Download Advanced Functional Programming: 4th International School, by Richard Bird, Jeremy Gibbons (auth.), Johan Jeuring, Simon PDF

By Richard Bird, Jeremy Gibbons (auth.), Johan Jeuring, Simon L. Peyton Jones (eds.)

This educational ebook provides seven revised lectures given via major researchers on the 4th overseas tuition on practical Programming, AFP 2002, in Oxford, united kingdom in August 2002.

The lectures awarded introduce instruments, language good points, domain-specific languages, challenge domain names, and programming tools. All lectures include workouts and useful assignments. The software program accompanying the lectures will be accessed from the AFP 2002 site. This ebook is designed to allow participants, small teams of scholars, and academics to review fresh paintings within the speedily constructing quarter of useful programming.

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Additional info for Advanced Functional Programming: 4th International School, AFP 2002, Oxford, UK, August 19-24, 2002. Revised Lectures

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In the case where the applied function is not vectorised, we replace the function by its vectorised variant and lift the function arguments. More precisely, we rewrite L f e1 · · · en vs to f ↑ (L e1 vs ) · · · (L en vs ). Much more interesting is, however, the case where the applied function is already vectorised. In fact, the treatment of this case is one of the central points An Approach to Fast Arrays in Haskell 37 of the flattening transformation, so we need to look into it more closely. Let us, for a moment, pretend that we are dealing with list operations.

Perhaps not surprisingly we went through many iterations of the development, considering different ways of expressing the concepts of streaming and stream inversion. The final constructions given above differ markedly from the versions given in the Summer School in August, 2002. None of these iterations would have been possible without the availability of a functional perspective, whose smooth proof theory enabled us to formulate theorems, prove them, and perhaps discard them, quite quickly. Whether or not the reader has followed all the details, we hope we have demonstrated that functional programming and equational reasoning are essential tools of thought for expressing and proving properties of complicated algorithms, and that the ability to define structured recursion operators, such as foldl , unfoldr , stream and destream, is critical for formulating and understanding patterns of computation.

The first is to define buffer bs = (foldl (λ x b → 2 × x + b) 0 cs, rs) where (cs, rs) = splitAt e (bs + + 1 : replicate (e − 1) 0) The definition of z uses the standard method for converting a bit string into a binary integer. This method is used in the final version of decode. But we also have to show how to maintain the representation (z , rs) during the destreaming process. We leave it as an exercise to show that buffer can also be computed by buffer = foldr op (w/2 , [ ]) bs op b (z , rs) = (y, r : rs) where (y, r ) = (w × b + z ) divMod 2 The point of this alternative is that we have foldr op (w/2 , [ ]) · concat = foldr (⊕) (w/2 , [ ]) where bs ⊕ (x , ds) = foldr op (x , ds) bs.

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