API Reference¶

Constants¶

`None`¶

As Lua dictionaries cannot distinguish between a value not being present and a value of nil, Llama.None exists to represent values that should be interpreted as nil. This is especially useful when removing values with Dictionary.merge.

Dictionary¶

Dictionaries are tables with key-value pairs.

Constructors¶

`fromLists`¶

Llama.Dictionary.fromLists(keys, values) -> dictionary

Returns a new dictionary constructed from keys and values. The lists are expected to be the same size.

Example:

local keys = { "foo", "bar", "baz" }
local values = { 1, 2, 3 }

Llama.Dictionary.fromLists(keys, values)

Results:

{
    foo = 1,
    bar = 2,
    baz = 3,
}

Copying¶

`copy`¶

Llama.Dictionary.copy(dictionary) -> dictionary

Returns a shallow copy of dictionary.

`copyDeep`¶

Llama.Dictionary.copyDeep(dictionary) -> dictionary

Returns a deep copy of dictionary.

Warning

Deep copying is more expensive than shallow copying and forces you to resort to the more expensive equalsDeep for value equality checking. Only use it when absolutely necessary.

Comparing¶

`equals`¶

Llama.Dictionary.equals(...dictionaries) -> result

Returns whether all dictionaries have shallow value equality.

`equalsDeep`¶

Llama.Dictionary.equalsDeep(...dictionaries) -> result

Returns whether all dictionaries have deep value equality.

Warning

Deep comparison is more expensive than shallow comparison. Only use it when absolutely necessary.

Persistent changes¶

`merge`¶

Llama.Dictionary.merge(...dictionaries) -> dictionary

Returns a new dictionary with all of the entries of dictionaries merged together. Later entries replace older ones, and Llama.None can be used to remove values.

Aliases
`join`

Example:

local a = {
    key = "value",
    foo = "bar",
    removeMe = 0,
}

local b = {
    removeMe = Llama.None,
    addMe = 1,
}

Llama.Dictionary.merge(a, b)

Results:

{
    key = "value",
    foo = "bar",
    addMe = 1,
}

`mergeDeep`¶

Llama.Dictionary.mergeDeep(...dictionaries) -> dictionary

Returns a new dictionary with all of the entries of dictionaries deeply merged together. Later entries replace older ones, and Llama.None can be used to remove values.

Aliases
`joinDeep`

Example:

local a = {
    key = "value",
    foo = "bar",
    dictionary = {
        foo = "foo",
        bar = "bar",
    },
    removeMe = 0,
}

local b = {
    removeMe = Llama.None,
    addMe = 1,
    dictionary = {
        baz = "baz",
    },
}

Llama.Dictionary.mergeDeep(a, b)

Results:

{
    key = "value",
    foo = "bar",
    addMe = 1,
    dictionary = {
        foo = "foo",
        bar = "bar",
        baz = "baz",
    },
}

Warning

Deep merging is more expensive than shallow merging and forces you to resort to the more expensive equalsDeep for value equality checking. Only use it when absolutely necessary.

`removeKey`¶

Llama.Dictionary.removeKey(dictionary, key) -> dictionary

Returns a new dictionary with the entry at key is removed from dictionary.

`removeKeys`¶

Llama.Dictionary.removeKeys(dictionary, ...keys) -> dictionary

Returns new dictionary with entries at keys are removed from dictionary.

`removeValue`¶

Llama.Dictionary.removeValue(dictionary, value) -> dictionary

Returns a new dictionary where any entry with value are removed from dictionary.

`removeValues`¶

Llama.Dictionary.removeValues(dictionary, ...values) -> dictionary

Returns a new dictionary where any entry with any values are removed from dictionary.

`set`¶

Llama.Dictionary.set(dictionary, key, value) -> dictionary

Returns a new dictionary with the entry at key in dictionary is set to value.

