feat: Set aztec private functions to be recursive (AztecProtocol#6192)

This PR marks aztec private functions as recursive.

noir/noir-repo/aztec_macros/src/transforms/functions.rs

@@ -3,8 +3,8 @@ use noirc_errors::Span;
 use noirc_frontend::ast;
 use noirc_frontend::ast::{
     BlockExpression, ConstrainKind, ConstrainStatement, Expression, ExpressionKind,
-    ForLoopStatement, ForRange, FunctionReturnType, Ident, Literal, NoirFunction, NoirStruct,
-    Param, PathKind, Pattern, Signedness, Statement, StatementKind, UnresolvedType,
+    ForLoopStatement, ForRange, FunctionKind, FunctionReturnType, Ident, Literal, NoirFunction,
+    NoirStruct, Param, PathKind, Pattern, Signedness, Statement, StatementKind, UnresolvedType,
     UnresolvedTypeData, Visibility,
 };
 
@@ -38,6 +38,7 @@ pub fn transform_function(
     let inputs_name = format!("{}ContextInputs", ty);
     let return_type_name = format!("{}CircuitPublicInputs", ty);
     let is_avm = ty == "Avm";
+    let is_private = ty == "Private";
 
     // Add check that msg sender equals this address and flag function as internal
     if is_internal {
@@ -107,6 +108,11 @@ pub fn transform_function(
     // Public functions should have unconstrained auto-inferred
     func.def.is_unconstrained = matches!(ty, "Public" | "Avm");
 
+    // Private functions need to be recursive
+    if is_private {
+        func.kind = FunctionKind::Recursive;
+    }
+
     Ok(())
 }