/usr/lib/hugs/packages/base/Data/Map.hs is in libhugs-base-bundled 98.200609.21-5.3ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 | {-# OPTIONS_GHC -fno-bang-patterns #-}
-----------------------------------------------------------------------------
-- |
-- Module : Data.Map
-- Copyright : (c) Daan Leijen 2002
-- License : BSD-style
-- Maintainer : libraries@haskell.org
-- Stability : provisional
-- Portability : portable
--
-- An efficient implementation of maps from keys to values (dictionaries).
--
-- Since many function names (but not the type name) clash with
-- "Prelude" names, this module is usually imported @qualified@, e.g.
--
-- > import Data.Map (Map)
-- > import qualified Data.Map as Map
--
-- The implementation of 'Map' is based on /size balanced/ binary trees (or
-- trees of /bounded balance/) as described by:
--
-- * Stephen Adams, \"/Efficient sets: a balancing act/\",
-- Journal of Functional Programming 3(4):553-562, October 1993,
-- <http://www.swiss.ai.mit.edu/~adams/BB>.
--
-- * J. Nievergelt and E.M. Reingold,
-- \"/Binary search trees of bounded balance/\",
-- SIAM journal of computing 2(1), March 1973.
--
-- Note that the implementation is /left-biased/ -- the elements of a
-- first argument are always preferred to the second, for example in
-- 'union' or 'insert'.
-----------------------------------------------------------------------------
module Data.Map (
-- * Map type
Map -- instance Eq,Show,Read
-- * Operators
, (!), (\\)
-- * Query
, null
, size
, member
, notMember
, lookup
, findWithDefault
-- * Construction
, empty
, singleton
-- ** Insertion
, insert
, insertWith, insertWithKey, insertLookupWithKey
, insertWith', insertWithKey'
-- ** Delete\/Update
, delete
, adjust
, adjustWithKey
, update
, updateWithKey
, updateLookupWithKey
, alter
-- * Combine
-- ** Union
, union
, unionWith
, unionWithKey
, unions
, unionsWith
-- ** Difference
, difference
, differenceWith
, differenceWithKey
-- ** Intersection
, intersection
, intersectionWith
, intersectionWithKey
-- * Traversal
-- ** Map
, map
, mapWithKey
, mapAccum
, mapAccumWithKey
, mapKeys
, mapKeysWith
, mapKeysMonotonic
-- ** Fold
, fold
, foldWithKey
-- * Conversion
, elems
, keys
, keysSet
, assocs
-- ** Lists
, toList
, fromList
, fromListWith
, fromListWithKey
-- ** Ordered lists
, toAscList
, fromAscList
, fromAscListWith
, fromAscListWithKey
, fromDistinctAscList
-- * Filter
, filter
, filterWithKey
, partition
, partitionWithKey
, mapMaybe
, mapMaybeWithKey
, mapEither
, mapEitherWithKey
, split
, splitLookup
-- * Submap
, isSubmapOf, isSubmapOfBy
, isProperSubmapOf, isProperSubmapOfBy
-- * Indexed
, lookupIndex
, findIndex
, elemAt
, updateAt
, deleteAt
-- * Min\/Max
, findMin
, findMax
, deleteMin
, deleteMax
, deleteFindMin
, deleteFindMax
, updateMin
, updateMax
, updateMinWithKey
, updateMaxWithKey
, minView
, maxView
-- * Debugging
, showTree
, showTreeWith
, valid
) where
import Prelude hiding (lookup,map,filter,foldr,foldl,null)
import qualified Data.Set as Set
import qualified Data.List as List
import Data.Monoid (Monoid(..))
import Data.Typeable
import Control.Applicative (Applicative(..), (<$>))
import Data.Traversable (Traversable(traverse))
import Data.Foldable (Foldable(foldMap))
{-
-- for quick check
import qualified Prelude
import qualified List
import Debug.QuickCheck
import List(nub,sort)
-}
{--------------------------------------------------------------------
Operators
--------------------------------------------------------------------}
infixl 9 !,\\ --
-- | /O(log n)/. Find the value at a key.
-- Calls 'error' when the element can not be found.
(!) :: Ord k => Map k a -> k -> a
m ! k = find k m
-- | /O(n+m)/. See 'difference'.
(\\) :: Ord k => Map k a -> Map k b -> Map k a
m1 \\ m2 = difference m1 m2
{--------------------------------------------------------------------
Size balanced trees.
--------------------------------------------------------------------}
-- | A Map from keys @k@ to values @a@.
data Map k a = Tip
| Bin {-# UNPACK #-} !Size !k a !(Map k a) !(Map k a)
type Size = Int
instance (Ord k) => Monoid (Map k v) where
mempty = empty
mappend = union
mconcat = unions
{--------------------------------------------------------------------
Query
--------------------------------------------------------------------}
-- | /O(1)/. Is the map empty?
null :: Map k a -> Bool
null t
= case t of
Tip -> True
Bin sz k x l r -> False
-- | /O(1)/. The number of elements in the map.
size :: Map k a -> Int
size t
= case t of
Tip -> 0
Bin sz k x l r -> sz
-- | /O(log n)/. Lookup the value at a key in the map.
--
-- The function will
-- @return@ the result in the monad or @fail@ in it the key isn't in the
-- map. Often, the monad to use is 'Maybe', so you get either
-- @('Just' result)@ or @'Nothing'@.
lookup :: (Monad m,Ord k) => k -> Map k a -> m a
lookup k t = case lookup' k t of
Just x -> return x
Nothing -> fail "Data.Map.lookup: Key not found"
lookup' :: Ord k => k -> Map k a -> Maybe a
lookup' k t
= case t of
Tip -> Nothing
Bin sz kx x l r
-> case compare k kx of
LT -> lookup' k l
GT -> lookup' k r
EQ -> Just x
lookupAssoc :: Ord k => k -> Map k a -> Maybe (k,a)
lookupAssoc k t
= case t of
Tip -> Nothing
Bin sz kx x l r
-> case compare k kx of
LT -> lookupAssoc k l
GT -> lookupAssoc k r
EQ -> Just (kx,x)
-- | /O(log n)/. Is the key a member of the map?
member :: Ord k => k -> Map k a -> Bool
member k m
= case lookup k m of
Nothing -> False
Just x -> True
-- | /O(log n)/. Is the key not a member of the map?
notMember :: Ord k => k -> Map k a -> Bool
notMember k m = not $ member k m
-- | /O(log n)/. Find the value at a key.
-- Calls 'error' when the element can not be found.
find :: Ord k => k -> Map k a -> a
find k m
= case lookup k m of
Nothing -> error "Map.find: element not in the map"
Just x -> x
-- | /O(log n)/. The expression @('findWithDefault' def k map)@ returns
-- the value at key @k@ or returns @def@ when the key is not in the map.
findWithDefault :: Ord k => a -> k -> Map k a -> a
findWithDefault def k m
= case lookup k m of
Nothing -> def
Just x -> x
{--------------------------------------------------------------------
Construction
--------------------------------------------------------------------}
-- | /O(1)/. The empty map.
empty :: Map k a
empty
= Tip
-- | /O(1)/. A map with a single element.
singleton :: k -> a -> Map k a
singleton k x
= Bin 1 k x Tip Tip
{--------------------------------------------------------------------
Insertion
--------------------------------------------------------------------}
-- | /O(log n)/. Insert a new key and value in the map.
-- If the key is already present in the map, the associated value is
-- replaced with the supplied value, i.e. 'insert' is equivalent to
-- @'insertWith' 'const'@.
insert :: Ord k => k -> a -> Map k a -> Map k a
insert kx x t
= case t of
Tip -> singleton kx x
Bin sz ky y l r
-> case compare kx ky of
LT -> balance ky y (insert kx x l) r
GT -> balance ky y l (insert kx x r)
EQ -> Bin sz kx x l r
-- | /O(log n)/. Insert with a combining function.