`update`¶

Llama.Dictionary.update(dictionary, key[, updater[, callback]]) -> dictionary

Returns a new dictionary with the entry at key is updated by updater. If the entry does not exist, callback is invoked and the entry is created from its return value.

updater and callback are expected to have the following signatures:

updater(value, key) -> value
callback(key) -> value

Example:

local dictionary = {
    foo = "foo",
    bar = "bar",
}

local function fooify(value)
    return "foo" .. value
end

Llama.Dictionary.update(dictionary, "bar", fooify)
Llama.Dictionary.update(dictionary, "baz", fooify, function()
    return "baz"
end)

Results:

{
    foo = "foo",
    bar = "foobar",
}

{
    foo = "foo",
    bar = "bar",
    baz = "baz",
}

Sequence algorithms¶

`filter`¶

Llama.Dictionary.filter(dictionary, filterer) -> dictionary

Returns a new dictionary with only the entries of dictionary for which filterer returns a truthy.

filterer is expected to have the following signature:

filterer(value, key) -> result

Example:

local dictionary = {
    foo1 = "foo",
    foo2 = "foo",
    bar1 = "bar",
}

local function onlyFoo(value)
    return value == "foo"
end

Llama.Dictionary.filter(dictionary, onlyFoo)

Results:

{
    foo1 = "foo",
    foo2 = "foo",
}

`flip`¶

Llama.Dictionary.flip(dictionary) -> dictionary

Returns a new dictionary with the keys and values of dictionary swapped.

Example:

local dictionary = {
    foo = "oof",
    bar = "rab",
    baz = "zab",
}

Llama.Dictionary.flip(dictionary)

Results:

{
    oof = "foo",
    rab = "bar",
    zab = "baz",
}

`map`¶

Llama.Dictionary.map(dictionary, mapper) -> dictionary

Returns a new dictionary with the values (and keys) of dictionary mapped over using mapper.

mapper is expected to have the following signature:

mapper(value, key) -> value[, key]

Example:

local dictionary = {
    foo = "foo",
    bar = "bar",
    baz = "baz",
}

local function fooify(value)
    return "foo" .. value
end

Llama.Dictionary.map(dictionary, fooify)

Results:

{
    foo = "foofoo",
    bar = "foobar",
    baz = "foobaz",
}

Reading values¶

`has`¶

Llama.Dictionary.has(dictionary, key) -> result

Returns whether dictionary has a value at the key.

`includes`¶

Llama.Dictionary.includes(dictionary, value) -> result

Returns whether dictionary includes a value.

Conversion¶

`keys`¶

Llama.Dictionary.keys(dictionary) -> list

Returns a list of dictionary's keys.

`values`¶

Llama.Dictionary.values(dictionary) -> list

Returns a list of dictionary's values.

Reducing¶

`count`¶

Llama.Dictionary.count(dictionary[, predicate]) -> result

Returns the number of entries in dictionary for which predicate returns a truthy. If predicate is not provided, count simply counts all of the entries in dictionary (useful since #dictionary does not give the number of dictionary entries, only the number of list entries).

predicate is expected to have the following signature:

predicate(value, key) -> result

Example:

local dictionary = {
    foo1 = "foo",
    foo2 = "foo",
    bar1 = "bar",
    bar2 = "bar",
}

local function onlyFoo(value)
    return value == "foo"
end

Llama.Dictionary.count(dictionary, onlyFoo)

Results:

`every`¶

Llama.Dictionary.every(dictionary, predicate) -> result

Returns whether predicate returns a truthy for all of dictionary's entries.

predicate is expected to have the following signature:

predicate(value, key) -> result

Example:

local a = {
    foo1 = "foo",
    foo2 = "foo",
}

local b = {
    foo = "foo",
    bar = "bar",
    baz = "baz",
}

local function onlyFoo(value)
    return value == "foo"
end

Llama.Dictionary.every(a, onlyFoo)
Llama.Dictionary.every(b, onlyFoo)

Results:

true
false

`some`¶

Llama.Dictionary.some(dictionary, predicate) -> result

Returns whether predicate returns a truthy for any of dictionary's entries.

predicate is expected to have the following signature:

predicate(value, key) -> result

Example:

local a = {
    bar1 = "bar",
    bar2 = "bar",
}

local b = {
    foo = "foo",
    bar = "bar",
    baz = "baz",
}

local function onlyFoo(value)
    return value == "foo"
end

Llama.Dictionary.some(a, onlyFoo)
Llama.Dictionary.every(b, onlyFoo)

Results:

false
true

Combination¶

`flatten`¶

Llama.Dictionary.flatten(dictionary[, depth]) -> dictionary

Returns a new dictionary with dictionary's entries flattened to depth or as deeply as possible if depth is not provided.

