The C11 and C++11 Concurrency Model

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| Blocked rmw l → lk l = Atomic
end
Some actions block forever, and the thread-local semantics must generate preexecutions
in which permanently blocked actions have no successors in sequenced-before
on the same thread:
let blocking observed actions sb =
(∀ a ∈ actions.
(is blocked rmw a ∨ is blocked lock a)
−→
¬ (∃ b ∈ actions. (a, b) ∈ sb))
The standard says that functions are ordered with respect to all other actions on the
same thread by sequenced-before, whether or not an order is imposed by the syntax of
the program; their sequencing is described as indeterminate (see Appendix A for the
rationale). All memory accesses on atomic and mutex locations are the result of calls to
library functions, and as a consequence, they are ordered with respect to all other actions
on the same thread by sequenced before. This property is captured by the following
conjunct of the well-formed-threads predicate:
let indeterminate sequencing Xo =
∀ a ∈ Xo.actions b ∈ Xo.actions.
(tid of a = tid of b) ∧ (a ≠ b) ∧
¬ (is at non atomic location Xo.lk a ∧ is at non atomic location Xo.lk b) −→
(a, b) ∈ Xo.sb ∨ (b, a) ∈ Xo.sb
We do not model the creation and joining of threads explicitly. Instead, the threadlocal
semantics provides us with the additional synchronises-with relation, that captures
parent-to-child thread creation ordering. The calculated relation sbasw is the transitive
closure of the union of sb and asw. This relation captures program order and the interthread
ordering induced by creating and joining threads. We require this relation to be
acyclic.
let sbasw Xo = transitiveClosure (Xo.sb ∪ Xo.asw)
In addition to the requirements above, well formed threads predicate provides the following
guarantees: all actions have a unique identifier (we require the projection of the
action identifier to be injective), the sb and asw relations only relate actions of the execution,
the sb relation must only relate actions on the same thread, the asw relation
must only relate actions on different threads, the sb and dd relations are both strict partial
orders, and the dd relation is a subset of the sb relation. The well formed threads
predicate: