Dictionaries

Cairo provides in its core library a dictionary-like type. The Felt252Dict<T> data type represents a collection of key-value pairs where each key is unique and associated with a corresponding value. This type of data structure is known differently across different programming languages such as maps, hash tables, associative arrays and many others.

The Felt252Dict<T> type is useful when you want to organize your data in a certain way for which using an Array<T> and indexing doesn't suffice. Cairo dictionaries also allow the programmer to easily simulate the existence of mutable memory when there is none.

Basic Use of Dictionaries

It is normal in other languages when creating a new dictionary to define the data types of both key and value. In Cairo, the key type is restricted to felt252, leaving only the possibility to specify the value data type, represented by T in Felt252Dict<T>.

The core functionality of a Felt252Dict<T> is implemented in the trait Felt252DictTrait which includes all basic operations. Among them we can find:

  1. insert(felt252, T) -> () to write values to a dictionary instance and
  2. get(felt252) -> T to read values from it.

These functions allow us to manipulate dictionaries like in any other language. In the following example, we create a dictionary to represent a mapping between individuals and their balance:

fn main() {
    let mut balances: Felt252Dict<u64> = Default::default();

    balances.insert('Alex', 100);
    balances.insert('Maria', 200);

    let alex_balance = balances.get('Alex');
    assert!(alex_balance == 100, "Balance is not 100");

    let maria_balance = balances.get('Maria');
    assert!(maria_balance == 200, "Balance is not 200");
}

We can create a new instance of Felt252Dict<u64> by using the default method of the Default trait and add two individuals, each one with their own balance, using the insert method. Finally, we check the balance of our users with the get method. These methods are defined in the Felt252DictTrait trait in the core library.

Throughout the book we have talked about how Cairo's memory is immutable, meaning you can only write to a memory cell once but the Felt252Dict<T> type represents a way to overcome this obstacle. We will explain how this is implemented later on in "Dictionaries Underneath".

Building upon our previous example, let us show a code example where the balance of the same user changes:

fn main() {
    let mut balances: Felt252Dict<u64> = Default::default();

    // Insert Alex with 100 balance
    balances.insert('Alex', 100);
    // Check that Alex has indeed 100 associated with him
    let alex_balance = balances.get('Alex');
    assert!(alex_balance == 100, "Alex balance is not 100");

    // Insert Alex again, this time with 200 balance
    balances.insert('Alex', 200);
    // Check the new balance is correct
    let alex_balance_2 = balances.get('Alex');
    assert!(alex_balance_2 == 200, "Alex balance is not 200");
}

Notice how in this example we added the 'Alex' individual twice, each time using a different balance and each time that we checked for its balance it had the last value inserted! Felt252Dict<T> effectively allows us to "rewrite" the stored value for any given key.

Before heading on and explaining how dictionaries are implemented it is worth mentioning that once you instantiate a Felt252Dict<T>, behind the scenes all keys have their associated values initialized as zero. This means that if for example, you tried to get the balance of an inexistent user you will get 0 instead of an error or an undefined value. This also means there is no way to delete data from a dictionary. Something to take into account when incorporating this structure into your code.

Until this point, we have seen all the basic features of Felt252Dict<T> and how it mimics the same behavior as the corresponding data structures in any other language, that is, externally of course. Cairo is at its core a non-deterministic Turing-complete programming language, very different from any other popular language in existence, which as a consequence means that dictionaries are implemented very differently as well!

In the following sections, we are going to give some insights about Felt252Dict<T> inner mechanisms and the compromises that were taken to make them work. After that, we are going to take a look at how to use dictionaries with other data structures as well as use the entry method as another way to interact with them.

Dictionaries Underneath

One of the constraints of Cairo's non-deterministic design is that its memory system is immutable, so in order to simulate mutability, the language implements Felt252Dict<T> as a list of entries. Each of the entries represents a time when a dictionary was accessed for reading/updating/writing purposes. An entry has three fields:

  1. A key field that identifies the key for this key-value pair of the dictionary.
  2. A previous_value field that indicates which previous value was held at key.
  3. A new_value field that indicates the new value that is held at key.

