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A big pass to stop Coq from complaining about missing locality annotations

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Adam Chlipala 2022-03-07 13:48:40 -05:00
parent b643755628
commit f3211734b9
16 changed files with 80 additions and 80 deletions
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24
AbstractInterpret.v
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@ -56,7 +56,7 @@ Record absint_sound (a : absint) : Prop := {
-> a.(Represents) n (a.(Join) x y) -> a.(Represents) n (a.(Join) x y)
}. }.
Hint Resolve TopSound ConstSound AddSound SubtractSound MultiplySound Global Hint Resolve TopSound ConstSound AddSound SubtractSound MultiplySound
AddMonotone SubtractMonotone MultiplyMonotone AddMonotone SubtractMonotone MultiplyMonotone
JoinSoundLeft JoinSoundRight : core. JoinSoundLeft JoinSoundRight : core.
@ -103,7 +103,7 @@ Proof.
cases (s $? x); equality. cases (s $? x); equality.
Qed. Qed.
Hint Resolve subsumed_refl : core. Global Hint Resolve subsumed_refl : core.
Lemma subsumed_use : forall a (s s' : astate a) x n t0 t, Lemma subsumed_use : forall a (s s' : astate a) x n t0 t,
s $? x = Some t0 s $? x = Some t0
@ -131,7 +131,7 @@ Proof.
equality. equality.
Qed. Qed.
Hint Resolve subsumed_use subsumed_use_empty : core. Global Hint Resolve subsumed_use subsumed_use_empty : core.
Lemma subsumed_trans : forall a (s1 s2 s3 : astate a), Lemma subsumed_trans : forall a (s1 s2 s3 : astate a),
subsumed s1 s2 subsumed s1 s2
@ -156,7 +156,7 @@ Proof.
invert H0; eauto. invert H0; eauto.
Qed. Qed.
Hint Resolve subsumed_merge_left : core. Global Hint Resolve subsumed_merge_left : core.
Lemma subsumed_add : forall a, absint_sound a Lemma subsumed_add : forall a, absint_sound a
-> forall (s1 s2 : astate a) x v1 v2, -> forall (s1 s2 : astate a) x v1 v2,
@ -170,7 +170,7 @@ Proof.
specialize (H0 x0); eauto. specialize (H0 x0); eauto.
Qed. Qed.
Hint Resolve subsumed_add : core. Global Hint Resolve subsumed_add : core.
(** * Flow-sensitive analysis *) (** * Flow-sensitive analysis *)
@ -190,7 +190,7 @@ Proof.
invert H1; eauto. invert H1; eauto.
Qed. Qed.
Hint Resolve compatible_add : core. Global Hint Resolve compatible_add : core.
(* A similar result follows about soundness of expression interpretation. *) (* A similar result follows about soundness of expression interpretation. *)
Theorem absint_interp_ok : forall a, absint_sound a Theorem absint_interp_ok : forall a, absint_sound a
@ -208,7 +208,7 @@ Proof.
assumption. assumption.
Qed. Qed.
Hint Resolve absint_interp_ok : core. Global Hint Resolve absint_interp_ok : core.
Definition astates (a : absint) := fmap cmd (astate a). Definition astates (a : absint) := fmap cmd (astate a).
@ -281,7 +281,7 @@ Inductive abs_step a : astate a * cmd -> astate a * cmd -> Prop :=
-> ss $? c' = Some s' -> ss $? c' = Some s'
-> abs_step (s, c) (s', c'). -> abs_step (s, c) (s', c').
Hint Constructors abs_step : core. Global Hint Constructors abs_step : core.
Definition absint_trsys a (c : cmd) := {| Definition absint_trsys a (c : cmd) := {|
Initial := {($0, c)}; Initial := {($0, c)};
@ -293,7 +293,7 @@ Inductive Rabsint a : valuation * cmd -> astate a * cmd -> Prop :=
compatible s v compatible s v
-> Rabsint (v, c) (s, c). -> Rabsint (v, c) (s, c).
Hint Constructors abs_step Rabsint : core. Global Hint Constructors abs_step Rabsint : core.
Theorem absint_simulates : forall a v c, Theorem absint_simulates : forall a v c,
absint_sound a absint_sound a
@ -351,7 +351,7 @@ Proof.
unfold subsumeds; simplify; eauto. unfold subsumeds; simplify; eauto.
Qed. Qed.
Hint Resolve subsumeds_refl : core. Global Hint Resolve subsumeds_refl : core.
Lemma subsumeds_add : forall a (ss1 ss2 : astates a) c s1 s2, Lemma subsumeds_add : forall a (ss1 ss2 : astates a) c s1 s2,
subsumeds ss1 ss2 subsumeds ss1 ss2
@ -363,7 +363,7 @@ Proof.
invert H1; eauto. invert H1; eauto.
Qed. Qed.
Hint Resolve subsumeds_add : core. Global Hint Resolve subsumeds_add : core.
Lemma subsumeds_empty : forall a (ss : astates a), Lemma subsumeds_empty : forall a (ss : astates a),
subsumeds $0 ss. subsumeds $0 ss.
@ -459,7 +459,7 @@ Proof.
cases (s $? x); eauto. cases (s $? x); eauto.
Qed. Qed.
Hint Resolve absint_interp_monotone : core. Global Hint Resolve absint_interp_monotone : core.
Lemma absint_step_monotone : forall a, absint_sound a Lemma absint_step_monotone : forall a, absint_sound a
-> forall (s : astate a) c wrap ss, -> forall (s : astate a) c wrap ss,

