Replace omega with lia

.gitignore

@@ -22,3 +22,4 @@ Deep.ml*
 Deeper.ml*
 DeeperWithFail.ml*
 *.dir-locals.el
+*.cache

CompilerCorrectness.v

@@ -1538,7 +1538,7 @@ Proof.
     repeat erewrite interp_agree in * by eassumption; eauto 10.
 
   assert (Hnu : noUnderscoreArith e = true) by assumption.
-  eapply flatten_Assign with (tempCount := 0) (dst := x) in Hnu; eauto.
+  eapply flatten_Assign with (tempCount := 0) (dst := x) in Hnu; try eassumption.
   first_order.
   do 3 eexists.
   split.
@@ -1659,8 +1659,8 @@ Proof.
     simplify; propositional; eauto.
 
   invert H1; simplify; subst.
-  assert (noUnderscore c2 = true) by eauto.
-  eapply flatten_ok' in H5; eauto.
+  assert (noUnderscore c2 = true) by eauto 4.
+  eapply flatten_ok' in H5; eauto 4.
   first_order.
   cases vc2; simplify; subst.
   pose proof (plug_total x0 (flattenContext C)).

FrapWithoutSets.v

@@ -1,4 +1,4 @@
-Require Import Eqdep String Arith Omega Program Sets Relations Map Var Invariant Bool ModelCheck.
+Require Import Eqdep String Arith Lia Program Sets Relations Map Var Invariant Bool ModelCheck.
 Export Ascii String Arith Sets Relations Map Var Invariant Bool ModelCheck.
 Require Import List.
 Export List ListNotations.
@@ -177,8 +177,8 @@ Ltac doSubtract :=
 Ltac simpl_maps :=
   repeat match goal with
          | [ |- context[add ?m ?k1 ?v $? ?k2] ] =>
-           (rewrite (@lookup_add_ne _ _ m k1 k2 v) by (congruence || omega))
-           || (rewrite (@lookup_add_eq _ _ m k1 k2 v) by (congruence || omega))
+           (rewrite (@lookup_add_ne _ _ m k1 k2 v) by (congruence || lia))
+           || (rewrite (@lookup_add_eq _ _ m k1 k2 v) by (congruence || lia))
          end.
 
 Ltac simplify := repeat (unifyTails; pose proof I);
@@ -203,7 +203,7 @@ Ltac linear_arithmetic := intros;
            | [ _ : context[min ?a ?b] |- _ ] =>
              let Heq := fresh "Heq" in destruct (Min.min_spec a b) as [[? Heq] | [? Heq]];
                rewrite Heq in *; clear Heq
-           end; omega.
+           end; lia.
 
 Ltac equality := intuition congruence.
 
@@ -333,8 +333,8 @@ Inductive ordering (n m : nat) :=
 | Gt (_ : n > m).
 
 Local Hint Constructors ordering.
-Local Hint Extern 1 (_ < _) => omega.
-Local Hint Extern 1 (_ > _) => omega.
+Local Hint Extern 1 (_ < _) => lia.
+Local Hint Extern 1 (_ > _) => lia.
 
 Theorem totally_ordered : forall n m, ordering n m.
 Proof.

HoareLogic.v

@@ -170,6 +170,7 @@ Qed.
 (* BEGIN syntax macros that won't be explained *)
 Coercion Const : nat >-> exp.
 Coercion Var : string >-> exp.
+Declare Scope cmd_scope.
 Notation "*[ e ]" := (Read e) : cmd_scope.
 Infix "+" := Plus : cmd_scope.
 Infix "-" := Minus : cmd_scope.
@@ -189,6 +190,7 @@ Notation "{{ I }} 'while' b 'loop' body 'done'" := (While_ I b body) (at level 7
 Notation "'assert' {{ I }}" := (Assert I) (at level 75).
 Delimit Scope cmd_scope with cmd.
 
