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nLab > Latest Changes: partial combinatory algebra

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- CommentRowNumber1.
- CommentAuthorTodd_Trimble
- CommentTimeAug 16th 2012
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Author: Todd_Trimble
Format: MarkdownItexI have been adding material to [[partial combinatory algebra]]. I plan on linking this to an article on functional completeness for cartesian closed categories, and on deduction theorems for various simple calculi.

I have been adding material to partial combinatory algebra.

I plan on linking this to an article on functional completeness for cartesian closed categories, and on deduction theorems for various simple calculi.
- CommentRowNumber2.
- CommentAuthorDaniil
- CommentTimeSep 3rd 2015
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Author: Daniil
Format: MarkdownItexThe change from the 16th revison to the 17th contains a typo. It [reads](http://ncatlab.org/nlab/revision/partial+combinatory+algebra/17): > let $Hom(f, g)$ be the set of $a$ in $A$ such that for all $x$ in $X$ and $a'$ in $f(x)$, $a$ is an element of $g(x)$, and $a a'$ is defined (that is, $a$ is applicable to $a'$. I changed it to > let $Hom(f, g)$ be the set of $a$ in $A$ such that for all $x$ in $X$ and $a'$ in $f(x)$, $a a'$ is defined (that is, $a$ is applicable to $a'$), and $a a'$ is an element of $g(x)$.

The change from the 16th revison to the 17th contains a typo. It reads:

let $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Hom</mi><mo stretchy="false">(</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">Hom(f, g)</annotation></semantics></math>$ be the set of $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math>$ in $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math>$ such that for all $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math>$ in $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math>$ and $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>′</mo></mrow><annotation encoding="application/x-tex">a'</annotation></semantics></math>$ in $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">f(x)</annotation></semantics></math>$ , $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math>$ is an element of $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>g</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">g(x)</annotation></semantics></math>$ , and $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mi>a</mi><mo>′</mo></mrow><annotation encoding="application/x-tex">a a'</annotation></semantics></math>$ is defined (that is, $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math>$ is applicable to $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>′</mo></mrow><annotation encoding="application/x-tex">a'</annotation></semantics></math>$ .

I changed it to

let $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Hom</mi><mo stretchy="false">(</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">Hom(f, g)</annotation></semantics></math>$ be the set of $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math>$ in $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math>$ such that for all $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math>$ in $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math>$ and $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>′</mo></mrow><annotation encoding="application/x-tex">a'</annotation></semantics></math>$ in $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">f(x)</annotation></semantics></math>$ , $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mi>a</mi><mo>′</mo></mrow><annotation encoding="application/x-tex">a a'</annotation></semantics></math>$ is defined (that is, $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math>$ is applicable to $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>′</mo></mrow><annotation encoding="application/x-tex">a'</annotation></semantics></math>$ ), and $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mi>a</mi><mo>′</mo></mrow><annotation encoding="application/x-tex">a a'</annotation></semantics></math>$ is an element of $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>g</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">g(x)</annotation></semantics></math>$ .
- CommentRowNumber3.
- CommentAuthorTodd_Trimble
- CommentTimeSep 3rd 2015
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Author: Todd_Trimble
Format: MarkdownItexYou made the right call. Thanks, Daniil.

You made the right call. Thanks, Daniil.
- CommentRowNumber4.
- CommentAuthorJames Francese
- CommentTimeNov 3rd 2019
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Author: James Francese
Format: MarkdownItexAdded some redirects. <a href="https://ncatlab.org/nlab/revision/diff/partial+combinatory+algebra/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/partial+combinatory+algebra/21">v21</a>, <a href="https://ncatlab.org/nlab/show/partial+combinatory+algebra">current</a>

Added some redirects.

diff, v21, current
- CommentRowNumber5.
- CommentAuthorjoseville
- CommentTimeDec 13th 2021
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Author: joseville
Format: MarkdownItexError and fix from https://math.stackexchange.com/a/4331329/833760 Special thanks to Taroccoesbrocco <a href="https://ncatlab.org/nlab/revision/diff/partial+combinatory+algebra/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/partial+combinatory+algebra/24">v24</a>, <a href="https://ncatlab.org/nlab/show/partial+combinatory+algebra">current</a>

Error and fix from https://math.stackexchange.com/a/4331329/833760 Special thanks to Taroccoesbrocco

diff, v24, current
- CommentRowNumber6.
- CommentAuthorjoseville
- CommentTimeDec 13th 2021
- PermaLink
Author: joseville
Format: MarkdownItexError and fix from https://math.stackexchange.com/a/4331329/833760 Special thanks to Taroccoesbrocco <a href="https://ncatlab.org/nlab/revision/diff/partial+combinatory+algebra/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/partial+combinatory+algebra/24">v24</a>, <a href="https://ncatlab.org/nlab/show/partial+combinatory+algebra">current</a>

Error and fix from https://math.stackexchange.com/a/4331329/833760 Special thanks to Taroccoesbrocco

diff, v24, current
- CommentRowNumber7.
- CommentAuthorjoseville
- CommentTimeDec 13th 2021
- PermaLink
Author: joseville
Format: MarkdownItexFix formatting <a href="https://ncatlab.org/nlab/revision/diff/partial+combinatory+algebra/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/partial+combinatory+algebra/24">v24</a>, <a href="https://ncatlab.org/nlab/show/partial+combinatory+algebra">current</a>

Fix formatting

diff, v24, current
- CommentRowNumber8.
- CommentAuthorjoseville
- CommentTimeDec 13th 2021
- PermaLink
Author: joseville
Format: MarkdownItexError and fix discussed here: https://math.stackexchange.com/a/4331329/833760 Special thanks to Taroccoesbrocco <a href="https://ncatlab.org/nlab/revision/diff/partial+combinatory+algebra/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/partial+combinatory+algebra/24">v24</a>, <a href="https://ncatlab.org/nlab/show/partial+combinatory+algebra">current</a>

Error and fix discussed here: https://math.stackexchange.com/a/4331329/833760 Special thanks to Taroccoesbrocco

diff, v24, current

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nLab > Latest Changes: partial combinatory algebra