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Revising before this week's lectures

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Adam Chlipala 2021-05-10 10:45:34 -04:00
parent 45fa64d69e
commit 8fdc4e2cfd
5 changed files with 29 additions and 29 deletions
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12
ConcurrentSeparationLogic.v
View file

@ -19,8 +19,8 @@ Set Asymmetric Patterns.
Notation heap := (fmap nat nat). Notation heap := (fmap nat nat).
Notation locks := (set nat). Notation locks := (set nat).
Hint Extern 1 (_ <= _) => linear_arithmetic : core. Local Hint Extern 1 (_ <= _) => linear_arithmetic : core.
Hint Extern 1 (@eq nat _ _) => linear_arithmetic : core. Local Hint Extern 1 (@eq nat _ _) => linear_arithmetic : core.
Ltac simp := repeat (simplify; subst; propositional; Ltac simp := repeat (simplify; subst; propositional;
try match goal with try match goal with
@ -206,7 +206,7 @@ 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
@ -502,7 +502,7 @@ Proof.
apply try_me_first_easy. apply try_me_first_easy.
Qed. Qed.
Hint Resolve try_ptsto_first : core. Local Hint Resolve try_ptsto_first : core.
(** ** The nonzero shared counter *) (** ** The nonzero shared counter *)
@ -837,7 +837,7 @@ Qed.
* book PDF for a sketch of the important technical devices and lemmas in this * book PDF for a sketch of the important technical devices and lemmas in this
* proof. *) * proof. *)
Hint Resolve himp_refl : core. Local Hint Resolve himp_refl : core.
Lemma invert_Return : forall linvs {result : Set} (r : result) P Q, Lemma invert_Return : forall linvs {result : Set} (r : result) P Q,
hoare_triple linvs P (Return r) Q hoare_triple linvs P (Return r) Q
@ -852,7 +852,7 @@ Proof.
rewrite IHhoare_triple; eauto. rewrite IHhoare_triple; eauto.
Qed. Qed.
Hint Constructors hoare_triple : core. Local Hint Constructors hoare_triple : core.
Lemma invert_Bind : forall linvs {result' result} (c1 : cmd result') (c2 : result' -> cmd result) P Q, Lemma invert_Bind : forall linvs {result' result} (c1 : cmd result') (c2 : result' -> cmd result) P Q,
hoare_triple linvs P (Bind c1 c2) Q hoare_triple linvs P (Bind c1 c2) Q

12
ConcurrentSeparationLogic_template.v
View file

@ -9,8 +9,8 @@ Set Asymmetric Patterns.
Notation heap := (fmap nat nat). Notation heap := (fmap nat nat).
Notation locks := (set nat). Notation locks := (set nat).
Hint Extern 1 (_ <= _) => linear_arithmetic : core. Local Hint Extern 1 (_ <= _) => linear_arithmetic : core.
Hint Extern 1 (@eq nat _ _) => linear_arithmetic : core. Local Hint Extern 1 (@eq nat _ _) => linear_arithmetic : core.
Ltac simp := repeat (simplify; subst; propositional; Ltac simp := repeat (simplify; subst; propositional;
try match goal with try match goal with
@ -187,7 +187,7 @@ 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
@ -483,7 +483,7 @@ Proof.
apply try_me_first_easy. apply try_me_first_easy.
Qed. Qed.
Hint Resolve try_ptsto_first : core. Local Hint Resolve try_ptsto_first : core.
(** ** The nonzero shared counter *) (** ** The nonzero shared counter *)
@ -752,7 +752,7 @@ Qed.
(** * Soundness proof *) (** * Soundness proof *)
Hint Resolve himp_refl : core. Local Hint Resolve himp_refl : core.
Lemma invert_Return : forall linvs {result : Set} (r : result) P Q, Lemma invert_Return : forall linvs {result : Set} (r : result) P Q,
hoare_triple linvs P (Return r) Q hoare_triple linvs P (Return r) Q
@ -767,7 +767,7 @@ Proof.
rewrite IHhoare_triple; eauto. rewrite IHhoare_triple; eauto.
Qed. Qed.
Hint Constructors hoare_triple : core. Local Hint Constructors hoare_triple : core.
Lemma invert_Bind : forall linvs {result' result} (c1 : cmd result') (c2 : result' -> cmd result) P Q, Lemma invert_Bind : forall linvs {result' result} (c1 : cmd result') (c2 : result' -> cmd result) P Q,
hoare_triple linvs P (Bind c1 c2) Q hoare_triple linvs P (Bind c1 c2) Q

