Meeting 16 - Higher-Order Fun

Author

Bor-Yuh Evan Chang

Published

Saturday, October 12, 2024

\(\newcommand{\TirName}[1]{\text{#1}} \newcommand{\inferrule}[3][]{ \let\and\qquad \begin{array}{@{}l@{}} \TirName{#1} \\ \displaystyle \frac{#2}{#3} \end{array} } \newcommand{\infer}[3][]{\inferrule[#1]{#2}{#3}} \)

What questions does your neighbor have?

Announcements

  • HW4 due Mon 10/21 6pm
  • Exam 1-2 feedback released
    • See CM Lawrence about errors grading
    • See me and TAs about how to improve for next time
  • Prof. Chang traveling next week

Today

Questions?

  • Review:
    • What is a higher-order function?

Questions?

Higher-Order Functions

Currying

res0: Int = 0
res1_0: Int => Int = ammonite.$sess.cmd1$Helper$$Lambda$1879/0x0000000800a84040@dbf2d1d
res1_1: Int = 42
incr: Int => Int = ammonite.$sess.cmd1$Helper$$Lambda$1881/0x0000000800a85840@5fe7816d
res1_3: Int = 42
plus: Int => Int => Int = ammonite.$sess.cmd2$Helper$$Lambda$1923/0x0000000800a9f040@566da122
res2_1: Int = 7
defined function plus
res3_1: Int = 7
incr: Int => Int = ammonite.$sess.cmd4$Helper$$Lambda$1940/0x0000000800aad840@615a8fd5
res4_1: Int = 42
defined function addToFactorial
tenFactorialPlus: Int => Int = ammonite.$sess.cmd5$Helper$$Lambda$1968/0x0000000800acd040@173d7df4
res6_1: Int = 3628847
res6_2: Int = 3628859

Collections and Callbacks

Map

res7: Int = 0
defined function increment
res8_1: List[Int] = List(2, 3, 4)
defined function double
res9_1: List[Int] = List(2, 4, 6)
defined function eachLength
res10_1: List[Int] = List(3, 7, 8)
defined function map
defined function increment
res12_1: List[Int] = List(2, 3, 4)
defined function double
res13_1: List[Int] = List(2, 4, 6)
defined function eachLength
res14_1: List[Int] = List(3, 7, 8)
res15: List[Int] = List(3, 6, 9)
res16_0: List[Int] = List(3, 6, 9)
res16_1: List[Int] = List(3, 6, 9)
res17_0: List[Int] = List(4, 7, 10)
res17_1: List[Int] = List(4, 7, 10)
res18_0: List[Int] = List(4, 7, 10)
res18_1: List[Int] = List(4, 7, 10)
res19_0: List[Int] = List(3, 6, 9)
res19_1: List[Int] = List(3, 6, 9)
res20: List[Int] = List(3, 9)
res21: List[Int] = List(3, 9)
res22_0: List[Int] = List(1, 3)
res22_1: List[Int] = List(1, 3)
res22_2: collection.WithFilter[Int, List[_]] = scala.collection.IterableOps$WithFilter@55e0d2ab
res22_3: List[Int] = List(1, 3)
res23_0: List[Int] = List(3, 9)
res23_1: List[Int] = List(1, 3)
res24: List[Int] = List(0, 4, 5, 0)
res25: List[Int] = List(0, 4, 5, 0)

FlatMap

defined function map
defined function flatMap
defined function duplicate
res28_1: List[Int] = List(1, 1, 2, 2, 3, 3)
mapped: List[List[Int]] = List(List(1, 1), List(2, 2), List(3, 3))
flattened: List[Int] = List(1, 1, 2, 2, 3, 3)

Exercise 1 Define map in terms of flatMap.

defined function map

Exercise 2 Define filter in terms of flatMap.

defined function filter

FoldRight

defined function addList
res32_1: Int = 10
defined function multList
res33_1: Int = 24
defined function foldRight
defined function addList
res35_1: Int = 10
defined function multList
res35_3: Int = 24
res36_0: Int = 10
res36_1: Int = 24
defined function foldRight

Exercise 3 Define map in terms of foldRight

defined function map

Exercise 4 Define append: (List[A], List[A]) => List[A] that appends together two lists into one list (i.e., returns l1 follows by l2) in terms of foldRight:

defined function append

FoldLeft

defined function foldLeft
res41: Int = 24

Exercise 5 Define reverse of a list in terms of foldLeft.

defined function reverse
res43: Int = 24
res44: Int = 24

Abstract Data Types

m: Map[Int, List[String]] = Map(
  2 -> List("two", "dos", "\u4e8c"),
  10 -> List("ten", "diez", "\u5341")
)
res46: Map[Int, String] = Map(2 -> "two", 10 -> "ten")
res47: List[String] = List("two", "ten")

Parallel and Distributed

Scala Parallel Collections Library

Run the following cell to load the Scala Parallel Collections library.

import $ivy.$                                                         , scala.collection.parallel.CollectionConverters._
par0to9999: collection.parallel.immutable.ParSeq[Int] = ParVector(0, 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, ...
sum: Int = 50005000