[coq] ohe.v: add eqb

coq/ohe.v

@@ -2,8 +2,15 @@
 From mathcomp Require Import all_ssreflect.
 Set Bullet Behavior "Strict Subproofs".
 
+(* Set Implicit Arguments. *)
+
 Require Import Bvector.
 
+Search (Vector.t _  _ -> Vector.t _  _ -> bool).
+Print BVeq.
+Print Vector.eqb.
+About Vector.eqb.
+
 (* Parameters: size and a flag indicating whether the mark has been made *)
 (* Valid values have flag set to true *)
 Inductive t: nat -> bool -> Type :=
@@ -13,6 +20,34 @@ Inductive t: nat -> bool -> Type :=
 | Mark: forall {n: nat},
     t n false -> t (S n) true.
 
+
+Fixpoint eqb {b1 b2: bool} {n1 n2: nat} (o1: t n1 b1) (o2: t n2 b2): bool.
+  case (Nat.eqb n1 n2) eqn:Hneq.
+  move/PeanoNat.Nat.eqb_spec: Hneq => Hneq.
+  refine (
+    match o1, o2 with
+    | Nil, Nil => true
+    | Pad n1' b1' o1', Pad n2' b2' o2' => _
+    | Mark n1' o1', Mark n2' o2' => _
+    | _, _ => false
+    end).
+  - move: n1' n2' o1' o2' => n1' n2'.
+    case (Nat.eqb n1' n2') eqn:Hneq'.
+    + move/PeanoNat.Nat.eqb_spec: Hneq' => Hneq'.
+      rewrite -Hneq'.
+      move => o1' o2'.
+      exact: eqb _ _ _ _ o1' o2'.
+    + exact: (fun _ _ => false).
+  - move: n1' n2' o1' o2' => n1' n2'.
+    case (Nat.eqb n1' n2') eqn:Hneq'.
+    + move/PeanoNat.Nat.eqb_spec: Hneq' => Hneq'.
+      rewrite -Hneq'.
+      move => o1' o2'.
+      exact: eqb _ _ _ _ o1' o2'.
+    + exact: (fun _ _ => false).
+  - exact: false.
+Defined.
+
 Fixpoint markCount_aux {n: nat} {b: bool} (a: t n b): nat :=
   match a with
   | Nil => 0
@@ -74,6 +109,7 @@ Compute markCount eg4.
 Compute markCount eg5.
 
 Compute to_bv eg5.
+(* = [false; false; true; false] : Bvector 4 *)
 
 Fixpoint genPad (z: nat): t z false :=
   match z with