feat!: prediction and joint queries take borrowed keys

`&[&[&K]]` was the worst shape in the API. At `K = String` — the
realistic case, where names arrive owned from a database or CSV — a
string literal was *impossible*, and asking "who wins" cost six lines
and four allocations of temporaries that all had to outlive the call:

    let ta = vec![a.to_string()];
    let ra: Vec<&String> = ta.iter().collect();
    ...
    self.history.predict_win_probabilities(&teams)

All seven `predict_*` / `expected_*` methods, `posterior_of`,
`posterior_of_at` and the `Joint` mirrors are now generic over the
borrowed key, the same way `current_skill` and `learning_curve` already
were. `member_skills` and `resolve_terms` only ever did two things with
a key — `keys.get` and `format!("{key:?}")` — and neither needed `K`.

    h.predict_win_probabilities(&[&["alice"], &["bob"]])   // K = String
    h.predict_win_probabilities(&[&["alice"], &["bob"]])   // K = &'static str
    h.posterior_of(&[("alice", 1.0), ("bob", -1.0)])

One spelling for both key types, and `K: Debug` becomes `Q: Debug`, so a
key type no longer has to be `Debug` to run a prediction. The old
`&[&[&"a"]]` spelling still compiles at the default key type, where `Q`
infers to `&str` and the two shapes coincide.

The one cost: `predict_outcome(&[])` can no longer infer `Q` — nothing
in an empty slice names it. It needs an annotation, and only on that
degenerate call.

`lookup` carried `ToOwned<Owned = K>`, copy-pasted from `intern`, which
genuinely needs it to create the entry. `lookup` never creates, and its
five neighbours all accept `h.f("alice")` already. Dropping the bound
strictly widens what compiles.

`HistoryBuilder::gamma` is shorthand for `.drift(ConstantDrift::new(g))`.
Drift is the most-tuned parameter after `sigma` and `GAMMA` is a public
constant, but setting it meant first discovering `ConstantDrift`, a type
a caller has no other reason to name. On the `ConstantDrift` builder
only, since `gamma` is that model's parameter rather than something
every `Drift` has, and rejecting a negative value for the same reason as
`sigma` and `beta`: it enters squared.

Refs #72 (items 2 and 3, plus the gamma shorthand; the type-parameter
reorder in item 1 is still open).

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ

src/history.rs

@@ -507,6 +507,32 @@ impl<T: Time, K: Eq + Hash + Clone> HistoryBuilder<T, ConstantDrift, NullObserve
     pub fn new() -> Self {
         Self::default()
     }
+
+    /// Set the drift rate, in skill units per unit of time.
+    ///
+    /// Shorthand for `.drift(ConstantDrift::new(gamma))`. Drift is the
+    /// most-tuned parameter after `sigma` and [`GAMMA`](crate::GAMMA) is a
+    /// public constant, but reaching it otherwise means first discovering
+    /// [`ConstantDrift`] — a type a caller has no other reason to name.
+    ///
+    /// Only on the `ConstantDrift` builder: `gamma` is that model's parameter,
+    /// not a property every [`Drift`] has. Use
+    /// [`drift`](HistoryBuilder::drift) for anything else.
+    ///
+    /// # Panics
+    ///
+    /// Panics unless `gamma` is finite and non-negative. Drift enters as
+    /// `gamma^2` per elapsed tick, so a negative value would behave as its
+    /// absolute value — the same sign-absorption already rejected for `sigma`
+    /// and `beta`.
+    pub fn gamma(self, gamma: f64) -> Self {
+        assert!(
+            gamma.is_finite() && gamma >= 0.0,
+            "gamma must be finite and non-negative (got {gamma}); it is only ever \
+             squared, so a negative value would silently behave as its absolute value"
+        );
+        self.drift(ConstantDrift::new(gamma))
+    }
 }
 
 impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O, K> {
@@ -531,7 +557,7 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     pub fn lookup<Q>(&self, key: &Q) -> Option<Index>
     where
         K: Borrow<Q>,
-        Q: Hash + Eq + ToOwned<Owned = K> + ?Sized,
+        Q: Hash + Eq + ?Sized,
     {
         self.keys.get(key)
     }
@@ -1128,9 +1154,10 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     /// reported rather than dropped — silently skipping them would turn a team
     /// of strangers into a confident-looking prediction about nobody, which is
     /// the failure this replaced.
-    fn member_skills(&self, teams: &[&[&K]]) -> Result<Vec<Vec<Gaussian>>, InferenceError>
+    fn member_skills<Q>(&self, teams: &[&[&Q]]) -> Result<Vec<Vec<Gaussian>>, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         if teams.len() < 2 {
             return Err(InferenceError::NotEnoughTeams { got: teams.len() });
@@ -1244,9 +1271,13 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     /// # Errors
     ///
     /// As `member_skills`.
-    fn performances(&self, teams: &[&[&K]]) -> Result<(Vec<Gaussian>, Vec<usize>), InferenceError>
+    fn performances<Q>(
+        &self,
+        teams: &[&[&Q]],
+    ) -> Result<(Vec<Gaussian>, Vec<usize>), InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         let skills = self.member_skills(teams)?;
 
