diff --git a/src/walker.rs b/src/walker.rs
index 316e65ed7..009203d80 100644
--- a/src/walker.rs
+++ b/src/walker.rs
@@ -1,5 +1,7 @@
+#![allow(missing_docs)]
 use std::rc::Rc;
 
+use itertools::Itertools;
 use lazy_static::__Deref;
 
 use crate::{ops::OpType, HugrView, Node};
@@ -16,31 +18,31 @@ pub enum WalkOrder {
     Postorder,
 }
 
-struct WalkerCallback<'a, T>(Box<dyn 'a + Fn(Node, OpType, &mut T) -> WalkResult>);
+struct WalkerCallback<'a, T, E>(Box<dyn 'a + Fn(Node, OpType, T) -> Result<T, E>>);
 
-impl<'a, T, F: 'a + Fn(Node, OpType, &mut T) -> WalkResult> From<F> for WalkerCallback<'a, T> {
+impl<'a, T, E, F: 'a + Fn(Node, OpType, T) -> Result<T, E>> From<F> for WalkerCallback<'a, T, E> {
     fn from(f: F) -> Self {
         Self(Box::new(f))
     }
 }
 
-pub struct Walker<'a, T> {
-    pre_callbacks: Vec<WalkerCallback<'a, T>>,
-    post_callbacks: Vec<WalkerCallback<'a, T>>,
+pub struct Walker<'a, T, E> {
+    pre_callbacks: Vec<WalkerCallback<'a, T, E>>,
+    post_callbacks: Vec<WalkerCallback<'a, T, E>>,
 }
 
-fn call_back<O, T>(
+fn call_back<O, T, E>(
     n: Node,
     o: OpType,
-    t: &mut T,
-    f: impl Fn(Node, O, &mut T) -> WalkResult,
-) -> WalkResult
+    t: T,
+    f: &impl Fn(Node, O, T) -> Result<T, E>,
+) -> Result<T, E>
 where
     OpType: TryInto<O>,
 {
     match o.try_into() {
         Ok(x) => f(n, x, t),
-        _ => WalkResult::Advance,
+        _ => Ok(t),
     }
 }
 
@@ -49,7 +51,7 @@ enum WorkItem {
     Callback(WalkOrder, Node),
 }
 
-impl<'a, T> Walker<'a, T> {
+impl<'a, T, E> Walker<'a, T, E> {
     pub fn new() -> Self {
         Self {
             pre_callbacks: Vec::new(),
@@ -57,7 +59,7 @@ impl<'a, T> Walker<'a, T> {
         }
     }
 
-    pub fn visit<O, F: 'a + Fn(Node, O, &mut T) -> WalkResult>(
+    pub fn visit<O, F: 'a + Fn(Node, O, T) -> Result<T, E>>(
         &mut self,
         walk_order: WalkOrder,
         f: F,
@@ -70,11 +72,11 @@ impl<'a, T> Walker<'a, T> {
             WalkOrder::Preorder => &mut self.pre_callbacks,
             WalkOrder::Postorder => &mut self.post_callbacks,
         };
-        callbacks.push((move |n, o, t: &'_ mut _| call_back(n, o, t, g.as_ref())).into());
+        callbacks.push((move |n, o, t| call_back(n, o, t, g.as_ref())).into());
         self
     }
 
-    pub fn walk(&self, hugr: impl HugrView, t: &mut T) {
+    pub fn walk(&self, hugr: impl HugrView, mut t: T) -> Result<T, E> {
         // We intentionally avoid recursion so that we can robustly accept very deep hugrs
         let mut worklist = vec![WorkItem::Visit(hugr.root())];
 
