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GADTs for dummies - Revision history
2024-03-19T11:57:42Z
Revision history for this page on the wiki
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https://wiki.haskell.org/index.php?title=GADTs_for_dummies&diff=66446&oldid=prev
Curry: /* Type functions */ Apply tag <hask>
2023-11-24T13:55:51Z
<p><span dir="auto"><span class="autocomment">Type functions: </span> Apply tag <hask></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:55, 24 November 2023</td>
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<td style="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;"><div>A <del class="diffchange diffchange-inline">"</del>data<del class="diffchange diffchange-inline">"</del> declaration is a way to declare both type constructor and data</div></td>
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<td style="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;"><div>A <ins class="diffchange diffchange-inline"><hask></ins>data<ins class="diffchange diffchange-inline"></hask></ins> declaration is a way to declare both type constructor and data</div></td>
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<td style="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;"><div>constructors. For example,</div></td>
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<td style="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;"></td>
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<td style="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;"><div>declares type constructor <del class="diffchange diffchange-inline">"</del>Either<del class="diffchange diffchange-inline">"</del> and two data constructors <del class="diffchange diffchange-inline">"</del>Left<del class="diffchange diffchange-inline">"</del></div></td>
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<td style="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;"><div>declares type constructor <ins class="diffchange diffchange-inline"><hask></ins>Either<ins class="diffchange diffchange-inline"></hask></ins> and two data constructors <ins class="diffchange diffchange-inline"><hask></ins>Left<ins class="diffchange diffchange-inline"></hask></ins></div></td>
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<td style="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;"><div>and <del class="diffchange diffchange-inline">"</del>Right<del class="diffchange diffchange-inline">"</del>. Ordinary Haskell functions work with data constructors:</div></td>
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<td style="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;"><div>and <ins class="diffchange diffchange-inline"><hask></ins>Right<ins class="diffchange diffchange-inline"></hask></ins>. Ordinary Haskell functions work with data constructors:</div></td>
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<td style="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;"><div><haskell></div></td>
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<td style="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;"><div>isLeft <del class="diffchange diffchange-inline">(Left</del> a<del class="diffchange diffchange-inline">)</del> <del class="diffchange diffchange-inline">=</del> <del class="diffchange diffchange-inline">True</del></div></td>
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<td style="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;"><div>isLeft <ins class="diffchange diffchange-inline">:: Either</ins> a <ins class="diffchange diffchange-inline">b -></ins> <ins class="diffchange diffchange-inline">Bool</ins></div></td>
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<td style="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;"><div>isLeft (<del class="diffchange diffchange-inline">Right</del> <del class="diffchange diffchange-inline">b</del>) = <del class="diffchange diffchange-inline">False</del></div></td>
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<td style="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;"><div>isLeft (<ins class="diffchange diffchange-inline">Left</ins> <ins class="diffchange diffchange-inline">_</ins>) = <ins class="diffchange diffchange-inline">True</ins></div></td>
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<td style="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;"></td>
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<td style="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;"><div>declares a TYPE FUNCTION named <del class="diffchange diffchange-inline">"</del>X<del class="diffchange diffchange-inline">"</del>. Its parameter <del class="diffchange diffchange-inline">"</del>a<del class="diffchange diffchange-inline">"</del> must be some type</div></td>
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<td style="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;"><div>declares a TYPE FUNCTION named <ins class="diffchange diffchange-inline"><hask></ins>X<ins class="diffchange diffchange-inline"></hask></ins>. Its parameter <ins class="diffchange diffchange-inline"><hask></ins>a<ins class="diffchange diffchange-inline"></hask></ins> must be some type</div></td>
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<td style="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;"><div>and it returns some type as its result. We can't use <del class="diffchange diffchange-inline">"</del>X<del class="diffchange diffchange-inline">"</del> on data values,</div></td>
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<td style="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;"><div>and it returns some type as its result. We can't use <ins class="diffchange diffchange-inline"><hask></ins>X<ins class="diffchange diffchange-inline"></hask></ins> on data values,</div></td>
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<td style="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;"><div>but we can use it on type values. Type constructors declared with</div></td>
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<td style="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;"><div>but we can use it on type values. Type constructors declared with</div></td>
