# Harden the ownership analysis for universal activation — Implementation Plan

> **Parent spec:** `docs/specs/0063-harden-ownership-analysis.md`
>
> **For agentic workers:** REQUIRED SUB-SKILL: use the
> `implement` skill to run this plan. Steps use `- [ ]`
> checkboxes for tracking.

**Goal:** Make the linearity analysis (`crates/ailang-check/src/linearity.rs`) correct under universal activation by exempting value-type binders from consume-tracking and treating function application as a borrow, plus a new `is_value_type` predicate.

**Architecture:** Two orthogonal additive changes inside `linearity.rs` (a value-type exemption gated on a per-binder `is_value` flag, and switching the `Term::App` callee walk from `Consume` to `Borrow`), plus one new shared predicate in `ailang-core::primitives`. No schema change, no hash reset, no codegen change. The analysis stays a pure diagnostic pass; the two existing diagnostic codes simply fire on a smaller, more correct set.

**Tech Stack:** `ailang-core` (primitives predicate), `ailang-check` (linearity pass + in-source unit tests + on-disk fixture tests), `examples/` (`.ail` fixtures).

---

**Files this plan creates or modifies:**

- Modify: `crates/ailang-core/src/primitives.rs` — add `is_value_type`; extend the `#[cfg(test)] mod tests` block.
- Modify: `crates/ailang-check/src/linearity.rs` — `BinderState.is_value`; `Checker.ctors`; `type_is_value` + `collect_value_pattern_binders` helpers; param/pattern/lam seeding; `use_var` short-circuit; `Term::App` callee borrow; `merge_states` carry; in-source tests.
- Create: `examples/fp_value.ail` — Class-1 value-type RED→GREEN fixture.
- Create: `examples/fp_hof.ail` — Class-2a own-fn-param RED→GREEN fixture.
- Create: `examples/fp_map.ail` — Class-2b borrow-fn-param RED→GREEN fixture.
- Create: `examples/real_consume.ail` — must-stay-RED heap double-consume fixture.
- Modify: `crates/ailang-check/tests/workspace.rs` — on-disk linearity assertions for the four fixtures.

---

## Task 1: `is_value_type` predicate

**Files:**
- Modify: `crates/ailang-core/src/primitives.rs`

- [ ] **Step 1: Write the failing test**

In `crates/ailang-core/src/primitives.rs`, inside the existing `#[cfg(test)] mod tests` block, add this test after `predicate_and_surface_name_agree`:

```rust
    /// `is_value_type` is the unboxed/no-RC subset of the primitives:
    /// it agrees with `is_primitive_name` on every name EXCEPT `Str`,
    /// which is a primitive zero-arity ctor but is heap-allocated
    /// (`ptr`, RC'd) — see drop.rs:490-492.
    #[test]
    fn value_type_is_primitive_minus_str() {
        for name in ["Int", "Bool", "Float", "Unit"] {
            assert!(is_value_type(name), "{name} must be a value type");
            assert!(is_primitive_name(name), "{name} must be a primitive");
        }
        // The sole divergence: Str is a primitive but NOT a value type.
        assert!(!is_value_type("Str"), "Str is heap-allocated, not a value type");
        assert!(is_primitive_name("Str"), "Str is still a primitive zero-arity ctor");
        // Non-primitives are neither.
        for name in ["List", "Foo", ""] {
            assert!(!is_value_type(name));
            assert!(!is_primitive_name(name));
        }
    }
```

- [ ] **Step 2: Run test to verify it fails**

Run: `cargo test -p ailang-core value_type_is_primitive_minus_str`
Expected: FAIL to compile — `cannot find function `is_value_type` in this scope`.

- [ ] **Step 3: Write minimal implementation**

In `crates/ailang-core/src/primitives.rs`, immediately after the closing `}` of `pub fn is_primitive_name`, insert:

```rust
/// Returns `true` iff `name` is an **unboxed value type** — no RC, no
/// heap slab, copied by value. This is the `Str`-excluding subset of
/// [`is_primitive_name`]: `Str` is a primitive zero-arity ctor but is
/// heap-allocated (`ptr`, RC-`dec`'d — codegen `drop.rs:490-492` lowers
/// only `Int`/`Bool`/`Float`/`Unit` to non-`ptr`). Used by the
/// linearity analysis to exempt value-type binders from
/// consume-tracking: a value type is never consumed, so multi-use is
/// always legal.
pub fn is_value_type(name: &str) -> bool {
    matches!(name, "Int" | "Bool" | "Float" | "Unit")
}
```

- [ ] **Step 4: Run test to verify it passes**

Run: `cargo test -p ailang-core value_type_is_primitive_minus_str`
Expected: PASS.

