### 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 multiset 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 xmonad
### Archives

- May 2015 (1)
- 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

# Category Archives: species

## 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

## Readers wanted!

tl;dr: Read a draft of my thesis and send me your feedback by September 9! Over the past year I’ve had several people say things along the lines of, “let me know if you want me to read through your … Continue reading

Posted in category theory, combinatorics, diagrams, grad school, math, species, writing
Tagged dissertation, feedback, readers, species, thesis
15 Comments

## Anafunctors

This is part four in a series of posts on avoiding the axiom of choice (part one, part two, part three). In my previous post, we considered the “Axiom of Protoequivalence”—that is, the statement that every fully faithful, essentially surjective … Continue reading

Posted in category theory, math, species
Tagged AC, anafunctor, axiom of choice, category, constructive, equivalence, functor, isomorphism, theory, types, unique
2 Comments

## AC and equivalence of categories

This is part three in a series of posts on avoiding the axiom of choice (part one, part two). In my previous post, I explained one place where the axiom of choice often shows up in category theory, namely, when … Continue reading

Posted in category theory, math, species
Tagged AC, axiom of choice, category, constructive, equivalence, functor, isomorphism, theory, types, unique
5 Comments

## Unique isomorphism and generalized “the”

This is part two in a series of posts on avoiding the axiom of choice; you can read part one here. In category theory, one is typically interested in specifying objects only up to unique isomorphism. In fact, definitions which … Continue reading

Posted in category theory, math, species
Tagged AC, axiom of choice, category, constructive, functor, isomorphism, theory, types, unique
8 Comments

## Avoiding the axiom of choice, part I

I’m hard at work on my dissertation, and plan to get back to doing a bit of blogging based on stuff I’m writing and thinking about, as a way of forcing myself to explain things clearly and to potentially get … Continue reading

Posted in math, species, category theory
Tagged AC, axiom of choice, category, constructive, theory, types
17 Comments

## Random binary trees with a size-limited 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
9 Comments