diff --git a/pil_analyzer/src/condenser.rs b/pil_analyzer/src/condenser.rs
index b11cbab51..50c17375a 100644
--- a/pil_analyzer/src/condenser.rs
+++ b/pil_analyzer/src/condenser.rs
@@ -1,20 +1,22 @@
 //! Component that turns data from the PILAnalyzer into Analyzed,
 //! i.e. it turns more complex expressions in identities to simpler expressions.
 
-use std::collections::HashMap;
+use std::{collections::HashMap, fmt::Display, rc::Rc};
 
 use ast::{
     analyzed::{
         AlgebraicExpression, AlgebraicReference, Analyzed, Expression, FunctionValueDefinition,
-        Identity, PolyID, PolynomialReference, PolynomialType, PublicDeclaration, Reference,
+        Identity, PolynomialReference, PolynomialType, PublicDeclaration, Reference,
         StatementIdentifier, Symbol, SymbolKind,
     },
-    evaluate_binary_operation, evaluate_unary_operation,
-    parsed::{visitor::ExpressionVisitable, IndexAccess, SelectedExpressions, UnaryOperator},
+    parsed::{visitor::ExpressionVisitable, SelectedExpressions, UnaryOperator},
 };
+use itertools::Itertools;
 use number::{DegreeType, FieldElement};
 
-use crate::evaluator;
+use crate::evaluator::{
+    self, evaluate, evaluate_function_call, Custom, EvalError, SymbolLookup, Value,
+};
 
 pub fn condense<T: FieldElement>(
     degree: Option<DegreeType>,
@@ -24,7 +26,6 @@ pub fn condense<T: FieldElement>(
     source_order: Vec<StatementIdentifier>,
 ) -> Analyzed<T> {
     let condenser = Condenser {
-        constants: compute_constants(&definitions),
         symbols: definitions.clone(),
     };
 
@@ -78,8 +79,6 @@ pub fn condense<T: FieldElement>(
 pub struct Condenser<T> {
     /// All the definitions from the PIL file.
     pub symbols: HashMap<String, (Symbol, Option<FunctionValueDefinition<T>>)>,
-    /// Definitions that evaluate to constant numbers.
-    pub constants: HashMap<String, T>,
 }
 
 impl<T: FieldElement> Condenser<T> {
@@ -125,143 +124,202 @@ impl<T: FieldElement> Condenser<T> {
     }
 
     pub fn condense_expression(&self, e: &Expression<T>) -> AlgebraicExpression<T> {
-        match e {
-            Expression::Reference(Reference::Poly(poly)) => {
-                if let Some(value) = self.constants.get(&poly.name) {
-                    return AlgebraicExpression::Number(*value);
+        evaluator::evaluate(e, &self)
+            .and_then(|result| {
+                // TODO at this point, we could also support arrays of constraints, but we would
+                // need to make it clear if an array is supported in this context (it is at statement level,
+                // but not inside a lookup for example).
+                match result {
+                    Value::Custom(Condensate { expr, .. }) => Ok(expr),
+                    Value::Number(n) => Ok(n.into()),
+                    _ => Err(EvalError::TypeError(format!(
+                        "Expected constraint, but got {result}"
+                    ))),
                 }
-                let symbol = &self
-                    .symbols
-                    .get(&poly.name)
-                    .unwrap_or_else(|| panic!("Symbol {} not found.", poly.name))
-                    .0;
+            })
+            .unwrap_or_else(|err| {
+                panic!("Error reducing expression to constraint:\nExpression: {e}\nError: {err:?}")
+            })
+    }
+}
 
-                assert!(
-                    symbol.length.is_none(),
-                    "Arrays cannot be used as a whole in this context, only individual array elements can be used."
-                );
+impl<'a, T: FieldElement> SymbolLookup<'a, T, Condensate<T>> for &'a Condenser<T> {
+    fn lookup(&self, name: &str) -> Result<Value<'a, T, Condensate<T>>, EvalError> {
+        let name = name.to_string();
+        let (symbol, value) = &self
+            .symbols
+            .get(&name)
+            .ok_or_else(|| EvalError::SymbolNotFound(format!("Symbol {name} not found.")))?;
 
