|
| 1 | +def pair(x, y): |
| 2 | + """ |
| 3 | + PRIMITIVE |
| 4 | + Makes a pair whose head (first component) is x and whose |
| 5 | + tail (second component) is y. |
| 6 | +
|
| 7 | + Parameters: |
| 8 | + x (value): given head |
| 9 | + y (value): given tail |
| 10 | +
|
| 11 | + Returns: |
| 12 | + pair: pair with x as head and y as tail |
| 13 | + """ |
| 14 | + pass |
| 15 | + |
| 16 | + |
| 17 | +def is_pair(x): |
| 18 | + """ |
| 19 | + PRIMITIVE |
| 20 | + Returns true if x is a pair and false otherwise. |
| 21 | +
|
| 22 | + Parameters: |
| 23 | + x (value): given value |
| 24 | +
|
| 25 | + Returns: |
| 26 | + boolean: whether x is a pair |
| 27 | + """ |
| 28 | + pass |
| 29 | + |
| 30 | + |
| 31 | +def head(p): |
| 32 | + """ |
| 33 | + PRIMITIVE |
| 34 | + Returns head (first component) of given pair p. |
| 35 | +
|
| 36 | + Parameters: |
| 37 | + p (pair): given pair |
| 38 | +
|
| 39 | + Returns: |
| 40 | + value: head of p |
| 41 | + """ |
| 42 | + pass |
| 43 | + |
| 44 | + |
| 45 | +def tail(p): |
| 46 | + """ |
| 47 | + PRIMITIVE |
| 48 | + Returns tail (second component) of given pair p. |
| 49 | +
|
| 50 | + Parameters: |
| 51 | + p (pair): given pair |
| 52 | +
|
| 53 | + Returns: |
| 54 | + value: tail of p |
| 55 | + """ |
| 56 | + pass |
| 57 | + |
| 58 | + |
| 59 | +def is_none(x): |
| 60 | + """ |
| 61 | + PRIMITIVE |
| 62 | + Returns true if x is the empty linked list None, and false otherwise. |
| 63 | +
|
| 64 | + Parameters: |
| 65 | + x (value): given value |
| 66 | +
|
| 67 | + Returns: |
| 68 | + boolean: whether x is None |
| 69 | + """ |
| 70 | + pass |
| 71 | + |
| 72 | + |
| 73 | +def is_linked_list(xs): |
| 74 | + """ |
| 75 | + PRIMITIVE |
| 76 | + Returns true if xs is a linked list as defined in the textbook, and |
| 77 | + false otherwise. |
| 78 | +
|
| 79 | + Parameters: |
| 80 | + xs (value): given value |
| 81 | +
|
| 82 | + Returns: |
| 83 | + boolean: whether xs is a linked list |
| 84 | + """ |
| 85 | + pass |
| 86 | + |
| 87 | + |
| 88 | +def linked_list(*values): |
| 89 | + """ |
| 90 | + PRIMITIVE |
| 91 | + Given n values, returns a linked list of length n. The elements of |
| 92 | + the linked list are the given values in the given order. |
| 93 | +
|
| 94 | + Parameters: |
| 95 | + value (value1, value2, ...values): given values |
| 96 | +
|
| 97 | + Returns: |
| 98 | + linked list: linked list containing all values |
| 99 | + """ |
| 100 | + pass |
| 101 | + |
| 102 | + |
| 103 | +def draw_data(value1, value2, *values): |
| 104 | + """ |
| 105 | + PRIMITIVE |
| 106 | + Visualizes the arguments in a separate drawing area in the Source |
| 107 | + Academy using box-and-pointer diagrams. |
| 108 | +
|
| 109 | + Parameters: |
| 110 | + value1 (value1, value2, ...values): given values |
| 111 | + """ |
| 112 | + pass |
| 113 | + |
| 114 | + |
| 115 | +def equal(xs, ys): |
| 116 | + """ |
| 117 | + Pure Function: Returns true if both have the same structure (pairs) |
| 118 | + and identical values at corresponding leaf positions. |
| 119 | + """ |
| 120 | + if is_pair(xs): |
| 121 | + return ( |
| 122 | + is_pair(ys) |
| 123 | + and equal(head(xs), head(ys)) |
| 124 | + and equal(tail(xs), tail(ys)) |
| 125 | + ) |
| 126 | + elif is_none(xs): |
| 127 | + return is_none(ys) |
| 128 | + elif is_int(xs): |
| 129 | + return is_int(ys) and xs == ys |
| 130 | + elif is_float(xs): |
| 131 | + return is_float(ys) and xs == ys |
| 132 | + elif is_boolean(xs): |
| 133 | + return is_boolean(ys) and ((xs and ys) or (not xs and not ys)) |
| 134 | + elif is_string(xs): |
| 135 | + return is_string(ys) and xs == ys |
| 136 | + else: |
