feat: Reject programs with unconditional recursion (#6292)

# Description

## Problem\*

Related to #4828 
Followup to #6291

## Summary\*

Added a new `ResolutionError::UnconditionalRecursion` which should
result in a warning or compilation error where the function body
recurses into the defining function with no alternative way to return.

## Additional Context


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

compiler/noirc_frontend/src/elaborator/lints.rs

@@ -6,11 +6,13 @@ use crate::{
         type_check::TypeCheckError,
     },
     hir_def::{
-        expr::{HirExpression, HirIdent, HirLiteral},
+        expr::{HirBlockExpression, HirExpression, HirIdent, HirLiteral},
         function::FuncMeta,
+        stmt::HirStatement,
+    },
+    node_interner::{
+        DefinitionId, DefinitionKind, ExprId, FuncId, FunctionModifiers, NodeInterner,
     },
-    node_interner::NodeInterner,
-    node_interner::{DefinitionKind, ExprId, FuncId, FunctionModifiers},
     Type,
 };
 
@@ -264,3 +266,77 @@ pub(crate) fn overflowing_int(
 fn func_meta_name_ident(func: &FuncMeta, modifiers: &FunctionModifiers) -> Ident {
     Ident(Spanned::from(func.name.location.span, modifiers.name.clone()))
 }
+
+/// Check that a recursive function *can* return without endlessly calling itself.
+pub(crate) fn unbounded_recursion<'a>(
+    interner: &'a NodeInterner,
+    func_id: FuncId,
+    func_name: impl FnOnce() -> &'a str,
+    func_span: Span,
+    body_id: ExprId,
+) -> Option<ResolverError> {
+    if !can_return_without_recursing(interner, func_id, body_id) {
+        Some(ResolverError::UnconditionalRecursion {
+            name: func_name().to_string(),
+            span: func_span,
+        })
+    } else {
+        None
+    }
+}
+
+/// Check if an expression will end up calling a specific function.
+fn can_return_without_recursing(interner: &NodeInterner, func_id: FuncId, expr_id: ExprId) -> bool {
+    let check = |e| can_return_without_recursing(interner, func_id, e);
+
+    let check_block = |block: HirBlockExpression| {
+        block.statements.iter().all(|stmt_id| match interner.statement(stmt_id) {
+            HirStatement::Let(s) => check(s.expression),
+            HirStatement::Assign(s) => check(s.expression),
+            HirStatement::Expression(e) => check(e),
+            HirStatement::Semi(e) => check(e),
+            // Rust doesn't seem to check the for loop body (it's bounds might mean it's never called).
+            HirStatement::For(e) => check(e.start_range) && check(e.end_range),
+            HirStatement::Constrain(_)
+            | HirStatement::Comptime(_)
+            | HirStatement::Break
+            | HirStatement::Continue
+            | HirStatement::Error => true,
+        })
+    };
+
+    match interner.expression(&expr_id) {
+        HirExpression::Ident(ident, _) => {
+            if ident.id == DefinitionId::dummy_id() {
+                return true;
+            }
+            let definition = interner.definition(ident.id);
+            if let DefinitionKind::Function(id) = definition.kind {
+                func_id != id
+            } else {
+                true
+            }
+        }
+        HirExpression::Block(b) => check_block(b),
+        HirExpression::Prefix(e) => check(e.rhs),
+        HirExpression::Infix(e) => check(e.lhs) && check(e.rhs),
+        HirExpression::Index(e) => check(e.collection) && check(e.index),
+        HirExpression::MemberAccess(e) => check(e.lhs),
+        HirExpression::Call(e) => check(e.func) && e.arguments.iter().cloned().all(check),
+        HirExpression::MethodCall(e) => check(e.object) && e.arguments.iter().cloned().all(check),
+        HirExpression::Cast(e) => check(e.lhs),
+        HirExpression::If(e) => {
+            check(e.condition) && (check(e.consequence) || e.alternative.map(check).unwrap_or(true))
+        }
+        HirExpression::Tuple(e) => e.iter().cloned().all(check),
+        HirExpression::Unsafe(b) => check_block(b),
+        // Rust doesn't check the lambda body (it might not be called).
+        HirExpression::Lambda(_)
+        | HirExpression::Literal(_)
+        | HirExpression::Constructor(_)
+        | HirExpression::Quote(_)
+        | HirExpression::Unquote(_)
+        | HirExpression::Comptime(_)
+        | HirExpression::Error => true,
+    }
+}

compiler/noirc_frontend/src/elaborator/mod.rs

@@ -470,6 +470,20 @@ impl<'context> Elaborator<'context> {
             self.check_for_unused_variables_in_scope_tree(func_scope_tree);
         }
 
