Add quot and rem operations

theories/F_mu_ref_conc/lang.v

@@ -11,7 +11,8 @@ Module lang.
   Instance loc_dec_eq : EqDecision loc := _.
 
   (** ** Expressions *)
-  Inductive binop := Mul | Add | Sub | Eq | Le | Lt | Xor.
+  Inductive binop :=
+    Mul | Add | Sub | Quot | Rem  | Eq | Le | Lt | Xor.
   
   Instance binop_dec_eq : EqDecision binop.
   Proof. solve_decision. Defined.
@@ -108,6 +109,8 @@ Module lang.
     | Mul, LitV (Nat a), LitV (Nat b) => Some $ LitV (Nat (a * b))
     | Add, LitV (Nat a), LitV (Nat b) => Some $ LitV (Nat (a + b))
     | Sub, LitV (Nat a), LitV (Nat b) => Some $ LitV (Nat (a - b))
+    | Quot, LitV (Nat a), LitV (Nat b) => Some $ LitV (Nat (a / b)%nat)
+    | Rem, LitV (Nat a), LitV (Nat b) => Some $ LitV (Nat (a `mod` b))
     | Eq, LitV (Nat a), LitV (Nat b) => Some $ LitV (Bool (if decide (a = b) then true else false))
     | Eq, LitV (Bool a), LitV (Bool b) => Some $ LitV (Bool (eqb a b))
     | Eq, LitV (Loc l1), LitV (Loc l2) => Some $ LitV (Bool (if decide (l1 = l2) then true else false))
@@ -181,9 +184,9 @@ Module lang.
   Instance binop_countable : Countable binop.
   Proof.
    refine (inj_countable' (λ op, match op with
-    | Mul => 0 | Add => 1 | Sub => 2 | Eq => 3 | Le => 4 | Lt => 5 | Xor => 6
+    | Mul => 0 | Add => 1 | Sub => 2 | Eq => 3 | Le => 4 | Lt => 5 | Xor => 6 | Quot => 7 | Rem => 8
     end) (λ n, match n with
-    | 0 => Mul | 1 => Add | 2 => Sub | 3 => Eq | 4 => Le | 5 => Lt | _ => Xor
+    | 0 => Mul | 1 => Add | 2 => Sub | 3 => Eq | 4 => Le | 5 => Lt | 6 => Xor | 7 => Quot | _ => Rem
     end) _); by intros [].
   Qed.
 

theories/F_mu_ref_conc/notation.v

@@ -61,6 +61,9 @@ Notation "e1 = e2" := (BinOp Eq e1%E e2%E) (at level 70) : expr_scope.
 Notation "e1 ⊕ e2" := (BinOp Xor e1%E e2%E) (at level 70) : expr_scope.
 Notation "¬ e" := (BinOp Xor e%E (Lit (Bool true))) (at level 75, right associativity) : expr_scope.
 
+Notation "e1 / e2" := (BinOp Quot e1%E e2%E) : expr_scope.
+Notation "e1 `mod` e2" := (BinOp Rem e1%E e2%E) : expr_scope.
+
 (* The unicode ← is already part of the notation "_ ← _; _" for bind. *)
 Notation "e1 <- e2" := (Store e1%E e2%E) (at level 80) : expr_scope.