2
ConcurrentSeparationLogic.v
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@ -474,7 +474,7 @@ Ltac use H := (eapply use_lemma; [ eapply H | cancel; auto ])
Ltac heq := intros; apply himp_heq; split. Ltac heq := intros; apply himp_heq; split.
(* Fancy theorem to help us rewrite within preconditions and postconditions *) (* Fancy theorem to help us rewrite within preconditions and postconditions *)
Instance hoare_triple_morphism : forall linvs A, Local Instance hoare_triple_morphism : forall linvs A,
Proper (heq ==> eq ==> (eq ==> heq) ==> iff) (@hoare_triple linvs A). Proper (heq ==> eq ==> (eq ==> heq) ==> iff) (@hoare_triple linvs A).
Proof. Proof.
Transparent himp. Transparent himp.

2
ConcurrentSeparationLogic_template.v
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@ -455,7 +455,7 @@ Ltac use H := (eapply use_lemma; [ eapply H | cancel ])
Ltac heq := intros; apply himp_heq; split. Ltac heq := intros; apply himp_heq; split.
(* Fancy theorem to help us rewrite within preconditions and postconditions *) (* Fancy theorem to help us rewrite within preconditions and postconditions *)
Instance hoare_triple_morphism : forall linvs A, Local Instance hoare_triple_morphism : forall linvs A,
Proper (heq ==> eq ==> (eq ==> heq) ==> iff) (@hoare_triple linvs A). Proper (heq ==> eq ==> (eq ==> heq) ==> iff) (@hoare_triple linvs A).
Proof. Proof.
Transparent himp. Transparent himp.

6
Connecting.v
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@ -769,7 +769,7 @@ Module MixedEmbedded(Import BW : BIT_WIDTH).
cases s; simp; eauto. cases s; simp; eauto.
Qed. Qed.
Instance hoare_triple_morphism : forall A, Local Instance hoare_triple_morphism : forall A,
Proper (heq ==> eq ==> (eq ==> heq) ==> iff) (@hoare_triple A). Proper (heq ==> eq ==> (eq ==> heq) ==> iff) (@hoare_triple A).
Proof. Proof.
Transparent himp. Transparent himp.
@ -874,8 +874,8 @@ Module MixedEmbedded(Import BW : BIT_WIDTH).
end; cancel. end; cancel.
Qed. Qed.
Hint Rewrite <- rev_alt. Local Hint Rewrite <- rev_alt.
Hint Rewrite rev_involutive. Local Hint Rewrite rev_involutive.
Opaque linkedList. Opaque linkedList.

