dvanhorn @ λ-calcul.us » Syntax http://dvanhorn.lambda-calcul.us Research weblog for David Van Horn Sat, 28 Aug 2010 13:39:54 +0000 http://wordpress.org/?v=2.9.2 en hourly 1 TLCA Open Problems http://dvanhorn.lambda-calcul.us/2009/06/08/tlca-open-problems/ http://dvanhorn.lambda-calcul.us/2009/06/08/tlca-open-problems/#comments Mon, 08 Jun 2009 19:03:01 +0000 dvanhorn http://dvanhorn.lambda-calcul.us/?p=115 I just came across the TLCA List of Open Problems, which includes 20 unsolved problems in the areas of:

  • Typed and untyped lambda-calculi as models of computation.
  • Proof-theory: Natural deduction, sequent calculi, cut elimination and normalization. Propositions as types, linear logic and proof nets.
  • Semantics: Denotational semantics, game semantics, realizability, categorical models.
  • Programming languages: Foundations of functional and object-oriented programming, proof search, logic programming, type checking.
  • Implementation: Abstract machines, parallel execution, optimal reduction, program optimization.

The problems are all interesting. I liked 6, 8, 12-14, 16-18 in particular.

]]> http://dvanhorn.lambda-calcul.us/2009/06/08/tlca-open-problems/feed/ 0 Sharing graph for call/cc http://dvanhorn.lambda-calcul.us/2008/04/06/sharing-graph-for-callcc/ http://dvanhorn.lambda-calcul.us/2008/04/06/sharing-graph-for-callcc/#comments Sun, 06 Apr 2008 22:35:37 +0000 dvanhorn http://dvanhorn.lambda-calcul.us/2008/04/06/sharing-graph-for-callcc/ Sharing graphs are, in my opinion, the syntax representation of the discriminating hacker. They work wonderfully well on whiteboards, napkins, and yellow pads of unruled paper. But typesetting them is an exercise left only for the true masochist. The best known solution to this problem is to become a full professor, leaving it up to sycophantic graduate students to obsess over. Shy of that, you might try typessetting them with Peter Neergaard’s proofnets package, PS Tricks, or XFig, as I have in the past with limited success. This weekend, I tried another approach: MetaPost.

The graph shown here is the sharing graph for call/cc; my favorite because there’s a straightforward reading of the graph that gives the usual operational understanding of call/cc. Understanding this graph goes a long way towards understanding sharing graphs in general and demonstrates their generalization of a term-based representation (which cannot express call/cc directly).

MetaPost was far more pleasant to deal with than the other approaches I’ve tried. And it looks like it will be straightforward to add graph annotations for either flow analysis or reduction. So for the time being at least, I’m going to use MetaPost for my dissertation figures.

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