Example:

local dictionary = {
    foo = "foo",
    foobar = {
        bar = "bar",
        barbaz = {
            baz = "baz",
        }
    }
}

Llama.Dictionary.flatten(dictionary)

Results:

{
    foo = "foo",
    bar = "bar",
    baz = "baz",
}

List¶

Lists are tables with index-value pairs.

Constructors¶

`create`¶

Llama.List.create(count, value) -> list

Creates a new list of count values.

Copying¶

`copy`¶

Llama.List.copy(list) -> list

Returns a shallow copy of list.

`copyDeep`¶

Llama.List.copyDeep(list) -> list

Returns a deep copy of list.

Warning

Deep copying is more expensive than shallow copying and forces you to resort to the more expensive equalsDeep for value equality checking. Only use it when absolutely necessary.

Comparing¶

`equals`¶

Llama.List.equals(...lists) -> result

Returns whether all lists have shallow value equality.

`equalsDeep`¶

Llama.List.equalsDeep(...lists) -> result

Returns whether all lists have deep value equality.

Warning

Deep comparison is more expensive than shallow comparison. Only use it when absolutely necessary.

Persistent changes¶

`concat`¶

Llama.List.concat(...lists) -> list

Returns a concatenation of all of the lists in lists.

Aliases
`join`

Example:

local a = { 1, 2, 3 }
local b = { 4, 5, 6 }

Llama.List.concat(a, b)

Results:

{ 1, 2, 3, 4, 5, 6 }

`concatDeep`¶

Llama.List.concatDeep(...lists) -> list

Returns a concatenation of all of the lists in lists with their sublists deep copied.

Aliases
`joinDeep`

Warning

Deep concatenating is more expensive than shallow concatenating and forces you to resort to the more expensive equalsDeep for value equality checking. Only use it when absolutely necessary.

`insert`¶

Llama.List.insert(list, index, ...values) -> list

Returns a new list with values inserted at index of list. If index is 0 or negative, insert inserts at index relative to the end of list.

`push`¶

Llama.List.push(list, ...values) -> list

Returns copy of list with values appended to the end of list.

Aliases
`append`

`pop`¶

Llama.List.pop(list[, numPops]) -> list

Returns copy of list with numPops values popped off the end of list.

`removeIndex`¶

Llama.List.removeIndex(list, index) -> list

Returns a new list where the entry in list at index is removed. If index is 0 or negative, removeIndex removes at index relative to the end of list.

`removeIndices`¶

Llama.List.removeIndices(list, ...indices) -> list

Returns a new list where all entries in list at indices is removed. If an index is 0 or negative, removeIndex removes at the index relative to the end of list.

`removeValue`¶

Llama.List.removeValue(list, value) -> list

Returns a new list with all entries of list with value removed.

`removeValues`¶

Llama.List.removeValues(list, ...values) -> list

Returns a new list with all entries of list with any values removed.

`set`¶

Llama.List.set(list, index, value) -> list

Returns a new list with index in list set to the value. If index is 0 or negative, set sets at index relative to the end of list.

`shift`¶

Llama.List.shift(list[, numPlaces]) -> list

Returns new list with numPlaces values shifted off the beginning of list.

Example:

local list = { "foo", "bar", "baz" }

Llama.List.shift(list)

Results:

{ "bar", "baz" }

`unshift`¶

Llama.List.unshift(list, ...values) -> list

Returns new list with values prepended to the beginning of list.

Example:

local list = { "baz" }

Llama.List.unshift(list, "foo", "bar")

Results:

{ "foo", "bar", "baz" }

`update`¶

Llama.List.update(list, index[, updater[, callback]]) -> list

Returns a new list with the entry at index being updated by updater. If the entry does not exist, callback is invoked and the entry is created from its return value.

updater and callback are expected to have the following signatures:

updater(value, index) -> value
callback(index) -> value

Example:

local list = { "foo", "bar" }

local function fooify(value)
    return "foo" .. value
end

Llama.List.update(list, 2, fooify)
Llama.List.update(list, 3, fooify, function()
    return "baz"
end)

Results:

{ "foo", "foobar" }

{ "foo", "bar", "baz" }

Sequence algorithms¶

`filter`¶

Llama.List.filter(list, filterer) -> list

Returns a new list with only the entries of list for which filterer returns a truthy.