-- @'insertWith' f key value mp@
-- will insert the pair (key, value) into @mp@ if key does
-- not exist in the map. If the key does exist, the function will
-- insert the pair @(key, f new_value old_value)@.
insertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWith f k x m
= insertWithKey (\k x y -> f x y) k x m
-- | Same as 'insertWith', but the combining function is applied strictly.
insertWith' :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWith' f k x m
= insertWithKey' (\k x y -> f x y) k x m
-- | /O(log n)/. Insert with a combining function.
-- @'insertWithKey' f key value mp@
-- will insert the pair (key, value) into @mp@ if key does
-- not exist in the map. If the key does exist, the function will
-- insert the pair @(key,f key new_value old_value)@.
-- Note that the key passed to f is the same key passed to 'insertWithKey'.
insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithKey f kx x t
= case t of
Tip -> singleton kx x
Bin sy ky y l r
-> case compare kx ky of
LT -> balance ky y (insertWithKey f kx x l) r
GT -> balance ky y l (insertWithKey f kx x r)
EQ -> Bin sy kx (f kx x y) l r
-- | Same as 'insertWithKey', but the combining function is applied strictly.
insertWithKey' :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithKey' f kx x t
= case t of
Tip -> singleton kx x
Bin sy ky y l r
-> case compare kx ky of
LT -> balance ky y (insertWithKey' f kx x l) r
GT -> balance ky y l (insertWithKey' f kx x r)
EQ -> let x' = f kx x y in seq x' (Bin sy kx x' l r)
-- | /O(log n)/. The expression (@'insertLookupWithKey' f k x map@)
-- is a pair where the first element is equal to (@'lookup' k map@)
-- and the second element equal to (@'insertWithKey' f k x map@).
insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> (Maybe a,Map k a)
insertLookupWithKey f kx x t
= case t of
Tip -> (Nothing, singleton kx x)
Bin sy ky y l r
-> case compare kx ky of
LT -> let (found,l') = insertLookupWithKey f kx x l in (found,balance ky y l' r)
GT -> let (found,r') = insertLookupWithKey f kx x r in (found,balance ky y l r')
EQ -> (Just y, Bin sy kx (f kx x y) l r)
{--------------------------------------------------------------------
Deletion
[delete] is the inlined version of [deleteWith (\k x -> Nothing)]
--------------------------------------------------------------------}
-- | /O(log n)/. Delete a key and its value from the map. When the key is not
-- a member of the map, the original map is returned.
delete :: Ord k => k -> Map k a -> Map k a
delete k t
= case t of
Tip -> Tip
Bin sx kx x l r
-> case compare k kx of
LT -> balance kx x (delete k l) r
GT -> balance kx x l (delete k r)
EQ -> glue l r
-- | /O(log n)/. Adjust a value at a specific key. When the key is not
-- a member of the map, the original map is returned.
adjust :: Ord k => (a -> a) -> k -> Map k a -> Map k a
adjust f k m
= adjustWithKey (\k x -> f x) k m
-- | /O(log n)/. Adjust a value at a specific key. When the key is not
-- a member of the map, the original map is returned.
adjustWithKey :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a
adjustWithKey f k m
= updateWithKey (\k x -> Just (f k x)) k m
-- | /O(log n)/. The expression (@'update' f k map@) updates the value @x@
-- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is
-- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
update :: Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a
update f k m
= updateWithKey (\k x -> f x) k m
-- | /O(log n)/. The expression (@'updateWithKey' f k map@) updates the
-- value @x@ at @k@ (if it is in the map). If (@f k x@) is 'Nothing',
-- the element is deleted. If it is (@'Just' y@), the key @k@ is bound
-- to the new value @y@.
updateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a
updateWithKey f k t
= case t of
Tip -> Tip
Bin sx kx x l r
-> case compare k kx of
LT -> balance kx x (updateWithKey f k l) r
GT -> balance kx x l (updateWithKey f k r)
EQ -> case f kx x of
Just x' -> Bin sx kx x' l r
Nothing -> glue l r
-- | /O(log n)/. Lookup and update.
updateLookupWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a,Map k a)
updateLookupWithKey f k t
= case t of
Tip -> (Nothing,Tip)
Bin sx kx x l r
-> case compare k kx of
LT -> let (found,l') = updateLookupWithKey f k l in (found,balance kx x l' r)
GT -> let (found,r') = updateLookupWithKey f k r in (found,balance kx x l r')
EQ -> case f kx x of
Just x' -> (Just x',Bin sx kx x' l r)
Nothing -> (Just x,glue l r)
-- | /O(log n)/. The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof.
-- 'alter' can be used to insert, delete, or update a value in a 'Map'.
-- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@
alter :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a
alter f k t
= case t of
Tip -> case f Nothing of
Nothing -> Tip
Just x -> singleton k x
Bin sx kx x l r
-> case compare k kx of
LT -> balance kx x (alter f k l) r
GT -> balance kx x l (alter f k r)
EQ -> case f (Just x) of
Just x' -> Bin sx kx x' l r
Nothing -> glue l r
{--------------------------------------------------------------------
Indexing
--------------------------------------------------------------------}
-- | /O(log n)/. Return the /index/ of a key. The index is a number from
-- /0/ up to, but not including, the 'size' of the map. Calls 'error' when
-- the key is not a 'member' of the map.
findIndex :: Ord k => k -> Map k a -> Int
findIndex k t
= case lookupIndex k t of
Nothing -> error "Map.findIndex: element is not in the map"
Just idx -> idx
-- | /O(log n)/. Lookup the /index/ of a key. The index is a number from
-- /0/ up to, but not including, the 'size' of the map.
lookupIndex :: (Monad m,Ord k) => k -> Map k a -> m Int
lookupIndex k t = case lookup 0 t of
Nothing -> fail "Data.Map.lookupIndex: Key not found."
Just x -> return x
where
lookup idx Tip = Nothing
lookup idx (Bin _ kx x l r)
= case compare k kx of
LT -> lookup idx l
GT -> lookup (idx + size l + 1) r
EQ -> Just (idx + size l)
-- | /O(log n)/. Retrieve an element by /index/. Calls 'error' when an
-- invalid index is used.
elemAt :: Int -> Map k a -> (k,a)
elemAt i Tip = error "Map.elemAt: index out of range"
elemAt i (Bin _ kx x l r)
= case compare i sizeL of
LT -> elemAt i l
GT -> elemAt (i-sizeL-1) r
EQ -> (kx,x)
where
sizeL = size l
-- | /O(log n)/. Update the element at /index/. Calls 'error' when an
-- invalid index is used.
updateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a
updateAt f i Tip = error "Map.updateAt: index out of range"
updateAt f i (Bin sx kx x l r)
= case compare i sizeL of
LT -> updateAt f i l
GT -> updateAt f (i-sizeL-1) r
EQ -> case f kx x of
Just x' -> Bin sx kx x' l r
Nothing -> glue l r
where
sizeL = size l
-- | /O(log n)/. Delete the element at /index/.