---

## Task 2: Application is a borrow

**Files:**
- Modify: `crates/ailang-check/src/linearity.rs` (`Term::App` arm at `:430-433`; in-source tests)

- [ ] **Step 1: Write the failing test**

In `crates/ailang-check/src/linearity.rs`, inside `#[cfg(test)] mod tests`, add a helper (after `fn_with_modes`, near `:1315`) and a test. The helper builds a fn with a single function-typed param `p0 : (mode (Int -> Int))` returning Int:

```rust
    /// A fn with one function-typed param `p0 : (mode (Int -> Int))`,
    /// returning Int. Used to exercise HOF application linearity.
    fn fn_with_fn_param(name: &str, mode: ParamMode, body: Term) -> Def {
        Def::Fn(FnDef {
            name: name.into(),
            ty: Type::Fn {
                params: vec![Type::Fn {
                    params: vec![Type::int()],
                    param_modes: vec![ParamMode::Own],
                    ret: Box::new(Type::int()),
                    ret_mode: ParamMode::Own,
                    effects: vec![],
                }],
                param_modes: vec![mode],
                ret: Box::new(Type::int()),
                ret_mode: ParamMode::Implicit,
                effects: vec![],
            },
            params: vec!["p0".into()],
            body,
            suppress: vec![],
            doc: None,
            export: None,
        })
    }

    /// Applying a function param more than once is a borrow each time,
    /// not a consume: `(app p0 (app p0 0))` must NOT fire
    /// use-after-consume. (Today the App callee is walked Consume, so
    /// the first application consumes `p0` and the second fires
    /// use-after-consume — this test is RED until Fix 2.)
    #[test]
    fn own_fn_param_applied_twice_is_clean() {
        let body = Term::App {
            callee: Box::new(Term::Var { name: "p0".into() }),
            args: vec![Term::App {
                callee: Box::new(Term::Var { name: "p0".into() }),
                args: vec![Term::Lit { lit: Literal::Int { value: 0 } }],
                tail: false,
            }],
            tail: false,
        };
        let m = Module {
            schema: ailang_core::SCHEMA.into(),
            name: "t".into(),
            kernel: false,
            imports: vec![],
            defs: vec![fn_with_fn_param("f", ParamMode::Own, body)],
        };
        let diags = check_module(&m);
        assert!(
            !diags.iter().any(|d| d.code == "use-after-consume"),
            "applying a function param is a borrow, not a consume; got {diags:?}"
        );
    }
```

- [ ] **Step 2: Run test to verify it fails**

Run: `cargo test -p ailang-check own_fn_param_applied_twice_is_clean`
Expected: FAIL — assertion fires; a `use-after-consume` diagnostic is present (the App callee is walked in `Position::Consume` today).

- [ ] **Step 3: Write minimal implementation**

In `crates/ailang-check/src/linearity.rs`, in the `Term::App { callee, args, .. }` arm (`:430-433`), change the callee walk. Replace:

```rust
            Term::App { callee, args, .. } => {
                // The callee itself is consumed (it's "the function value");
                // for var-callees this is typically a global fn ref.
                self.walk(callee, Position::Consume);
```

with:

```rust
            Term::App { callee, args, .. } => {
                // Applying a function value READS it (a borrow): the value
                // stays live for further applications and is dropped at
                // scope close like any other binder. For a global fn-ref
                // callee this is a no-op (globals are untracked, so
                // `use_var` returns early either way); for a tracked
                // function-typed binder (a HOF param) it stops application
                // from consuming the binder. The `consumed` check still
                // runs in Borrow position, so applying an already-consumed
                // function value still fires use-after-consume.
                self.walk(callee, Position::Borrow);
```

- [ ] **Step 4: Run test to verify it passes**

Run: `cargo test -p ailang-check own_fn_param_applied_twice_is_clean`
Expected: PASS.

