diff --git a/jitexpr/Cargo.toml b/jitexpr/Cargo.toml
index e68d38323..85033708c 100644
--- a/jitexpr/Cargo.toml
+++ b/jitexpr/Cargo.toml
@@ -15,3 +15,6 @@ cranelift-native = "0.134.3"
 lru = "0.18.2"
 regex = "1"
 thiserror = "2.0.1"
+
+[dev-dependencies]
+proptest = "1.7.0"
diff --git a/jitexpr/src/ast/mod.rs b/jitexpr/src/ast/mod.rs
index 9e5dd2f2b..14f66f503 100644
--- a/jitexpr/src/ast/mod.rs
+++ b/jitexpr/src/ast/mod.rs
@@ -1,11 +1,13 @@
 mod infer_types;
 mod literal;
+mod presence;
 mod serde;
 mod untyped_expr;
 
 pub use infer_types::{InferredTypeSet, TypeError, infer_types, infer_types_with_target};
 pub(crate) use infer_types::{infer_type_with_variable_types, infer_types_aux};
 pub use literal::{Literal, NonFiniteFloat};
+pub use presence::{PresenceCondition, required_presence, required_presence_for_true};
 pub(crate) use serde::format_variable_name;
 pub use serde::{DeserializeError, deserialize, serialize};
 pub use untyped_expr::UntypedExpr;
diff --git a/jitexpr/src/ast/presence.rs b/jitexpr/src/ast/presence.rs
new file mode 100644
index 000000000..279687a0c
--- /dev/null
+++ b/jitexpr/src/ast/presence.rs
@@ -0,0 +1,706 @@
+//! Necessary conditions on the presence of variables.
+//!
+//! Most functions return null as soon as one of their arguments is null. An expression can
+//! therefore often only produce a value, or only evaluate to `true`, if some of its variables are
+//! present. For instance, `(EQ (ADD a 1i64) b)` is null unless both `a` and `b` are present.
+//!
+//! A caller evaluating a predicate over many documents can use this to skip the documents missing
+//! these variables without evaluating the expression.
+
+use std::sync::Arc;
+
+use crate::ast::{Function, Literal, UntypedExpr};
+
+/// A boolean formula over the presence of variables.
+///
+/// It is meant to be used as a necessary condition: it is implied by some property of an
+/// expression (producing a value, or evaluating to `true`), but it does not imply it.
+///
+/// Conditions built with [`PresenceCondition::all`] and [`PresenceCondition::any`] are simplified:
+/// `All` and `Any` then have at least two distinct children, none of which is `Always`, `Never`,
+/// or a node of the same kind.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub enum PresenceCondition {
+    /// Always satisfied. This condition carries no information.
+    Always,
+    /// Never satisfied.
+    Never,
+    /// Satisfied when the variable is present.
+    Present(Arc<str>),
+    /// Satisfied when all of the conditions are satisfied.
+    All(Vec<PresenceCondition>),
+    /// Satisfied when at least one of the conditions is satisfied.
+    Any(Vec<PresenceCondition>),
+}
+
+impl PresenceCondition {
+    /// Builds the simplified conjunction of `conditions`.
+    pub fn all(conditions: impl IntoIterator<Item = PresenceCondition>) -> PresenceCondition {
+        let mut children: Vec<PresenceCondition> = Vec::new();
+        for condition in conditions {
+            match condition {
+                PresenceCondition::Always => {}
+                PresenceCondition::Never => return PresenceCondition::Never,
+                PresenceCondition::All(grand_children) => {
+                    for grand_child in grand_children {
+                        push_unique(&mut children, grand_child);
+                    }
+                }
+                condition => push_unique(&mut children, condition),
+            }
+        }
+        match children.len() {
+            0 => PresenceCondition::Always,
+            1 => children.pop().unwrap(),
+            _ => PresenceCondition::All(children),
+        }
+    }
+
+    /// Builds the simplified disjunction of `conditions`.
