Version: 1.1.0

# Tuples, Lists, Sets

Apart from complex data types such as `maps` and `records`, LIGO also features `tuples`, `lists` and `sets`.

## Tuples​

Tuples gather a given number of values in a specific order and those values, called components, can be retrieved by their index (position). Probably the most common tuple is the pair. For example, if we were storing coordinates on a two dimensional grid we might use a pair `[x, y]` to store the coordinates `x` and `y`. There is a specific order, so `[y, x]` is not equal to `[x, y]` in general. The number of components is part of the type of a tuple, so, for example, we cannot add an extra component to a pair and obtain a triple of the same type: `[x, y]` has always a different type from `[x, y, z]`, whereas `[y, x]` might have the same type as `[x, y]`.

Like records, tuple components can be of arbitrary types.

### Defining Tuples​

Unlike a record, tuple types do not have to be defined before they can be used. However below we will give them names by type aliasing.

type two_people = [string, string]; // Alias
const friends: two_people = ["Alice", "Johnson"];

### Destructuring​

If we want to get the first and second names of the `two_people` type, we can use destructuring. Destructuring a tuple allows you to give names to the elements inside the tuple.

let [person_a, person_b] = friends;

This also works in functions:

let first_person_fun = ([person_a, _person_b]: two_people) => person_a;
let alice = first_person_fun(friends);

note: the leading underscore to indicate that the argument `_person_b` is unused.

and within a code block:

let destruct_tuple = (x : [ int , [int , nat] ]) : nat => {
let [a,[b,c]] = x ;
return c
};
let destruct_record = (x : { a : int , b : string }) : int => {
let { a , b } = x ;
return a
};

note: nested patterns in record destructuring are not yet available

### Accessing Components​

Accessing the components of a tuple in OCaml is achieved by pattern matching. LIGO currently supports tuple patterns only in the parameters of functions, not in pattern matching. However, we can access components by their position in their tuple, which cannot be done in OCaml. Tuple components are zero-indexed, that is, the first component has index `0`.

const first_name_component = friends;

## Lists​

Lists are linear collections of elements of the same type. Linear means that, in order to reach an element in a list, we must visit all the elements before (sequential access). Elements can be repeated, as only their order in the collection matters. The first element is called the head, and the sub-list after the head is called the tail. For those familiar with algorithmic data structure, you can think of a list a stack, where the top is written on the left.

💡 Lists are needed when returning operations from a smart contract's main function.

### Defining Lists​

const empty_list: list<int> = list([]);
const my_list = list([1, 2, 2]); // The head is 1, the tail is list([2, 2])

Lists can be augmented by adding an element before the head (or, in terms of stack, by pushing an element on top). This operation is usually called consing in functional languages.

In JsLIGO, the cons operator is infix and noted `, ...`. It is not symmetric: on the left lies the element to cons, and, on the right, a list on which to cons.

const larger_list = list([5, ...my_list]); // [5,1,2,2]

### Accessing list elements​

You cannot access element directly in list but you can access the first element, the head or the rest of the list, the tail. The two function to access those are `List.head_opt` and `List.tail_opt`

const tail: option<list<int>> = List.tail_opt(my_list); // [2,2]

However, the canonical way to destructure lists is using pattern matching.

### Functional Iteration over Lists​

A functional iterator is a function that traverses a data structure and calls in turn a given function over the elements of that structure to compute some value. Another approach is possible in JsLIGO: loops (see the relevant section).

There are three kinds of functional iterations over LIGO lists: the iterated operation, the map operation (not to be confused with the map data structure) and the fold operation.

#### Iterated Operation over Lists​

The first, the iterated operation, is an iteration over the list with a unit return value. It is useful to enforce certain invariants on the element of a list, or fail.

For example you might want to check that each value inside of a list is within a certain range, and fail otherwise. The predefined functional iterator implementing the iterated operation over lists is called `List.iter`.