---

## Task 3: Value-type exemption

**Files:**
- Modify: `crates/ailang-check/src/linearity.rs` (`BinderState` `:181-192`; `Checker` `:408-420`; `Checker` literal `:351-356`; param install `:361-370`; `walk_arm` `:638-652`; `Term::Lam` `:541-560`; `use_var` `:683-690`; `merge_states` `:781-787`; new helpers; in-source tests)

- [ ] **Step 1: Write the failing tests**

In `crates/ailang-check/src/linearity.rs`, inside `#[cfg(test)] mod tests`, add a helper and three tests:

```rust
    /// A fn with one `(own (con Int))` value-type param `p0`, returning
    /// Int. Used to exercise the value-type exemption.
    fn fn_with_int_own(name: &str, body: Term) -> Def {
        Def::Fn(FnDef {
            name: name.into(),
            ty: Type::Fn {
                params: vec![Type::Con { name: "Int".into(), args: vec![] }],
                param_modes: vec![ParamMode::Own],
                ret: Box::new(Type::int()),
                ret_mode: ParamMode::Implicit,
                effects: vec![],
            },
            params: vec!["p0".into()],
            body,
            suppress: vec![],
            doc: None,
            export: None,
        })
    }

    /// A value-type param read in two consume positions
    /// (`(seq p0 p0)`) must NOT fire use-after-consume: an `Int` has no
    /// refcount and is never consumed. RED until Fix 1.
    #[test]
    fn value_param_multi_read_is_clean() {
        let body = Term::Seq {
            lhs: Box::new(Term::Var { name: "p0".into() }),
            rhs: Box::new(Term::Var { name: "p0".into() }),
        };
        let m = Module {
            schema: ailang_core::SCHEMA.into(),
            name: "t".into(),
            kernel: false,
            imports: vec![],
            defs: vec![fn_with_int_own("f", body)],
        };
        let diags = check_module(&m);
        assert!(
            !diags.iter().any(|d| d.code == "use-after-consume"),
            "a value-type param is never consumed; multi-read is legal; got {diags:?}"
        );
    }

    /// Type-gating guard: a HEAP param (`List`) consumed twice in a ctor
    /// (`(term-ctor Pair Pair p0 p0)`) MUST still fire use-after-consume
    /// after the fix — the exemption is value-type-only, not blanket.
    /// (Green today and after the fix; a regression guard, not RED-first.)
    #[test]
    fn heap_param_multi_consume_still_errors() {
        let body = Term::Ctor {
            type_name: "Pair".into(),
            ctor: "Pair".into(),
            args: vec![
                Term::Var { name: "p0".into() },
                Term::Var { name: "p0".into() },
            ],
        };
        let m = Module {
            schema: ailang_core::SCHEMA.into(),
            name: "t".into(),
            kernel: false,
            imports: vec![],
            defs: vec![fn_with_modes("f", vec![ParamMode::Own], body)],
        };
        let diags = check_module(&m);
        assert!(
            diags.iter().any(|d| d.code == "use-after-consume"),
            "a heap param consumed twice must still error; got {diags:?}"
        );
    }

    /// A borrow function param applied AND passed (the recursive-HOF
    /// shape `map_int`) must be clean: application is a borrow, and the
    /// param starts borrowed, so neither use-after-consume nor
    /// consume-while-borrowed should fire. Covered by Fix 2 (App
    /// borrow); this asserts the borrow-param variant. RED until Fix 2.
    #[test]
    fn borrow_fn_param_applied_is_clean() {
        let body = Term::App {
            callee: Box::new(Term::Var { name: "p0".into() }),
            args: vec![Term::Lit { lit: Literal::Int { value: 0 } }],
            tail: false,
        };
        let m = Module {
            schema: ailang_core::SCHEMA.into(),
            name: "t".into(),
            kernel: false,
            imports: vec![],
            defs: vec![fn_with_fn_param("f", ParamMode::Borrow, body)],
        };
        let diags = check_module(&m);
        assert!(
            !diags.iter().any(|d| {
                d.code == "use-after-consume" || d.code == "consume-while-borrowed"
            }),
            "applying a borrow function param is a clean read; got {diags:?}"
        );
    }
```

- [ ] **Step 2: Run tests to verify they fail (the RED ones) / pass (the guard)**

Run: `cargo test -p ailang-check value_param_multi_read_is_clean heap_param_multi_consume_still_errors borrow_fn_param_applied_is_clean`
Expected: `value_param_multi_read_is_clean` FAILS (use-after-consume fires today); `borrow_fn_param_applied_is_clean` PASSES (already fixed by Task 2's App-borrow change); `heap_param_multi_consume_still_errors` PASSES (regression guard, green today).

