|
| 1 | +# Assignable-to relation |
| 2 | + |
| 3 | +The `is_assignable_to(S, T)` relation below checks if type `S` is assignable to type `T` (target). |
| 4 | +This allows us to check if a type `S` can be used in a context where a type `T` is expected |
| 5 | +(function arguments, variable assignments). See the [typing documentation] for a precise definition |
| 6 | +of this concept. |
| 7 | + |
| 8 | +## Basic types |
| 9 | + |
| 10 | +### Fully static |
| 11 | + |
| 12 | +Fully static types participate in subtyping. If a type `S` is a subtype of `T`, `S` will also be |
| 13 | +assignable to `T`. Two equivalent types are subtypes of each other: |
| 14 | + |
| 15 | +```py |
| 16 | +from knot_extensions import static_assert, is_assignable_to |
| 17 | + |
| 18 | +class Parent: ... |
| 19 | +class Child1(Parent): ... |
| 20 | +class Child2(Parent): ... |
| 21 | +class Grandchild(Child1, Child2): ... |
| 22 | +class Unrelated: ... |
| 23 | + |
| 24 | +static_assert(is_assignable_to(int, int)) |
| 25 | +static_assert(is_assignable_to(Parent, Parent)) |
| 26 | +static_assert(is_assignable_to(Child1, Parent)) |
| 27 | +static_assert(is_assignable_to(Grandchild, Parent)) |
| 28 | +static_assert(is_assignable_to(Unrelated, Unrelated)) |
| 29 | + |
| 30 | +static_assert(not is_assignable_to(str, int)) |
| 31 | +static_assert(not is_assignable_to(object, int)) |
| 32 | +static_assert(not is_assignable_to(Parent, Child1)) |
| 33 | +static_assert(not is_assignable_to(Unrelated, Parent)) |
| 34 | +static_assert(not is_assignable_to(Child1, Child2)) |
| 35 | +``` |
| 36 | + |
| 37 | +### Gradual types |
| 38 | + |
| 39 | +Gradual types do not participate in subtyping, but can still be assignable to other types (and |
| 40 | +static types can be assignable to gradual types): |
| 41 | + |
| 42 | +```py |
| 43 | +from knot_extensions import static_assert, is_assignable_to, Unknown |
| 44 | +from typing import Any |
| 45 | + |
| 46 | +static_assert(is_assignable_to(Unknown, Literal[1])) |
| 47 | +static_assert(is_assignable_to(Any, Literal[1])) |
| 48 | +static_assert(is_assignable_to(Literal[1], Unknown)) |
| 49 | +static_assert(is_assignable_to(Literal[1], Any)) |
| 50 | +``` |
| 51 | + |
| 52 | +## Literal types |
| 53 | + |
| 54 | +### Boolean literals |
| 55 | + |
| 56 | +`Literal[True]` and `Literal[False]` are both subtypes of (and therefore assignable to) `bool`, |
| 57 | +which is in turn a subtype of `int`: |
| 58 | + |
| 59 | +```py |
| 60 | +from knot_extensions import static_assert, is_assignable_to |
| 61 | +from typing import Literal |
| 62 | + |
| 63 | +static_assert(is_assignable_to(Literal[True], Literal[True])) |
| 64 | +static_assert(is_assignable_to(Literal[True], bool)) |
| 65 | +static_assert(is_assignable_to(Literal[True], int)) |
| 66 | + |
| 67 | +static_assert(not is_assignable_to(Literal[True], Literal[False])) |
| 68 | +static_assert(not is_assignable_to(bool, Literal[True])) |
| 69 | +``` |
| 70 | + |
| 71 | +### Integer literals |
| 72 | + |
| 73 | +```py |
| 74 | +from knot_extensions import static_assert, is_assignable_to |
| 75 | +from typing import Literal |
| 76 | + |
| 77 | +static_assert(is_assignable_to(Literal[1], Literal[1])) |
| 78 | +static_assert(is_assignable_to(Literal[1], int)) |
| 79 | + |
| 80 | +static_assert(not is_assignable_to(Literal[1], Literal[2])) |
| 81 | +static_assert(not is_assignable_to(int, Literal[1])) |
| 82 | +static_assert(not is_assignable_to(Literal[1], str)) |
| 83 | +``` |
| 84 | + |
