feat: Add std::meta::typ::fresh_type_variable (#5948)

# Description

## Problem\*

Resolves #5873

## Summary\*

Adds a metaprogramming function to create new type variables. Vaguely
useful sometimes for impl searches to get the value of other types used
in the impl search.

## Additional Context



## Documentation\*

Check one:
- [ ] No documentation needed.
- [x] Documentation included in this PR.
- [ ] **[For Experimental Features]** Documentation to be submitted in a
separate PR.

# 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.

---------

Co-authored-by: Tom French <15848336+TomAFrench@users.noreply.github.com>

Author: jfecher

compiler/noirc_frontend/src/hir/comptime/interpreter/builtin.rs

@@ -96,6 +96,7 @@ impl<'local, 'context> Interpreter<'local, 'context> {
             "expr_resolve" => expr_resolve(self, arguments, location),
             "is_unconstrained" => Ok(Value::Bool(true)),
             "fmtstr_quoted_contents" => fmtstr_quoted_contents(interner, arguments, location),
+            "fresh_type_variable" => fresh_type_variable(interner),
             "function_def_add_attribute" => function_def_add_attribute(self, arguments, location),
             "function_def_body" => function_def_body(interner, arguments, location),
             "function_def_has_named_attribute" => {
@@ -680,11 +681,10 @@ fn type_as_constant(
     location: Location,
 ) -> IResult<Value> {
     type_as(arguments, return_type, location, |typ| {
-        if let Type::Constant(n) = typ {
-            Some(Value::U32(n))
-        } else {
-            None
-        }
+        // Prefer to use `evaluate_to_u32` over matching on `Type::Constant`
+        // since arithmetic generics may be `Type::InfixExpr`s which evaluate to
+        // constants but are not actually the `Type::Constant` variant.
+        typ.evaluate_to_u32().map(Value::U32)
     })
 }
 
@@ -786,7 +786,7 @@ where
     F: FnOnce(Type) -> Option<Value>,
 {
     let value = check_one_argument(arguments, location)?;
-    let typ = get_type(value)?;
+    let typ = get_type(value)?.follow_bindings();
 
     let option_value = f(typ);
 
@@ -815,13 +815,13 @@ fn type_get_trait_impl(
     let typ = get_type(typ)?;
     let (trait_id, generics) = get_trait_constraint(constraint)?;
 
-    let option_value = match interner.try_lookup_trait_implementation(
+    let option_value = match interner.lookup_trait_implementation(
         &typ,
         trait_id,
         &generics.ordered,
         &generics.named,
     ) {
-        Ok((TraitImplKind::Normal(trait_impl_id), _)) => Some(Value::TraitImpl(trait_impl_id)),
+        Ok(TraitImplKind::Normal(trait_impl_id)) => Some(Value::TraitImpl(trait_impl_id)),
         _ => None,
     };
 
@@ -840,7 +840,7 @@ fn type_implements(
     let (trait_id, generics) = get_trait_constraint(constraint)?;
 
     let implements = interner
-        .try_lookup_trait_implementation(&typ, trait_id, &generics.ordered, &generics.named)
+        .lookup_trait_implementation(&typ, trait_id, &generics.ordered, &generics.named)
         .is_ok();
     Ok(Value::Bool(implements))
 }
@@ -1736,6 +1736,11 @@ fn fmtstr_quoted_contents(
     Ok(Value::Quoted(Rc::new(tokens)))
 }
 
+// fn fresh_type_variable() -> Type
+fn fresh_type_variable(interner: &NodeInterner) -> IResult<Value> {
+    Ok(Value::Type(interner.next_type_variable()))
+}
+
 // fn add_attribute<let N: u32>(self, attribute: str<N>)
 fn function_def_add_attribute(
     interpreter: &mut Interpreter,

compiler/noirc_frontend/src/hir/comptime/value.rs

@@ -655,7 +655,7 @@ impl<'value, 'interner> Display for ValuePrinter<'value, 'interner> {
             }
             Value::ModuleDefinition(_) => write!(f, "(module)"),
             Value::Zeroed(typ) => write!(f, "(zeroed {typ})"),
-            Value::Type(typ) => write!(f, "{}", typ),
+            Value::Type(typ) => write!(f, "{:?}", typ),
             Value::Expr(ExprValue::Expression(expr)) => {
                 write!(f, "{}", remove_interned_in_expression_kind(self.interner, expr.clone()))
             }

docs/docs/noir/standard_library/meta/typ.md

@@ -5,6 +5,30 @@ title: Type
 `std::meta::typ` contains methods on the built-in `Type` type used for representing
 a type in the source program.
 