filterer is expected to have the following signature:

filterer(value, index) -> result

Example:

local list = { "foo", "foo", "bar" }

local function onlyFoo(value)
    return value == "foo"
end

Llama.List.filter(list, onlyFoo)

Results:

{ "foo", "foo" }

`map`¶

Llama.List.map(list, mapper) -> list

Returns a new list with the values of list mapped over using mapper.

mapper is expected to have the following signature:

mapper(value, index) -> value

Example:

local list = { "foo", "bar", "baz" }

local function fooify(value)
    return "foo" .. value
end

Llama.List.map(list, fooify)

Results:

{ "foofoo", "foobar", "foobaz" }

`reverse`¶

Llama.List.reverse(list) -> list

Returns a new list with the entries of list reversed.

Example:

local list = { 1, 2, 3 }

Llama.List.reverse(list)

Results:

{ 3, 2, 1 }

`sort`¶

Llama.list.sort(list[, comparator]) -> list

Returns a new list with the entries of list sorted by comparator if given. comparator should return true if the first argument should come before the second, and false otherwise.

comparator is expected to have the following signature:

comparator(a, b) -> result

`zip`¶

Llama.list.zip(...lists) -> list

Returns a new list of lists "zipped" together. The length of list is the length of the shortest provided list.

Example:

local a = { "foo", "bar", "baz" }
local b = { 1, 2, 3, 4 }

Llama.List.zip(a, b)

Results:

{
    { "foo", 1 },
    { "bar", 2 },
    { "baz", 3 },
}

`zipAll`¶

Llama.list.zipAll(...lists) -> list

Returns a new list of lists "zipped" together. zipAll zips as much as possible, filling in nil values with Llama.None

Example:

local a = { "foo", "bar", "baz" }
local b = { 1, 2, 3, 4 }

Llama.List.zipAll(a, b)

Results:

{
    { "foo", 1 },
    { "bar", 2 },
    { "baz", 3 },
    { Llama.None, 4 },
}

Creating subsets¶

`slice`¶

Llama.List.slice(list[, from[, to]]) -> list

Returns a new list sliced from list. If from is not provided, slice slices from the beginning of list. If to is not provided, slice slices to the end of list.

Example:

local list = { 1, 2, 3, 4, 5 }

Llama.List.slice(list, 1, 3)

{ 1, 2, 3 }

Reading values¶

`first`¶

Llama.List.first(list) -> result

Returns the first value in list.

`last`¶

Llama.List.last(list) -> result

Returns the last value in list.

`includes`¶

Llama.List.includes(list, value) -> result

Returns whether list includes a value.

Finding a value¶

`find`¶

Llama.List.find(list, value[, from]) -> index

Returns the first index from from if provided for which list has value. If from is 0 or negative, find searches from from relative to the end of list.

`findLast`¶

Llama.List.findLast(list, value[, from]) -> index

Returns the last index from from if provided for which list has value. If from is 0 or negative, findLast searches from from relative to the end of list.

`findWhere`¶

Llama.List.findWhere(list, predicate[, from]) -> index

Returns the first index from from if provided for which list's value satisfies predicate. If from is 0 or negative, findWhere searches from from relative to the end of list.

predicate is expected to have the following signature:

predicate(value, index) -> result

`findWhereLast`¶

Llama.List.findWhereLast(list, predicate[, from]) -> index

Returns the last index from from if provided for which list's value satisfies predicate. If from is 0 or negative, findWhereLast searches from from relative to the end of list.

predicate is expected to have the following signature:

predicate(value, index) -> result

Conversion¶

`toSet`¶

Llama.List.toSet(list) -> list

Returns a new set created from list.

Reducing¶

`count`¶

Llama.List.count(list[, predicate]) -> result

Returns the number of entries in list for which predicate returns a truthy. If no predicate is provided, count simply counts all of the entries in list.

predicate is expected to have the following signature:

predicate(value, index) -> result

Example:

local list = { "foo", "foo", "bar" }

local function onlyFoo(value)
    return value == "foo"
end

Llama.List.count(list, onlyFoo)

Results:

`every`¶

Llama.List.every(list, predicate) -> result

Returns whether predicate returns a truthy for all of list's entries.

