feat: add definitions for From and Into traits to Noir prelude (#4169)

# Description

## Problem\*

Supercedes #4148 

## Summary\*

This PR adds a definition of `From` and `Into` traits into the Noir
prelude. I've provided implementations for the primitive types along
with the trivial general implementations of the traits.

## Additional Context



## Documentation\*

Check one:
- [ ] No documentation needed.
- [ ] Documentation included in this PR.
- [x] **[Exceptional Case]** Documentation to be submitted in a separate
PR.
Will document once codegen is up.
# PR Checklist\*

- [x] I have tested the changes locally.
- [x] I have formatted the changes with [Prettier](https://prettier.io/)
and/or `cargo fmt` on default settings.

noir_stdlib/src/convert.nr

@@ -0,0 +1,56 @@
+trait From<T> {
+    fn from(input: T) -> Self;
+}
+
+impl<T> From<T> for T {
+  fn from(input: T) -> T {
+      input
+  }
+}
+
+trait Into<T> {
+    fn into(input: Self) -> T;
+}
+
+impl<T, U> Into<T> for U where T: From<U> {
+  fn into(input: U) -> T {
+      T::from(input)
+  }
+}
+
+// Unsigned integers
+impl From<u8> for u16 { fn from(value: u8) -> u16 { value as u16 } }
+
+impl From<u8> for u32 { fn from(value: u8) -> u32 { value as u32 } }
+impl From<u16> for u32 { fn from(value: u16) -> u32 { value as u32 } }
+
+impl From<u8> for u64 { fn from(value: u8) -> u64 { value as u64 } }
+impl From<u16> for u64 { fn from(value: u16) -> u64 { value as u64 } }
+impl From<u32> for u64 { fn from(value: u32) -> u64 { value as u64 } }
+
+impl From<u8> for Field { fn from(value: u8) -> Field { value as Field } }
+impl From<u16> for Field { fn from(value: u16) -> Field { value as Field } }
+impl From<u32> for Field { fn from(value: u32) -> Field { value as Field } }
+impl From<u64> for Field { fn from(value: u64) -> Field { value as Field } }
+
+// Signed integers
+impl From<i8> for i16 { fn from(value: i8) -> i16 { value as i16 } }
+
+impl From<i8> for i32 { fn from(value: i8) -> i32 { value as i32 } }
+impl From<i16> for i32 { fn from(value: i16) -> i32 { value as i32 } }
+
+impl From<i8> for i64 { fn from(value: i8) -> i64 { value as i64 } }
+impl From<i16> for i64 { fn from(value: i16) -> i64 { value as i64 } }
+impl From<i32> for i64 { fn from(value: i32) -> i64 { value as i64 } }
+
+// Booleans
+impl From<bool> for u8 { fn from(value: bool) -> u8 { value as u8 } }
+impl From<bool> for u16 { fn from(value: bool) -> u16 { value as u16 } }
+impl From<bool> for u32 { fn from(value: bool) -> u32 { value as u32 } }
+impl From<bool> for u64 { fn from(value: bool) -> u64 { value as u64 } }
+impl From<bool> for i8 { fn from(value: bool) -> i8 { value as i8 } }
+impl From<bool> for i16 { fn from(value: bool) -> i16 { value as i16 } }
+impl From<bool> for i32 { fn from(value: bool) -> i32 { value as i32 } }
+impl From<bool> for i64 { fn from(value: bool) -> i64 { value as i64 } }
+impl From<bool> for Field { fn from(value: bool) -> Field { value as Field } }
+

noir_stdlib/src/lib.nr

@@ -16,6 +16,7 @@ mod ec;
 mod unsafe;
 mod collections;
 mod compat;
+mod convert;
 mod option;
 mod string;
 mod test;

noir_stdlib/src/prelude.nr

@@ -4,3 +4,4 @@ use crate::{print, println, assert_constant};
 use crate::uint128::U128;
 use crate::cmp::{Eq, Ord};
 use crate::default::Default;
+use crate::convert::{From, Into};

test_programs/compile_success_empty/trait_generics/src/main.nr

@@ -1,4 +1,3 @@
-
 fn main() {
     let xs: [Field; 1] = [3];
     let ys: [u32; 1] = [3];
@@ -8,21 +7,21 @@ fn main() {
     assert_eq(15, sum_static(Data { a: 5, b: 10 }));
 }
 
-fn foo<T, U>(x: T, u: U) where T: Into<U>, U: Eq {
+fn foo<T, U>(x: T, u: U) where T: MyInto<U>, U: Eq {
     assert(x.into() == u);
 }
 
-trait Into<T> {
+trait MyInto<T> {
     fn into(self) -> T;
 }
 
-impl<T, U, N> Into<[U; N]> for [T; N] where T: Into<U> {
+impl<T, U, N> MyInto<[U; N]> for [T; N] where T: MyInto<U> {
     fn into(self) -> [U; N] {
         self.map(|x: T| x.into())
     }
 }
 
-impl Into<u32> for Field {
+impl MyInto<u32> for Field {
     fn into(self) -> u32 {
         self as u32
     }