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sanctuary-type-classes\n\nThe [Fantasy Land Specification][FL] \"specifies interoperability of common\nalgebraic structures\" by defining a number of type classes. For each type\nclass, it states laws which every member of a type must obey in order for\nthe type to be a member of the type class. In order for the Maybe type to\nbe considered a [Functor][], for example, every `Maybe a` value must have\na `fantasy-land/map` method which obeys the identity and composition laws.\n\nThis project provides:\n\n - [`TypeClass`](#TypeClass), a function for defining type classes;\n - one `TypeClass` value for each Fantasy Land type class;\n - lawful Fantasy Land methods for JavaScript's built-in types;\n - one function for each Fantasy Land method; and\n - several functions derived from these functions.\n\n## Type-class hierarchy\n\n
\n Setoid   Semigroupoid  Semigroup   Foldable        Functor      Contravariant  Filterable\n(equals)    (compose)    (concat)   (reduce)         (map)        (contramap)    (filter)\n    |           |           |           \\         / | | | | \\\n    |           |           |            \\       /  | | | |  \\\n    |           |           |             \\     /   | | | |   \\\n    |           |           |              \\   /    | | | |    \\\n    |           |           |               \\ /     | | | |     \\\n   Ord      Category     Monoid         Traversable | | | |      \\\n  (lte)       (id)       (empty)        (traverse)  / | | \\       \\\n                            |                      /  | |  \\       \\\n                            |                     /   / \\   \\       \\\n                            |             Profunctor /   \\ Bifunctor \\\n                            |              (promap) /     \\ (bimap)   \\\n                            |                      /       \\           \\\n                          Group                   /         \\           \\\n                         (invert)               Alt        Apply      Extend\n                                               (alt)        (ap)     (extend)\n                                                /           / \\           \\\n                                               /           /   \\           \\\n                                              /           /     \\           \\\n                                             /           /       \\           \\\n                                            /           /         \\           \\\n                                          Plus    Applicative    Chain      Comonad\n                                         (zero)       (of)      (chain)    (extract)\n                                            \\         / \\         / \\\n                                             \\       /   \\       /   \\\n                                              \\     /     \\     /     \\\n                                               \\   /       \\   /       \\\n                                                \\ /         \\ /         \\\n                                            Alternative    Monad     ChainRec\n                                                                    (chainRec)\n
\n\n## API\n\n#### `TypeClass :: (String, String, Array TypeClass, a -⁠> Boolean) -⁠> TypeClass`\n\nThe arguments are:\n\n - the name of the type class, prefixed by its npm package name;\n - the documentation URL of the type class;\n - an array of dependencies; and\n - a predicate which accepts any JavaScript value and returns `true`\n if the value satisfies the requirements of the type class; `false`\n otherwise.\n\nExample:\n\n```javascript\n// hasMethod :: String -> a -> Boolean\nconst hasMethod = name => x => x != null && typeof x[name] == 'function';\n\n// Foo :: TypeClass\nconst Foo = Z.TypeClass (\n 'my-package/Foo',\n 'http://example.com/my-package#Foo',\n [],\n hasMethod ('foo')\n);\n\n// Bar :: TypeClass\nconst Bar = Z.TypeClass (\n 'my-package/Bar',\n 'http://example.com/my-package#Bar',\n [Foo],\n hasMethod ('bar')\n);\n```\n\nTypes whose values have a `foo` method are members of the Foo type class.