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Prevent more warnings for Coq 8.10

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Adam Chlipala 2020-02-08 15:15:38 -05:00
parent 0ed668481d
commit c611524a96
7 changed files with 61 additions and 61 deletions
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24
AbstractInterpret.v
View file

@ -58,7 +58,7 @@ Record absint_sound (a : absint) : Prop := {
Hint Resolve TopSound ConstSound AddSound SubtractSound MultiplySound Hint Resolve TopSound ConstSound AddSound SubtractSound MultiplySound
AddMonotone SubtractMonotone MultiplyMonotone AddMonotone SubtractMonotone MultiplyMonotone
JoinSoundLeft JoinSoundRight. JoinSoundLeft JoinSoundRight : core.
@ -103,7 +103,7 @@ Proof.
cases (s $? x); equality. cases (s $? x); equality.
Qed. Qed.
Hint Resolve subsumed_refl. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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,

31
CompilerCorrectness_template.v
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@ -26,6 +26,7 @@ Inductive cmd :=
Coercion Const : nat >-> arith. Coercion Const : nat >-> arith.
Coercion Var : var >-> arith. Coercion Var : var >-> arith.
Declare Scope arith_scope.
Infix "+" := Plus : arith_scope. Infix "+" := Plus : arith_scope.
Infix "-" := Minus : arith_scope. Infix "-" := Minus : arith_scope.
Infix "*" := Times : arith_scope. Infix "*" := Times : arith_scope.
@ -100,7 +101,7 @@ Inductive generate : valuation * cmd -> list (option nat) -> Prop :=
-> generate vc' ns -> generate vc' ns
-> generate vc (Some n :: ns). -> generate vc (Some n :: ns).
Hint Constructors plug step0 cstep generate. Hint Constructors plug step0 cstep generate : core.
Definition traceInclusion (vc1 vc2 : valuation * cmd) := Definition traceInclusion (vc1 vc2 : valuation * cmd) :=
forall ns, generate vc1 ns -> generate vc2 ns. forall ns, generate vc1 ns -> generate vc2 ns.
@ -130,8 +131,8 @@ Example month_boundaries_in_days :=
done done
done. done.
Hint Extern 1 (interp _ _ = _) => simplify; equality. Hint Extern 1 (interp _ _ = _) => simplify; equality : core.
Hint Extern 1 (interp _ _ <> _) => simplify; equality. Hint Extern 1 (interp _ _ <> _) => simplify; equality : core.
Theorem first_few_values : Theorem first_few_values :
generate ($0, month_boundaries_in_days) [Some 28; Some 56]. generate ($0, month_boundaries_in_days) [Some 28; Some 56].
@ -250,7 +251,7 @@ Proof.
equality. equality.
Qed. Qed.
Hint Resolve peel_cseq. Hint Resolve peel_cseq : core.
Lemma plug_deterministic : forall v C c1 c2, plug C c1 c2 Lemma plug_deterministic : forall v C c1 c2, plug C c1 c2
-> forall l vc1, step0 (v, c1) l vc1 -> forall l vc1, step0 (v, c1) l vc1
@ -438,7 +439,7 @@ Proof.
invert H4. invert H4.
Qed. Qed.
Hint Resolve silent_generate_fwd silent_generate_bwd generate_Skip. Hint Resolve silent_generate_fwd silent_generate_bwd generate_Skip : core.
Section simulation_skipping. Section simulation_skipping.
Variable R : nat -> valuation * cmd -> valuation * cmd -> Prop. Variable R : nat -> valuation * cmd -> valuation * cmd -> Prop.
@ -526,7 +527,7 @@ Section simulation_skipping.
clear; induct 1; eauto. clear; induct 1; eauto.
Qed. Qed.
Hint Resolve step_to_termination. Hint Resolve step_to_termination : core.
Lemma R_Skip : forall n vc1 v, Lemma R_Skip : forall n vc1 v,
R n vc1 (v, Skip) R n vc1 (v, Skip)
@ -592,9 +593,9 @@ Section simulation_skipping.
Qed. Qed.
End simulation_skipping. End simulation_skipping.
Hint Extern 1 (_ < _) => linear_arithmetic. Hint Extern 1 (_ < _) => linear_arithmetic : core.
Hint Extern 1 (_ >= _) => linear_arithmetic. Hint Extern 1 (_ >= _) => linear_arithmetic : core.
Hint Extern 1 (_ <> _) => linear_arithmetic. Hint Extern 1 (_ <> _) => linear_arithmetic : core.
Lemma cfold_ok : forall v c, Lemma cfold_ok : forall v c,
(v, c) =| (v, cfold c). (v, c) =| (v, cfold c).
@ -835,7 +836,7 @@ Section simulation_multiple.
(* We won't comment on the other proof details, though they could be (* We won't comment on the other proof details, though they could be
* interesting reading. *) * interesting reading. *)
Hint Constructors generateN. Hint Constructors generateN : core.
Lemma generateN_fwd : forall sc vc ns, Lemma generateN_fwd : forall sc vc ns,
generateN sc vc ns generateN sc vc ns
@ -844,7 +845,7 @@ Section simulation_multiple.
induct 1; eauto. induct 1; eauto.
Qed. Qed.
Hint Resolve generateN_fwd. Hint Resolve generateN_fwd : core.
Lemma generateN_bwd : forall vc ns, Lemma generateN_bwd : forall vc ns,
generate vc ns generate vc ns
@ -1061,7 +1062,7 @@ Proof.
first_order. first_order.
Qed. Qed.
Hint Resolve agree_add agree_add_tempVar_fwd agree_add_tempVar_bwd agree_add_tempVar_bwd_prime agree_refl. Hint Resolve agree_add agree_add_tempVar_fwd agree_add_tempVar_bwd agree_add_tempVar_bwd_prime agree_refl : core.
Lemma silent_csteps_front : forall c v1 v2 c1 c2, Lemma silent_csteps_front : forall c v1 v2 c1 c2,
silent_cstep^* (v1, c1) (v2, c2) silent_cstep^* (v1, c1) (v2, c2)
@ -1072,7 +1073,7 @@ Proof.
eauto 6. eauto 6.
Qed. Qed.
Hint Resolve silent_csteps_front. Hint Resolve silent_csteps_front : core.
Lemma tempVar_contra : forall n1 n2, Lemma tempVar_contra : forall n1 n2,
tempVar n1 = tempVar n2 tempVar n1 = tempVar n2
@ -1083,7 +1084,7 @@ Proof.
first_order. first_order.
Qed. Qed.
Hint Resolve tempVar_contra. Hint Resolve tempVar_contra : core.
Lemma self_prime_contra : forall s, Lemma self_prime_contra : forall s,
(s ++ "'")%string = s -> False. (s ++ "'")%string = s -> False.
@ -1091,7 +1092,7 @@ Proof.
induct s; simplify; equality. induct s; simplify; equality.
Qed. Qed.
Hint Resolve self_prime_contra. Hint Resolve self_prime_contra : core.
Opaque tempVar. Opaque tempVar.

