Nest abstract rewriting systems under formal systems.

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

@@ -1,44 +0,0 @@
----
-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.

notes/formal-system/abstract-rewriting.md

@@ -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.