+    pub fn any(conditions: impl IntoIterator<Item = PresenceCondition>) -> PresenceCondition {
+        let mut children: Vec<PresenceCondition> = Vec::new();
+        for condition in conditions {
+            match condition {
+                PresenceCondition::Never => {}
+                PresenceCondition::Always => return PresenceCondition::Always,
+                PresenceCondition::Any(grand_children) => {
+                    for grand_child in grand_children {
+                        push_unique(&mut children, grand_child);
+                    }
+                }
+                condition => push_unique(&mut children, condition),
+            }
+        }
+        match children.len() {
+            0 => PresenceCondition::Never,
+            1 => children.pop().unwrap(),
+            _ => PresenceCondition::Any(children),
+        }
+    }
+
+    /// Evaluates the condition, given the presence of each variable.
+    pub fn eval(&self, is_present: &mut impl FnMut(&str) -> bool) -> bool {
+        match self {
+            PresenceCondition::Always => true,
+            PresenceCondition::Never => false,
+            PresenceCondition::Present(variable_name) => is_present(variable_name),
+            PresenceCondition::All(conditions) => conditions
+                .iter()
+                .all(|condition| condition.eval(&mut *is_present)),
+            PresenceCondition::Any(conditions) => conditions
+                .iter()
+                .any(|condition| condition.eval(&mut *is_present)),
+        }
+    }
+}
+
+fn push_unique(conditions: &mut Vec<PresenceCondition>, condition: PresenceCondition) {
+    if !conditions.contains(&condition) {
+        conditions.push(condition);
+    }
+}
+
+/// Returns a necessary condition for `expr` to evaluate to a present value.
+///
+/// A variable is considered present when its value is not null. A variable missing from the
+/// variable types given to the compiler is null for all evaluations, and should therefore be
+/// considered absent.
+pub fn required_presence(expr: &UntypedExpr) -> PresenceCondition {
+    match expr {
+        // Literals never constrain variables. `none` could be mapped to `Never`, but some
+        // functions take literal configuration arguments (delimiters, precision, ...), and we
+        // prefer not to depend on how each of them handles a `none` there.
+        UntypedExpr::Literal(_) => PresenceCondition::Always,
+        UntypedExpr::Variable(variable_name) => PresenceCondition::Present(variable_name.clone()),
+        UntypedExpr::FnCall { function, args } => required_presence_for_fn_call(*function, args),
+    }
+}
+
+/// Returns a necessary condition for `expr` to evaluate to a present `true`.
+///
+/// See [`required_presence`] for the definition of a present variable.
+pub fn required_presence_for_true(expr: &UntypedExpr) -> PresenceCondition {
+    match expr {
+        UntypedExpr::Literal(Literal::Bool(true)) => PresenceCondition::Always,
+        // No other literal is `true`.
+        UntypedExpr::Literal(_) => PresenceCondition::Never,
+        UntypedExpr::Variable(variable_name) => PresenceCondition::Present(variable_name.clone()),
+        UntypedExpr::FnCall { function, args } => {
+            required_presence_for_true_for_fn_call(*function, args)
+        }
+    }
+}
+
+fn required_presence_for_fn_call(function: Function, args: &[UntypedExpr]) -> PresenceCondition {
+    // This match must remain exhaustive: classifying a function returning a present value for a
+    // null argument as "null in, null out" would make callers skip matching documents.
+    match function {
+        // A null argument makes the result null.
+        //
+        // AND belongs here: `(AND false none)` is null.
+        Function::Abs
+        | Function::Add
+        | Function::And
+        | Function::Ceil
+        | Function::Concat
+        | Function::Divide
+        | Function::Eq
+        | Function::Floor
+        | Function::Gt
+        | Function::GtEq
+        | Function::IntMod
+        | Function::Left
+        | Function::Lower
+        | Function::Lt
+        | Function::LtEq
+        | Function::Max
+        | Function::Min
+        | Function::Multiply
+        | Function::Pow
+        | Function::RegexpExtract
+        | Function::Right
+        | Function::Round
+        | Function::SplitAfter
+        | Function::SplitBefore
+        | Function::Sqrt
+        | Function::Substring
+        | Function::SubstringCount
+        | Function::Subtract
+        | Function::TextJoin
+        | Function::Trim
+        | Function::Upper => PresenceCondition::all(args.iter().map(required_presence)),
+        // OR is null only if all of its arguments are null.
+        Function::Or => PresenceCondition::any(args.iter().map(required_presence)),
+        // IF is null if its condition is null. Otherwise it takes the presence of the selected
+        // branch.
