Require Import Ltac2.Init.

Ltac2 and x y :=
  match x with
  | true => y
  | false => false
  end.

Ltac2 or x y :=
  match x with
  | true => true
  | false => y
  end.

Ltac2 impl x y :=
  match x with
  | true => y
  | false => true
  end.

Ltac2 neg x :=
  match x with
  | true => false
  | false => true
  end.

Ltac2 xor x y :=
  match x with
  | true
    => match y with
       | true => false
       | false => true
       end
  | false
    => match y with
       | true => true
       | false => false
       end
  end.

Ltac2 equal x y :=
  match x with
  | true
    => match y with
       | true => true
       | false => false
       end
  | false
    => match y with
       | true => false
       | false => true
       end
  end.

Ltac2 Notation x(self) "&&" y(thunk(self)) : 2 :=
  match x with
  | true => y ()
  | false => false
  end.

Ltac2 Notation x(self) "||" y(thunk(self)) : 3 :=
  match x with
  | true => true
  | false => y ()
  end.

#[deprecated(note="Use Bool.equal", since="8.14")]
Ltac2 eq := equal.