src/Pure/library.ML
author clasohm
Tue Oct 24 13:41:06 1995 +0100 (1995-10-24)
changeset 1290 ee8f41456d28
parent 955 aa0c5f9daf5b
child 1364 8ea1a962ad72
permissions -rw-r--r--
added space_explode and relative_path
wenzelm@41
     1
(*  Title:      Pure/library.ML
clasohm@0
     2
    ID:         $Id$
wenzelm@233
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@0
     4
    Copyright   1992  University of Cambridge
clasohm@0
     5
wenzelm@233
     6
Basic library: functions, options, pairs, booleans, lists, integers,
wenzelm@233
     7
strings, lists as sets, association lists, generic tables, balanced trees,
wenzelm@233
     8
input / output, timing, filenames, misc functions.
clasohm@0
     9
*)
clasohm@0
    10
clasohm@0
    11
wenzelm@233
    12
(** functions **)
clasohm@0
    13
wenzelm@233
    14
(*handy combinators*)
wenzelm@233
    15
fun curry f x y = f (x, y);
wenzelm@233
    16
fun uncurry f (x, y) = f x y;
wenzelm@233
    17
fun I x = x;
wenzelm@233
    18
fun K x y = x;
clasohm@0
    19
wenzelm@380
    20
(*reverse apply*)
wenzelm@410
    21
infix |>;
wenzelm@410
    22
fun (x |> f) = f x;
wenzelm@380
    23
wenzelm@233
    24
(*combine two functions forming the union of their domains*)
wenzelm@233
    25
infix orelf;
wenzelm@233
    26
fun f orelf g = fn x => f x handle Match => g x;
clasohm@0
    27
wenzelm@233
    28
(*application of (infix) operator to its left or right argument*)
wenzelm@233
    29
fun apl (x, f) y = f (x, y);
wenzelm@233
    30
fun apr (f, y) x = f (x, y);
clasohm@0
    31
wenzelm@233
    32
(*functional for pairs*)
wenzelm@233
    33
fun pairself f (x, y) = (f x, f y);
clasohm@0
    34
wenzelm@233
    35
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
    36
fun funpow n f x =
wenzelm@233
    37
  let fun rep (0, x) = x
wenzelm@233
    38
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
    39
  in rep (n, x) end;
wenzelm@160
    40
wenzelm@160
    41
wenzelm@160
    42
wenzelm@233
    43
(** options **)
clasohm@0
    44
clasohm@0
    45
datatype 'a option = None | Some of 'a;
clasohm@0
    46
clasohm@0
    47
exception OPTION of string;
clasohm@0
    48
clasohm@0
    49
fun the (Some x) = x
clasohm@0
    50
  | the None = raise OPTION "the";
clasohm@0
    51
wenzelm@255
    52
fun if_none None y = y
wenzelm@255
    53
  | if_none (Some x) _ = x;
wenzelm@255
    54
clasohm@0
    55
fun is_some (Some _) = true
clasohm@0
    56
  | is_some None = false;
clasohm@0
    57
clasohm@0
    58
fun is_none (Some _) = false
clasohm@0
    59
  | is_none None = true;
clasohm@0
    60
wenzelm@233
    61
fun apsome f (Some x) = Some (f x)
wenzelm@233
    62
  | apsome _ None = None;
clasohm@0
    63
wenzelm@233
    64
wenzelm@233
    65
wenzelm@233
    66
(** pairs **)
wenzelm@233
    67
wenzelm@233
    68
fun pair x y = (x, y);
wenzelm@233
    69
fun rpair x y = (y, x);
wenzelm@233
    70
wenzelm@233
    71
fun fst (x, y) = x;
wenzelm@233
    72
fun snd (x, y) = y;
wenzelm@233
    73
wenzelm@233
    74
fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
wenzelm@233
    75
fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
wenzelm@233
    76
wenzelm@233
    77
fun swap (x, y) = (y, x);
wenzelm@233
    78
wenzelm@233
    79
(*apply the function to a component of a pair*)
wenzelm@233
    80
fun apfst f (x, y) = (f x, y);
wenzelm@233
    81
fun apsnd f (x, y) = (x, f y);
wenzelm@233
    82
wenzelm@233
    83
wenzelm@233
    84
wenzelm@233
    85
(** booleans **)
wenzelm@233
    86
wenzelm@233
    87
(* equality *)
wenzelm@233
    88
wenzelm@233
    89
fun equal x y = x = y;
wenzelm@233
    90
fun not_equal x y = x <> y;
wenzelm@233
    91
wenzelm@233
    92
wenzelm@233
    93
(* operators for combining predicates *)
wenzelm@233
    94
wenzelm@233
    95
infix orf;
wenzelm@233
    96
fun p orf q = fn x => p x orelse q x;
wenzelm@233
    97
wenzelm@233
    98
infix andf;
wenzelm@233
    99
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   100
wenzelm@233
   101
fun notf p x = not (p x);
clasohm@0
   102
wenzelm@233
   103
wenzelm@233
   104
(* predicates on lists *)
wenzelm@233
   105
wenzelm@233
   106
fun orl [] = false
wenzelm@233
   107
  | orl (x :: xs) = x orelse orl xs;
wenzelm@233
   108
wenzelm@233
   109
fun andl [] = true
wenzelm@233
   110
  | andl (x :: xs) = x andalso andl xs;
wenzelm@233
   111
wenzelm@233
   112
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   113
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   114
  let fun boolf [] = false
wenzelm@233
   115
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   116
  in boolf end;
wenzelm@233
   117
wenzelm@233
   118
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   119
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   120