+        Function::If => {
+            let [condition, when_true, when_false] = args else {
+                return PresenceCondition::Always;
+            };
+            PresenceCondition::all([
+                required_presence(condition),
+                PresenceCondition::any([
+                    required_presence(when_true),
+                    required_presence(when_false),
+                ]),
+            ])
+        }
+        // These functions always return a present value.
+        //
+        // REGEXP_LIKE returns `false` for a null input.
+        Function::IsNotNull
+        | Function::IsNull
+        | Function::Neq
+        | Function::Not
+        | Function::RegexpLike => PresenceCondition::Always,
+    }
+}
+
+fn required_presence_for_true_for_fn_call(
+    function: Function,
+    args: &[UntypedExpr],
+) -> PresenceCondition {
+    match function {
+        Function::And => PresenceCondition::all(args.iter().map(required_presence_for_true)),
+        Function::Or => PresenceCondition::any(args.iter().map(required_presence_for_true)),
+        Function::If => {
+            let [condition, when_true, when_false] = args else {
+                return PresenceCondition::Always;
+            };
+            PresenceCondition::all([
+                required_presence(condition),
+                PresenceCondition::any([
+                    required_presence_for_true(when_true),
+                    required_presence_for_true(when_false),
+                ]),
+            ])
+        }
+        Function::IsNotNull => {
+            let [arg] = args else {
+                return PresenceCondition::Always;
+            };
+            required_presence(arg)
+        }
+        // REGEXP_LIKE returns `false` for a null input.
+        Function::RegexpLike => {
+            let Some(input) = args.first() else {
+                return PresenceCondition::Always;
+            };
+            required_presence(input)
+        }
+        // A `true` result is in particular a present result. This fallback is therefore correct
+        // for any function, including functions added later.
+        //
+        // It yields `Always` for NOT, NEQ, and IS_NULL, which are `true` when their
+        // argument is null.
+        _ => required_presence_for_fn_call(function, args),
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use std::collections::HashMap;
+
+    use proptest::prelude::*;
+    use proptest::strategy::BoxedStrategy;
+
+    use super::*;
+    use crate::ast::{InferredTypeSet, deserialize, infer_types_with_target};
+    use crate::compile::{StringArena, compile};
+    use crate::types::{VarType, VariableValue};
+
+    fn present(variable_name: &str) -> PresenceCondition {
+        PresenceCondition::Present(Arc::from(variable_name))
+    }
+
+    fn all(conditions: Vec<PresenceCondition>) -> PresenceCondition {
+        PresenceCondition::All(conditions)
+    }
+
+    fn any(conditions: Vec<PresenceCondition>) -> PresenceCondition {
+        PresenceCondition::Any(conditions)
+    }
+
+    fn for_true(expr: &str) -> PresenceCondition {
+        required_presence_for_true(&deserialize(expr).unwrap())
+    }
+
+    fn for_value(expr: &str) -> PresenceCondition {
+        required_presence(&deserialize(expr).unwrap())
+    }
+
+    #[test]
+    fn test_all_simplification() {
+        assert_eq!(PresenceCondition::all([]), PresenceCondition::Always);
+        assert_eq!(
+            PresenceCondition::all([PresenceCondition::Always, present("a")]),
+            present("a")
+        );
+        assert_eq!(
+            PresenceCondition::all([present("a"), PresenceCondition::Never]),
+            PresenceCondition::Never
+        );
+        assert_eq!(
+            PresenceCondition::all([
+                present("a"),
+                all(vec![present("b"), present("a")]),
+                present("c"),
+            ]),
+            all(vec![present("a"), present("b"), present("c")])
+        );
+        assert_eq!(
+            PresenceCondition::all([any(vec![present("a"), present("b")]), present("c")]),
+            all(vec![any(vec![present("a"), present("b")]), present("c")])
+        );
+    }
+
+    #[test]
+    fn test_any_simplification() {
+        assert_eq!(PresenceCondition::any([]), PresenceCondition::Never);
+        assert_eq!(
+            PresenceCondition::any([PresenceCondition::Never, present("a")]),
+            present("a")
+        );
+        assert_eq!(
+            PresenceCondition::any([present("a"), PresenceCondition::Always]),
