pl/frap
1
0
Fork 0
mirror of https://github.com/achlipala/frap.git synced 2024-11-27 23:06:20 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions

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

Browse source
This commit is contained in:
Adam Chlipala 2022-03-07 13:48:40 -05:00
parent b643755628
commit f3211734b9
16 changed files with 80 additions and 80 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

24
AbstractInterpret.v
View file

@ -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
View file

@ -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
View file

@ -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
View file

@ -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
View file

@ -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
View file

@ -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
View file

@ -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
View file

@ -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
View file

@ -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. *)