| 85 | +### String literals and `LiteralString` |
| 86 | + |
| 87 | +All string-literal types are subtypes of (and therefore assignable to) `LiteralString`, which is in |
| 88 | +turn a subtype of `str`: |
| 89 | + |
| 90 | +```py |
| 91 | +from knot_extensions import static_assert, is_assignable_to |
| 92 | +from typing_extensions import Literal, LiteralString |
| 93 | + |
| 94 | +static_assert(is_assignable_to(Literal["foo"], Literal["foo"])) |
| 95 | +static_assert(is_assignable_to(Literal["foo"], LiteralString)) |
| 96 | +static_assert(is_assignable_to(Literal["foo"], str)) |
| 97 | + |
| 98 | +static_assert(is_assignable_to(LiteralString, str)) |
| 99 | + |
| 100 | +static_assert(not is_assignable_to(Literal["foo"], Literal["bar"])) |
| 101 | +static_assert(not is_assignable_to(str, Literal["foo"])) |
| 102 | +static_assert(not is_assignable_to(str, LiteralString)) |
| 103 | +``` |
| 104 | + |
| 105 | +### Byte literals |
| 106 | + |
| 107 | +```py |
| 108 | +from knot_extensions import static_assert, is_assignable_to |
| 109 | +from typing_extensions import Literal, LiteralString |
| 110 | + |
| 111 | +static_assert(is_assignable_to(Literal[b"foo"], bytes)) |
| 112 | +static_assert(is_assignable_to(Literal[b"foo"], Literal[b"foo"])) |
| 113 | + |
| 114 | +static_assert(not is_assignable_to(Literal[b"foo"], str)) |
| 115 | +static_assert(not is_assignable_to(Literal[b"foo"], LiteralString)) |
| 116 | +static_assert(not is_assignable_to(Literal[b"foo"], Literal[b"bar"])) |
| 117 | +static_assert(not is_assignable_to(Literal[b"foo"], Literal["foo"])) |
| 118 | +static_assert(not is_assignable_to(Literal["foo"], Literal[b"foo"])) |
| 119 | +``` |
| 120 | + |
| 121 | +## `type[…]` and class literals |
| 122 | + |
| 123 | +In the following tests, `TypeOf[str]` is a singleton type with a single inhabitant, the class `str`. |
| 124 | +This contrasts with `type[str]`, which represents "all possible subclasses of `str`". |
| 125 | + |
| 126 | +Both `TypeOf[str]` and `type[str]` are subtypes of `type` and `type[object]`, which both represent |
| 127 | +"all possible instances of `type`"; therefore both `type[str]` and `TypeOf[str]` are assignable to |
| 128 | +`type`. `type[Any]`, on the other hand, represents a type of unknown size or inhabitants, but which |
| 129 | +is known to be no larger than the set of possible objects represented by `type`. |
| 130 | + |
| 131 | +```py |
| 132 | +from knot_extensions import static_assert, is_assignable_to, Unknown, TypeOf |
| 133 | +from typing import Any |
| 134 | + |
| 135 | +static_assert(is_assignable_to(type, type)) |
| 136 | +static_assert(is_assignable_to(type[object], type[object])) |
| 137 | + |
| 138 | +static_assert(is_assignable_to(type, type[object])) |
| 139 | +static_assert(is_assignable_to(type[object], type)) |
| 140 | + |
| 141 | +static_assert(is_assignable_to(type[str], type[object])) |
| 142 | +static_assert(is_assignable_to(TypeOf[str], type[object])) |
| 143 | +static_assert(is_assignable_to(type[str], type)) |
| 144 | +static_assert(is_assignable_to(TypeOf[str], type)) |
| 145 | + |
| 146 | +static_assert(is_assignable_to(type[str], type[str])) |
| 147 | +static_assert(is_assignable_to(TypeOf[str], type[str])) |
| 148 | + |
| 149 | +static_assert(not is_assignable_to(TypeOf[int], type[str])) |
| 150 | +static_assert(not is_assignable_to(type, type[str])) |
| 151 | +static_assert(not is_assignable_to(type[object], type[str])) |
| 152 | + |