- [ ] **Step 3a: Add the `is_value` field to `BinderState`**

Replace the `BinderState` struct (`:181-192`):

```rust
#[derive(Debug, Default, Clone)]
struct BinderState {
    /// `true` once the binder has been used in a Consume position.
    /// Subsequent uses (in any position) trigger `use-after-consume`.
    consumed: bool,
    /// Number of currently-live borrows of this binder. ...
    borrow_count: u32,
}
```

with (keep the existing doc comments on `consumed`/`borrow_count` verbatim; only the field is added):

```rust
#[derive(Debug, Default, Clone)]
struct BinderState {
    /// `true` once the binder has been used in a Consume position.
    /// Subsequent uses (in any position) trigger `use-after-consume`.
    consumed: bool,
    /// Number of currently-live borrows of this binder. Incremented
    /// when a Borrow-position use starts (in a fn-call arg slot or as
    /// the initial state of a `Borrow` parameter); decremented when
    /// the borrow ends. Consume while `> 0` triggers
    /// `consume-while-borrowed`.
    borrow_count: u32,
    /// `true` if this binder has an unboxed value type
    /// (`Int`/`Bool`/`Float`/`Unit`). A value type has no refcount and
    /// is never consumed, so `use_var` skips all consume bookkeeping
    /// for it. Invariant per binder; set at the introduction site
    /// (param / pattern / lam) where the type is locally available.
    is_value: bool,
}
```

- [ ] **Step 3b: Add the type-is-value helper**

In `crates/ailang-check/src/linearity.rs`, immediately after the `is_heap_type` function (`:164`), add:

```rust
/// `true` iff `t` is an unboxed value type (`Int`/`Bool`/`Float`/`Unit`).
/// The `Str`-excluding counterpart of `is_heap_type`'s primitive check —
/// see `ailang_core::primitives::is_value_type`.
fn type_is_value(t: &Type) -> bool {
    matches!(t, Type::Con { name, .. } if ailang_core::primitives::is_value_type(name))
}
```

- [ ] **Step 3c: Add the `ctors` field to `Checker` and the value-binder pattern helper**

Replace the `Checker` struct field list (`:408-420`) — add the `ctors` field after `def_name`:

```rust
struct Checker<'a> {
    /// Top-level symbol → type. Used to look up the param_modes of an
    /// `App` callee that resolves to a global fn def.
    globals: &'a HashMap<String, Type>,
    /// Diagnostic accumulator (shared with the module-level walk).
    diags: &'a mut Vec<Diagnostic>,
    /// Name of the fn currently being checked (becomes
    /// [`Diagnostic::def`]).
    def_name: &'a str,
    /// ctor name → field types. Used to type pattern binders so a
    /// value-typed sub-binder (`Cons(h, t)` with `h: Int`) is exempted
    /// from consume-tracking. Mirrors the `ctors` map built in
    /// `check_module_with_visible`.
    ctors: &'a HashMap<String, Vec<Type>>,
    /// Live binder state, keyed by name. Modified in place; lexical
    /// scoping is restored by [`Checker::with_binder`].
    binders: HashMap<String, BinderState>,
}
```

Then add this free function after `collect_pattern_binders` (`:775`):

```rust
/// Collect the names of pattern binders that have an unboxed value
/// type, by walking the pattern alongside the ctor field types.
/// Mirrors `pattern_has_consumed_heap_binder_at`'s descent: a
/// `Pattern::Var` directly under a ctor field of value type is added;
/// a top-level `Pattern::Var` (whole-scrutinee binder, `declared_ty ==
/// None`) is conservatively treated as heap and never added.
fn collect_value_pattern_binders(
    pat: &Pattern,
    declared_ty: Option<&Type>,
    ctors: &HashMap<String, Vec<Type>>,
    out: &mut Vec<String>,
) {
    match pat {
        Pattern::Wild | Pattern::Lit { .. } => {}
        Pattern::Var { name } => {
            if let Some(t) = declared_ty {
                if type_is_value(t) {
                    out.push(name.clone());
                }
            }
        }
        Pattern::Ctor { ctor, fields } => {
            let field_tys: &[Type] = ctors.get(ctor).map(|v| v.as_slice()).unwrap_or(&[]);
            for (i, f) in fields.iter().enumerate() {
                collect_value_pattern_binders(f, field_tys.get(i), ctors, out);
            }
        }
    }
}
```