\nMembers of the Foo type class whose values have a `bar` method are also\nmembers of the Bar type class.\n\nEach `TypeClass` value has a `test` field: a function which accepts\nany JavaScript value and returns `true` if the value satisfies the\ntype class's predicate and the predicates of all the type class's\ndependencies; `false` otherwise.\n\n`TypeClass` values may be used with [sanctuary-def][type-classes]\nto define parametrically polymorphic functions which verify their\ntype-class constraints at run time.\n\n#### `Setoid :: TypeClass`\n\n`TypeClass` value for [Setoid][].\n\n```javascript\n> Setoid.test (null)\ntrue\n```\n\n#### `Ord :: TypeClass`\n\n`TypeClass` value for [Ord][].\n\n```javascript\n> Ord.test (0)\ntrue\n\n> Ord.test (Math.sqrt)\nfalse\n```\n\n#### `Semigroupoid :: TypeClass`\n\n`TypeClass` value for [Semigroupoid][].\n\n```javascript\n> Semigroupoid.test (Math.sqrt)\ntrue\n\n> Semigroupoid.test (0)\nfalse\n```\n\n#### `Category :: TypeClass`\n\n`TypeClass` value for [Category][].\n\n```javascript\n> Category.test (Math.sqrt)\ntrue\n\n> Category.test (0)\nfalse\n```\n\n#### `Semigroup :: TypeClass`\n\n`TypeClass` value for [Semigroup][].\n\n```javascript\n> Semigroup.test ('')\ntrue\n\n> Semigroup.test (0)\nfalse\n```\n\n#### `Monoid :: TypeClass`\n\n`TypeClass` value for [Monoid][].\n\n```javascript\n> Monoid.test ('')\ntrue\n\n> Monoid.test (0)\nfalse\n```\n\n#### `Group :: TypeClass`\n\n`TypeClass` value for [Group][].\n\n```javascript\n> Group.test (Sum (0))\ntrue\n\n> Group.test ('')\nfalse\n```\n\n#### `Filterable :: TypeClass`\n\n`TypeClass` value for [Filterable][].\n\n```javascript\n> Filterable.test ({})\ntrue\n\n> Filterable.test ('')\nfalse\n```\n\n#### `Functor :: TypeClass`\n\n`TypeClass` value for [Functor][].\n\n```javascript\n> Functor.test ([])\ntrue\n\n> Functor.test ('')\nfalse\n```\n\n#### `Bifunctor :: TypeClass`\n\n`TypeClass` value for [Bifunctor][].\n\n```javascript\n> Bifunctor.test (Pair ('foo') (64))\ntrue\n\n> Bifunctor.test ([])\nfalse\n```\n\n#### `Profunctor :: TypeClass`\n\n`TypeClass` value for [Profunctor][].\n\n```javascript\n> Profunctor.test (Math.sqrt)\ntrue\n\n> Profunctor.test ([])\nfalse\n```\n\n#### `Apply :: TypeClass`\n\n`TypeClass` value for [Apply][].\n\n```javascript\n> Apply.test ([])\ntrue\n\n> Apply.test ('')\nfalse\n```\n\n#### `Applicative :: TypeClass`\n\n`TypeClass` value for [Applicative][].\n\n```javascript\n> Applicative.test ([])\ntrue\n\n> Applicative.test ({})\nfalse\n```\n\n#### `Chain :: TypeClass`\n\n`TypeClass` value for [Chain][].\n\n```javascript\n> Chain.test ([])\ntrue\n\n> Chain.test ({})\nfalse\n```\n\n#### `ChainRec :: TypeClass`\n\n`TypeClass` value for [ChainRec][].\n\n```javascript\n> ChainRec.test ([])\ntrue\n\n> ChainRec.test ({})\nfalse\n```\n\n#### `Monad :: TypeClass`\n\n`TypeClass` value for [Monad][].\n\n```javascript\n> Monad.test ([])\ntrue\n\n> Monad.test ({})\nfalse\n```\n\n#### `Alt :: TypeClass`\n\n`TypeClass` value for [Alt][].\n\n```javascript\n> Alt.test ({})\ntrue\n\n> Alt.test ('')\nfalse\n```\n\n#### `Plus :: TypeClass`\n\n`TypeClass` value for [Plus][].\n\n```javascript\n> Plus.test ({})\ntrue\n\n> Plus.test ('')\nfalse\n```\n\n#### `Alternative :: TypeClass`\n\n`TypeClass` value for [Alternative][].\n\n```javascript\n> Alternative.test ([])\ntrue\n\n> Alternative.test ({})\nfalse\n```\n\n#### `Foldable :: TypeClass`\n\n`TypeClass` value for [Foldable][].\n\n```javascript\n> Foldable.test ({})\ntrue\n\n> Foldable.test ('')\nfalse\n```\n\n#### `Traversable :: TypeClass`\n\n`TypeClass` value for [Traversable][].\n\n```javascript\n> Traversable.test ([])\ntrue\n\n> Traversable.test ('')\nfalse\n```\n\n#### `Extend :: TypeClass`\n\n`TypeClass` value for [Extend][].\n\n```javascript\n> Extend.test ([])\ntrue\n\n> Extend.test ({})\nfalse\n```\n\n#### `Comonad :: TypeClass`\n\n`TypeClass` value for [Comonad][].\n\n```javascript\n> Comonad.test (Identity (0))\ntrue\n\n> Comonad.test ([])\nfalse\n```\n\n#### `Contravariant :: TypeClass`\n\n`TypeClass` value for [Contravariant][].\n\n```javascript\n> Contravariant.test (Math.sqrt)\ntrue\n\n> Contravariant.test ([])\nfalse\n```\n\n#### `equals :: (a, b) -⁠> Boolean`\n\nReturns `true` if its arguments are of the same type and equal according\nto the type's [`fantasy-land/equals`][] method; `false` otherwise.