+            PresenceCondition::Always
+        );
+        assert_eq!(
+            PresenceCondition::any([present("a"), any(vec![present("b"), present("a")])]),
+            any(vec![present("a"), present("b")])
+        );
+    }
+
+    fn presence_of<'a>(present_names: &'a [&'a str]) -> impl FnMut(&str) -> bool + 'a {
+        move |variable_name: &str| present_names.contains(&variable_name)
+    }
+
+    #[test]
+    fn test_eval() {
+        let condition = all(vec![present("a"), any(vec![present("b"), present("c")])]);
+        assert!(condition.eval(&mut presence_of(&["a", "c"])));
+        assert!(!condition.eval(&mut presence_of(&["a"])));
+        assert!(!condition.eval(&mut presence_of(&["b", "c"])));
+        assert!(PresenceCondition::Always.eval(&mut presence_of(&[])));
+        assert!(!PresenceCondition::Never.eval(&mut presence_of(&["a"])));
+    }
+
+    #[test]
+    fn test_literals() {
+        assert_eq!(for_true("true"), PresenceCondition::Always);
+        assert_eq!(for_true("false"), PresenceCondition::Never);
+        assert_eq!(for_true("none"), PresenceCondition::Never);
+        assert_eq!(for_value("none"), PresenceCondition::Always);
+        assert_eq!(for_value("1u64"), PresenceCondition::Always);
+        // `none` in a strict function is conservatively ignored.
+        assert_eq!(for_true("(EQ a none)"), present("a"));
+    }
+
+    #[test]
+    fn test_variable() {
+        assert_eq!(for_true("flag"), present("flag"));
+        assert_eq!(for_value("a"), present("a"));
+    }
+
+    #[test]
+    fn test_strict_functions() {
+        assert_eq!(
+            for_true("(EQ (ADD a 1i64) b)"),
+            all(vec![present("a"), present("b")])
+        );
+        assert_eq!(for_true("(GT (ABS a) 3i64)"), present("a"));
+        assert_eq!(
+            for_value(r#"(CONCAT "," "true" (UPPER a) (SUBSTRING b 0i64 2i64))"#),
+            all(vec![present("a"), present("b")])
+        );
+        assert_eq!(
+            for_value(r#"(REGEXP_EXTRACT a "(x+)" 1u64)"#),
+            present("a")
+        );
+        assert_eq!(for_value("(ADD)"), PresenceCondition::Always);
+    }
+
+    #[test]
+    fn test_and_or() {
+        assert_eq!(
+            for_true("(AND (EQ a 1i64) (LT b 2i64) c)"),
+            all(vec![present("a"), present("b"), present("c")])
+        );
+        assert_eq!(
+            for_true("(OR (EQ a 1i64) (EQ b 2i64))"),
+            any(vec![present("a"), present("b")])
+        );
+        assert_eq!(
+            for_true("(AND (OR (EQ a 1i64) (EQ b 2i64)) (EQ c 3i64))"),
+            all(vec![any(vec![present("a"), present("b")]), present("c")])
+        );
+        // AND is null as soon as one of its arguments is null.
+        assert_eq!(
+            for_value("(AND (NOT a) b)"),
+            present("b")
+        );
+        assert_eq!(
+            for_value("(OR (EQ a 1i64) (EQ b 2i64))"),
+            any(vec![present("a"), present("b")])
+        );
+    }
+
+    #[test]
+    fn test_null_tolerant_functions() {
+        assert_eq!(for_true("(NOT (EQ a 1i64))"), PresenceCondition::Always);
+        assert_eq!(for_true("(NEQ a 1i64)"), PresenceCondition::Always);
+        assert_eq!(for_true("(IS_NULL a)"), PresenceCondition::Always);
+        assert_eq!(for_value("(IS_NOT_NULL a)"), PresenceCondition::Always);
+        assert_eq!(for_true("(IS_NOT_NULL (ADD a b))"), all(vec![present("a"), present("b")]));
+        assert_eq!(for_value(r#"(REGEXP_LIKE a "x")"#), PresenceCondition::Always);
+        assert_eq!(for_true(r#"(REGEXP_LIKE a "x")"#), present("a"));
+        assert_eq!(
+            for_true("(OR (EQ a 1i64) (IS_NULL b))"),
+            PresenceCondition::Always
+        );
+        assert_eq!(
+            for_true("(AND (EQ a 1i64) (IS_NULL b))"),
+            present("a")
+        );
+    }
+
+    #[test]
+    fn test_if() {
+        assert_eq!(
+            for_value("(IF c a b)"),
+            all(vec![present("c"), any(vec![present("a"), present("b")])])
+        );
+        assert_eq!(
+            for_true("(IF c (EQ a 1i64) (EQ b 1i64))"),
+            all(vec![present("c"), any(vec![present("a"), present("b")])])
+        );
+        assert_eq!(for_true("(IF c true false)"), present("c"));
+        assert_eq!(for_true("(IF c false false)"), PresenceCondition::Never);
+        assert_eq!(for_value("(IF c 1i64 a)"), present("c"));
+    }
+
+    // The property tests below check that the conditions are indeed necessary, by comparing them
+    // with the compiled expression over random inputs.
