https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&feed=atom&action=history
The Monad.Reader/Issue5/Number Param Types - Revision history
2024-03-19T02:56:32Z
Revision history for this page on the wiki
MediaWiki 1.35.5
https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=48117&oldid=prev
Henk-Jan van Tuyl: Updated some links
2012-08-09T11:34:49Z
<p>Updated some links</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:34, 9 August 2012</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><span id="Fridlender"></span>Daniel Fridlender and Mia Indrika: Do we Need Dependent Types? BRICS Report Series RS-01-10, March 2001. [http://www.brics.dk/RS/01/10/] </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><span id="mcomp"></span>Oleg Kiselyov: Polyvariadic composition. October 31, 2003. [http://<del class="diffchange diffchange-inline">pobox</del>.<del class="diffchange diffchange-inline">com/~oleg</del>/ftp/Haskell/<del class="diffchange diffchange-inline">types</del>.<del class="diffchange diffchange-inline">scm{{{</del>#<del class="diffchange diffchange-inline">}}}</del>polyvar-comp] </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><span id="mcomp"></span>Oleg Kiselyov: Polyvariadic composition. October 31, 2003. [http://<ins class="diffchange diffchange-inline">okmij</ins>.<ins class="diffchange diffchange-inline">org</ins>/ftp/Haskell/<ins class="diffchange diffchange-inline">polyvariadic</ins>.<ins class="diffchange diffchange-inline">html</ins>#polyvar-comp] </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><span id="Kreye"></span>Dietmar Kreye: A Compilation Scheme for a Hierarchy of Array Types. Proc. 3th International Workshop on Implementation of Functional Languages (IFL’01).</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><span id="Okasaki99"></span>Chris Okasaki: From fast exponentiation to square matrices: An adventure in types. Proc. fourth ACM SIGPLAN International Conference on<del class="diffchange diffchange-inline"> </del> Functional Programming (ICFP ’99), Paris, France, September 27-29,<del class="diffchange diffchange-inline"> </del> pp. 28 - 35, 1999 [http://www.<del class="diffchange diffchange-inline">eecs.usma</del>.edu/<del class="diffchange diffchange-inline">Personnel</del>/<del class="diffchange diffchange-inline">okasaki</del>/<del class="diffchange diffchange-inline">pubs</del>.<del class="diffchange diffchange-inline">html{{{</del>#<del class="diffchange diffchange-inline">}}}</del>icfp99] </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><span id="Okasaki99"></span>Chris Okasaki: From fast exponentiation to square matrices: An adventure in types. Proc. fourth ACM SIGPLAN International Conference on Functional Programming (ICFP ’99), Paris, France, September 27-29, pp. 28 - 35, 1999 [http://www.<ins class="diffchange diffchange-inline">westpoint</ins>.edu/<ins class="diffchange diffchange-inline">eecs</ins>/<ins class="diffchange diffchange-inline">SitePages</ins>/<ins class="diffchange diffchange-inline">Chris%20Okasaki</ins>.<ins class="diffchange diffchange-inline">aspx</ins>#icfp99] </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><span id="Haskell-list-quote"></span>Dominic Steinitz: Re: Polymorphic Recursion / Rank-2 Confusion. Message posted on the Haskell mailing list on Sep 21 2003. [http://www.haskell.org/pipermail/haskell/2003-September/012726.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;"><div><span id="Xi98"></span>Hongwei Xi, Frank Pfenning: Eliminating Array Bound Checking Through Dependent Types. Proc. ACM SIGPLAN Conference on Programming Language Design and Implementation, pp. 249—257, 1998. [http://www-2.cs.cmu.edu/~hwxi/] </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><span id="Xi98"></span>Hongwei Xi, Frank Pfenning: Eliminating Array Bound Checking Through Dependent Types. Proc. ACM SIGPLAN Conference on Programming Language Design and Implementation, pp. 249—257, 1998. [http://www-2.cs.cmu.edu/~hwxi/] </div></td>
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Henk-Jan van Tuyl
https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=48095&oldid=prev
Henk-Jan van Tuyl at 21:57, 8 August 2012
2012-08-08T21:57:14Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:57, 8 August 2012</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>Overall we demonstrate a practical dependent-type-like system that is just a Haskell library. The basics of the number-parameterized types are written in Haskell98.</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, number-parameterized types, type arithmetic, decimal types, type-directed programming.</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, number-parameterized types, type arithmetic, decimal types, type-directed programming.</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>therefore becomes more readable, reliable, and fast. Number-parameterized types when expressed in signatures also provide a better documentation of the code and let the invariants be checked across module boundaries.</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>therefore becomes more readable, reliable, and fast. Number-parameterized types when expressed in signatures also provide a better documentation of the code and let the invariants be checked across module boundaries.</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="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>In this paper, we develop realizations of number-parameterized types in Haskell that indeed have all the above advantages. The numeric parameter is specified in ''decimal'' rather than in binary, which makes types smaller and far easier to read. Type error messages also become more comprehensible. The programmer may write or the compiler can infer equality constraints (e.g., two argument</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>In this paper, we develop realizations of number-parameterized types in Haskell that indeed have all the above advantages. The numeric parameter is specified in ''decimal'' rather than in binary, which makes types smaller and far easier to read. Type error messages also become more comprehensible. The programmer may write or the compiler can infer equality constraints (e.g., two argument<ins class="diffchange diffchange-inline"> vectors of a function must be of the same size), arithmetic constraints (e.g., one vector must be larger by some amount), and inequality constraints (e.g., the size of the argument vector must be at least one). The violations of the constraints are detected at compile time. We can remove run-time tag checks in functions like <hask>vhead</hask>, which are statically assured to receive a non-empty vector.</ins></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>vectors of a function must be of the same size), arithmetic constraints (e.g., one vector must be larger by some amount), and inequality constraints (e.g., the size of the argument vector must be at least one). The violations of the constraints are detected at compile time. We can remove run-time tag checks in functions like <hask>vhead</hask>, which are statically assured to receive a non-empty vector.</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>
