### Pages

### Categories

- AC
- algorithm
- announcement
- applicative
- art
- axiom of choice
- balanced
- Beeminder
- bijection
- BlogLiterately
- category
- collaborative editing
- combinatorial species
- combinatorics
- competitive
- constructive
- contest
- darcs
- data
- design
- diagrams
- dissertation
- drawing
- DSL
- EDSL
- enumeration
- feedback
- functional
- functional programming
- functor
- GHC
- ghci
- graphics
- hackathon
- Hac φ
- haskell
- ICFP
- isomorphism
- Kattis
- library
- log
- monad
- monads
- monoid
- multiset
- music
- paper
- parsing
- partitions
- patch theory
- pedagogy
- Philadelphia
- pictures
- productivity
- programming
- QuickCheck
- random
- release
- sampling
- sets
- species
- symposium
- talk
- teaching
- test
- theory
- translation
- tree
- tutorial
- type
- type-level
- Typeclassopedia
- types
- virtual
- workshop

### Archives

- July 2020 (2)
- June 2020 (3)
- May 2020 (4)
- April 2020 (2)
- March 2020 (2)
- February 2020 (4)
- December 2019 (1)
- November 2019 (1)
- October 2019 (1)
- July 2019 (1)
- May 2019 (2)
- April 2019 (2)
- March 2019 (1)
- February 2019 (3)
- November 2018 (1)
- October 2018 (3)
- June 2018 (1)
- May 2018 (4)
- April 2018 (1)
- March 2018 (2)
- February 2018 (3)
- January 2018 (1)
- November 2017 (1)
- September 2017 (1)
- June 2017 (1)
- May 2017 (1)
- April 2017 (1)
- March 2017 (1)
- February 2017 (4)
- January 2017 (3)
- November 2016 (2)
- October 2016 (2)
- September 2016 (3)
- August 2016 (4)
- July 2016 (1)
- June 2016 (1)
- May 2016 (3)
- April 2016 (2)
- March 2016 (3)
- February 2016 (1)
- November 2015 (2)
- 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: types

## 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
5 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 category theory, math, species
Tagged AC, axiom of choice, category, constructive, theory, types
17 Comments

## 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

## Typed type-level programming: status report

A few people have been bugging me (you know who you are ;-) about the current status of the project to allow automatic “lifting” of Haskell data constructors to the type level, to allow for typed type-level programming. I’ve written … Continue reading

Posted in haskell, projects
Tagged extension, GHC, hacking, lifting, progress, refactoring, types
Leave a comment

## On a Problem of sigfpe

> {-# LANGUAGE TypeFamilies, EmptyDataDecls, TypeOperators, GADTs #-} At the end of his most recent blog post, Divided Differences and the Tomography of Types, Dan Piponi left his readers with a challenge: In preparation for the next installment, here’s a … Continue reading

## Typed type-level programming in Haskell, part IV: collapsing types and kinds

In Part III, we saw how the current state of the art in Haskell type-level programming leaves some things to be desired: it requires duplicating both data declarations and code, and even worse, it’s untyped. What to do? Currently, GHC’s … Continue reading

## Typed type-level programming in Haskell, part II: type families

In my previous post, we saw how multi-parameter type classes with functional dependencies in Haskell allow us to do type-level programming in a logic programming style. (If you’re not clear on why this corresponds to a logic programming style, see … Continue reading