-- Defined as (@'deleteAt' i map = 'updateAt' (\k x -> 'Nothing') i map@).
deleteAt :: Int -> Map k a -> Map k a
deleteAt i map
= updateAt (\k x -> Nothing) i map
{--------------------------------------------------------------------
Minimal, Maximal
--------------------------------------------------------------------}
-- | /O(log n)/. The minimal key of the map.
findMin :: Map k a -> (k,a)
findMin (Bin _ kx x Tip r) = (kx,x)
findMin (Bin _ kx x l r) = findMin l
findMin Tip = error "Map.findMin: empty map has no minimal element"
-- | /O(log n)/. The maximal key of the map.
findMax :: Map k a -> (k,a)
findMax (Bin _ kx x l Tip) = (kx,x)
findMax (Bin _ kx x l r) = findMax r
findMax Tip = error "Map.findMax: empty map has no maximal element"
-- | /O(log n)/. Delete the minimal key.
deleteMin :: Map k a -> Map k a
deleteMin (Bin _ kx x Tip r) = r
deleteMin (Bin _ kx x l r) = balance kx x (deleteMin l) r
deleteMin Tip = Tip
-- | /O(log n)/. Delete the maximal key.
deleteMax :: Map k a -> Map k a
deleteMax (Bin _ kx x l Tip) = l
deleteMax (Bin _ kx x l r) = balance kx x l (deleteMax r)
deleteMax Tip = Tip
-- | /O(log n)/. Update the value at the minimal key.
updateMin :: (a -> Maybe a) -> Map k a -> Map k a
updateMin f m
= updateMinWithKey (\k x -> f x) m
-- | /O(log n)/. Update the value at the maximal key.
updateMax :: (a -> Maybe a) -> Map k a -> Map k a
updateMax f m
= updateMaxWithKey (\k x -> f x) m
-- | /O(log n)/. Update the value at the minimal key.
updateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a
updateMinWithKey f t
= case t of
Bin sx kx x Tip r -> case f kx x of
Nothing -> r
Just x' -> Bin sx kx x' Tip r
Bin sx kx x l r -> balance kx x (updateMinWithKey f l) r
Tip -> Tip
-- | /O(log n)/. Update the value at the maximal key.
updateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a
updateMaxWithKey f t
= case t of
Bin sx kx x l Tip -> case f kx x of
Nothing -> l
Just x' -> Bin sx kx x' l Tip
Bin sx kx x l r -> balance kx x l (updateMaxWithKey f r)
Tip -> Tip
-- | /O(log n)/. Retrieves the minimal key of the map, and the map stripped from that element
-- @fail@s (in the monad) when passed an empty map.
minView :: Monad m => Map k a -> m (Map k a, (k,a))
minView Tip = fail "Map.minView: empty map"
minView x = return (swap $ deleteFindMin x)
-- | /O(log n)/. Retrieves the maximal key of the map, and the map stripped from that element
-- @fail@s (in the monad) when passed an empty map.
maxView :: Monad m => Map k a -> m (Map k a, (k,a))
maxView Tip = fail "Map.maxView: empty map"
maxView x = return (swap $ deleteFindMax x)
swap (a,b) = (b,a)
{--------------------------------------------------------------------
Union.
--------------------------------------------------------------------}
-- | The union of a list of maps:
-- (@'unions' == 'Prelude.foldl' 'union' 'empty'@).
unions :: Ord k => [Map k a] -> Map k a
unions ts
= foldlStrict union empty ts
-- | The union of a list of maps, with a combining operation:
-- (@'unionsWith' f == 'Prelude.foldl' ('unionWith' f) 'empty'@).
unionsWith :: Ord k => (a->a->a) -> [Map k a] -> Map k a
unionsWith f ts
= foldlStrict (unionWith f) empty ts
-- | /O(n+m)/.
-- The expression (@'union' t1 t2@) takes the left-biased union of @t1@ and @t2@.
-- It prefers @t1@ when duplicate keys are encountered,
-- i.e. (@'union' == 'unionWith' 'const'@).
-- The implementation uses the efficient /hedge-union/ algorithm.
-- Hedge-union is more efficient on (bigset `union` smallset)
union :: Ord k => Map k a -> Map k a -> Map k a
union Tip t2 = t2
union t1 Tip = t1
union t1 t2 = hedgeUnionL (const LT) (const GT) t1 t2
-- left-biased hedge union
hedgeUnionL cmplo cmphi t1 Tip
= t1
hedgeUnionL cmplo cmphi Tip (Bin _ kx x l r)
= join kx x (filterGt cmplo l) (filterLt cmphi r)
hedgeUnionL cmplo cmphi (Bin _ kx x l r) t2
= join kx x (hedgeUnionL cmplo cmpkx l (trim cmplo cmpkx t2))
(hedgeUnionL cmpkx cmphi r (trim cmpkx cmphi t2))
where
cmpkx k = compare kx k
-- right-biased hedge union
hedgeUnionR cmplo cmphi t1 Tip
= t1
hedgeUnionR cmplo cmphi Tip (Bin _ kx x l r)
= join kx x (filterGt cmplo l) (filterLt cmphi r)
hedgeUnionR cmplo cmphi (Bin _ kx x l r) t2
= join kx newx (hedgeUnionR cmplo cmpkx l lt)
(hedgeUnionR cmpkx cmphi r gt)
where
cmpkx k = compare kx k
lt = trim cmplo cmpkx t2
(found,gt) = trimLookupLo kx cmphi t2
newx = case found of
Nothing -> x
Just (_,y) -> y
{--------------------------------------------------------------------
Union with a combining function
--------------------------------------------------------------------}
-- | /O(n+m)/. Union with a combining function. The implementation uses the efficient /hedge-union/ algorithm.
unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a
unionWith f m1 m2
= unionWithKey (\k x y -> f x y) m1 m2
-- | /O(n+m)/.
-- Union with a combining function. The implementation uses the efficient /hedge-union/ algorithm.
-- Hedge-union is more efficient on (bigset `union` smallset).
unionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a
unionWithKey f Tip t2 = t2
unionWithKey f t1 Tip = t1
unionWithKey f t1 t2 = hedgeUnionWithKey f (const LT) (const GT) t1 t2
hedgeUnionWithKey f cmplo cmphi t1 Tip
= t1
hedgeUnionWithKey f cmplo cmphi Tip (Bin _ kx x l r)
= join kx x (filterGt cmplo l) (filterLt cmphi r)
hedgeUnionWithKey f cmplo cmphi (Bin _ kx x l r) t2
= join kx newx (hedgeUnionWithKey f cmplo cmpkx l lt)
(hedgeUnionWithKey f cmpkx cmphi r gt)
where
cmpkx k = compare kx k
lt = trim cmplo cmpkx t2
(found,gt) = trimLookupLo kx cmphi t2
newx = case found of
Nothing -> x
Just (_,y) -> f kx x y
{--------------------------------------------------------------------
Difference
--------------------------------------------------------------------}
-- | /O(n+m)/. Difference of two maps.
-- The implementation uses an efficient /hedge/ algorithm comparable with /hedge-union/.
difference :: Ord k => Map k a -> Map k b -> Map k a
difference Tip t2 = Tip
difference t1 Tip = t1
difference t1 t2 = hedgeDiff (const LT) (const GT) t1 t2
hedgeDiff cmplo cmphi Tip t
= Tip
hedgeDiff cmplo cmphi (Bin _ kx x l r) Tip
= join kx x (filterGt cmplo l) (filterLt cmphi r)
hedgeDiff cmplo cmphi t (Bin _ kx x l r)
= merge (hedgeDiff cmplo cmpkx (trim cmplo cmpkx t) l)
(hedgeDiff cmpkx cmphi (trim cmpkx cmphi t) r)
where
cmpkx k = compare kx k
-- | /O(n+m)/. Difference with a combining function.
-- The implementation uses an efficient /hedge/ algorithm comparable with /hedge-union/.
differenceWith :: Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
differenceWith f m1 m2
= differenceWithKey (\k x y -> f x y) m1 m2
-- | /O(n+m)/. Difference with a combining function. When two equal keys are
-- encountered, the combining function is applied to the key and both values.
-- If it returns 'Nothing', the element is discarded (proper set difference). If
-- it returns (@'Just' y@), the element is updated with a new value @y@.
-- The implementation uses an efficient /hedge/ algorithm comparable with /hedge-union/.
differenceWithKey :: Ord k => (k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
differenceWithKey f Tip t2 = Tip
differenceWithKey f t1 Tip = t1
differenceWithKey f t1 t2 = hedgeDiffWithKey f (const LT) (const GT) t1 t2
hedgeDiffWithKey f cmplo cmphi Tip t
= Tip
hedgeDiffWithKey f cmplo cmphi (Bin _ kx x l r) Tip
= join kx x (filterGt cmplo l) (filterLt cmphi r)
hedgeDiffWithKey f cmplo cmphi t (Bin _ kx x l r)
= case found of
Nothing -> merge tl tr
Just (ky,y) ->
case f ky y x of
Nothing -> merge tl tr
Just z -> join ky z tl tr
where
cmpkx k = compare kx k
lt = trim cmplo cmpkx t
(found,gt) = trimLookupLo kx cmphi t
tl = hedgeDiffWithKey f cmplo cmpkx lt l
tr = hedgeDiffWithKey f cmpkx cmphi gt r
{--------------------------------------------------------------------
Intersection
--------------------------------------------------------------------}
-- | /O(n+m)/. Intersection of two maps. The values in the first
-- map are returned, i.e. (@'intersection' m1 m2 == 'intersectionWith' 'const' m1 m2@).
intersection :: Ord k => Map k a -> Map k b -> Map k a
intersection m1 m2
= intersectionWithKey (\k x y -> x) m1 m2
-- | /O(n+m)/. Intersection with a combining function.
intersectionWith :: Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c
intersectionWith f m1 m2
= intersectionWithKey (\k x y -> f x y) m1 m2
-- | /O(n+m)/. Intersection with a combining function.