+## Functions
+
+#include_code fresh_type_variable noir_stdlib/src/meta/typ.nr rust
+
+Creates and returns an unbound type variable. This is a special kind of type internal
+to type checking which will type check with any other type. When it is type checked
+against another type it will also be set to that type. For example, if `a` is a type
+variable and we have the type equality `(a, i32) = (u8, i32)`, the compiler will set
+`a` equal to `u8`.
+
+Unbound type variables will often be rendered as `_` while printing them. Bound type
+variables will appear as the type they are bound to.
+
+This can be used in conjunction with functions which internally perform type checks
+such as `Type::implements` or `Type::get_trait_impl` to potentially grab some of the types used.
+
+Note that calling `Type::implements` or `Type::get_trait_impl` on a type variable will always
+fail.
+
+Example:
+
+#include_code serialize-setup test_programs/compile_success_empty/comptime_type/src/main.nr rust
+#include_code fresh-type-variable-example test_programs/compile_success_empty/comptime_type/src/main.nr rust
+
 ## Methods
 
 ### as_array

noir_stdlib/src/meta/typ.nr

@@ -1,6 +1,11 @@
 use crate::cmp::Eq;
 use crate::option::Option;
 
+#[builtin(fresh_type_variable)]
+// docs:start:fresh_type_variable
+pub fn fresh_type_variable() -> Type {}
+// docs:end:fresh_type_variable
+
 impl Type {
     #[builtin(type_as_array)]
 // docs:start:as_array

test_programs/compile_success_empty/comptime_type/src/main.nr

@@ -19,6 +19,18 @@ struct StructDoesNotImplementSomeTrait {
 
 }
 
+// docs:start:serialize-setup
+trait Serialize<let N: u32> {}
+
+impl Serialize<1> for Field {}
+
+impl<T, let N: u32, let M: u32> Serialize<N * M> for [T; N]
+    where T: Serialize<M> {}
+
+impl<T, U, let N: u32, let M: u32> Serialize<N + M> for (T, U)
+    where T: Serialize<N>, U: Serialize<M> {}
+// docs:end:serialize-setup
+
 fn main() {
     comptime
     {
@@ -115,6 +127,29 @@ fn main() {
         let str_type = quote { str<10> }.as_type();
         let constant = str_type.as_str().unwrap();
         assert_eq(constant.as_constant().unwrap(), 10);
+
+        // Check std::meta::typ::fresh_type_variable
+        // docs:start:fresh-type-variable-example
+        let typevar1 = std::meta::typ::fresh_type_variable();
+        let constraint = quote { Serialize<$typevar1> }.as_trait_constraint();
+        let field_type = quote { Field }.as_type();
+
+        // Search for a trait impl (binding typevar1 to 1 when the impl is found):
+        assert(field_type.implements(constraint));
+
+        // typevar1 should be bound to the "1" generic now:
+        assert_eq(typevar1.as_constant().unwrap(), 1);
+
+        // If we want to do the same with a different type, we need to
+        // create a new type variable now that `typevar1` is bound
+        let typevar2 = std::meta::typ::fresh_type_variable();
+        let constraint = quote { Serialize<$typevar2> }.as_trait_constraint();
+        let array_type = quote { [(Field, Field); 5] }.as_type();
+        assert(array_type.implements(constraint));
+
+        // Now typevar2 should be bound to the serialized pair size 2 times the array length 5
+        assert_eq(typevar2.as_constant().unwrap(), 10);
+        // docs:end:fresh-type-variable-example
     }
 }