  let fun boolf [] = true
wenzelm@233
   121
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   122
  in boolf end;
clasohm@0
   123
wenzelm@233
   124
wenzelm@380
   125
(* flags *)
wenzelm@380
   126
wenzelm@380
   127
fun set flag = (flag := true; true);
wenzelm@380
   128
fun reset flag = (flag := false; false);
wenzelm@380
   129
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   130
wenzelm@380
   131
wenzelm@233
   132
wenzelm@233
   133
(** lists **)
wenzelm@233
   134
wenzelm@233
   135
exception LIST of string;
wenzelm@233
   136
wenzelm@233
   137
fun null [] = true
wenzelm@233
   138
  | null (_ :: _) = false;
wenzelm@233
   139
wenzelm@233
   140
fun hd [] = raise LIST "hd"
wenzelm@233
   141
  | hd (x :: _) = x;
wenzelm@233
   142
wenzelm@233
   143
fun tl [] = raise LIST "tl"
wenzelm@233
   144
  | tl (_ :: xs) = xs;
wenzelm@233
   145
wenzelm@233
   146
fun cons x xs = x :: xs;
wenzelm@233
   147
wenzelm@233
   148
wenzelm@233
   149
(* fold *)
wenzelm@233
   150
wenzelm@233
   151
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   152
wenzelm@233
   153
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   154
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   155
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   156
  let fun itl (e, [])  = e
wenzelm@233
   157
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   158
  in  itl end;
wenzelm@233
   159
wenzelm@233
   160
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   161
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   162
fun foldr f (l, e) =
wenzelm@233
   163
  let fun itr [] = e
wenzelm@233
   164
        | itr (a::l) = f(a, itr l)
wenzelm@233
   165
  in  itr l  end;
wenzelm@233
   166
wenzelm@233
   167
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   168
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   169
fun foldr1 f l =
wenzelm@233
   170
  let fun itr [x] = x                       (* FIXME [] case: elim warn (?) *)
wenzelm@233
   171
        | itr (x::l) = f(x, itr l)
wenzelm@233
   172
  in  itr l  end;
wenzelm@233
   173
wenzelm@233
   174
wenzelm@233
   175
(* basic list functions *)
wenzelm@233
   176
wenzelm@233
   177
(*length of a list, should unquestionably be a standard function*)
wenzelm@233
   178
local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
wenzelm@233
   179
        | length1 (n, x :: xs) = length1 (n + 1, xs)
wenzelm@233
   180
in  fun length l = length1 (0, l) end;
wenzelm@233
   181
wenzelm@233
   182
(*take the first n elements from a list*)
wenzelm@233
   183
fun take (n, []) = []
wenzelm@233
   184
  | take (n, x :: xs) =
wenzelm@233
   185
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   186
wenzelm@233
   187
(*drop the first n elements from a list*)
wenzelm@233
   188
fun drop (n, []) = []
wenzelm@233
   189
  | drop (n, x :: xs) =
wenzelm@233
   190
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   191
wenzelm@233
   192
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   193
  raise EXCEPTION if list too short*)
wenzelm@233
   194
fun nth_elem NL =
wenzelm@233
   195
  (case drop NL of
wenzelm@233
   196
    [] => raise LIST "nth_elem"
wenzelm@233
   197
  | x :: _ => x);
wenzelm@233
   198
wenzelm@233
   199
(*last element of a list*)
wenzelm@233
   200
fun last_elem [] = raise LIST "last_elem"
wenzelm@233
   201
  | last_elem [x] = x
wenzelm@233
   202
  | last_elem (_ :: xs) = last_elem xs;
wenzelm@233
   203
wenzelm@233
   204
(*find the position of an element in a list*)
wenzelm@233
   205
fun find (x, ys) =
wenzelm@233
   206
  let fun f (y :: ys, i) = if x = y then i else f (ys, i + 1)
wenzelm@233
   207
        | f (_, _) = raise LIST "find"
wenzelm@233
   208
  in f (ys, 0) end;
wenzelm@233
   209
wenzelm@233
   210
(*flatten a list of lists to a list*)
wenzelm@233
   211
fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
wenzelm@233
   212
wenzelm@233
   213
wenzelm@233
   214
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   215
  (proc x1; ...; proc xn) for side effects*)
wenzelm@233
   216
fun seq (proc: 'a -> unit) : 'a list -> unit =
wenzelm@233
   217
  let fun seqf [] = ()
wenzelm@233
   218
        | seqf (x :: xs) = (proc x; seqf xs)
wenzelm@233
   219
  in seqf end;
wenzelm@233
   220
wenzelm@233
   221
wenzelm@233
   222
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   223
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   224
  | separate _ xs = xs;
wenzelm@233
   225
wenzelm@233
   226
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   227
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   228
  let fun rep (0, xs) = xs
wenzelm@233
   229
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   230
  in
wenzelm@233
   231