-- Intersection is more efficient on (bigset `intersection` smallset)
--intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c
--intersectionWithKey f Tip t = Tip
--intersectionWithKey f t Tip = Tip
--intersectionWithKey f t1 t2 = intersectWithKey f t1 t2
--
--intersectWithKey f Tip t = Tip
--intersectWithKey f t Tip = Tip
--intersectWithKey f t (Bin _ kx x l r)
-- = case found of
-- Nothing -> merge tl tr
-- Just y -> join kx (f kx y x) tl tr
-- where
-- (lt,found,gt) = splitLookup kx t
-- tl = intersectWithKey f lt l
-- tr = intersectWithKey f gt r
intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c
intersectionWithKey f Tip t = Tip
intersectionWithKey f t Tip = Tip
intersectionWithKey f t1@(Bin s1 k1 x1 l1 r1) t2@(Bin s2 k2 x2 l2 r2) =
if s1 >= s2 then
let (lt,found,gt) = splitLookupWithKey k2 t1
tl = intersectionWithKey f lt l2
tr = intersectionWithKey f gt r2
in case found of
Just (k,x) -> join k (f k x x2) tl tr
Nothing -> merge tl tr
else let (lt,found,gt) = splitLookup k1 t2
tl = intersectionWithKey f l1 lt
tr = intersectionWithKey f r1 gt
in case found of
Just x -> join k1 (f k1 x1 x) tl tr
Nothing -> merge tl tr
{--------------------------------------------------------------------
Submap
--------------------------------------------------------------------}
-- | /O(n+m)/.
-- This function is defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
isSubmapOf :: (Ord k,Eq a) => Map k a -> Map k a -> Bool
isSubmapOf m1 m2
= isSubmapOfBy (==) m1 m2
{- | /O(n+m)/.
The expression (@'isSubmapOfBy' f t1 t2@) returns 'True' if
all keys in @t1@ are in tree @t2@, and when @f@ returns 'True' when
applied to their respective values. For example, the following
expressions are all 'True':
> isSubmapOfBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
> isSubmapOfBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
> isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)])
But the following are all 'False':
> isSubmapOfBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)])
> isSubmapOfBy (<) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
> isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)])
-}
isSubmapOfBy :: Ord k => (a->b->Bool) -> Map k a -> Map k b -> Bool
isSubmapOfBy f t1 t2
= (size t1 <= size t2) && (submap' f t1 t2)
submap' f Tip t = True
submap' f t Tip = False
submap' f (Bin _ kx x l r) t
= case found of
Nothing -> False
Just y -> f x y && submap' f l lt && submap' f r gt
where
(lt,found,gt) = splitLookup kx t
-- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
-- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@).
isProperSubmapOf :: (Ord k,Eq a) => Map k a -> Map k a -> Bool
isProperSubmapOf m1 m2
= isProperSubmapOfBy (==) m1 m2
{- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
@m1@ and @m2@ are not equal,
all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
applied to their respective values. For example, the following
expressions are all 'True':
> isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
But the following are all 'False':
> isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
> isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
> isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
-}
isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool
isProperSubmapOfBy f t1 t2
= (size t1 < size t2) && (submap' f t1 t2)
{--------------------------------------------------------------------
Filter and partition
--------------------------------------------------------------------}
-- | /O(n)/. Filter all values that satisfy the predicate.
filter :: Ord k => (a -> Bool) -> Map k a -> Map k a
filter p m
= filterWithKey (\k x -> p x) m
-- | /O(n)/. Filter all keys\/values that satisfy the predicate.
filterWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> Map k a
filterWithKey p Tip = Tip
filterWithKey p (Bin _ kx x l r)
| p kx x = join kx x (filterWithKey p l) (filterWithKey p r)
| otherwise = merge (filterWithKey p l) (filterWithKey p r)
-- | /O(n)/. partition the map according to a predicate. The first
-- map contains all elements that satisfy the predicate, the second all
-- elements that fail the predicate. See also 'split'.
partition :: Ord k => (a -> Bool) -> Map k a -> (Map k a,Map k a)
partition p m
= partitionWithKey (\k x -> p x) m
-- | /O(n)/. partition the map according to a predicate. The first
-- map contains all elements that satisfy the predicate, the second all
-- elements that fail the predicate. See also 'split'.
partitionWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> (Map k a,Map k a)
partitionWithKey p Tip = (Tip,Tip)
partitionWithKey p (Bin _ kx x l r)
| p kx x = (join kx x l1 r1,merge l2 r2)
| otherwise = (merge l1 r1,join kx x l2 r2)
where
(l1,l2) = partitionWithKey p l
(r1,r2) = partitionWithKey p r
-- | /O(n)/. Map values and collect the 'Just' results.
mapMaybe :: Ord k => (a -> Maybe b) -> Map k a -> Map k b
mapMaybe f m
= mapMaybeWithKey (\k x -> f x) m
-- | /O(n)/. Map keys\/values and collect the 'Just' results.
mapMaybeWithKey :: Ord k => (k -> a -> Maybe b) -> Map k a -> Map k b
mapMaybeWithKey f Tip = Tip
mapMaybeWithKey f (Bin _ kx x l r) = case f kx x of
Just y -> join kx y (mapMaybeWithKey f l) (mapMaybeWithKey f r)
Nothing -> merge (mapMaybeWithKey f l) (mapMaybeWithKey f r)
-- | /O(n)/. Map values and separate the 'Left' and 'Right' results.
mapEither :: Ord k => (a -> Either b c) -> Map k a -> (Map k b, Map k c)
mapEither f m
= mapEitherWithKey (\k x -> f x) m
-- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results.
mapEitherWithKey :: Ord k =>
(k -> a -> Either b c) -> Map k a -> (Map k b, Map k c)
mapEitherWithKey f Tip = (Tip, Tip)
mapEitherWithKey f (Bin _ kx x l r) = case f kx x of
Left y -> (join kx y l1 r1, merge l2 r2)
Right z -> (merge l1 r1, join kx z l2 r2)
where
(l1,l2) = mapEitherWithKey f l
(r1,r2) = mapEitherWithKey f r
{--------------------------------------------------------------------
Mapping
--------------------------------------------------------------------}
-- | /O(n)/. Map a function over all values in the map.
map :: (a -> b) -> Map k a -> Map k b
map f m
= mapWithKey (\k x -> f x) m
-- | /O(n)/. Map a function over all values in the map.
mapWithKey :: (k -> a -> b) -> Map k a -> Map k b
mapWithKey f Tip = Tip
mapWithKey f (Bin sx kx x l r)
= Bin sx kx (f kx x) (mapWithKey f l) (mapWithKey f r)
-- | /O(n)/. The function 'mapAccum' threads an accumulating
-- argument through the map in ascending order of keys.
mapAccum :: (a -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
mapAccum f a m
= mapAccumWithKey (\a k x -> f a x) a m
-- | /O(n)/. The function 'mapAccumWithKey' threads an accumulating
-- argument through the map in ascending order of keys.
mapAccumWithKey :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
mapAccumWithKey f a t
= mapAccumL f a t
-- | /O(n)/. The function 'mapAccumL' threads an accumulating
-- argument throught the map in ascending order of keys.
mapAccumL :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
mapAccumL f a t
= case t of
Tip -> (a,Tip)
Bin sx kx x l r
-> let (a1,l') = mapAccumL f a l
(a2,x') = f a1 kx x
(a3,r') = mapAccumL f a2 r
in (a3,Bin sx kx x' l' r')
-- | /O(n)/. The function 'mapAccumR' threads an accumulating
-- argument throught the map in descending order of keys.
mapAccumR :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
mapAccumR f a t
= case t of
Tip -> (a,Tip)
Bin sx kx x l r
-> let (a1,r') = mapAccumR f a r
(a2,x') = f a1 kx x
(a3,l') = mapAccumR f a2 l
in (a3,Bin sx kx x' l' r')
-- | /O(n*log n)/.