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<td style="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;"><div><del class="diffchange diffchange-inline">"</del>data<del class="diffchange diffchange-inline">"</del> statements and type functions declared with <del class="diffchange diffchange-inline">"</del>type<del class="diffchange diffchange-inline">"</del> statements</div></td>
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<td style="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;"><div><ins class="diffchange diffchange-inline"><hask></ins>data<ins class="diffchange diffchange-inline"></hask></ins> statements and type functions declared with <ins class="diffchange diffchange-inline"><hask></ins>type<ins class="diffchange diffchange-inline"></hask></ins> statements</div></td>
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<td style="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;"><div>can be used together to build arbitrarily complex types. In such</div></td>
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<td style="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;"><div>can be used together to build arbitrarily complex types. In such</div></td>
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<td style="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;"><div>"computations" type constructors serves as basic "values" and type</div></td>
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<td style="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;"><div>"computations" type constructors serves as basic "values" and type</div></td>
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Curry
https://wiki.haskell.org/index.php?title=GADTs_for_dummies&diff=64800&oldid=prev
Tomjaguarpaw: Remove dead link
2021-10-26T11:36:15Z
<p>Remove dead link</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:36, 26 October 2021</td>
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<td style="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;"><div>( http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.2636 ). Most of</div></td>
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<td style="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;"><div>this article comes from his work.</div></td>
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<td style="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;"><div>this article comes from his work.</div></td>
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<td style="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;"></td>
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<td style="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;"><div>A great demonstration of type-level arithmetic is in the TypeNats package,</div></td>
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<td style="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;"><div>which "defines type-level natural numbers and arithmetic operations on</div></td>
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<td style="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;"><div>them including addition, subtraction, multiplication, division and GCD"</div></td>
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<td style="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;"><div>( darcs get --partial --tag '0.1' http://www.eecs.tufts.edu/~rdocki01/typenats/ )</div></td>
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<td style="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;"></td>
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<td style="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;"></td>
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<td style="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;"><div>I should also mention here [http://okmij.org/ftp/Haskell/types.html Oleg Kiselyov's page on type-level programming in Haskell].</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>I should also mention here [http://okmij.org/ftp/Haskell/types.html Oleg Kiselyov's page on type-level programming in Haskell].</div></td>
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Tomjaguarpaw
https://wiki.haskell.org/index.php?title=GADTs_for_dummies&diff=64431&oldid=prev
Yakushima: slightly less paranoid-sounding rephrase
2021-06-10T10:49:48Z
<p>slightly less paranoid-sounding rephrase</p>
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<td style="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;"></td>
<td class="diff-marker"> </td>
<td style="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;"></td>
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<td class="diff-marker">−</td>
<td style="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;"><div>For a long time, I didn't understand what <del class="diffchange diffchange-inline">GADTs</del> were or how they could be used. It <del class="diffchange diffchange-inline">was sort</del> <del class="diffchange diffchange-inline">of</del> a conspiracy of silence &mdash; people who understood GADTs thought</div></td>
<td class="diff-marker">+</td>
<td style="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;"><div>For a long time, I didn't understand what <ins class="diffchange diffchange-inline">[[Generalised algebraic datatype]]s</ins> were or how they could be used. It <ins class="diffchange diffchange-inline">almost</ins> <ins class="diffchange diffchange-inline">seemed</ins> a conspiracy of silence &mdash; people who understood GADTs thought</div></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>that everything was obvious and didn't need further explanation, but I still</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>that everything was obvious and didn't need further explanation, but I still</div></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>couldn't understand them.</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>couldn't understand them.</div></td>
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<td class="diff-marker"> </td>
<td style="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;"></td>
<td class="diff-marker"> </td>
<td style="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;"></td>
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<tr>
<td class="diff-marker"> </td>