predicate is expected to have the following signature:

predicate(value, index) -> result

Example:

local a = { "foo", "foo" }
local b = { "foo", "foo", "bar" }

local function onlyFoo(value)
    return value == "foo"
end

Llama.List.every(a, onlyFoo)
Llama.List.every(b, onlyFoo)

Results:

true
false

`some`¶

Llama.List.some(list, predicate) -> result

Returns whether predicate returns a truthy for any of list's entries.

predicate is expected to have the following signature:

predicate(value, key) -> result

Example:

local a = { "bar", "bar" }
local b = { "foo", "bar", "baz" }

local function onlyFoo(value)
    return value == "foo"
end

Llama.List.some(a, onlyFoo)
Llama.List.some(b, onlyFoo)

Results:

false
true

`reduce`¶

Llama.List.reduce(list, reducer[, initialReduction]) -> value

Reduces list to a single value, from left to right. If initialReduction is not provided, reduce uses the first value in list.

reducer is expected to have the following signature:

reducer(reduction, value, key) -> reduction

Example:

local list = { 1, 2, 3 }

local function add(reduction, value)
    return reduction = reduction + value
end

Llama.List.reduce(list, add)

Results:

`reduceRight`¶

Llama.List.reduceRight(list, reducer[, initialReduction]) -> value

Reduces list to a single value, from right to left. If initialReduction is not provided, reduceRight uses the last value in list.

reducer is expected to have the following signature:

reducer(reduction, value, key) -> reduction

Example:

local list = { 1, 2, 3 }

local function subtract(reduction, value)
    return reduction = reduction - value
end

Llama.List.reduceRight(list, subtract)

Results:

Combination¶

`flatten`¶

Llama.List.flatten(list[, depth]) -> list

Returns a new list with all of list's entries flattened to depth or as deeply as possible if depth is not provided.

Example:

local list = {
    "foo",
    {
        "bar",
        {
            "baz",
        }
    }
}

Llama.List.flatten(list)

Results:

{ "foo", "bar", "baz" }

`splice`¶

Llama.List.splice(list, from, to, ...values) -> list

Returns a new list with values replacing the values between from and to in list.

Example:

local list = { "foo", 2, 3}

Llama.List.splice(list, 2, 3, "bar", "baz")

Results:

{ "foo", "bar", "baz" }

Set¶

Sets are tables where each value may only occur once.

Constructors¶

`fromList`¶

Llama.Set.fromList(list) -> set

Creates a set from list.

Example:

local list = { "foo", "bar", "baz" }

Llama.Set.fromList(list)

Results:

{
    foo = true,
    bar = true,
    baz = true,
}

Copying¶

`copy`¶

Llama.Set.copy(set) -> set

Returns a shallow copy of set.

Comparing¶

`isSubset`¶

Llama.Set.isSubset(subset, superset) -> result

Returns whether subset is a subset of superset.

Example:

local a = {
    foo = true,
    bar = true,
}

local b = {
    foo = true,
    bar = true,
    baz = true,
}

Llama.Set.isSubset(a, b)
Llama.Set.isSubset(b, a)

Results:

true
false

`isSuperset`¶

Llama.Set.isSuperset(superset, subset) -> result

Returns whether superset is a superset of subset.

Example:

local a = {
    foo = true,
    bar = true,
    baz = true,
}

local b = {
    foo = true,
    bar = true,
}

Llama.Set.isSuperset(a, b)
Llama.Set.isSuperset(b, a)

Results:

true
false

Persistent changes¶

`add`¶

Llama.Set.add(set, ...values) -> set

Returns a new set with values added to set.

Example:

local set = {
    foo = true,
    bar = true,
}

Llama.Set.add(set, "baz")

Results:

{
    foo = true,
    bar = true,
    baz = true,
}

`subtract`¶

Llama.Set.subtract(set, ...values) -> set

Returns a new set with values subtracted from set.

Example:

local set = {
    foo = true,
    bar = true,
    baz = true,
}

Llama.Set.subtract(set, "baz")

Results:

{
    foo = true,
    bar = true,
}

`union`¶

Llama.Set.union(...sets) -> set

Returns a new set with all of the values of sets combined.

Example:

local a = {
    foo = true,
    bar = true,
}

local b = {
    bar = true,
    baz = true,
}

Llama.Set.union(a, b)

Results:

{
    foo = true,
    bar = true,
    baz = true,
}

`intersection`¶

Llama.Set.intersection(...sets) -> set

Returns a new set with only the values of sets that intersect.

