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archivesThe Experimental Effectiveness of Mathematical ProofThe Experimental Effectiveness of Mathematical Proof
I thought I had already posted this, but apparently not. Consider this paper the main gauntlet thrown down to those who insist that mathematical logic, the Curry-Howard Isomorphism, etc. might be fine for "algorithmic code" (as if there were any other kind) but is somehow inapplicable the moment a system interacts with the "real" or "outside" world (as if software weren't real). Update: the author is Alexandre Miquel, and the citation is "Chapitre du livre Anachronismes logiques, à paraître dans la collection Logique, Langage, Sciences, Philosophie, aux Publications de la Sorbonne. Éd.: Myriam Quatrini et Samuel Tronçon, 2010." By Paul Snively at 2011-10-30 16:05 | Functional | Lambda Calculus | Logic/Declarative | Semantics | 32 comments | other blogs | 15799 reads
Foundations of InferenceFoundations of Inference, Kevin H. Knuth, John Skilling, arXiv:1008.4831v1 [math.PR]
For those of us who find ourselves compelled by the view of probability as a generalization of logic that is isomorphic to (algorithmic, as if there were any other kind) information theory, here is some recent i-dotting and t-crossing. The connection to Curry-Howard or, if you prefer, Krivine's classical realizability is something I hope to explore in the near future. Extensible Programming with First-Class CasesExtensible Programming with First-Class Cases, by Matthias Blume, Umut A. Acar, and Wonseok Chae:
This is an elegant solution to the expression problem for languages with pattern matching. This paper was posted twice in LtU comments, but it definitely deserves its own story. Previous solutions to the exression problem are rather more involved, like Garrigue's use of recursion and polymorphic variants, because they lack support for extensible records which makes this solution so elegant. Extensible records and first-class cases unify object-oriented and functional paradigms on a deeper level, since they enable first-class messages to be directly encoded. Add a sensible system for dynamics, and I argue you have most of the power people claim of dynamic languages without sacrificing the safety of static typing. By naasking at 2011-10-30 21:41 | Functional | Software Engineering | Theory | Type Theory | 33 comments | other blogs | 41859 reads
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