| 153 | +static_assert(is_assignable_to(type[Any], type[Any])) |
| 154 | +static_assert(is_assignable_to(type[Any], type[object])) |
| 155 | +static_assert(is_assignable_to(type[object], type[Any])) |
| 156 | +static_assert(is_assignable_to(type, type[Any])) |
| 157 | +static_assert(is_assignable_to(type[Any], type[str])) |
| 158 | +static_assert(is_assignable_to(type[str], type[Any])) |
| 159 | +static_assert(is_assignable_to(TypeOf[str], type[Any])) |
| 160 | + |
| 161 | +static_assert(is_assignable_to(type[Unknown], type[Unknown])) |
| 162 | +static_assert(is_assignable_to(type[Unknown], type[object])) |
| 163 | +static_assert(is_assignable_to(type[object], type[Unknown])) |
| 164 | +static_assert(is_assignable_to(type, type[Unknown])) |
| 165 | +static_assert(is_assignable_to(type[Unknown], type[str])) |
| 166 | +static_assert(is_assignable_to(type[str], type[Unknown])) |
| 167 | +static_assert(is_assignable_to(TypeOf[str], type[Unknown])) |
| 168 | + |
| 169 | +static_assert(is_assignable_to(type[Unknown], type[Any])) |
| 170 | +static_assert(is_assignable_to(type[Any], type[Unknown])) |
| 171 | + |
| 172 | +static_assert(not is_assignable_to(object, type[Any])) |
| 173 | +static_assert(not is_assignable_to(str, type[Any])) |
| 174 | + |
| 175 | +class Meta(type): ... |
| 176 | + |
| 177 | +static_assert(is_assignable_to(type[Any], Meta)) |
| 178 | +static_assert(is_assignable_to(type[Unknown], Meta)) |
| 179 | +static_assert(is_assignable_to(Meta, type[Any])) |
| 180 | +static_assert(is_assignable_to(Meta, type[Unknown])) |
| 181 | +``` |
| 182 | + |
| 183 | +## Tuple types |
| 184 | + |
| 185 | +```py |
| 186 | +from knot_extensions import static_assert, is_assignable_to |
| 187 | +from typing import Literal, Any |
| 188 | + |
| 189 | +static_assert(is_assignable_to(tuple[()], tuple[()])) |
| 190 | +static_assert(is_assignable_to(tuple[int], tuple[int])) |
| 191 | +static_assert(is_assignable_to(tuple[int], tuple[Any])) |
| 192 | +static_assert(is_assignable_to(tuple[Any], tuple[int])) |
| 193 | +static_assert(is_assignable_to(tuple[int, str], tuple[int, str])) |
| 194 | +static_assert(is_assignable_to(tuple[Literal[1], Literal[2]], tuple[int, int])) |
| 195 | +static_assert(is_assignable_to(tuple[Any, Literal[2]], tuple[int, int])) |
| 196 | +static_assert(is_assignable_to(tuple[Literal[1], Any], tuple[int, int])) |
| 197 | + |
| 198 | +static_assert(not is_assignable_to(tuple[()], tuple[int])) |
| 199 | +static_assert(not is_assignable_to(tuple[int], tuple[str])) |
| 200 | +static_assert(not is_assignable_to(tuple[int], tuple[int, str])) |
| 201 | +static_assert(not is_assignable_to(tuple[int, str], tuple[int])) |
| 202 | +static_assert(not is_assignable_to(tuple[int, int], tuple[Literal[1], int])) |
| 203 | +static_assert(not is_assignable_to(tuple[Any, Literal[2]], tuple[int, str])) |
| 204 | +``` |
| 205 | + |
| 206 | +## Union types |
| 207 | + |
| 208 | +```py |
| 209 | +from knot_extensions import static_assert, is_assignable_to, Unknown |
| 210 | +from typing import Literal, Any |
| 211 | + |
| 212 | +static_assert(is_assignable_to(int, int | str)) |
| 213 | +static_assert(is_assignable_to(str, int | str)) |
| 214 | +static_assert(is_assignable_to(int | str, int | str)) |
| 215 | +static_assert(is_assignable_to(str | int, int | str)) |
| 216 | +static_assert(is_assignable_to(Literal[1], int | str)) |
| 217 | +static_assert(is_assignable_to(Literal[1], Unknown | str)) |
| 218 | +static_assert(is_assignable_to(Literal[1] | Literal[2], Literal[1] | Literal[2])) |
