742 lines
20 KiB
Markdown
742 lines
20 KiB
Markdown
---
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id: sets-lists-tuples
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title: Tuples, Lists, Sets
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---
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Apart from complex data types such as `maps` and `records`, LIGO also
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features `tuples`, `lists` and `sets`.
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## Tuples
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Tuples gather a given number of values in a specific order and those
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values, called *components*, can be retrieved by their index
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(position). Probably the most common tuple is the *pair*. For
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example, if we were storing coordinates on a two dimensional grid we
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might use a pair `(x,y)` to store the coordinates `x` and `y`. There
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is a *specific order*, so `(y,x)` is not equal to `(x,y)` in
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general. The number of components is part of the type of a tuple, so,
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for example, we cannot add an extra component to a pair and obtain a
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triple of the same type: `(x,y)` has always a different type from
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`(x,y,z)`, whereas `(y,x)` might have the same type as `(x,y)`.
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Like records, tuple components can be of arbitrary types.
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### Defining Tuples
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Unlike [a record](language-basics/maps-records.md), tuple types do not
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have to be defined before they can be used. However below we will give
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them names by *type aliasing*.
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<!--DOCUSAURUS_CODE_TABS-->
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<!--Pascaligo-->
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```pascaligo group=tuple
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type full_name is string * string // Alias
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const full_name : full_name = ("Alice", "Johnson")
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```
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<!--CameLIGO-->
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```cameligo group=tuple
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type full_name = string * string // Alias
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let full_name : full_name = ("Alice", "Johnson") // Optional parentheses
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```
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<!--ReasonLIGO-->
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```reasonligo group=tuple
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type full_name = (string, string); // Alias
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let full_name : full_name = ("Alice", "Johnson");
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```
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<!--END_DOCUSAURUS_CODE_TABS-->
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### Accessing Components
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Accessing the components of a tuple in OCaml is achieved by
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[pattern matching](language-basics/unit-option-pattern-matching.md). LIGO
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currently supports tuple patterns only in the parameters of functions,
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not in pattern matching. However, we can access components by their
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position in their tuple, which cannot be done in OCaml. *Tuple
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components are zero-indexed*, that is, the first component has index
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`0`.
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<!--DOCUSAURUS_CODE_TABS-->
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<!--PascaLIGO-->
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```pascaligo group=tuple
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const first_name : string = full_name.0
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```
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<!--CameLIGO-->
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```cameligo group=tuple
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let first_name : string = full_name.0
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```
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<!--ReasonLIGO-->
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```reasonligo group=tuple
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let first_name : string = full_name[0];
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```
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<!--END_DOCUSAURUS_CODE_TABS-->
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## Lists
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Lists are linear collections of elements of the same type. Linear
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means that, in order to reach an element in a list, we must visit all
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the elements before (sequential access). Elements can be repeated, as
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only their order in the collection matters. The first element is
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called the *head*, and the sub-list after the head is called the
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*tail*. For those familiar with algorithmic data structure, you can
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think of a list a *stack*, where the top is written on the left.
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> 💡 Lists are needed when returning operations from a smart
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> contract's main function.
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### Defining Lists
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<!--DOCUSAURUS_CODE_TABS-->
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<!--PascaLIGO-->
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```pascaligo group=lists
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const empty_list : list (int) = nil // Or list []
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const my_list : list (int) = list [1; 2; 2] // The head is 1
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```
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<!--CameLIGO-->
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```cameligo group=lists
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let empty_list : int list = []
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let my_list : int list = [1; 2; 2] // The head is 1
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```
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<!--ReasonLIGO-->
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```reasonligo group=lists
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let empty_list : list (int) = [];
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let my_list : list (int) = [1, 2, 2]; // The head is 1
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```
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<!--END_DOCUSAURUS_CODE_TABS-->
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### Adding to Lists
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Lists can be augmented by adding an element before the head (or, in
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terms of stack, by *pushing an element on top*). This operation is
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usually called *consing* in functional languages.
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<!--DOCUSAURUS_CODE_TABS-->
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<!--PascaLIGO-->
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In PascaLIGO, the *cons operator* is infix and noted `#`. It is not
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symmetric: on the left lies the element to cons, and, on the right, a
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list on which to cons. (The symbol is helpfully asymmetric to remind
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you of that.)