+        Ok(if matches!(symbol.kind, SymbolKind::Poly(_)) {
+            if symbol.is_array() {
+                Value::Array(
+                    symbol
+                        .array_elements()
+                        .map(|(name, poly_id)| {
+                            AlgebraicExpression::Reference(AlgebraicReference {
+                                name,
+                                poly_id,
+                                next: false,
+                            })
+                            .into()
+                        })
+                        .collect(),
+                )
+            } else {
                 AlgebraicExpression::Reference(AlgebraicReference {
-                    name: poly.name.clone(),
+                    name,
                     poly_id: symbol.into(),
                     next: false,
                 })
+                .into()
             }
-            Expression::Reference(Reference::LocalVar(_, _)) => {
-                panic!("Local variables not allowed here.")
-            }
-            Expression::Number(n) => AlgebraicExpression::Number(*n),
-            Expression::BinaryOperation(left, op, right) => {
-                match (
-                    self.condense_expression(left),
-                    self.condense_expression(right),
-                ) {
-                    (AlgebraicExpression::Number(l), AlgebraicExpression::Number(r)) => {
-                        AlgebraicExpression::Number(evaluate_binary_operation(l, *op, r))
-                    }
-                    (l, r) => AlgebraicExpression::BinaryOperation(
-                        Box::new(l),
-                        (*op).try_into().unwrap(),
-                        Box::new(r),
-                    ),
+        } else {
+            match value {
+                Some(FunctionValueDefinition::Expression(value)) => {
+                    evaluator::evaluate(value, self)?
                 }
+                _ => Err(EvalError::Unsupported(
+                    "Cannot evaluate arrays and queries.".to_string(),
+                ))?,
             }
-            Expression::UnaryOperation(op, inner) => {
-                let inner = self.condense_expression(inner);
-                if *op == UnaryOperator::Next {
-                    let AlgebraicExpression::Reference(reference) = inner else {
-                        panic!(
-                            "Can apply \"'\" operator only directly to columns in this context."
-                        );
+        })
+    }
+
+    fn lookup_public_reference(
+        &self,
+        name: &str,
+    ) -> Result<Value<'a, T, Condensate<T>>, EvalError> {
+        Ok(AlgebraicExpression::PublicReference(name.to_string()).into())
+    }
+
+    fn eval_function_application(
+        &self,
+        function: Condensate<T>,
+        arguments: &[Rc<Value<'a, T, Condensate<T>>>],
+    ) -> Result<Value<'a, T, Condensate<T>>, EvalError> {
+        match function.expr {
+            AlgebraicExpression::Reference(AlgebraicReference {
+                name,
+                poly_id,
+                next,
+            }) if poly_id.ptype == PolynomialType::Constant => {
+                let arguments = if next {
+                    assert_eq!(arguments.len(), 1);
+                    let Value::Number(arg) = *arguments[0] else {
+                        return Err(EvalError::TypeError(
+                            "Expected numeric argument when evaluating function with next ref."
+                                .to_string(),
+                        ));
                     };
-
-                    assert!(!reference.next, "Double application of \"'\"");
-                    AlgebraicExpression::Reference(AlgebraicReference {
-                        next: true,
-                        ..reference
-                    })
+                    vec![Rc::new(Value::Number(arg + 1.into()))]
                 } else {
-                    match inner {
-                        AlgebraicExpression::Number(n) => {
-                            AlgebraicExpression::Number(evaluate_unary_operation(*op, n))
-                        }
-                        _ => AlgebraicExpression::UnaryOperation(
-                            (*op).try_into().unwrap(),
-                            Box::new(inner),
-                        ),
+                    arguments.to_vec()
+                };
+
+                match self.symbols[&name].1.as_ref() {
+                    Some(FunctionValueDefinition::Expression(v)) => {
+                        let function = evaluate(v, self)?;
+                        evaluate_function_call(function, arguments, self)
                     }
+                    None => Err(EvalError::SymbolNotFound(format!(
+                        "Symbol not found in function call: {name}"
+                    ))),
+                    _ => Err(EvalError::Unsupported(format!(
+                        "Cannot evaluate arrays or queries: {name}"
+                    ))),
                 }
             }
-            Expression::PublicReference(r) => AlgebraicExpression::PublicReference(r.clone()),
-            Expression::IndexAccess(IndexAccess { array, index }) => {
-                let array_symbol = match array.as_ref() {
-                    ast::parsed::Expression::Reference(Reference::Poly(PolynomialReference {
-                        name,
-                        poly_id: _,
-                    })) => {
-                        &self
-                            .symbols
-                            .get(name)
-                            .unwrap_or_else(|| panic!("Symbol {name} not found."))
-                            .0
-                    }
-                    _ => panic!("Expected direct reference before array index access."),
-                };
-                let Some(length) = array_symbol.length else {
-                    panic!("Array-access for non-array {}.", array_symbol.absolute_name);
-                };
+            _ => Err(EvalError::TypeError(format!(
+                "Function application not supported: {function}({})",
+                arguments.iter().format(", ")
+            ))),
+        }
+    }
 