4
DeepAndShallowEmbeddings.v
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@ -19,7 +19,7 @@ Local Hint Extern 1 (@eq nat _ _) => linear_arithmetic : core.
Example h0 : heap := $0 $+ (0, 2) $+ (1, 1) $+ (2, 8) $+ (3, 6). Example h0 : heap := $0 $+ (0, 2) $+ (1, 1) $+ (2, 8) $+ (3, 6).
Hint Rewrite max_l max_r using linear_arithmetic : core. Local Hint Rewrite max_l max_r using linear_arithmetic : core.
Ltac simp := repeat (simplify; subst; propositional; Ltac simp := repeat (simplify; subst; propositional;
try match goal with try match goal with
@ -1214,7 +1214,7 @@ Module DeeperWithFail.
reflexivity. reflexivity.
Qed. Qed.
Hint Rewrite firstn_nochange fold_left_firstn using linear_arithmetic : core. Local Hint Rewrite firstn_nochange fold_left_firstn using linear_arithmetic : core.
(* Here's the soundness theorem for [heapfold], relying on a hypothesis of (* Here's the soundness theorem for [heapfold], relying on a hypothesis of
* soundness for [combine]. *) * soundness for [combine]. *)

4
DeepAndShallowEmbeddings_template.v
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@ -14,7 +14,7 @@ Local Hint Extern 1 (@eq nat _ _) => linear_arithmetic : core.
Example h0 : heap := $0 $+ (0, 2) $+ (1, 1) $+ (2, 8) $+ (3, 6). Example h0 : heap := $0 $+ (0, 2) $+ (1, 1) $+ (2, 8) $+ (3, 6).
Hint Rewrite max_l max_r using linear_arithmetic : core. Local Hint Rewrite max_l max_r using linear_arithmetic : core.
Ltac simp := repeat (simplify; subst; propositional; Ltac simp := repeat (simplify; subst; propositional;
try match goal with try match goal with
@ -1044,7 +1044,7 @@ Module DeeperWithFail.
reflexivity. reflexivity.
Qed. Qed.
Hint Rewrite firstn_nochange fold_left_firstn using linear_arithmetic : core. Local Hint Rewrite firstn_nochange fold_left_firstn using linear_arithmetic : core.
Theorem heapfold_ok : forall {A : Set} (init : A) combine Theorem heapfold_ok : forall {A : Set} (init : A) combine
(ls : list nat) (f : A -> nat -> A), (ls : list nat) (f : A -> nat -> A),

16
DependentInductiveTypes.v
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@ -1091,7 +1091,7 @@ Proof.
induct s; substring. induct s; substring.
Qed. Qed.
Hint Rewrite substring_all substring_none. Local Hint Rewrite substring_all substring_none.
Lemma substring_split : forall s m, Lemma substring_split : forall s m,
substring 0 m s ++ substring m (length s - m) s = s. substring 0 m s ++ substring m (length s - m) s = s.
@ -1115,7 +1115,7 @@ Proof.
rewrite IHs1; auto. rewrite IHs1; auto.
Qed. Qed.
Hint Rewrite <- minus_n_O. Local Hint Rewrite <- minus_n_O.
Lemma substring_app_snd : forall s2 s1 n, Lemma substring_app_snd : forall s2 s1 n,
length s1 = n length s1 = n
@ -1124,7 +1124,7 @@ Proof.
induct s1; simplify; subst; simplify; auto. induct s1; simplify; subst; simplify; auto.
Qed. Qed.
Hint Rewrite substring_app_fst substring_app_snd using solve [trivial]. Local Hint Rewrite substring_app_fst substring_app_snd using solve [trivial].
(* BOREDOM'S END! *) (* BOREDOM'S END! *)
@ -1227,7 +1227,7 @@ Proof.
induct s; substring. induct s; substring.
Qed. Qed.
Hint Rewrite app_empty_end. Local Hint Rewrite app_empty_end.
Lemma substring_self : forall s n, Lemma substring_self : forall s n,
n <= 0 n <= 0
@ -1243,8 +1243,8 @@ Proof.
induct s; substring. induct s; substring.
Qed. Qed.
Hint Rewrite substring_self substring_empty using linear_arithmetic. Local Hint Rewrite substring_self substring_empty using linear_arithmetic.
Hint Rewrite substring_split. Local Hint Rewrite substring_split.
Lemma substring_split' : forall s n m, Lemma substring_split' : forall s n m,
substring n m s ++ substring (n + m) (length s - (n + m)) s substring n m s ++ substring (n + m) (length s - (n + m)) s
@ -1308,7 +1308,7 @@ Proof.
simplify; cases m; simplify; eauto using substring_suffix_emp'. simplify; cases m; simplify; eauto using substring_suffix_emp'.
Qed. Qed.
Hint Rewrite substring_stack substring_stack' substring_suffix using linear_arithmetic. Local Hint Rewrite substring_stack substring_stack' substring_suffix using linear_arithmetic.
Lemma minus_minus : forall n m1 m2, Lemma minus_minus : forall n m1 m2,
m1 + m2 <= n m1 + m2 <= n
@ -1322,7 +1322,7 @@ Proof.
linear_arithmetic. linear_arithmetic.
Qed. Qed.
Hint Rewrite minus_minus plus_n_Sm' using linear_arithmetic. Local Hint Rewrite minus_minus plus_n_Sm' using linear_arithmetic.
(* BOREDOM VANQUISHED! *) (* BOREDOM VANQUISHED! *)