    if n < 0 then raise LIST "replicate"
wenzelm@233
   232
    else rep (n, [])
wenzelm@233
   233
  end;
wenzelm@233
   234
wenzelm@233
   235
wenzelm@233
   236
(* filter *)
wenzelm@233
   237
wenzelm@233
   238
(*copy the list preserving elements that satisfy the predicate*)
wenzelm@233
   239
fun filter (pred: 'a->bool) : 'a list -> 'a list =
clasohm@0
   240
  let fun filt [] = []
wenzelm@233
   241
        | filt (x :: xs) = if pred x then x :: filt xs else filt xs
wenzelm@233
   242
  in filt end;
clasohm@0
   243
clasohm@0
   244
fun filter_out f = filter (not o f);
clasohm@0
   245
clasohm@0
   246
wenzelm@233
   247
fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
wenzelm@233
   248
  | mapfilter f (x :: xs) =
wenzelm@233
   249
      (case f x of
wenzelm@233
   250
        None => mapfilter f xs
wenzelm@233
   251
      | Some y => y :: mapfilter f xs);
wenzelm@233
   252
wenzelm@233
   253
wenzelm@380
   254
fun find_first _ [] = None
wenzelm@380
   255
  | find_first pred (x :: xs) =
wenzelm@380
   256
      if pred x then Some x else find_first pred xs;
wenzelm@380
   257
wenzelm@380
   258
wenzelm@233
   259
(* lists of pairs *)
wenzelm@233
   260
wenzelm@380
   261
fun map2 _ ([], []) = []
wenzelm@380
   262
  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
wenzelm@380
   263
  | map2 _ _ = raise LIST "map2";
wenzelm@380
   264
wenzelm@380
   265
fun exists2 _ ([], []) = false
wenzelm@380
   266
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
wenzelm@380
   267
  | exists2 _ _ = raise LIST "exists2";
wenzelm@380
   268
wenzelm@380
   269
fun forall2 _ ([], []) = true
wenzelm@380
   270
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
wenzelm@380
   271
  | forall2 _ _ = raise LIST "forall2";
wenzelm@380
   272
wenzelm@233
   273
(*combine two lists forming a list of pairs:
wenzelm@233
   274
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   275
infix ~~;
wenzelm@233
   276
fun [] ~~ [] = []
wenzelm@233
   277
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@233
   278
  | _ ~~ _ = raise LIST "~~";
wenzelm@233
   279
wenzelm@233
   280
wenzelm@233
   281
(*inverse of ~~; the old 'split':
wenzelm@233
   282
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
wenzelm@233
   283
fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
wenzelm@233
   284
wenzelm@233
   285
wenzelm@233
   286
(* prefixes, suffixes *)
wenzelm@233
   287
wenzelm@233
   288
infix prefix;
wenzelm@233
   289
fun [] prefix _ = true
wenzelm@233
   290
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   291
  | _ prefix _ = false;
wenzelm@233
   292
wenzelm@233
   293
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   294
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   295
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   296
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   297
        | take (rxs, x :: xs) =
wenzelm@255
   298
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   299
  in  take([], xs)  end;
wenzelm@233
   300
wenzelm@233
   301
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   302
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   303
fun take_suffix _ [] = ([], [])
wenzelm@233
   304
  | take_suffix pred (x :: xs) =
wenzelm@233
   305
      (case take_suffix pred xs of
wenzelm@233
   306
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   307
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   308
wenzelm@233
   309
wenzelm@233
   310
wenzelm@233
   311
(** integers **)
wenzelm@233
   312
wenzelm@233
   313
fun inc i = i := ! i + 1;
wenzelm@233
   314
fun dec i = i := ! i - 1;
wenzelm@233
   315
wenzelm@233
   316
wenzelm@233
   317
(* lists of integers *)
wenzelm@233
   318
wenzelm@233
   319
(*make the list [from, from + 1, ..., to]*)
wenzelm@233
   320
infix upto;
wenzelm@233
   321
fun from upto to =
wenzelm@233
   322
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   323
wenzelm@233
   324
(*make the list [from, from - 1, ..., to]*)
wenzelm@233
   325
infix downto;
wenzelm@233
   326
fun from downto to =
wenzelm@233
   327
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   328
wenzelm@233
   329
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   330
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   331
  | downto0 ([], n) = n = ~1;
wenzelm@233
   332
wenzelm@233
   333
wenzelm@233
   334
(* operations on integer lists *)
clasohm@0
   335
wenzelm@233
   336
fun sum [] = 0
wenzelm@233
   337
  | sum (n :: ns) = n + sum ns;
wenzelm@233
   338
wenzelm@233
   339
fun max [m:int] = m
wenzelm@233
   340
  | max (m :: n :: ns) = if m > n then max (m :: ns) else max (n :: ns)
wenzelm@233
   341
  | max [] = raise LIST "max";
wenzelm@233
   342
wenzelm@233
   343
fun min [m:int] = m