| 219 | +static_assert(is_assignable_to(Literal[1] | Literal[2], int)) |
| 220 | +static_assert(is_assignable_to(Literal[1] | None, int | None)) |
| 221 | +static_assert(is_assignable_to(Any, int | str)) |
| 222 | +static_assert(is_assignable_to(Any | int, int)) |
| 223 | +static_assert(is_assignable_to(str, int | Any)) |
| 224 | + |
| 225 | +static_assert(not is_assignable_to(int | None, int)) |
| 226 | +static_assert(not is_assignable_to(int | None, str | None)) |
| 227 | +static_assert(not is_assignable_to(Literal[1] | None, int)) |
| 228 | +static_assert(not is_assignable_to(Literal[1] | None, str | None)) |
| 229 | +static_assert(not is_assignable_to(Any | int | str, int)) |
| 230 | +``` |
| 231 | + |
| 232 | +## Intersection types |
| 233 | + |
| 234 | +```py |
| 235 | +from knot_extensions import static_assert, is_assignable_to, Intersection, Not |
| 236 | +from typing_extensions import Any, Literal |
| 237 | + |
| 238 | +class Parent: ... |
| 239 | +class Child1(Parent): ... |
| 240 | +class Child2(Parent): ... |
| 241 | +class Grandchild(Child1, Child2): ... |
| 242 | +class Unrelated: ... |
| 243 | + |
| 244 | +static_assert(is_assignable_to(Intersection[Child1, Child2], Child1)) |
| 245 | +static_assert(is_assignable_to(Intersection[Child1, Child2], Child2)) |
| 246 | +static_assert(is_assignable_to(Intersection[Child1, Child2], Parent)) |
| 247 | +static_assert(is_assignable_to(Intersection[Child1, Parent], Parent)) |
| 248 | + |
| 249 | +static_assert(is_assignable_to(Intersection[Parent, Unrelated], Parent)) |
| 250 | +static_assert(is_assignable_to(Intersection[Child1, Unrelated], Child1)) |
| 251 | + |
| 252 | +static_assert(is_assignable_to(Intersection[Child1, Not[Child2]], Child1)) |
| 253 | +static_assert(is_assignable_to(Intersection[Child1, Not[Child2]], Parent)) |
| 254 | +static_assert(is_assignable_to(Intersection[Child1, Not[Grandchild]], Parent)) |
| 255 | + |
| 256 | +static_assert(is_assignable_to(Intersection[Child1, Child2], Intersection[Child1, Child2])) |
| 257 | +static_assert(is_assignable_to(Intersection[Child1, Child2], Intersection[Child2, Child1])) |
| 258 | +static_assert(is_assignable_to(Grandchild, Intersection[Child1, Child2])) |
| 259 | + |
| 260 | +static_assert(not is_assignable_to(Parent, Intersection[Parent, Unrelated])) |
| 261 | +static_assert(not is_assignable_to(int, Intersection[int, Not[Literal[1]]])) |
| 262 | +static_assert(not is_assignable_to(int, Not[int])) |
| 263 | +static_assert(not is_assignable_to(int, Not[Literal[1]])) |
| 264 | + |
| 265 | +static_assert(not is_assignable_to(Intersection[Any, Parent], Unrelated)) |
| 266 | + |
| 267 | +# TODO: The following assertions should not fail (see https://github.com/astral-sh/ruff/issues/14899) |
| 268 | +# error: [static-assert-error] |
| 269 | +static_assert(is_assignable_to(Intersection[Any, int], int)) |
| 270 | + |
| 271 | +# error: [static-assert-error] |
| 272 | +static_assert(is_assignable_to(Intersection[Unrelated, Any], Intersection[Unrelated, Any])) |
| 273 | +# error: [static-assert-error] |
| 274 | +static_assert(is_assignable_to(Intersection[Unrelated, Any], Intersection[Unrelated, Not[Any]])) |
| 275 | +# error: [static-assert-error] |
| 276 | +static_assert(is_assignable_to(Intersection[Unrelated, Any], Not[tuple[Unrelated, Any]])) |
| 277 | +``` |
| 278 | + |
| 279 | +## General properties |
| 280 | + |
| 281 | +See also: our property tests in `property_tests.rs`. |
| 282 | + |
