6328c3a · rowtype-yoga/purescript-native

git.iko.soy/rowtype-yoga/purescript-native

Merge pull request #932 from purescript/prelude-docs

Prelude documentation

commit6328c3ac232b1b8cd422a0926679284237a51000 authorPhil Freeman <paf31@cantab.net> dateMon 2 Mar 2015, 13:31 (12 years ago) parent388a369 8ebc617

3 files changed+315−49

compare with golang

unifiedsplit

prelude/README.md+158−25 prelude/images/Prelude.png prelude/prelude.purs+157−24

prelude/README.md+158−25

@@ -72,6 +72,8 @@ element `id`, just composable morphisms.

7272

7373- Associativity: `p <<< (q <<< r) = (p <<< q) <<< r`

7474

75+One example of a `Semigroupoid` is the function type constructor `(->)`, with `(<<<)` defined

76+as function composition.

7577

7678#### `semigroupoidArr`

7779

@@ -86,6 +88,7 @@ instance semigroupoidArr :: Semigroupoid Prim.Function

8688(>>>) :: forall a b c d. (Semigroupoid a) => a b c -> a c d -> a b d

8789```

8890

91+Forwards composition, or `(<<<)` with its arguments reversed.

8992

9093#### `Category`

9194

@@ -160,12 +163,9 @@ length (groupBy productCategory (filter isInStock (products)))

160163(:) :: forall a. a -> [a] -> [a]

161164```

162165

163−Attaches an element to the front of a list.

164−

165−```purescript

166−1 : [2, 3, 4] = [1, 2, 3, 4]

167−```

166+An infix alias for `cons`.

168167

168+Note, the running time of this function is `O(n)`.

169169

170170#### `cons`

171171

@@ -173,6 +173,13 @@ Attaches an element to the front of a list.

173173cons :: forall a. a -> [a] -> [a]

174174```

175175

176+Attaches an element to the front of an array, creating a new array.

177+

178+```purescript

179+cons 1 [2, 3, 4] = [1, 2, 3, 4]

180+```

181+

182+Note, the running time of this function is `O(n)`.

176183

177184#### `Show`

178185

@@ -181,6 +188,10 @@ class Show a where

181188 show :: a -> String

182189```

183190

191+The `Show` type class represents those types which can be converted into a human-readable `String` representation.

192+

193+While not required, it is recommended that for any expression `x`, the string `show x` be executable PureScript code

194+which evaluates to the same value as the expression `x`.

184195

185196#### `showUnit`

186197

@@ -224,10 +235,12 @@ class Functor f where

224235 (<$>) :: forall a b. (a -> b) -> f a -> f b

225236```

226237

227−A `Functor` is intuitively a type which can be mapped over, and more formally a mapping

228−between [`Category`](#category)s that preserves structure.

238+A `Functor` is a type constructor which supports a mapping operation `(<$>)`.

239+

240+`(<$>)` can be used to turn functions `a -> b` into functions `f a -> f b` whose argument and return

241+types use the type constructor `f` to represent some computational context.

229242

230−`Functor`s should obey the following rules.

243+`Functor` instances should satisfy the following laws:

231244

232245- Identity: `(<$>) id = id`

233246- Composition: `(<$>) (f <<< g) = (<$> f) <<< (<$> g)`

@@ -239,6 +252,11 @@ between [`Category`](#category)s that preserves structure.

239252(<#>) :: forall f a b. (Functor f) => f a -> (a -> b) -> f b

240253```

241254

255+`(<#>)` is `(<$>)` with its arguments flipped. For example:

256+

257+```purescript

258+[1, 2, 3] <#> \n -> n * n

259+```

242260

243261#### `void`

244262

@@ -246,6 +264,16 @@ between [`Category`](#category)s that preserves structure.

246264void :: forall f a. (Functor f) => f a -> f Unit

247265```

248266

267+The `void` function is used to ignore the type wrapped by a [`Functor`](#functor), replacing it with `Unit` and

268+keeping only the type information provided by the type constructor itself.