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```pascaligo group=lists
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const larger_list : list (int) = 5 # my_list // [5;1;2;2]
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```
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<!--CameLIGO-->
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In CameLIGO, the *cons operator* is infix and noted `::`. It is not
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symmetric: on the left lies the element to cons, and, on the right, a
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list on which to cons.
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```cameligo group=lists
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let larger_list : int list = 5 :: my_list // [5;1;2;2]
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```
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<!--ReasonLIGO-->
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In ReasonLIGO, the *cons operator* is infix and noted `, ...`. It is
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not symmetric: on the left lies the element to cons, and, on the
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right, a list on which to cons.
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```reasonligo group=lists
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let larger_list : list (int) = [5, ...my_list]; // [5,1,2,2]
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```
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<!--END_DOCUSAURUS_CODE_TABS-->
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### Functional Iteration over Lists
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A *functional iterator* is a function that traverses a data structure
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and calls in turn a given function over the elements of that structure
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to compute some value. Another approach is possible in PascaLIGO:
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*loops* (see the relevant section).
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There are three kinds of functional iterations over LIGO lists: the
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*iterated operation*, the *map operation* (not to be confused with the
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*map data structure*) and the *fold operation*.
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> 💡 Lists can be iterated, folded or mapped to different values. You
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> can find additional examples
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> [here](https://gitlab.com/ligolang/ligo/tree/dev/src/test/contracts)
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> and other built-in operators
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> [here](https://gitlab.com/ligolang/ligo/blob/dev/src/passes/operators/operators.ml#L59)
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#### Iterated Operation over Lists
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The first, the *iterated operation*, is an iteration over the list
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with a unit return value. It is useful to enforce certain invariants
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on the element of a list, or fail. For example you might want to check
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that each value inside of a list is within a certain range, and fail
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otherwise.
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<!--DOCUSAURUS_CODE_TABS-->
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<!--PascaLIGO-->
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In PascaLIGO, the predefined functional iterator implementing the
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iterated operation over lists is called `list_iter`.
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In the following example, a list is iterated to check that all its
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elements (integers) are greater than `3`:
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```pascaligo group=lists
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function iter_op (const l : list (int)) : unit is
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block {
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function iterated (const i : int) : unit is
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if i > 2 then Unit else (failwith ("Below range.") : unit)
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} with list_iter (iterated, l)
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```
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> The iterated function must be pure, that is, it cannot mutate
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> variables.
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<!--CameLIGO-->
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In CameLIGO, the predefined functional iterator implementing the
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iterated operation over lists is called `List.iter`.
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In the following example, a list is iterated to check that all its
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elements (integers) are greater than `3`:
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```cameligo group=lists
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let iter_op (l : int list) : unit =
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let predicate = fun (i : int) -> assert (i > 3)
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in List.iter predicate l
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```
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<!--ReasonLIGO-->
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In ReasonLIGO, the predefined functional iterator implementing the
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iterated operation over lists is called `List.iter`.
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In the following example, a list is iterated to check that all its
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elements (integers) are greater than `3`:
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```reasonligo group=lists
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let iter_op = (l : list (int)) : unit => {
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let predicate = (i : int) => assert (i > 3);
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List.iter (predicate, l);
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};
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```
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<!--END_DOCUSAURUS_CODE_TABS-->
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#### Mapped Operation over Lists
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We may want to change all the elements of a given list by applying to
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them a function. This is called a *map operation*, not to be confused
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with the map data structure.
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<!--DOCUSAURUS_CODE_TABS-->
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<!--PascaLIGO-->
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In PascaLIGO, the predefined functional iterator implementing the
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mapped operation over lists is called `list_map` and is used as
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follows:
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```pascaligo group=lists
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function increment (const i : int): int is i + 1
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// Creates a new list with all elements incremented by 1
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const plus_one : list (int) = list_map (increment, larger_list)
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```
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> The mapped function must be pure, that is, it cannot mutate
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> variables.
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<!--CameLIGO-->
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In CameLIGO, the predefined functional iterator implementing the
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mapped operation over lists is called `List.map` and is used as
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follows:
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```cameligo group=lists
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let increment (i : int) : int = i + 1
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// Creates a new list with all elements incremented by 1
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let plus_one : int list = List.map increment larger_list
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```
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<!--ReasonLIGO-->
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In ReasonLIGO, the predefined functional iterator implementing the
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mapped operation over lists is called `List.map` and is used as
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follows:
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```reasonligo group=lists
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let increment = (i : int) : int => i + 1;
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// Creates a new list with all elements incremented by 1
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let plus_one : list (int) = List.map (increment, larger_list);
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```
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<!--END_DOCUSAURUS_CODE_TABS-->
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#### Folded Operation over Lists
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A *folded operation* is the most general of iterations. The folded
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function takes two arguments: an *accumulator* and the structure
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*element* at hand, with which it then produces a new accumulator. This
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enables having a partial result that becomes complete when the
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traversal of the data structure is over.