wenzelm@233
   344
  | min (m :: n :: ns) = if m < n then min (m :: ns) else min (n :: ns)
wenzelm@233
   345
  | min [] = raise LIST "min";
wenzelm@233
   346
wenzelm@233
   347
wenzelm@233
   348
(* convert integers to strings *)
wenzelm@233
   349
wenzelm@233
   350
(*expand the number in the given base;
wenzelm@233
   351
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   352
fun radixpand (base, num) : int list =
wenzelm@233
   353
  let
wenzelm@233
   354
    fun radix (n, tail) =
wenzelm@233
   355
      if n < base then n :: tail
wenzelm@233
   356
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   357
  in radix (num, []) end;
wenzelm@233
   358
wenzelm@233
   359
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   360
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   361
fun radixstring (base, zerochar, num) =
wenzelm@233
   362
  let val offset = ord zerochar;
wenzelm@233
   363
      fun chrof n = chr (offset + n)
wenzelm@233
   364
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   365
wenzelm@233
   366
wenzelm@233
   367
fun string_of_int n =
wenzelm@233
   368
  if n < 0 then "~" ^ radixstring (10, "0", ~n) else radixstring (10, "0", n);
wenzelm@233
   369
wenzelm@233
   370
wenzelm@233
   371
wenzelm@233
   372
(** strings **)
wenzelm@233
   373
wenzelm@233
   374
fun is_letter ch =
wenzelm@233
   375
  ord "A" <= ord ch andalso ord ch <= ord "Z" orelse
wenzelm@233
   376
  ord "a" <= ord ch andalso ord ch <= ord "z";
wenzelm@233
   377
wenzelm@233
   378
fun is_digit ch =
wenzelm@233
   379
  ord "0" <= ord ch andalso ord ch <= ord "9";
wenzelm@233
   380
wenzelm@233
   381
(*letter or _ or prime (')*)
wenzelm@233
   382
fun is_quasi_letter "_" = true
wenzelm@233
   383
  | is_quasi_letter "'" = true
wenzelm@233
   384
  | is_quasi_letter ch = is_letter ch;
wenzelm@233
   385
lcp@512
   386
(*white space: blanks, tabs, newlines, formfeeds*)
wenzelm@233
   387
val is_blank : string -> bool =
lcp@512
   388
  fn " " => true | "\t" => true | "\n" => true | "\^L" => true | _ => false;
wenzelm@233
   389
wenzelm@233
   390
val is_letdig = is_quasi_letter orf is_digit;
wenzelm@233
   391
wenzelm@233
   392
wenzelm@233
   393
(*lower all chars of string*)
wenzelm@233
   394
val to_lower =
wenzelm@233
   395
  let
wenzelm@233
   396
    fun lower ch =
wenzelm@233
   397
      if ch >= "A" andalso ch <= "Z" then
wenzelm@233
   398
        chr (ord ch - ord "A" + ord "a")
wenzelm@233
   399
      else ch;
wenzelm@233
   400
  in implode o (map lower) o explode end;
wenzelm@233
   401
wenzelm@233
   402
lcp@512
   403
(*enclose in brackets*)
lcp@512
   404
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@255
   405
wenzelm@233
   406
(*simple quoting (does not escape special chars)*)
lcp@512
   407
val quote = enclose "\"" "\"";
wenzelm@233
   408
wenzelm@233
   409
(*space_implode "..." (explode "hello"); gives "h...e...l...l...o"*)
wenzelm@233
   410
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   411
wenzelm@255
   412
val commas = space_implode ", ";
wenzelm@380
   413
val commas_quote = commas o map quote;
wenzelm@255
   414
wenzelm@233
   415
(*concatenate messages, one per line, into a string*)
wenzelm@255
   416
val cat_lines = space_implode "\n";
wenzelm@233
   417
clasohm@1290
   418
(*space_explode "." "h.e..l.lo"; gives ["h", "e", "l", "lo"]*)
clasohm@1290
   419
fun space_explode sep s =
clasohm@1290
   420
  let fun divide [] "" = []
clasohm@1290
   421
        | divide [] part = [part]
clasohm@1290
   422
        | divide (c::s) part =
clasohm@1290
   423
            if c = sep then
clasohm@1290
   424
              (if part = "" then divide s "" else part :: divide s "")
clasohm@1290
   425
            else divide s (part ^ c)
clasohm@1290
   426
  in divide (explode s) "" end;
wenzelm@233
   427
wenzelm@233
   428
wenzelm@233
   429
(** lists as sets **)
wenzelm@233
   430
wenzelm@233
   431
(*membership in a list*)
wenzelm@233
   432
infix mem;
wenzelm@233
   433
fun x mem [] = false
wenzelm@233
   434
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   435
clasohm@0
   436
(*generalized membership test*)
wenzelm@233
   437
fun gen_mem eq (x, []) = false
wenzelm@233
   438
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   439
wenzelm@233
   440
wenzelm@233
   441
(*insertion into list if not already there*)
wenzelm@233
   442
infix ins;
wenzelm@233
   443
fun x ins xs = if x mem xs then xs else x :: xs;
clasohm@0
   444
clasohm@0
   445
(*generalized insertion*)
wenzelm@233
   446
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   447
wenzelm@233
   448
wenzelm@233
   449
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   450
infix union;
wenzelm@233
   451
fun xs union [] = xs
wenzelm@233