| 283 | +### Everything is assignable to `object` |
| 284 | + |
| 285 | +`object` is Python's top type; the set of all possible objects at runtime: |
| 286 | + |
| 287 | +```py |
| 288 | +from knot_extensions import static_assert, is_assignable_to, Unknown |
| 289 | +from typing import Literal, Any |
| 290 | + |
| 291 | +static_assert(is_assignable_to(str, object)) |
| 292 | +static_assert(is_assignable_to(Literal[1], object)) |
| 293 | +static_assert(is_assignable_to(object, object)) |
| 294 | +static_assert(is_assignable_to(type, object)) |
| 295 | +static_assert(is_assignable_to(Any, object)) |
| 296 | +static_assert(is_assignable_to(Unknown, object)) |
| 297 | +static_assert(is_assignable_to(type[object], object)) |
| 298 | +static_assert(is_assignable_to(type[str], object)) |
| 299 | +static_assert(is_assignable_to(type[Any], object)) |
| 300 | +``` |
| 301 | + |
| 302 | +### Every type is assignable to `Any` / `Unknown` |
| 303 | + |
| 304 | +`Any` and `Unknown` are gradual types. They could materialize to any given type at runtime, and so |
| 305 | +any type is assignable to them: |
| 306 | + |
| 307 | +```py |
| 308 | +from knot_extensions import static_assert, is_assignable_to, Unknown |
| 309 | +from typing import Literal, Any |
| 310 | + |
| 311 | +static_assert(is_assignable_to(str, Any)) |
| 312 | +static_assert(is_assignable_to(Literal[1], Any)) |
| 313 | +static_assert(is_assignable_to(object, Any)) |
| 314 | +static_assert(is_assignable_to(type, Any)) |
| 315 | +static_assert(is_assignable_to(Any, Any)) |
| 316 | +static_assert(is_assignable_to(Unknown, Any)) |
| 317 | +static_assert(is_assignable_to(type[object], Any)) |
| 318 | +static_assert(is_assignable_to(type[str], Any)) |
| 319 | +static_assert(is_assignable_to(type[Any], Any)) |
| 320 | + |
| 321 | +static_assert(is_assignable_to(str, Unknown)) |
| 322 | +static_assert(is_assignable_to(Literal[1], Unknown)) |
| 323 | +static_assert(is_assignable_to(object, Unknown)) |
| 324 | +static_assert(is_assignable_to(type, Unknown)) |
| 325 | +static_assert(is_assignable_to(Any, Unknown)) |
| 326 | +static_assert(is_assignable_to(Unknown, Unknown)) |
| 327 | +static_assert(is_assignable_to(type[object], Unknown)) |
| 328 | +static_assert(is_assignable_to(type[str], Unknown)) |
| 329 | +static_assert(is_assignable_to(type[Any], Unknown)) |
| 330 | +``` |
| 331 | + |
| 332 | +### `Never` is assignable to every type |
| 333 | + |
| 334 | +`Never` is Python's bottom type: the empty set, a type with no inhabitants. It is therefore |
| 335 | +assignable to any arbitrary type. |
| 336 | + |
| 337 | +```py |
| 338 | +from knot_extensions import static_assert, is_assignable_to, Unknown |
| 339 | +from typing_extensions import Never, Any |
| 340 | + |
| 341 | +static_assert(is_assignable_to(Never, str)) |
| 342 | +static_assert(is_assignable_to(Never, Literal[1])) |
| 343 | +static_assert(is_assignable_to(Never, object)) |
| 344 | +static_assert(is_assignable_to(Never, type)) |
| 345 | +static_assert(is_assignable_to(Never, Any)) |
| 346 | +static_assert(is_assignable_to(Never, Unknown)) |
| 347 | +static_assert(is_assignable_to(Never, type[object])) |
| 348 | +static_assert(is_assignable_to(Never, type[str])) |
| 349 | +static_assert(is_assignable_to(Never, type[Any])) |
| 350 | +``` |
| 351 | + |
| 352 | +[typing documentation]: https://typing.readthedocs.io/en/latest/spec/concepts.html#the-assignable-to-or-consistent-subtyping-relation |
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