Category Archives: math

Random binary trees with a size-limited critical Boltzmann sampler

Posted on April 25, 2013 by

Today I’d like to talk about generating random trees. First, some imports and such (this post is literate Haskell). > {-# LANGUAGE GeneralizedNewtypeDeriving #-} > > module BoltzmannTrees where > > import Control.Applicative > import Control.Arrow ((&&&)) > import Control.Lens … Continue reading →

Posted in combinatorics, haskell, math, species | Tagged , , , , , | 7 Comments

The algebra of species: primitives

Posted on January 7, 2013 by

[This is the fifth in a series of posts about combinatorial species. Previous posts: And now, back to your regularly scheduled combinatorial species; Decomposing data structures; Combinatorial species definition, Species definition clarification and exercises.] Recall that a species is a … Continue reading →

Posted in math, species | Tagged , , , , , , | 5 Comments

Species definition clarification and exercises

Posted on December 6, 2012 by

[This is the fourth in a series of posts about combinatorial species. Previous posts: And now, back to your regularly scheduled combinatorial species; Decomposing data structures; Combinatorial species definition.] In my previous post I neglected to mention something quite crucial, … Continue reading →

Posted in math, species | Tagged , , , | 2 Comments

Combinatorial species definition

Posted on November 20, 2012 by

Continuing from my previous post, recall that the goal of species is to have a unified theory of containers with labeled1 locations. So, how do we actually specify such things (leaving aside for the moment the question of how we … Continue reading →

Posted in math, species | Tagged , , , , | 5 Comments

foldr is made of monoids

Posted on November 5, 2012 by

> import Data.Monoid In his recent blog post What is foldr made of?, Tom Ellis made the clever observation that foldr is equivalent in power to the combination of map and compose, where > compose :: [a -> a] -> … Continue reading →

Posted in haskell, math | Tagged , , , , | 15 Comments

Decomposing data structures

Posted on October 27, 2012 by

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 →

Posted in math, species | Tagged , , , | 9 Comments

And now, back to your regularly scheduled combinatorial species

Posted on October 17, 2012 by

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 →

Posted in combinatorics, math, writing | Tagged , | 10 Comments

Generating plane tilings with diagrams

Posted on November 12, 2011 by

I’ve finally set up a diagrams-contrib package to serve as a home for user contributions to the diagrams project—generation of specialized diagrams, fun or instructive examples, half-baked ideas, stuff which is not sufficiently polished or general to go in the … Continue reading →

Posted in diagrams, haskell, math, projects | Tagged , , | 1 Comment

Themes on Streams, Part II

Posted on May 20, 2011 by

In a previous post I claimed that comonad structures on R -> a are in one-to-one 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 , , , , | 2 Comments

Themes on Streams

Posted on May 9, 2011 by

> {-# 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 →

Posted in haskell, math | Tagged , , , , , | 3 Comments