horse/prob: begin work on kfl statistics

horse/prob/kfl.kk

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+module horse/prob/kfl
+
+// kfl is a semiring of probabilities formed by vibes.
+pub type kfl
+  // Effectively if not literally impossible events.
+  Impossible
+  // Not worth aiming for, but can technically still happen.
+  Probably-Not
+  // You expect it not to happen most of the time, but it might still be worth
+  // trying for it if you're being forced to play to your outs.
+  Doubtful
+  // More likely that it won't happen, but a success isn't surprising.
+  Unlikely
+  // Either it does or it doesn't.
+  Mayhapsibly
+  // Decent chance it doesn't happen, but you still expect it to.
+  Probably
+  // You expect it to happen most of the time, but accept that there will be failures.
+  Most-Likely
+  // Very close to guaranteed, but technically with a small chance to fail.
+  Cry-If-Not
+  // Absolutely guaranteed events.
+  Guaranteed
+
+// Automatically generated.
+// Comparison of the `kfl` type.
+pub fun kfl/cmp(this : kfl, other : kfl) : e order
+  match (this, other)
+    (Impossible, Impossible) -> Eq
+    (Impossible, _) -> Lt
+    (_, Impossible) -> Gt
+    (Probably-Not, Probably-Not) -> Eq
+    (Probably-Not, _) -> Lt
+    (_, Probably-Not) -> Gt
+    (Doubtful, Doubtful) -> Eq
+    (Doubtful, _) -> Lt
+    (_, Doubtful) -> Gt
+    (Unlikely, Unlikely) -> Eq
+    (Unlikely, _) -> Lt
+    (_, Unlikely) -> Gt
+    (Mayhapsibly, Mayhapsibly) -> Eq
+    (Mayhapsibly, _) -> Lt
+    (_, Mayhapsibly) -> Gt
+    (Probably, Probably) -> Eq
+    (Probably, _) -> Lt
+    (_, Probably) -> Gt
+    (Most-Likely, Most-Likely) -> Eq
+    (Most-Likely, _) -> Lt
+    (_, Most-Likely) -> Gt
+    (Cry-If-Not, Cry-If-Not) -> Eq
+    (Cry-If-Not, _) -> Lt
+    (_, Cry-If-Not) -> Gt
+    (Guaranteed, Guaranteed) -> Eq
+
+// Shows a string representation of the `kfl` type.
+pub fun kfl/show(this : kfl) : e string
+  match this
+    Impossible -> "impossible"
+    Probably-Not -> "probably not"
+    Doubtful -> "doubtful"
+    Unlikely -> "unlikely"
+    Mayhapsibly -> "mayhapsibly"
+    Probably -> "probably"
+    Most-Likely -> "most likely"
+    Cry-If-Not -> "cry if not"
+    Guaranteed -> "guaranteed"
+
+// KFL multiplication, or the probability of cooccurrence of two independent events.
+pub fun kfl/(*)(a: kfl, b: kfl): e kfl
+  val (l, h) = match a.cmp(b) // this operation is commutative
+    Gt -> (b, a)
+    _ -> (a, b)
+  match (l, h)
+    (Impossible, _) -> Impossible
+    (Probably-Not, Guaranteed) -> Probably-Not
+    (Probably-Not, _) -> Impossible
+    (Doubtful, Guaranteed) -> Doubtful
+    (Doubtful, Cry-If-Not) -> Doubtful
+    (Doubtful, Most-Likely) -> Probably-Not
+    (Doubtful, _) -> Impossible
+    (Unlikely, Guaranteed) -> Unlikely
+    (Unlikely, Cry-If-Not) -> Unlikely
+    (Unlikely, Most-Likely) -> Doubtful
+    (Unlikely, Probably) -> Doubtful
+    (Unlikely, Mayhapsibly) -> Probably-Not
+    (Unlikely, _) -> Probably-Not // (Unlikely, Unlikely) because commutative
+    (Mayhapsibly, Guaranteed) -> Mayhapsibly
+    (Mayhapsibly, Cry-If-Not) -> Mayhapsibly
+    (Mayhapsibly, Most-Likely) -> Unlikely
+    (Mayhapsibly, Probably) -> Unlikely
+    (Mayhapsibly, _) -> Unlikely
+    (Probably, Guaranteed) -> Probably
+    (Probably, Cry-If-Not) -> Probably
+    (Probably, Most-Likely) -> Mayhapsibly
+    (Probably, _) -> Unlikely
+    (Most-Likely, Guaranteed) -> Most-Likely
+    (Most-Likely, Cry-If-Not) -> Most-Likely
+    (Most-Likely, _) -> Probably
+    (Cry-If-Not, Guaranteed) -> Guaranteed
+    (Cry-If-Not, _) -> Cry-If-Not
+    (Guaranteed, _) -> Guaranteed