17
Imp.v
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@ -19,6 +19,7 @@ Inductive cmd :=
Coercion Const : nat >-> arith. Coercion Const : nat >-> arith.
Coercion Var : var >-> arith. Coercion Var : var >-> arith.
Declare Scope arith_scope.
Infix "+" := Plus : arith_scope. Infix "+" := Plus : arith_scope.
Infix "-" := Minus : arith_scope. Infix "-" := Minus : arith_scope.
Infix "*" := Times : arith_scope. Infix "*" := Times : arith_scope.
@ -89,7 +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. 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')
@ -99,7 +100,7 @@ Proof.
cases y; eauto. cases y; eauto.
Qed. Qed.
Hint Resolve step_star_Seq. 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).
@ -117,7 +118,7 @@ Proof.
end; eauto. end; eauto.
Qed. Qed.
Hint Resolve small_big''. 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''
@ -127,7 +128,7 @@ Proof.
cases y; eauto. cases y; eauto.
Qed. Qed.
Hint Resolve small_big'. 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'.
@ -175,7 +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. 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')
@ -186,7 +187,7 @@ Proof.
end; eauto. end; eauto.
Qed. Qed.
Hint Resolve step_cstep. 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')
@ -195,7 +196,7 @@ Proof.
invert 1; eauto. invert 1; eauto.
Qed. Qed.
Hint Resolve step0_step. 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
@ -208,7 +209,7 @@ Proof.
end; eauto. end; eauto.
Qed. Qed.
Hint Resolve cstep_step'. 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')