If we try implementing Felt252Dict<T> using high-level structures we would internally define it as Array<Entry<T>> where each Entry<T> has information about what key-value pair it represents and the previous and new values it holds. The definition of Entry<T> would be:

struct Entry<T> {
    key: felt252,
    previous_value: T,
    new_value: T,
}

For each time we interact with a Felt252Dict<T>, a new Entry<T> will be registered:

  • A get would register an entry where there is no change in state, and previous and new values are stored with the same value.
  • An insert would register a new Entry<T> where the new_value would be the element being inserted, and the previous_value the last element inserted before this. In case it is the first entry for a certain key, then the previous value will be zero.

The use of this entry list shows how there isn't any rewriting, just the creation of new memory cells per Felt252Dict<T> interaction. Let's show an example of this using the balances dictionary from the previous section and inserting the users 'Alex' and 'Maria':

struct Entry<T> {
    key: felt252,
    previous_value: T,
    new_value: T,
}

fn main() {
    let mut balances: Felt252Dict<u64> = Default::default();
    balances.insert('Alex', 100_u64);
    balances.insert('Maria', 50_u64);
    balances.insert('Alex', 200_u64);
    balances.get('Maria');
}

These instructions would then produce the following list of entries:

keypreviousnew
Alex0100
Maria050
Alex100200
Maria5050

Notice that since 'Alex' was inserted twice, it appears twice and the previous and current values are set properly. Also reading from 'Maria' registered an entry with no change from previous to current values.

This approach to implementing Felt252Dict<T> means that for each read/write operation, there is a scan for the whole entry list in search of the last entry with the same key. Once the entry has been found, its new_value is extracted and used on the new entry to be added as the previous_value. This means that interacting with Felt252Dict<T> has a worst-case time complexity of O(n) where n is the number of entries in the list.

If you pour some thought into alternate ways of implementing Felt252Dict<T> you'd surely find them, probably even ditching completely the need for a previous_value field, nonetheless, since Cairo is not your normal language this won't work. One of the purposes of Cairo is, with the STARK proof system, to generate proofs of computational integrity. This means that you need to verify that program execution is correct and inside the boundaries of Cairo restrictions. One of those boundary checks consists of "dictionary squashing" and that requires information on both previous and new values for every entry.

Squashing Dictionaries

To verify that the proof generated by a Cairo program execution that used a Felt252Dict<T> is correct, we need to check that there wasn't any illegal tampering with the dictionary. This is done through a method called squash_dict that reviews each entry of the entry list and checks that access to the dictionary remains coherent throughout the execution.

The process of squashing is as follows: given all entries with certain key k, taken in the same order as they were inserted, verify that the ith entry new_value is equal to the ith + 1 entry previous_value.

For example, given the following entry list:

keypreviousnew
Alex0150
Maria0100
Charles070
Maria100250
Alex15040
Alex40300
Maria250190
Alex30090

After squashing, the entry list would be reduced to:

keypreviousnew
Alex090
Maria0190
Charles070

In case of a change on any of the values of the first table, squashing would have failed during runtime.

Dictionary Destruction

If you run the examples from "Basic Use of Dictionaries" section, you'd notice that there was never a call to squash dictionary, but the program compiled successfully nonetheless. What happened behind the scene was that squash was called automatically via the Felt252Dict<T> implementation of the Destruct<T> trait. This call occurred just before the balance dictionary went out of scope.

The Destruct<T> trait represents another way of removing instances out of scope apart from Drop<T>. The main difference between these two is that Drop<T> is treated as a no-op operation, meaning it does not generate new CASM while Destruct<T> does not have this restriction. The only type which actively uses the Destruct<T> trait is Felt252Dict<T>, for every other type Destruct<T> and Drop<T> are synonyms. You can read more about these traits in Drop and Destruct section of Appendix C.

Later in "Dictionaries as Struct Members" section, we will have a hands-on example where we implement the Destruct<T> trait for a custom type.