+        // Check that the body can return without calling the function.
+        if let FunctionKind::Normal | FunctionKind::Recursive = kind {
+            self.run_lint(|elaborator| {
+                lints::unbounded_recursion(
+                    elaborator.interner,
+                    id,
+                    || elaborator.interner.definition_name(func_meta.name.id),
+                    func_meta.name.location.span,
+                    hir_func.as_expr(),
+                )
+                .map(Into::into)
+            });
+        }
+
         let meta = self
             .interner
             .func_meta

compiler/noirc_frontend/src/hir/resolution/errors.rs

@@ -29,6 +29,8 @@ pub enum ResolverError {
     UnusedVariable { ident: Ident },
     #[error("Unused {}", item.item_type())]
     UnusedItem { ident: Ident, item: UnusedItem },
+    #[error("Unconditional recursion")]
+    UnconditionalRecursion { name: String, span: Span },
     #[error("Could not find variable in this scope")]
     VariableNotDeclared { name: String, span: Span },
     #[error("path is not an identifier")]
@@ -213,6 +215,15 @@ impl<'a> From<&'a ResolverError> for Diagnostic {
                 diagnostic.unnecessary = true;
                 diagnostic
             }
+            ResolverError::UnconditionalRecursion { name, span} => {
+                let mut diagnostic = Diagnostic::simple_warning(
+                    format!("function `{name}` cannot return without recursing"),
+                    "function cannot return without recursing".to_string(),
+                    *span,
+                );
+                diagnostic.unnecessary = true;
+                diagnostic
+            }
             ResolverError::VariableNotDeclared { name, span } => Diagnostic::simple_error(
                 format!("cannot find `{name}` in this scope "),
                 "not found in this scope".to_string(),

compiler/noirc_frontend/src/tests.rs

@@ -122,7 +122,7 @@ pub(crate) fn get_program_errors(src: &str) -> Vec<(CompilationError, FileId)> {
 fn assert_no_errors(src: &str) {
     let errors = get_program_errors(src);
     if !errors.is_empty() {
-        panic!("Expected no errors, got: {:?}", errors);
+        panic!("Expected no errors, got: {:?}; src = {src}", errors);
     }
 }
 
@@ -3390,6 +3390,136 @@ fn arithmetic_generics_rounding_fail() {
     assert_eq!(errors.len(), 1);
 }
 
+#[test]
+fn unconditional_recursion_fail() {
+    let srcs = vec![
+        r#"
+        fn main() {
+            main()
+        }
+        "#,
+        r#"
+        fn main() -> pub bool {
+            if main() { true } else { false }
+        }
+        "#,
+        r#"
+        fn main() -> pub bool {
+            if true { main() } else { main() }
+        }
+        "#,
+        r#"
+        fn main() -> pub u64 {
+            main() + main()
+        }
+        "#,
+        r#"
+        fn main() -> pub u64 {
+            1 + main()
+        }
+        "#,
+        r#"
+        fn main() -> pub bool {
+            let _ = main();
+            true
+        }
+        "#,
+        r#"
+        fn main(a: u64, b: u64) -> pub u64 {
+            main(a + b, main(a, b))
+        }
+        "#,
+        r#"
+        fn main() -> pub u64 {
+            foo(1, main())
+        }
+        fn foo(a: u64, b: u64) -> u64 { 
+            a + b
+        }
+        "#,
+        r#"
+        fn main() -> pub u64 {
+            let (a, b) = (main(), main());
+            a + b
+        }
+        "#,
+        r#"
+        fn main() -> pub u64 {
+            let mut sum = 0;
+            for i in 0 .. main() {
+                sum += i;
+            }
+            sum
+        }
+        "#,
+    ];
+
+    for src in srcs {
+        let errors = get_program_errors(src);
+        assert!(
+            !errors.is_empty(),
+            "expected 'unconditional recursion' error, got nothing; src = {src}"
+        );
+
+        for (error, _) in errors {
+            let CompilationError::ResolverError(ResolverError::UnconditionalRecursion { .. }) =
+                error
+            else {
+                panic!("Expected an 'unconditional recursion' error, got {:?}; src = {src}", error);
+            };
+        }
+    }
+}
+
+#[test]
+fn unconditional_recursion_pass() {
+    let srcs = vec![
+        r#"
+        fn main() {
+            if false { main(); }
+        }
+        "#,
+        r#"
+        fn main(i: u64) -> pub u64 {
+            if i == 0 { 0 } else { i + main(i-1) }
+        }
+        "#,
+        // Only immediate self-recursion is detected.
+        r#"
+        fn main() {
+            foo();
+        }
+        fn foo() {
+            bar();
+        }
+        fn bar() {
+            foo();
+        }
+        "#,
+        // For loop bodies are not checked.
+        r#"
+        fn main() -> pub u64 {
+            let mut sum = 0;
+            for _ in 0 .. 10 {
+                sum += main();
+            }
+            sum
+        }
+        "#,
+        // Lambda bodies are not checked.
+        r#"
+        fn main() {
+            let foo = || main();
+            foo();
+        }
+        "#,
+    ];
+
+    for src in srcs {
+        assert_no_errors(src);
+    }
+}
+
 #[test]
 fn uses_self_in_import() {
     let src = r#"

noir_stdlib/src/meta/mod.nr

@@ -259,6 +259,8 @@ mod tests {
         let _: MyOtherStruct = MyOtherStruct { my_other_field: 2 };
         let _ = derive_do_nothing(crate::panic::panic(f""));
         let _ = derive_do_nothing_alt(crate::panic::panic(f""));
-        remove_unused_warnings();
+        if false {
+            remove_unused_warnings();
+        }
     }
 }