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Category Archives: math
Decomposing data structures
So, what are combinatorial species? As a very weak first approximation, you can think of them as a generalization of algebraic data types.1 That doesn’t really say much about what they are, but at least it does explain why programmers … Continue reading
And now, back to your regularly scheduled combinatorial species
I’ve already mentioned this to people here and there, but haven’t yet announced it publically, so here it is: Stephanie Weirich and I have been awarded a grant from the NSF to study the intersection of combinatorial species and (functional) … Continue reading
Generating plane tilings with diagrams
I’ve finally set up a diagramscontrib package to serve as a home for user contributions to the diagrams project—generation of specialized diagrams, fun or instructive examples, halfbaked ideas, stuff which is not sufficiently polished or general to go in the … Continue reading
Themes on Streams, Part II
In a previous post I claimed that comonad structures on R > a are in onetoone correspondence with monoid structures on R. In this post and the next I’ll justify that claim. Characterizing comonads on R > a Suppose we … Continue reading
Posted in haskell, math
Tagged comonad, free theorem, functor, parametricity, representable
2 Comments
Themes on Streams
> {# LANGUAGE DeriveFunctor, FlexibleInstances #} Recall that a stream is a countably infinite sequence of values: > data Stream a = a :> Stream a > deriving (Functor, Show) > > sHead (a :> _) = a > sTail … Continue reading
Math.OEIS needs a new maintainer
Summary: the OEIS has switched servers and the oeis package needs updating to match, so I’m looking for someone to take over development. All the rest is padding in the form of entertaining stories. Recently, Michael Snoyman’s wonderful packdeps tool … Continue reading
Things I have learned about vector spaces
Work on the diagrams library is coming along rather nicely. I’ll have more to say about it soon, but for now here are two things I have learned recently: Normals transform as the inverse transpose (see Subject 5.27). Be very … Continue reading
Species and Functors and Types, Oh My!
My paper on combinatorial species and the species library (an improved version of my previous ICFP submission) has been accepted to the 2010 Haskell Symposium! I look forward to seeing people in Baltimore in September, and in the meantime the … Continue reading
Posted in combinatorics, haskell, math, writing
Tagged 2010, combinatorics, haskell, paper, species, symposium
2 Comments
Math.Combinatorics.Multiset and Sawada’s algorithm
I’ve uploaded a new version of my Math.Combinatorics.Multiset library (see the previous announcement here). I’ve added a few more fairly simple algorithms (splitting a multiset into two pieces in all possible ways; finding all sizek submultisets of a multiset), and … Continue reading