In the following example, a list is iterated to check that all its elements (integers) are strictly greater than `3`.

const assert_all_greater_than_three = (l: list<int>): unit => {
let predicate = i => assert(i > 3);
List.iter(predicate, l);
};

#### Mapped Operation over Lists​

We may want to change all the elements of a given list by applying to them a function. This is called a map operation, not to be confused with the map data structure. The predefined functional iterator implementing the mapped operation over lists is called `List.map` and is used as follows.

const increment = i => i + 1;
// Creates a new list with all elements incremented by 1
const plus_one: list<int> = List.map(increment, larger_list); // [6,2,3,3]

#### Folded Operation over Lists​

A folded operation is the most general of iterations. The folded function takes two arguments: an accumulator and the structure element at hand, with which it then produces a new accumulator. This enables having a partial result that becomes complete when the traversal of the data structure is over. Folding can be done in two ways, labelled with the directions left and right. One way to tell them apart is to look where the folded function, and the fold itself, keep the accumulator in their signatures. Take for example a function `f`, a list `[1; 2; 3; 4; 5]`, and an accumulator that's just an empty list. A rough approximation of the result of a left fold would look like `f(f(f(f(f([], 1), 2), 3), 4), 5)`, while a right fold would instead look like `f(1, f(2, f(3, f(4, f(5, [])))))`.

The left fold operation has a function signature of `List.fold_left (a -> x -> a) -> a -> x list -> a`, while the right fold operation has `List.fold_right (x -> a -> a) -> x list -> a -> a`. Here is an example of their use.

const sum = ([result, i]: [int, int]) => result + i;
const sum_of_elements: int = List.fold (sum, my_list, 0);

## Sets​

Sets are unordered collections of values of the same type, like lists are ordered collections. Like the mathematical sets and lists, sets can be empty and, if not, elements of sets in LIGO are unique, whereas they can be repeated in a list.

### Empty Sets​

In JsLIGO, the empty set is denoted by the predefined value `Set.empty`.

const my_empty_set: set<int> = Set.empty;

### Non-empty Sets​

In JsLIGO, you can define a non-empty set using the `Set.literal` function which takes a list of elements & returns a set.

let my_set: set<int> = Set.literal(list([3, 2, 2, 1]));

You can check that `2` is not repeated in `my_set` by using the LIGO compiler like this (the output will sort the elements of the set, but that order is not significant for the compiler):

ligo run evaluate-expr gitlab-pages/docs/language-basics/src/sets-lists-tuples/sets.jsligo my_set

### Adding an element to a Set​

You can add an element to a set, using `Set.add` function.

const with_999: set<int> = Set.add(999, my_set);

### Set Membership​

In JsLIGO, the predefined predicate `Set.mem` tests for membership in a set as follows:

const contains_3: bool = Set.mem(3, my_set);

### Cardinal of Sets​

The predefined function `Set.size` returns the number of elements in a given set as follows.

const cardinal: nat = Set.size(my_set);

### Updating Sets​

There are two ways to update a set, that is to add or remove from it.

In JsLIGO, we can use the predefined functions `Set.add` and `Set.remove`. We update a given set by creating another one, with or without some elements.

const larger_set: set<int> = Set.add(4, my_set);
const smaller_set: set<int> = Set.remove(3, my_set);

### Functional Iteration over Sets​

A functional iterator is a function that traverses a data structure and calls in turn a given function over the elements of that structure to compute some value. Another approach is possible in JsLIGO: loops (see the relevant section).

There are three kinds of functional iterations over LIGO maps: the iterated operation, the mapped operation (not to be confused with the map data structure) and the folded operation.

#### Iterated Operation​

The first, the iterated operation, is an iteration over the map with no return value: its only use is to produce side-effects. This can be useful if for example you would like to check that each value inside of a map is within a certain range, and fail with an error otherwise.

The predefined functional iterator implementing the iterated operation over sets is called `Set.iter`. In the following example, a set is iterated to check that all its elements (integers) are greater than `3`.

const assert_all_greater_than_three = s => {
let predicate = i => assert(i > 3);
Set.iter(predicate, s);
};

#### Folded Operation​

A folded operation is the most general of iterations. The folded function takes two arguments: an accumulator and the structure element at hand, with which it then produces a new accumulator. This enables having a partial result that becomes complete when the traversal of the data structure is over.

The predefined fold over sets is called `Set.fold`, however an additional function, `Set.fold_right`, has been added with the signature ```val fold_right : ('acc * 'elt -> 'acc) * 'elt set * 'acc -> 'acc```.

const sum = ([acc, i]: [int, int]) => acc + i;
const sum_of_elements = Set.fold (sum, my_set, 0);