\n\n`fantasy-land/equals` implementations are provided for the following\nbuilt-in types: Null, Undefined, Boolean, Number, Date, RegExp, String,\nArray, Arguments, Error, Object, and Function.\n\nThe algorithm supports circular data structures. Two arrays are equal\nif they have the same index paths and for each path have equal values.\nTwo arrays which represent `[1, [1, [1, [1, [1, ...]]]]]`, for example,\nare equal even if their internal structures differ. Two objects are equal\nif they have the same property paths and for each path have equal values.\n\n```javascript\n> equals (0, -0)\ntrue\n\n> equals (NaN, NaN)\ntrue\n\n> equals (Cons (1, Cons (2, Nil)), Cons (1, Cons (2, Nil)))\ntrue\n\n> equals (Cons (1, Cons (2, Nil)), Cons (2, Cons (1, Nil)))\nfalse\n```\n\n#### `lt :: (a, b) -⁠> Boolean`\n\nReturns `true` if its arguments are of the same type and the first is\nless than the second according to the type's [`fantasy-land/lte`][]\nmethod; `false` otherwise.\n\nThis function is derived from [`lte`](#lte).\n\nSee also [`gt`](#gt) and [`gte`](#gte).\n\n```javascript\n> lt (0, 0)\nfalse\n\n> lt (0, 1)\ntrue\n\n> lt (1, 0)\nfalse\n```\n\n#### `lte :: (a, b) -⁠> Boolean`\n\nReturns `true` if its arguments are of the same type and the first\nis less than or equal to the second according to the type's\n[`fantasy-land/lte`][] method; `false` otherwise.\n\n`fantasy-land/lte` implementations are provided for the following\nbuilt-in types: Null, Undefined, Boolean, Number, Date, String, Array,\nArguments, and Object.\n\nThe algorithm supports circular data structures in the same manner as\n[`equals`](#equals).\n\nSee also [`lt`](#lt), [`gt`](#gt), and [`gte`](#gte).\n\n```javascript\n> lte (0, 0)\ntrue\n\n> lte (0, 1)\ntrue\n\n> lte (1, 0)\nfalse\n```\n\n#### `gt :: (a, b) -⁠> Boolean`\n\nReturns `true` if its arguments are of the same type and the first is\ngreater than the second according to the type's [`fantasy-land/lte`][]\nmethod; `false` otherwise.\n\nThis function is derived from [`lte`](#lte).\n\nSee also [`lt`](#lt) and [`gte`](#gte).\n\n```javascript\n> gt (0, 0)\nfalse\n\n> gt (0, 1)\nfalse\n\n> gt (1, 0)\ntrue\n```\n\n#### `gte :: (a, b) -⁠> Boolean`\n\nReturns `true` if its arguments are of the same type and the first\nis greater than or equal to the second according to the type's\n[`fantasy-land/lte`][] method; `false` otherwise.\n\nThis function is derived from [`lte`](#lte).\n\nSee also [`lt`](#lt) and [`gt`](#gt).\n\n```javascript\n> gte (0, 0)\ntrue\n\n> gte (0, 1)\nfalse\n\n> gte (1, 0)\ntrue\n```\n\n#### `min :: Ord a => (a, a) -⁠> a`\n\nReturns the smaller of its two arguments.\n\nThis function is derived from [`lte`](#lte).\n\nSee also [`max`](#max).\n\n```javascript\n> min (10, 2)\n2\n\n> min (new Date ('1999-12-31'), new Date ('2000-01-01'))\nnew Date ('1999-12-31')\n\n> min ('10', '2')\n'10'\n```\n\n#### `max :: Ord a => (a, a) -⁠> a`\n\nReturns the larger of its two arguments.\n\nThis function is derived from [`lte`](#lte).\n\nSee also [`min`](#min).\n\n```javascript\n> max (10, 2)\n10\n\n> max (new Date ('1999-12-31'), new Date ('2000-01-01'))\nnew Date ('2000-01-01')\n\n> max ('10', '2')\n'2'\n```\n\n#### `clamp :: Ord a => (a, a, a) -⁠> a`\n\nTakes a lower bound, an upper bound, and a value of the same type.\nReturns the value if it is within the bounds; the nearer bound otherwise.\n\nThis function is derived from [`min`](#min) and [`max`](#max).\n\n```javascript\n> clamp (0, 100, 42)\n42\n\n> clamp (0, 100, -1)\n0\n\n> clamp ('A', 'Z', '~')\n'Z'\n```\n\n#### `compose :: Semigroupoid c => (c j k, c i j) -⁠> c i k`\n\nFunction wrapper for [`fantasy-land/compose`][].\n\n`fantasy-land/compose` implementations are provided for the following\nbuilt-in types: Function.\n\n```javascript\n> compose (Math.sqrt, x => x + 1) (99)\n10\n```\n\n#### `id :: Category c => TypeRep c -⁠> c`\n\nFunction wrapper for [`fantasy-land/id`][].\n\n`fantasy-land/id` implementations are provided for the following\nbuilt-in types: Function.\n\n```javascript\n> id (Function) ('foo')\n'foo'\n```\n\n#### `concat :: Semigroup a => (a, a) -⁠> a`\n\nFunction wrapper for [`fantasy-land/concat`][].