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	<id>https://fascipedia.org/index.php?action=history&amp;feed=atom&amp;title=Type_theory</id>
	<title>Type theory - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://fascipedia.org/index.php?action=history&amp;feed=atom&amp;title=Type_theory"/>
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	<updated>2026-04-06T02:23:20Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.39.2</generator>
	<entry>
		<id>https://fascipedia.org/index.php?title=Type_theory&amp;diff=49323&amp;oldid=prev</id>
		<title>𝗔𝗿𝗰𝗵𝗮𝗻𝗴𝗲𝗹: Text replacement - &quot;\[\[Category(.*) of (.*)\]\]&quot; to &quot;&quot;</title>
		<link rel="alternate" type="text/html" href="https://fascipedia.org/index.php?title=Type_theory&amp;diff=49323&amp;oldid=prev"/>
		<updated>2024-02-22T01:54:11Z</updated>

		<summary type="html">&lt;p&gt;Text replacement - &amp;quot;\[\[Category(.*) of (.*)\]\]&amp;quot; to &amp;quot;&amp;quot;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 16:54, 21 February 2024&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The topic of ''type [[theory]]'' is fundamental both in [[logic]] and computer Science &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Science]]. We limit ourselves here to sketch some aspects that are important in logic. For the importance of types in computer Science [[Category:Science]]&lt;/del&gt;, for instance:&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The topic of ''type [[theory]]'' is fundamental both in [[logic]] and computer Science , for instance:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Reynolds 1983 and 1985.  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Reynolds 1983 and 1985.  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Paradoxes and Russell's Type Theories  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Paradoxes and Russell's Type Theories  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>𝗔𝗿𝗰𝗵𝗮𝗻𝗴𝗲𝗹</name></author>
	</entry>
	<entry>
		<id>https://fascipedia.org/index.php?title=Type_theory&amp;diff=17116&amp;oldid=prev</id>
		<title>Bacchus: Text replacement - &quot;science&quot; to &quot;Science Category:Science&quot;</title>
		<link rel="alternate" type="text/html" href="https://fascipedia.org/index.php?title=Type_theory&amp;diff=17116&amp;oldid=prev"/>
		<updated>2023-02-14T02:54:43Z</updated>

		<summary type="html">&lt;p&gt;Text replacement - &amp;quot;science&amp;quot; to &amp;quot;Science &lt;a href=&quot;/index.php/Category:Science&quot; title=&quot;Category:Science&quot;&gt;Category:Science&lt;/a&gt;&amp;quot;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 17:54, 13 February 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The topic of ''type [[theory]]'' is fundamental both in [[logic]] and computer &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;science&lt;/del&gt;. We limit ourselves here to sketch some aspects that are important in logic. For the importance of types in computer &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;science&lt;/del&gt;, for instance:&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The topic of ''type [[theory]]'' is fundamental both in [[logic]] and computer &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Science [[Category:Science]]&lt;/ins&gt;. We limit ourselves here to sketch some aspects that are important in logic. For the importance of types in computer &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Science [[Category:Science]]&lt;/ins&gt;, for instance:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Reynolds 1983 and 1985.  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Reynolds 1983 and 1985.  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Paradoxes and Russell's Type Theories  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Paradoxes and Russell's Type Theories  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Bacchus</name></author>
	</entry>
	<entry>
		<id>https://fascipedia.org/index.php?title=Type_theory&amp;diff=16774&amp;oldid=prev</id>
		<title>Bacchus: Text replacement - &quot;theory&quot; to &quot;theory&quot;</title>
		<link rel="alternate" type="text/html" href="https://fascipedia.org/index.php?title=Type_theory&amp;diff=16774&amp;oldid=prev"/>
		<updated>2023-02-10T05:11:32Z</updated>

		<summary type="html">&lt;p&gt;Text replacement - &amp;quot;theory&amp;quot; to &amp;quot;&lt;a href=&quot;/index.php/Theory&quot; title=&quot;Theory&quot;&gt;theory&lt;/a&gt;&amp;quot;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:11, 9 February 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The topic of ''type theory'' is fundamental both in [[logic]] and computer science. We limit ourselves here to sketch some aspects that are important in logic. For the importance of types in computer science, for instance:&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The topic of ''type &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[&lt;/ins&gt;theory&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]]&lt;/ins&gt;'' is fundamental both in [[logic]] and computer science. We limit ourselves here to sketch some aspects that are important in logic. For the importance of types in computer science, for instance:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Reynolds 1983 and 1985.  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Reynolds 1983 and 1985.  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Paradoxes and Russell's Type Theories  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Paradoxes and Russell's Type Theories  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Simple Type Theory and the λ -Calculus.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Simple Type Theory and the λ -Calculus.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Church's type theory, aka simple type theory, is a formal logical language which includes classical first-order and propositional logic, but is more expressive in a practical sense. It is used, with some modifications and enhancements, in most modern applications of type theory.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Church's type &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[&lt;/ins&gt;theory&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]]&lt;/ins&gt;, aka simple type &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[&lt;/ins&gt;theory&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]]&lt;/ins&gt;, is a formal logical language which includes classical first-order and propositional logic, but is more expressive in a practical sense. It is used, with some modifications and enhancements, in most modern applications of type &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[&lt;/ins&gt;theory&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]]&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Definitions]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Definitions]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Bacchus</name></author>
	</entry>
	<entry>
		<id>https://fascipedia.org/index.php?title=Type_theory&amp;diff=11003&amp;oldid=prev</id>
		<title>Bacchus: Created page with &quot;The topic of ''type theory'' is fundamental both in logic and computer science. We limit ourselves here to sketch some aspects that are important in logic. For the importance of types in computer science, for instance: # Reynolds 1983 and 1985.  # Paradoxes and Russell's Type Theories  # Simple Type Theory and the λ -Calculus.  Church's type theory, aka simple type theory, is a formal logical language which includes classical first-order and propositional logic, but...&quot;</title>
		<link rel="alternate" type="text/html" href="https://fascipedia.org/index.php?title=Type_theory&amp;diff=11003&amp;oldid=prev"/>
		<updated>2022-12-17T22:41:07Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;The topic of &amp;#039;&amp;#039;type theory&amp;#039;&amp;#039; is fundamental both in &lt;a href=&quot;/index.php/Logic&quot; title=&quot;Logic&quot;&gt;logic&lt;/a&gt; and computer science. We limit ourselves here to sketch some aspects that are important in logic. For the importance of types in computer science, for instance: # Reynolds 1983 and 1985.  # Paradoxes and Russell&amp;#039;s Type Theories  # Simple Type Theory and the λ -Calculus.  Church&amp;#039;s type theory, aka simple type theory, is a formal logical language which includes classical first-order and propositional logic, but...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;The topic of ''type theory'' is fundamental both in [[logic]] and computer science. We limit ourselves here to sketch some aspects that are important in logic. For the importance of types in computer science, for instance:&lt;br /&gt;
# Reynolds 1983 and 1985. &lt;br /&gt;
# Paradoxes and Russell's Type Theories &lt;br /&gt;
# Simple Type Theory and the λ -Calculus.&lt;br /&gt;
&lt;br /&gt;
Church's type theory, aka simple type theory, is a formal logical language which includes classical first-order and propositional logic, but is more expressive in a practical sense. It is used, with some modifications and enhancements, in most modern applications of type theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Definitions]]&lt;/div&gt;</summary>
		<author><name>Bacchus</name></author>
	</entry>
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