Merge branch 'master' of https://gitlab.mpi-sws.org/FP/iris-coq

_CoqProject

@@ -34,7 +34,7 @@ theories/base_logic/hlist.v
 theories/base_logic/soundness.v
 theories/base_logic/double_negation.v
 theories/base_logic/deprecated.v
-theories/base_logic/fix.v
+theories/base_logic/fixpoint.v
 theories/base_logic/lib/iprop.v
 theories/base_logic/lib/own.v
 theories/base_logic/lib/saved_prop.v

opam

@@ -13,5 +13,5 @@ remove: ["sh" "-c" "rm -rf '%{lib}%/coq/user-contrib/iris'"]
 depends: [
   "coq" { (>= "8.6.1" & < "8.8~") }
   "coq-mathcomp-ssreflect" { ((>= "1.6.1" & < "1.7~") | (= "dev")) }
-  "coq-stdpp" { ((= "dev.2017-09-18.1") | (= "dev")) }
+  "coq-stdpp" { ((= "dev.2017-09-18.4") | (= "dev")) }
 ]

theories/base_logic/fix.v → theories/base_logic/fixpoint.v

@@ -5,9 +5,9 @@ Import uPred.
 
 (** Least and greatest fixpoint of a monotone function, defined entirely inside
     the logic.  *)
-
-Definition uPred_mono_pred {M A} (F : (A → uPred M) → (A → uPred M)) :=
-  ∀ Φ Ψ, ((□ ∀ x, Φ x → Ψ x) → ∀ x, F Φ x → F Ψ x)%I.
+Class BIMonoPred {M A} (F : (A → uPred M) → (A → uPred M)) :=
+  bi_mono_pred Φ Ψ : ((□ ∀ x, Φ x -∗ Ψ x) → ∀ x, F Φ x -∗ F Ψ x)%I.
+Arguments bi_mono_pred {_ _ _ _} _ _.
 
 Definition uPred_least_fixpoint {M A} (F : (A → uPred M) → (A → uPred M))
     (x : A) : uPred M :=
@@ -18,13 +18,12 @@ Definition uPred_greatest_fixpoint {M A} (F : (A → uPred M) → (A → uPred M
   (∃ Φ, □ (∀ x, Φ x → F Φ x) ∧ Φ x)%I.
 
 Section least.
-  Context {M : ucmraT}.
-  Context {A} (F : (A → uPred M) → (A → uPred M)) (Hmono : uPred_mono_pred F).
+  Context {M A} (F : (A → uPred M) → (A → uPred M)) `{!BIMonoPred F}.
 
   Lemma least_fixpoint_unfold_2 x : F (uPred_least_fixpoint F) x ⊢ uPred_least_fixpoint F x.
   Proof.
     iIntros "HF" (Φ) "#Hincl".
-    iApply "Hincl". iApply (Hmono _ Φ); last done.
+    iApply "Hincl". iApply (bi_mono_pred _ Φ); last done.
     iIntros "!#" (y) "Hy". iApply "Hy". done.
   Qed.
 
@@ -32,7 +31,7 @@ Section least.
     uPred_least_fixpoint F x ⊢ F (uPred_least_fixpoint F) x.
   Proof.
     iIntros "HF". iApply "HF". iIntros "!#" (y) "Hy".
-    iApply Hmono; last done. iIntros "!#" (z) "?".
+    iApply bi_mono_pred; last done. iIntros "!#" (z) "?".
     by iApply least_fixpoint_unfold_2.
   Qed.
 
@@ -48,13 +47,13 @@ Section least.
 End least.
 
 Section greatest.
-  Context {M : ucmraT} {A} (F : (A → uPred M) → (A → uPred M)) (Hmono : uPred_mono_pred F).
+  Context {M A} (F : (A → uPred M) → (A → uPred M)) `{!BIMonoPred F}.
 
   Lemma greatest_fixpoint_unfold_1 x :
     uPred_greatest_fixpoint F x ⊢ F (uPred_greatest_fixpoint F) x.
   Proof.
     iDestruct 1 as (Φ) "[#Hincl HΦ]".
-    iApply (Hmono Φ (uPred_greatest_fixpoint F)).
+    iApply (bi_mono_pred Φ (uPred_greatest_fixpoint F)).
     - iIntros "!#" (y) "Hy". iExists Φ. auto.
     - by iApply "Hincl".
   Qed.
@@ -63,7 +62,7 @@ Section greatest.
     F (uPred_greatest_fixpoint F) x ⊢ uPred_greatest_fixpoint F x.
   Proof.
     iIntros "HF". iExists (F (uPred_greatest_fixpoint F)).
-    iIntros "{$HF} !#" (y) "Hy". iApply (Hmono with "[] Hy").
+    iIntros "{$HF} !#" (y) "Hy". iApply (bi_mono_pred with "[] Hy").
     iIntros "!#" (z) "?". by iApply greatest_fixpoint_unfold_1.
   Qed.
 

theories/heap_lang/lang.v

@@ -139,6 +139,84 @@ Proof.
  refine (λ v v', cast_if (decide (of_val v = of_val v'))); abstract naive_solver.
 Defined.
 
