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SessionTypes: example of an online store

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Adam Chlipala 2018-05-13 10:27:15 -04:00
parent af4a09c047
commit 9f247b8375
1 changed files with 85 additions and 1 deletions
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86
SessionTypes.v
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@ -40,7 +40,11 @@ Definition addN (k : nat) (input output : channel) : proc :=
!!output(n + k);
Done.
Ltac hasty := simplify; repeat (constructor; simplify).
Ltac hasty := simplify; repeat ((constructor; simplify)
|| match goal with
| [ |- hasty _ (match ?E with _ => _ end) ] => cases E
| [ |- hasty (match ?E with _ => _ end) _ ] => cases E
end).
Theorem addN_typed : forall k input output,
hasty (addN k input output) (???input(_ : nat); !!!output(_ : nat); TDone).
@ -69,6 +73,68 @@ Proof.
hasty.
Qed.
(** ** Example *)
Section online_store.
Variables request_product in_stock_or_not send_payment_info payment_success add_review : channel.
Definition customer (product payment_info : string) :=
!!request_product(product);
??in_stock_or_not(worked : bool);
if worked then
!!send_payment_info(payment_info);
??payment_success(worked_again : bool);
if worked_again then
!!add_review((product, "awesome"));
Done
else
Done
else
Done.
Definition customer_type :=
(!!!request_product(_ : string);
???in_stock_or_not(worked : bool);
if worked then
!!!send_payment_info(_ : string);
???payment_success(worked_again : bool);
if worked_again then
!!!add_review(_ : (string * string)%type);
TDone
else
TDone
else
TDone)%st.
Theorem customer_hasty : forall product payment_info,
hasty (customer product payment_info) customer_type.
Proof.
hasty.
Qed.
Definition merchant (in_stock payment_checker : string -> bool) :=
??request_product(product : string);
if in_stock product then
!!in_stock_or_not(true);
??send_payment_info(payment_info : string);
if payment_checker payment_info then
!!payment_success(true);
??add_review(_ : (string * string)%type);
Done
else
!!payment_success(false);
Done
else
!!in_stock_or_not(false);
Done.
Theorem merchant_hasty : forall in_stock payment_checker,
hasty (merchant in_stock payment_checker) (complement customer_type).
Proof.
hasty.
Qed.
End online_store.
(** * Parallel execution preserves the existence of complementary session types. *)
@ -149,3 +215,21 @@ Proof.
Unshelve.
assumption.
Qed.
Example online_store_no_deadlock : forall request_product in_stock_or_not
send_payment_info payment_success add_review
product payment_info in_stock payment_checker,
invariantFor (trsys_of (customer request_product in_stock_or_not
send_payment_info payment_success add_review
product payment_info
|| merchant request_product in_stock_or_not
send_payment_info payment_success add_review
in_stock payment_checker))
(fun pr => pr = (Done || Done)
\/ exists l' pr', lstep pr l' pr').
Proof.
simplify.
eapply no_deadlock with (t := customer_type request_product in_stock_or_not
send_payment_info payment_success add_review);
hasty.
Qed.