https://wiki.haskell.org/index.php?title=Show_instance_for_functions&feed=atom&action=history
Show instance for functions - Revision history
2024-03-19T03:19:45Z
Revision history for this page on the wiki
MediaWiki 1.35.5
https://wiki.haskell.org/index.php?title=Show_instance_for_functions&diff=60583&oldid=prev
Hairy Dude: /* Theoretical answer */ this "mathematical" means "set-theoretic"; other notions of function (e.g. Martin-Löf type theory) aren't defined by their graph type theory
2016-02-01T00:30:28Z
<p><span dir="auto"><span class="autocomment">Theoretical answer: </span> this "mathematical" means "set-theoretic"; other notions of function (e.g. Martin-Löf type theory) aren't defined by their graph type theory</span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:30, 1 February 2016</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>Functional programming is about 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;"><div>Functional programming is about functions.</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>A mathematical function is entirely defined by its graph, that is by pairs of objects (argument, value).</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 mathematical<ins class="diffchange diffchange-inline"> (precisely, set-theoretic)</ins> function is entirely defined by its graph, that is by pairs of objects (argument, value).</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>*<math> \sqrt{\ } = \{(0,0), (1,1), (4,2), (9,3), \dots \} </math></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>*<math> \sqrt{\ } = \{(0,0), (1,1), (4,2), (9,3), \dots \} </math></div></td>
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Hairy Dude
https://wiki.haskell.org/index.php?title=Show_instance_for_functions&diff=60582&oldid=prev
Hairy Dude: /* Practical answer */ optimized to nothing
2016-02-01T00:27:40Z
<p><span dir="auto"><span class="autocomment">Practical answer: </span> optimized to nothing</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;"></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>The Haskell compiler doesn't maintain the expressions as they are, but translates them to machine code or some other low-level representation.</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>The Haskell compiler doesn't maintain the expressions as they are, but translates them to machine code or some other low-level representation.</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>The function <hask>\x -> x - x + x :: Int -> Int</hask> might have been optimized to <hask>\x -> x :: Int -> Int</hask>.</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>The function <hask>\x -> x - x + x :: Int -> Int</hask> might have been optimized to <hask>\x -> x :: Int -> Int</hask><ins class="diffchange diffchange-inline">. If it's used anywhere, it might have been inlined and optimized to nothing</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;"><div>The variable name <hask>x</hask> is not stored anywhere.</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>The variable name <hask>x</hask> is not stored anywhere.</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>You might have thought, that Haskell is like a scripting language, maintaining expressions at runtime.</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>You might have thought, that Haskell is like a scripting language, maintaining expressions at runtime.</div></td>
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Hairy Dude
https://wiki.haskell.org/index.php?title=Show_instance_for_functions&diff=59452&oldid=prev
Dmwit: /* Theoretical answer */
2015-02-25T18:52:22Z
<p><span dir="auto"><span class="autocomment">Theoretical answer</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:52, 25 February 2015</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>Code to do this is available in the [http://hackage.haskell.org/package/universe-reverse-instances universe-reverse-instances] package (which is also installed when installing the top-level [http://hackage.haskell.org/package/universe universe] 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>One could do this for enumerable argument types, but it is not in the standard libraries.</div></td>
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Dmwit
https://wiki.haskell.org/index.php?title=Show_instance_for_functions&diff=33469&oldid=prev
Boris: Statement that 2*x is faster than x+x is doubtful because generally (*) is slower than (+), but (*) by power of 2 may be optimized by shifts... New example is more clear I think.
