No cell names.

executor/src/witgen/jit/block_machine_processor.rs

@@ -147,7 +147,7 @@ impl<'a, T: FieldElement> BlockMachineProcessor<'a, T> {
                 queue_items.push(QueueItem::variable_assignment(
                     value,
                     Variable::IntermediateCell(Cell {
-                        column_name: name.clone(),
+                        column_name: "cell",
                         id: poly_id.id,
                         row_offset,
                     }),
@@ -219,12 +219,12 @@ impl<'a, T: FieldElement> BlockMachineProcessor<'a, T> {
         for (column_id, row_offsets) in written_rows_per_column(&code) {
             for (outside, inside) in self.conflicting_row_offsets(&row_offsets) {
                 let first_var = Variable::WitnessCell(Cell {
-                    column_name: String::new(),
+                    column_name: "cell",
                     id: column_id,
                     row_offset: outside,
                 });
                 let second_var = Variable::WitnessCell(Cell {
-                    column_name: String::new(),
+                    column_name: "cell",
                     id: column_id,
                     row_offset: inside,
                 });

executor/src/witgen/jit/compiler.rs

@@ -684,7 +684,7 @@ mod tests {
 
     fn cell(column_name: &str, id: u64, row_offset: i32) -> Variable {
         Variable::WitnessCell(Cell {
-            column_name: column_name.to_string(),
+            column_name: "cell",
             row_offset,
             id,
         })
@@ -1011,7 +1011,7 @@ extern \"C\" fn witgen(
     fn fixed_column_access() {
         let a = cell("a", 0, 0);
         let x = Variable::FixedCell(Cell {
-            column_name: "X".to_string(),
+            column_name: "cell",
             id: 15,
             row_offset: 6,
         });

executor/src/witgen/jit/effect.rs

@@ -226,7 +226,7 @@ mod test {
 
     fn var(id: u64) -> Variable {
         Variable::WitnessCell(Cell {
-            column_name: format!("v{id}"),
+            column_name: "cell",
             id,
             row_offset: 0,
         })

executor/src/witgen/jit/single_step_processor.rs

@@ -92,7 +92,7 @@ impl<'a, T: FieldElement> SingleStepProcessor<'a, T> {
                 queue_items.push(QueueItem::variable_assignment(
                     value,
                     Variable::IntermediateCell(Cell {
-                        column_name: name.clone(),
+                        column_name: "cell",
                         id: poly_id.id,
                         row_offset,
                     }),
@@ -115,7 +115,7 @@ impl<'a, T: FieldElement> SingleStepProcessor<'a, T> {
 
     fn cell(&self, id: PolyID, row_offset: i32) -> Variable {
         Variable::WitnessCell(Cell {
-            column_name: self.fixed_data.column_name(&id).to_string(),
+            column_name: "cell",
             id: id.id,
             row_offset,
         })

executor/src/witgen/jit/variable.rs

@@ -1,6 +1,8 @@
 use std::{
     fmt::{self, Display, Formatter},
     hash::{Hash, Hasher},
+    rc::Rc,
+    sync::Arc,
 };
 
 use powdr_ast::analyzed::{AlgebraicReference, PolyID, PolynomialType};
@@ -43,7 +45,7 @@ impl Variable {
     /// Create a variable from an algebraic reference.
     pub fn from_reference(r: &AlgebraicReference, row_offset: i32) -> Self {
         let cell = Cell {
-            column_name: r.name.clone(),
+            column_name: "cell",
             id: r.poly_id.id,
             row_offset: r.next as i32 + row_offset,
         };
@@ -88,7 +90,7 @@ pub struct MachineCallVariable {
 #[derive(Debug, Clone, Eq)]
 pub struct Cell {
     /// Name of the column, used only for display purposes.
-    pub column_name: String,
+    pub column_name: &'static str,
     pub id: u64,
     pub row_offset: i32,
 }

executor/src/witgen/jit/witgen_inference.rs

@@ -643,6 +643,8 @@ impl<T: FieldElement, Q: QueryCallback<T>> CanProcessCall<T> for &MutableState<'
 
 #[cfg(test)]
 mod test {
+    use std::sync::Arc;
+
     use powdr_ast::analyzed::{PolyID, PolynomialIdentity, PolynomialType};
     use powdr_number::GoldilocksField;
     use pretty_assertions::assert_eq;
@@ -693,7 +695,7 @@ mod test {
         let known_cells = known_cells.iter().map(|(name, row_offset)| {
             let id = fixed_data.try_column_by_name(name).unwrap().id;
             Variable::WitnessCell(Cell {
-                column_name: name.to_string(),
+                column_name: "cell",
                 id,
                 row_offset: *row_offset,
             })