-- @'mapKeys' f s@ is the map obtained by applying @f@ to each key of @s@.
--
-- The size of the result may be smaller if @f@ maps two or more distinct
-- keys to the same new key. In this case the value at the smallest of
-- these keys is retained.
mapKeys :: Ord k2 => (k1->k2) -> Map k1 a -> Map k2 a
mapKeys = mapKeysWith (\x y->x)
-- | /O(n*log n)/.
-- @'mapKeysWith' c f s@ is the map obtained by applying @f@ to each key of @s@.
--
-- The size of the result may be smaller if @f@ maps two or more distinct
-- keys to the same new key. In this case the associated values will be
-- combined using @c@.
mapKeysWith :: Ord k2 => (a -> a -> a) -> (k1->k2) -> Map k1 a -> Map k2 a
mapKeysWith c f = fromListWith c . List.map fFirst . toList
where fFirst (x,y) = (f x, y)
-- | /O(n)/.
-- @'mapKeysMonotonic' f s == 'mapKeys' f s@, but works only when @f@
-- is strictly monotonic.
-- /The precondition is not checked./
-- Semi-formally, we have:
--
-- > and [x < y ==> f x < f y | x <- ls, y <- ls]
-- > ==> mapKeysMonotonic f s == mapKeys f s
-- > where ls = keys s
mapKeysMonotonic :: (k1->k2) -> Map k1 a -> Map k2 a
mapKeysMonotonic f Tip = Tip
mapKeysMonotonic f (Bin sz k x l r) =
Bin sz (f k) x (mapKeysMonotonic f l) (mapKeysMonotonic f r)
{--------------------------------------------------------------------
Folds
--------------------------------------------------------------------}
-- | /O(n)/. Fold the values in the map, such that
-- @'fold' f z == 'Prelude.foldr' f z . 'elems'@.
-- For example,
--
-- > elems map = fold (:) [] map
--
fold :: (a -> b -> b) -> b -> Map k a -> b
fold f z m
= foldWithKey (\k x z -> f x z) z m
-- | /O(n)/. Fold the keys and values in the map, such that
-- @'foldWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
-- For example,
--
-- > keys map = foldWithKey (\k x ks -> k:ks) [] map
--
foldWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b
foldWithKey f z t
= foldr f z t
-- | /O(n)/. In-order fold.
foldi :: (k -> a -> b -> b -> b) -> b -> Map k a -> b
foldi f z Tip = z
foldi f z (Bin _ kx x l r) = f kx x (foldi f z l) (foldi f z r)
-- | /O(n)/. Post-order fold.
foldr :: (k -> a -> b -> b) -> b -> Map k a -> b
foldr f z Tip = z
foldr f z (Bin _ kx x l r) = foldr f (f kx x (foldr f z r)) l
-- | /O(n)/. Pre-order fold.
foldl :: (b -> k -> a -> b) -> b -> Map k a -> b
foldl f z Tip = z
foldl f z (Bin _ kx x l r) = foldl f (f (foldl f z l) kx x) r
{--------------------------------------------------------------------
List variations
--------------------------------------------------------------------}
-- | /O(n)/.
-- Return all elements of the map in the ascending order of their keys.
elems :: Map k a -> [a]
elems m
= [x | (k,x) <- assocs m]
-- | /O(n)/. Return all keys of the map in ascending order.
keys :: Map k a -> [k]
keys m
= [k | (k,x) <- assocs m]
-- | /O(n)/. The set of all keys of the map.
keysSet :: Map k a -> Set.Set k
keysSet m = Set.fromDistinctAscList (keys m)
-- | /O(n)/. Return all key\/value pairs in the map in ascending key order.
assocs :: Map k a -> [(k,a)]
assocs m
= toList m
{--------------------------------------------------------------------
Lists
use [foldlStrict] to reduce demand on the control-stack
--------------------------------------------------------------------}
-- | /O(n*log n)/. Build a map from a list of key\/value pairs. See also 'fromAscList'.
fromList :: Ord k => [(k,a)] -> Map k a
fromList xs
= foldlStrict ins empty xs
where
ins t (k,x) = insert k x t
-- | /O(n*log n)/. Build a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
fromListWith :: Ord k => (a -> a -> a) -> [(k,a)] -> Map k a
fromListWith f xs
= fromListWithKey (\k x y -> f x y) xs
-- | /O(n*log n)/. Build a map from a list of key\/value pairs with a combining function. See also 'fromAscListWithKey'.
fromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k,a)] -> Map k a
fromListWithKey f xs
= foldlStrict ins empty xs
where
ins t (k,x) = insertWithKey f k x t
-- | /O(n)/. Convert to a list of key\/value pairs.
toList :: Map k a -> [(k,a)]
toList t = toAscList t
-- | /O(n)/. Convert to an ascending list.
toAscList :: Map k a -> [(k,a)]
toAscList t = foldr (\k x xs -> (k,x):xs) [] t
-- | /O(n)/.
toDescList :: Map k a -> [(k,a)]
toDescList t = foldl (\xs k x -> (k,x):xs) [] t
{--------------------------------------------------------------------
Building trees from ascending/descending lists can be done in linear time.
Note that if [xs] is ascending that:
fromAscList xs == fromList xs
fromAscListWith f xs == fromListWith f xs
--------------------------------------------------------------------}
-- | /O(n)/. Build a map from an ascending list in linear time.
-- /The precondition (input list is ascending) is not checked./
fromAscList :: Eq k => [(k,a)] -> Map k a
fromAscList xs
= fromAscListWithKey (\k x y -> x) xs
-- | /O(n)/. Build a map from an ascending list in linear time with a combining function for equal keys.
-- /The precondition (input list is ascending) is not checked./
fromAscListWith :: Eq k => (a -> a -> a) -> [(k,a)] -> Map k a
fromAscListWith f xs
= fromAscListWithKey (\k x y -> f x y) xs
-- | /O(n)/. Build a map from an ascending list in linear time with a
-- combining function for equal keys.
-- /The precondition (input list is ascending) is not checked./
fromAscListWithKey :: Eq k => (k -> a -> a -> a) -> [(k,a)] -> Map k a
fromAscListWithKey f xs
= fromDistinctAscList (combineEq f xs)
where
-- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs]
combineEq f xs
= case xs of
[] -> []
[x] -> [x]
(x:xx) -> combineEq' x xx
combineEq' z [] = [z]
combineEq' z@(kz,zz) (x@(kx,xx):xs)
| kx==kz = let yy = f kx xx zz in combineEq' (kx,yy) xs
| otherwise = z:combineEq' x xs
-- | /O(n)/. Build a map from an ascending list of distinct elements in linear time.
-- /The precondition is not checked./
fromDistinctAscList :: [(k,a)] -> Map k a
fromDistinctAscList xs
= build const (length xs) xs
where
-- 1) use continutations so that we use heap space instead of stack space.
-- 2) special case for n==5 to build bushier trees.
build c 0 xs = c Tip xs
build c 5 xs = case xs of
((k1,x1):(k2,x2):(k3,x3):(k4,x4):(k5,x5):xx)
-> c (bin k4 x4 (bin k2 x2 (singleton k1 x1) (singleton k3 x3)) (singleton k5 x5)) xx
build c n xs = seq nr $ build (buildR nr c) nl xs
where
nl = n `div` 2
nr = n - nl - 1
buildR n c l ((k,x):ys) = build (buildB l k x c) n ys
buildB l k x c r zs = c (bin k x l r) zs
{--------------------------------------------------------------------
Utility functions that return sub-ranges of the original
tree. Some functions take a comparison function as argument to
allow comparisons against infinite values. A function [cmplo k]
should be read as [compare lo k].