   452
  | [] union ys = ys
wenzelm@233
   453
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   454
clasohm@0
   455
(*generalized union*)
wenzelm@233
   456
fun gen_union eq (xs, []) = xs
wenzelm@233
   457
  | gen_union eq ([], ys) = ys
wenzelm@233
   458
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   459
wenzelm@233
   460
wenzelm@233
   461
(*intersection*)
wenzelm@233
   462
infix inter;
wenzelm@233
   463
fun [] inter ys = []
wenzelm@233
   464
  | (x :: xs) inter ys =
wenzelm@233
   465
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   466
wenzelm@233
   467
wenzelm@233
   468
(*subset*)
wenzelm@233
   469
infix subset;
wenzelm@233
   470
fun [] subset ys = true
wenzelm@233
   471
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   472
wenzelm@233
   473
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
wenzelm@233
   474
wenzelm@233
   475
wenzelm@265
   476
(*eq_set*)
wenzelm@265
   477
wenzelm@265
   478
fun eq_set (xs, ys) =
wenzelm@265
   479
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@265
   480
wenzelm@265
   481
wenzelm@233
   482
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   483
infix \;
wenzelm@233
   484
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   485
  | [] \ x = [];
wenzelm@233
   486
wenzelm@233
   487
infix \\;
wenzelm@233
   488
val op \\ = foldl (op \);
clasohm@0
   489
wenzelm@233
   490
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   491
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@233
   492
wenzelm@233
   493
val gen_rems = foldl o gen_rem;
wenzelm@233
   494
wenzelm@233
   495
wenzelm@233
   496
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   497
  first of equal elements*)
wenzelm@233
   498
fun gen_distinct eq lst =
wenzelm@233
   499
  let
wenzelm@233
   500
    val memb = gen_mem eq;
clasohm@0
   501
wenzelm@233
   502
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   503
      | dist (rev_seen, x :: xs) =
wenzelm@233
   504
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   505
          else dist (x :: rev_seen, xs);
wenzelm@233
   506
  in
wenzelm@233
   507
    dist ([], lst)
wenzelm@233
   508
  end;
wenzelm@233
   509
wenzelm@233
   510
val distinct = gen_distinct (op =);
wenzelm@233
   511
wenzelm@233
   512
wenzelm@233
   513
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   514
fun findrep [] = []
wenzelm@233
   515
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   516
wenzelm@233
   517
wenzelm@255
   518
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   519
  order, takes first of equal elements*)
wenzelm@255
   520
fun gen_duplicates eq lst =
wenzelm@255
   521
  let
wenzelm@255
   522
    val memb = gen_mem eq;
wenzelm@255
   523
wenzelm@255
   524
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   525
      | dups (rev_dups, x :: xs) =
wenzelm@255
   526
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   527
            dups (rev_dups, xs)
wenzelm@255
   528
          else dups (x :: rev_dups, xs);
wenzelm@255
   529
  in
wenzelm@255
   530
    dups ([], lst)
wenzelm@255
   531
  end;
wenzelm@255
   532
wenzelm@255
   533
val duplicates = gen_duplicates (op =);
wenzelm@255
   534
wenzelm@255
   535
wenzelm@233
   536
wenzelm@233
   537
(** association lists **)
clasohm@0
   538
wenzelm@233
   539
(*association list lookup*)
wenzelm@233
   540
fun assoc ([], key) = None
wenzelm@233
   541
  | assoc ((keyi, xi) :: pairs, key) =
wenzelm@233
   542
      if key = keyi then Some xi else assoc (pairs, key);
wenzelm@233
   543
wenzelm@233
   544
fun assocs ps x =
wenzelm@233
   545
  (case assoc (ps, x) of
wenzelm@233
   546
    None => []
wenzelm@233
   547
  | Some ys => ys);
wenzelm@233
   548
wenzelm@255
   549
(*two-fold association list lookup*)
wenzelm@255
   550
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
   551
  (case assoc (aal, key1) of
wenzelm@255
   552
    Some al => assoc (al, key2)
wenzelm@255
   553
  | None => None);
wenzelm@255
   554
wenzelm@233
   555
(*generalized association list lookup*)
wenzelm@233
   556
fun gen_assoc eq ([], key) = None
wenzelm@233
   557
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
wenzelm@233
   558
      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
wenzelm@233
   559
wenzelm@233
   560
(*association list update*)
wenzelm@233
   561
fun overwrite (al, p as (key, _)) =
wenzelm@233
   562
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
   563
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
   564
        | over [] = [p]
wenzelm@233
   565
  in over al end;
wenzelm@233
   566
wenzelm@233
   567
wenzelm@233
   568
wenzelm@233
   569
(** generic tables **)
clasohm@0
   570
wenzelm@233
   571