\n\n`fantasy-land/concat` implementations are provided for the following\nbuilt-in types: String, Array, and Object.\n\n```javascript\n> concat ('abc', 'def')\n'abcdef'\n\n> concat ([1, 2, 3], [4, 5, 6])\n[1, 2, 3, 4, 5, 6]\n\n> concat ({x: 1, y: 2}, {y: 3, z: 4})\n{x: 1, y: 3, z: 4}\n\n> concat (Cons ('foo', Cons ('bar', Cons ('baz', Nil))), Cons ('quux', Nil))\nCons ('foo', Cons ('bar', Cons ('baz', Cons ('quux', Nil))))\n```\n\n#### `empty :: Monoid m => TypeRep m -⁠> m`\n\nFunction wrapper for [`fantasy-land/empty`][].\n\n`fantasy-land/empty` implementations are provided for the following\nbuilt-in types: String, Array, and Object.\n\n```javascript\n> empty (String)\n''\n\n> empty (Array)\n[]\n\n> empty (Object)\n{}\n\n> empty (List)\nNil\n```\n\n#### `invert :: Group g => g -⁠> g`\n\nFunction wrapper for [`fantasy-land/invert`][].\n\n```javascript\n> invert (Sum (5))\nSum (-5)\n```\n\n#### `filter :: Filterable f => (a -⁠> Boolean, f a) -⁠> f a`\n\nFunction wrapper for [`fantasy-land/filter`][]. Discards every element\nwhich does not satisfy the predicate.\n\n`fantasy-land/filter` implementations are provided for the following\nbuilt-in types: Array and Object.\n\nSee also [`reject`](#reject).\n\n```javascript\n> filter (x => x % 2 == 1, [1, 2, 3])\n[1, 3]\n\n> filter (x => x % 2 == 1, {x: 1, y: 2, z: 3})\n{x: 1, z: 3}\n\n> filter (x => x % 2 == 1, Cons (1, Cons (2, Cons (3, Nil))))\nCons (1, Cons (3, Nil))\n\n> filter (x => x % 2 == 1, Nothing)\nNothing\n\n> filter (x => x % 2 == 1, Just (0))\nNothing\n\n> filter (x => x % 2 == 1, Just (1))\nJust (1)\n```\n\n#### `reject :: Filterable f => (a -⁠> Boolean, f a) -⁠> f a`\n\nDiscards every element which satisfies the predicate.\n\nThis function is derived from [`filter`](#filter).\n\n```javascript\n> reject (x => x % 2 == 1, [1, 2, 3])\n[2]\n\n> reject (x => x % 2 == 1, {x: 1, y: 2, z: 3})\n{y: 2}\n\n> reject (x => x % 2 == 1, Cons (1, Cons (2, Cons (3, Nil))))\nCons (2, Nil)\n\n> reject (x => x % 2 == 1, Nothing)\nNothing\n\n> reject (x => x % 2 == 1, Just (0))\nJust (0)\n\n> reject (x => x % 2 == 1, Just (1))\nNothing\n```\n\n#### `map :: Functor f => (a -⁠> b, f a) -⁠> f b`\n\nFunction wrapper for [`fantasy-land/map`][].\n\n`fantasy-land/map` implementations are provided for the following\nbuilt-in types: Array, Object, and Function.\n\n```javascript\n> map (Math.sqrt, [1, 4, 9])\n[1, 2, 3]\n\n> map (Math.sqrt, {x: 1, y: 4, z: 9})\n{x: 1, y: 2, z: 3}\n\n> map (Math.sqrt, s => s.length) ('Sanctuary')\n3\n\n> map (Math.sqrt, Pair ('foo') (64))\nPair ('foo') (8)\n\n> map (Math.sqrt, Nil)\nNil\n\n> map (Math.sqrt, Cons (1, Cons (4, Cons (9, Nil))))\nCons (1, Cons (2, Cons (3, Nil)))\n```\n\n#### `flip :: Functor f => (f (a -⁠> b), a) -⁠> f b`\n\nMaps over the given functions, applying each to the given value.\n\nThis function is derived from [`map`](#map).\n\n```javascript\n> flip (x => y => x + y, '!') ('foo')\n'foo!'\n\n> flip ([Math.floor, Math.ceil], 1.5)\n[1, 2]\n\n> flip ({floor: Math.floor, ceil: Math.ceil}, 1.5)\n{floor: 1, ceil: 2}\n\n> flip (Cons (Math.floor, Cons (Math.ceil, Nil)), 1.5)\nCons (1, Cons (2, Nil))\n```\n\n#### `bimap :: Bifunctor f => (a -⁠> b, c -⁠> d, f a c) -⁠> f b d`\n\nFunction wrapper for [`fantasy-land/bimap`][].\n\n```javascript\n> bimap (s => s.toUpperCase (), Math.sqrt, Pair ('foo') (64))\nPair ('FOO') (8)\n```\n\n#### `mapLeft :: Bifunctor f => (a -⁠> b, f a c) -⁠> f b c`\n\nMaps the given function over the left side of a Bifunctor.\n\n```javascript\n> mapLeft (Math.sqrt, Pair (64) (9))\nPair (8) (9)\n```\n\n#### `promap :: Profunctor p => (a -⁠> b, c -⁠> d, p b c) -⁠> p a d`\n\nFunction wrapper for [`fantasy-land/promap`][].\n\n`fantasy-land/promap` implementations are provided for the following\nbuilt-in types: Function.\n\n```javascript\n> promap (Math.abs, x => x + 1, Math.sqrt) (-100)\n11\n```\n\n#### `ap :: Apply f => (f (a -⁠> b), f a) -⁠> f b`\n\nFunction wrapper for [`fantasy-land/ap`][].\n\n`fantasy-land/ap` implementations are provided for the following\nbuilt-in types: Array, Object, and Function.