- [ ] **Step 3d: Wire `ctors` into the `Checker` literal and seed param `is_value`**

Replace the `Checker` construction + param install loop in `check_fn` (`:351-370`):

```rust
    let mut checker = Checker {
        globals,
        diags,
        def_name: &f.name,
        binders: HashMap::new(),
    };

    // Install fn parameters as binders, with initial `borrow_count = 1`
    // for `Borrow` params (the caller's outer borrow stays live for the
    // body's whole duration) and `0` for `Own` params.
    for (name, mode) in f.params.iter().zip(param_modes.iter()) {
        let initial = BinderState {
            consumed: false,
            borrow_count: match mode {
                ParamMode::Borrow => 1,
                ParamMode::Own | ParamMode::Implicit => 0,
            },
        };
        checker.binders.insert(name.clone(), initial);
    }
```

with:

```rust
    let mut checker = Checker {
        globals,
        diags,
        def_name: &f.name,
        ctors,
        binders: HashMap::new(),
    };

    // Install fn parameters as binders, with initial `borrow_count = 1`
    // for `Borrow` params (the caller's outer borrow stays live for the
    // body's whole duration) and `0` for `Own` params. A value-type
    // param starts `is_value = true` and is exempt from consume-tracking.
    for (i, (name, mode)) in f.params.iter().zip(param_modes.iter()).enumerate() {
        let initial = BinderState {
            consumed: false,
            borrow_count: match mode {
                ParamMode::Borrow => 1,
                ParamMode::Own | ParamMode::Implicit => 0,
            },
            is_value: param_tys.get(i).map(type_is_value).unwrap_or(false),
        };
        checker.binders.insert(name.clone(), initial);
    }
```

- [ ] **Step 3e: Seed `is_value` for pattern binders in `walk_arm`**

Replace the binder-install loop in `walk_arm` (`:638-644`):

```rust
    fn walk_arm(&mut self, arm: &Arm, pos: Position) {
        let names = collect_pattern_binders(&arm.pat);
        let mut saved: HashMap<String, Option<BinderState>> = HashMap::new();
        for n in &names {
            saved.insert(n.clone(), self.binders.remove(n));
            self.binders.insert(n.clone(), BinderState::default());
        }
```

with:

```rust
    fn walk_arm(&mut self, arm: &Arm, pos: Position) {
        let names = collect_pattern_binders(&arm.pat);
        let mut value_names: Vec<String> = Vec::new();
        collect_value_pattern_binders(&arm.pat, None, self.ctors, &mut value_names);
        let mut saved: HashMap<String, Option<BinderState>> = HashMap::new();
        for n in &names {
            saved.insert(n.clone(), self.binders.remove(n));
            let st = BinderState {
                is_value: value_names.contains(n),
                ..BinderState::default()
            };
            self.binders.insert(n.clone(), st);
        }
```

- [ ] **Step 3f: Seed `is_value` for lam params in `Term::Lam`**

Replace the `Term::Lam` arm's destructure and param-install loop (`:541-552`):

```rust
            Term::Lam { params, body, .. } => {
                // Lam captures cross the linearity boundary: any free
                // var of the body is implicitly consumed by closure
                // construction (we don't yet model captured-borrow
                // discipline; that is 18c.3 territory). For 18c.2 we
                // walk the body with the lam's own params as fresh
                // binders.
                let mut saved_for_params: HashMap<String, Option<BinderState>> = HashMap::new();
                for p in params {
                    saved_for_params.insert(p.clone(), self.binders.remove(p));
                    self.binders.insert(p.clone(), BinderState::default());
                }
```

