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This instructional ebook offers seven rigorously revised lectures given on the sixth foreign institution on sensible Programming, AFP 2008, in Heijen, The Netherlands in might 2008.
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Extra resources for Advanced Functional Programming: 6th International School, AFP 2008, Heijen, The Netherlands, May 2008, Revised Lectures
4525, pp. 80–93. Springer, Heidelberg (2007) 67. : Self-adjusting top trees. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (2005) 68. : Dynamic trees as search trees via euler tours, applied to the network simplex algorithm. Mathematical Programming 78, 167–177 (1997) 69. : INC: A Language for Incremental Computations. ACM Transactions on Programming Languages and Systems 13(2), 211–236 (1991) Spider Spinning for Dummies Richard S. uk Oh what a tangled web we weave when ﬁrst we practise to derive.
Spider spinning has a twist: we want the generation to be loopless, meaning that the ﬁrst transition should be produced in linear time in the size of the nest, and each subsequent transition in constant time. Note carefully that the idea of a loopless algorithm is deﬁned in terms of the transitions between bit strings, not the bit strings themselves. Writing out a bit string is not possible in constant time. Knuth and Ruskey gave an algorithm for spider spinning but it wasn’t loopless. There is a program, SPIDERS, on Knuth’s web site  that does perform loopless spider spinning.
When the program is not stable, we often need to choose a diﬀerent algorithm. , applying reduce [1,2,3,4] with addition operation yields 10. A typical implementation of reduce (shown below) traverses the list from left to right while maintaining an accumulator of the partial results for the visited preﬁx. afun reduce f base l = let mfun red (l,a) = case get $ l of NIL => put a | CONS(h,t) => red $ (t,f(h,a)) in red $ (l,base) end This implementation of reduce is not stable. To see why let’s consider adding integer elements of a list with inputs that diﬀer by a single key.