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Nest abstract rewriting systems under formal systems.

c-declarations
Joshua Potter 2024-07-21 06:54:03 -06:00
parent 6ba651c41b
commit b9504d7857
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notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
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notes/abstract-rewriting-systems/normal-form.md
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---
title: Normal Form
TARGET DECK: Obsidian::STEM
FILE TAGS: ars::normal
tags:
- ars
---
## Overview
An object is said to be in **normal form** if it cannot be reduced any further. Examples of normal form include:
* [[truth-tables|Conjunctive Normal Form]]
* [[truth-tables|Disjunctive Normal Form]]
* [[pred-logic#Identifiers|Prenex Normal Form]]
* [[beta-reduction#Normal Form|β-normal forms]]
%%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.
<!--ID: 1707675146194-->
END%%
%%ANKI
Basic
What zero-order logical normal form(s) have only $\land$ and $\lor$ operators?
Back: CNF and DNF.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1707675369145-->
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.
<!--ID: 1707675369187-->
END%%
## Bibliography
* Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.

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notes/abstract-rewriting-systems/index.md → notes/formal-system/abstract-rewriting.md
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@ -1,15 +1,23 @@
---
title: Abstract Rewriting Systems
TARGET DECK: Obsidian::STEM
FILE TAGS: ars
FILE TAGS: formal-system::abstract-rewriting
tags:
- ars
- abstract-rewriting
- formal-system
---
## Overview
In an **abstract rewriting system** (ARS), an object is said to be in **normal form** if it cannot be rewritten any further, i.e. it is irreducible. An object is said to be in **canonical form** if it is presented in the "standard" representation (where "standard" is defined per field).
Examples of normal form include:
* [[truth-tables|Conjunctive Normal Form]]
* [[truth-tables|Disjunctive Normal Form]]
* [[pred-logic#Identifiers|Prenex Normal Form]]
* [[beta-reduction#Normal Form|β-normal forms]]
In most fields, a canoncial form specifies a *unique* representation.
%%ANKI
@ -59,6 +67,30 @@ Reference: “Canonical Form,” in _Wikipedia_, January 7, 2024, [https://en.wi
<!--ID: 1719067812833-->
END%%
%%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.
<!--ID: 1707675146194-->
END%%
%%ANKI
Basic
What zero-order logical normal form(s) have only $\land$ and $\lor$ operators?
Back: CNF and DNF.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1707675369145-->
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.
<!--ID: 1707675369187-->
END%%
## Confluence
**Confluence** is the property by which two different terms can be further reduced to one common term. That is to say, confluence is a property of rewriting systems describing which terms in such a system can be rewritten in more than one way.