Duane’s Quick Posts

As I've worked in Haskell over the past several months, I've noticed that my mind has kind of implicitly modeled functional programming as a visual/mechanical representation of concepts.  I'd like to make the ideas more explicit, however, so I'm writing this post and cooking up some graphics.  I wonder if others have similar "internal representations" of functions, and if perhaps others might suggest improvements over my model.

The basic idea is that a function is a semi-circle with inputs on one side (left) and the output at the right.  Colors represent types.  Here is a function that takes one input and produces one output (of the same type):

Haskell would type this as "a -> a".  Next, we have a function that takes one type and returns a different type... e.g. a hashing function might take a string and return an integer:

(Please ignore the vertical stripe, it's an artifact of my poor Inkscape skills).  We can also create functions with more than one input, of course, so here is a binary function.  It might be the '+' operator, or some other binary operator, e.g. "a -> a -> a":

Haskell and many other languages also have the concept of higher-order functions, i.e. functions that take functions as inputs.  Here is a function that takes a binary function as input, along with another input, to produce an output of the same type:

There exist polymorphic types in many languages as well.  In Haskell, for example, the list is a polymorphic type--it is a linked list of any type you want.  I imagine these polymorphic types as "banded colors" so that the bands contain another type (color).  Here is what the "head" function might look like ("head" returns the first element in a list):

Finally, here is a composite of all of the above visualizations.  The "map" function in Haskell is a function that takes a function and a list, and applies that function to each element in the list, returning a new list with the "mapped" elements:

The type signature for the "map" function in Haskell is "(a -> b) -> [a] -> [b]".

With these functions visualized, one could make a kind of "drag and drop" interface for Haskell programming, although that isn't really my intention.  I admit this is a little convoluted even for the purpose of visualization, but at least it's a starting place.  Does anyone know of another system or better representation?

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The semester is over, my final project was a success (at least in that I passed the class) and it's time now to release the game I made for Graphics 455: Silkworm!

                           

Click here to download:

Silkworm_Game_written_in_Haske.zip (720 KB)

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Class is now done.  My last final exam was yesterday. More than any previous semester, I used a wide variety of computing tools to finish my work in class.  Here are a few of the ones I put to use:

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I really don't like blogging about this kind of thing, but the battle between my stomach and my conscience often leads to a win for the conscience.  The United States should be a world leader in moral capacity and ethical treatment of even the vilest of characters.  Somehow, we failed at that role between 2002 and 2007.  FireDogLake reports:

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I liked this article by John Sviokla about why people are willing to work for nothing: it's a different economy altogether.  Once a person has left the ground-level of income-for-survival and is flying in the upper stratosphere of meaning, purpose and contribution it makes little sense to desecrate that higher ideal with a token payment in dollars.

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Wow.  Just in case Github wasn't already the coolest social site for coders, it now has "issues"---a bug tracking area for each software project.  And it gives everyone the ability to vote for the issues they most want fixed!

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This New York Times article talks about the malleability of intelligence and the recent evidence that shows IQ is not quite as genetic as was once thought.  Anyway, this little snippet kind of blew me away:

Another indication of malleability is that I.Q. has risen sharply over time. Indeed, the average I.Q. of a person in 1917 would amount to only 73 on today’s I.Q. test. Half the population of 1917 would be considered mentally retarded by today’s measurements, Professor Nisbett says.

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This adventure took longer than I expected, so I am posting what I've found here for others.  The goal is to create a CD with a custom icon for Mac OS X, with one caveat---it needs to be created on a Linux system.  The software to use on Linux is called "cdrtools" and includes a command-line tool, "mkisofs".  You can also install cdrtools on the Mac (using the MacPorts system) for testing purposes with "sudo port install cdrtools".  Here's the recipe:

mkisofs -hfs -r -V 'My CD' -o mycd.iso mycd/

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When I first heard about the attempted spying on our US infrastructure and subsequent early discovery of the infiltration, I thought "Oh, whew, good thing we caught them."  But on second thought, Robert Graham has a good point: is this another one of those Bush-era "few facts and government officials said" stories?  Could it be part of a PR campaign to convince us that we need to give the president power to "switch off the internet" so to speak?

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