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