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<!--DOCUSAURUS_CODE_TABS-->
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<!--PascaLIGO-->
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In PascaLIGO, the predefined functional iterator implementing the
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folded operation over lists is called `list_fold` and is used as
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follows:
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```pascaligo group=lists
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function sum (const acc : int; const i : int): int is acc + i
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const sum_of_elements : int = list_fold (sum, my_list, 0)
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```
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> The folded function must be pure, that is, it cannot mutate
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> variables.
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<!--CameLIGO-->
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In CameLIGO, the predefined functional iterator implementing the folded
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operation over lists is called `List.fold` and is used as follows:
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```cameligo group=lists
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let sum (acc, i: int * int) : int = acc + i
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let sum_of_elements : int = List.fold sum my_list 0
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```
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<!--ReasonLIGO-->
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In ReasonLIGO, the predefined functional iterator implementing the
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folded operation over lists is called `List.fold` and is used as
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follows:
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```reasonligo group=lists
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let sum = ((result, i): (int, int)): int => result + i;
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let sum_of_elements : int = List.fold (sum, my_list, 0);
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```
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<!--END_DOCUSAURUS_CODE_TABS-->
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## Sets
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Sets are unordered collections of values of the same type, like lists
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are ordered collections. Like the mathematical sets and lists, sets
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can be empty and, if not, elements of sets in LIGO are *unique*,
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whereas they can be repeated in a list.
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### Empty Sets
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<!--DOCUSAURUS_CODE_TABS-->
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<!--PascaLIGO-->
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In PascaLIGO, the notation for sets is similar to that for lists,
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except the keyword `set` is used before:
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```pascaligo group=sets
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const my_set : set (int) = set []
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```
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<!--CameLIGO-->
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In CameLIGO, the empty set is denoted by the predefined value
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`Set.empty`.
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```cameligo group=sets
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let my_set : int set = Set.empty
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```
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<!--ReasonLIGO-->
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In ReasonLIGO, the empty set is denoted by the predefined value
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`Set.empty`.
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```reasonligo group=sets
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let my_set : set (int) = Set.empty;
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```
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<!--END_DOCUSAURUS_CODE_TABS-->
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### Non-empty Sets
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<!--DOCUSAURUS_CODE_TABS-->
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<!--PascaLIGO-->
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In PascaLIGO, the notation for sets is similar to that for lists,
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except the keyword `set` is used before:
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```pascaligo group=sets
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const my_set : set (int) = set [3; 2; 2; 1]
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```
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You can check that `2` is not repeated in `my_set` by using the LIGO
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compiler like this (the output will sort the elements of the set, but
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that order is not significant for the compiler):
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```shell
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ligo evaluate-value
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gitlab-pages/docs/language-basics/src/sets-lists-tuples/sets.ligo my_set
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# Outputs: { 3 ; 2 ; 1 }
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```
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<!--CameLIGO-->
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In CameLIGO, there is no predefined syntactic construct for sets: you
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must build your set by adding to the empty set. (This is the way in
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OCaml.)
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```cameligo group=sets
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let my_set : int set =
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Set.add 3 (Set.add 2 (Set.add 2 (Set.add 1 (Set.empty : int set))))
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```
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You can check that `2` is not repeated in `my_set` by using the LIGO
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compiler like this (the output will sort the elements of the set, but
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that order is not significant for the compiler):
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```shell
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ligo evaluate-value
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gitlab-pages/docs/language-basics/src/sets-lists-tuples/sets.mligo my_set
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# Outputs: { 3 ; 2 ; 1 }
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```
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<!--ReasonLIGO-->
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In ReasonLIGO, there is no predefined syntactic construct for sets:
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you must build your set by adding to the empty set. (This is the way
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in OCaml.)