16
DependentInductiveTypes_template.v
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@ -507,7 +507,7 @@ Proof.
induct s; substring. induct s; substring.
Qed. Qed.
Hint Rewrite substring_all substring_none. Local Hint Rewrite substring_all substring_none.
Lemma substring_split : forall s m, Lemma substring_split : forall s m,
substring 0 m s ++ substring m (length s - m) s = s. substring 0 m s ++ substring m (length s - m) s = s.
@ -531,7 +531,7 @@ Proof.
rewrite IHs1; auto. rewrite IHs1; auto.
Qed. Qed.
Hint Rewrite <- minus_n_O. Local Hint Rewrite <- minus_n_O.
Lemma substring_app_snd : forall s2 s1 n, Lemma substring_app_snd : forall s2 s1 n,
length s1 = n length s1 = n
@ -540,7 +540,7 @@ Proof.
induct s1; simplify; subst; simplify; auto. induct s1; simplify; subst; simplify; auto.
Qed. Qed.
Hint Rewrite substring_app_fst substring_app_snd using solve [trivial]. Local Hint Rewrite substring_app_fst substring_app_snd using solve [trivial].
(* BOREDOM'S END! *) (* BOREDOM'S END! *)
@ -609,7 +609,7 @@ Proof.
induct s; substring. induct s; substring.
Qed. Qed.
Hint Rewrite app_empty_end. Local Hint Rewrite app_empty_end.
Lemma substring_self : forall s n, Lemma substring_self : forall s n,
n <= 0 n <= 0
@ -625,8 +625,8 @@ Proof.
induct s; substring. induct s; substring.
Qed. Qed.
Hint Rewrite substring_self substring_empty using linear_arithmetic. Local Hint Rewrite substring_self substring_empty using linear_arithmetic.
Hint Rewrite substring_split. Local Hint Rewrite substring_split.
Lemma substring_split' : forall s n m, Lemma substring_split' : forall s n m,
substring n m s ++ substring (n + m) (length s - (n + m)) s substring n m s ++ substring (n + m) (length s - (n + m)) s
@ -690,7 +690,7 @@ Proof.
simplify; cases m; simplify; eauto using substring_suffix_emp'. simplify; cases m; simplify; eauto using substring_suffix_emp'.
Qed. Qed.
Hint Rewrite substring_stack substring_stack' substring_suffix using linear_arithmetic. Local Hint Rewrite substring_stack substring_stack' substring_suffix using linear_arithmetic.
Lemma minus_minus : forall n m1 m2, Lemma minus_minus : forall n m1 m2,
m1 + m2 <= n m1 + m2 <= n
@ -704,7 +704,7 @@ Proof.
linear_arithmetic. linear_arithmetic.
Qed. Qed.
Hint Rewrite minus_minus plus_n_Sm' using linear_arithmetic. Local Hint Rewrite minus_minus plus_n_Sm' using linear_arithmetic.
(* BOREDOM VANQUISHED! *) (* BOREDOM VANQUISHED! *)

