1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
|
datatype t = datatype Basis.list
val show = fn [a] (_ : show a) =>
let
fun show' (ls : list a) =
case ls of
[] => "[]"
| x :: ls => show x ^ " :: " ^ show' ls
in
mkShow show'
end
val eq = fn [a] (_ : eq a) =>
let
fun eq' (ls1 : list a) ls2 =
case (ls1, ls2) of
([], []) => True
| (x1 :: ls1, x2 :: ls2) => x1 = x2 && eq' ls1 ls2
| _ => False
in
mkEq eq'
end
fun foldl [a] [b] (f : a -> b -> b) =
let
fun foldl' acc ls =
case ls of
[] => acc
| x :: ls => foldl' (f x acc) ls
in
foldl'
end
val rev = fn [a] =>
let
fun rev' acc (ls : list a) =
case ls of
[] => acc
| x :: ls => rev' (x :: acc) ls
in
rev' []
end
fun foldr [a] [b] f (acc : b) (ls : list a) = foldl f acc (rev ls)
fun foldlAbort [a] [b] f =
let
fun foldlAbort' acc ls =
case ls of
[] => Some acc
| x :: ls =>
case f x acc of
None => None
| Some acc' => foldlAbort' acc' ls
in
foldlAbort'
end
val length = fn [a] =>
let
fun length' acc (ls : list a) =
case ls of
[] => acc
| _ :: ls => length' (acc + 1) ls
in
length' 0
end
fun foldlMapAbort [a] [b] [c] f =
let
fun foldlMapAbort' ls' acc ls =
case ls of
[] => Some (rev ls', acc)
| x :: ls =>
case f x acc of
None => None
| Some (x', acc') => foldlMapAbort' (x' :: ls') acc' ls
in
foldlMapAbort' []
end
val revAppend = fn [a] =>
let
fun ra (ls : list a) acc =
case ls of
[] => acc
| x :: ls => ra ls (x :: acc)
in
ra
end
fun append [a] (ls1 : t a) (ls2 : t a) = revAppend (rev ls1) ls2
fun mp [a] [b] f =
let
fun mp' acc ls =
case ls of
[] => rev acc
| x :: ls => mp' (f x :: acc) ls
in
mp' []
end
fun mapi [a] [b] f =
let
fun mp' n acc ls =
case ls of
[] => rev acc
| x :: ls => mp' (n + 1) (f n x :: acc) ls
in
mp' 0 []
end
fun mapPartial [a] [b] f =
let
fun mp' acc ls =
case ls of
[] => rev acc
| x :: ls => mp' (case f x of
None => acc
| Some y => y :: acc) ls
in
mp' []
end
fun mapX [a] [ctx ::: {Unit}] f =
let
fun mapX' ls =
case ls of
[] => <xml/>
| x :: ls => <xml>{f x}{mapX' ls}</xml>
in
mapX'
end
fun mapXi [a] [ctx ::: {Unit}] f =
let
fun mapX' i ls =
case ls of
[] => <xml/>
| x :: ls => <xml>{f i x}{mapX' (i + 1) ls}</xml>
in
mapX' 0
end
fun mapM [m ::: (Type -> Type)] (_ : monad m) [a] [b] f =
let
fun mapM' acc ls =
case ls of
[] => return (rev acc)
| x :: ls => x' <- f x; mapM' (x' :: acc) ls
in
mapM' []
end
fun mapPartialM [m ::: (Type -> Type)] (_ : monad m) [a] [b] f =
let
fun mapPartialM' acc ls =
case ls of
[] => return (rev acc)
| x :: ls =>
v <- f x;
mapPartialM' (case v of
None => acc
| Some x' => x' :: acc) ls
in
mapPartialM' []
end
fun mapXM [m ::: (Type -> Type)] (_ : monad m) [a] [ctx ::: {Unit}] f =
let
fun mapXM' ls =
case ls of
[] => return <xml/>
| x :: ls =>
this <- f x;
rest <- mapXM' ls;
return <xml>{this}{rest}</xml>
in
mapXM'
end
fun filter [a] f =
let
fun fil acc ls =
case ls of
[] => rev acc
| x :: ls => fil (if f x then x :: acc else acc) ls
in
fil []
end
fun exists [a] f =
let
fun ex ls =
case ls of
[] => False
| x :: ls =>
if f x then
True
else
ex ls
in
ex
end
fun foldlMap [a] [b] [c] f =
let
fun fold ls' st ls =
case ls of
[] => (rev ls', st)
| x :: ls =>
case f x st of
(y, st) => fold (y :: ls') st ls
in
fold []
end
fun find [a] f =
let
fun find' ls =
case ls of
[] => None
| x :: ls =>
if f x then
Some x
else
find' ls
in
find'
end
fun search [a] [b] f =
let
fun search' ls =
case ls of
[] => None
| x :: ls =>
case f x of
None => search' ls
| v => v
in
search'
end
fun foldlM [m] (_ : monad m) [a] [b] f =
let
fun foldlM' acc ls =
case ls of
[] => return acc
| x :: ls =>
acc <- f x acc;