with:

```rust
            Term::Lam { params, param_tys, body, .. } => {
                // Lam captures cross the linearity boundary: any free
                // var of the body is implicitly consumed by closure
                // construction (we don't yet model captured-borrow
                // discipline; that is 18c.3 territory). For 18c.2 we
                // walk the body with the lam's own params as fresh
                // binders; a value-typed lam param is exempt from
                // consume-tracking.
                let mut saved_for_params: HashMap<String, Option<BinderState>> = HashMap::new();
                for (i, p) in params.iter().enumerate() {
                    saved_for_params.insert(p.clone(), self.binders.remove(p));
                    let st = BinderState {
                        is_value: param_tys.get(i).map(type_is_value).unwrap_or(false),
                        ..BinderState::default()
                    };
                    self.binders.insert(p.clone(), st);
                }
```

- [ ] **Step 3g: Short-circuit the consume arm in `use_var`**

Replace the `Position::Consume` arm in `use_var` (`:683-690`):

```rust
            Position::Consume => {
                if state.borrow_count > 0 {
                    self.diags
                        .push(make_consume_while_borrowed(self.def_name, name));
                    return;
                }
                state.consumed = true;
            }
```

with:

```rust
            Position::Consume => {
                // A value type has no refcount and is never consumed;
                // multi-use in any position is legal.
                if state.is_value {
                    return;
                }
                if state.borrow_count > 0 {
                    self.diags
                        .push(make_consume_while_borrowed(self.def_name, name));
                    return;
                }
                state.consumed = true;
            }
```

- [ ] **Step 3h: Carry `is_value` through `merge_states`**

Replace `merge_states` (`:781-787`):

```rust
fn merge_states(into: &mut HashMap<String, BinderState>, other: &HashMap<String, BinderState>) {
    for (name, s) in other {
        let entry = into.entry(name.clone()).or_default();
        entry.consumed = entry.consumed || s.consumed;
        entry.borrow_count = entry.borrow_count.max(s.borrow_count);
    }
}
```

with (add the `is_value` carry — invariant per binder, but `or_default()` would otherwise reset a value binder present only in `other` to `false`):

```rust
fn merge_states(into: &mut HashMap<String, BinderState>, other: &HashMap<String, BinderState>) {
    for (name, s) in other {
        let entry = into.entry(name.clone()).or_default();
        entry.consumed = entry.consumed || s.consumed;
        entry.borrow_count = entry.borrow_count.max(s.borrow_count);
        // is_value is invariant per binder; the OR recovers it when the
        // binder reached `into` via a fresh `or_default()`.
        entry.is_value = entry.is_value || s.is_value;
    }
}
```

- [ ] **Step 4: Build and run the linearity tests**

Run: `cargo build -p ailang-check`
Expected: 0 errors (every `BinderState` / `Checker` literal compiles; the `..Default::default()` tail and the explicit `is_value` field cover all sites).

Run: `cargo test -p ailang-check value_param_multi_read_is_clean heap_param_multi_consume_still_errors borrow_fn_param_applied_is_clean own_fn_param_applied_twice_is_clean`
Expected: all PASS.

---

## Task 4: On-disk fixtures and assertions

**Files:**
- Create: `examples/fp_value.ail`, `examples/fp_hof.ail`, `examples/fp_map.ail`, `examples/real_consume.ail`
- Modify: `crates/ailang-check/tests/workspace.rs`

- [ ] **Step 1: Create the four fixtures**

Create `examples/fp_value.ail`:

```ail
(module fp_value
  (fn sum_explicit
    (doc "value-type param read multiple times")
    (type (fn-type (params (own (con Int))) (ret (own (con Int)))))
    (params n)
    (body (if (app eq n 0) 0 (app + n (app sum_explicit (app - n 1))))))
  (fn main
    (type (fn-type (params) (ret (own (con Unit))) (effects IO)))
    (params)
    (body (app print (app sum_explicit 10)))))
```

Create `examples/fp_hof.ail`:

```ail
(module fp_hof
  (fn apply_thrice
    (doc "apply a function param three times")
    (type (fn-type
            (params (own (fn-type (params (own (con Int))) (ret (own (con Int))))) (own (con Int)))
            (ret (own (con Int)))))
    (params f x)
    (body (app f (app f (app f x)))))
  (fn main
    (type (fn-type (params) (ret (own (con Unit))) (effects IO)))
    (params)
    (body (app print (app apply_thrice (lam (params (typed y (con Int))) (ret (con Int)) (body (app + y 1))) 0)))))
```