+Declare Scope reset_scope.
 Infix "+" := plus : reset_scope.
 Infix "-" := Init.Nat.sub : reset_scope.
 Infix "*" := mult : reset_scope.
@@ -351,8 +353,6 @@ Proof.
   apply HtAssign.
   simplify.
   t.
-  ring [H0].
-  (* This variant of [ring] suggests a hypothesis to use in the proof. *)
   simplify.
   t.
 Qed.
@@ -368,7 +368,6 @@ Theorem fact_ok_snazzy : forall n,
   {{_&v ~> v $! "acc" = fact n}}.
 Proof.
   ht.
-  ring [H0].
 Qed.
 
 (** ** Selection sort *)
@@ -384,10 +383,10 @@ Proof.
   ht.
 Qed.
 
-Hint Resolve leq_f.
-Hint Extern 1 (@eq nat _ _) => linear_arithmetic.
-Hint Extern 1 (_ < _) => linear_arithmetic.
-Hint Extern 1 (_ <= _) => linear_arithmetic.
+Hint Resolve leq_f : core.
+Hint Extern 1 (@eq nat _ _) => linear_arithmetic : core.
+Hint Extern 1 (_ < _) => linear_arithmetic : core.
+Hint Extern 1 (_ <= _) => linear_arithmetic : core.
 (* We also register [linear_arithmetic] as a step to try during proof search. *)
 
 (* These invariants are fairly hairy, but probably the best way to understand
@@ -471,7 +470,7 @@ Inductive step : heap * valuation * cmd -> heap * valuation * cmd -> Prop :=
   a h v
   -> step (h, v, Assert a) (h, v, Skip).
 
-Hint Constructors step.
+Hint Constructors step : core.
 
 Definition trsys_of (st : heap * valuation * cmd) := {|
   Initial := {st};

TypesAndMutation.v

@@ -205,7 +205,7 @@ Module References.
 
       -> heapty ht h.
                  
-  Hint Constructors value plug step0 step hasty heapty.
+  Hint Constructors value plug step0 step hasty heapty : core.
 
 
   (* Perhaps surprisingly, this language admits well-typed, nonterminating
@@ -222,7 +222,7 @@ Module References.
     repeat (econstructor; simplify).
   Qed.
 
-  Hint Resolve lookup_add_eq.
+  Hint Resolve lookup_add_eq : core.
 
   Ltac loopy := propositional; subst; simplify;
     repeat match goal with
@@ -293,7 +293,7 @@ Module References.
 
   Ltac t := simplify; propositional; repeat (t0; simplify); try equality; eauto 7.
 
-  Hint Extern 2 (exists _ : _ * _, _) => eexists (_ $+ (_, _), _).
+  Hint Extern 2 (exists _ : _ * _, _) => eexists (_ $+ (_, _), _) : core.
 
   (* Progress is quite straightforward. *)
   Lemma progress : forall ht h, heapty ht h
@@ -323,7 +323,7 @@ Module References.
     cases (x ==v x'); simplify; eauto.
   Qed.
 
-  Hint Resolve weakening_override.
+  Hint Resolve weakening_override : core.
 
   Lemma weakening : forall H G e t,
     hasty H G e t
@@ -333,7 +333,7 @@ Module References.
     induct 1; t.
   Qed.
 
-  Hint Resolve weakening.
+  Hint Resolve weakening : core.
 
   Lemma hasty_change : forall H G e t,
     hasty H G e t
@@ -343,7 +343,7 @@ Module References.
     t.
   Qed.
 
-  Hint Resolve hasty_change.
+  Hint Resolve hasty_change : core.
 
   Lemma substitution : forall H G x t' e t e',
     hasty H (G $+ (x, t')) e t
@@ -353,7 +353,7 @@ Module References.
     induct 1; t.
   Qed.
 
-  Hint Resolve substitution.
+  Hint Resolve substitution : core.
 
   (* A new property: expanding the heap typing preserves typing. *)
   Lemma heap_weakening : forall H G e t,
@@ -364,7 +364,7 @@ Module References.
     induct 1; t.
   Qed.
 
-  Hint Resolve heap_weakening.
+  Hint Resolve heap_weakening : core.
 
   (* A property about extending heap typings *)
   Lemma heap_override : forall H h k t t0 l,
@@ -378,7 +378,7 @@ Module References.
     apply H2 in H0; t.
   Qed.
 
-  Hint Resolve heap_override.
+  Hint Resolve heap_override : core.
 
