Short-Circuit

Overview

The $\mathbf{\text{cand}}$ and $\mathbf{\text{cor}}$ operator allows short-circuiting evaluation in the case of undefined ($U$) values.

Laws

Associativity

Given propositions $E1$, $E2$, and $E3$,

• $E1\mathbf{\text{ cand }}(E2\mathbf{\text{ cand }}E3)=(E1\mathbf{\text{ cand }}E2)\mathbf{\text{ cand }}E3$
• $E1\mathbf{\text{ cor }}(E2\mathbf{\text{ cor }}E3)=(E1\mathbf{\text{ cor }}E2)\mathbf{\text{ cor }}E3$

Distributivity

Given propositions $E1$, $E2$, and $E3$,

• $E1\mathbf{\text{ cand }}(E2\mathbf{\text{ cor }}E3)=(E1\mathbf{\text{ cand }}E2)\mathbf{\text{ cor }}(E1\mathbf{\text{ cand }}E3)$
• $E1\mathbf{\text{ cor }}(E2\mathbf{\text{ cand }}E3)=(E1\mathbf{\text{ cor }}E2)\mathbf{\text{ cand }}(E1\mathbf{\text{ cor }}E3)$

De Morgan's Laws

Given propositions $E1$ and $E2$,

• $\mathrm{\neg }(E1\mathbf{\text{ cand }}E2)=\mathrm{\neg }E1\mathbf{\text{ cor }}\mathrm{\neg }E2$
• $\mathrm{\neg }(E1\mathbf{\text{ cor }}E2)=\mathrm{\neg }E1\mathbf{\text{ cand }}\mathrm{\neg }E2$