[Haskell-cafe] Visualizing Typed Functions
Duane Johnson
duane.johnson at gmail.com
Thu May 7 17:01:47 EDT 2009
I'm not sure what the policy is on posting with graphical attachments,
but I'll give this a tentative try. In case this does not come
through with images, I've also posted this on my blog at
http://blog.inquirylabs.com/2009/05/07/visualizing-typed-functions/
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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
binary function that takes a binary function as input, along with
another input, to produce an output of the same type:
I imagine polymorphic types as "banded colors" so that the bands
contain another type (color). Lists are polymorphic types. 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 is "(a -> b) -> [a] ->
[b]". I wonder what a Monad would look like...
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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