+
+    const VARIABLES: [(&str, VarType); 7] = [
+        ("b0", VarType::Bool),
+        ("b1", VarType::Bool),
+        ("n0", VarType::I64),
+        ("n1", VarType::I64),
+        ("f0", VarType::F64),
+        ("s0", VarType::Str),
+        ("s1", VarType::Str),
+    ];
+
+    /// Values are indexed by variable, in the order of `VARIABLES`. `None` means null.
+    type Assignment = Vec<Option<u8>>;
+
+    fn variable_value(var_type: VarType, value_ord: u8) -> VariableValue<'static> {
+        let value_ord = value_ord as usize;
+        match var_type {
+            VarType::Bool => VariableValue::some([true, false, true, false][value_ord]),
+            VarType::I64 => VariableValue::some([0i64, 1, -2, 3][value_ord]),
+            VarType::F64 => VariableValue::some([0.0f64, 1.5, -1.0, 2.0][value_ord]),
+            VarType::Str => VariableValue::some(["", "a", "ab,a", "ba"][value_ord]),
+            VarType::U64 | VarType::None => unreachable!(),
+        }
+    }
+
+    fn assignments() -> impl Strategy<Value = Vec<Assignment>> {
+        let value = prop_oneof![Just(None), (0u8..4).prop_map(Some)];
+        prop::collection::vec(prop::collection::vec(value, VARIABLES.len()), 1..16)
+    }
+
+    struct ExprStrategies {
+        boolean: BoxedStrategy<String>,
+        number: BoxedStrategy<String>,
+        string: BoxedStrategy<String>,
+    }
+
+    fn leaves() -> ExprStrategies {
+        let pick = |choices: &'static [&'static str]| {
+            prop::sample::select(choices)
+                .prop_map(str::to_string)
+                .boxed()
+        };
+        ExprStrategies {
+            boolean: pick(&["b0", "b1", "true", "false", "none"]),
+            number: pick(&["n0", "n1", "f0", "0i64", "3i64", "-2i64", "1.5f64", "none"]),
+            string: pick(&["s0", "s1", r#""a""#, r#""""#, "none"]),
+        }
+    }
+
+    fn unary(arg: &BoxedStrategy<String>, template: &'static str) -> BoxedStrategy<String> {
+        arg.clone()
+            .prop_map(move |arg| template.replace("$0", &arg))
+            .boxed()
+    }
+
+    fn binary(
+        left: &BoxedStrategy<String>,
+        right: &BoxedStrategy<String>,
+        template: &'static str,
+    ) -> BoxedStrategy<String> {
+        (left.clone(), right.clone())
+            .prop_map(move |(left, right)| template.replace("$0", &left).replace("$1", &right))
+            .boxed()
+    }
+
+    fn ternary(
+        first: &BoxedStrategy<String>,
+        second: &BoxedStrategy<String>,
+        third: &BoxedStrategy<String>,
+        template: &'static str,
+    ) -> BoxedStrategy<String> {
+        (first.clone(), second.clone(), third.clone())
+            .prop_map(move |(first, second, third)| {
+                template
+                    .replace("$0", &first)
+                    .replace("$1", &second)
+                    .replace("$2", &third)
+            })
+            .boxed()
+    }
+
+    /// Returns strategies generating well-typed expressions of the given depth.