16
Map.v
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@ -136,9 +136,9 @@ Module Type S.
Hint Extern 1 => match goal with 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. end : core.
Hint Resolve includes_lookup includes_add empty_includes. 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 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.
@ -152,7 +152,7 @@ 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. 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'
@ -267,9 +267,9 @@ Module Type S.
-> disjoint h3 h2. -> disjoint h3 h2.
End splitting. End splitting.
Hint Immediate disjoint_comm split_comm. Hint Immediate disjoint_comm split_comm : core.
Hint Immediate split_empty_bwd disjoint_hemp disjoint_hemp' split_assoc1 split_assoc2. 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. Hint Immediate disjoint_assoc1 disjoint_assoc2 split_join split_disjoint disjoint_assoc3 : core.
End S. End S.
Module M : S. Module M : S.
@ -593,7 +593,7 @@ Module M : S.
Definition split (h h1 h2 : fmap K V) : Prop := Definition split (h h1 h2 : fmap K V) : Prop :=
h = h1 $++ h2. h = h1 $++ h2.
Hint Extern 2 (_ <> _) => congruence. Hint Extern 2 (_ <> _) => congruence : core.
Ltac splt := unfold disjoint, split, join, lookup in *; intros; subst; Ltac splt := unfold disjoint, split, join, lookup in *; intros; subst;
try match goal with try match goal with
@ -661,7 +661,7 @@ Module M : S.
splt. splt.
Qed. Qed.
Hint Immediate disjoint_comm split_comm. Hint Immediate disjoint_comm split_comm : core.
Lemma split_assoc1 : forall h h1 h' h2 h3, Lemma split_assoc1 : forall h h1 h' h2 h3,
split h h1 h' split h h1 h'

2
ModelCheck.v
View file

@ -143,7 +143,7 @@ Proof.
eauto. eauto.
Qed. Qed.
Local Hint Constructors invariantViaSimulation. Local Hint Constructors invariantViaSimulation : core.
Theorem invariant_simulates : forall state1 state2 (R : state1 -> state2 -> Prop) Theorem invariant_simulates : forall state1 state2 (R : state1 -> state2 -> Prop)
(sys1 : trsys state1) (sys2 : trsys state2) (inv2 : state2 -> Prop), (sys1 : trsys state1) (sys2 : trsys state2) (inv2 : state2 -> Prop),

