fix(docs): Update other constructor refs in docs to use initializer

docs/docs/developers/contracts/writing_contracts/functions/initializers.md

@@ -0,0 +1,32 @@
+---
+title: How to write an initializer function
+---
+
+This page explains how to write an initializer function.
+
+To learn more about initializers, read [this](./main.md#initializer-functions).
+
+Initializers are regular functions that set an "initialized" flag (a nullifier) for the contract. A contract can only be initialized once, and contract functions can only be called after the contract has been initialized, much like a constructor. However, if a contract defines no initializers, it can be called at any time. Additionally, you can define as many initializer functions in a contract as you want, both private and public.
+
+## Annotate with `#[aztec(private)]` and `#[aztec(initializer)]`
+
+
+Define your initiaizer like so:
+
+```rust
+#[aztec(private)]
+#[aztec(initializer)]
+fn constructor(){
+    // function logic here
+}
+```
+
+## Initializer with logic
+
+Initializers are commonly used to set an admin, such as this example:
+
+#include_code constructor /noir-projects/noir-contracts/contracts/token_contract/src/main.nr rust
+
+Here, the initializer is calling a public function. It can also call a private function. Learn more about calling functions from functions [here](../functions/call_functions.md).
+
+To see constructors in action, check out the [Aztec.nr getting started guide](../../../getting_started/aztecnr-getting-started.md).

docs/docs/developers/contracts/writing_contracts/functions/main.md

@@ -6,17 +6,13 @@ Functions serve as the building blocks of smart contracts. Functions can be eith
 
 For a more practical guide of using multiple types of functions, follow the [token tutorial](../../../tutorials/writing_token_contract.md).
 
-Currently, any function is "mutable" in the sense that it might alter state. However, we also support support static calls, similarly to EVM. A static call is essentially a call that does not alter state (it keeps state static). 
+Currently, any function is "mutable" in the sense that it might alter state. However, we also support support static calls, similarly to EVM. A static call is essentially a call that does not alter state (it keeps state static).
 
-## Constructors
+## Initializer functions
 
-Every smart contract has a private `constructor` function which is called when the contract is deployed. 
+Smart contracts may have one, or many, initializer functions which are called when the contract is deployed.
 
-A special constructor function must be declared within a contract's scope.
-
-A constructor doesn't have a name, because its purpose is clear: to initialize contract state.
-In Aztec terminology, a constructor is always a 'private function' (i.e. it cannot be a public function).
-A constructor behaves almost identically to any other function. It is just important for Aztec to be able to identify this function as special: it may only be called once, and will not be deployed as part of the contract.
+Initializers are regular functions that set an "initialized" flag (a nullifier) for the contract. A contract can only be initialized once, and contract functions can only be called after the contract has been initialized, much like a constructor. However, if a contract defines no initializers, it can be called at any time. Additionally, you can define as many initializer functions in a contract as you want, both private and public.
 
 ## Oracles
 
@@ -26,7 +22,7 @@ Explore this section to learn:
 
 - [How function visibility works in Aztec](./visibility.md)
 - [Public, private, and unconstrained functions](./public_private_unconstrained.md), and how to write them
-- How to write a [constructor](./write_constructor.md)
+- How to write an [initializer function](./initializers.md)
 - [Calling functions from within the same smart contract and from different contracts](./call_functions.md), including calling private functions from private functions, public from public, and even private from public
 - [Oracles](../oracles/main.md) and how Aztec smart contracts might use them
-- [How functions work under the hood](./inner_workings.md)
+- [How functions work under the hood](./inner_workings.md)

docs/docs/developers/limitations/main.md

@@ -29,7 +29,7 @@ Help shape and define:
 
 - It is a testing environment, it is insecure, unaudited and does not generate any proofs, its only for testing purposes;
 - Constructors can not call nor alter public state
-  - The constructor is executed exclusively in private domain, WITHOUT the ability to call public functions or alter public state. This means to set initial storage values, you need to follow a pattern similar to [proxies in Ethereum](https://blog.openzeppelin.com/proxy-patterns), where you `initialize` the contract with values after it have been deployed, see [constructor](../contracts/writing_contracts/functions/write_constructor.md).
+  - The constructor is executed exclusively in private domain, WITHOUT the ability to call public functions or alter public state. This means to set initial storage values, you need to follow a pattern similar to [proxies in Ethereum](https://blog.openzeppelin.com/proxy-patterns), where you `initialize` the contract with values after it have been deployed, see [initializer functions](../contracts/writing_contracts/functions/initializers.md).
   - Beware that what you think of as a `view` could alter state ATM! Notably the account could alter state or re-enter whenever the account contract's `is_valid` function is called.
 - `msg_sender` is currently leaking when doing private -> public calls
   - The `msg_sender` will always be set, if you call a public function from the private world, the `msg_sender` will be set to the private caller's address. See [function context](../contracts/writing_contracts/functions/context.md).

docs/sidebars.js

@@ -338,7 +338,7 @@ const sidebars = {
             "developers/contracts/writing_contracts/layout",
             "developers/contracts/writing_contracts/example_contract",
             {
-              label: "Functions and Constructors",
+              label: "Functions and Initializers",
               type: "category",
               link: {
                 type: "doc",
@@ -349,7 +349,7 @@ const sidebars = {
                 "developers/contracts/writing_contracts/functions/public_private_unconstrained",
                 "developers/contracts/writing_contracts/functions/visibility",
                 "developers/contracts/writing_contracts/functions/call_functions",
-                "developers/contracts/writing_contracts/functions/write_constructor",
+                "developers/contracts/writing_contracts/functions/initializers",
                 "developers/contracts/writing_contracts/functions/compute_note_hash_and_nullifier",
                 "developers/contracts/writing_contracts/functions/inner_workings",
               ],