Mark Dominus (陶敏修)
mjd@pobox.com
Archive:
| 2025: | JFMAMJ |
| JAS | |
| 2024: | JFMAMJ |
| JASOND | |
| 2023: | JFMAMJ |
| JASOND | |
| 2022: | JFMAMJ |
| JASOND | |
| 2021: | JFMAMJ |
| JASOND | |
| 2020: | JFMAMJ |
| JASOND | |
| 2019: | JFMAMJ |
| JASOND | |
| 2018: | JFMAMJ |
| JASOND | |
| 2017: | JFMAMJ |
| JASOND | |
| 2016: | JFMAMJ |
| JASOND | |
| 2015: | JFMAMJ |
| JASOND | |
| 2014: | JFMAMJ |
| JASOND | |
| 2013: | JFMAMJ |
| JASOND | |
| 2012: | JFMAMJ |
| JASOND | |
| 2011: | JFMAMJ |
| JASOND | |
| 2010: | JFMAMJ |
| JASOND | |
| 2009: | JFMAMJ |
| JASOND | |
| 2008: | JFMAMJ |
| JASOND | |
| 2007: | JFMAMJ |
| JASOND | |
| 2006: | JFMAMJ |
| JASOND | |
| 2005: | OND |
Subtopics:
| Mathematics | 245 |
| Programming | 99 |
| Language | 95 |
| Miscellaneous | 75 |
| Book | 50 |
| Tech | 49 |
| Etymology | 35 |
| Haskell | 33 |
| Oops | 30 |
| Unix | 27 |
| Cosmic Call | 25 |
| Math SE | 25 |
| Law | 22 |
| Physics | 21 |
| Perl | 17 |
| Biology | 16 |
| Brain | 15 |
| Calendar | 15 |
| Food | 15 |
Comments disabled
Tue, 03 Jan 2012
Eta-reduction in Haskell and English
The other day Katara and I were putting together a model, and she asked
what a certain small green part was for. I said "It's a thing for
connecting a thing to another thing."
Katara objected that this was a completely unhelpful explanation, but I disagreed. I would have agreed that it was an excessively verbose explanation, but she didn't argue that point.
Later, it occurred to me that Haskell has a syntax for eliding unnecessary variables in cases like this. In Haskell, one can abbreviate the expression
λx → λy → x + y
to just (+). (Perl users may find it helpful to know that
the Perl equivalent of the expression above is sub { my ($x) = @_;
return sub { my ($y) = @_; return $x + $y } }.) This is an
example of a general transformation called η-reduction. In general, for
any function f, λx → f x is a
function that takes an argument x and returns f x. But
that's exactly what f does. So we can replace the longer
version with the shorter version, and that's η-reduction, or we can go the
other way, which is η-expansion.Anyway, once I thought of this it occurred to me that, just like the longer expression could be reduced to (+), my original explanation that the small green part was "a thing for connecting a thing to another thing" could be η-reduced to "a connector".
Perhaps if I had said that in the first place Katara would not have complained.
Happy new year, all readers.
[Other articles in category /lang] permanent link