[trim cmplo cmphi t] A tree that is either empty or where [cmplo k == LT]
and [cmphi k == GT] for the key [k] of the root.
[filterGt cmp t] A tree where for all keys [k]. [cmp k == LT]
[filterLt cmp t] A tree where for all keys [k]. [cmp k == GT]
[split k t] Returns two trees [l] and [r] where all keys
in [l] are <[k] and all keys in [r] are >[k].
[splitLookup k t] Just like [split] but also returns whether [k]
was found in the tree.
--------------------------------------------------------------------}
{--------------------------------------------------------------------
[trim lo hi t] trims away all subtrees that surely contain no
values between the range [lo] to [hi]. The returned tree is either
empty or the key of the root is between @lo@ and @hi@.
--------------------------------------------------------------------}
trim :: (k -> Ordering) -> (k -> Ordering) -> Map k a -> Map k a
trim cmplo cmphi Tip = Tip
trim cmplo cmphi t@(Bin sx kx x l r)
= case cmplo kx of
LT -> case cmphi kx of
GT -> t
le -> trim cmplo cmphi l
ge -> trim cmplo cmphi r
trimLookupLo :: Ord k => k -> (k -> Ordering) -> Map k a -> (Maybe (k,a), Map k a)
trimLookupLo lo cmphi Tip = (Nothing,Tip)
trimLookupLo lo cmphi t@(Bin sx kx x l r)
= case compare lo kx of
LT -> case cmphi kx of
GT -> (lookupAssoc lo t, t)
le -> trimLookupLo lo cmphi l
GT -> trimLookupLo lo cmphi r
EQ -> (Just (kx,x),trim (compare lo) cmphi r)
{--------------------------------------------------------------------
[filterGt k t] filter all keys >[k] from tree [t]
[filterLt k t] filter all keys <[k] from tree [t]
--------------------------------------------------------------------}
filterGt :: Ord k => (k -> Ordering) -> Map k a -> Map k a
filterGt cmp Tip = Tip
filterGt cmp (Bin sx kx x l r)
= case cmp kx of
LT -> join kx x (filterGt cmp l) r
GT -> filterGt cmp r
EQ -> r
filterLt :: Ord k => (k -> Ordering) -> Map k a -> Map k a
filterLt cmp Tip = Tip
filterLt cmp (Bin sx kx x l r)
= case cmp kx of
LT -> filterLt cmp l
GT -> join kx x l (filterLt cmp r)
EQ -> l
{--------------------------------------------------------------------
Split
--------------------------------------------------------------------}
-- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@ where
-- the keys in @map1@ are smaller than @k@ and the keys in @map2@ larger than @k@. Any key equal to @k@ is found in neither @map1@ nor @map2@.
split :: Ord k => k -> Map k a -> (Map k a,Map k a)
split k Tip = (Tip,Tip)
split k (Bin sx kx x l r)
= case compare k kx of
LT -> let (lt,gt) = split k l in (lt,join kx x gt r)
GT -> let (lt,gt) = split k r in (join kx x l lt,gt)
EQ -> (l,r)
-- | /O(log n)/. The expression (@'splitLookup' k map@) splits a map just
-- like 'split' but also returns @'lookup' k map@.
splitLookup :: Ord k => k -> Map k a -> (Map k a,Maybe a,Map k a)
splitLookup k Tip = (Tip,Nothing,Tip)
splitLookup k (Bin sx kx x l r)
= case compare k kx of
LT -> let (lt,z,gt) = splitLookup k l in (lt,z,join kx x gt r)
GT -> let (lt,z,gt) = splitLookup k r in (join kx x l lt,z,gt)
EQ -> (l,Just x,r)
-- | /O(log n)/.
splitLookupWithKey :: Ord k => k -> Map k a -> (Map k a,Maybe (k,a),Map k a)
splitLookupWithKey k Tip = (Tip,Nothing,Tip)
splitLookupWithKey k (Bin sx kx x l r)
= case compare k kx of
LT -> let (lt,z,gt) = splitLookupWithKey k l in (lt,z,join kx x gt r)
GT -> let (lt,z,gt) = splitLookupWithKey k r in (join kx x l lt,z,gt)
EQ -> (l,Just (kx, x),r)
-- | /O(log n)/. Performs a 'split' but also returns whether the pivot
-- element was found in the original set.
splitMember :: Ord k => k -> Map k a -> (Map k a,Bool,Map k a)
splitMember x t = let (l,m,r) = splitLookup x t in
(l,maybe False (const True) m,r)
{--------------------------------------------------------------------
Utility functions that maintain the balance properties of the tree.
All constructors assume that all values in [l] < [k] and all values
in [r] > [k], and that [l] and [r] are valid trees.
In order of sophistication:
[Bin sz k x l r] The type constructor.
[bin k x l r] Maintains the correct size, assumes that both [l]
and [r] are balanced with respect to each other.
[balance k x l r] Restores the balance and size.
Assumes that the original tree was balanced and
that [l] or [r] has changed by at most one element.
[join k x l r] Restores balance and size.
Furthermore, we can construct a new tree from two trees. Both operations
assume that all values in [l] < all values in [r] and that [l] and [r]
are valid:
[glue l r] Glues [l] and [r] together. Assumes that [l] and
[r] are already balanced with respect to each other.
[merge l r] Merges two trees and restores balance.
Note: in contrast to Adam's paper, we use (<=) comparisons instead
of (<) comparisons in [join], [merge] and [balance].
Quickcheck (on [difference]) showed that this was necessary in order
to maintain the invariants. It is quite unsatisfactory that I haven't
been able to find out why this is actually the case! Fortunately, it
doesn't hurt to be a bit more conservative.
--------------------------------------------------------------------}
{--------------------------------------------------------------------
Join
--------------------------------------------------------------------}
join :: Ord k => k -> a -> Map k a -> Map k a -> Map k a
join kx x Tip r = insertMin kx x r
join kx x l Tip = insertMax kx x l
join kx x l@(Bin sizeL ky y ly ry) r@(Bin sizeR kz z lz rz)
| delta*sizeL <= sizeR = balance kz z (join kx x l lz) rz
| delta*sizeR <= sizeL = balance ky y ly (join kx x ry r)
| otherwise = bin kx x l r
-- insertMin and insertMax don't perform potentially expensive comparisons.
insertMax,insertMin :: k -> a -> Map k a -> Map k a
insertMax kx x t
= case t of
Tip -> singleton kx x
Bin sz ky y l r
-> balance ky y l (insertMax kx x r)
insertMin kx x t
= case t of
Tip -> singleton kx x
Bin sz ky y l r
-> balance ky y (insertMin kx x l) r
{--------------------------------------------------------------------
[merge l r]: merges two trees.
--------------------------------------------------------------------}
merge :: Map k a -> Map k a -> Map k a
merge Tip r = r
merge l Tip = l
merge l@(Bin sizeL kx x lx rx) r@(Bin sizeR ky y ly ry)
| delta*sizeL <= sizeR = balance ky y (merge l ly) ry
| delta*sizeR <= sizeL = balance kx x lx (merge rx r)
| otherwise = glue l r
{--------------------------------------------------------------------
[glue l r]: glues two trees together.
Assumes that [l] and [r] are already balanced with respect to each other.