<td style="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;"><div>Now that I have an idea of how it works, I think that it was really obvious. :) So, I want to share my understanding of GADTs. Maybe the way I realized how GADTs work could help</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>Now that I have an idea of how it works, I think that it was really obvious. :) So, I want to share my understanding of GADTs. Maybe the way I realized how GADTs work could help</div></td>
</tr>
<tr>
<td class="diff-marker">−</td>
<td style="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;"><div>someone else. <del class="diffchange diffchange-inline">See also [[Generalised algebraic datatype]]</del></div></td>
<td class="diff-marker">+</td>
<td style="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;"><div>someone else. </div></td>
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<td class="diff-marker"> </td>
<td style="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;"></td>
<td class="diff-marker"> </td>
<td style="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;"></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>There are plenty of GADT-related papers, but the best one for beginners</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>There are plenty of GADT-related papers, but the best one for beginners</div></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>Phantom types is another name of GADT. You should also know that this</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>Phantom types is another name of GADT. You should also know that this</div></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>paper uses old GADT syntax. This paper is a must-read because it</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>paper uses old GADT syntax. This paper is a must-read because it</div></td>
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<td class="diff-marker">−</td>
<td style="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;"><div>contains <del class="diffchange diffchange-inline">numerous</del> examples of practical GADT usage - a theme completely</div></td>
<td class="diff-marker">+</td>
<td style="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;"><div>contains <ins class="diffchange diffchange-inline">several</ins> examples of practical GADT usage - a theme completely</div></td>
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<td class="diff-marker">−</td>
<td style="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;"><div>omitted from <del class="diffchange diffchange-inline">my</del> article. <del class="diffchange diffchange-inline">The</del> paper outlines how to do binary compression<del class="diffchange diffchange-inline"> on datatypes,</del></div></td>
<td class="diff-marker">+</td>
<td style="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;"><div>omitted from <ins class="diffchange diffchange-inline">this</ins> article. <ins class="diffchange diffchange-inline">For example, the</ins> paper outlines how to do binary compression</div></td>
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<td colspan="2" class="diff-empty"> </td>
<td class="diff-marker">+</td>
<td style="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;"><div>on datatypes without using typeclasses,</div></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>and suggests how to make a kind of printf function.</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>and suggests how to make a kind of printf function.</div></td>
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<td class="diff-marker"> </td>
<td style="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;"></td>
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<td style="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;"></td>
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Yakushima
https://wiki.haskell.org/index.php?title=GADTs_for_dummies&diff=64430&oldid=prev
Yakushima: rearranged to suggest practical uses
2021-06-10T10:43:48Z
<p>rearranged to suggest practical uses</p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:43, 10 June 2021</td>
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<td colspan="2" class="diff-lineno">Line 8:</td>
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<td class="diff-marker"> </td>
<td style="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;"><div>Now that I have an idea of how it works, I think that it was really obvious. :) So, I want to share my understanding of GADTs. Maybe the way I realized how GADTs work could help</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>Now that I have an idea of how it works, I think that it was really obvious. :) So, I want to share my understanding of GADTs. Maybe the way I realized how GADTs work could help</div></td>
</tr>
<tr>
<td class="diff-marker"> </td>
<td style="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;"><div>someone else. See also [[Generalised algebraic datatype]]</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>someone else. See also [[Generalised algebraic datatype]]</div></td>
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<td style="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;"></td>
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<td class="diff-marker"><a class="mw-diff-movedpara-right" title="Paragraph was moved. Click to jump to old location." href="#movedpara_3_2_lhs">⚫</a></td>
<td style="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;"><div><a name="movedpara_1_1_rhs"></a>There are plenty of GADT-related papers, but the best one for beginners</div></td>
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<td colspan="2" class="diff-empty"> </td>
<td class="diff-marker"><a class="mw-diff-movedpara-right" title="Paragraph was moved. Click to jump to old location." href="#movedpara_3_3_lhs">⚫</a></td>
<td style="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;"><div><a name="movedpara_1_2_rhs"></a>is [http://www.cs.ox.ac.uk/ralf.hinze/publications/With.pdf "Fun with phantom types"].</div></td>
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<td colspan="2" class="diff-empty"> </td>
<td class="diff-marker"><a class="mw-diff-movedpara-right" title="Paragraph was moved. Click to jump to old location." href="#movedpara_3_4_lhs">⚫</a></td>
<td style="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;"><div><a name="movedpara_1_3_rhs"></a>Phantom types is another name of GADT. You should also know that this</div></td>
