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Avoid a notation conflict

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Adam Chlipala 2016-02-25 11:54:03 -05:00
parent a583e1d0d4
commit 4889f08ac4
1 changed files with 13 additions and 13 deletions
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26
OperationalSemantics.v
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@ -37,13 +37,13 @@ Infix "*" := Times : arith_scope.
Delimit Scope arith_scope with arith. Delimit Scope arith_scope with arith.
Notation "x <- e" := (Assign x e%arith) (at level 75). Notation "x <- e" := (Assign x e%arith) (at level 75).
Infix ";;" := Sequence (at level 76). (* This one changed slightly, to avoid parsing clashes. *) Infix ";;" := Sequence (at level 76). (* This one changed slightly, to avoid parsing clashes. *)
Notation "'when' e 'do' then_ 'else' else_ 'done'" := (If e%arith then_ else_) (at level 75, e at level 0). Notation "'when' e 'loop' then_ 'else' else_ 'done'" := (If e%arith then_ else_) (at level 75, e at level 0).
Notation "'while' e 'do' body 'done'" := (While e%arith body) (at level 75). Notation "'while' e 'loop' body 'done'" := (While e%arith body) (at level 75).
(* Here's an adaptation of our factorial example from Chapter 3. *) (* Here's an adaptation of our factorial example from Chapter 3. *)
Example factorial := Example factorial :=
"output" <- 1;; "output" <- 1;;
while "input" do while "input" loop
"output" <- "output" * "input";; "output" <- "output" * "input";;
"input" <- "input" - 1 "input" <- "input" - 1
done. done.
@ -159,7 +159,7 @@ Fixpoint fact (n : nat) : nat :=
end. end.
Example factorial_loop := Example factorial_loop :=
while "input" do while "input" loop
"output" <- "output" * "input";; "output" <- "output" * "input";;
"input" <- "input" - 1 "input" <- "input" - 1
done. done.
@ -518,13 +518,13 @@ Inductive isEven : nat -> Prop :=
| EvenSS : forall n, isEven n -> isEven (S (S n)). | EvenSS : forall n, isEven n -> isEven (S (S n)).
Definition my_loop := Definition my_loop :=
while "n" do while "n" loop
"a" <- "a" + "n";; "a" <- "a" + "n";;
"n" <- "n" - 2 "n" <- "n" - 2
done. done.
Definition all_programs := { Definition all_programs := {
(while "n" do (while "n" loop
"a" <- "a" + "n";; "a" <- "a" + "n";;
"n" <- "n" - 2 "n" <- "n" - 2
done), done),
@ -535,23 +535,23 @@ Definition all_programs := {
("n" <- "n" - 2), ("n" <- "n" - 2),
(("a" <- "a" + "n";; (("a" <- "a" + "n";;
"n" <- "n" - 2);; "n" <- "n" - 2);;
while "n" do while "n" loop
"a" <- "a" + "n";; "a" <- "a" + "n";;
"n" <- "n" - 2 "n" <- "n" - 2
done), done),
((Skip;; ((Skip;;
"n" <- "n" - 2);; "n" <- "n" - 2);;
while "n" do while "n" loop
"a" <- "a" + "n";; "a" <- "a" + "n";;
"n" <- "n" - 2 "n" <- "n" - 2
done), done),
("n" <- "n" - 2;; ("n" <- "n" - 2;;
while "n" do while "n" loop
"a" <- "a" + "n";; "a" <- "a" + "n";;
"n" <- "n" - 2 "n" <- "n" - 2
done), done),
(Skip;; (Skip;;
while "n" do while "n" loop
"a" <- "a" + "n";; "a" <- "a" + "n";;
"n" <- "n" - 2 "n" <- "n" - 2
done), done),
@ -583,7 +583,7 @@ Proof.
Qed. Qed.
Lemma manually_proved_invariant' : Lemma manually_proved_invariant' :
invariantFor (trsys_of ($0 $+ ("n", 0) $+ ("a", 0)) (while "n" do "a" <- "a" + "n";; "n" <- "n" - 2 done)) invariantFor (trsys_of ($0 $+ ("n", 0) $+ ("a", 0)) (while "n" loop "a" <- "a" + "n";; "n" <- "n" - 2 done))
(fun s => all_programs (snd s) (fun s => all_programs (snd s)
/\ exists n a, fst s $? "n" = Some n /\ exists n a, fst s $? "n" = Some n
/\ fst s $? "a" = Some a /\ fst s $? "a" = Some a
@ -680,7 +680,7 @@ Hint Constructors isEven.
Hint Resolve isEven_minus2 isEven_plus. Hint Resolve isEven_minus2 isEven_plus.
Lemma manually_proved_invariant'_snazzy : Lemma manually_proved_invariant'_snazzy :
invariantFor (trsys_of ($0 $+ ("n", 0) $+ ("a", 0)) (while "n" do "a" <- "a" + "n";; "n" <- "n" - 2 done)) invariantFor (trsys_of ($0 $+ ("n", 0) $+ ("a", 0)) (while "n" loop "a" <- "a" + "n";; "n" <- "n" - 2 done))
(fun s => all_programs (snd s) (fun s => all_programs (snd s)
/\ exists n a, fst s $? "n" = Some n /\ exists n a, fst s $? "n" = Some n
/\ fst s $? "a" = Some a /\ fst s $? "a" = Some a
@ -700,7 +700,7 @@ Proof.
Qed. Qed.
Theorem manually_proved_invariant : Theorem manually_proved_invariant :
invariantFor (trsys_of ($0 $+ ("n", 0) $+ ("a", 0)) (while "n" do "a" <- "a" + "n";; "n" <- "n" - 2 done)) invariantFor (trsys_of ($0 $+ ("n", 0) $+ ("a", 0)) (while "n" loop "a" <- "a" + "n";; "n" <- "n" - 2 done))
(fun s => exists a, fst s $? "a" = Some a /\ isEven a). (fun s => exists a, fst s $? "a" = Some a /\ isEven a).
Proof. Proof.
eapply invariant_weaken. eapply invariant_weaken.