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+(* 
+ * CoqUp: Verified high-level synthesis.
+ * Copyright (C) 2019-2020 Yann Herklotz <yann@yannherklotz.com>
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ *)
+
+Module Option.
+
+Definition default {T : Type} (x : T) (u : option T) : T :=
+  match u with
+  | Some y => y
+  | _ => x
+  end.
+
+Definition map {S : Type} {T : Type} (f : S -> T) (u : option S) : option T :=
+  match u with
+  | Some y => Some (f y)
+  | _ => None
+  end.
+
+Definition liftA2 {T : Type} (f : T -> T -> T) (a : option T) (b : option T) : option T :=
+  match a with
+  | Some x => map (f x) b
+  | _ => None
+  end.
+
+End Option.