--------------------------------------------------------------------}
glue :: Map k a -> Map k a -> Map k a
glue Tip r = r
glue l Tip = l
glue l r
| size l > size r = let ((km,m),l') = deleteFindMax l in balance km m l' r
| otherwise = let ((km,m),r') = deleteFindMin r in balance km m l r'
-- | /O(log n)/. Delete and find the minimal element.
deleteFindMin :: Map k a -> ((k,a),Map k a)
deleteFindMin t
= case t of
Bin _ k x Tip r -> ((k,x),r)
Bin _ k x l r -> let (km,l') = deleteFindMin l in (km,balance k x l' r)
Tip -> (error "Map.deleteFindMin: can not return the minimal element of an empty map", Tip)
-- | /O(log n)/. Delete and find the maximal element.
deleteFindMax :: Map k a -> ((k,a),Map k a)
deleteFindMax t
= case t of
Bin _ k x l Tip -> ((k,x),l)
Bin _ k x l r -> let (km,r') = deleteFindMax r in (km,balance k x l r')
Tip -> (error "Map.deleteFindMax: can not return the maximal element of an empty map", Tip)
{--------------------------------------------------------------------
[balance l x r] balances two trees with value x.
The sizes of the trees should balance after decreasing the
size of one of them. (a rotation).
[delta] is the maximal relative difference between the sizes of
two trees, it corresponds with the [w] in Adams' paper.
[ratio] is the ratio between an outer and inner sibling of the
heavier subtree in an unbalanced setting. It determines
whether a double or single rotation should be performed
to restore balance. It is correspondes with the inverse
of $\alpha$ in Adam's article.
Note that:
- [delta] should be larger than 4.646 with a [ratio] of 2.
- [delta] should be larger than 3.745 with a [ratio] of 1.534.
- A lower [delta] leads to a more 'perfectly' balanced tree.
- A higher [delta] performs less rebalancing.
- Balancing is automatic for random data and a balancing
scheme is only necessary to avoid pathological worst cases.
Almost any choice will do, and in practice, a rather large
[delta] may perform better than smaller one.
Note: in contrast to Adam's paper, we use a ratio of (at least) [2]
to decide whether a single or double rotation is needed. Allthough
he actually proves that this ratio is needed to maintain the
invariants, his implementation uses an invalid ratio of [1].
--------------------------------------------------------------------}
delta,ratio :: Int
delta = 5
ratio = 2
balance :: k -> a -> Map k a -> Map k a -> Map k a
balance k x l r
| sizeL + sizeR <= 1 = Bin sizeX k x l r
| sizeR >= delta*sizeL = rotateL k x l r
| sizeL >= delta*sizeR = rotateR k x l r
| otherwise = Bin sizeX k x l r
where
sizeL = size l
sizeR = size r
sizeX = sizeL + sizeR + 1
-- rotate
rotateL k x l r@(Bin _ _ _ ly ry)
| size ly < ratio*size ry = singleL k x l r
| otherwise = doubleL k x l r
rotateR k x l@(Bin _ _ _ ly ry) r
| size ry < ratio*size ly = singleR k x l r
| otherwise = doubleR k x l r
-- basic rotations
singleL k1 x1 t1 (Bin _ k2 x2 t2 t3) = bin k2 x2 (bin k1 x1 t1 t2) t3
singleR k1 x1 (Bin _ k2 x2 t1 t2) t3 = bin k2 x2 t1 (bin k1 x1 t2 t3)
doubleL k1 x1 t1 (Bin _ k2 x2 (Bin _ k3 x3 t2 t3) t4) = bin k3 x3 (bin k1 x1 t1 t2) (bin k2 x2 t3 t4)
doubleR k1 x1 (Bin _ k2 x2 t1 (Bin _ k3 x3 t2 t3)) t4 = bin k3 x3 (bin k2 x2 t1 t2) (bin k1 x1 t3 t4)
{--------------------------------------------------------------------
The bin constructor maintains the size of the tree
--------------------------------------------------------------------}
bin :: k -> a -> Map k a -> Map k a -> Map k a
bin k x l r
= Bin (size l + size r + 1) k x l r
{--------------------------------------------------------------------
Eq converts the tree to a list. In a lazy setting, this
actually seems one of the faster methods to compare two trees
and it is certainly the simplest :-)
--------------------------------------------------------------------}
instance (Eq k,Eq a) => Eq (Map k a) where
t1 == t2 = (size t1 == size t2) && (toAscList t1 == toAscList t2)
{--------------------------------------------------------------------
Ord
--------------------------------------------------------------------}
instance (Ord k, Ord v) => Ord (Map k v) where
compare m1 m2 = compare (toAscList m1) (toAscList m2)
{--------------------------------------------------------------------
Functor
--------------------------------------------------------------------}
instance Functor (Map k) where
fmap f m = map f m
instance Traversable (Map k) where
traverse f Tip = pure Tip
traverse f (Bin s k v l r)
= flip (Bin s k) <$> traverse f l <*> f v <*> traverse f r
instance Foldable (Map k) where
foldMap _f Tip = mempty
foldMap f (Bin _s _k v l r)
= foldMap f l `mappend` f v `mappend` foldMap f r
{--------------------------------------------------------------------
Read
--------------------------------------------------------------------}
instance (Ord k, Read k, Read e) => Read (Map k e) where
readsPrec p = readParen (p > 10) $ \ r -> do
("fromList",s) <- lex r
(xs,t) <- reads s
return (fromList xs,t)
-- parses a pair of things with the syntax a:=b
readPair :: (Read a, Read b) => ReadS (a,b)
readPair s = do (a, ct1) <- reads s
(":=", ct2) <- lex ct1
(b, ct3) <- reads ct2
return ((a,b), ct3)
{--------------------------------------------------------------------
Show
--------------------------------------------------------------------}
instance (Show k, Show a) => Show (Map k a) where
showsPrec d m = showParen (d > 10) $
showString "fromList " . shows (toList m)
showMap :: (Show k,Show a) => [(k,a)] -> ShowS
showMap []
= showString "{}"
showMap (x:xs)
= showChar '{' . showElem x . showTail xs
where
showTail [] = showChar '}'
showTail (x:xs) = showString ", " . showElem x . showTail xs
showElem (k,x) = shows k . showString " := " . shows x
-- | /O(n)/. Show the tree that implements the map. The tree is shown
-- in a compressed, hanging format.
showTree :: (Show k,Show a) => Map k a -> String
showTree m
= showTreeWith showElem True False m
where
showElem k x = show k ++ ":=" ++ show x
{- | /O(n)/. The expression (@'showTreeWith' showelem hang wide map@) shows
the tree that implements the map. Elements are shown using the @showElem@ function. If @hang@ is
'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
@wide@ is 'True', an extra wide version is shown.
> Map> let t = fromDistinctAscList [(x,()) | x <- [1..5]]
> Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True False t
> (4,())
> +--(2,())
> | +--(1,())
> | +--(3,())
> +--(5,())
>
> Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True True t
> (4,())
> |
> +--(2,())
> | |
> | +--(1,())
> | |
> | +--(3,())
> |
> +--(5,())
>
> Map> putStrLn $ showTreeWith (\k x -> show (k,x)) False True t
> +--(5,())
> |
> (4,())
> |
> | +--(3,())
> | |
> +--(2,())
> |
> +--(1,())
-}
showTreeWith :: (k -> a -> String) -> Bool -> Bool -> Map k a -> String
showTreeWith showelem hang wide t
| hang = (showsTreeHang showelem wide [] t) ""
| otherwise = (showsTree showelem wide [] [] t) ""
showsTree :: (k -> a -> String) -> Bool -> [String] -> [String] -> Map k a -> ShowS
showsTree showelem wide lbars rbars t
= case t of
Tip -> showsBars lbars . showString "|\n"
Bin sz kx x Tip Tip
-> showsBars lbars . showString (showelem kx x) . showString "\n"
Bin sz kx x l r
-> showsTree showelem wide (withBar rbars) (withEmpty rbars) r .
showWide wide rbars .
showsBars lbars . showString (showelem kx x) . showString "\n" .
showWide wide lbars .
showsTree showelem wide (withEmpty lbars) (withBar lbars) l
showsTreeHang :: (k -> a -> String) -> Bool -> [String] -> Map k a -> ShowS
showsTreeHang showelem wide bars t
= case t of
Tip -> showsBars bars . showString "|\n"
Bin sz kx x Tip Tip
-> showsBars bars . showString (showelem kx x) . showString "\n"
Bin sz kx x l r
-> showsBars bars . showString (showelem kx x) . showString "\n" .