@@ -1310,9 +1341,10 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     /// — the fit did not converge — and `InvalidParameter` if `beta` is zero
     /// and every skill is a point mass, leaving no performance distribution to
     /// predict from.
-    pub fn predict_quality(&self, teams: &[&[&K]]) -> Result<f64, InferenceError>
+    pub fn predict_quality<Q>(&self, teams: &[&[&Q]]) -> Result<f64, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         let groups = self.member_skills(teams)?;
         let group_refs: Vec<&[Gaussian]> = groups.iter().map(Vec::as_slice).collect();
@@ -1448,14 +1480,15 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     ///
     /// `row_for` picks which appearance of a competitor the caller means —
     /// their latest, or the one at a given time.
-    fn resolve_terms(
+    fn resolve_terms<Q>(
         &self,
-        terms: &[(&K, f64)],
+        terms: &[(&Q, f64)],
         width: usize,
         row_for: impl Fn(Index) -> Option<(usize, usize)>,
     ) -> Result<ResolvedTerms, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         let mut contrast = vec![0.0; width];
         let mut unseen: BTreeMap<String, f64> = BTreeMap::new();
@@ -1557,9 +1590,10 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     /// `UnknownKey` for a competitor the history has never seen, and
     /// `JointUnavailable` for ranked events or a system that is not
     /// positive-definite.
-    pub fn posterior_of(&self, terms: &[(&K, f64)]) -> Result<Gaussian, InferenceError>
+    pub fn posterior_of<Q>(&self, terms: &[(&Q, f64)]) -> Result<Gaussian, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         self.joint()?.posterior_of(terms)
     }
@@ -1579,9 +1613,14 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     ///
     /// As [`History::posterior_of`], plus `UnknownKey` for a competitor with no
     /// appearance at or before `time`.
-    pub fn posterior_of_at(&self, time: T, terms: &[(&K, f64)]) -> Result<Gaussian, InferenceError>
+    pub fn posterior_of_at<Q>(
+        &self,
+        time: T,
+        terms: &[(&Q, f64)],
+    ) -> Result<Gaussian, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         self.joint()?.posterior_of_at(time, terms)
     }
@@ -1625,13 +1664,14 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     ///
     /// As [`History::posterior_of`], plus `MismatchedShape` unless exactly two
     /// teams are supplied and `EmptyTeam` for an empty one.
-    pub fn expected_variance_reduction(
+    pub fn expected_variance_reduction<Q>(
         &self,
-        teams: &[&[&K]],
+        teams: &[&[&Q]],
-        target: &[(&K, f64)],
+        target: &[(&Q, f64)],
     ) -> Result<f64, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         self.joint()?.expected_variance_reduction(teams, target)
     }
@@ -1747,9 +1787,10 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     /// `UnknownKey` under [`UnknownKeys::Reject`](crate::UnknownKeys::Reject),
     /// and `JointUnavailable` if the history is empty or holds ranked events in
     /// *any* slice — not merely the latest one.
-    pub fn predict_margin(&self, teams: &[&[&K]]) -> Result<Gaussian, InferenceError>
+    pub fn predict_margin<Q>(&self, teams: &[&[&Q]]) -> Result<Gaussian, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         if teams.len() != 2 {
             return Err(InferenceError::MismatchedShape {
@@ -1759,7 +1800,7 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
             });
         }
 
-        let mut terms: Vec<(&K, f64)> = Vec::new();
+        let mut terms: Vec<(&Q, f64)> = Vec::new();
         let mut performance_noise = 0.0;
 
         for (team_idx, team) in teams.iter().enumerate() {
@@ -1824,9 +1865,10 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     /// — the fit did not converge — and `InvalidParameter` if `beta` is zero
     /// and every skill is a point mass, leaving no performance distribution to
     /// predict from.
-    pub fn expected_information_gain(&self, teams: &[&[&K]]) -> Result<f64, InferenceError>
+    pub fn expected_information_gain<Q>(&self, teams: &[&[&Q]]) -> Result<f64, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         let skills = self.member_skills(teams)?;
 