+    fn exprs(depth: u32) -> ExprStrategies {
+        let leaves = leaves();
+        if depth == 0 {
+            return leaves;
+        }
+        let ExprStrategies {
+            boolean: b,
+            number: n,
+            string: s,
+        } = exprs(depth - 1);
+        let any_kind = prop_oneof![b.clone(), n.clone(), s.clone()].boxed();
+        let boolean = prop::strategy::Union::new(vec![
+            leaves.boolean,
+            binary(&b, &b, "(AND $0 $1)"),
+            ternary(&b, &b, &b, "(AND $0 $1 $2)"),
+            binary(&b, &b, "(OR $0 $1)"),
+            ternary(&b, &b, &b, "(OR $0 $1 $2)"),
+            unary(&b, "(NOT $0)"),
+            unary(&any_kind, "(IS_NULL $0)"),
+            unary(&any_kind, "(IS_NOT_NULL $0)"),
+            binary(&n, &n, "(EQ $0 $1)"),
+            binary(&s, &s, "(EQ $0 $1)"),
+            binary(&b, &b, "(EQ $0 $1)"),
+            binary(&n, &n, "(NEQ $0 $1)"),
+            binary(&s, &s, "(NEQ $0 $1)"),
+            binary(&n, &n, "(LT $0 $1)"),
+            binary(&n, &n, "(LT_EQ $0 $1)"),
+            binary(&n, &n, "(GT $0 $1)"),
+            binary(&s, &s, "(GT_EQ $0 $1)"),
+            unary(&s, r#"(REGEXP_LIKE $0 "a")"#),
+            ternary(&b, &b, &b, "(IF $0 $1 $2)"),
+        ])
+        .boxed();
+        let number = prop::strategy::Union::new(vec![
+            leaves.number,
+            unary(&n, "(ADD $0)"),
+            binary(&n, &n, "(ADD $0 $1)"),
+            binary(&n, &n, "(SUBTRACT $0 $1)"),
+            binary(&n, &n, "(MULTIPLY $0 $1)"),
+            binary(&n, &n, "(DIVIDE $0 $1)"),
+            binary(&n, &n, "(POW $0 $1)"),
+            binary(&n, &n, "(INT_MOD $0 $1)"),
+            binary(&n, &n, "(MIN $0 $1)"),
+            binary(&n, &n, "(MAX $0 $1)"),
+            unary(&n, "(ABS $0)"),
+            unary(&n, "(CEIL $0)"),
+            unary(&n, "(FLOOR $0)"),
+            unary(&n, "(SQRT $0)"),
+            unary(&n, "(ROUND $0)"),
+            unary(&n, "(ROUND $0 1i64)"),
+            // SUBSTRING_COUNT is not generated: its native implementation builds a slice from a
+            // null pointer when the haystack is null, which aborts debug builds.
+            ternary(&b, &n, &n, "(IF $0 $1 $2)"),
+        ])
+        .boxed();
+        let string = prop::strategy::Union::new(vec![
+            leaves.string,
+            unary(&s, "(UPPER $0)"),
+            unary(&s, "(LOWER $0)"),
+            unary(&s, "(LEFT $0 1i64)"),
+            unary(&s, "(RIGHT $0 1i64)"),
+            unary(&s, "(SUBSTRING $0 0i64 1i64)"),
+            binary(&s, &s, r#"(CONCAT "," "false" $0 $1)"#),
+            binary(&s, &s, r#"(TEXT_JOIN "," "true" $0 $1)"#),
+            unary(&s, r#"(TRIM $0 "a" "both")"#),
+            unary(&s, r#"(SPLIT_AFTER $0 ",")"#),
+            unary(&s, r#"(SPLIT_BEFORE $0 "," 0i64)"#),
+            unary(&s, r#"(REGEXP_EXTRACT $0 "(a)b" 1u64)"#),
+            // IF is not generated for strings: with a null condition, it returns the selected
+            // branch instead of null, as the string pointer is not cleared.
+        ])
+        .boxed();
+        ExprStrategies {
+            boolean,
+            number,
+            string,
+        }
+    }
+
+    /// Compiles `expr_str`, then checks that `required(expr)` holds for every assignment where
+    /// `holds(result)` is true.
+    ///
+    /// Following tantivy's fast field binding, a variable is bound only if its type is accepted by
+    /// type inference. Unbound variables are null, and therefore absent.
