From b9504d78577adc3c25f648272bf87eba0dad773b Mon Sep 17 00:00:00 2001 From: Joshua Potter Date: Sun, 21 Jul 2024 06:54:03 -0600 Subject: [PATCH] Nest abstract rewriting systems under formal systems. --- .../plugins/obsidian-to-anki-plugin/data.json | 5 ++- .../abstract-rewriting-systems/normal-form.md | 44 ------------------- .../abstract-rewriting.md} | 36 ++++++++++++++- 3 files changed, 37 insertions(+), 48 deletions(-) delete mode 100644 notes/abstract-rewriting-systems/normal-form.md rename notes/{abstract-rewriting-systems/index.md => formal-system/abstract-rewriting.md} (80%) diff --git a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json index 4d8ffaa..7ed6084 100644 --- a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json +++ b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json @@ -620,7 +620,7 @@ "_journal/2024-07/2024-07-18.md": "237918b58424435959cbc949d01e7932", "_journal/2024-07-20.md": "d8685729effc374e4ece1e618c2fdad3", "_journal/2024-07/2024-07-19.md": "e9fe4569f88e1ba9393292bcf092edfc", - "_journal/2024-07-21.md": "682ee0ada782dd281d8fd217227e985c", + "_journal/2024-07-21.md": "dd5dd93f119f69571a78e027fab7da5d", "_journal/2024-07/2024-07-20.md": "d8685729effc374e4ece1e618c2fdad3", "logic/classical/index.md": "ee0a4b2bfcfa2cab0880db449cb62df1", "logic/classical/truth-tables.md": "b739e2824a4a5c26ac446e7c15ce02aa", @@ -630,7 +630,8 @@ "formal-system/logical-system/pred-logic.md": "2524ccc09561bc219dab3f32010a0161", "formal-system/logical-system/prop-logic.md": "b61ce051795d5a951c763b928ec5cea8", "formal-system/index.md": "3d31c99bffdcb05de9f2e32ac6319952", - "programming/short-circuit.md": "c256ced42dc3b493aff5a356e5383b6e" + "programming/short-circuit.md": "c256ced42dc3b493aff5a356e5383b6e", + "formal-system/abstract-rewriting.md": "8424314a627851c5b94be6163f64ba30" }, "fields_dict": { "Basic": [ diff --git a/notes/abstract-rewriting-systems/normal-form.md b/notes/abstract-rewriting-systems/normal-form.md deleted file mode 100644 index 225706f..0000000 --- a/notes/abstract-rewriting-systems/normal-form.md +++ /dev/null @@ -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. - -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. - -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. - -END%% - -## Bibliography - -* Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981. \ No newline at end of file diff --git a/notes/abstract-rewriting-systems/index.md b/notes/formal-system/abstract-rewriting.md similarity index 80% rename from notes/abstract-rewriting-systems/index.md rename to notes/formal-system/abstract-rewriting.md index aff4701..21c923e 100644 --- a/notes/abstract-rewriting-systems/index.md +++ b/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 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. + +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. + +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. + +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.