</tr>
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<td colspan="2" class="diff-empty"> </td>
<td class="diff-marker"><a class="mw-diff-movedpara-right" title="Paragraph was moved. Click to jump to old location." href="#movedpara_3_5_lhs">⚫</a></td>
<td style="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;"><div><a name="movedpara_1_4_rhs"></a>paper uses old GADT syntax. This paper is a must-read because it</div></td>
</tr>
<tr>
<td colspan="2" class="diff-empty"> </td>
<td class="diff-marker"><a class="mw-diff-movedpara-right" title="Paragraph was moved. Click to jump to old location." href="#movedpara_3_6_lhs">⚫</a></td>
<td style="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;"><div><a name="movedpara_1_5_rhs"></a>contains numerous examples of practical GADT usage - a theme completely</div></td>
</tr>
<tr>
<td colspan="2" class="diff-empty"> </td>
<td class="diff-marker">+</td>
<td style="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;"><div>omitted from my article. The paper outlines how to do binary compression on datatypes,</div></td>
</tr>
<tr>
<td colspan="2" class="diff-empty"> </td>
<td class="diff-marker">+</td>
<td style="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;"><div>and suggests how to make a kind of printf function.</div></td>
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<td class="diff-marker"> </td>
<td style="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;"></td>
<td class="diff-marker"> </td>
<td style="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;"></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>== Type functions ==</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>== Type functions ==</div></td>
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<td style="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;"></td>
<td class="diff-marker"> </td>
<td style="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;"></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>I should also mention here [http://okmij.org/ftp/Haskell/types.html Oleg Kiselyov's page on type-level programming in Haskell].</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>I should also mention here [http://okmij.org/ftp/Haskell/types.html Oleg Kiselyov's page on type-level programming in Haskell].</div></td>
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<td class="diff-marker"><a class="mw-diff-movedpara-left" title="Paragraph was moved. Click to jump to new location." href="#movedpara_1_1_rhs">⚫</a></td>
<td style="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;"><div><a name="movedpara_3_2_lhs"></a>There are plenty of GADT-related papers, but the best one for beginners</div></td>
<td colspan="2" class="diff-empty"> </td>
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<td class="diff-marker"><a class="mw-diff-movedpara-left" title="Paragraph was moved. Click to jump to new location." href="#movedpara_1_2_rhs">⚫</a></td>
<td style="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;"><div><a name="movedpara_3_3_lhs"></a>is [http://www.cs.ox.ac.uk/ralf.hinze/publications/With.pdf "Fun with phantom types"].</div></td>
<td colspan="2" class="diff-empty"> </td>
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<td class="diff-marker"><a class="mw-diff-movedpara-left" title="Paragraph was moved. Click to jump to new location." href="#movedpara_1_3_rhs">⚫</a></td>
<td style="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;"><div><a name="movedpara_3_4_lhs"></a>Phantom types is another name of GADT. You should also know that this</div></td>
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<td class="diff-marker"><a class="mw-diff-movedpara-left" title="Paragraph was moved. Click to jump to new location." href="#movedpara_1_4_rhs">⚫</a></td>
<td style="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;"><div><a name="movedpara_3_5_lhs"></a>paper uses old GADT syntax. This paper is a must-read because it</div></td>
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<td class="diff-marker"><a class="mw-diff-movedpara-left" title="Paragraph was moved. Click to jump to new location." href="#movedpara_1_5_rhs">⚫</a></td>
<td style="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;"><div><a name="movedpara_3_6_lhs"></a>contains numerous examples of practical GADT usage - a theme completely</div></td>
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<td style="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;"><div>omitted from my article.</div></td>
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<td style="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;"></td>
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<td style="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;"></td>
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Yakushima
https://wiki.haskell.org/index.php?title=GADTs_for_dummies&diff=60119&oldid=prev
Goens: typo
2015-09-16T21:57:25Z
<p>typo</p>
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<td style="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;"></td>
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<td style="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;"><div>declares type constructor "Either" and two data constructors "Left"</div></td>
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<td style="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;"><div>declares type constructor "Either" and two data constructors "Left"</div></td>
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<td style="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;"><div>and "Right". Ordinary Haskell functions <del class="diffchange diffchange-inline">works</del> with data constructors:</div></td>
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<td style="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;"><div>and "Right". Ordinary Haskell functions <ins class="diffchange diffchange-inline">work</ins> with data constructors:</div></td>
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<td style="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;"><div><haskell></div></td>
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Goens
https://wiki.haskell.org/index.php?title=GADTs_for_dummies&diff=58676&oldid=prev
Rethab: Fixed link to 'Faking it: Simulating..'