-                let index = evaluator::evaluate_expression(index, &self.symbols)
-                    .and_then(|v| v.try_to_number())
-                    .expect("Index needs to be constant number.")
-                    .to_degree();
-                assert!(
-                    index < length,
-                    "Array access to index {index} for array of length {length}: {}",
-                    array_symbol.absolute_name,
-                );
-                let poly_id: PolyID = array_symbol.into();
-                AlgebraicExpression::Reference(AlgebraicReference {
-                    poly_id: PolyID {
-                        id: poly_id.id + index,
-                        ..poly_id
-                    },
-                    name: array_symbol.array_element_name(index),
-                    next: false,
-                })
+    fn eval_binary_operation(
+        &self,
+        left: Value<'a, T, Condensate<T>>,
+        op: ast::parsed::BinaryOperator,
+        right: Value<'a, T, Condensate<T>>,
+    ) -> Result<Value<'a, T, Condensate<T>>, EvalError> {
+        let left: Condensate<T> = left.try_into()?;
+        let right: Condensate<T> = right.try_into()?;
+        Ok(AlgebraicExpression::BinaryOperation(
+            Box::new(left.expr),
+            op.try_into().map_err(EvalError::TypeError)?,
+            Box::new(right.expr),
+        )
+        .into())
+    }
+
+    fn eval_unary_operation(
+        &self,
+        op: UnaryOperator,
+        inner: Condensate<T>,
+    ) -> Result<Value<'a, T, Condensate<T>>, EvalError> {
+        if op == UnaryOperator::Next {
+            let AlgebraicExpression::Reference(reference) = inner.expr else {
+                return Err(EvalError::TypeError(format!(
+                    "Expected column for \"'\" operator, but got: {inner}"
+                )));
+            };
+
+            if reference.next {
+                return Err(EvalError::TypeError(format!(
+                    "Double application of \"'\" on: {reference}"
+                )));
             }
-            Expression::String(_) => panic!("Strings are not allowed here."),
-            Expression::Tuple(_) => panic!(),
-            Expression::LambdaExpression(_) => panic!(),
-            Expression::ArrayLiteral(_) => panic!(),
-            Expression::FunctionCall(_) => panic!(),
-            Expression::FreeInput(_) => panic!(),
-            Expression::MatchExpression(_, _) => panic!(),
+            Ok(AlgebraicExpression::Reference(AlgebraicReference {
+                next: true,
+                ..reference
+            })
+            .into())
+        } else {
+            Ok(AlgebraicExpression::UnaryOperation(
+                op.try_into().map_err(EvalError::TypeError)?,
+                Box::new(inner.expr),
+            )
+            .into())
         }
     }
 }
 