\n\n```javascript\n> ap ([Math.sqrt, x => x * x], [1, 4, 9, 16, 25])\n[1, 2, 3, 4, 5, 1, 16, 81, 256, 625]\n\n> ap ({a: Math.sqrt, b: x => x * x}, {a: 16, b: 10, c: 1})\n{a: 4, b: 100}\n\n> ap (s => n => s.slice (0, n), s => Math.ceil (s.length / 2)) ('Haskell')\n'Hask'\n\n> ap (Identity (Math.sqrt), Identity (64))\nIdentity (8)\n\n> ap (Cons (Math.sqrt, Cons (x => x * x, Nil)), Cons (16, Cons (100, Nil)))\nCons (4, Cons (10, Cons (256, Cons (10000, Nil))))\n```\n\n#### `lift2 :: Apply f => (a -⁠> b -⁠> c, f a, f b) -⁠> f c`\n\nLifts `a -> b -> c` to `Apply f => f a -> f b -> f c` and returns the\nresult of applying this to the given arguments.\n\nThis function is derived from [`map`](#map) and [`ap`](#ap).\n\nSee also [`lift3`](#lift3).\n\n```javascript\n> lift2 (x => y => Math.pow (x, y), [10], [1, 2, 3])\n[10, 100, 1000]\n\n> lift2 (x => y => Math.pow (x, y), Identity (10), Identity (3))\nIdentity (1000)\n```\n\n#### `lift3 :: Apply f => (a -⁠> b -⁠> c -⁠> d, f a, f b, f c) -⁠> f d`\n\nLifts `a -> b -> c -> d` to `Apply f => f a -> f b -> f c -> f d` and\nreturns the result of applying this to the given arguments.\n\nThis function is derived from [`map`](#map) and [`ap`](#ap).\n\nSee also [`lift2`](#lift2).\n\n```javascript\n> lift3 (x => y => z => x + z + y,\n. ['<', '['],\n. ['>', ']'],\n. ['foo', 'bar', 'baz'])\n[ '', '', '',\n. '', '[bar>', '[baz>',\n. '[foo]', '[bar]', '[baz]' ]\n\n> lift3 (x => y => z => x + z + y,\n. Identity ('<'),\n. Identity ('>'),\n. Identity ('baz'))\nIdentity ('')\n```\n\n#### `apFirst :: Apply f => (f a, f b) -⁠> f a`\n\nCombines two effectful actions, keeping only the result of the first.\nEquivalent to Haskell's `(<*)` function.\n\nThis function is derived from [`lift2`](#lift2).\n\nSee also [`apSecond`](#apSecond).\n\n```javascript\n> apFirst ([1, 2], [3, 4])\n[1, 1, 2, 2]\n\n> apFirst (Identity (1), Identity (2))\nIdentity (1)\n```\n\n#### `apSecond :: Apply f => (f a, f b) -⁠> f b`\n\nCombines two effectful actions, keeping only the result of the second.\nEquivalent to Haskell's `(*>)` function.\n\nThis function is derived from [`lift2`](#lift2).\n\nSee also [`apFirst`](#apFirst).\n\n```javascript\n> apSecond ([1, 2], [3, 4])\n[3, 4, 3, 4]\n\n> apSecond (Identity (1), Identity (2))\nIdentity (2)\n```\n\n#### `of :: Applicative f => (TypeRep f, a) -⁠> f a`\n\nFunction wrapper for [`fantasy-land/of`][].\n\n`fantasy-land/of` implementations are provided for the following\nbuilt-in types: Array and Function.\n\n```javascript\n> of (Array, 42)\n[42]\n\n> of (Function, 42) (null)\n42\n\n> of (List, 42)\nCons (42, Nil)\n```\n\n#### `append :: (Applicative f, Semigroup (f a)) => (a, f a) -⁠> f a`\n\nReturns the result of appending the first argument to the second.\n\nThis function is derived from [`concat`](#concat) and [`of`](#of).\n\nSee also [`prepend`](#prepend).\n\n```javascript\n> append (3, [1, 2])\n[1, 2, 3]\n\n> append (3, Cons (1, Cons (2, Nil)))\nCons (1, Cons (2, Cons (3, Nil)))\n```\n\n#### `prepend :: (Applicative f, Semigroup (f a)) => (a, f a) -⁠> f a`\n\nReturns the result of prepending the first argument to the second.\n\nThis function is derived from [`concat`](#concat) and [`of`](#of).\n\nSee also [`append`](#append).\n\n```javascript\n> prepend (1, [2, 3])\n[1, 2, 3]\n\n> prepend (1, Cons (2, Cons (3, Nil)))\nCons (1, Cons (2, Cons (3, Nil)))\n```\n\n#### `chain :: Chain m => (a -⁠> m b, m a) -⁠> m b`\n\nFunction wrapper for [`fantasy-land/chain`][].\n\n`fantasy-land/chain` implementations are provided for the following\nbuilt-in types: Array and Function.\n\n```javascript\n> chain (x => [x, x], [1, 2, 3])\n[1, 1, 2, 2, 3, 3]\n\n> chain (x => x % 2 == 1 ? of (List, x) : Nil,\n. Cons (1, Cons (2, Cons (3, Nil))))\nCons (1, Cons (3, Nil))\n\n> chain (n => s => s.slice (0, n),\n. s => Math.ceil (s.length / 2))\n. ('Haskell')\n'Hask'\n```\n\n#### `join :: Chain m => m (m a) -⁠> m a`\n\nRemoves one level of nesting from a nested monadic structure.\n\nThis function is derived from [`chain`](#chain).\n\n```javascript\n> join ([[1], [2], [3]])\n[1, 2, 3]\n\n> join ([[[1, 2, 3]]])\n[[1, 2, 3]]\n\n> join (Identity (Identity (1)))\nIdentity (1)\n```\n\n#### `chainRec :: ChainRec m => (TypeRep m, (a -⁠> c, b -⁠> c, a) -⁠> m c, a) -⁠> m b`\n\nFunction wrapper for [`fantasy-land/chainRec`][].