| 137 | + return False |
| 138 | + |
| 139 | + |
| 140 | +def length(xs): |
| 141 | + """ |
| 142 | + Returns the length of the linked list xs. |
| 143 | + """ |
| 144 | + return _length(xs, 0) |
| 145 | + |
| 146 | + |
| 147 | +def _length(xs, acc): |
| 148 | + return acc if is_none(xs) else _length(tail(xs), acc + 1) |
| 149 | + |
| 150 | + |
| 151 | +def map_linked_list(f, xs): |
| 152 | + """ |
| 153 | + Returns a linked list that results from linked list xs by element-wise |
| 154 | + application of unary function f. |
| 155 | + """ |
| 156 | + return _map_linked_list(f, xs, None) |
| 157 | + |
| 158 | + |
| 159 | +def _map_linked_list(f, xs, acc): |
| 160 | + return ( |
| 161 | + reverse(acc) |
| 162 | + if is_none(xs) |
| 163 | + else _map_linked_list(f, tail(xs), pair(f(head(xs)), acc)) |
| 164 | + ) |
| 165 | + |
| 166 | + |
| 167 | +def build_linked_list(fun, n): |
| 168 | + """ |
| 169 | + Makes a linked list with n elements by applying the unary function fun |
| 170 | + to the numbers 0 to n - 1. |
| 171 | + """ |
| 172 | + return _build_linked_list(n - 1, fun, None) |
| 173 | + |
| 174 | + |
| 175 | +def _build_linked_list(i, fun, already_built): |
| 176 | + return ( |
| 177 | + already_built |
| 178 | + if i < 0 |
| 179 | + else _build_linked_list(i - 1, fun, pair(fun(i), already_built)) |
| 180 | + ) |
| 181 | + |
| 182 | + |
| 183 | +def for_each(fun, xs): |
| 184 | + """ |
| 185 | + Applies the unary function fun to every element of the linked list xs. |
| 186 | + """ |
| 187 | + if is_none(xs): |
| 188 | + return True |
| 189 | + else: |
| 190 | + fun(head(xs)) # Side effect happens here if fun is not pure |
| 191 | + return for_each(fun, tail(xs)) |
| 192 | + |
| 193 | + |
| 194 | +def linked_list_to_string(xs): |
| 195 | + """ |
| 196 | + Returns a string that represents linked list xs using the text-based |
| 197 | + box-and-pointer notation. |
| 198 | + """ |
| 199 | + return _linked_list_to_string(xs, lambda x: x) |
| 200 | + |
| 201 | + |
| 202 | +def _linked_list_to_string(xs, cont): |
| 203 | + if is_none(xs): |
| 204 | + return cont("None") |
| 205 | + elif is_pair(xs): |
| 206 | + return _linked_list_to_string( |
| 207 | + head(xs), |
| 208 | + lambda x_str: _linked_list_to_string( |
| 209 | + tail(xs), lambda y_str: cont(f"[{x_str},{y_str}]") |
| 210 | + ), |
| 211 | + ) |
| 212 | + else: |
| 213 | + return cont(stringify(xs)) |
| 214 | + |
| 215 | + |
| 216 | +def reverse(xs): |
| 217 | + """ |
| 218 | + Returns linked list xs in reverse order. |
| 219 | + """ |
| 220 | + return _reverse(xs, None) |
| 221 | + |
| 222 | + |
| 223 | +def _reverse(original, reversed_acc): |
| 224 | + return ( |
| 225 | + reversed_acc |
| 226 | + if is_none(original) |
| 227 | + else _reverse(tail(original), pair(head(original), reversed_acc)) |
| 228 | + ) |
| 229 | + |
| 230 | + |
| 231 | +def append(xs, ys): |
| 232 | + """ |
| 233 | + Returns a linked list that results from appending the linked list ys |
| 234 | + to the linked list xs. |
| 235 | + """ |
| 236 | + return _append(xs, ys, lambda x: x) |
| 237 | + |
| 238 | + |
| 239 | +def _append(xs, ys, cont): |
| 240 | + return ( |
| 241 | + cont(ys) |
| 242 | + if is_none(xs) |
| 243 | + else _append(tail(xs), ys, lambda zs: cont(pair(head(xs), zs))) |
| 244 | + ) |
| 245 | + |
| 246 | + |
| 247 | +def member(v, xs): |
| 248 | + """ |
| 249 | + Returns first postfix sub-linked list whose head is identical to v |
| 250 | + (using ==). Returns None if the element does not occur in the linked |
| 251 | + list. |
| 252 | + """ |
| 253 | + if is_none(xs): |
| 254 | + return None |
| 255 | + elif v == head(xs): |