269+

270+`void` is often useful when using `do` notation to change the return type of a monadic computation:

271+

272+```purescript

273+main = forE 1 10 \n -> void do

274+ print n

275+ print (n * n)

276+```

249277

250278#### `Apply`

251279

@@ -254,13 +282,24 @@ class (Functor f) <= Apply f where

254282 (<*>) :: forall a b. f (a -> b) -> f a -> f b

255283```

256284

257−`Apply`s are intuitively [`Applicative`](#applicative)s less `pure`, and more formally a

258−strong lax semi-monoidal endofunctor.

285+The `Apply` class provides the `(<*>)` which is used to apply a function to an argument under a type constructor.

286+

287+`Apply` can be used to lift functions of two or more arguments to work on values wrapped with the type constructor `f`.

288+It might also be understood in terms of the `lift2` function:

289+

290+```purescript

291+lift2 :: forall f a b c. (Apply f) => (a -> b -> c) -> f a -> f b -> f c

292+lift2 f a b = f <$> a <*> b

293+```

294+

295+`(<*>)` is recovered from `lift2` as `lift2 ($)`. That is, `(<*>)` lifts the function application operator `($)` to arguments

296+wrapped with the type constructor `f`.

259297

260−`Apply`s should obey the following rule.

298+`Apply` instances should satisfy the following law:

261299

262300- Associative Composition: `(<<<) <$> f <*> g <*> h = f <*> (g <*> h)`

263301

302+Formally, `Apply` represents a strong lax semi-monoidal endofunctor.

264303

265304#### `Applicative`

266305

@@ -269,10 +308,14 @@ class (Apply f) <= Applicative f where

269308 pure :: forall a. a -> f a

270309```

271310

272−`Applicative`s are [`Functor`](#functor)s which can be "applied" by sequencing composition

273−(`<*>`) or embedding pure expressions (`pure`).

311+The `Applicative` type class extends the [`Apply`](#apply) type class with a `pure` function, which can be used to

312+create values of type `f a` from values of type `a`.

274313

275−`Applicative`s should obey the following rules.

314+Where [`Apply`](#apply) provides the ability to lift functions of two or more arguments to functions whose arguments are wrapped using `f`,

315+and [`Functor`](#functor) provides the ability to lift functions of one argument, `pure` can be seen as the function which lifts functions of

316+_zero_ arguments. That is, `Applicative` functors support a lifting operation for any number of function arguments.

317+

318+`Applicative` instances should satisfy the following laws:

276319

277320- Identity: `(pure id) <*> v = v`

278321- Composition: `(pure <<<) <*> f <*> g <*> h = f <*> (g <*> h)`

@@ -286,6 +329,15 @@ class (Apply f) <= Applicative f where

286329liftA1 :: forall f a b. (Applicative f) => (a -> b) -> f a -> f b

287330```

288331

332+`liftA1` provides a default implementation of `(<$>)` for any [`Applicative`](#applicative) functor,

333+without using `(<$>)` as provided by the [`Functor`](#functor)-[`Applicative`](#applicative) superclass relationship.

334+

335+`liftA1` can therefore be used to write [`Functor`](#functor) instances as follows:

336+

337+```purescript

338+instance functorF :: Functor F where

339+ (<$>) = liftA1

340+```

289341

290342#### `Bind`

291343

@@ -294,12 +346,33 @@ class (Apply m) <= Bind m where

294346 (>>=) :: forall a b. m a -> (a -> m b) -> m b

295347```

296348

297−A `Bind` is an [`Apply`](#apply) with a bind operation which sequentially composes actions.

349+The `Bind` type class extends the [`Apply`](#apply) type class with a "bind" operation `(>>=)` which composes computations

350+in sequence, using the return value of one computation to determine the next computation.

351+

352+The `>>=` operator can also be expressed using `do` notation, as follows:

353+

354+```purescript

355+x >>= f = do y <- x

356+ f y

357+```

358+

359+where the function argument of `f` is given the name `y`.

360+

361+`Bind` instances should satisfy the following law:

298362

299−`Bind`s should obey the following rule.