\n\n`fantasy-land/chainRec` implementations are provided for the following\nbuilt-in types: Array.\n\n```javascript\n> chainRec (\n. Array,\n. (next, done, s) => s.length == 2 ? [s + '!', s + '?'].map (done)\n. : [s + 'o', s + 'n'].map (next),\n. ''\n. )\n['oo!', 'oo?', 'on!', 'on?', 'no!', 'no?', 'nn!', 'nn?']\n```\n\n#### `alt :: Alt f => (f a, f a) -⁠> f a`\n\nFunction wrapper for [`fantasy-land/alt`][].\n\n`fantasy-land/alt` implementations are provided for the following\nbuilt-in types: Array and Object.\n\n```javascript\n> alt ([1, 2, 3], [4, 5, 6])\n[1, 2, 3, 4, 5, 6]\n\n> alt (Nothing, Nothing)\nNothing\n\n> alt (Nothing, Just (1))\nJust (1)\n\n> alt (Just (2), Just (3))\nJust (2)\n```\n\n#### `zero :: Plus f => TypeRep f -⁠> f a`\n\nFunction wrapper for [`fantasy-land/zero`][].\n\n`fantasy-land/zero` implementations are provided for the following\nbuilt-in types: Array and Object.\n\n```javascript\n> zero (Array)\n[]\n\n> zero (Object)\n{}\n\n> zero (Maybe)\nNothing\n```\n\n#### `reduce :: Foldable f => ((b, a) -⁠> b, b, f a) -⁠> b`\n\nFunction wrapper for [`fantasy-land/reduce`][].\n\n`fantasy-land/reduce` implementations are provided for the following\nbuilt-in types: Array and Object.\n\n```javascript\n> reduce ((xs, x) => [x].concat (xs), [], [1, 2, 3])\n[3, 2, 1]\n\n> reduce (concat, '', Cons ('foo', Cons ('bar', Cons ('baz', Nil))))\n'foobarbaz'\n```\n\n#### `size :: Foldable f => f a -⁠> Integer`\n\nReturns the number of elements of the given structure.\n\nThis function is derived from [`reduce`](#reduce).\n\n```javascript\n> size ([])\n0\n\n> size (['foo', 'bar', 'baz'])\n3\n\n> size (Nil)\n0\n\n> size (Cons ('foo', Cons ('bar', Cons ('baz', Nil))))\n3\n```\n\n#### `all :: Foldable f => (a -⁠> Boolean, f a) -⁠> Boolean`\n\nReturns `true` if all the elements of the structure satisfy the\npredicate; `false` otherwise.\n\nThis function is derived from [`reduce`](#reduce).\n\nSee also [`any`](#any) and [`none`](#none).\n\n```javascript\n> all (Number.isInteger, [])\ntrue\n\n> all (Number.isInteger, [1, 2, 3])\ntrue\n\n> all (Number.isInteger, [0, 0.25, 0.5, 0.75, 1])\nfalse\n```\n\n#### `any :: Foldable f => (a -⁠> Boolean, f a) -⁠> Boolean`\n\nReturns `true` if any element of the structure satisfies the predicate;\n`false` otherwise.\n\nThis function is derived from [`reduce`](#reduce).\n\nSee also [`all`](#all) and [`none`](#none).\n\n```javascript\n> any (Number.isInteger, [])\nfalse\n\n> any (Number.isInteger, [1, 2, 3])\ntrue\n\n> any (Number.isInteger, [0, 0.25, 0.5, 0.75, 1])\ntrue\n```\n\n#### `none :: Foldable f => (a -⁠> Boolean, f a) -⁠> Boolean`\n\nReturns `true` if none of the elements of the structure satisfies the\npredicate; `false` otherwise.\n\nThis function is derived from [`any`](#any). `none (pred, foldable)` is\nequivalent to `!(any (pred, foldable))`.\n\nSee also [`all`](#all).\n\n```javascript\n> none (Number.isInteger, [])\ntrue\n\n> none (Number.isInteger, [0, 0.25, 0.5, 0.75, 1])\nfalse\n```\n\n#### `elem :: (Setoid a, Foldable f) => (a, f a) -⁠> Boolean`\n\nTakes a value and a structure and returns `true` if the\nvalue is an element of the structure; `false` otherwise.\n\nThis function is derived from [`equals`](#equals) and\n[`reduce`](#reduce).\n\n```javascript\n> elem ('c', ['a', 'b', 'c'])\ntrue\n\n> elem ('x', ['a', 'b', 'c'])\nfalse\n\n> elem (3, {x: 1, y: 2, z: 3})\ntrue\n\n> elem (8, {x: 1, y: 2, z: 3})\nfalse\n\n> elem (0, Just (0))\ntrue\n\n> elem (0, Just (1))\nfalse\n\n> elem (0, Nothing)\nfalse\n```\n\n#### `intercalate :: (Monoid m, Foldable f) => (m, f m) -⁠> m`\n\nConcatenates the elements of the given structure, separating each pair\nof adjacent elements with the given separator.\n\nThis function is derived from [`concat`](#concat), [`empty`](#empty),\nand [`reduce`](#reduce).\n\n```javascript\n> intercalate (', ', [])\n''\n\n> intercalate (', ', ['foo', 'bar', 'baz'])\n'foo, bar, baz'\n\n> intercalate (', ', Nil)\n''\n\n> intercalate (', ', Cons ('foo', Cons ('bar', Cons ('baz', Nil))))\n'foo, bar, baz'\n\n> intercalate ([0, 0, 0], [])\n[]\n\n> intercalate ([0, 0, 0], [[1], [2, 3], [4, 5, 6], [7, 8], [9]])\n[1, 0, 0, 0, 2, 3, 0, 0, 0, 4, 5, 6, 0, 0, 0, 7, 8, 0, 0, 0, 9]\n```\n\n#### `foldMap :: (Monoid m, Foldable f) => (TypeRep m, a -⁠> m, f a) -⁠> m`\n\nDeconstructs a foldable by mapping every element to a monoid and\nconcatenating the results.