(*Tables are supposed to be 'efficient' encodings of lists of elements distinct
wenzelm@233
   572
  wrt. an equality "eq". The extend and merge operations below are optimized
wenzelm@233
   573
  for long-term space efficiency.*)
wenzelm@233
   574
wenzelm@233
   575
(*append (new) elements to a table*)
wenzelm@233
   576
fun generic_extend _ _ _ tab [] = tab
wenzelm@233
   577
  | generic_extend eq dest_tab mk_tab tab1 lst2 =
wenzelm@233
   578
      let
wenzelm@233
   579
        val lst1 = dest_tab tab1;
wenzelm@233
   580
        val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   581
      in
wenzelm@233
   582
        if null new_lst2 then tab1
wenzelm@233
   583
        else mk_tab (lst1 @ new_lst2)
wenzelm@233
   584
      end;
clasohm@0
   585
wenzelm@233
   586
(*append (new) elements of 2nd table to 1st table*)
wenzelm@233
   587
fun generic_merge eq dest_tab mk_tab tab1 tab2 =
wenzelm@233
   588
  let
wenzelm@233
   589
    val lst1 = dest_tab tab1;
wenzelm@233
   590
    val lst2 = dest_tab tab2;
wenzelm@233
   591
    val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   592
  in
wenzelm@233
   593
    if null new_lst2 then tab1
wenzelm@233
   594
    else if gen_subset eq (lst1, lst2) then tab2
wenzelm@233
   595
    else mk_tab (lst1 @ new_lst2)
wenzelm@233
   596
  end;
clasohm@0
   597
wenzelm@233
   598
wenzelm@233
   599
(*lists as tables*)
wenzelm@233
   600
val extend_list = generic_extend (op =) I I;
wenzelm@233
   601
val merge_lists = generic_merge (op =) I I;
wenzelm@233
   602
wenzelm@380
   603
fun merge_rev_lists xs [] = xs
wenzelm@380
   604
  | merge_rev_lists [] ys = ys
wenzelm@380
   605
  | merge_rev_lists xs (y :: ys) =
wenzelm@380
   606
      (if y mem xs then I else cons y) (merge_rev_lists xs ys);
wenzelm@380
   607
clasohm@0
   608
clasohm@0
   609
wenzelm@233
   610
(** balanced trees **)
wenzelm@233
   611
wenzelm@233
   612
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
   613
wenzelm@233
   614
(*balanced folding; avoids deep nesting*)
wenzelm@233
   615
fun fold_bal f [x] = x
wenzelm@233
   616
  | fold_bal f [] = raise Balance
wenzelm@233
   617
  | fold_bal f xs =
wenzelm@233
   618
      let val k = length xs div 2
wenzelm@233
   619
      in  f (fold_bal f (take(k, xs)),
wenzelm@233
   620
             fold_bal f (drop(k, xs)))
wenzelm@233
   621
      end;
wenzelm@233
   622
wenzelm@233
   623
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
   624
fun access_bal (f, g, x) n i =
wenzelm@233
   625
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
   626
          if n=1 then x else
wenzelm@233
   627
          let val n2 = n div 2
wenzelm@233
   628
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
   629
                       else g (acc (n-n2) (i-n2))
wenzelm@233
   630
          end
wenzelm@233
   631
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
   632
wenzelm@233
   633
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
   634
fun accesses_bal (f, g, x) n =
wenzelm@233
   635
  let fun acc n =
wenzelm@233
   636
          if n=1 then [x] else
wenzelm@233
   637
          let val n2 = n div 2
wenzelm@233
   638
              val acc2 = acc n2
wenzelm@233
   639
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
   640
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
   641
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
   642
wenzelm@233
   643
wenzelm@233
   644
wenzelm@233
   645
(** input / output **)
wenzelm@233
   646
wenzelm@233
   647
fun prs s = output (std_out, s);
wenzelm@233
   648
fun writeln s = prs (s ^ "\n");
wenzelm@233
   649
wenzelm@233
   650
wenzelm@233
   651
(*print error message and abort to top level*)
wenzelm@233
   652
exception ERROR;
wenzelm@233
   653
fun error msg = (writeln msg; raise ERROR);
wenzelm@380
   654
fun sys_error msg = (writeln "*** SYSTEM ERROR ***"; error msg);
wenzelm@233
   655
wenzelm@233
   656
fun assert p msg = if p then () else error msg;
wenzelm@233
   657
fun deny p msg = if p then error msg else ();
wenzelm@233
   658
lcp@544
   659
(*Assert pred for every member of l, generating a message if pred fails*)
lcp@544
   660
fun assert_all pred l msg_fn = 
lcp@544
   661
  let fun asl [] = ()
lcp@544
   662
	| asl (x::xs) = if pred x then asl xs
lcp@544
   663
	                else error (msg_fn x)
lcp@544
   664
  in  asl l  end;
wenzelm@233
   665
wenzelm@233
   666
(* FIXME close file (?) *)
wenzelm@233
   667
(*for the "test" target in Makefiles -- signifies successful termination*)
wenzelm@233
   668
fun maketest msg =
wenzelm@233
   669
  (writeln msg; output (open_out "test", "Test examples ran successfully\n"));
wenzelm@233
   670
wenzelm@233
   671
wenzelm@233
   672
(*print a list surrounded by the brackets lpar and rpar, with comma separator