26
Relations.v
View file

@ -12,7 +12,7 @@ Section trc.
-> trc y z -> trc y z
-> trc x z. -> trc x z.
Hint Constructors trc. Hint Constructors trc : core.
Theorem trc_one : forall x y, R x y Theorem trc_one : forall x y, R x y
-> trc x y. -> trc x y.
@ -20,7 +20,7 @@ Section trc.
eauto. eauto.
Qed. Qed.
Hint Resolve trc_one. Hint Resolve trc_one : core.
Theorem trc_trans : forall x y, trc x y Theorem trc_trans : forall x y, trc x y
-> forall z, trc y z -> forall z, trc y z
@ -29,7 +29,7 @@ Section trc.
induction 1; eauto. induction 1; eauto.
Qed. Qed.
Hint Resolve trc_trans. Hint Resolve trc_trans : core.
Inductive trcEnd : A -> A -> Prop := Inductive trcEnd : A -> A -> Prop :=
| TrcEndRefl : forall x, trcEnd x x | TrcEndRefl : forall x, trcEnd x x
@ -38,7 +38,7 @@ Section trc.
-> R y z -> R y z
-> trcEnd x z. -> trcEnd x z.
Hint Constructors trcEnd. Hint Constructors trcEnd : core.
Lemma TrcFront' : forall x y z, Lemma TrcFront' : forall x y z,
R x y R x y
@ -48,7 +48,7 @@ Section trc.
induction 2; eauto. induction 2; eauto.
Qed. Qed.
Hint Resolve TrcFront'. Hint Resolve TrcFront' : core.
Theorem trc_trcEnd : forall x y, trc x y Theorem trc_trcEnd : forall x y, trc x y
-> trcEnd x y. -> trcEnd x y.
@ -56,7 +56,7 @@ Section trc.
induction 1; eauto. induction 1; eauto.
Qed. Qed.
Hint Resolve trc_trcEnd. Hint Resolve trc_trcEnd : core.
Lemma TrcBack' : forall x y z, Lemma TrcBack' : forall x y z,
trc x y trc x y
@ -66,7 +66,7 @@ Section trc.
induction 1; eauto. induction 1; eauto.
Qed. Qed.
Hint Resolve TrcBack'. Hint Resolve TrcBack' : core.
Theorem trcEnd_trans : forall x y, trcEnd x y Theorem trcEnd_trans : forall x y, trcEnd x y
-> forall z, trcEnd y z -> forall z, trcEnd y z
@ -75,7 +75,7 @@ Section trc.
induction 1; eauto. induction 1; eauto.
Qed. Qed.
Hint Resolve trcEnd_trans. Hint Resolve trcEnd_trans : core.
Theorem trcEnd_trc : forall x y, trcEnd x y Theorem trcEnd_trc : forall x y, trcEnd x y
-> trc x y. -> trc x y.
@ -83,7 +83,7 @@ Section trc.
induction 1; eauto. induction 1; eauto.
Qed. Qed.
Hint Resolve trcEnd_trc. Hint Resolve trcEnd_trc : core.
Inductive trcLiteral : A -> A -> Prop := Inductive trcLiteral : A -> A -> Prop :=
| TrcLiteralRefl : forall x, trcLiteral x x | TrcLiteralRefl : forall x, trcLiteral x x
@ -93,7 +93,7 @@ Section trc.
| TrcInclude : forall x y, R x y | TrcInclude : forall x y, R x y
-> trcLiteral x y. -> trcLiteral x y.
Hint Constructors trcLiteral. Hint Constructors trcLiteral : core.
Theorem trc_trcLiteral : forall x y, trc x y Theorem trc_trcLiteral : forall x y, trc x y
-> trcLiteral x y. -> trcLiteral x y.
@ -107,7 +107,7 @@ Section trc.
induction 1; eauto. induction 1; eauto.
Qed. Qed.
Hint Resolve trc_trcLiteral trcLiteral_trc. Hint Resolve trc_trcLiteral trcLiteral_trc : core.
Theorem trcEnd_trcLiteral : forall x y, trcEnd x y Theorem trcEnd_trcLiteral : forall x y, trcEnd x y
-> trcLiteral x y. -> trcLiteral x y.
@ -121,10 +121,10 @@ Section trc.
induction 1; eauto. induction 1; eauto.
Qed. Qed.
Hint Resolve trcEnd_trcLiteral trcLiteral_trcEnd. Hint Resolve trcEnd_trcLiteral trcLiteral_trcEnd : core.
End trc. End trc.
Notation "R ^*" := (trc R) (at level 0). Notation "R ^*" := (trc R) (at level 0).
Notation "*^ R" := (trcEnd R) (at level 0). Notation "*^ R" := (trcEnd R) (at level 0).
Hint Constructors trc. Hint Constructors trc : core.

6
Sets.v
View file

@ -1,4 +1,4 @@
Require Import Classical FunctionalExtensionality List. Require Import Bool Classical FunctionalExtensionality List.
Set Implicit Arguments. Set Implicit Arguments.
@ -131,7 +131,7 @@ Section properties.
Qed. Qed.
End properties. End properties.
Hint Resolve subseteq_refl subseteq_In. Hint Resolve subseteq_refl subseteq_In : core.
(*Hint Rewrite union_constant.*) (*Hint Rewrite union_constant.*)
@ -506,8 +506,6 @@ Section setexpr.
destruct (member a ns2); simpl in *; auto; congruence. destruct (member a ns2); simpl in *; auto; congruence.
Qed. Qed.
Require Import Bool.
Theorem compare_sets : forall env e1 e2, Theorem compare_sets : forall env e1 e2,
let nf1 := normalize_setexpr e1 in let nf1 := normalize_setexpr e1 in
let nf2 := normalize_setexpr e2 in let nf2 := normalize_setexpr e2 in