Add the opion monad file

1 files changed, 66 insertions, 0 deletions

diff --git a/src/common/Optionmonad.v b/src/common/Optionmonad.v
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+++ b/src/common/Optionmonad.v
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+(*
+ * Vericert: Verified high-level synthesis.
+ * Copyright (C) 2022 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/>.
+ *)
+
+From vericert Require Import Monad.
+From Coq Require Import Lists.List.
+
+Module Option <: Monad.
+
+  Definition mon := option.
+
+  Definition ret {A: Type} (x: A) := Some x.
+
+  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.
+
+  Definition bind {A B : Type} (f : option A) (g : A -> option B) : option B :=
+    match f with
+    | Some a => g a
+    | _ => None
+    end.
+
+  Definition bind2 {A B C : Type} (f : mon (A * B)) (g : A -> B -> option C) : option C :=
+    match f with
+    | Some (a, b) => g a b
+    | _ => None
+    end.
+
+  Definition join {A : Type} (a : option (option A)) : option A :=
+    match a with
+    | None => None
+    | Some a' => a'
+    end.
+
+End Option.
+
+Module OptionExtra := MonadExtra(Option).