\n\nThis function is derived from [`concat`](#concat), [`empty`](#empty),\nand [`reduce`](#reduce).\n\n```javascript\n> foldMap (String, f => f.name, [Math.sin, Math.cos, Math.tan])\n'sincostan'\n```\n\n#### `reverse :: (Applicative f, Foldable f, Monoid (f a)) => f a -⁠> f a`\n\nReverses the elements of the given structure.\n\nThis function is derived from [`concat`](#concat), [`empty`](#empty),\n[`of`](#of), and [`reduce`](#reduce).\n\n```javascript\n> reverse ([1, 2, 3])\n[3, 2, 1]\n\n> reverse (Cons (1, Cons (2, Cons (3, Nil))))\nCons (3, Cons (2, Cons (1, Nil)))\n```\n\n#### `sort :: (Ord a, Applicative f, Foldable f, Monoid (f a)) => f a -⁠> f a`\n\nPerforms a [stable sort][] of the elements of the given structure,\nusing [`lte`](#lte) for comparisons.\n\nThis function is derived from [`lte`](#lte), [`concat`](#concat),\n[`empty`](#empty), [`of`](#of), and [`reduce`](#reduce).\n\nSee also [`sortBy`](#sortBy).\n\n```javascript\n> sort (['foo', 'bar', 'baz'])\n['bar', 'baz', 'foo']\n\n> sort ([Just (2), Nothing, Just (1)])\n[Nothing, Just (1), Just (2)]\n\n> sort (Cons ('foo', Cons ('bar', Cons ('baz', Nil))))\nCons ('bar', Cons ('baz', Cons ('foo', Nil)))\n```\n\n#### `sortBy :: (Ord b, Applicative f, Foldable f, Monoid (f a)) => (a -⁠> b, f a) -⁠> f a`\n\nPerforms a [stable sort][] of the elements of the given structure,\nusing [`lte`](#lte) to compare the values produced by applying the\ngiven function to each element of the structure.\n\nThis function is derived from [`lte`](#lte), [`concat`](#concat),\n[`empty`](#empty), [`of`](#of), and [`reduce`](#reduce).\n\nSee also [`sort`](#sort).\n\n```javascript\n> sortBy (s => s.length, ['red', 'green', 'blue'])\n['red', 'blue', 'green']\n\n> sortBy (s => s.length, ['black', 'white'])\n['black', 'white']\n\n> sortBy (s => s.length, ['white', 'black'])\n['white', 'black']\n\n> sortBy (s => s.length, Cons ('red', Cons ('green', Cons ('blue', Nil))))\nCons ('red', Cons ('blue', Cons ('green', Nil)))\n```\n\n#### `traverse :: (Applicative f, Traversable t) => (TypeRep f, a -⁠> f b, t a) -⁠> f (t b)`\n\nFunction wrapper for [`fantasy-land/traverse`][].\n\n`fantasy-land/traverse` implementations are provided for the following\nbuilt-in types: Array and Object.\n\nSee also [`sequence`](#sequence).\n\n```javascript\n> traverse (Array, x => x, [[1, 2, 3], [4, 5]])\n[[1, 4], [1, 5], [2, 4], [2, 5], [3, 4], [3, 5]]\n\n> traverse (Identity, x => Identity (x + 1), [1, 2, 3])\nIdentity ([2, 3, 4])\n```\n\n#### `sequence :: (Applicative f, Traversable t) => (TypeRep f, t (f a)) -⁠> f (t a)`\n\nInverts the given `t (f a)` to produce an `f (t a)`.\n\nThis function is derived from [`traverse`](#traverse).\n\n```javascript\n> sequence (Array, Identity ([1, 2, 3]))\n[Identity (1), Identity (2), Identity (3)]\n\n> sequence (Identity, [Identity (1), Identity (2), Identity (3)])\nIdentity ([1, 2, 3])\n```\n\n#### `extend :: Extend w => (w a -⁠> b, w a) -⁠> w b`\n\nFunction wrapper for [`fantasy-land/extend`][].\n\n`fantasy-land/extend` implementations are provided for the following\nbuilt-in types: Array and Function.\n\n```javascript\n> extend (ss => ss.join (''), ['x', 'y', 'z'])\n['xyz', 'yz', 'z']\n\n> extend (f => f ([3, 4]), reverse) ([1, 2])\n[4, 3, 2, 1]\n```\n\n#### `duplicate :: Extend w => w a -⁠> w (w a)`\n\nAdds one level of nesting to a comonadic structure.\n\nThis function is derived from [`extend`](#extend).\n\n```javascript\n> duplicate (Identity (1))\nIdentity (Identity (1))\n\n> duplicate ([1])\n[[1]]\n\n> duplicate ([1, 2, 3])\n[[1, 2, 3], [2, 3], [3]]\n\n> duplicate (reverse) ([1, 2]) ([3, 4])\n[4, 3, 2, 1]\n```\n\n#### `extract :: Comonad w => w a -⁠> a`\n\nFunction wrapper for [`fantasy-land/extract`][].\n\n```javascript\n> extract (Identity (42))\n42\n```\n\n#### `contramap :: Contravariant f => (b -⁠> a, f a) -⁠> f b`\n\nFunction wrapper for [`fantasy-land/contramap`][].\n\n`fantasy-land/contramap` implementations are provided for the following\nbuilt-in types: Function.