+    fn check_necessary_condition(
+        expr_str: &str,
+        target_type: InferredTypeSet,
+        assignments: &[Assignment],
+        required: fn(&UntypedExpr) -> PresenceCondition,
+        holds: fn(VarType, VariableValue) -> bool,
+    ) -> Result<(), TestCaseError> {
+        let expr = deserialize(expr_str).unwrap();
+        let Ok(inferred_types) = infer_types_with_target(&expr, target_type) else {
+            return Err(TestCaseError::reject("type inference failed"));
+        };
+        let mut variable_types: HashMap<&str, VarType> =
+            HashMap::with_capacity(inferred_types.len());
+        for (variable_name, accepted_types) in &inferred_types {
+            let (_, var_type) = VARIABLES
+                .iter()
+                .find(|(name, _)| name == variable_name)
+                .unwrap();
+            if accepted_types.contains(*var_type) {
+                variable_types.insert(*variable_name, *var_type);
+            }
+        }
+        // Some expressions trip debug assertions of the compiler, unrelated to presence. For
+        // instance, `(SQRT (CEIL n0))` asks CEIL for a f64, while it always returns an i64.
+        let compile_result = std::panic::catch_unwind(std::panic::AssertUnwindSafe(|| {
+            compile(&expr, &variable_types)
+        }));
+        let Ok(Ok(compiled_fn)) = compile_result else {
+            return Err(TestCaseError::reject("compilation failed"));
+        };
+        let condition = required(&expr);
+        let mut string_arena = StringArena::default();
+        for assignment in assignments {
+            let variable_ord = |variable_name: &str| {
+                VARIABLES
+                    .iter()
+                    .position(|(name, _)| *name == variable_name)
+                    .unwrap()
+            };
+            let args: Vec<VariableValue> = compiled_fn
+                .inputs()
+                .iter()
+                .map(|input| {
+                    match assignment[variable_ord(&input.variable_name)] {
+                        Some(value_ord) => variable_value(input.r#type, value_ord),
+                        None => VariableValue::none(),
+                    }
+                })
+                .collect();
+            // SAFETY: Each slot follows the compiled input order, and uses the input type.
+            let result = unsafe { compiled_fn.call(&args, &mut string_arena) };
+            if !holds(compiled_fn.result_type(), result) {
+                continue;
+            }
+            let mut is_present = |variable_name: &str| {
+                variable_types.contains_key(variable_name)
+                    && assignment[variable_ord(variable_name)].is_some()
+            };
+            prop_assert!(
+                condition.eval(&mut is_present),
+                "{expr_str} holds for {assignment:?}, but {condition:?} does not"
+            );
+        }
+        Ok(())
+    }
+
+    fn is_true(result_type: VarType, result: VariableValue) -> bool {
+        // SAFETY: The union member is selected with the result type.
+        result_type == VarType::Bool && unsafe { result.as_bool() } == Some(true)
+    }
+
+    fn is_present(result_type: VarType, result: VariableValue) -> bool {
+        // SAFETY: The union member is selected with the result type.
+        unsafe {
+            match result_type {
+                VarType::Bool => result.as_bool().is_some(),
+                VarType::F64 => result.as_f64().is_some(),
+                VarType::U64 => result.as_u64().is_some(),
+                VarType::I64 => result.as_i64().is_some(),
+                VarType::Str => result.as_str().is_some(),
+                VarType::None => false,
+            }
+        }
+    }
+
+    proptest! {
+        #![proptest_config(ProptestConfig::with_cases(512))]
+
+        #[test]
+        fn proptest_required_presence_for_true_is_necessary(
+            expr in exprs(3).boolean,
+            assignments in assignments(),
+        ) {
+            check_necessary_condition(
+                &expr,
+                InferredTypeSet::BOOLEAN,
+                &assignments,
+                required_presence_for_true,
+                is_true,
+            )?;
+        }
+
+        #[test]
+        fn proptest_required_presence_is_necessary(
+            expr in prop_oneof![exprs(3).boolean, exprs(3).number, exprs(3).string],
+            assignments in assignments(),
+        ) {
+            check_necessary_condition(
+                &expr,
+                InferredTypeSet::ALL,
+                &assignments,
+                required_presence,
+                is_present,
+            )?;
+        }
+    }
+}