By Lex Augusteijn (auth.), S. Doaitse Swierstra, José N. Oliveira, Pedro R. Henriques (eds.)
This booklet originates from the 3rd summer time university on complicated practical Programming, held in Barga, Portugal, in September 1998. The lectures offered are precise at person scholars and programming pros in addition to at small learn teams and academics who desire to turn into familiar with fresh paintings within the quickly constructing quarter of practical programming.
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Read Online or Download Advanced Functional Programming: Third International School, AFP’98, Braga, Portugal, September 12-19, 1998, Revised Lectures PDF
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Additional resources for Advanced Functional Programming: Third International School, AFP’98, Braga, Portugal, September 12-19, 1998, Revised Lectures
MapTree id • (mapTree g k) 46 Roland Backhouse et al. Notational convention Conventionally, the same notation is used for the type mapping and the function mapping of a functor, and we follow that convention here. Moreover, when applicable, we use the name of the type mapping. So, from here on, for function f , we write List f rather than mapList f . 5 Consider the following datatype declarations. Each defines a mapping from types to types. For example, Error maps the type a to the type Error a.
The extractions that we have particular use for are the identity functor Id, which is the same as Ex10 , and the binary functors Ex20 and Ex21 , for which we use the more convenient notations Par and Rec. (The reason for this choice of identifiers will become evident in chapter 3. When defining recursive datatypes like List , we identify a binary “pattern functor”. ) The sum functor The binary sum functor + gives the “disjoint union” of two types. We write it as an infix operator.
What is its complexity? Can you write it as a hylomorphism with O(log n) complexity? The exponent n can be divided by 2 and the recursive results can be multiplied. > pow2 x = leaftree_hylo (destruct,(id,(*))) where > destruct 0 = Left 1 > destruct 1 = Left x > destruct n | even n = Right (n/2,n/2) > | otherwise = Right (n/2,n/2+1) The complexity is O(n), since the hylomorphism has no information about the two recursively being identical. This can be fixed by using a list hylomorphism, that uses only one recursively call and squaring the result of that call.
Advanced Functional Programming: Third International School, AFP’98, Braga, Portugal, September 12-19, 1998, Revised Lectures by Lex Augusteijn (auth.), S. Doaitse Swierstra, José N. Oliveira, Pedro R. Henriques (eds.)