14
ProgramDerivation.v
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@ -327,7 +327,7 @@ Inductive RefineMethods {state1 state2} (R : state1 -> state2 -> Prop)
-> RefineMethods R (MethodsCons {| MethodName := name; MethodBody := f1 |} ms1) -> RefineMethods R (MethodsCons {| MethodName := name; MethodBody := f1 |} ms1)
(MethodsCons {| MethodName := name; MethodBody := f2 |} ms2). (MethodsCons {| MethodName := name; MethodBody := f2 |} ms2).
Hint Constructors RefineMethods : core. Local Hint Constructors RefineMethods : core.
(* When does [adt2] refine [adt1]? When there exists a simulation relation, (* When does [adt2] refine [adt1]? When there exists a simulation relation,
* with respect to which the constructors and methods all satisfy the usual * with respect to which the constructors and methods all satisfy the usual
@ -360,7 +360,7 @@ Definition split_counter := ADT {
and method "value"[[self, _]] = ret (self, fst self + snd self) and method "value"[[self, _]] = ret (self, fst self + snd self)
}. }.
Hint Extern 1 (@eq nat _ _) => simplify; linear_arithmetic : core. Local Hint Extern 1 (@eq nat _ _) => simplify; linear_arithmetic : core.
(* Here is why the new implementation is correct. *) (* Here is why the new implementation is correct. *)
Theorem split_counter_ok : adt_refine counter split_counter. Theorem split_counter_ok : adt_refine counter split_counter.
@ -393,7 +393,7 @@ Proof.
subst; eauto. subst; eauto.
Qed. Qed.
Hint Immediate RefineMethods_refl : core. Local Hint Immediate RefineMethods_refl : core.
Theorem refine_refl : forall names (adt1 : adt names), Theorem refine_refl : forall names (adt1 : adt names),
adt_refine adt1 adt1. adt_refine adt1 adt1.
@ -422,7 +422,7 @@ Proof.
first_order. first_order.
Qed. Qed.
Hint Resolve RefineMethods_trans : core. Local Hint Resolve RefineMethods_trans : core.
Theorem refine_trans : forall names (adt1 adt2 adt3 : adt names), Theorem refine_trans : forall names (adt1 adt2 adt3 : adt names),
adt_refine adt1 adt2 adt_refine adt1 adt2
@ -497,7 +497,7 @@ Proof.
simplify; subst; eauto. simplify; subst; eauto.
Qed. Qed.
Hint Resolve ReplaceMethod_ok : core. Local Hint Resolve ReplaceMethod_ok : core.
(* It is OK to replace a method body if the new refines the old as a [comp]. *) (* It is OK to replace a method body if the new refines the old as a [comp]. *)
Theorem refine_method : forall state name (oldbody newbody : state -> nat -> comp (state * nat)) Theorem refine_method : forall state name (oldbody newbody : state -> nat -> comp (state * nat))
@ -553,7 +553,7 @@ Proof.
eauto. eauto.
Qed. Qed.
Hint Resolve RepChangeMethods_ok : core. Local Hint Resolve RepChangeMethods_ok : core.
Theorem refine_rep : forall state1 state2 (absfunc : state2 -> state1) Theorem refine_rep : forall state1 state2 (absfunc : state2 -> state1)
names (ms1 : methods state1 names) (ms2 : methods state2 names) names (ms1 : methods state1 names) (ms2 : methods state2 names)
@ -688,7 +688,7 @@ Proof.
eauto. eauto.
Qed. Qed.
Hint Resolve CachingMethods_ok : core. Local Hint Resolve CachingMethods_ok : core.
Theorem refine_cache : forall state name (func : state -> nat) Theorem refine_cache : forall state name (func : state -> nat)
names (ms1 : methods state names) (ms2 : methods (state * nat) names) names (ms1 : methods state names) (ms2 : methods (state * nat) names)

