PCG Nodes

$$\begin{array}{llr}i& & \text{(Integer)}\\ v& & \text{(MIR Local)}\\ c& & \text{(MIR Constant)}\\ b& & \text{(MIR Basic Block Index)}\\ l& ::=b[i]& \text{(MIR Location)}\\ p& & \text{(MIR Place)}\\ \ell & ::=& \text{(Label)}\\ & \mid \text{start}b& \\ & \mid \text{loop}b& \\ & \mid \text{prepare}l& \\ & \mid \text{before-collapse}l& \\ & \mid \text{before-ref-assignment}l& \\ & \mid \text{mid}l& \\ & \mid \text{after}l& \\ \tilde{p}& ::=& \text{(Maybe-Labelled Place)}\\ & \mid p& \text{(Current Place)}\\ & \mid p\mathtt{at}\ell & \text{(Labelled Place)}\\ \hat{p}& ::=& \text{(PCG Place)}\\ & \mid \tilde{p}& \text{(Maybe-Labelled Place)}\\ & \mid remote(v)& \text{(Remote Place)}\\ rp& ::=& \text{(Lifetime Projection)}\\ & \mid \hat{p}\downarrow r& \text{(Place Projection)}\\ & \mid \hat{p}\downarrow r\text{at}\ell & \text{(Snapshot of Place Projection)}\\ & \mid \hat{p}\downarrow r\text{at}\text{FUTURE}& \text{(Placeholder Projection)}\\ & \mid c\downarrow r& \text{(Constant Projection)}\\ n& ::=\hat{p}|rp& \text{(PCG Node)}\end{array}$$

Associated Place

The associated place of a PCG node $n$ is defined by the partial function $p(n)$ :

• $p(p)=p$
• $p(p\text{at}\ell )=p$
• $p(rp)=p(base(rp))$

Where $base(rp)$ is the base of the lifetime projection $rp$ as defined here.

Local PCG Nodes

A PCG node $n$ is a local node if it has an associated place $p(n)$.