\n\n```javascript\n> contramap (s => s.length, Math.sqrt) ('Sanctuary')\n3\n```\n\n[Alt]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#alt\n[Alternative]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#alternative\n[Applicative]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#applicative\n[Apply]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#apply\n[Bifunctor]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#bifunctor\n[Category]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#category\n[Chain]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#chain\n[ChainRec]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#chainrec\n[Comonad]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#comonad\n[Contravariant]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#contravariant\n[Extend]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#extend\n[FL]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1\n[Filterable]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#filterable\n[Foldable]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#foldable\n[Functor]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#functor\n[Group]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#group\n[Monad]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#monad\n[Monoid]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#monoid\n[Ord]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#ord\n[Plus]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#plus\n[Profunctor]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#profunctor\n[Semigroup]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#semigroup\n[Semigroupoid]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#semigroupoid\n[Setoid]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#setoid\n[Traversable]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#traversable\n[`fantasy-land/alt`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#alt-method\n[`fantasy-land/ap`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#ap-method\n[`fantasy-land/bimap`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#bimap-method\n[`fantasy-land/chain`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#chain-method\n[`fantasy-land/chainRec`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#chainrec-method\n[`fantasy-land/compose`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#compose-method\n[`fantasy-land/concat`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#concat-method\n[`fantasy-land/contramap`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#contramap-method\n[`fantasy-land/empty`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#empty-method\n[`fantasy-land/equals`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#equals-method\n[`fantasy-land/extend`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#extend-method\n[`fantasy-land/extract`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#extract-method\n[`fantasy-land/filter`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#filter-method\n[`fantasy-land/id`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#id-method\n[`fantasy-land/invert`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#invert-method\n[`fantasy-land/lte`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#lte-method\n[`fantasy-land/map`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#map-method\n[`fantasy-land/of`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#of-method\n[`fantasy-land/promap`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#promap-method\n[`fantasy-land/reduce`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#reduce-method\n[`fantasy-land/traverse`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#traverse-method\n[`fantasy-land/zero`]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#zero-method\n[stable sort]: https://en.wikipedia.org/wiki/Sorting_algorithm#Stability\n[type-classes]: https://github.com/sanctuary-js/sanctuary-def#type-classes\n","_attachments":{},"homepage":"https://github.com/sanctuary-js/sanctuary-type-classes#readme","bugs":{"url":"https://github.com/sanctuary-js/sanctuary-type-classes/issues"},"license":"MIT"}