2014-08-19T05:06:23Z
<p>Fixed link to 'Faking it: Simulating..'</p>
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<td style="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;"><div>The best paper on type level arithmetic using type classes I've seen</div></td>
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<td style="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;"><div>is "Faking it: simulating dependent types in Haskell"</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>is "Faking it: simulating dependent types in Haskell"</div></td>
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<td style="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;"><div>( http://<del class="diffchange diffchange-inline">www</del>.<del class="diffchange diffchange-inline">cs</del>.<del class="diffchange diffchange-inline">nott</del>.<del class="diffchange diffchange-inline">ac.uk</del>/<del class="diffchange diffchange-inline">~ctm</del>/<del class="diffchange diffchange-inline">faking</del>.<del class="diffchange diffchange-inline">ps</del>.<del class="diffchange diffchange-inline">gz</del> ). Most of</div></td>
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<td style="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;"><div>( http://<ins class="diffchange diffchange-inline">citeseerx</ins>.<ins class="diffchange diffchange-inline">ist</ins>.<ins class="diffchange diffchange-inline">psu</ins>.<ins class="diffchange diffchange-inline">edu</ins>/<ins class="diffchange diffchange-inline">viewdoc</ins>/<ins class="diffchange diffchange-inline">summary?doi=10.1.1</ins>.<ins class="diffchange diffchange-inline">22</ins>.<ins class="diffchange diffchange-inline">2636</ins> ). Most of</div></td>
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<td style="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;"><div>this article comes from his work.</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>this article comes from his work.</div></td>
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Rethab
https://wiki.haskell.org/index.php?title=GADTs_for_dummies&diff=58393&oldid=prev
Dfeuer: /* Further reading */ Fixed broken link; make links links
2014-06-29T20:50:28Z
<p><span dir="auto"><span class="autocomment">Further reading: </span> Fixed broken link; make links links</span></p>
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<td style="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;"><div>( darcs get --partial --tag '0.1' http://www.eecs.tufts.edu/~rdocki01/typenats/ )</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>( darcs get --partial --tag '0.1' http://www.eecs.tufts.edu/~rdocki01/typenats/ )</div></td>
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<td style="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;"></td>
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<td style="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;"></td>
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<td class="diff-marker">−</td>
<td style="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;"><div>I should also mention here Oleg Kiselyov's page on type-level</div></td>
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<td style="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;"><div>I should also mention here<ins class="diffchange diffchange-inline"> [http://okmij.org/ftp/Haskell/types.html</ins> Oleg Kiselyov's page on type-level<ins class="diffchange diffchange-inline"> programming in Haskell].</ins></div></td>
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<td style="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;"><div>programming in Haskell: http://okmij.org/ftp/Haskell/types.html</div></td>
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<td style="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;"></td>
<td class="diff-marker"> </td>
<td style="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;"></td>
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<td style="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;"></td>
<td class="diff-marker"> </td>
<td style="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;"></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>There are plenty of GADT-related papers, but the best one for beginners</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>There are plenty of GADT-related papers, but the best one for beginners</div></td>
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<td class="diff-marker">−</td>
<td style="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;"><div>is "Fun with phantom types"</div></td>
<td class="diff-marker">+</td>
<td style="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;"><div>is<ins class="diffchange diffchange-inline"> [http://www.cs.ox.ac.uk/ralf.hinze/publications/With.pdf</ins> "Fun with phantom types"<ins class="diffchange diffchange-inline">].</ins></div></td>
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<td class="diff-marker">−</td>
<td style="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;"><div>(http://www.informatik.uni-bonn.de/~ralf/publications/With.pdf).</div></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>Phantom types is another name of GADT. You should also know that this</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>Phantom types is another name of GADT. You should also know that this</div></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>paper uses old GADT syntax. This paper is a must-read because it</div></td>
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<td style="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;"><div>paper uses old GADT syntax. This paper is a must-read because it</div></td>
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<td style="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;"><div>Other GADT-related papers:</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>Other GADT-related papers:</div></td>
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<td class="diff-marker"> </td>
<td style="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;"></td>
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<td style="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;"></td>
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<td style="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;"><div>"Dynamic Optimization for Functional Reactive Programming using</div></td>
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<td style="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;"><div><ins class="diffchange diffchange-inline">* [http://www.cs.nott.ac.uk/~nhn/Publications/icfp2005.pdf </ins>"Dynamic Optimization for Functional Reactive Programming using<ins class="diffchange diffchange-inline"> Generalized Algebraic Data Types"]</ins></div></td>
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<td class="diff-marker">−</td>
<td style="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;"><div>Generalized Algebraic Data Types"</div></td>
<td colspan="2" class="diff-empty"> </td>
</tr>
<tr>
<td class="diff-marker">−</td>
<td style="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;"><div>http://www.cs.nott.ac.uk/~nhn/Publications/icfp2005.pdf</div></td>
<td colspan="2" class="diff-empty"> </td>
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<td class="diff-marker"> </td>
<td style="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;"></td>
<td class="diff-marker"> </td>
<td style="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;"></td>
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<tr>
<td class="diff-marker">−</td>
<td style="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;"><div>"Phantom <del class="diffchange diffchange-inline">types</del>" (actually more scientific version of "Fun with phantom types")</div></td>
<td class="diff-marker">+</td>
<td style="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;"><div><ins class="diffchange diffchange-inline">* [http://citeseer.ist.psu.edu/rd/0,606209,1,0.25,Download/http:qSqqSqwww.informatik.uni-bonn.deqSq~ralfqSqpublicationsqSqPhantom.ps.gz </ins>"Phantom <ins class="diffchange diffchange-inline">Types</ins>"<ins class="diffchange diffchange-inline">]</ins> (actually<ins class="diffchange diffchange-inline"> a</ins> more scientific version of "Fun with phantom types")</div></td>
</tr>
<tr>
<td class="diff-marker">−</td>
<td style="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;"><div>http://citeseer.ist.psu.edu/rd/0,606209,1,0.25,Download/http:qSqqSqwww.informatik.uni-bonn.deqSq~ralfqSqpublicationsqSqPhantom.ps.gz</div></td>
<td colspan="2" class="diff-empty"> </td>
</tr>
<tr>
<td class="diff-marker"> </td>
<td style="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;"></td>
<td class="diff-marker"> </td>
<td style="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;"></td>
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<td class="diff-marker">−</td>
<td style="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;"><div><del class="diffchange diffchange-inline">"Phantom types and subtyping"</del> http://arxiv.org/ps/cs.PL/0403034</div></td>
<td class="diff-marker">+</td>
<td style="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;"><div><ins class="diffchange diffchange-inline">*</ins> <ins class="diffchange diffchange-inline">[</ins>http://arxiv.org/ps/cs.PL/0403034<ins class="diffchange diffchange-inline"> "Phantom types and subtyping"]</ins></div></td>
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<td class="diff-marker"> </td>
<td style="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;"></td>
<td class="diff-marker"> </td>
<td style="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;"></td>
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<tr>
<td class="diff-marker">−</td>
<td style="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;"><div>"Existentially quantified type classes" by Stuckey, Sulzmann and Wazny (URL?)</div></td>
<td class="diff-marker">+</td>
<td style="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;"><div><ins class="diffchange diffchange-inline">* </ins>"Existentially quantified type classes" by Stuckey, Sulzmann and Wazny (URL?)</div></td>
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</table>
Dfeuer
https://wiki.haskell.org/index.php?title=GADTs_for_dummies&diff=58389&oldid=prev
Dfeuer: /* Back to real Haskell - type classes */ Fixed second Replace instance to match the rest—in its original form it made no sense.
2014-06-29T20:13:36Z
<p><span dir="auto"><span class="autocomment">Back to real Haskell - type classes: </span> Fixed second Replace instance to match the rest—in its original form it made no sense.</span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:13, 29 June 2014</td>
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<td style="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;"><div>class Replace t a b res</div></td>
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<td style="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;"><div>class Replace t a b res</div></td>
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<td style="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;"><div>instance Replace t a a t</div></td>
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<td style="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;"><div>instance Replace t a a t</div></td>
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<td style="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;"><div>instance Replace <del class="diffchange diffchange-inline">[</del>t<del class="diffchange diffchange-inline">]</del> a b <del class="diffchange diffchange-inline">[Replace t a b]</del></div></td>
<td class="diff-marker">+</td>
<td style="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;"><div>instance <ins class="diffchange diffchange-inline">(</ins>Replace t a b <ins class="diffchange diffchange-inline">res)</ins></div></td>
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<td style="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;"><div> => Replace [t] a b [res]</div></td>
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<td style="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;"><div>instance (Replace t a b res)</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>instance (Replace t a b res)</div></td>
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<td class="diff-marker"> </td>
<td style="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;"><div> => Replace (Set t) a b (Set res)</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div> => Replace (Set t) a b (Set res)</div></td>
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<td style="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;"><div>UNIFICATION</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>UNIFICATION</div></td>
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<td style="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;"><div>...</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>...</div></td>
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<td style="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;"></td>
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<td style="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;"></td>
<td class="diff-marker"> </td>
<td style="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;"></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>== Back to GADTs ==</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>== Back to GADTs ==</div></td>
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Dfeuer
https://wiki.haskell.org/index.php?title=GADTs_for_dummies&diff=56425&oldid=prev
Davesque at 01:42, 20 July 2013
2013-07-20T01:42:35Z
<p></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 01:42, 20 July 2013</td>
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<td colspan="2" class="diff-lineno">Line 6:</td>
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<td style="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;"><div>couldn't understand them.</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>couldn't understand them.</div></td>
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<td style="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;"></td>
<td class="diff-marker"> </td>
<td style="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;"></td>
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<td class="diff-marker">−</td>
<td style="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;"><div>Now that I have an idea how it works, I think that it was really obvious. :) So, I want to share my understanding of GADTs. Maybe the way I realized how GADTs work could help</div></td>
<td class="diff-marker">+</td>
<td style="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;"><div>Now that I have an idea<ins class="diffchange diffchange-inline"> of</ins> how it works, I think that it was really obvious. :) So, I want to share my understanding of GADTs. Maybe the way I realized how GADTs work could help</div></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>someone else. See also [[Generalised algebraic datatype]]</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>someone else. See also [[Generalised algebraic datatype]]</div></td>
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<td class="diff-marker"> </td>
<td style="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;"></td>
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Davesque
https://wiki.haskell.org/index.php?title=GADTs_for_dummies&diff=56424&oldid=prev
Davesque at 01:42, 20 July 2013
2013-07-20T01:42:00Z
<p></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 01:42, 20 July 2013</td>
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<td style="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;"><div>[[Category:Language extensions]]</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>[[Category:Language extensions]]</div></td>
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<td style="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;"></td>
<td class="diff-marker"> </td>
<td style="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;"></td>
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<td class="diff-marker">−</td>
<td style="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;"><div>For a long time, I didn't understand what GADTs were or how they could be used. It was sort of a conspiracy of silence <del class="diffchange diffchange-inline">-</del> people who understood GADTs thought</div></td>
<td class="diff-marker">+</td>
<td style="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;"><div>For a long time, I didn't understand what GADTs were or how they could be used. It was sort of a conspiracy of silence <ins class="diffchange diffchange-inline">&mdash;</ins> people who understood GADTs thought</div></td>
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<tr>
<td class="diff-marker"> </td>
<td style="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;"><div>that everything was obvious and didn't need further explanation, but I still</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>that everything was obvious and didn't need further explanation, but I still</div></td>
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<td class="diff-marker"> </td>
<td style="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;"><div>couldn't understand them.</div></td>
<td class="diff-marker"> </td>
<td style="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;"><div>couldn't understand them.</div></td>
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Davesque