   (* A higher-level property, stated via [heapty] *)
   Lemma heapty_extend : forall H h l t v,
@@ -394,12 +394,11 @@ Module References.
     invert H0; eauto 6.
     apply H3 in H0; t.
 
-    rewrite lookup_add_ne by linear_arithmetic.
     apply H4.
     linear_arithmetic.
   Qed.
 
-  Hint Resolve heapty_extend.
+  Hint Resolve heapty_extend : core.
 
   (* The old cases of preservation proceed as before, and we need to fiddle with
    * the heap in the new cases.  Note a crucial change to the theorem statement:
@@ -445,7 +444,7 @@ Module References.
     assumption.
   Qed.
 
-  Hint Resolve preservation0.
+  Hint Resolve preservation0 : core.
 
   (* This lemma gets more complicated, too, to accommodate heap typings. *)
   Lemma generalize_plug : forall H e1 C e1',
@@ -482,7 +481,7 @@ Module References.
     eauto.
   Qed.
 
-  Hint Resolve progress preservation.
+  Hint Resolve progress preservation : core.
 
   (* We'll need this fact for the base case of invariant induction. *)
   Lemma heapty_empty : heapty $0 $0.
@@ -490,7 +489,7 @@ Module References.
     exists 0; t.
   Qed.
 
-  Hint Resolve heapty_empty.
+  Hint Resolve heapty_empty : core.
 
   (* Now there isn't much more to the proof of type safety.  The crucial overall
    * insight is a strengthened invariant that quantifies existentially over a
@@ -504,7 +503,7 @@ Module References.
     apply invariant_weaken with (invariant1 := fun he' => exists H,
                                                    hasty H $0 (snd he') t
                                                    /\ heapty H (fst he')); eauto.
-    apply invariant_induction; simplify; eauto.
+    apply invariant_induction; simplify.
     propositional.
     subst; simplify.
     eauto.
@@ -593,7 +592,7 @@ Module GarbageCollection.
 
     -> step (h, e) (h', e).
 
-  Hint Constructors step.
+  Hint Constructors step : core.
 
   Definition trsys_of (e : exp) := {|
     Initial := {($0, e)};
@@ -632,10 +631,10 @@ Module GarbageCollection.
     assumption.
   Qed.
 
-  Hint Resolve reachableLocFromExp_trans.
-  Hint Extern 1 (_ \in _) => simplify; solve [ sets ].
-  Hint Extern 1 (_ \subseteq _) => simplify; solve [ sets ].
-  Hint Constructors reachableLoc reachableLocFromExp.
+  Hint Resolve reachableLocFromExp_trans : core.
+  Hint Extern 1 (_ \in _) => simplify; solve [ sets ] : core.
+  Hint Extern 1 (_ \subseteq _) => simplify; solve [ sets ] : core.
+  Hint Constructors reachableLoc reachableLocFromExp : core.
 
   (* Typing is preserved by moving to a heap typing that only needs to preserve
    * the mappings for *reachable* locations. *)
@@ -685,9 +684,9 @@ Module GarbageCollection.
 
     (* The case for the original [step] rule proceeds exactly the same way as
      * before. *)
-    eapply generalize_plug in H; eauto.
+    eapply generalize_plug in H; eauto 3.
     invert H; propositional.
-    eapply preservation0 in H6; eauto.
+    eapply preservation0 in H6; eauto 3.
     invert H6; propositional.
     eauto.
 
@@ -731,7 +730,7 @@ Module GarbageCollection.
     equality.
   Qed.
 
-  Hint Resolve progress preservation.
+  Hint Resolve progress preservation : core.
 
   (* The safety proof itself is anticlimactic, looking the same as before. *)
   Theorem safety : forall e t, hasty $0 $0 e t
@@ -743,7 +742,7 @@ Module GarbageCollection.
     apply invariant_weaken with (invariant1 := fun he' => exists H,
                                                    hasty H $0 (snd he') t
                                                    /\ heapty H (fst he')); eauto.
-    apply invariant_induction; simplify; eauto.
+    apply invariant_induction; simplify.
     propositional.
     subst; simplify.
     eauto.