notebook/notes/abstract-rewriting-systems/normal-form.md

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---
title: Normal Form
TARGET DECK: Obsidian::STEM
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FILE TAGS: ars::normal
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tags:
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- ars
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---
## Overview
An object is said to be in **normal form** if it cannot be reduced any further. Examples of normal form include:
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* [[truth-tables|Conjunctive Normal Form]]
* [[truth-tables|Disjunctive Normal Form]]
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* [[pred-logic#Identifiers|Prenex Normal Form]]
* [[beta-reduction#Normal Form|β-normal forms]]
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%%ANKI
Basic
What does it mean for an object to be in normal form?
Back: It cannot be rewritten/reduced any further.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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%%ANKI
Basic
What zero-order logical normal form(s) have only $\land$ and $\lor$ operators?
Back: CNF and DNF.
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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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END%%
%%ANKI
Basic
What first-order logical normal form(s) writes bound identifiers before free ones?
Back: PNF
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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END%%
## Bibliography
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* Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.