</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>Although we come close to the dependent-type programming, we do not extend either a compiler or the language. Our system is a regular Haskell library. In fact, the basic number-parameterized types can be implemented entirely in Haskell98. Advanced operations such as type arithmetic require commonly supported Haskell98 extensions to multi-parameter classes with functional dependencies and higher-ranked types.</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>Although we come close to the dependent-type programming, we do not extend either a compiler or the language. Our system is a regular Haskell library. In fact, the basic number-parameterized types can be implemented entirely in Haskell98. Advanced operations such as type arithmetic require commonly supported Haskell98 extensions to multi-parameter classes with functional dependencies and higher-ranked types.</div></td>
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<td colspan="2" class="diff-lineno">Line 322:</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> listVec' size elems = Vec $ listArray (0,(c2num size)-1) elems</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> listVec' size elems = Vec $ listArray (0,(c2num size)-1) elems</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></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></haskell></div></td>
</tr>
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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 implementations of the polymorphic functions <hask>listVec</hask>, <hask>vec</hask>, <hask>vlength_t</hask>, <hask>vlength</hask>, <hask>vat</hask>, <hask>velems</hask>, and <hask>vzipWith</hask> are precisely the same</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 implementations of the polymorphic functions <hask>listVec</hask>, <hask>vec</hask>, <hask>vlength_t</hask>, <hask>vlength</hask>, <hask>vat</hask>, <hask>velems</hask>, and <hask>vzipWith</hask> are precisely the same<ins class="diffchange diffchange-inline"> as those in section [[#Encoding the number parameter in type constructors, in unary|Encoding the number parameter in type constructors, in unary]]. We elide the code for the sake of space. We introduce a few sample vectors, using the decimal notation this time:</ins></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>as those in section [[#Encoding the number parameter in type constructors, in unary|Encoding the number parameter in type constructors, in unary]]. We elide the code for the sake of space. We introduce a few sample vectors, using the decimal notation this time:</div></td>
<td colspan="2" class="diff-empty"> </td>
</tr>
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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><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><haskell></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> v12c = listVec (D1,D2) $ take 12 ['a'..'z']</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> v12c = listVec (D1,D2) $ take 12 ['a'..'z']</div></td>
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Henk-Jan van Tuyl
https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=48094&oldid=prev
Henk-Jan van Tuyl: Changed section links to better human readable versions
2012-08-08T21:52:38Z
<p>Changed section links to better human readable versions</p>
<a href="https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=48094&oldid=48093">Show changes</a>
Henk-Jan van Tuyl
https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=48093&oldid=prev
Henk-Jan van Tuyl: Added a link to the Cayenne site, Category:Proposals and Category:Community
2012-08-08T21:33:55Z
<p>Added a link to the Cayenne site, Category:Proposals and Category:Community</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 21:33, 8 August 2012</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>== References ==</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="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><span id="Cayenne"></span>Augustsson, L. Cayenne — a language with dependent types. Proc. ACM SIGPLAN International Conference on Functional Programming, pp. 239—250, 1998.</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><span id="Cayenne"></span>Augustsson, L. Cayenne — a language with dependent types. Proc. ACM SIGPLAN International Conference on Functional Programming, pp. 239—250, 1998.<ins class="diffchange diffchange-inline">[http://www.augustsson.net/Darcs/Cayenne/html/]</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="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><span id="Blume01"></span>Matthias Blume: No-Longer-Foreign: Teaching an ML compiler to speak C “natively.” In BABEL’01: First workshop on multi-language infrastructure and interoperability, September 2001, Firenze, Italy. [http://people.cs.uchicago.edu/~blume/pub.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;"><div><span id="Blume01"></span>Matthias Blume: No-Longer-Foreign: Teaching an ML compiler to speak C “natively.” In BABEL’01: First workshop on multi-language infrastructure and interoperability, September 2001, Firenze, Italy. [http://people.cs.uchicago.edu/~blume/pub.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;"><div><span id="XiThesis"></span>Hongwei Xi: Dependent Types in Practical Programming. Ph.D thesis, Carnegie Mellon University, September 1998. [http://www.cs.bu.edu/~hwxi/]</div></td>
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Henk-Jan van Tuyl
https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=48092&oldid=prev
Henk-Jan van Tuyl: More reformatting; removed remark about needing reformatting
2012-08-08T21:28:38Z
<p>More reformatting; removed remark about needing reformatting</p>
<a href="https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=48092&oldid=48089">Show changes</a>
Henk-Jan van Tuyl
https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=48089&oldid=prev
Henk-Jan van Tuyl: Partially corrected formatting
2012-08-08T20:57:03Z
<p>Partially corrected formatting</p>
<a href="https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=48089&oldid=23690">Show changes</a>
Henk-Jan van Tuyl
https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=23690&oldid=prev
Sergio at 05:51, 26 October 2008
2008-10-26T05:51:13Z
<p></p>
<a href="https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=23690&oldid=23604">Show changes</a>
Sergio
https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=23604&oldid=prev
Sergio at 06:33, 22 October 2008
2008-10-22T06:33:22Z
<p></p>
<a href="https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=23604&oldid=20842">Show changes</a>
Sergio
https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=20842&oldid=prev
WouterSwierstra at 14:26, 9 May 2008
2008-05-09T14:26:18Z
<p></p>
<a href="https://wiki.haskell.org/index.php?title=The_Monad.Reader/Issue5/Number_Param_Types&diff=20842">Show changes</a>
WouterSwierstra