More Dictionaries

Up to this point, we have given a comprehensive overview of the functionality of Felt252Dict<T> as well as how and why it is implemented in a certain way. If you haven't understood all of it, don't worry because in this section we will have some more examples using dictionaries.

We will start by explaining the entry method which is part of a dictionary basic functionality included in Felt252DictTrait<T> which we didn't mention at the beginning. Soon after, we will see examples of how to use Felt252Dict<T> with other complex types such as Array<T>.

Entry and Finalize

In the "Dictionaries Underneath" section, we explained how Felt252Dict<T> internally worked. It was a list of entries for each time the dictionary was accessed in any manner. It would first find the last entry given a certain key and then update it accordingly to whatever operation it was executing. The Cairo language gives us the tools to replicate this ourselves through the entry and finalize methods.

The entry method comes as part of Felt252DictTrait<T> with the purpose of creating a new entry given a certain key. Once called, this method takes ownership of the dictionary and returns the entry to update. The method signature is as follows:

fn entry(self: Felt252Dict<T>, key: felt252) -> (Felt252DictEntry<T>, T) nopanic

The first input parameter takes ownership of the dictionary while the second one is used to create the appropriate entry. It returns a tuple containing a Felt252DictEntry<T>, which is the type used by Cairo to represent dictionary entries, and a T representing the value held previously. The nopanic notation simply indicates that the function is guaranteed to never panic.

The next thing to do is to update the entry with the new value. For this, we use the finalize method which inserts the entry and returns ownership of the dictionary:

fn finalize(self: Felt252DictEntry<T>, new_value: T) -> Felt252Dict<T>

This method receives the entry and the new value as parameters, and returns the updated dictionary.

Let us see an example using entry and finalize. Imagine we would like to implement our own version of the get method from a dictionary. We should then do the following:

  1. Create the new entry to add using the entry method.
  2. Insert back the entry where the new_value equals the previous_value.
  3. Return the value.

Implementing our custom get would look like this:

use core::dict::Felt252DictEntryTrait;

fn custom_get<T, +Felt252DictValue<T>, +Drop<T>, +Copy<T>>(
    ref dict: Felt252Dict<T>, key: felt252
) -> T {
    // Get the new entry and the previous value held at `key`
    let (entry, prev_value) = dict.entry(key);

    // Store the value to return
    let return_value = prev_value;

    // Update the entry with `prev_value` and get back ownership of the dictionary
    dict = entry.finalize(prev_value);

    // Return the read value
    return_value
}

The ref keyword means that the ownership of the variable will be given back at the end of the function. This concept will be explained in more detail in the "References and Snapshots" section.

Implementing the insert method would follow a similar workflow, except for inserting a new value when finalizing. If we were to implement it, it would look like the following:

use core::dict::Felt252DictEntryTrait;

fn custom_insert<T, +Felt252DictValue<T>, +Destruct<T>, +Drop<T>>(
    ref dict: Felt252Dict<T>, key: felt252, value: T
) {
    // Get the last entry associated with `key`
    // Notice that if `key` does not exist, `_prev_value` will
    // be the default value of T.
    let (entry, _prev_value) = dict.entry(key);

    // Insert `entry` back in the dictionary with the updated value,
    // and receive ownership of the dictionary
    dict = entry.finalize(value);
}

As a finalizing note, these two methods are implemented in a similar way to how insert and get are implemented for Felt252Dict<T>. This code shows some example usage:

use core::dict::Felt252DictEntryTrait;

fn custom_get<T, +Felt252DictValue<T>, +Drop<T>, +Copy<T>>(
    ref dict: Felt252Dict<T>, key: felt252
) -> T {
    // Get the new entry and the previous value held at `key`
    let (entry, prev_value) = dict.entry(key);

    // Store the value to return
    let return_value = prev_value;

    // Update the entry with `prev_value` and get back ownership of the dictionary
    dict = entry.finalize(prev_value);

