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Turn off some warnings
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Adam Chlipala
parent
19d915fb37
commit
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4 changed files with 75 additions and 64 deletions
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@ -3,6 +3,8 @@
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* Author: Adam Chlipala
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* License: https://creativecommons.org/licenses/by-nc-nd/4.0/ *)
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Set Warnings "-notation-overridden". (* <-- needed while we play with defining one
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* of the book's notations ourselves locally *)
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Require Import Frap TransitionSystems.
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Set Implicit Arguments.
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@ -3,6 +3,8 @@
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* Author: Adam Chlipala
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* License: https://creativecommons.org/licenses/by-nc-nd/4.0/ *)
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Set Warnings "-notation-overridden". (* <-- needed while we play with defining one
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* of the book's notations ourselves locally *)
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Require Import Frap TransitionSystems.
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Set Implicit Arguments.
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@ -175,28 +177,64 @@ Qed.
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Theorem factorial_ok_2 :
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invariantFor (factorial_sys 2) (fact_correct 2).
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Proof.
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Admitted.
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simplify.
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eapply invariant_weaken.
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apply multiStepClosure_ok.
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simplify.
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rewrite fact_init_is.
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eapply MscStep.
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apply oneStepClosure_split.
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simplify.
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invert H.
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simplify.
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apply singleton_in.
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apply oneStepClosure_empty.
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simplify.
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eapply MscStep.
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apply oneStepClosure_split.
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simplify.
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invert H.
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simplify.
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apply singleton_in.
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apply oneStepClosure_split.
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simplify.
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invert H.
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simplify.
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apply singleton_in.
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apply oneStepClosure_empty.
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simplify.
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eapply MscStep.
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apply oneStepClosure_split.
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simplify.
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invert H.
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simplify.
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apply singleton_in.
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apply oneStepClosure_split.
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simplify.
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invert H.
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simplify.
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apply singleton_in.
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apply oneStepClosure_split.
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simplify.
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invert H.
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simplify.
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apply singleton_in.
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apply oneStepClosure_empty.
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simplify.
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apply MscDone.
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apply prove_oneStepClosure; simplify.
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assumption.
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propositional; subst; invert H0; simplify; propositional.
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simplify.
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unfold fact_correct.
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propositional; subst; trivial.
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Qed.
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(* BEGIN CODE THAT WILL NOT BE EXPLAINED IN DETAIL! *)
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@ -404,25 +442,10 @@ Proof.
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assumption.
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Qed.
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Theorem add2_ok :
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(*Theorem add2_ok :
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invariantFor add2_sys add2_correct.
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Proof.
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Admitted.
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Admitted.*)
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Inductive add2_bthread :=
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| BRead
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@ -488,7 +511,7 @@ Qed.
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Hint Rewrite add2_init_is.
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(* Now, let's verify the original system. *)
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(*Theorem add2_ok :
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Theorem add2_ok :
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invariantFor add2_sys add2_correct.
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Proof.
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(* First step: strengthen the invariant. We leave an underscore for the
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@ -597,7 +620,7 @@ Proof.
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invert H1.
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propositional.
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Qed.*)
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Qed.
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(** * Another abstraction example *)
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@ -1373,35 +1396,17 @@ Qed.
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Theorem twoadd2_ok :
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invariantFor (parallel twoadd_sys twoadd_sys) (twoadd_correct (private := _)).
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Proof.
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Admitted.
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eapply invariant_weaken.
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eapply invariant_simulates.
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apply withInterference_abstracts.
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apply withInterference_parallel.
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apply twoadd_ok.
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apply twoadd_ok.
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unfold twoadd_correct.
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invert 1.
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assumption.
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Qed.
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(* In fact, this modularity technique is so powerful that we now get correctness
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* for any number of threads, "for free"! Here's a tactic definition, which we
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@ -85,6 +85,8 @@ Proof.
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Qed.
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(* Transitive-reflexive closure is so common that it deserves a shorthand notation! *)
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Set Warnings "-notation-overridden". (* <-- needed while we play with defining one
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* of the book's notations ourselves locally *)
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Notation "R ^*" := (trc R) (at level 0).
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(* Now let's use it to execute the factorial program. *)
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@ -50,6 +50,8 @@ Inductive trc {A} (R : A -> A -> Prop) : A -> A -> Prop :=
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-> trc R x z.
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(* Transitive-reflexive closure is so common that it deserves a shorthand notation! *)
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Set Warnings "-notation-overridden". (* <-- needed while we play with defining one
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* of the book's notations ourselves locally *)
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Notation "R ^*" := (trc R) (at level 0).
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(* Now let's use it to execute the factorial program. *)
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