foldlM' acc ls
in
foldlM'
end
fun foldlMi [m] (_ : monad m) [a] [b] f =
let
fun foldlMi' i acc ls =
case ls of
[] => return acc
| x :: ls =>
acc <- f i x acc;
foldlMi' (i + 1) acc ls
in
foldlMi' 0
end
fun filterM [m] (_ : monad m) [a] (p : a -> m bool) =
let
fun filterM' (acc : list a) (xs : list a) : m (list a) =
case xs of
[] => return (rev acc)
| x :: xs =>
c <- p x;
filterM' (if c then x :: acc else acc) xs
in
filterM' []
end
fun all [m] f =
let
fun all' ls =
case ls of
[] => True
| x :: ls => f x && all' ls
in
all'
end
fun app [m] (_ : monad m) [a] f =
let
fun app' ls =
case ls of
[] => return ()
| x :: ls =>
f x;
app' ls
in
app'
end
fun mapQuery [tables ::: {{Type}}] [exps ::: {Type}] [t ::: Type]
[tables ~ exps] (q : sql_query [] [] tables exps)
(f : $(exps ++ map (fn fields :: {Type} => $fields) tables) -> t) =
ls <- query q
(fn fs acc => return (f fs :: acc))
[];
return (rev ls)
fun mapQueryM [tables ::: {{Type}}] [exps ::: {Type}] [t ::: Type]
[tables ~ exps] (q : sql_query [] [] tables exps)
(f : $(exps ++ map (fn fields :: {Type} => $fields) tables) -> transaction t) =
ls <- query q
(fn fs acc => v <- f fs; return (v :: acc))
[];
return (rev ls)
fun mapQueryPartialM [tables ::: {{Type}}] [exps ::: {Type}] [t ::: Type]
[tables ~ exps] (q : sql_query [] [] tables exps)
(f : $(exps ++ map (fn fields :: {Type} => $fields) tables) -> transaction (option t)) =
ls <- query q
(fn fs acc => v <- f fs;
return (case v of
None => acc
| Some v => v :: acc))
[];
return (rev ls)
fun sort [a] (gt : a -> a -> bool) (ls : t a) : t a =
let
fun split ls acc1 acc2 =
case ls of
[] => (rev acc1, rev acc2)
| x :: [] => (rev (x :: acc1), rev acc2)
| x1 :: x2 :: ls' => split ls' (x1 :: acc1) (x2 :: acc2)
fun merge ls1 ls2 acc =
case (ls1, ls2) of
([], _) => revAppend acc ls2
| (_, []) => revAppend acc ls1
| (x1 :: ls1', x2 :: ls2') => if gt x1 x2 then merge ls1 ls2' (x2 :: acc) else merge ls1' ls2 (x1 :: acc)
fun sort' ls =
case ls of
[] => ls
| _ :: [] => ls
| _ =>
let
val (ls1, ls2) = split ls [] []
in
merge (sort' ls1) (sort' ls2) []
end
in
sort' ls
end
val nth [a] =
let
fun nth (ls : list a) (n : int) : option a =
case ls of
[] => None
| x :: ls' =>
if n <= 0 then
Some x
else
nth ls' (n-1)
in
nth
end
fun replaceNth [a] (ls : list a) (n : int) (v : a) : list a =
let
fun repNth (ls : list a) (n : int) (acc : list a) =
case ls of
[] => rev acc
| x :: ls' => if n <= 0 then
revAppend acc (v :: ls')
else
repNth ls' (n-1) (x :: acc)
in
repNth ls n []
end
fun assoc [a] [b] (_ : eq a) (x : a) =
let
fun assoc' (ls : list (a * b)) =
case ls of
[] => None
| (y, z) :: ls =>
if x = y then
Some z
else
assoc' ls
in
assoc'
end
fun assocAdd [a] [b] (_ : eq a) (x : a) (y : b) (ls : t (a * b)) =
case assoc x ls of
None => (x, y) :: ls
| Some _ => ls
fun recToList [a ::: Type] [r ::: {Unit}] (fl : folder r)
= @foldUR [a] [fn _ => list a] (fn [nm ::_] [rest ::_] [[nm] ~ rest] x xs =>
x :: xs) [] fl
fun take [a] (n : int) (xs : list a) : list a =
if n <= 0 then
[]
else
case xs of
[] => []
| x :: xs => x :: take (n-1) xs
fun drop [a] (n : int) (xs : list a) : list a =
if n <= 0 then
xs
else
case xs of
[] => []
| x :: xs => drop (n-1) xs
fun splitAt [a] (n : int) (xs : list a) : list a * list a =
(take n xs, drop n xs)
fun mapXiM [m ::: Type -> Type] (_ : monad m) [a] [ctx ::: {Unit}] (f : int -> a -> m (xml ctx [] [])) : t a -> m (xml ctx [] []) =
let
fun mapXiM' i ls =
case ls of
[] => return <xml/>
| x :: ls =>
this <- f i x;
rest <- mapXiM' (i+1) ls;
return <xml>{this}{rest}</xml>
in
mapXiM' 0
end
|