wenzelm@233
   673
  print nothing for empty list*)
wenzelm@233
   674
fun print_list (lpar, rpar, pre: 'a -> unit) (l : 'a list) =
wenzelm@233
   675
  let fun prec x = (prs ","; pre x)
wenzelm@233
   676
  in
wenzelm@233
   677
    (case l of
wenzelm@233
   678
      [] => ()
wenzelm@233
   679
    | x::l => (prs lpar; pre x; seq prec l; prs rpar))
wenzelm@233
   680
  end;
wenzelm@233
   681
wenzelm@233
   682
(*print a list of items separated by newlines*)
wenzelm@233
   683
fun print_list_ln (pre: 'a -> unit) : 'a list -> unit =
wenzelm@233
   684
  seq (fn x => (pre x; writeln ""));
wenzelm@233
   685
wenzelm@233
   686
wenzelm@233
   687
val print_int = prs o string_of_int;
wenzelm@233
   688
wenzelm@233
   689
wenzelm@233
   690
wenzelm@233
   691
(** timing **)
wenzelm@233
   692
wenzelm@233
   693
(*unconditional timing function*)
wenzelm@233
   694
val timeit = cond_timeit true;
wenzelm@233
   695
wenzelm@233
   696
(*timed application function*)
wenzelm@233
   697
fun timeap f x = timeit (fn () => f x);
wenzelm@233
   698
wenzelm@233
   699
(*timed "use" function, printing filenames*)
wenzelm@233
   700
fun time_use fname = timeit (fn () =>
wenzelm@233
   701
  (writeln ("\n**** Starting " ^ fname ^ " ****"); use fname;
wenzelm@233
   702
   writeln ("\n**** Finished " ^ fname ^ " ****")));
wenzelm@233
   703
lcp@955
   704
(*For Makefiles: use the file, but exit with error code if errors found.*)
lcp@955
   705
fun exit_use fname = use fname handle _ => exit 1;
wenzelm@233
   706
wenzelm@233
   707
wenzelm@233
   708
(** filenames **)
wenzelm@233
   709
clasohm@1290
   710
(*Convert UNIX filename of the form "path/file" to "path/" and "file";
wenzelm@233
   711
  if filename contains no slash, then it returns "" and "file"*)
wenzelm@233
   712
val split_filename =
wenzelm@233
   713
  (pairself implode) o take_suffix (not_equal "/") o explode;
wenzelm@233
   714
wenzelm@233
   715
val base_name = #2 o split_filename;
wenzelm@233
   716
clasohm@1290
   717
(*Merge splitted filename (path and file);
wenzelm@233
   718
  if path does not end with one a slash is appended*)
wenzelm@233
   719
fun tack_on "" name = name
wenzelm@233
   720
  | tack_on path name =
wenzelm@233
   721
      if last_elem (explode path) = "/" then path ^ name
wenzelm@233
   722
      else path ^ "/" ^ name;
wenzelm@233
   723
clasohm@1290
   724
(*Remove the extension of a filename, i.e. the part after the last '.'*)
wenzelm@233
   725
val remove_ext = implode o #1 o take_suffix (not_equal ".") o explode;
wenzelm@233
   726
clasohm@1290
   727
(*Make relative path to reach an absolute location from a different one*)
clasohm@1290
   728
fun relative_path cur_path dest_path =
clasohm@1290
   729
  let (*Remove common beginning of both paths and make relative path*)
clasohm@1290
   730
      fun mk_relative [] [] = []
clasohm@1290
   731
        | mk_relative [] ds = ds
clasohm@1290
   732
        | mk_relative cs [] = map (fn _ => "..") cs
clasohm@1290
   733
        | mk_relative (c::cs) (d::ds) =
clasohm@1290
   734
            if c = d then mk_relative cs ds
clasohm@1290
   735
            else ".." :: map (fn _ => "..") cs @ (d::ds);
clasohm@1290
   736
  in if cur_path = "" orelse hd (explode cur_path) <> "/" orelse
clasohm@1290
   737
        dest_path = "" orelse hd (explode dest_path) <> "/" then
clasohm@1290
   738
       error "Relative or empty path passed to relative_path"
clasohm@1290
   739
     else ();
clasohm@1290
   740
     space_implode "/" (mk_relative (space_explode "/" cur_path)
clasohm@1290
   741
                                    (space_explode "/" dest_path))
clasohm@1290
   742
  end;
wenzelm@233
   743
wenzelm@233
   744
wenzelm@233
   745
(** misc functions **)
wenzelm@233
   746
wenzelm@233
   747
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
   748
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
   749
  let fun keypair x = (x, keyfun x)
wenzelm@233
   750
  in map keypair end;
clasohm@0
   751
wenzelm@233
   752
(*given a list of (x, key) pairs and a searchkey
clasohm@0
   753
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
   754
fun keyfilter [] searchkey = []
wenzelm@233
   755
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
   756
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
   757
      else keyfilter pairs searchkey;
clasohm@0
   758
clasohm@0
   759
clasohm@0
   760
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
   761
  Preserves order of elements in both lists.*)
clasohm@0
   762
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
clasohm@0
   763
    let fun part ([], answer) = answer
wenzelm@233
   764
          | part (x::xs, (ys, ns)) = if pred(x)
wenzelm@233
   765
            then  part (xs, (x::ys, ns))
