cs
1.587 +	    in  implode lets :: scanwords is_let rest  end;
1.588 +  in  scan1 (#2 (take_prefix (not o is_let) cs))  end;
```