Pages

Categories
 abstraction AC algorithm announcement applicative art axiom of choice Bell numbers BlogLiterately category category theory collaborative editing combinatorial combinatorial species combinatorics constraints constructive cycles darcs data diagrams drawing DSL EDSL feedback FringeDC functional functional programming functor GHC ghci grad school graphics hackathon Hac φ haskell ICFP isomorphism knowledge library lifting list lists monad Monad.Reader monads monoid monoids multiset music paper partitions patch theory pedagogy Philadelphia pictures preorder programming QuickCheck reading release species symposium talk text theory translation tutorial typelevel type classes Typeclassopedia types unique UPenn xmonad
Archives
 June 2014 (2)
 May 2014 (2)
 January 2014 (2)
 October 2013 (1)
 August 2013 (1)
 July 2013 (1)
 May 2013 (1)
 April 2013 (3)
 March 2013 (2)
 January 2013 (2)
 December 2012 (2)
 November 2012 (4)
 October 2012 (3)
 August 2012 (4)
 July 2012 (5)
 June 2012 (1)
 March 2012 (1)
 January 2012 (1)
 November 2011 (4)
 October 2011 (3)
 September 2011 (2)
 August 2011 (2)
 July 2011 (2)
 June 2011 (1)
 May 2011 (6)
 April 2011 (2)
 March 2011 (1)
 February 2011 (3)
 January 2011 (1)
 December 2010 (2)
 November 2010 (3)
 October 2010 (1)
 September 2010 (1)
 August 2010 (3)
 July 2010 (2)
 June 2010 (3)
 May 2010 (3)
 April 2010 (3)
 March 2010 (2)
 February 2010 (1)
 January 2010 (1)
 December 2009 (2)
 October 2009 (3)
 September 2009 (2)
 August 2009 (4)
 July 2009 (7)
 June 2009 (1)
 May 2009 (2)
 April 2009 (1)
 March 2009 (2)
 February 2009 (3)
 January 2009 (3)
 December 2008 (2)
 September 2008 (2)
 August 2008 (1)
 July 2008 (3)
 June 2008 (1)
 April 2008 (4)
 March 2008 (4)
 February 2008 (4)
 January 2008 (2)
 December 2007 (4)
 October 2007 (2)
 September 2007 (2)
 August 2007 (3)
 June 2007 (2)
Top Posts
Blogroll
Fun
Personal
Meta
Category Archives: combinatorics
Random binary trees with a sizelimited critical Boltzmann sampler
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 Boltzmann, generation, QuickCheck, random, sampler, tree
7 Comments
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
Unordered tuples and type algebra
At Hac Phi a few weekends ago (which, by the way, was awesome), Dan Doel told me about a certain curiosity in type algebra, and we ended up working out a bunch more details together with Gershom Bazerman, Scott Walck, … Continue reading
Counting linear lambda terms: choice and correspondence
In my last post, I showed how to write down polymorphic types with numbers of linear inhabitants given by products of factorials and Mersenne numbers, but left open the question of types with five linear inhabitants in particular, and whether … Continue reading
Counting linear lambda terms: Mersenne numbers
In a previous post I posed the challenge of coming up with polymorphic types admitting certain numbers of linear inhabitants. (If you didn’t see the previous post and want to puzzle over an interesting lambdacalculus based problem, stop reading now … Continue reading
Posted in combinatorics
18 Comments
Counting linear lambda terms
Just a little something with which I’ve been idly occupying spare brain cycles lately… read on for an interesting puzzle. Warm up: counting lambda terms Consider a strippeddown version of Haskell’s type system with only natural numbers, polymorphism, functions, and … Continue reading
Posted in combinatorics
Tagged combinatorics, lambda, linear, polymorphism, System F, terms
10 Comments
Species subtraction made simple
> {# OPTIONS_GHC fnowarnmissingmethods #} > module Virtual where > > import Control.Applicative > import Test.QuickCheck Yesterday on #haskell, augur asked me to explain how subtraction works for combinatorial species. (For an introduction to species, see my paper from the … Continue reading
Posted in combinatorics, haskell
Tagged data, haskell, integers, natural, numbers, species, structures, subtraction
14 Comments
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
Functional pearl on combinatorial species
I’ve just submitted a Functional Pearl to ICFP explaining combinatorial species in a way that is (hopefully) accessible and interesting to functional programmers. You can read the draft here — as always, comments, suggestions, etc. are welcome (although it’s too … Continue reading