Create `examples/fp_map.ail`:

```ail
(module fp_map
  (data IntList
    (doc "boxed list")
    (ctor Nil)
    (ctor Cons (con Int) (con IntList)))
  (fn map_int
    (doc "recursive HOF: f applied AND passed to the recursive call")
    (type (fn-type
            (params (borrow (fn-type (params (own (con Int))) (ret (own (con Int))))) (own (con IntList)))
            (ret (own (con IntList)))))
    (params f xs)
    (body (match xs
      (case (pat-ctor Nil) (term-ctor IntList Nil))
      (case (pat-ctor Cons h t) (term-ctor IntList Cons (app f h) (app map_int f t)))))))
```

Create `examples/real_consume.ail`:

```ail
(module real_consume
  (data Box
    (doc "heap cell")
    (ctor Box (con Int)))
  (data Pair
    (doc "two boxes")
    (ctor Pair (con Box) (con Box)))
  (fn dup
    (doc "MUST STAY an error: a heap param consumed twice without clone")
    (type (fn-type (params (own (con Box))) (ret (own (con Pair)))))
    (params b)
    (body (term-ctor Pair Pair b b))))
```

- [ ] **Step 2: Verify the fixtures check clean / error as designed**

Run: `cargo build -p ail && for f in fp_value fp_hof fp_map real_consume; do echo "== $f =="; ./target/debug/ail check examples/$f.ail; echo "exit=$?"; done`
Expected: `fp_value`, `fp_hof`, `fp_map` each exit 0 (clean, post-fix); `real_consume` exits 1 with `[use-after-consume] dup: \`b\` is used after it was already consumed`.

- [ ] **Step 3: Add the on-disk assertions**

In `crates/ailang-check/tests/workspace.rs`, append after `borrow_own_demo_is_linearity_clean` (`:720`):

```rust
/// #56 Fix 1+2: under universal activation the linearity analysis must
/// not false-fire on value-type params or on applied function params.
/// These three fixtures use explicit-mode signatures (so the analysis
/// is active today) and were RED before the hardening (docs/specs/0063).
#[test]
fn harden_ownership_false_positives_are_clean() {
    for name in ["fp_value", "fp_hof", "fp_map"] {
        let entry = examples_dir().join(format!("{name}.ail"));
        let ws = load_workspace(&entry).unwrap_or_else(|e| panic!("load {name}: {e:?}"));
        let diags = check_workspace(&ws);
        let lin: Vec<&ailang_check::Diagnostic> = diags
            .iter()
            .filter(|d| d.code == "use-after-consume" || d.code == "consume-while-borrowed")
            .collect();
        assert!(lin.is_empty(), "{name} must be linearity-clean; got: {lin:#?}");
    }
}

/// #56 type-gating: the exemption is value-type-only. A heap param
/// consumed twice (`real_consume.dup`, `(term-ctor Pair Pair b b)`) MUST
/// still fire use-after-consume — proving the fix did not blanket-silence
/// genuine multi-consume.
#[test]
fn harden_ownership_heap_double_consume_still_errors() {
    let entry = examples_dir().join("real_consume.ail");
    let ws = load_workspace(&entry).expect("load real_consume");
    let diags = check_workspace(&ws);
    assert!(
        diags.iter().any(|d| d.code == "use-after-consume"),
        "real_consume.dup must still fire use-after-consume; got: {diags:#?}"
    );
}
```

- [ ] **Step 4: Run the on-disk assertions**

Run: `cargo test -p ailang-check --test workspace harden_ownership`
Expected: both `harden_ownership_false_positives_are_clean` and `harden_ownership_heap_double_consume_still_errors` PASS.

- [ ] **Step 5: Full workspace regression**

Run: `cargo test --workspace`
Expected: PASS (no regressions; per the typed-MIR re-synth strictness memory, the whole suite is the net, not just e2e).

Run: `python3 bench/check.py && python3 bench/compile_check.py`
Expected: both report clean (the analysis is diagnostic-only; no compile-baseline shift expected).
