Short-Circuit

Overview

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

Laws

Associativity

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

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

Distributivity

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

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

De Morgan’s Laws

Given propositions $E1$ and $E2$,

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

Bibliography

• Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.