14
ProgramDerivation_template.v
View file

@ -187,7 +187,7 @@ Inductive RefineMethods {state1 state2} (R : state1 -> state2 -> Prop)
-> RefineMethods R (MethodsCons {| MethodName := name; MethodBody := f1 |} ms1) -> RefineMethods R (MethodsCons {| MethodName := name; MethodBody := f1 |} ms1)
(MethodsCons {| MethodName := name; MethodBody := f2 |} ms2). (MethodsCons {| MethodName := name; MethodBody := f2 |} ms2).
Hint Constructors RefineMethods : core. Local Hint Constructors RefineMethods : core.
Record adt_refine {names} (adt1 adt2 : adt names) : Prop := { Record adt_refine {names} (adt1 adt2 : adt names) : Prop := {
ArRel : AdtState adt1 -> AdtState adt2 -> Prop; ArRel : AdtState adt1 -> AdtState adt2 -> Prop;
@ -214,7 +214,7 @@ Definition split_counter := ADT {
and method "value"[[self, _]] = ret (self, fst self + snd self) and method "value"[[self, _]] = ret (self, fst self + snd self)
}. }.
Hint Extern 1 (@eq nat _ _) => simplify; linear_arithmetic : core. Local Hint Extern 1 (@eq nat _ _) => simplify; linear_arithmetic : core.
Theorem split_counter_ok : adt_refine counter split_counter. Theorem split_counter_ok : adt_refine counter split_counter.
Proof. Proof.
@ -232,7 +232,7 @@ Proof.
subst; eauto. subst; eauto.
Qed. Qed.
Hint Immediate RefineMethods_refl : core. Local Hint Immediate RefineMethods_refl : core.
Theorem refine_refl : forall names (adt1 : adt names), Theorem refine_refl : forall names (adt1 : adt names),
adt_refine adt1 adt1. adt_refine adt1 adt1.
@ -261,7 +261,7 @@ Proof.
first_order. first_order.
Qed. Qed.
Hint Resolve RefineMethods_trans : core. Local Hint Resolve RefineMethods_trans : core.
Theorem refine_trans : forall names (adt1 adt2 adt3 : adt names), Theorem refine_trans : forall names (adt1 adt2 adt3 : adt names),
adt_refine adt1 adt2 adt_refine adt1 adt2
@ -324,7 +324,7 @@ Proof.
simplify; subst; eauto. simplify; subst; eauto.
Qed. Qed.
Hint Resolve ReplaceMethod_ok : core. Local Hint Resolve ReplaceMethod_ok : core.
Theorem refine_method : forall state name (oldbody newbody : state -> nat -> comp (state * nat)) Theorem refine_method : forall state name (oldbody newbody : state -> nat -> comp (state * nat))
names (ms1 ms2 : methods state names) constr, names (ms1 ms2 : methods state names) constr,
@ -369,7 +369,7 @@ Proof.
eauto. eauto.
Qed. Qed.
Hint Resolve RepChangeMethods_ok : core. Local Hint Resolve RepChangeMethods_ok : core.
Theorem refine_rep : forall state1 state2 (absfunc : state2 -> state1) Theorem refine_rep : forall state1 state2 (absfunc : state2 -> state1)
names (ms1 : methods state1 names) (ms2 : methods state2 names) names (ms1 : methods state1 names) (ms2 : methods state2 names)
@ -460,7 +460,7 @@ Proof.
eauto. eauto.
Qed. Qed.
Hint Resolve CachingMethods_ok : core. Local Hint Resolve CachingMethods_ok : core.
Theorem refine_cache : forall state name (func : state -> nat) Theorem refine_cache : forall state name (func : state -> nat)
names (ms1 : methods state names) (ms2 : methods (state * nat) names) names (ms1 : methods state names) (ms2 : methods (state * nat) names)

2
frap_book.tex
View file

@ -5377,7 +5377,7 @@ $$\begin{array}{rrcl}
$$\infer{\smallstep{(h, l, x \leftarrow c_1; c_2(x))}{(h', l', x \leftarrow c'_1; c_2(x))}}{ $$\infer{\smallstep{(h, l, x \leftarrow c_1; c_2(x))}{(h', l', x \leftarrow c'_1; c_2(x))}}{
\smallstep{(h, l, c_1)}{(h', l', c'_1)} \smallstep{(h, l, c_1)}{(h', l', c'_1)}
} }
\quad \infer{\smallstep{(h, l, x \leftarrow \mt{Return} \; v; c_2(x))}{(h, k, c_2(v))}}{}$$ \quad \infer{\smallstep{(h, l, x \leftarrow \mt{Return} \; v; c_2(x))}{(h, l, c_2(v))}}{}$$
$$\infer{\smallstep{(h, l, \mt{Loop} \; i \; f)}{(h, l, x \leftarrow f(i); \mt{match} \; x \; \mt{with} \; \mt{Done}(a) \Rightarrow \mt{Return} \; a \mid \mt{Again}(a) \Rightarrow \mt{Loop} \; a \; f)}}{}$$ $$\infer{\smallstep{(h, l, \mt{Loop} \; i \; f)}{(h, l, x \leftarrow f(i); \mt{match} \; x \; \mt{with} \; \mt{Done}(a) \Rightarrow \mt{Return} \; a \mid \mt{Again}(a) \Rightarrow \mt{Loop} \; a \; f)}}{}$$