begin coding bro-tree for benchmarks

bench/bro-tree.sml

@@ -0,0 +1,57 @@
+structure BroTree =
+struct
+  (* implementation of 1-2 brother tree ported from:
+   * https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL-Data_Structures/document.pdf
+   * *)
+  datatype bro =
+    N0
+  | N1 of bro
+  | N2 of bro * string * bro
+  | L2 of string
+  | N3 of bro * string * bro * string * bro
+
+  val empty = N0
+
+  fun n1 bro =
+    case bro of
+      L2 str => N2 (N0, str, N0)
+    | N3 (t1, a1, t2, a2, t3) => N2 (N2 (t1, a1, t2), a2, N1 t3)
+    | t => N1 t
+
+  fun n2Left (t1, str, t2) =
+    case (t1, str, t2) of
+      (L2 a1, a2, t) => N3 (N0, a2, N0, a2, t)
+    | (N3 (t1, a1, t2, a2, t3), a3, N1 t4) =>
+        N2 (N2 (t1, a1, t2), a2, N2 (t2, a3, t4))
+    | (N3 (t1, a1, t2, a2, t3), a3, t4) =>
+        N3 (N2 (t1, a1, t2), a2, N1 t3, a3, t4)
+    | (t1, a1, t2) => N2 (t1, a1, t2)
+
+  fun n2Right (t1, str, t2) =
+    case (t1, str, t2) of
+      (t1, a1, L2 a2) => N3 (t1, a2, N0, a2, N0)
+    | (N1 t1, a1, N3 (t2, a2, t3, a3, t4)) =>
+        N2 (N2 (t1, a1, t2), a2, N2 (t3, a3, t4))
+    | (t1, a1, N3 (t2, a2, t3, a3, t4)) =>
+        N3 (t1, a2, N1 t2, a2, N2 (t3, a3, t4))
+    | (t1, a1, t2) => N2 (t1, a1, t2)
+
+  fun ins (str, tree) =
+    case tree of
+      N0 => L2 str
+    | N1 t => n1 (ins (str, t))
+    | N2 (l, a, r) =>
+        if str < a then n2Left (ins (str, l), a, r)
+        else if str > a then n2Right (l, a, ins (str, r))
+        else N2 (l, a, r)
+    | _ => raise Match (*impossible case*)
+
+  fun insRoot tree =
+    case tree of
+      L2 str => N2 (N0, str, N0)
+    | N3 (t1, a1, t2, a2, t3) => N2 (N2 (t1, a2, t2), a2, N1 t3)
+    | tree => tree
+
+  fun insert (str, tree) =
+    insRoot (ins (str, tree))
+end