143 lines
5.0 KiB
Markdown
143 lines
5.0 KiB
Markdown
---
|
||
title: Short-Circuit
|
||
TARGET DECK: Obsidian::STEM
|
||
FILE TAGS: logic
|
||
tags:
|
||
- logic
|
||
---
|
||
|
||
## Overview
|
||
|
||
The $\textbf{cand}$ and $\textbf{cor}$ operator allows short-circuiting evaluation in the case of undefined ($U$) values.
|
||
|
||
%%ANKI
|
||
Basic
|
||
What truth values do short-circuit evaluation operators act on?
|
||
Back: $T$, $F$, and $U$
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
<!--ID: 1707317708622-->
|
||
END%%
|
||
|
||
%%ANKI
|
||
Basic
|
||
What C operator corresponds to $\textbf{cand}$?
|
||
Back: `&&`
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
Tags: c
|
||
<!--ID: 1707316606004-->
|
||
END%%
|
||
|
||
%%ANKI
|
||
Basic
|
||
Why is $\textbf{cand}$ named the way it is?
|
||
Back: It is short for **c**onditional **and**.
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
<!--ID: 1707317708625-->
|
||
END%%
|
||
|
||
%%ANKI
|
||
Basic
|
||
How is $p \textbf{ cand } q$ written as a conditional?
|
||
Back: $\textbf{if } p \textbf{ then } q \textbf{ else } F$
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
<!--ID: 1707317708627-->
|
||
END%%
|
||
|
||
%%ANKI
|
||
Basic
|
||
When can $\textbf{cand}$ evaluate to a non-$U$ value despite being given a $U$ operand?
|
||
Back: $F \textbf{ cand } U = F$
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
<!--ID: 1707317708628-->
|
||
END%%
|
||
|
||
%%ANKI
|
||
Basic
|
||
What C operator corresponds to $\textbf{cor}$?
|
||
Back: `||`
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
Tags: c
|
||
<!--ID: 1707316606007-->
|
||
END%%
|
||
|
||
%%ANKI
|
||
Basic
|
||
Why is $\textbf{cor}$ named the way it is?
|
||
Back: It is short for **c**onditional **or**.
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
<!--ID: 1707317708630-->
|
||
END%%
|
||
|
||
%%ANKI
|
||
Basic
|
||
How is $p \textbf{ cor } q$ written as a conditional?
|
||
Back: $\textbf{if } p \textbf{ then } T \textbf{ else } q$
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
<!--ID: 1707317708632-->
|
||
END%%
|
||
|
||
%%ANKI
|
||
Basic
|
||
When can $\textbf{cor}$ evaluate to a non-$U$ value despite being given a $U$ operand?
|
||
Back: $T \textbf{ cor } U = T$
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
<!--ID: 1707317708633-->
|
||
END%%
|
||
|
||
* Associative Laws
|
||
* $E1 \textbf{ cand } (E2 \textbf{ cand } E3) = (E1 \textbf{ cand } E2) \textbf{ cand } E3$
|
||
* $E1 \textbf{ cor } (E2 \textbf{ cor } E3) = (E1 \textbf{ cor } E2) \textbf{ cor } E3$
|
||
|
||
%%ANKI
|
||
Basic
|
||
Which of the short-circuit logical operators do the commutative laws apply to?
|
||
Back: Neither of them.
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
<!--ID: 1707317708635-->
|
||
END%%
|
||
|
||
%%ANKI
|
||
Basic
|
||
Which of the short-circuit logical operators do the associative laws apply to?
|
||
Back: $\textbf{cand}$ and $\textbf{cor}$
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
<!--ID: 1707317708636-->
|
||
END%%
|
||
|
||
* Distributive Laws
|
||
* $E1 \textbf{ cand } (E2 \textbf{ cor } E3) = (E1 \textbf{ cand } E2) \textbf{ cor } (E1 \textbf{ cand } E3)$
|
||
* $E1 \textbf{ cor } (E2 \textbf{ cand } E3) = (E1 \textbf{ cor } E2) \textbf{ cand } (E1 \textbf{ cor } E3)$
|
||
|
||
%%ANKI
|
||
Basic
|
||
What is the distributive law of e.g. $\textbf{cor}$ over $\textbf{cand}$?
|
||
Back: $E1 \textbf{ cor } (E2 \textbf{ cand } E3) = (E1 \textbf{ cor } E2) \textbf{ cand } (E1 \textbf{ cor } E3)$
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
<!--ID: 1707317708638-->
|
||
END%%
|
||
|
||
* De Morgan's Laws
|
||
* $\neg (E1 \textbf{ cand } E2) = \neg E1 \textbf{ cor } \neg E2$
|
||
* $\neg (E1 \textbf{ cor } E2) = \neg E1 \textbf{ cand } \neg E2$
|
||
|
||
%%ANKI
|
||
Basic
|
||
Which of the short-circuit logical operators do De Morgan's Laws apply to?
|
||
Back: $\textbf{cand}$ and $\textbf{cor}$
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
<!--ID: 1707317708640-->
|
||
END%%
|
||
|
||
%%ANKI
|
||
Basic
|
||
What is De Morgan's Law of e.g. $\textbf{cor}$?
|
||
Back: $\neg (E1 \textbf{ cor } E2) = \neg E1 \textbf{ cand } \neg E2$
|
||
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
||
<!--ID: 1707317708642-->
|
||
END%%
|
||
|
||
Gries lists other "Laws" but they don't seem as important to note here. What's worth noting is that the other [[equiv-trans#Equivalence Schemas|equivalence schemas]] still apply if we can limit operands to just $T$ and $F$.
|
||
|
||
## References
|
||
|
||
* Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981. |