+Instance base_lit_countable : Countable base_lit.
+Proof.
+ refine (inj_countable' (λ l, match l with
+  | LitInt n => inl (inl n) | LitBool b => inl (inr b)
+  | LitUnit => inr (inl ()) | LitLoc l => inr (inr l)
+  end) (λ l, match l with
+  | inl (inl n) => LitInt n | inl (inr b) => LitBool b
+  | inr (inl ()) => LitUnit | inr (inr l) => LitLoc l
+  end) _); by intros [].
+Qed.
+Instance un_op_finite : Countable un_op.
+Proof.
+ refine (inj_countable' (λ op, match op with NegOp => 0 | MinusUnOp => 1 end)
+  (λ n, match n with 0 => NegOp | _ => MinusUnOp end) _); by intros [].
+Qed.
+Instance bin_op_countable : Countable bin_op.
+Proof.
+ refine (inj_countable' (λ op, match op with
+  | PlusOp => 0 | MinusOp => 1 | LeOp => 2 | LtOp => 3 | EqOp => 4
+  end) (λ n, match n with
+  | 0 => PlusOp | 1 => MinusOp | 2 => LeOp | 3 => LtOp | _ => EqOp
+  end) _); by intros [].
+Qed.
+Instance binder_countable : Countable binder.
+Proof.
+ refine (inj_countable' (λ b, match b with BNamed s => Some s | BAnon => None end)
+  (λ b, match b with Some s => BNamed s | None => BAnon end) _); by intros [].
+Qed.
+Instance expr_countable : Countable expr.
+Proof.
+ set (enc := fix go e :=
+  match e with
+  | Var x => GenLeaf (inl (inl x))
+  | Rec f x e => GenNode 0 [GenLeaf (inl (inr f)); GenLeaf (inl (inr x)); go e]
+  | App e1 e2 => GenNode 1 [go e1; go e2]
+  | Lit l => GenLeaf (inr (inl l))
+  | UnOp op e => GenNode 2 [GenLeaf (inr (inr (inl op))); go e]
+  | BinOp op e1 e2 => GenNode 3 [GenLeaf (inr (inr (inr op))); go e1; go e2]
+  | If e0 e1 e2 => GenNode 4 [go e0; go e1; go e2]
+  | Pair e1 e2 => GenNode 5 [go e1; go e2]
+  | Fst e => GenNode 6 [go e]
+  | Snd e => GenNode 7 [go e]
+  | InjL e => GenNode 8 [go e]
+  | InjR e => GenNode 9 [go e]
+  | Case e0 e1 e2 => GenNode 10 [go e0; go e1; go e2]
+  | Fork e => GenNode 11 [go e]
+  | Alloc e => GenNode 12 [go e]
+  | Load e => GenNode 13 [go e]
+  | Store e1 e2 => GenNode 14 [go e1; go e2]
+  | CAS e0 e1 e2 => GenNode 15 [go e0; go e1; go e2]
+  end).
+ set (dec := fix go e :=
+  match e with
+  | GenLeaf (inl (inl x)) => Var x
+  | GenNode 0 [GenLeaf (inl (inr f)); GenLeaf (inl (inr x)); e] => Rec f x (go e)
+  | GenNode 1 [e1; e2] => App (go e1) (go e2)
+  | GenLeaf (inr (inl l)) => Lit l
+  | GenNode 2 [GenLeaf (inr (inr (inl op))); e] => UnOp op (go e)
+  | GenNode 3 [GenLeaf (inr (inr (inr op))); e1; e2] => BinOp op (go e1) (go e2)
+  | GenNode 4 [e0; e1; e2] => If (go e0) (go e1) (go e2)
+  | GenNode 5 [e1; e2] => Pair (go e1) (go e2)
+  | GenNode 6 [e] => Fst (go e)
+  | GenNode 7 [e] => Snd (go e)
+  | GenNode 8 [e] => InjL (go e)
+  | GenNode 9 [e] => InjR (go e)
+  | GenNode 10 [e0; e1; e2] => Case (go e0) (go e1) (go e2)
+  | GenNode 11 [e] => Fork (go e)
+  | GenNode 12 [e] => Alloc (go e)
+  | GenNode 13 [e] => Load (go e)
+  | GenNode 14 [e1; e2] => Store (go e1) (go e2)
+  | GenNode 15 [e0; e1; e2] => CAS (go e0) (go e1) (go e2)
+  | _ => Lit LitUnit (* dummy *)
+  end).
+ refine (inj_countable' enc dec _). intros e. induction e; f_equal/=; auto.
+Qed.
+Instance val_countable : Countable val.
+Proof. refine (inj_countable of_val to_val _); auto using to_of_val. Qed.
+
 Instance expr_inhabited : Inhabited expr := populate (Lit LitUnit).
 Instance val_inhabited : Inhabited val := populate (LitV LitUnit).