10
FirstClassFunctions.v
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@ -354,7 +354,7 @@ Proof.
trivial. trivial.
Qed. Qed.
Hint Rewrite dnot_dnot. Global Hint Rewrite dnot_dnot.
Lemma map_identity : forall A (f : A -> A) (ls : list A), Lemma map_identity : forall A (f : A -> A) (ls : list A),
(forall x, x = f x) (forall x, x = f x)
@ -363,7 +363,7 @@ Proof.
induct ls; simplify; equality. induct ls; simplify; equality.
Qed. Qed.
Hint Rewrite map_identity map_map using assumption. Global Hint Rewrite map_identity map_map using assumption.
Lemma map_same : forall A B (f1 f2 : A -> B) ls, Lemma map_same : forall A B (f1 f2 : A -> B) ls,
(forall x, f1 x = f2 x) (forall x, f1 x = f2 x)
@ -399,9 +399,9 @@ Proof.
apply filter_same; assumption. apply filter_same; assumption.
Qed. Qed.
Hint Resolve List_map_same List_filter_same : core. Global Hint Resolve List_map_same List_filter_same : core.
Hint Extern 5 (_ = match _ with Bool _ => _ | _ => _ end) => Global Hint Extern 5 (_ = match _ with Bool _ => _ | _ => _ end) =>
match goal with match goal with
| [ H : forall x : dyn, _ |- _ ] => rewrite <- H | [ H : forall x : dyn, _ |- _ ] => rewrite <- H
end : core. end : core.
@ -493,7 +493,7 @@ Proof.
induct d; simplify; linear_arithmetic. induct d; simplify; linear_arithmetic.
Qed. Qed.
Hint Immediate dsize_positive : core. Global Hint Immediate dsize_positive : core.
Lemma sum_map_monotone : forall A (f1 f2 : A -> nat) ds, Lemma sum_map_monotone : forall A (f1 f2 : A -> nat) ds,
(forall x, f1 x <= f2 x) (forall x, f1 x <= f2 x)

4
HoareLogic.v
View file

@ -316,7 +316,7 @@ Proof.
simplify; subst; auto. simplify; subst; auto.
Qed. Qed.
Hint Rewrite <- minus_n_O. Local Hint Rewrite <- minus_n_O.
Lemma fact_rec : forall n, Lemma fact_rec : forall n,
n > 0 n > 0
@ -325,7 +325,7 @@ Proof.
simplify; cases n; simplify; linear_arithmetic. simplify; cases n; simplify; linear_arithmetic.
Qed. Qed.
Hint Rewrite fact_base fact_rec using linear_arithmetic. Local Hint Rewrite fact_base fact_rec using linear_arithmetic.
(* Note the careful choice of loop invariant below. It may look familiar from (* Note the careful choice of loop invariant below. It may look familiar from
* earlier chapters' proofs! *) * earlier chapters' proofs! *)