wenzelm@233
   766
            else  part (xs, (ys, x::ns))
wenzelm@233
   767
    in  part (rev ys, ([], []))  end;
clasohm@0
   768
clasohm@0
   769
clasohm@0
   770
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
   771
    let fun part [] = []
wenzelm@233
   772
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
   773
                           in (x::xs)::(part xs') end
clasohm@0
   774
    in part end;
clasohm@0
   775
clasohm@0
   776
wenzelm@233
   777
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
   778
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
   779
fun partition_list p i j =
wenzelm@233
   780
  let fun part k xs =
wenzelm@233
   781
            if k>j then
clasohm@0
   782
              (case xs of [] => []
clasohm@0
   783
                         | _ => raise LIST "partition_list")
clasohm@0
   784
            else
wenzelm@233
   785
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
   786
            in  ns :: part(k+1)rest  end
clasohm@0
   787
  in  part i end;
clasohm@0
   788
clasohm@0
   789
wenzelm@233
   790
(* sorting *)
wenzelm@233
   791
wenzelm@233
   792
(*insertion sort; stable (does not reorder equal elements)
wenzelm@233
   793
  'less' is less-than test on type 'a*)
wenzelm@233
   794
fun sort (less: 'a*'a -> bool) =
clasohm@0
   795
  let fun insert (x, []) = [x]
wenzelm@233
   796
        | insert (x, y::ys) =
wenzelm@233
   797
              if less(y, x) then y :: insert (x, ys) else x::y::ys;
clasohm@0
   798
      fun sort1 [] = []
clasohm@0
   799
        | sort1 (x::xs) = insert (x, sort1 xs)
clasohm@0
   800
  in  sort1  end;
clasohm@0
   801
wenzelm@41
   802
(*sort strings*)
wenzelm@41
   803
val sort_strings = sort (op <= : string * string -> bool);
wenzelm@41
   804
wenzelm@41
   805
wenzelm@233
   806
(* transitive closure (not Warshall's algorithm) *)
clasohm@0
   807
wenzelm@233
   808
fun transitive_closure [] = []
wenzelm@233
   809
  | transitive_closure ((x, ys)::ps) =
wenzelm@233
   810
      let val qs = transitive_closure ps
wenzelm@233
   811
          val zs = foldl (fn (zs, y) => assocs qs y union zs) (ys, ys)
wenzelm@233
   812
          fun step(u, us) = (u, if x mem us then zs union us else us)
wenzelm@233
   813
      in (x, zs) :: map step qs end;
clasohm@0
   814
clasohm@0
   815
wenzelm@233
   816
(* generating identifiers *)
clasohm@0
   817
clasohm@0
   818
local
wenzelm@233
   819
  val a = ord "a" and z = ord "z" and A = ord "A" and Z = ord "Z"
wenzelm@233
   820
  and k0 = ord "0" and k9 = ord "9"
clasohm@0
   821
in
clasohm@0
   822
clasohm@0
   823
(*Increment a list of letters like a reversed base 26 number.
wenzelm@233
   824
  If head is "z", bumps chars in tail.
clasohm@0
   825
  Digits are incremented as if they were integers.
clasohm@0
   826
  "_" and "'" are not changed.
wenzelm@233
   827
  For making variants of identifiers.*)
clasohm@0
   828
clasohm@0
   829
fun bump_int_list(c::cs) = if c="9" then "0" :: bump_int_list cs else
wenzelm@233
   830
        if k0 <= ord(c) andalso ord(c) < k9 then chr(ord(c)+1) :: cs
wenzelm@233
   831
        else "1" :: c :: cs
clasohm@0
   832
  | bump_int_list([]) = error("bump_int_list: not an identifier");
clasohm@0
   833
wenzelm@233
   834
fun bump_list([], d) = [d]
wenzelm@233
   835
  | bump_list(["'"], d) = [d, "'"]
wenzelm@233
   836
  | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
wenzelm@233
   837
  | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
wenzelm@233
   838
  | bump_list("9"::cs, _) = "0" :: bump_int_list cs
wenzelm@233
   839
  | bump_list(c::cs, _) = let val k = ord(c)
wenzelm@233
   840
        in if (a <= k andalso k < z) orelse (A <= k andalso k < Z) orelse
wenzelm@233
   841
              (k0 <= k andalso k < k9) then chr(k+1) :: cs else
wenzelm@233
   842
           if c="'" orelse c="_" then c :: bump_list(cs, "") else
wenzelm@233
   843
                error("bump_list: not legal in identifier: " ^
wenzelm@233
   844
                        implode(rev(c::cs)))
wenzelm@233
   845
        end;
clasohm@0
   846
clasohm@0
   847
end;
clasohm@0
   848
wenzelm@233
   849
fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
wenzelm@41
   850
wenzelm@41
   851
wenzelm@233
   852
(* lexical scanning *)
clasohm@0
   853
wenzelm@233
   854
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
   855
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
   856
fun scanwords is_let cs =
clasohm@0
   857
  let fun scan1 [] = []
wenzelm@233
   858
        | scan1 cs =
wenzelm@233
   859
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
   860
            in implode lets :: scanwords is_let rest end;
wenzelm@233
   861
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
   862