2010-02-05T11:21:29Z
<p>Statement that 2*x is faster than x+x is doubtful because generally (*) is slower than (+), but (*) by power of 2 may be optimized by shifts... New example is more clear I think.</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:21, 5 February 2010</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>Why is there a Show instance, but it only prints the 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;"></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">Text.Show.FunctPrelude</del>> :m + Text.Show.Functions</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">Prelude</ins>> :m + Text.Show.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;"><div> Prelude Text.Show.Functions> show Char.ord</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> Prelude Text.Show.Functions> show Char.ord</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;"><div>The Haskell compiler doesn't maintain the expressions as they are, but translates them to machine code or some other low-level representation.</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>The Haskell compiler doesn't maintain the expressions as they are, but translates them to machine code or some other low-level representation.</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>The function <hask>\x -> x+x :: Int -> Int</hask> might have been optimized to <hask>\x -> <del class="diffchange diffchange-inline">2*</del>x :: Int -> Int</hask>.</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>The function <hask>\x -> x<ins class="diffchange diffchange-inline"> - x </ins>+<ins class="diffchange diffchange-inline"> </ins>x :: Int -> Int</hask> might have been optimized to <hask>\x -> x :: Int -> Int</hask>.</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>The variable name <hask>x</hask> is not stored anywhere.</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>The variable name <hask>x</hask> is not stored anywhere.</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>You might have thought, that Haskell is like a scripting language, maintaining expressions at runtime.</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>You might have thought, that Haskell is like a scripting language, maintaining expressions at runtime.</div></td>
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Boris
https://wiki.haskell.org/index.php?title=Show_instance_for_functions&diff=17664&oldid=prev
Lemming: give the lambda expression the fixed type Int -> Int in order to avoid effects of strange Num instance
2007-12-18T21:30:01Z
<p>give the lambda expression the fixed type Int -> Int in order to avoid effects of strange Num instance</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 Haskell compiler doesn't maintain the expressions as they are, but translates them to machine code or some other low-level representation.</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>The Haskell compiler doesn't maintain the expressions as they are, but translates them to machine code or some other low-level representation.</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>The function <hask>\x -> x+x</hask> might have been optimized to <hask>\x -> 2*x</hask>.</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>The function <hask>\x -> x+x<ins class="diffchange diffchange-inline"> :: Int -> Int</ins></hask> might have been optimized to <hask>\x -> 2*x<ins class="diffchange diffchange-inline"> :: Int -> Int</ins></hask>.</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>The variable name <hask>x</hask> is not stored anywhere.</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>The variable name <hask>x</hask> is not stored anywhere.</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>You might have thought, that Haskell is like a scripting language, maintaining expressions at runtime.</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>You might have thought, that Haskell is like a scripting language, maintaining expressions at runtime.</div></td>
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Lemming
https://wiki.haskell.org/index.php?title=Show_instance_for_functions&diff=17661&oldid=prev
DonStewart: /* Question */
2007-12-18T16:59:10Z
<p><span dir="auto"><span class="autocomment">Question</span></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>Why is there no <hask>Show</hask> instance for functions for showable argument and value types?</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>Why can't I enter <hask>\x -> x+x</hask> into GHCi or Hugs and get the same expression as answer?</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>Why can't I enter <hask>\x -> x+x</hask> into GHCi or Hugs and get the same expression as answer?</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>Why is there a Show instance, but it only prints the 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;"></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> Text.Show.FunctPrelude> :m + Text.Show.Functions</div></td>
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DonStewart
https://wiki.haskell.org/index.php?title=Show_instance_for_functions&diff=17658&oldid=prev
Lemming: explanation
2007-12-18T14:45:22Z
<p>explanation</p>
<p><b>New page</b></p><div>== Question ==<br />
<br />
Why is there no <hask>Show</hask> instance for functions for showable argument and value types?<br />
Why can't I enter <hask>\x -> x+x</hask> into GHCi or Hugs and get the same expression as answer?<br />
<br />
== Answer ==<br />
<br />
=== Practical answer ===<br />
<br />
The Haskell compiler doesn't maintain the expressions as they are, but translates them to machine code or some other low-level representation.<br />
The function <hask>\x -> x+x</hask> might have been optimized to <hask>\x -> 2*x</hask>.<br />
The variable name <hask>x</hask> is not stored anywhere.<br />
You might have thought, that Haskell is like a scripting language, maintaining expressions at runtime.<br />
This is not the case.<br />
[[Lambda abstraction|Lambda expression]]s are just [[anonymous function]]s.<br />
You will not find a possibility to request the name of a variable at runtime,<br />
or inspect the structure of a function definition.<br />
You can also not receive an expression from the program user, which invokes variables of your program, and evaluate it accordingly.<br />
That is, Haskell is not [[reflexive language|reflexive]].<br />
Everything can be compiled.<br />
A slight exception is [[hs-plugins]].<br />
<br />
=== Theoretical answer ===<br />
<br />
Functional programming is about functions.<br />
A mathematical function is entirely defined by its graph, that is by pairs of objects (argument, value).<br />
E.g.<br />
*<math> \sqrt{\ } = \{(0,0), (1,1), (4,2), (9,3), \dots \} </math><br />
*<math> (\lambda x.\ x+x) = \{(0,0), (1,2), (2,4), (3,6), \dots \} </math><br />
Since the graphs of <math> \lambda x.\ x+x </math> and <math> \lambda x.\ 2\cdot x </math> are equal<br />
these both expressions denote the same function.<br />
Now imagine both terms would be echoed by Hugs or GHCi as they are.<br />
This would mean that equal functions lead to different output.<br />
The interactive Haskell environments use the regular <hask>show</hask> function,<br />
and thus it would mean <math> \mathrm{show}(\lambda x.\ x+x) \ne \mathrm{show}(\lambda x.\ 2\cdot x) </math>.<br />
This would break [[referential transparency]].<br />
<br />
It follows that the only sensible way to show functions is to show their graph.<br />
<haskell><br />
Prelude> \x -> x+x<br />
functionFromGraph [(0,0), (1,2), (2,4), (3,6),<br />
Interrupted.<br />
</haskell><br />
<br />
One could do this for enumerable argument types, but it is not in the standard libraries.<br />
<br />
== Source ==<br />
<br />
http://www.haskell.org/pipermail/haskell-cafe/2006-April/015161.html<br />
<br />
[[Category:FAQ]]</div>
Lemming