showWide wide bars .
showsTreeHang showelem wide (withBar bars) l .
showWide wide bars .
showsTreeHang showelem wide (withEmpty bars) r
showWide wide bars
| wide = showString (concat (reverse bars)) . showString "|\n"
| otherwise = id
showsBars :: [String] -> ShowS
showsBars bars
= case bars of
[] -> id
_ -> showString (concat (reverse (tail bars))) . showString node
node = "+--"
withBar bars = "| ":bars
withEmpty bars = " ":bars
{--------------------------------------------------------------------
Typeable
--------------------------------------------------------------------}
mapTc = mkTyCon "Map"; instance Typeable2 Map where { typeOf2 _ = mkTyConApp mapTc [] }; instance Typeable a => Typeable1 (Map a) where { typeOf1 = typeOf1Default }; instance (Typeable a, Typeable b) => Typeable (Map a b) where { typeOf = typeOfDefault }
{--------------------------------------------------------------------
Assertions
--------------------------------------------------------------------}
-- | /O(n)/. Test if the internal map structure is valid.
valid :: Ord k => Map k a -> Bool
valid t
= balanced t && ordered t && validsize t
ordered t
= bounded (const True) (const True) t
where
bounded lo hi t
= case t of
Tip -> True
Bin sz kx x l r -> (lo kx) && (hi kx) && bounded lo (<kx) l && bounded (>kx) hi r
-- | Exported only for "Debug.QuickCheck"
balanced :: Map k a -> Bool
balanced t
= case t of
Tip -> True
Bin sz kx x l r -> (size l + size r <= 1 || (size l <= delta*size r && size r <= delta*size l)) &&
balanced l && balanced r
validsize t
= (realsize t == Just (size t))
where
realsize t
= case t of
Tip -> Just 0
Bin sz kx x l r -> case (realsize l,realsize r) of
(Just n,Just m) | n+m+1 == sz -> Just sz
other -> Nothing
{--------------------------------------------------------------------
Utilities
--------------------------------------------------------------------}
foldlStrict f z xs
= case xs of
[] -> z
(x:xx) -> let z' = f z x in seq z' (foldlStrict f z' xx)
{-
{--------------------------------------------------------------------
Testing
--------------------------------------------------------------------}
testTree xs = fromList [(x,"*") | x <- xs]
test1 = testTree [1..20]
test2 = testTree [30,29..10]
test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
{--------------------------------------------------------------------
QuickCheck
--------------------------------------------------------------------}
qcheck prop
= check config prop
where
config = Config
{ configMaxTest = 500
, configMaxFail = 5000
, configSize = \n -> (div n 2 + 3)
, configEvery = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
}
{--------------------------------------------------------------------
Arbitrary, reasonably balanced trees
--------------------------------------------------------------------}
instance (Enum k,Arbitrary a) => Arbitrary (Map k a) where
arbitrary = sized (arbtree 0 maxkey)
where maxkey = 10000
arbtree :: (Enum k,Arbitrary a) => Int -> Int -> Int -> Gen (Map k a)
arbtree lo hi n
| n <= 0 = return Tip
| lo >= hi = return Tip
| otherwise = do{ x <- arbitrary
; i <- choose (lo,hi)
; m <- choose (1,30)
; let (ml,mr) | m==(1::Int)= (1,2)
| m==2 = (2,1)
| m==3 = (1,1)
| otherwise = (2,2)
; l <- arbtree lo (i-1) (n `div` ml)
; r <- arbtree (i+1) hi (n `div` mr)
; return (bin (toEnum i) x l r)
}
{--------------------------------------------------------------------
Valid tree's
--------------------------------------------------------------------}
forValid :: (Show k,Enum k,Show a,Arbitrary a,Testable b) => (Map k a -> b) -> Property
forValid f
= forAll arbitrary $ \t ->
-- classify (balanced t) "balanced" $
classify (size t == 0) "empty" $
classify (size t > 0 && size t <= 10) "small" $
classify (size t > 10 && size t <= 64) "medium" $
classify (size t > 64) "large" $
balanced t ==> f t
forValidIntTree :: Testable a => (Map Int Int -> a) -> Property
forValidIntTree f
= forValid f
forValidUnitTree :: Testable a => (Map Int () -> a) -> Property
forValidUnitTree f
= forValid f
prop_Valid
= forValidUnitTree $ \t -> valid t
{--------------------------------------------------------------------
Single, Insert, Delete
--------------------------------------------------------------------}
prop_Single :: Int -> Int -> Bool
prop_Single k x
= (insert k x empty == singleton k x)
prop_InsertValid :: Int -> Property
prop_InsertValid k
= forValidUnitTree $ \t -> valid (insert k () t)
prop_InsertDelete :: Int -> Map Int () -> Property
prop_InsertDelete k t
= (lookup k t == Nothing) ==> delete k (insert k () t) == t
prop_DeleteValid :: Int -> Property
prop_DeleteValid k
= forValidUnitTree $ \t ->
valid (delete k (insert k () t))
{--------------------------------------------------------------------
Balance
--------------------------------------------------------------------}
prop_Join :: Int -> Property
prop_Join k
= forValidUnitTree $ \t ->
let (l,r) = split k t
in valid (join k () l r)
prop_Merge :: Int -> Property
prop_Merge k
= forValidUnitTree $ \t ->
let (l,r) = split k t
in valid (merge l r)
{--------------------------------------------------------------------
Union
--------------------------------------------------------------------}
prop_UnionValid :: Property
prop_UnionValid
= forValidUnitTree $ \t1 ->
forValidUnitTree $ \t2 ->
valid (union t1 t2)
prop_UnionInsert :: Int -> Int -> Map Int Int -> Bool
prop_UnionInsert k x t
= union (singleton k x) t == insert k x t
prop_UnionAssoc :: Map Int Int -> Map Int Int -> Map Int Int -> Bool
prop_UnionAssoc t1 t2 t3
= union t1 (union t2 t3) == union (union t1 t2) t3
prop_UnionComm :: Map Int Int -> Map Int Int -> Bool
prop_UnionComm t1 t2
= (union t1 t2 == unionWith (\x y -> y) t2 t1)
prop_UnionWithValid
= forValidIntTree $ \t1 ->
forValidIntTree $ \t2 ->
valid (unionWithKey (\k x y -> x+y) t1 t2)
prop_UnionWith :: [(Int,Int)] -> [(Int,Int)] -> Bool
prop_UnionWith xs ys
= sum (elems (unionWith (+) (fromListWith (+) xs) (fromListWith (+) ys)))
== (sum (Prelude.map snd xs) + sum (Prelude.map snd ys))
prop_DiffValid
= forValidUnitTree $ \t1 ->
forValidUnitTree $ \t2 ->
valid (difference t1 t2)
prop_Diff :: [(Int,Int)] -> [(Int,Int)] -> Bool
prop_Diff xs ys
= List.sort (keys (difference (fromListWith (+) xs) (fromListWith (+) ys)))
== List.sort ((List.\\) (nub (Prelude.map fst xs)) (nub (Prelude.map fst ys)))
prop_IntValid
= forValidUnitTree $ \t1 ->
forValidUnitTree $ \t2 ->
valid (intersection t1 t2)
prop_Int :: [(Int,Int)] -> [(Int,Int)] -> Bool
prop_Int xs ys
= List.sort (keys (intersection (fromListWith (+) xs) (fromListWith (+) ys)))
== List.sort (nub ((List.intersect) (Prelude.map fst xs) (Prelude.map fst ys)))
{--------------------------------------------------------------------
Lists
--------------------------------------------------------------------}
prop_Ordered
= forAll (choose (5,100)) $ \n ->
let xs = [(x,()) | x <- [0..n::Int]]
in fromAscList xs == fromList xs
prop_List :: [Int] -> Bool
prop_List xs
= (sort (nub xs) == [x | (x,()) <- toList (fromList [(x,()) | x <- xs])])
-}
|