363+- Associativity: `(x >>= f) >>= g = x >>= (\k => f k >>= g)`

300364

301−- Associativity: `forall f g x. (x >>= f) >>= g = x >>= (\k => f k >>= g)`

365+Or, expressed using `do` notation:

302366

367+- Associativity: `do { z <- do { y <- x ; f y } ; g z } = do { k <- x ; do { y <- f k ; g y } }`

368+

369+Associativity tells us that we can regroup operations which use do-notation, so that we can unambiguously write, for example:

370+

371+```purescript

372+do x <- m1

373+ y <- m2 x

374+ m3 x y

375+```

303376

304377#### `Monad`

305378

@@ -307,14 +380,19 @@ A `Bind` is an [`Apply`](#apply) with a bind operation which sequentially compos

307380class (Applicative m, Bind m) <= Monad m where

308381```

309382

310−`Monad` is a class which can be intuitively thought of as an abstract datatype of actions or

311−more formally though of as a monoid in the category of endofunctors.

383+The `Monad` type class combines the operations of the `Bind` and `Applicative` type classes. Therefore, `Monad` instances

384+represent type constructors which support sequential composition, and also lifting of functions of arbitrary arity.

312385

313−`Monad`s should obey the following rules.

386+`Monad` instances should satisfy the following laws:

314387

315388- Left Identity: `pure x >>= f = f x`

316389- Right Identity: `x >>= pure = x`

317390

391+Or, expressed using `do` notation:

392+

393+- Left Identity: `do { y <- pure x ; f y } = f x`

394+- Right Identity: `do { y <- x ; pure y } = x`

395+

318396

319397#### `return`

320398

@@ -322,6 +400,7 @@ more formally though of as a monoid in the category of endofunctors.

322400return :: forall m a. (Monad m) => a -> m a

323401```

324402

403+`return` is an alias for `pure`.

325404

326405#### `liftM1`

327406

@@ -329,6 +408,15 @@ return :: forall m a. (Monad m) => a -> m a

329408liftM1 :: forall m a b. (Monad m) => (a -> b) -> m a -> m b

330409```

331410

411+`liftM1` provides a default implementation of `(<$>)` for any [`Monad`](#monad),

412+without using `(<$>)` as provided by the [`Functor`](#functor)-[`Monad`](#monad) superclass relationship.

413+

414+`liftM1` can therefore be used to write [`Functor`](#functor) instances as follows:

415+

416+```purescript

417+instance functorF :: Functor F where

418+ (<$>) = liftM1

419+```

332420

333421#### `ap`

334422

@@ -336,6 +424,15 @@ liftM1 :: forall m a b. (Monad m) => (a -> b) -> m a -> m b

336424ap :: forall m a b. (Monad m) => m (a -> b) -> m a -> m b

337425```

338426

427+`ap` provides a default implementation of `(<*>)` for any [`Monad`](#monad),

428+without using `(<*>)` as provided by the [`Apply`](#apply)-[`Monad`](#monad) superclass relationship.

429+

430+`ap` can therefore be used to write [`Apply`](#apply) instances as follows:

431+

432+```purescript

433+instance applyF :: Apply F where

434+ (<*>) = ap

435+```

339436

340437#### `functorArr`

341438

@@ -384,8 +481,8 @@ class Semiring a where

384481

385482Addition and multiplication, satisfying the following laws:

386483

387−- `a` is a commutative monoid under addition with identity element zero

388−- `a` is a monoid under multiplication with identity element one

484+- `a` is a commutative monoid under addition

485+- `a` is a monoid under multiplication

389486- multiplication distributes over addition

390487- multiplication by `zero` annihilates `a`

391488

@@ -485,6 +582,10 @@ newtype Unit

485582 = Unit { }

486583```

487584

585+The `Unit` type has a single inhabitant, called `unit`. It represents values with no computational content.

586+

587+`Unit` is often used, wrapped in a monadic type constructor, as the return type of a computation where only

588+the _effects_ are important.

488589

489590#### `unit`

490591

@@ -492,6 +593,7 @@ newtype Unit

492593unit :: Unit

493594```

494595

596+`unit` is the sole inhabitant of the `Unit` type.

495597

496598#### `Eq`

497599

@@ -501,7 +603,16 @@ class Eq a where

501603 (/=) :: a -> a -> Boolean

502604```

503605

504−Class for types that have an equality comparison.

606+The `Eq` type class represents types which support decidable equality.

