switch the language over to integers

tests.v is temporarily broken

heap_lang/derived.v

@@ -32,28 +32,28 @@ Proof.
   by rewrite -wp_let //= ?gsubst_correct ?subst_empty ?to_of_val.
 Qed.
 
-Lemma wp_le E (n1 n2 : nat) P Q :
+Lemma wp_le E (n1 n2 : Z) P Q :
   (n1 ≤ n2 → P ⊑ ▷ Q (LitV $ LitBool true)) →
   (n2 < n1 → P ⊑ ▷ Q (LitV $ LitBool false)) →
-  P ⊑ wp E (BinOp LeOp (Lit $ LitNat n1) (Lit $ LitNat n2)) Q.
+  P ⊑ wp E (BinOp LeOp (Lit $ LitInt n1) (Lit $ LitInt n2)) Q.
 Proof.
   intros. rewrite -wp_bin_op //; [].
   destruct (bool_decide_reflect (n1 ≤ n2)); by eauto with omega.
 Qed.
 
-Lemma wp_lt E (n1 n2 : nat) P Q :
+Lemma wp_lt E (n1 n2 : Z) P Q :
   (n1 < n2 → P ⊑ ▷ Q (LitV $ LitBool true)) →
   (n2 ≤ n1 → P ⊑ ▷ Q (LitV $ LitBool false)) →
-  P ⊑ wp E (BinOp LtOp (Lit $ LitNat n1) (Lit $ LitNat n2)) Q.
+  P ⊑ wp E (BinOp LtOp (Lit $ LitInt n1) (Lit $ LitInt n2)) Q.
 Proof.
   intros. rewrite -wp_bin_op //; [].
   destruct (bool_decide_reflect (n1 < n2)); by eauto with omega.
 Qed.
 
-Lemma wp_eq E (n1 n2 : nat) P Q :
+Lemma wp_eq E (n1 n2 : Z) P Q :
   (n1 = n2 → P ⊑ ▷ Q (LitV $ LitBool true)) →
   (n1 ≠ n2 → P ⊑ ▷ Q (LitV $ LitBool false)) →
-  P ⊑ wp E (BinOp EqOp (Lit $ LitNat n1) (Lit $ LitNat n2)) Q.
+  P ⊑ wp E (BinOp EqOp (Lit $ LitInt n1) (Lit $ LitInt n2)) Q.
 Proof.
   intros. rewrite -wp_bin_op //; [].
   destruct (bool_decide_reflect (n1 = n2)); by eauto with omega.

heap_lang/heap_lang.v

@@ -2,13 +2,15 @@ Require Export program_logic.language prelude.strings.
 Require Import prelude.gmap.
 
 Module heap_lang.
+Open Scope Z_scope.
+
 (** Expressions and vals. *)
 Definition loc := positive. (* Really, any countable type. *)
 
 Inductive base_lit : Set :=
-  | LitNat (n : nat) | LitBool (b : bool) | LitUnit.
+  | LitInt (n : Z) | LitBool (b : bool) | LitUnit.
 Inductive un_op : Set :=
-  | NegOp.
+  | NegOp | MinusUnOp.
 Inductive bin_op : Set :=
   | PlusOp | MinusOp | LeOp | LtOp | EqOp.
 
@@ -152,16 +154,17 @@ Fixpoint subst (e : expr) (x : string) (v : val) : expr :=
 Definition un_op_eval (op : un_op) (l : base_lit) : option base_lit :=
   match op, l with
   | NegOp, LitBool b => Some (LitBool (negb b))
+  | MinusUnOp, LitInt n => Some (LitInt (- n))
   | _, _ => None
   end.
 
 Definition bin_op_eval (op : bin_op) (l1 l2 : base_lit) : option base_lit :=
   match op, l1, l2 with
-  | PlusOp, LitNat n1, LitNat n2 => Some $ LitNat (n1 + n2)
-  | MinusOp, LitNat n1, LitNat n2 => Some $ LitNat (n1 - n2)
-  | LeOp, LitNat n1, LitNat n2 => Some $ LitBool $ bool_decide (n1 ≤ n2)
-  | LtOp, LitNat n1, LitNat n2 => Some $ LitBool $ bool_decide (n1 < n2)
-  | EqOp, LitNat n1, LitNat n2 => Some $ LitBool $ bool_decide (n1 = n2)
+  | PlusOp, LitInt n1, LitInt n2 => Some $ LitInt (n1 + n2)
+  | MinusOp, LitInt n1, LitInt n2 => Some $ LitInt (n1 - n2)
+  | LeOp, LitInt n1, LitInt n2 => Some $ LitBool $ bool_decide (n1 ≤ n2)
+  | LtOp, LitInt n1, LitInt n2 => Some $ LitBool $ bool_decide (n1 < n2)
+  | EqOp, LitInt n1, LitInt n2 => Some $ LitBool $ bool_decide (n1 = n2)
   | _, _, _ => None
   end.
 

heap_lang/notation.v

@@ -4,7 +4,7 @@ Delimit Scope lang_scope with L.
 Bind Scope lang_scope with expr val.
 Arguments wp {_ _} _ _%L _.
 
-Coercion LitNat : nat >-> base_lit.
+Coercion LitInt : Z >-> base_lit.
 Coercion LitBool : bool >-> base_lit.
 (** No coercion from base_lit to expr. This makes is slightly easier to tell
    apart language and Coq expressions. *)
@@ -22,6 +22,8 @@ Notation "e1 + e2" := (BinOp PlusOp e1%L e2%L)
   (at level 50, left associativity) : lang_scope.
 Notation "e1 - e2" := (BinOp MinusOp e1%L e2%L)
   (at level 50, left associativity) : lang_scope.
+Notation "- e" := (UnOp MinusUnOp e%L) (at level 35, right associativity) : lang_scope.
+Notation "~ e" := (UnOp NegOp e%L) (at level 75, right associativity) : lang_scope.
 Notation "e1 ≤ e2" := (BinOp LeOp e1%L e2%L) (at level 70) : lang_scope.
 Notation "e1 < e2" := (BinOp LtOp e1%L e2%L) (at level 70) : lang_scope.
 Notation "e1 = e2" := (BinOp EqOp e1%L e2%L) (at level 70) : lang_scope.