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Deriving parallel tree scans
The post Deriving list scans explored folds and scans on lists and showed how the usual, efficient scan implementations can be derived from simpler specifications. Let’s see now how to apply the same...
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Composable parallel scanning
The post Deriving list scans gave a simple specification of the list-scanning functions scanl and scanr, and then transformed those specifications into the standard optimized implementations. Next,...
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Parallel tree scanning by composition
My last few blog posts have been on the theme of scans, and particularly on parallel scans. In Composable parallel scanning, I tackled parallel scanning in a very general setting. There are five...
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A third view on trees
A few recent posts have played with trees from two perspectives. The more commonly used I call "top-down", because the top-level structure is most immediately apparent. A top-down binary tree is...
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Parallel speculative addition via memoization
I’ve been thinking much more about parallel computation for the last couple of years, especially since starting to work at Tabula a year ago. Until getting into parallelism explicitly, I’d naïvely...
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Reimagining matrices
The function of the imagination is notto make strange things settled, so much asto make settled things strange.- G.K. Chesterton Why is matrix multiplication defined so very differently from matrix...
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From Haskell to hardware via cartesian closed categories
Since fall of last year, I’ve been working at Tabula, a Silicon Valley start-up developing an innovative programmable hardware architecture called “Spacetime”, somewhat similar to an FPGA, but much...
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Overloading lambda
Haskell’s type class facility is a powerful abstraction mechanism. Using it, we can overload multiple interpretations onto a single vocabulary, with each interpretation corresponding to a different...
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Optimizing CCCs
In the post Overloading lambda, I gave a translation from a typed lambda calculus into the vocabulary of cartesian closed categories (CCCs). This simple translation leads to unnecessarily complex...
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Circuits as a bicartesian closed category
My previous few posts have been about cartesian closed categories (CCCs). In From Haskell to hardware via cartesian closed categories, I gave a brief motivation: typed lambda expressions and the CCC...
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