607+

608+`Eq` instances should satisfy the following laws:

609+

610+- Reflexivity: `x == x = true`

611+- Symmetry: `x == y = y == x`

612+- Transitivity: if `x == y` and `y == z` then `x == z`

613+- Negation: `x /= y = not (x == y)`

614+

615+`(/=)` may be implemented in terms of `(==)`, but it might give a performance improvement to implement it separately.

505616

506617#### `refEq`

507618

@@ -561,6 +672,11 @@ data Ordering

561672 | EQ

562673```

563674

675+The `Ordering` data type represents the three possible outcomes of comparing two values:

676+

677+`LT` - The first value is _less than_ the second.

678+`GT` - The first value is _greater than_ the second.

679+`EQ` - The first value is _equal to_ or _incomparable to_ the second.

564680

565681#### `eqOrdering`

566682

@@ -590,9 +706,9 @@ class (Eq a) <= Ord a where

590706 compare :: a -> a -> Ordering

591707```

592708

593−Class for types that have ordered comparisons.

709+The `Ord` type class represents types which support comparisons.

594710

595−Represents a partially ordered set satisfying the following laws:

711+`Ord` instances should satisfy the laws of _partially orderings_:

596712

597713- Reflexivity: `a <= a`

598714- Antisymmetry: if `a <= b` and `b <= a` then `a = b`

@@ -605,6 +721,7 @@ Represents a partially ordered set satisfying the following laws:

605721(<) :: forall a. (Ord a) => a -> a -> Boolean

606722```

607723

724+Test whether one value is _strictly less than_ another.

608725

609726#### `(>)`

610727

@@ -612,6 +729,7 @@ Represents a partially ordered set satisfying the following laws:

612729(>) :: forall a. (Ord a) => a -> a -> Boolean

613730```

614731

732+Test whether one value is _strictly greater than_ another.

615733

616734#### `(<=)`

617735

@@ -619,6 +737,7 @@ Represents a partially ordered set satisfying the following laws:

619737(<=) :: forall a. (Ord a) => a -> a -> Boolean

620738```

621739

740+Test whether one value is _non-strictly less than_ another.

622741

623742#### `(>=)`

624743

@@ -626,6 +745,7 @@ Represents a partially ordered set satisfying the following laws:

626745(>=) :: forall a. (Ord a) => a -> a -> Boolean

627746```

628747

748+Test whether one value is _non-strictly greater than_ another.

629749

630750#### `ordUnit`

631751

@@ -675,6 +795,7 @@ class Bits b where

675795 complement :: b -> b

676796```

677797

798+The `Bits` type class identifies types which support bitwise operations.

678799

679800#### `bitsNumber`

680801

@@ -692,6 +813,10 @@ class BoolLike b where

692813 not :: b -> b

693814```

694815

816+The `BoolLike` type class identifies types which support Boolean operations.

817+

818+`BoolLike` instances are required to satisfy the laws of a _Boolean algebra_.

819+

695820

696821#### `boolLikeBoolean`

697822

@@ -707,6 +832,13 @@ class Semigroup a where

707832 (<>) :: a -> a -> a

708833```

709834

835+The `Semigroup` type class identifies an associative operation on a type.

836+

837+`Semigroup` instances are required to satisfy the following law:

838+

839+- Associativity: `(x <> y) <> z = x <> (y <> z)`

840+

841+For example, the `String` type is an instance of `Semigroup`, where `(<>)` is defined to be string concatenation.

710842

711843#### `semigroupUnit`

712844

@@ -735,6 +867,7 @@ instance semigroupArr :: (Semigroup s') => Semigroup (s -> s')

735867(++) :: forall s. (Semigroup s) => s -> s -> s

736868```

737869

870+`(++)` is an alias for `(<>)`.

738871

739872

740873## Module Data.Function

prelude/images/Prelude.png

Binary file not shown.

prelude/prelude.purs+157−24

@@ -79,12 +79,15 @@ module Prelude

7979 -- |

8080 -- | - Associativity: `p <<< (q <<< r) = (p <<< q) <<< r`

8181 -- |

82+ -- | One example of a `Semigroupoid` is the function type constructor `(->)`, with `(<<<)` defined

83+ -- | as function composition.

