feat: LSP inlay type hints on lambda parameters (#5639)

# Description

## Problem

Resolves #5640

## Summary


![image](https://github.com/user-attachments/assets/e9caa443-3ffb-4a99-a5f0-ba79e1f1d106)


## Additional Context

None.

## Documentation

Check one:
- [x] No documentation needed.
- [ ] 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.

tooling/lsp/src/requests/inlay_hint.rs

@@ -251,7 +251,15 @@ impl<'a> InlayHintCollector<'a> {
                     self.collect_in_expression(expression);
                 }
             }
-            ExpressionKind::Lambda(lambda) => self.collect_in_expression(&lambda.body),
+            ExpressionKind::Lambda(lambda) => {
+                for (pattern, typ) in &lambda.parameters {
+                    if matches!(typ.typ, UnresolvedTypeData::Unspecified) {
+                        self.collect_in_pattern(pattern);
+                    }
+                }
+
+                self.collect_in_expression(&lambda.body);
+            }
             ExpressionKind::Parenthesized(parenthesized) => {
                 self.collect_in_expression(parenthesized);
             }
@@ -895,6 +903,34 @@ mod inlay_hints_tests {
         );
     }
 
+    #[test]
+    async fn test_type_inlay_hints_in_lambda() {
+        let inlay_hints = get_inlay_hints(102, 105, type_hints()).await;
+        assert_eq!(inlay_hints.len(), 1);
+
+        let position = Position { line: 104, character: 35 };
+
+        let inlay_hint = &inlay_hints[0];
+        assert_eq!(inlay_hint.position, position);
+
+        if let InlayHintLabel::LabelParts(labels) = &inlay_hint.label {
+            assert_eq!(labels.len(), 2);
+            assert_eq!(labels[0].value, ": ");
+            assert_eq!(labels[0].location, None);
+            assert_eq!(labels[1].value, "i32");
+        } else {
+            panic!("Expected InlayHintLabel::LabelParts, got {:?}", inlay_hint.label);
+        }
+
+        assert_eq!(
+            inlay_hint.text_edits,
+            Some(vec![TextEdit {
+                range: Range { start: position, end: position },
+                new_text: ": i32".to_string(),
+            }])
+        );
+    }
+
     #[test]
     async fn test_do_not_panic_when_given_line_is_too_big() {
         let inlay_hints = get_inlay_hints(0, 100000, type_hints()).await;

tooling/lsp/test_programs/inlay_hints/src/main.nr

@@ -94,4 +94,13 @@ fn call_yet_another_function() {
 
 fn struct_member_hint() {
     let SomeStruct { one } = SomeStruct { one: 1 };
-}
+}
+
+fn some_map<T, U>(x: T, f: fn(T) -> U) -> U {
+    f(x)
+}
+
+fn hint_on_lambda_parameter() {
+    let value: i32 = 1;
+    let _: i32 = some_map(value, |x| x + 1);
+}