Memory Model Background Definitions

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Basic Definitions

These definitions are essentially due to Sebastian Burckhardt.

Definition

P -- set of procesors, is {1,...,n} for some natural number n

A -- set of target addresses

V -- set of values

i(a) -- initial value of locations a in A; ranges over V

Event structure

E -- set of events

t(e) in {load, store, sync} -- type of event e in E

p(e) in P -- processor that executes event e in E

a(e) in A -- storage address used by event e in E

v(e) in V --value loaded or stored by event e in E

Derived notation

E(p) -- events executed by processor p = {e in E | p(e) = p}

L -- load events = {e in E | t(e)=load}

S -- store events = {e in E | t(e)=store}

X -- load or store events = L u S

F -- fence events = {e in E | t(e)=fence}

L(p) -- for p a processor, loads executed by p = L intersect E(p)

S(p) -- for p a processor, stores executed by p = S intersect E(p)

F(p) -- for p a processor, fences executed by p = F intersect E(p)

S(a) -- for a an address, store events to a = {s in S | a(s)=a}

S(l) -- for l a load, store events to address a(l) = S(a(l))

L(s) -- for s a store, load events to address a(s) = L(s(l))

We shall use per-process partial orders, <p, where p a processor. By a slight abuse of notation, we shall permit < to be subscripted with events rather than just processes. Thus d <d e is taken to be shorthand for d <p e, where p=p(d).