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206 changes: 206 additions & 0 deletions README.md
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<a href="https://github.com/fantasyland/fantasy-land"><img alt="Fantasy Land" src="https://raw.githubusercontent.com/fantasyland/fantasy-land/master/logo.png" width="75" height="75" align="left"></a>

# sanctuary-identity

Identity is the simplest container type: a value of type `Identity a`
always contains exactly one value, of type `a`.

`Identity a` satisfies the following [Fantasy Land][] specifications:

```javascript
> const Useless = require ('sanctuary-useless')

> S.map (k => k + ' '.repeat (16 - k.length) +
. (Z[k].test (Identity (Useless)) ? '\u2705 ' :
. Z[k].test (Identity (['foo'])) ? '\u2705 * ' :
. /* otherwise */ '\u274C '))
. (S.keys (Z.filter ($.test ([]) ($.TypeClass), Z)))
[ 'Setoid ✅ * ', // if ‘a’ satisfies Setoid
. 'Ord ✅ * ', // if ‘a’ satisfies Ord
. 'Semigroupoid ❌ ',
. 'Category ❌ ',
. 'Semigroup ✅ * ', // if ‘a’ satisfies Semigroup
. 'Monoid ❌ ',
. 'Group ❌ ',
. 'Filterable ❌ ',
. 'Functor ✅ ',
. 'Bifunctor ❌ ',
. 'Profunctor ❌ ',
. 'Apply ✅ ',
. 'Applicative ✅ ',
. 'Chain ✅ ',
. 'ChainRec ✅ ',
. 'Monad ✅ ',
. 'Alt ❌ ',
. 'Plus ❌ ',
. 'Alternative ❌ ',
. 'Foldable ✅ ',
. 'Traversable ✅ ',
. 'Extend ✅ ',
. 'Comonad ✅ ',
. 'Contravariant ❌ ' ]
```

#### <a name="Identity" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L117">`Identity :: a -⁠> Identity a`</a>

Identity's sole data constructor. Additionally, it serves as the
Identity [type representative][].

```javascript
> Identity (42)
Identity (42)
```

#### <a name="Identity.@@type" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L141">`Identity.@@type :: String`</a>

Identity [type identifier][].

```javascript
> type (Identity (42))
'sanctuary-identity/Identity@1'

> type.parse (type (Identity (42)))
{namespace: 'sanctuary-identity', name: 'Identity', version: 1}
```

#### <a name="Identity.fantasy-land/of" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L154">`Identity.fantasy-land/of :: a -⁠> Identity a`</a>

`of (Identity) (x)` is equivalent to `Identity (x)`.

```javascript
> S.of (Identity) (42)
Identity (42)
```

#### <a name="Identity.fantasy-land/chainRec" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L167">`Identity.fantasy-land/chainRec :: ((a -⁠> c, b -⁠> c, a) -⁠> Identity c, a) -⁠> Identity b`</a>

```javascript
> Z.chainRec (
. Identity,
. (next, done, x) => Identity (x >= 0 ? done (x * x) : next (x + 1)),
. 8
. )
Identity (64)

> Z.chainRec (
. Identity,
. (next, done, x) => Identity (x >= 0 ? done (x * x) : next (x + 1)),
. -8
. )
Identity (0)
```

#### <a name="Identity.prototype.@@show" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L190">`Identity#@@show :: Showable a => Identity a ~> () -⁠> String`</a>

`show (Identity (x))` is equivalent to `'Identity (' + show (x) + ')'`.

```javascript
> show (Identity (['foo', 'bar', 'baz']))
'Identity (["foo", "bar", "baz"])'
```

#### <a name="Identity.prototype.fantasy-land/equals" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L202">`Identity#fantasy-land/equals :: Setoid a => Identity a ~> Identity a -⁠> Boolean`</a>

`Identity (x)` is equal to `Identity (y)` [iff][] `x` is equal to `y`
according to [`Z.equals`][].

```javascript
> S.equals (Identity ([1, 2, 3])) (Identity ([1, 2, 3]))
true

> S.equals (Identity ([1, 2, 3])) (Identity ([3, 2, 1]))
false
```

#### <a name="Identity.prototype.fantasy-land/lte" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L218">`Identity#fantasy-land/lte :: Ord a => Identity a ~> Identity a -⁠> Boolean`</a>

`Identity (x)` is less than or equal to `Identity (y)` [iff][] `x` is
less than or equal to `y` according to [`Z.lte`][].

```javascript
> S.filter (S.lte (Identity (1)))
. ([Identity (0), Identity (1), Identity (2)])
[Identity (0), Identity (1)]
```

#### <a name="Identity.prototype.fantasy-land/concat" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L232">`Identity#fantasy-land/concat :: Semigroup a => Identity a ~> Identity a -⁠> Identity a`</a>

`concat (Identity (x)) (Identity (y))` is equivalent to
`Identity (concat (x) (y))`.

```javascript
> S.concat (Identity ([1, 2, 3])) (Identity ([4, 5, 6]))
Identity ([1, 2, 3, 4, 5, 6])
```

#### <a name="Identity.prototype.fantasy-land/map" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L245">`Identity#fantasy-land/map :: Identity a ~> (a -⁠> b) -⁠> Identity b`</a>

`map (f) (Identity (x))` is equivalent to `Identity (f (x))`.

```javascript
> S.map (Math.sqrt) (Identity (64))
Identity (8)
```

#### <a name="Identity.prototype.fantasy-land/ap" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L257">`Identity#fantasy-land/ap :: Identity a ~> Identity (a -⁠> b) -⁠> Identity b`</a>

`ap (Identity (f)) (Identity (x))` is equivalent to `Identity (f (x))`.

```javascript
> S.ap (Identity (Math.sqrt)) (Identity (64))
Identity (8)
```

#### <a name="Identity.prototype.fantasy-land/chain" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L269">`Identity#fantasy-land/chain :: Identity a ~> (a -⁠> Identity b) -⁠> Identity b`</a>

`chain (f) (Identity (x))` is equivalent to `f (x)`.

```javascript
> S.chain (n => Identity (n + 1)) (Identity (99))
Identity (100)
```

#### <a name="Identity.prototype.fantasy-land/reduce" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L281">`Identity#fantasy-land/reduce :: Identity a ~> ((b, a) -⁠> b, b) -⁠> b`</a>

`reduce (f) (x) (Identity (y))` is equivalent to `f (x) (y)`.

```javascript
> S.reduce (S.concat) ([1, 2, 3]) (Identity ([4, 5, 6]))
[1, 2, 3, 4, 5, 6]
```

#### <a name="Identity.prototype.fantasy-land/traverse" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L293">`Identity#fantasy-land/traverse :: Applicative f => Identity a ~> (TypeRep f, a -⁠> f b) -⁠> f (Identity b)`</a>

`traverse (_) (f) (Identity (x))` is equivalent to
`map (Identity) (f (x))`.

```javascript
> S.traverse (Array) (x => [x + 1, x + 2, x + 3]) (Identity (100))
[Identity (101), Identity (102), Identity (103)]
```

#### <a name="Identity.prototype.fantasy-land/extend" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L306">`Identity#fantasy-land/extend :: Identity a ~> (Identity a -⁠> b) -⁠> Identity b`</a>

`extend (f) (Identity (x))` is equivalent to
`Identity (f (Identity (x)))`.

```javascript
> S.extend (S.reduce (S.add) (1)) (Identity (99))
Identity (100)
```

#### <a name="Identity.prototype.fantasy-land/extract" href="https://github.com/sanctuary-js/sanctuary-identity/blob/v1.0.0/index.js#L319">`Identity#fantasy-land/extract :: Identity a ~> () -⁠> a`</a>

`extract (Identity (x))` is equivalent to `x`.

```javascript
> S.extract (Identity (42))
42
```

[Fantasy Land]: https://github.com/fantasyland/fantasy-land/tree/v3.5.0
[`Z.equals`]: https://github.com/sanctuary-js/sanctuary-type-classes/tree/v9.0.0#equals
[`Z.lte`]: https://github.com/sanctuary-js/sanctuary-type-classes/tree/v9.0.0#lte
[iff]: https://en.wikipedia.org/wiki/If_and_only_if
[type identifier]: https://github.com/sanctuary-js/sanctuary-type-identifiers/tree/v2.0.1
[type representative]: https://github.com/fantasyland/fantasy-land/tree/v3.5.0#type-representatives
2 changes: 1 addition & 1 deletion package.json
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@@ -1,6 +1,6 @@
{
"name": "sanctuary-identity",
"version": "0.0.0",
"version": "1.0.0",
"description": "Fantasy Land -compliant Identity type",
"license": "MIT",
"repository": {
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