16
Imp.v
View file

@ -90,7 +90,7 @@ Inductive step : valuation * cmd -> valuation * cmd -> Prop :=
interp e v = 0 interp e v = 0
-> step (v, While e body) (v, Skip). -> step (v, While e body) (v, Skip).
Hint Constructors trc step eval : core. Global Hint Constructors trc step eval : core.
Lemma step_star_Seq : forall v c1 c2 v' c1', Lemma step_star_Seq : forall v c1 c2 v' c1',
step^* (v, c1) (v', c1') step^* (v, c1) (v', c1')
@ -100,7 +100,7 @@ Proof.
cases y; eauto. cases y; eauto.
Qed. Qed.
Hint Resolve step_star_Seq : core. Global Hint Resolve step_star_Seq : core.
Theorem big_small : forall v c v', eval v c v' Theorem big_small : forall v c v', eval v c v'
-> step^* (v, c) (v', Skip). -> step^* (v, c) (v', Skip).
@ -118,7 +118,7 @@ Proof.
end; eauto. end; eauto.
Qed. Qed.
Hint Resolve small_big'' : core. Global Hint Resolve small_big'' : core.
Lemma small_big' : forall v c v' c', step^* (v, c) (v', c') Lemma small_big' : forall v c v' c', step^* (v, c) (v', c')
-> forall v'', eval v' c' v'' -> forall v'', eval v' c' v''
@ -128,7 +128,7 @@ Proof.
cases y; eauto. cases y; eauto.
Qed. Qed.
Hint Resolve small_big' : core. Global Hint Resolve small_big' : core.
Theorem small_big : forall v c v', step^* (v, c) (v', Skip) Theorem small_big : forall v c v', step^* (v, c) (v', Skip)
-> eval v c v'. -> eval v c v'.
@ -176,7 +176,7 @@ Inductive cstep : valuation * cmd -> valuation * cmd -> Prop :=
-> plug C c' c2 -> plug C c' c2
-> cstep (v, c1) (v', c2). -> cstep (v, c1) (v', c2).
Hint Constructors plug step0 cstep : core. Global Hint Constructors plug step0 cstep : core.
Theorem step_cstep : forall v c v' c', Theorem step_cstep : forall v c v' c',
step (v, c) (v', c') step (v, c) (v', c')
@ -187,7 +187,7 @@ Proof.
end; eauto. end; eauto.
Qed. Qed.
Hint Resolve step_cstep : core. Global Hint Resolve step_cstep : core.
Lemma step0_step : forall v c v' c', Lemma step0_step : forall v c v' c',
step0 (v, c) (v', c') step0 (v, c) (v', c')
@ -196,7 +196,7 @@ Proof.
invert 1; eauto. invert 1; eauto.
Qed. Qed.
Hint Resolve step0_step : core. Global Hint Resolve step0_step : core.
Lemma cstep_step' : forall C c0 c, Lemma cstep_step' : forall C c0 c,
plug C c0 c plug C c0 c
@ -209,7 +209,7 @@ Proof.
end; eauto. end; eauto.
Qed. Qed.
Hint Resolve cstep_step' : core. Global Hint Resolve cstep_step' : core.
Theorem cstep_step : forall v c v' c', Theorem cstep_step : forall v c v' c',
cstep (v, c) (v', c') cstep (v, c) (v', c')

24
Map.v
View file

@ -133,17 +133,17 @@ Module Type S.
lookup (restrict P m) k = Some v lookup (restrict P m) k = Some v
-> P k. -> P k.
Hint Extern 1 => match goal with Global Hint Extern 1 => match goal with
| [ H : lookup (empty _ _) _ = Some _ |- _ ] => | [ H : lookup (empty _ _) _ = Some _ |- _ ] =>
rewrite lookup_empty in H; discriminate rewrite lookup_empty in H; discriminate
end : core. end : core.
Hint Resolve includes_lookup includes_add empty_includes : core. Global Hint Resolve includes_lookup includes_add empty_includes : core.
Hint Rewrite lookup_empty lookup_add_eq lookup_add_ne lookup_remove_eq lookup_remove_ne Global Hint Rewrite lookup_empty lookup_add_eq lookup_add_ne lookup_remove_eq lookup_remove_ne
lookup_merge lookup_restrict_true lookup_restrict_false using congruence. lookup_merge lookup_restrict_true lookup_restrict_false using congruence.
Hint Rewrite dom_empty dom_add. Global Hint Rewrite dom_empty dom_add.
Ltac maps_equal := Ltac maps_equal :=
apply fmap_ext; intros; apply fmap_ext; intros;
@ -152,17 +152,17 @@ Module Type S.
| [ |- context[lookup (add _ ?k _) ?k' ] ] => destruct (classic (k = k')); subst | [ |- context[lookup (add _ ?k _) ?k' ] ] => destruct (classic (k = k')); subst
end). end).
Hint Extern 3 (_ = _) => maps_equal : core. Global Hint Extern 3 (_ = _) => maps_equal : core.
Axiom lookup_split : forall A B (m : fmap A B) k v k' v', Axiom lookup_split : forall A B (m : fmap A B) k v k' v',
(m $+ (k, v)) $? k' = Some v' (m $+ (k, v)) $? k' = Some v'
-> (k' <> k /\ m $? k' = Some v') \/ (k' = k /\ v' = v). -> (k' <> k /\ m $? k' = Some v') \/ (k' = k /\ v' = v).
Hint Rewrite merge_empty1 merge_empty2 using solve [ eauto 1 ]. Global Hint Rewrite merge_empty1 merge_empty2 using solve [ eauto 1 ].
Hint Rewrite merge_empty1_alt merge_empty2_alt using congruence. Global Hint Rewrite merge_empty1_alt merge_empty2_alt using congruence.
Hint Rewrite merge_add1 using solve [ eauto | unfold Sets.In; autorewrite with core in *; simpl in *; try (normalize_set; simpl); intuition congruence ]. Global Hint Rewrite merge_add1 using solve [ eauto | unfold Sets.In; autorewrite with core in *; simpl in *; try (normalize_set; simpl); intuition congruence ].
Hint Rewrite merge_add1_alt using solve [ congruence | unfold Sets.In; autorewrite with core in *; simpl in *; try (normalize_set; simpl); intuition congruence ]. Global Hint Rewrite merge_add1_alt using solve [ congruence | unfold Sets.In; autorewrite with core in *; simpl in *; try (normalize_set; simpl); intuition congruence ].
Axiom includes_intro : forall K V (m1 m2 : fmap K V), Axiom includes_intro : forall K V (m1 m2 : fmap K V),
(forall k v, m1 $? k = Some v -> m2 $? k = Some v) (forall k v, m1 $? k = Some v -> m2 $? k = Some v)
@ -267,9 +267,9 @@ Module Type S.
-> disjoint h3 h2. -> disjoint h3 h2.
End splitting. End splitting.
Hint Immediate disjoint_comm split_comm : core. Global Hint Immediate disjoint_comm split_comm : core.
Hint Immediate split_empty_bwd disjoint_hemp disjoint_hemp' split_assoc1 split_assoc2 : core. Global Hint Immediate split_empty_bwd disjoint_hemp disjoint_hemp' split_assoc1 split_assoc2 : core.
Hint Immediate disjoint_assoc1 disjoint_assoc2 split_join split_disjoint disjoint_assoc3 : core. Global Hint Immediate disjoint_assoc1 disjoint_assoc2 split_join split_disjoint disjoint_assoc3 : core.
End S. End S.
Module M : S. Module M : S.