-/// Returns a HashMap of all symbols that have a constant single value.
-fn compute_constants<T: FieldElement>(
-    definitions: &HashMap<String, (Symbol, Option<FunctionValueDefinition<T>>)>,
-) -> HashMap<String, T> {
-    definitions
-        .iter()
-        .filter_map(|(name, (symbol, value))| {
-            // TODO we could try to compute anything that evaluates to a "value" here.
-            if symbol.kind == SymbolKind::Constant() {
-                let Some(FunctionValueDefinition::Expression(value)) = value else {
-                    panic!();
-                };
-                Ok(value)
-                    .and_then(|value| {
-                        evaluator::evaluate_expression(value, definitions)?.try_to_number()
-                    })
-                    .map(|value| (name.to_owned(), value))
-                    .ok()
-            } else {
-                None
-            }
-        })
-        .collect()
+#[derive(Clone)]
+struct Condensate<T> {
+    pub expr: AlgebraicExpression<T>,
+}
+
+impl<T: PartialEq> PartialEq for Condensate<T> {
+    fn eq(&self, other: &Self) -> bool {
+        self.expr == other.expr
+    }
+}
+
+impl<T: Display> Display for Condensate<T> {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        write!(f, "{}", self.expr)
+    }
+}
+
+impl<T: FieldElement> Custom for Condensate<T> {}
+
+impl<'a, T: FieldElement> TryFrom<Value<'a, T, Self>> for Condensate<T> {
+    type Error = EvalError;
+
+    fn try_from(value: Value<'a, T, Self>) -> Result<Self, Self::Error> {
+        match value {
+            Value::Number(n) => Ok(Self { expr: n.into() }),
+            Value::Custom(v) => Ok(v),
+            value => Err(EvalError::TypeError(format!(
+                "Expected algebraic expression, got {value}"
+            ))),
+        }
+    }
+}
+
+impl<'a, T: FieldElement> From<AlgebraicExpression<T>> for Value<'a, T, Condensate<T>> {
+    fn from(expr: AlgebraicExpression<T>) -> Self {
+        Value::Custom(Condensate { expr })
+    }
 }
diff --git a/pil_analyzer/src/evaluator.rs b/pil_analyzer/src/evaluator.rs
index 9f9cc8031..62726fd34 100644
--- a/pil_analyzer/src/evaluator.rs
+++ b/pil_analyzer/src/evaluator.rs
@@ -3,7 +3,10 @@ use std::{collections::HashMap, fmt::Display, rc::Rc};
 use ast::{
     analyzed::{Expression, FunctionValueDefinition, Reference, Symbol},
     evaluate_binary_operation, evaluate_unary_operation,
-    parsed::{display::quote, FunctionCall, LambdaExpression, MatchArm, MatchPattern},
+    parsed::{
+        display::quote, BinaryOperator, FunctionCall, LambdaExpression, MatchArm, MatchPattern,
+        UnaryOperator,
+    },
 };
 use itertools::Itertools;
 use number::FieldElement;
@@ -199,6 +202,23 @@ pub trait SymbolLookup<'a, T, C> {
         function: C,
         arguments: &[Rc<Value<'a, T, C>>],
     ) -> Result<Value<'a, T, C>, EvalError>;
+
+    fn eval_binary_operation(
+        &self,
+        _left: Value<'a, T, C>,
+        _op: BinaryOperator,
+        _right: Value<'a, T, C>,
+    ) -> Result<Value<'a, T, C>, EvalError> {
+        unreachable!()
+    }
+
+    fn eval_unary_operation(
+        &self,
+        _op: UnaryOperator,
+        _inner: C,
+    ) -> Result<Value<'a, T, C>, EvalError> {
+        unreachable!()
+    }
 }
 
 mod internal {
@@ -228,16 +248,27 @@ mod internal {
                     .collect::<Result<_, _>>()?,
             ),
             Expression::BinaryOperation(left, op, right) => {
-                Value::Number(evaluate_binary_operation(
-                    evaluate(left, locals, symbols)?.try_to_number()?,
-                    *op,
-                    evaluate(right, locals, symbols)?.try_to_number()?,
-                ))
+                let left = evaluate(left, locals, symbols)?;
+                let right = evaluate(right, locals, symbols)?;
+                match (&left, &right) {
+                    (Value::Custom(_), _) | (_, Value::Custom(_)) => {
+                        symbols.eval_binary_operation(left, *op, right)?
+                    }
+                    (Value::Number(l), Value::Number(r)) => {
+                        Value::Number(evaluate_binary_operation(*l, *op, *r))
+                    }
+                    _ => Err(EvalError::TypeError(format!(
+                        "Operator {op} not supported on types: {left} {op} {right}"
+                    )))?,
+                }
             }
-            Expression::UnaryOperation(op, expr) => Value::Number(evaluate_unary_operation(
-                *op,
-                evaluate(expr, locals, symbols)?.try_to_number()?,
-            )),
+            Expression::UnaryOperation(op, expr) => match evaluate(expr, locals, symbols)? {
+                Value::Custom(inner) => symbols.eval_unary_operation(*op, inner)?,
+                Value::Number(n) => Value::Number(evaluate_unary_operation(*op, n)),
+                inner => Err(EvalError::TypeError(format!(
+                    "Operator {op} not supported on types: {op} {inner}"
+                )))?,
+            },
             Expression::LambdaExpression(lambda) => {
                 // TODO only copy the part of the environment that is actually referenced?
                 (Closure {
diff --git a/pil_analyzer/src/pil_analyzer.rs b/pil_analyzer/src/pil_analyzer.rs
index 402e37196..60d9dbec3 100644
--- a/pil_analyzer/src/pil_analyzer.rs
+++ b/pil_analyzer/src/pil_analyzer.rs
@@ -834,7 +834,7 @@ namespace N(65536);
     }
 
