Places

A place $p$ is a tuple of a local $v$ and a projection.

Place Expansion

A set of places $\overline{p}$ is a place expansion iff there exists a base $p$ such that:

• $p$ is an enum type and $\overline{p}=\{p@V\}$ and $V$ is a variant of $p$
• $p$ is a struct or tuple type and $\overline{p}$ is the set of places obtained by projecting $p$ with each of the fields in the type of $p$
• $p$ is a reference-typed field and $\overline{p}=\{\ast p\}$
• $p$ is an array or slice and $\overline{p}=p[i]$ (TODO: more cases)

If there is such a $p$, then that $p$ is unique, and $\overline{p}$ is an expansion of $p$.

Owned Places

A place is owned iff it does not project from the dereference of a reference-typed place.

Place Liveness

A place $p$ is live at a location $l$ iff there exists a location $l^{\prime }$ and a control flow-path $c$ from $l$ to $l^{\prime }$ where a place conflicting with $p$ is used at $l^{\prime }$ and there are no assignments of any places conflicting with $p$ along c.

Place Prefix

A place $p$ is a prefix of a place $p^{\prime }$ iff:

• $p$ and $p^{\prime }$ have the same local, and
• The projection of $p$ is a prefix of the projection of $p^{\prime }$

Note that $p$ is a prefix of itself.

A place $p$ is a strict prefix of $p^{\prime }$ iff $p$ is a prefix of $p^{\prime }$ and $p\ne p^{\prime }$.