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```reasonligo group=sets
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let my_set : set (int) =
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Set.add (3, Set.add (2, Set.add (2, Set.add (1, Set.empty : set (int)))));
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```
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You can check that `2` is not repeated in `my_set` by using the LIGO
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compiler like this (the output will sort the elements of the set, but
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that order is not significant for the compiler):
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```shell
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ligo evaluate-value
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gitlab-pages/docs/language-basics/src/sets-lists-tuples/sets.religo my_set
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# Outputs: { 3 ; 2 ; 1 }
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```
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<!--END_DOCUSAURUS_CODE_TABS-->
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### Set Membership
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<!--DOCUSAURUS_CODE_TABS-->
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<!--PascaLIGO-->
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PascaLIGO features a special keyword `contains` that operates like an
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infix operator checking membership in a set.
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```pascaligo group=sets
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const contains_3 : bool = my_set contains 3
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```
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<!--CameLIGO-->
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In CameLIGO, the predefined predicate `Set.mem` tests for membership
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in a set as follows:
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```cameligo group=sets
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let contains_3 : bool = Set.mem 3 my_set
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```
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<!--ReasonLIGO-->
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In ReasonLIGO, the predefined predicate `Set.mem` tests for membership
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in a set as follows:
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```reasonligo group=sets
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let contains_3 : bool = Set.mem (3, my_set);
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```
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<!--END_DOCUSAURUS_CODE_TABS-->
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### Cardinal of Sets
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<!--DOCUSAURUS_CODE_TABS-->
|
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<!--PascaLIGO-->
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In PascaLIGO, the predefined function `size` returns the number of
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elements in a given set as follows:
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```pascaligo group=sets
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const set_size : nat = size (my_set)
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```
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<!--CameLIGO-->
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In CameLIGO, the predefined function `Set.size` returns the number of
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elements in a given set as follows:
|
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```cameligo group=sets
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let set_size : nat = Set.size my_set
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```
|
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<!--ReasonLIGO-->
|
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In ReasonLIGO, the predefined function `Set.size` returns the number
|
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of elements in a given set as follows:
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```reasonligo group=sets
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let set_size : nat = Set.size (my_set);
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```
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<!--END_DOCUSAURUS_CODE_TABS-->
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### Updating Sets
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<!--DOCUSAURUS_CODE_TABS-->
|
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|
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<!--PascaLIGO-->
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In PascaLIGO, there are two ways to update a set, that is to add or
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remove from it. Either we create a new set from the given one, or we
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modify it in-place. First, let us consider the former way:
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```pascaligo group=sets
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const larger_set : set (int) = set_add (4, my_set)
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const smaller_set : set (int) = set_remove (3, my_set)
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```
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If we are in a block, we can use an instruction to modify the set
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bound to a given variable. This is called a *patch*. It is only
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possible to add elements by means of a patch, not remove any: it is
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the union of two sets.
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In the following example, the parameter set `s` of function `update`
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is augmented (as the `with s` shows) to include `4` and `7`, that is,
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this instruction is equivalent to perform the union of two sets, one
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that is modified in-place, and the other given as a literal
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(extensional definition).
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```pascaligo group=sets
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function update (var s : set (int)) : set (int) is block {
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patch s with set [4; 7]
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} with s
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const new_set : set (int) = update (my_set)
|
|
```
|
|
|
|
<!--CameLIGO-->
|
|
|
|
In CameLIGO, we update a given set by creating another one, with or
|
|
without some elements.
|
|
|
|
```cameligo group=sets
|
|
let larger_set : int set = Set.add 4 my_set
|
|
|
|
let smaller_set : int set = Set.remove 3 my_set
|
|
```
|
|
|
|
<!--ReasonLIGO-->
|
|
|
|
In ReasonLIGO, we update a given set by creating another one, with or
|
|
without some elements.
|
|
|
|
```reasonligo group=sets
|
|
let larger_set : set (int) = Set.add (4, my_set);
|
|
|
|
let smaller_set : set (int) = Set.remove (3, my_set);
|
|
```
|
|
<!--END_DOCUSAURUS_CODE_TABS-->
|
|
|
|
|
|
### 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 PascaLIGO:
|
|
*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.
|
|
|
|
<!--DOCUSAURUS_CODE_TABS-->
|
|
|
|
<!--PascaLIGO-->
|
|
|
|
In PascaLIGO, 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`:
|
|
|
|
```pascaligo group=sets
|
|
function iter_op (const s : set (int)) : unit is
|
|
block {
|
|
function iterated (const i : int) : unit is
|
|
if i > 2 then Unit else (failwith ("Below range.") : unit)
|
|
} with set_iter (iterated, s)
|
|
```
|
|
|
|
> The iterated function must be pure, that is, it cannot mutate
|
|
> variables.