8284 class Semigroupoid a where

8385 (<<<) :: forall b c d. a c d -> a b c -> a b d

8486

8587 instance semigroupoidArr :: Semigroupoid (->) where

8688 (<<<) f g x = f (g x)

8789

90+ -- | Forwards composition, or `(<<<)` with its arguments reversed.

8891 (>>>) :: forall a b c d. (Semigroupoid a) => a b c -> a c d -> a b d

8992 (>>>) f g = g <<< f

9093

@@ -143,15 +146,19 @@ module Prelude

143146

144147 infixr 6 :

145148

146− -- | Attaches an element to the front of a list.

147− -- |

148− -- | ```purescript

149− -- | 1 : [2, 3, 4] = [1, 2, 3, 4]

150− -- | ```

149+ -- | An infix alias for `cons`.

151150 -- |

151+ -- | Note, the running time of this function is `O(n)`.

152152 (:) :: forall a. a -> [a] -> [a]

153153 (:) = cons

154154

155+ -- | Attaches an element to the front of an array, creating a new array.

156+ -- |

157+ -- | ```purescript

158+ -- | cons 1 [2, 3, 4] = [1, 2, 3, 4]

159+ -- | ```

160+ -- |

161+ -- | Note, the running time of this function is `O(n)`.

155162 foreign import cons

156163 """

157164 function cons(e) {

@@ -161,6 +168,10 @@ module Prelude

161168 }

162169 """ :: forall a. a -> [a] -> [a]

163170

171+ -- | The `Show` type class represents those types which can be converted into a human-readable `String` representation.

172+ -- |

173+ -- | While not required, it is recommended that for any expression `x`, the string `show x` be executable PureScript code

174+ -- | which evaluates to the same value as the expression `x`.

164175 class Show a where

165176 show :: a -> String

166177

@@ -210,10 +221,12 @@ module Prelude

210221 infixl 4 <$>

211222 infixl 1 <#>

212223

213− -- | A `Functor` is intuitively a type which can be mapped over, and more formally a mapping

214− -- | between [`Category`](#category)s that preserves structure.

224+ -- | A `Functor` is a type constructor which supports a mapping operation `(<$>)`.

225+ -- |

226+ -- | `(<$>)` can be used to turn functions `a -> b` into functions `f a -> f b` whose argument and return

227+ -- | types use the type constructor `f` to represent some computational context.

215228 -- |

216− -- | `Functor`s should obey the following rules.

229+ -- | `Functor` instances should satisfy the following laws:

217230 -- |

218231 -- | - Identity: `(<$>) id = id`

219232 -- | - Composition: `(<$>) (f <<< g) = (<$> f) <<< (<$> g)`

@@ -221,28 +234,58 @@ module Prelude

221234 class Functor f where

222235 (<$>) :: forall a b. (a -> b) -> f a -> f b

223236

237+ -- | `(<#>)` is `(<$>)` with its arguments flipped. For example:

238+ -- |

239+ -- | ```purescript

240+ -- | [1, 2, 3] <#> \n -> n * n

241+ -- | ```

224242 (<#>) :: forall f a b. (Functor f) => f a -> (a -> b) -> f b

225243 (<#>) fa f = f <$> fa

226244

245+ -- | The `void` function is used to ignore the type wrapped by a [`Functor`](#functor), replacing it with `Unit` and

246+ -- | keeping only the type information provided by the type constructor itself.

247+ -- |

248+ -- | `void` is often useful when using `do` notation to change the return type of a monadic computation:

249+ -- |

250+ -- | ```purescript

251+ -- | main = forE 1 10 \n -> void do

252+ -- | print n

253+ -- | print (n * n)

254+ -- | ```

227255 void :: forall f a. (Functor f) => f a -> f Unit

228256 void fa = const unit <$> fa

229257

230258 infixl 4 <*>

231259

232− -- | `Apply`s are intuitively [`Applicative`](#applicative)s less `pure`, and more formally a

233− -- | strong lax semi-monoidal endofunctor.

260+ -- | The `Apply` class provides the `(<*>)` which is used to apply a function to an argument under a type constructor.

261+ -- |

262+ -- | `Apply` can be used to lift functions of two or more arguments to work on values wrapped with the type constructor `f`.