    // Return the read value
    return_value
}

fn custom_insert<T, +Felt252DictValue<T>, +Destruct<T>, +Drop<T>>(
    ref dict: Felt252Dict<T>, key: felt252, value: T
) {
    // Get the last entry associated with `key`
    // Notice that if `key` does not exist, `_prev_value` will
    // be the default value of T.
    let (entry, _prev_value) = dict.entry(key);

    // Insert `entry` back in the dictionary with the updated value,
    // and receive ownership of the dictionary
    dict = entry.finalize(value);
}

fn main() {
    let mut dict: Felt252Dict<u64> = Default::default();

    custom_insert(ref dict, '0', 100);

    let val = custom_get(ref dict, '0');

    assert!(val == 100, "Expecting 100");
}

Dictionaries of Types not Supported Natively

One restriction of Felt252Dict<T> that we haven't talked about is the trait Felt252DictValue<T>. This trait defines the zero_default method which is the one that gets called when a value does not exist in the dictionary. This is implemented by some common data types, such as most unsigned integers, bool and felt252 - but it is not implemented for more complex ones types such as arrays, structs (including u256), and other types from the core library. This means that making a dictionary of types not natively supported is not a straightforward task, because you would need to write a couple of trait implementations in order to make the data type a valid dictionary value type. To compensate this, you can wrap your type inside a Nullable<T>.

Nullable<T> is a smart pointer type that can either point to a value or be null in the absence of value. It is usually used in Object Oriented Programming Languages when a reference doesn't point anywhere. The difference with Option is that the wrapped value is stored inside a Box<T> data type. The Box<T> type is a smart pointer that allows us to use a dedicated boxed_segment memory segment for our data, and access this segment using a pointer that can only be manipulated in one place at a time. See Smart Pointers Chapter for more information.

Let's show using an example. We will try to store a Span<felt252> inside a dictionary. For that, we will use Nullable<T> and Box<T>. Also, we are storing a Span<T> and not an Array<T> because the latter does not implement the Copy<T> trait which is required for reading from a dictionary.

use core::nullable::{NullableTrait, match_nullable, FromNullableResult};

fn main() {
    // Create the dictionary
    let mut d: Felt252Dict<Nullable<Span<felt252>>> = Default::default();

    // Create the array to insert
    let a = array![8, 9, 10];

    // Insert it as a `Span`
    d.insert(0, NullableTrait::new(a.span()));

//...

In this code snippet, the first thing we did was to create a new dictionary d. We want it to hold a Nullable<Span>. After that, we created an array and filled it with values.

The last step is inserting the array as a span inside the dictionary. Notice that we do this using the new function of the NullableTrait.

Once the element is inside the dictionary, and we want to get it, we follow the same steps but in reverse order. The following code shows how to achieve that:

//...

    // Get value back
    let val = d.get(0);

    // Search the value and assert it is not null
    let span = match match_nullable(val) {
        FromNullableResult::Null => panic!("No value found"),
        FromNullableResult::NotNull(val) => val.unbox(),
    };

    // Verify we are having the right values
    assert!(*span.at(0) == 8, "Expecting 8");
    assert!(*span.at(1) == 9, "Expecting 9");
    assert!(*span.at(2) == 10, "Expecting 10");
}

Here we:

  1. Read the value using get.
  2. Verified it is non-null using the match_nullable function.
  3. Unwrapped the value inside the box and asserted it was correct.

The complete script would look like this:

use core::nullable::{NullableTrait, match_nullable, FromNullableResult};

fn main() {
    // Create the dictionary
    let mut d: Felt252Dict<Nullable<Span<felt252>>> = Default::default();

    // Create the array to insert
    let a = array![8, 9, 10];

    // Insert it as a `Span`
    d.insert(0, NullableTrait::new(a.span()));

    // Get value back
    let val = d.get(0);

    // Search the value and assert it is not null
    let span = match match_nullable(val) {
        FromNullableResult::Null => panic!("No value found"),
        FromNullableResult::NotNull(val) => val.unbox(),
    };

    // Verify we are having the right values
    assert!(*span.at(0) == 8, "Expecting 8");
    assert!(*span.at(1) == 9, "Expecting 9");
    assert!(*span.at(2) == 10, "Expecting 10");
}