horse/prob: add basic distribution operations

horse/prob/pmf.kk

@@ -34,3 +34,25 @@ pub tail fun foldl(p: pmf<s, v>, init: a, f: (a, s, v) -> e a): e a
 // Convert the distribution to a list of entries.
 pub fun pmf/list(p: pmf<s, v>): list<(s, v)>
   p.foldl(Nil) fn(l, s, v) Cons((s, v), l)
+
+// Distribution of cooccurrence of two events described by their distributions.
+pub fun (*)(a: pmf<s, v>, b: pmf<s, v>, ?s/cmp: (a: s, b: s) -> order, ?v/(*): (a: v, b: v) -> e v): e pmf<s, v>
+  match a
+    End -> End
+    Event(sa, va, nexta) -> match b
+      End -> End
+      Event(sb, vb, nextb) -> match sa.cmp(sb)
+        Lt -> nexta * b
+        Eq -> Event(sa, va * vb, nexta * nextb)
+        Gt -> a * nextb
+
+// Distribution of occurrence of at least one of two events described by their distributions.
+pub fun (+)(a: pmf<s, v>, b: pmf<s, v>, ?s/cmp: (a: s, b: s) -> order, ?v/(+): (a: v, b: v) -> e v): e pmf<s, v>
+  match a
+    End -> b
+    Event(sa, va, nexta) -> match b
+      End -> a
+      Event(sb, vb, nextb) -> match sa.cmp(sb)
+        Lt -> Event(sa, va, nexta + b)
+        Eq -> Event(sa, va + vb, nexta + nextb)
+        Gt -> Event(sb, vb, a + nextb)