263+ -- | It might also be understood in terms of the `lift2` function:

264+ -- |

265+ -- | ```purescript

266+ -- | lift2 :: forall f a b c. (Apply f) => (a -> b -> c) -> f a -> f b -> f c

267+ -- | lift2 f a b = f <$> a <*> b

268+ -- | ```

269+ -- |

270+ -- | `(<*>)` is recovered from `lift2` as `lift2 ($)`. That is, `(<*>)` lifts the function application operator `($)` to arguments

271+ -- | wrapped with the type constructor `f`.

234272 -- |

235− -- | `Apply`s should obey the following rule.

273+ -- | `Apply` instances should satisfy the following law:

236274 -- |

237275 -- | - Associative Composition: `(<<<) <$> f <*> g <*> h = f <*> (g <*> h)`

238276 -- |

277+ -- | Formally, `Apply` represents a strong lax semi-monoidal endofunctor.

239278 class (Functor f) <= Apply f where

240279 (<*>) :: forall a b. f (a -> b) -> f a -> f b

241280

242− -- | `Applicative`s are [`Functor`](#functor)s which can be "applied" by sequencing composition

243− -- | (`<*>`) or embedding pure expressions (`pure`).

281+ -- | The `Applicative` type class extends the [`Apply`](#apply) type class with a `pure` function, which can be used to

282+ -- | create values of type `f a` from values of type `a`.

283+ -- |

284+ -- | Where [`Apply`](#apply) provides the ability to lift functions of two or more arguments to functions whose arguments are wrapped using `f`,

285+ -- | and [`Functor`](#functor) provides the ability to lift functions of one argument, `pure` can be seen as the function which lifts functions of

286+ -- | _zero_ arguments. That is, `Applicative` functors support a lifting operation for any number of function arguments.

244287 -- |

245− -- | `Applicative`s should obey the following rules.

288+ -- | `Applicative` instances should satisfy the following laws:

246289 -- |

247290 -- | - Identity: `(pure id) <*> v = v`

248291 -- | - Composition: `(pure <<<) <*> f <*> g <*> h = f <*> (g <*> h)`

@@ -252,38 +295,92 @@ module Prelude

252295 class (Apply f) <= Applicative f where

253296 pure :: forall a. a -> f a

254297

298+ -- | `liftA1` provides a default implementation of `(<$>)` for any [`Applicative`](#applicative) functor,

299+ -- | without using `(<$>)` as provided by the [`Functor`](#functor)-[`Applicative`](#applicative) superclass relationship.

300+ -- |

301+ -- | `liftA1` can therefore be used to write [`Functor`](#functor) instances as follows:

302+ -- |

303+ -- | ```purescript

304+ -- | instance functorF :: Functor F where

305+ -- | (<$>) = liftA1

306+ -- | ```

255307 liftA1 :: forall f a b. (Applicative f) => (a -> b) -> f a -> f b

256308 liftA1 f a = pure f <*> a

257309

258310 infixl 1 >>=

259311

260− -- | A `Bind` is an [`Apply`](#apply) with a bind operation which sequentially composes actions.

261− -- |

262− -- | `Bind`s should obey the following rule.

312+ -- | The `Bind` type class extends the [`Apply`](#apply) type class with a "bind" operation `(>>=)` which composes computations

313+ -- | in sequence, using the return value of one computation to determine the next computation.

314+ -- |

315+ -- | The `>>=` operator can also be expressed using `do` notation, as follows:

316+ -- |

317+ -- | ```purescript

318+ -- | x >>= f = do y <- x

319+ -- | f y

320+ -- | ```

321+ -- |

322+ -- | where the function argument of `f` is given the name `y`.

