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

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
 
@@ -29,4 +25,4 @@ Explore this section to learn:
 - How to write a [constructor](./write_constructor.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/contracts/writing_contracts/functions/write_constructor.md

@@ -2,36 +2,31 @@
 title: How to write a constructor
 ---
 
-This page explains how to write a constructor function.
+This page explains how to write a constructor (or initializer) function.
 
-To learn more about constructors, read [this](./main.md#constructors).
+To learn more about constructors/initializers, read [this](./main.md#initializer-functions).
 
-## Annotate with `#[aztec(private)]`
+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.
 
-Currently, all constructors in Aztec must be private.
+## Annotate with `#[aztec(private)]` and `#[aztec(initializer)]`
 
-Define your constructor like so:
 
-```rust
-#[aztec(private)]
-fn constructor()
-```
-
-## Option 1: Empty constructor
-
-Your constructor does not need to do anything; you can leave it blank like so:
+Define your initiaizer like so:
 
 ```rust
 #[aztec(private)]
-fn constructor() {}
+#[aztec(initializer)]
+fn constructor(){
+    // function logic here
+}
 ```
 
-## Option 2: Constructor with logic
+## Initializer with logic
 
-Constructors are commonly used to set an admin, such as this example:
+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 constructor is calling a public function. It can also call a private function. Learn more about calling functions from functions [here](../functions/call_functions.md).
+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).