     #[test]
-    #[should_panic = "Arrays cannot be used as a whole in this context"]
+    #[should_panic = "Operator - not supported on types"]
     fn no_direct_array_references() {
         let input = r#"namespace N(16);
     col witness y[3];
@@ -845,7 +845,7 @@ namespace N(65536);
     }
 
     #[test]
-    #[should_panic = "Array access to index 3 for array of length 3"]
+    #[should_panic = "Tried to access element 3 of array of size 3."]
     fn no_out_of_bounds() {
         let input = r#"namespace N(16);
     col witness y[3];
@@ -865,4 +865,74 @@ namespace N(65536);
         let formatted = process_pil_file_contents::<GoldilocksField>(input).to_string();
         assert_eq!(formatted, input);
     }
+
+    #[test]
+    fn symbolic_functions() {
+        let input = r#"namespace N(16);
+    let last_row = 15;
+    let ISLAST = |i| match i { last_row => 1, _ => 0 };
+    let x;
+    let y;
+    let constrain_equal_expr = |A, B| A - B;
+    let on_regular_row = |cond| (1 - ISLAST) * cond;
+    on_regular_row(constrain_equal_expr(x', y)) = 0;
+    on_regular_row(constrain_equal_expr(y', x + y)) = 0;
+    "#;
+        let expected = r#"constant last_row = 15;
+namespace N(16);
+    col fixed ISLAST(i) { match i { last_row => 1, _ => 0, } };
+    col witness x;
+    col witness y;
+    let constrain_equal_expr = |A, B| (A - B);
+    col fixed on_regular_row(cond) { ((1 - N.ISLAST) * cond) };
+    ((1 - N.ISLAST) * (N.x' - N.y)) = 0;
+    ((1 - N.ISLAST) * (N.y' - (N.x + N.y))) = 0;
+"#;
+        let formatted = process_pil_file_contents::<GoldilocksField>(input).to_string();
+        assert_eq!(formatted, expected);
+    }
+
+    #[test]
+    fn next_op_on_param() {
+        let input = r#"namespace N(16);
+    let last_row = 15;
+    let ISLAST = |i| match i { last_row => 1, _ => 0 };
+    let x;
+    let y;
+    let next_is_seven = |t| t' - 7;
+    next_is_seven(y) = 0;
+    "#;
+        let expected = r#"constant last_row = 15;
+namespace N(16);
+    col fixed ISLAST(i) { match i { last_row => 1, _ => 0, } };
+    col witness x;
+    col witness y;
+    col fixed next_is_seven(t) { (t' - 7) };
+    (N.y' - 7) = 0;
+"#;
+        let formatted = process_pil_file_contents::<GoldilocksField>(input).to_string();
+        assert_eq!(formatted, expected);
+    }
+
+    #[test]
+    fn fixed_concrete_and_symbolic() {
+        let input = r#"namespace N(16);
+    let last_row = 15;
+    let ISLAST = |i| match i { last_row => 1, _ => 0, };
+    let x;
+    let y;
+    y - ISLAST(3) = 0;
+    x - ISLAST = 0;
+    "#;
+        let expected = r#"constant last_row = 15;
+namespace N(16);
+    col fixed ISLAST(i) { match i { last_row => 1, _ => 0, } };
+    col witness x;
+    col witness y;
+    (N.y - 0) = 0;
+    (N.x - N.ISLAST) = 0;
+"#;
+        let formatted = process_pil_file_contents::<GoldilocksField>(input).to_string();
+        assert_eq!(formatted, expected);
+    }
 }