|
|
|
|
<!--CameLIGO-->
|
|
|
|
In CameLIGO, 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`:
|
|
|
|
```cameligo group=sets
|
|
let iter_op (s : int set) : unit =
|
|
let predicate = fun (i : int) -> assert (i > 3)
|
|
in Set.iter predicate s
|
|
```
|
|
|
|
<!--ReasonLIGO-->
|
|
|
|
In ReasonLIGO, 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`:
|
|
|
|
```reasonligo group=sets
|
|
let iter_op = (s : set (int)) : unit => {
|
|
let predicate = (i : int) => assert (i > 3);
|
|
Set.iter (predicate, s);
|
|
};
|
|
```
|
|
|
|
<!--END_DOCUSAURUS_CODE_TABS-->
|
|
|
|
|
|
#### Mapped Operation (NOT IMPLEMENTED YET)
|
|
|
|
We may want to change all the elements of a given set by applying to
|
|
them a function. This is called a *mapped operation*, not to be
|
|
confused with the map data structure.
|
|
|
|
<!--DOCUSAURUS_CODE_TABS-->
|
|
|
|
<!--PascaLIGO-->
|
|
|
|
In PascaLIGO, the predefined functional iterator implementing the
|
|
mapped operation over sets is called `set_map` and is used as follows:
|
|
|
|
```pascaligo skip
|
|
function increment (const i : int): int is i + 1
|
|
|
|
// Creates a new set with all elements incremented by 1
|
|
const plus_one : set (int) = set_map (increment, larger_set)
|
|
```
|
|
|
|
<!--CameLIGO-->
|
|
|
|
In CameLIGO, the predefined functional iterator implementing the
|
|
mapped operation over sets is called `Set.map` and is used as follows:
|
|
|
|
```cameligo skip
|
|
let increment (i : int) : int = i + 1
|
|
|
|
// Creates a new set with all elements incremented by 1
|
|
let plus_one : int set = Set.map increment larger_set
|
|
```
|
|
|
|
<!--ReasonLIGO-->
|
|
|
|
In ReasonLIGO, the predefined functional iterator implementing the
|
|
mapped operation over sets is called `Set.map` and is used as follows:
|
|
|
|
```reasonligo skip
|
|
let increment = (i : int) : int => i + 1;
|
|
|
|
// Creates a new set with all elements incremented by 1
|
|
let plus_one : set (int) = Set.map (increment, larger_set);
|
|
```
|
|
|
|
<!--END_DOCUSAURUS_CODE_TABS-->
|
|
|
|
#### 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.
|
|
|
|
<!--DOCUSAURUS_CODE_TABS-->
|
|
|
|
<!--PascaLIGO-->
|
|
|
|
In PascaLIGO, the predefined functional iterator implementing the
|
|
folded operation over sets is called `set_fold` and is used as
|
|
follows:
|
|
|
|
```pascaligo group=sets
|
|
function sum (const acc : int; const i : int): int is acc + i
|
|
|
|
const sum_of_elements : int = set_fold (sum, my_set, 0)
|
|
```
|
|
|
|
> The folded function must be pure, that is, it cannot mutate
|
|
> variables.
|
|
|
|
It is possible to use a *loop* over a set as well.
|
|
|
|
```pascaligo group=sets
|
|
function loop (const s : set (int)) : int is block {
|
|
var sum : int := 0;
|
|
for element in set s block {
|
|
sum := sum + element
|
|
}
|
|
} with sum
|
|
```
|
|
|
|
<!--CameLIGO-->
|
|
|
|
In CameLIGO, the predefined fold over sets is called `Set.fold`.
|
|
|
|
```cameligo group=sets
|
|
let sum (acc, i : int * int) : int = acc + i
|
|
|
|
let sum_of_elements : int = Set.fold sum my_set 0
|
|
```
|
|
|
|
<!--ReasonLIGO-->
|
|
|
|
In ReasonLIGO, the predefined fold over sets is called `Set.fold`.
|
|
|
|
```reasonligo group=sets
|
|
let sum = ((acc, i) : (int, int)) : int => acc + i;
|
|
|
|
let sum_of_elements : int = Set.fold (sum, my_set, 0);
|
|
```
|
|
<!--END_DOCUSAURUS_CODE_TABS-->
|