### Pages

### Categories

- abstraction AC announcement applicative art axiom of choice Beeminder Bell numbers blogging BlogLiterately category category theory collaborative editing combinatorial combinatorial species combinatorics constructive cycles darcs data diagrams differentiation dissertation drawing DSL EDSL feedback FringeDC functional functional programming functor GHC ghci grad school graphics hackathon Hac φ haskell ICFP isomorphism knowledge library list lists monad Monad.Reader monads monoid monoids music partitions patch theory pedagogy Philadelphia pictures preorder productivity programming QuickCheck reading release species talk text theory translation tutorial type-level type classes Typeclassopedia types unique UPenn workshop xmonad
### Archives

- October 2015 (1)
- August 2015 (2)
- July 2015 (1)
- June 2015 (3)
- May 2015 (2)
- April 2015 (1)
- March 2015 (1)
- August 2014 (3)
- 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

# Tag Archives: combinatorics

## Pan-Galactic Division in Haskell

Summary: given an injective function , it is possible to constructively “divide by ” to obtain an injection , as shown recently by Peter Doyle and Cecil Qiu and expounded by Richard Schwartz. Their algorithm is nontrivial to come up … Continue reading

## 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 stripped-down 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 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

## Species operations: differentiation

Continuing my series describing my new combinatorial species library, today we’ll take a look at the operation of differentiation. You may remember that the Species type class has an Algebra.Differential constraint, which, as I previously explained, transitively implies an Algebra.Ring … Continue reading

Posted in combinatorics, haskell, math
Tagged combinatorial species, combinatorics, differentiation
1 Comment

## Primitive species and species operations, part II

In my previous post, I began describing the primitive species and species operations supported by my combinatorial species library; we looked at the ring structure on species, that is, the primitive species and , and the operations of species sum … Continue reading

Posted in combinatorics, haskell, math
Tagged combinatorial species, combinatorics, cycles, sets, singletons
2 Comments

## Primitive species and species operations

In this second post about my new combinatorial species library, I plan to begin writing about the species DSL itself: what are the primitive combinatorial species and the primitive operations on species? (The first post described the concept of combinatorial … Continue reading

Posted in combinatorics, haskell, math
Tagged combinatorial species, combinatorics, DSL, primitives
3 Comments

## Introducing Math.Combinatorics.Species!

I have just uploaded to Hackage version 0.1 of the species package, a Haskell library for computing with combinatorial species. Much like David Amos’s great series of posts introducing his Haskell for Maths library, I plan to write a series … Continue reading

Posted in combinatorics, haskell, math, projects
Tagged combinatorial species, combinatorics
14 Comments