323+ -- |

324+ -- | `Bind` instances should satisfy the following law:

263325 -- |

264− -- | - Associativity: `forall f g x. (x >>= f) >>= g = x >>= (\k => f k >>= g)`

326+ -- | - Associativity: `(x >>= f) >>= g = x >>= (\k => f k >>= g)`

265327 -- |

328+ -- | Or, expressed using `do` notation:

329+ -- |

330+ -- | - Associativity: `do { z <- do { y <- x ; f y } ; g z } = do { k <- x ; do { y <- f k ; g y } }`

331+ -- |

332+ -- | Associativity tells us that we can regroup operations which use do-notation, so that we can unambiguously write, for example:

333+ -- |

334+ -- | ```purescript

335+ -- | do x <- m1

336+ -- | y <- m2 x

337+ -- | m3 x y

338+ -- | ```

266339 class (Apply m) <= Bind m where

267340 (>>=) :: forall a b. m a -> (a -> m b) -> m b

268341

269− -- | `Monad` is a class which can be intuitively thought of as an abstract datatype of actions or

270− -- | more formally though of as a monoid in the category of endofunctors.

342+ -- | The `Monad` type class combines the operations of the `Bind` and `Applicative` type classes. Therefore, `Monad` instances

343+ -- | represent type constructors which support sequential composition, and also lifting of functions of arbitrary arity.

271344 -- |

272− -- | `Monad`s should obey the following rules.

345+ -- | `Monad` instances should satisfy the following laws:

273346 -- |

274347 -- | - Left Identity: `pure x >>= f = f x`

275348 -- | - Right Identity: `x >>= pure = x`

276349 -- |

350+ -- | Or, expressed using `do` notation:

351+ -- |

352+ -- | - Left Identity: `do { y <- pure x ; f y } = f x`

353+ -- | - Right Identity: `do { y <- x ; pure y } = x`

354+ -- |

277355 class (Applicative m, Bind m) <= Monad m

278356

357+ -- | `return` is an alias for `pure`.

279358 return :: forall m a. (Monad m) => a -> m a

280359 return = pure

281360

361+ -- | `liftM1` provides a default implementation of `(<$>)` for any [`Monad`](#monad),

362+ -- | without using `(<$>)` as provided by the [`Functor`](#functor)-[`Monad`](#monad) superclass relationship.

363+ -- |

364+ -- | `liftM1` can therefore be used to write [`Functor`](#functor) instances as follows:

365+ -- |

366+ -- | ```purescript

367+ -- | instance functorF :: Functor F where

368+ -- | (<$>) = liftM1

369+ -- | ```

282370 liftM1 :: forall m a b. (Monad m) => (a -> b) -> m a -> m b

283371 liftM1 f a = do

284372 a' <- a

285373 return (f a')

286374

375+ -- | `ap` provides a default implementation of `(<*>)` for any [`Monad`](#monad),

376+ -- | without using `(<*>)` as provided by the [`Apply`](#apply)-[`Monad`](#monad) superclass relationship.

377+ -- |

378+ -- | `ap` can therefore be used to write [`Apply`](#apply) instances as follows:

379+ -- |

380+ -- | ```purescript

381+ -- | instance applyF :: Apply F where

382+ -- | (<*>) = ap

383+ -- | ```

287384 ap :: forall m a b. (Monad m) => m (a -> b) -> m a -> m b

288385 ap f a = do

289386 f' <- f

@@ -417,15 +514,29 @@ module Prelude

417514

418515 instance numNumber :: Num Number

419516

517+ -- | The `Unit` type has a single inhabitant, called `unit`. It represents values with no computational content.

518+ -- |

519+ -- | `Unit` is often used, wrapped in a monadic type constructor, as the return type of a computation where only

520+ -- | the _effects_ are important.

420521 newtype Unit = Unit {}

421522

523+ -- | `unit` is the sole inhabitant of the `Unit` type.

422524 unit :: Unit

423525 unit = Unit {}

424526

425527 infix 4 ==

426528 infix 4 /=

427529

428− -- | Class for types that have an equality comparison.

530+ -- | The `Eq` type class represents types which support decidable equality.

531+ -- |

532+ -- | `Eq` instances should satisfy the following laws:

533+ -- |

534+ -- | - Reflexivity: `x == x = true`

535+ -- | - Symmetry: `x == y = y == x`

536+ -- | - Transitivity: if `x == y` and `y == z` then `x == z`

537+ -- | - Negation: `x /= y = not (x == y)`

538+ -- |

539+ -- | `(/=)` may be implemented in terms of `(==)`, but it might give a performance improvement to implement it separately.

