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Proofreading AbstractInterpretation

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Adam Chlipala 2018-03-18 20:45:46 -04:00
parent a48d85c84c
commit f46bed19bb
1 changed files with 5 additions and 5 deletions
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10
AbstractInterpretation.v
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@ -359,11 +359,11 @@ Qed.
Definition astate (a : absint) := fmap var a. Definition astate (a : absint) := fmap var a.
(* An abstract state maps variables to abstract elements. The idea is that each (* An abstract state maps variables to abstract elements. The idea is that each
* variable should take on a concrete valuable represented by its associated * variable should take on a concrete value represented by its associated
* abstract value. These are only finite maps, so missing variables are allowed * abstract value. These are only finite maps, so missing variables are allowed
* to take arbitrary values. *) * to take arbitrary values. *)
(* An easy think to do with an [astate] is evaluate an expression into another (* An easy thing to do with an [astate] is evaluate an expression into another
* abstract element. *) * abstract element. *)
Fixpoint absint_interp (e : arith) a (s : astate a) : a := Fixpoint absint_interp (e : arith) a (s : astate a) : a :=
match e with match e with
@ -460,7 +460,7 @@ Definition insensitive_compatible a (s : astate a) (v : valuation) : Prop :=
-> (exists n, v $? x = Some n -> (exists n, v $? x = Some n
/\ a.(Represents) n xa) /\ a.(Represents) n xa)
\/ (forall n, a.(Represents) n xa). \/ (forall n, a.(Represents) n xa).
(* That is, when a variable is mapped to some abstract element, either thhat (* That is, when a variable is mapped to some abstract element, either that
* variable has a compatible concrete value, or the variable has no value and * variable has a compatible concrete value, or the variable has no value and
* that element actually accepts all values (i.e., is probably [Top]). *) * that element actually accepts all values (i.e., is probably [Top]). *)
@ -1198,7 +1198,7 @@ Qed.
* Note the arguments to this predicate, called like * Note the arguments to this predicate, called like
* [interpret ss worklist ss']. [ss] is the state we're starting from, and * [interpret ss worklist ss']. [ss] is the state we're starting from, and
* [ss'] is the final invariatn we calculcate. [worklist] includes only those * [ss'] is the final invariatn we calculcate. [worklist] includes only those
* command/[astate] paris that we didn't already explore outward from. It would * command/[astate] pairs that we didn't already explore outward from. It would
* be pointless to continually explore from all the points we already * be pointless to continually explore from all the points we already
* processed! *) * processed! *)
Inductive interpret a : astates a -> astates a -> astates a -> Prop := Inductive interpret a : astates a -> astates a -> astates a -> Prop :=
@ -1325,7 +1325,7 @@ Proof.
invert H6; propositional; eauto. invert H6; propositional; eauto.
Qed. Qed.
(* Let's skip descriving this lemma, to move to the main event below. *) (* Let's skip describing this lemma, to move to the main event below. *)
Lemma interpret_sound' : forall c a, absint_sound a Lemma interpret_sound' : forall c a, absint_sound a
-> forall ss worklist ss' : astates a, interpret ss worklist ss' -> forall ss worklist ss' : astates a, interpret ss worklist ss'
-> ss $? c = Some $0 -> ss $? c = Some $0