6
SepCancel.v
View file

@ -82,7 +82,7 @@ Module Make(Import S : SEP).
transitivity proved by heq_trans transitivity proved by heq_trans
as heq_rel. as heq_rel.
Instance himp_heq_mor : Proper (heq ==> heq ==> iff) himp. Global Instance himp_heq_mor : Proper (heq ==> heq ==> iff) himp.
Proof. Proof.
hnf; intros; hnf; intros. hnf; intros; hnf; intros.
apply himp_heq in H; apply himp_heq in H0. apply himp_heq in H; apply himp_heq in H0.
@ -104,7 +104,7 @@ Module Make(Import S : SEP).
auto using star_cancel. auto using star_cancel.
Qed. Qed.
Instance exis_iff_morphism (A : Type) : Global Instance exis_iff_morphism (A : Type) :
Proper (pointwise_relation A heq ==> heq) (@exis A). Proper (pointwise_relation A heq ==> heq) (@exis A).
Proof. Proof.
hnf; intros; apply himp_heq; intuition. hnf; intros; apply himp_heq; intuition.
@ -120,7 +120,7 @@ Module Make(Import S : SEP).
apply himp_heq in H0; intuition eauto. apply himp_heq in H0; intuition eauto.
Qed. Qed.
Instance exis_imp_morphism (A : Type) : Global Instance exis_imp_morphism (A : Type) :
Proper (pointwise_relation A himp ==> himp) (@exis A). Proper (pointwise_relation A himp ==> himp) (@exis A).
Proof. Proof.
hnf; intros. hnf; intros.