Example:

local a = {
    foo = true,
    bar = true,
}

local b = {
    bar = true,
    baz = true,
}

Llama.Set.intersection(a, b)

Results:

{
    bar = true,
}

Sequence algorithms¶

`filter`¶

Llama.Set.filter(set, filterer) -> set

Returns a new set with only the entries of the set for which the filterer returns a truthy.

filterer is expected to have the following signature:

filterer(value) -> result

Example:

local set = {
    [1] = true,
    [2] = true,
    [3] = true,
    [4] = true,
    [5] = true,
}

local function onlyEvens(value)
    return value % 2 == 0
end

Llama.Set.filter(set, onlyEvens)

Results:

{
    [2] = true,
    [4] = true,
}

`map`¶

Llama.Set.map(set, mapper) -> set

Returns a new set with the values (and keys) of dictionary mapped using the mapper.

mapper is expected to have the following signature:

mapper(value) -> value

Example:

local set = {
    foo = true,
    bar = true,
    baz = true,
}

local function fooify(value)
    return "foo" .. value
end

Llama.Set.map(set, fooify)

Results:

{
    foofoo = true,
    foobar = true,
    foobaz = true,
}

Reading values¶

`has`¶

Llama.Set.has(set, value) -> result

Returns whether set has value.

`equalObjects`¶

Llama.equalObjects(...objects) -> result

Returns whether the items have reference equality.

`isEmpty`¶

Llama.isEmpty(table) -> result

Returns whether the table is empty.

API Reference¶

Constants¶

None¶

Dictionary¶

Constructors¶

fromLists¶

Copying¶

copy¶

copyDeep¶

Comparing¶

equals¶

equalsDeep¶

Persistent changes¶

merge¶

mergeDeep¶

removeKey¶

removeKeys¶

removeValue¶

removeValues¶

set¶

update¶

Sequence algorithms¶

filter¶

flip¶

map¶

Reading values¶

has¶

includes¶

Conversion¶

keys¶

values¶

Reducing¶

count¶

every¶

some¶

Combination¶

flatten¶

List¶

Constructors¶

create¶

Copying¶

copy¶

copyDeep¶

Comparing¶

equals¶

equalsDeep¶

Persistent changes¶

concat¶

concatDeep¶

insert¶

push¶

pop¶

removeIndex¶

removeIndices¶

removeValue¶

removeValues¶

set¶

shift¶

unshift¶

update¶

Sequence algorithms¶

filter¶

map¶

reverse¶

sort¶

zip¶

zipAll¶

Creating subsets¶

slice¶

Reading values¶

first¶

last¶

includes¶

Finding a value¶

find¶

findLast¶

findWhere¶

findWhereLast¶

Conversion¶

toSet¶

`None`¶

`fromLists`¶

`copy`¶

`copyDeep`¶

`equals`¶

`equalsDeep`¶

`merge`¶

`mergeDeep`¶

`removeKey`¶

`removeKeys`¶

`removeValue`¶

`removeValues`¶

`set`¶

`update`¶

`filter`¶

`flip`¶

`map`¶

`has`¶

`includes`¶

`keys`¶

`values`¶

`count`¶

`every`¶

`some`¶

`flatten`¶

`create`¶

`copy`¶

`copyDeep`¶

`equals`¶

`equalsDeep`¶

`concat`¶

`concatDeep`¶

`insert`¶

`push`¶

`pop`¶

`removeIndex`¶

`removeIndices`¶

`removeValue`¶

`removeValues`¶

`set`¶

`shift`¶

`unshift`¶

`update`¶

`filter`¶

`map`¶

`reverse`¶

`sort`¶

`zip`¶

`zipAll`¶

`slice`¶

`first`¶

`last`¶

`includes`¶

`find`¶

`findLast`¶

`findWhere`¶

`findWhereLast`¶

`toSet`¶

`count`¶

`every`¶

`some`¶

`reduce`¶

`reduceRight`¶

`flatten`¶

`splice`¶

`fromList`¶

`copy`¶

`isSubset`¶

`isSuperset`¶

`add`¶

`subtract`¶

`union`¶

`intersection`¶

`filter`¶

`map`¶

`has`¶

`equalObjects`¶

`isEmpty`¶