| 256 | + return xs |
| 257 | + else: |
| 258 | + return member(v, tail(xs)) |
| 259 | + |
| 260 | + |
| 261 | +def remove(v, xs): |
| 262 | + """ |
| 263 | + Returns a linked list that results from xs by removing the first item |
| 264 | + from xs that is identical (==) to v. |
| 265 | + """ |
| 266 | + return _remove(v, xs, None) |
| 267 | + |
| 268 | + |
| 269 | +def _remove(v, xs, acc): |
| 270 | + if is_none(xs): |
| 271 | + return append(reverse(acc), xs) |
| 272 | + elif v == head(xs): |
| 273 | + return append(reverse(acc), tail(xs)) |
| 274 | + else: |
| 275 | + return _remove(v, tail(xs), pair(head(xs), acc)) |
| 276 | + |
| 277 | + |
| 278 | +def remove_all(v, xs): |
| 279 | + """ |
| 280 | + Returns a linked list that results from xs by removing all items from |
| 281 | + xs that are identical (==) to v. |
| 282 | + """ |
| 283 | + return _remove_all(v, xs, None) |
| 284 | + |
| 285 | + |
| 286 | +def _remove_all(v, xs, acc): |
| 287 | + if is_none(xs): |
| 288 | + return append(reverse(acc), xs) |
| 289 | + elif v == head(xs): |
| 290 | + return _remove_all(v, tail(xs), acc) |
| 291 | + else: |
| 292 | + return _remove_all(v, tail(xs), pair(head(xs), acc)) |
| 293 | + |
| 294 | + |
| 295 | +def enum_linked_list(start, end): |
| 296 | + """ |
| 297 | + Makes a linked list with elements from start to end (inclusive). |
| 298 | + """ |
| 299 | + return _enum_linked_list(start, end, None) |
| 300 | + |
| 301 | + |
| 302 | +def _enum_linked_list(start, end, acc): |
| 303 | + return ( |
| 304 | + reverse(acc) |
| 305 | + if start > end |
| 306 | + else _enum_linked_list(start + 1, end, pair(start, acc)) |
| 307 | + ) |
| 308 | + |
| 309 | + |
| 310 | +def list_ref(xs, n): |
| 311 | + """ |
| 312 | + Returns the element of linked list xs at position n (0-indexed). |
| 313 | + """ |
| 314 | + if n == 0: |
| 315 | + if is_none(xs): |
| 316 | + raise IndexError( |
| 317 | + "linked_list_ref: index out of bounds on None linked list" |
| 318 | + ) |
| 319 | + return head(xs) |
| 320 | + else: |
| 321 | + if is_none(xs): |
| 322 | + raise IndexError("linked_list_ref: index out of bounds") |
| 323 | + return list_ref(tail(xs), n - 1) |
| 324 | + |
| 325 | + |
| 326 | +def accumulate_linked_list(f, initial, xs): |
| 327 | + """ |
| 328 | + Applies binary function f to the elements of xs from right-to-left |
| 329 | + order. |
| 330 | + """ |
| 331 | + return _accumulate_linked_list(f, initial, xs, lambda x: x) |
| 332 | + |
| 333 | + |
| 334 | +def _accumulate_linked_list(f, initial, xs, cont): |
| 335 | + if is_none(xs): |
| 336 | + return cont(initial) |
| 337 | + else: |
| 338 | + # Recursive CPS call: Process tail, then apply f with head, |
| 339 | + # then pass to continuation |
| 340 | + return _accumulate_linked_list( |
| 341 | + f, |
| 342 | + initial, |
| 343 | + tail(xs), |
| 344 | + lambda x_accumulated_from_tail: cont( |
| 345 | + f(head(xs), x_accumulated_from_tail) |
| 346 | + ), |
| 347 | + ) |
| 348 | + |
| 349 | + |
| 350 | +def filter_linked_list(pred, xs): |
| 351 | + """ |
| 352 | + Returns a linked list that contains only those elements for which the |
| 353 | + one-argument function pred returns true. |
| 354 | + """ |
| 355 | + return _filter_linked_list(pred, xs, None) |
| 356 | + |
| 357 | + |
| 358 | +def _filter_linked_list(pred, xs, acc): |
| 359 | + if is_none(xs): |
| 360 | + return reverse(acc) |
| 361 | + else: |
| 362 | + if pred(head(xs)): |
| 363 | + return _filter_linked_list(pred, tail(xs), pair(head(xs), acc)) |
| 364 | + else: |
| 365 | + return _filter_linked_list(pred, tail(xs), acc) |
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