@@ -1884,9 +1926,10 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     /// — the fit did not converge — and `InvalidParameter` if `beta` is zero
     /// and every skill is a point mass, leaving no performance distribution to
     /// predict from.
-    pub fn predict_win_probabilities(&self, teams: &[&[&K]]) -> Result<Vec<f64>, InferenceError>
+    pub fn predict_win_probabilities<Q>(&self, teams: &[&[&Q]]) -> Result<Vec<f64>, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         let (performances, sizes) = self.performances(teams)?;
         Ok(crate::predict::win_probabilities(
@@ -1938,9 +1981,10 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     /// — the fit did not converge — and `InvalidParameter` if `beta` is zero
     /// and every skill is a point mass, leaving no performance distribution to
     /// predict from.
-    pub fn predict_outcome(&self, teams: &[&[&K]]) -> Result<Prediction, InferenceError>
+    pub fn predict_outcome<Q>(&self, teams: &[&[&Q]]) -> Result<Prediction, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         if teams.len() > crate::MAX_PREDICTED_TEAMS {
             return Err(InferenceError::TooManyTeams {
@@ -1987,9 +2031,10 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     /// — the fit did not converge — and `InvalidParameter` if `beta` is zero
     /// and every skill is a point mass, leaving no performance distribution to
     /// predict from.
-    pub fn predict_ranking(&self, teams: &[&[&K]], ranks: &[u32]) -> Result<f64, InferenceError>
+    pub fn predict_ranking<Q>(&self, teams: &[&[&Q]], ranks: &[u32]) -> Result<f64, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         if ranks.len() != teams.len() {
             return Err(InferenceError::MismatchedShape {
@@ -2877,9 +2922,10 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> Joint<'_, T, D,
     /// # Errors
     ///
     /// `UnknownKey` for a competitor the history has never seen.
-    pub fn posterior_of(&self, terms: &[(&K, f64)]) -> Result<Gaussian, InferenceError>
+    pub fn posterior_of<Q>(&self, terms: &[(&Q, f64)]) -> Result<Gaussian, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         let resolved = self
             .history
@@ -2895,9 +2941,14 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> Joint<'_, T, D,
     /// # Errors
     ///
     /// `UnknownKey` for a competitor with no appearance at or before `time`.
-    pub fn posterior_of_at(&self, time: T, terms: &[(&K, f64)]) -> Result<Gaussian, InferenceError>
+    pub fn posterior_of_at<Q>(
+        &self,
+        time: T,
+        terms: &[(&Q, f64)],
+    ) -> Result<Gaussian, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         let as_of = self.rows_as_of(time);
         let resolved = self
@@ -2932,13 +2983,14 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> Joint<'_, T, D,
     ///
     /// `MismatchedShape` unless exactly two teams are supplied, `EmptyTeam` for
     /// an empty one, and `UnknownKey` for an unseen competitor.
-    pub fn expected_variance_reduction(
+    pub fn expected_variance_reduction<Q>(
         &self,
-        teams: &[&[&K]],
+        teams: &[&[&Q]],
-        target: &[(&K, f64)],
+        target: &[(&Q, f64)],
     ) -> Result<f64, InferenceError>
     where
-        K: std::fmt::Debug,
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized + std::fmt::Debug,
     {
         if teams.len() != 2 {
             return Err(InferenceError::MismatchedShape {
@@ -2950,7 +3002,7 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> Joint<'_, T, D,
 
         // The candidate matchup, expressed as the same kind of linear
         // functional as the target.
-        let mut matchup: Vec<(&K, f64)> = Vec::new();
+        let mut matchup: Vec<(&Q, f64)> = Vec::new();
         let mut noise = self.history.score_sigma * self.history.score_sigma;
         for (team_idx, team) in teams.iter().enumerate() {
             if team.is_empty() {