429540 class Eq a where

430541 (==) :: a -> a -> Boolean

431542 (/=) :: a -> a -> Boolean

@@ -483,6 +594,11 @@ module Prelude

483594 (==) xs ys = eqArrayImpl (==) xs ys

484595 (/=) xs ys = not (xs == ys)

485596

597+ -- | The `Ordering` data type represents the three possible outcomes of comparing two values:

598+ -- |

599+ -- | `LT` - The first value is _less than_ the second.

600+ -- | `GT` - The first value is _greater than_ the second.

601+ -- | `EQ` - The first value is _equal to_ or _incomparable to_ the second.

486602 data Ordering = LT | GT | EQ

487603

488604 instance eqOrdering :: Eq Ordering where

@@ -502,9 +618,9 @@ module Prelude

502618 (<>) GT _ = GT

503619 (<>) EQ y = y

504620

505− -- | Class for types that have ordered comparisons.

621+ -- | The `Ord` type class represents types which support comparisons.

506622 -- |

507− -- | Represents a partially ordered set satisfying the following laws:

623+ -- | `Ord` instances should satisfy the laws of _partially orderings_:

508624 -- |

509625 -- | - Reflexivity: `a <= a`

510626 -- | - Antisymmetry: if `a <= b` and `b <= a` then `a = b`

@@ -515,6 +631,7 @@ module Prelude

515631

516632 infixl 4 <

517633

634+ -- | Test whether one value is _strictly less than_ another.

518635 (<) :: forall a. (Ord a) => a -> a -> Boolean

519636 (<) a1 a2 = case a1 `compare` a2 of

520637 LT -> true

@@ -522,6 +639,7 @@ module Prelude

522639

523640 infixl 4 >

524641

642+ -- | Test whether one value is _strictly greater than_ another.

525643 (>) :: forall a. (Ord a) => a -> a -> Boolean

526644 (>) a1 a2 = case a1 `compare` a2 of

527645 GT -> true

@@ -529,6 +647,7 @@ module Prelude

529647

530648 infixl 4 <=

531649

650+ -- | Test whether one value is _non-strictly less than_ another.

532651 (<=) :: forall a. (Ord a) => a -> a -> Boolean

533652 (<=) a1 a2 = case a1 `compare` a2 of

534653 GT -> false

@@ -536,6 +655,7 @@ module Prelude

536655

537656 infixl 4 >=

538657

658+ -- | Test whether one value is _non-strictly greater than_ another.

539659 (>=) :: forall a. (Ord a) => a -> a -> Boolean

540660 (>=) a1 a2 = case a1 `compare` a2 of

541661 LT -> false

@@ -586,6 +706,7 @@ module Prelude

586706 infixl 10 .|.

587707 infixl 10 .^.

588708

709+ -- | The `Bits` type class identifies types which support bitwise operations.

589710 class Bits b where

590711 (.&.) :: b -> b -> b

591712 (.|.) :: b -> b -> b

@@ -668,6 +789,10 @@ module Prelude

668789 infixr 2 ||

669790 infixr 3 &&

670791

792+ -- | The `BoolLike` type class identifies types which support Boolean operations.

793+ -- |

794+ -- | `BoolLike` instances are required to satisfy the laws of a _Boolean algebra_.

795+ -- |

671796 class BoolLike b where

672797 (&&) :: b -> b -> b

673798 (||) :: b -> b -> b

@@ -705,6 +830,13 @@ module Prelude

705830

706831 infixr 5 <>

707832

833+ -- | The `Semigroup` type class identifies an associative operation on a type.

834+ -- |

835+ -- | `Semigroup` instances are required to satisfy the following law:

836+ -- |

837+ -- | - Associativity: `(x <> y) <> z = x <> (y <> z)`

838+ -- |

839+ -- | For example, the `String` type is an instance of `Semigroup`, where `(<>)` is defined to be string concatenation.

708840 class Semigroup a where

709841 (<>) :: a -> a -> a

710842

@@ -728,6 +860,7 @@ module Prelude

728860

729861 infixr 5 ++

730862

863+ -- | `(++)` is an alias for `(<>)`.

731864 (++) :: forall s. (Semigroup s) => s -> s -> s

732865 (++) = (<>)

733866