@@ -83,7 +85,9 @@ impl<'a, T> Walker<'a, T> {
                 WorkItem::Visit(n) => {
                     worklist.push(WorkItem::Callback(WalkOrder::Postorder, n));
                     // TODO we should add children in topological order
-                    worklist.extend(hugr.children(n).map(WorkItem::Visit));
+                    let mut children = hugr.children(n).collect_vec();
+                    children.reverse();
+                    worklist.extend(children.into_iter().map(WorkItem::Visit));
                     worklist.push(WorkItem::Callback(WalkOrder::Preorder, n));
                 }
                 WorkItem::Callback(order, n) => {
@@ -91,27 +95,26 @@ impl<'a, T> Walker<'a, T> {
                         WalkOrder::Preorder => &self.pre_callbacks,
                         WalkOrder::Postorder => &self.post_callbacks,
                     };
+                    let optype = hugr.get_optype(n);
                     for cb in callbacks.iter() {
                         // this clone is unfortunate, to avoid this we would need a TryInto variant:
                         // try_into(&O) -> Option<&T>
-                        if cb.0.as_ref()(n, hugr.get_optype(n).clone(), t) == WalkResult::Interrupt
-                        {
-                            return;
-                        }
+                        t = cb.0.as_ref()(n, optype.clone(), t)?;
                     }
                 }
             }
         }
+        Ok(t)
     }
 }
 
 #[cfg(test)]
 mod test {
-    use std::{error::Error, iter::empty};
+    use std::error::Error;
 
     use crate::types::Signature;
     use crate::{
-        builder::{Container, HugrBuilder, ModuleBuilder},
+        builder::{Container, HugrBuilder, ModuleBuilder, SubContainer},
         extension::{ExtensionRegistry, ExtensionSet},
         type_row,
         types::FunctionType,
@@ -119,48 +122,50 @@ mod test {
 
     use super::*;
 
+    #[test]
     fn test1() -> Result<(), Box<dyn Error>> {
         let mut module_builder = ModuleBuilder::new();
         let sig = Signature {
             signature: FunctionType::new(type_row![], type_row![]),
             input_extensions: ExtensionSet::new(),
         };
-        module_builder.define_function("f1", sig.clone());
-        module_builder.define_function("f2", sig.clone());
+        module_builder
+            .define_function("f1", sig.clone())?
+            .finish_sub_container()?;
+        module_builder
+            .define_function("f2", sig.clone())?
+            .finish_sub_container()?;
 
         let hugr = module_builder.finish_hugr(&ExtensionRegistry::new())?;
 
-        let mut s = String::new();
-        Walker::<String>::new()
-            .visit(WalkOrder::Preorder, |_, crate::ops::Module, r| {
-                r.extend("pre".chars());
-                r.extend(['m']);
-                WalkResult::Advance
+        let s = Walker::<String, Box<dyn Error>>::new()
+            .visit(WalkOrder::Preorder, |_, crate::ops::Module, mut r| {
+                r += "prem";
+                Ok(r)
             })
-            .visit(WalkOrder::Postorder, |_, crate::ops::Module, r| {
-                r.extend("post".chars());
-                r.extend(['n']);
-                WalkResult::Advance
+            .visit(WalkOrder::Postorder, |_, crate::ops::Module, mut r| {
+                r += "postm";
+                Ok(r)
             })
             .visit(
                 WalkOrder::Preorder,
-                |_, crate::ops::FuncDecl { ref name, .. }, r| {
-                    r.extend("pre".chars());
-                    r.extend(name.chars());
-                    WalkResult::Advance
+                |_, crate::ops::FuncDefn { ref name, .. }, mut r| {
+                    r += "pre";
+                    r += name.as_ref();
+                    Ok(r)
                 },
             )
             .visit(
                 WalkOrder::Postorder,
-                |_, crate::ops::FuncDecl { ref name, .. }, r| {
-                    r.extend("post".chars());
-                    r.extend(name.chars());
-                    WalkResult::Advance
+                |_, crate::ops::FuncDefn { ref name, .. }, mut r| {
+                    r += "post";
+                    r += name.as_ref();
+                    Ok(r)
                 },
             )
-            .walk(&hugr, &mut s);
+            .walk(&hugr, String::new())?;
 
-        assert_eq!(s, "prempref1pref2postf2postf1postn");
-        Ok(())
+        assert_eq!(s, "prempref1postf1pref2postf2postm");
+        Ok::<(), Box<dyn Error>>(())
     }
 }