tests/key_ergonomics.rs

@@ -0,0 +1,119 @@
+//! The realistic program: keys arrive owned, queries are written with literals.
+//!
+//! Every prediction and joint query used to take `&[&[&K]]`, which at
+//! `K = String` made a string literal *impossible* — the shape required three
+//! levels of temporaries that all had to outlive the call. They are generic
+//! over the borrowed key now, so one spelling works at both key types.
+//!
+//! Both key types are exercised in every test, because the point is that the
+//! spelling is the same.
+
+use trueskill_tt::{ConstantDrift, History, NullObserver};
+
+type Owned = History<i64, ConstantDrift, NullObserver, String>;
+type Borrowed = History<i64, ConstantDrift, NullObserver, &'static str>;
+
+fn owned() -> Owned {
+    let mut h: Owned = History::builder().key_type::<String>().build();
+    for t in 1..=4 {
+        h.record_winner(&"alice".to_string(), &"bob".to_string(), t)
+            .expect("ingests");
+    }
+    h.converge().expect("converges");
+    h
+}
+
+fn borrowed() -> Borrowed {
+    let mut h = History::default();
+    for t in 1..=4 {
+        h.record_winner(&"alice", &"bob", t).expect("ingests");
+    }
+    h.converge().expect("converges");
+    h
+}
+
+#[test]
+fn predictions_take_literals_at_either_key_type() {
+    let teams: &[&[&str]] = &[&["alice"], &["bob"]];
+
+    let a = owned()
+        .predict_win_probabilities(teams)
+        .expect("K = String");
+    let b = borrowed()
+        .predict_win_probabilities(teams)
+        .expect("K = &'static str");
+
+    assert_eq!(a, b, "the same fit through the same spelling");
+    assert!(a[0] > a[1], "alice won every game");
+}
+
+#[test]
+fn every_team_shaped_query_accepts_the_same_slice() {
+    let h = owned();
+    let teams: &[&[&str]] = &[&["alice"], &["bob"]];
+
+    h.predict_quality(teams).expect("quality");
+    let _ = h.predict_outcome(teams).expect("outcome");
+    h.predict_ranking(teams, &[0, 1]).expect("ranking");
+    h.expected_information_gain(teams)
+        .expect("information gain");
+}
+
+#[test]
+fn linear_combinations_take_bare_keys() {
+    // `&[(&K, f64)]` at `K = String` meant `&[(&String, f64)]` — no literals.
+    let h = owned();
+    let terms: &[(&str, f64)] = &[("alice", 1.0), ("bob", -1.0)];
+
+    // Ranked history, so the joint is unavailable — but the *call* compiles,
+    // which is what this pins. The error proves it reached the joint check
+    // rather than failing to resolve a key.
+    let err = h
+        .posterior_of(terms)
+        .expect_err("ranked history has no joint");
+    assert!(
+        format!("{err}").contains("ranked"),
+        "expected the joint-unavailable path, got {err}"
+    );
+}
+
+#[test]
+fn lookup_accepts_a_borrowed_key_like_its_neighbours() {
+    // `lookup` carried `ToOwned<Owned = K>`, copy-pasted from `intern`, which
+    // genuinely needs it to create the entry. `lookup` never creates.
+    let h = owned();
+    assert!(h.lookup("alice").is_some());
+    assert!(h.lookup("nobody").is_none());
+
+    // Control: its neighbours already accepted this and must still.
+    assert!(h.current_skill("alice").is_some());
+    assert!(h.rating("alice").is_some());
+}
+
+#[test]
+fn gamma_sets_drift_without_naming_constant_drift() {
+    let mut a: Borrowed = History::builder().gamma(0.5).build();
+    let mut b: Borrowed = History::builder().drift(ConstantDrift::new(0.5)).build();
+
+    for h in [&mut a, &mut b] {
+        h.record_winner(&"x", &"y", 1).unwrap();
+        h.record_winner(&"y", &"x", 100).unwrap();
+        h.converge().unwrap();
+    }
+
+    let (ga, gb) = (a.current_skill("x").unwrap(), b.current_skill("x").unwrap());
+    assert_eq!((ga.mu(), ga.sigma()), (gb.mu(), gb.sigma()));
+
+    // Control: the shorthand is not a no-op — a different gamma differs.
+    let mut c: Borrowed = History::builder().gamma(0.0).build();
+    c.record_winner(&"x", &"y", 1).unwrap();
+    c.record_winner(&"y", &"x", 100).unwrap();
+    c.converge().unwrap();
+    assert_ne!(c.current_skill("x").unwrap().sigma(), ga.sigma());
+}
+
+#[test]
+#[should_panic(expected = "gamma must be finite and non-negative")]
+fn a_negative_gamma_is_rejected_rather_than_squared_away() {
+    let _: Borrowed = History::builder().gamma(-0.5).build();
+}

tests/prediction.rs

@@ -60,8 +60,12 @@ fn degenerate_team_shapes_are_errors_rather_than_panics() {
         h.predict_outcome(&[&[&"a"]]).unwrap_err(),
         InferenceError::NotEnoughTeams { got: 1, .. }
     ),);
+    // An empty team list cannot infer the key type — nothing in `&[]` names it.
+    // The annotation is the cost of `predict_*` being generic over the borrowed
+    // key, and it only bites on the degenerate call.
+    let none: &[&[&str]] = &[];
     assert!(matches!(
-        h.predict_outcome(&[]).unwrap_err(),
+        h.predict_outcome(none).unwrap_err(),
         InferenceError::NotEnoughTeams { got: 0, .. }
     ),);
     assert!(matches!(