10
SeparationLogic.v
View file

@ -181,7 +181,7 @@ Module Import S <: SEP.
t. t.
Qed. Qed.
Hint Resolve split_empty_bwd' : core. Local Hint Resolve split_empty_bwd' : core.
Theorem extra_lift : forall (P : Prop) p, Theorem extra_lift : forall (P : Prop) p,
P P
@ -1161,8 +1161,8 @@ Proof.
end; cancel. end; cancel.
Qed. Qed.
Hint Rewrite <- rev_alt. Local Hint Rewrite <- rev_alt.
Hint Rewrite rev_involutive. Local Hint Rewrite rev_involutive.
(* Let's hide the definition of [linkedList], so that we *only* reason about it (* Let's hide the definition of [linkedList], so that we *only* reason about it
* via the two lemmas we just proved. *) * via the two lemmas we just proved. *)
@ -1302,8 +1302,8 @@ Qed.
Opaque linkedList linkedListSegment. Opaque linkedList linkedListSegment.
(* A few algebraic properties of list operations: *) (* A few algebraic properties of list operations: *)
Hint Rewrite <- app_assoc. Local Hint Rewrite <- app_assoc.
Hint Rewrite app_length app_nil_r. Local Hint Rewrite app_length app_nil_r.
(* We tie a few of them together into this lemma. *) (* We tie a few of them together into this lemma. *)
Lemma move_along : forall A (ls : list A) x2 x1 x0 x, Lemma move_along : forall A (ls : list A) x2 x1 x0 x,

12
SeparationLogic_template.v
View file

@ -165,7 +165,7 @@ Module Import S <: SEP.
t. t.
Qed. Qed.
Hint Resolve split_empty_bwd' : core. Global Hint Resolve split_empty_bwd' : core.
Theorem extra_lift : forall (P : Prop) p, Theorem extra_lift : forall (P : Prop) p,
P P
@ -398,7 +398,7 @@ Qed.
(* Fancy theorem to help us rewrite within preconditions and postconditions *) (* Fancy theorem to help us rewrite within preconditions and postconditions *)
Instance hoare_triple_morphism : forall A, Local Instance hoare_triple_morphism : forall A,
Proper (heq ==> eq ==> (eq ==> heq) ==> iff) (@hoare_triple A). Proper (heq ==> eq ==> (eq ==> heq) ==> iff) (@hoare_triple A).
Proof. Proof.
Transparent himp. Transparent himp.
@ -542,8 +542,8 @@ Proof.
end; cancel. end; cancel.
Qed. Qed.
Hint Rewrite <- rev_alt. Local Hint Rewrite <- rev_alt.
Hint Rewrite rev_involutive. Local Hint Rewrite rev_involutive.
(* Let's hide the definition of [linkedList], so that we *only* reason about it (* Let's hide the definition of [linkedList], so that we *only* reason about it
* via the two lemmas we just proved. *) * via the two lemmas we just proved. *)
@ -590,8 +590,8 @@ Admitted.
(* ** Computing the length of a linked list *) (* ** Computing the length of a linked list *)
(* A few algebraic properties of list operations: *) (* A few algebraic properties of list operations: *)
Hint Rewrite <- app_assoc. Local Hint Rewrite <- app_assoc.
Hint Rewrite app_length app_nil_r. Local Hint Rewrite app_length app_nil_r.
(* We tie a few of them together into this lemma. *) (* We tie a few of them together into this lemma. *)
Lemma move_along : forall A (ls : list A) x2 x1 x0 x, Lemma move_along : forall A (ls : list A) x2 x1 x0 x,

4
SubsetTypes.v
View file

@ -536,7 +536,7 @@ Notation "e1 ;; e2" := (if e1 then e2 else ??)
* [hasType] proof obligation, and [eauto] makes short work of them when we add * [hasType] proof obligation, and [eauto] makes short work of them when we add
* [hasType]'s constructors as hints. *) * [hasType]'s constructors as hints. *)
Local Hint Constructors hasType. Local Hint Constructors hasType : core.
Definition typeCheck : forall e : exp, {{t | hasType e t}}. Definition typeCheck : forall e : exp, {{t | hasType e t}}.
refine (fix F (e : exp) : {{t | hasType e t}} := refine (fix F (e : exp) : {{t | hasType e t}} :=
@ -589,7 +589,7 @@ Qed.
(* Now we can define the type-checker. Its type expresses that it only fails on (* Now we can define the type-checker. Its type expresses that it only fails on
* untypable expressions. *) * untypable expressions. *)
Local Hint Resolve hasType_det. Local Hint Resolve hasType_det : core.
(* The lemma [hasType_det] will also be useful for proving proof obligations (* The lemma [hasType_det] will also be useful for proving proof obligations
* with contradictory contexts. *) * with contradictory contexts. *)