Generic and Indexed Programming: International Spring by Nate Foster, Kazutaka Matsuda, Janis Voigtländer (auth.),

By Nate Foster, Kazutaka Matsuda, Janis Voigtländer (auth.), Jeremy Gibbons (eds.)

Generic programming is set making courses extra generally acceptable through unique varieties of parametrization---not simply alongside the size of values or of sorts, but in addition of items corresponding to the form of information, algebraic buildings, thoughts, computational paradigms, etc. listed programming is a light-weight kind of dependently typed programming, constraining flexibility by way of permitting one to country and fee relationships among parameters: that the shapes of 2 arguments agree, that an encoded price fits a few sort, that values transmitted alongside a channel agree to the said protocol, and so forth. the 2 forces of genericity and indexing stability one another well, concurrently selling and controlling generality. The five lectures integrated during this booklet stem from the Spring institution on accepted and listed Programming, held in Oxford, united kingdom, in March 2010 as a final task of the accepted and listed programming undertaking at Oxford which happened within the years 2006-2010.

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Extra info for Generic and Indexed Programming: International Spring School, SSGIP 2010, Oxford, UK, March 22-26, 2010, Revised Lectures

Example text

Put (vi , (Just ci , ri )) i ∈ {1, . . put (vi , (Nothing, ri )) i ∈ {m + 1, . . , n} c if mc = Just c [ ] if mc = Nothing and ri = take (length (content vi )) r(i−1) for i ∈ {1, . . , n} and ri = drop (length (content vi )) r(i−1) for i ∈ {1, . . , n} and [c1 , . . , cm ] = The get and res components are straightforward generalizations of the corresponding components of the product lens. The put function, however, is different—it handles cases where the view and the rigid complement have different lengths.

To see that these changes do not affect the semantics of lenses in any significant way, observe that, given a “classic” lens l, we can build a basic lens as follows: 28 N. Foster, K. Matsuda, and J. Voigtl¨ ander + (a) positional (b) best match (c) best non-crossing (d) actual operations Fig. 2. get refers to the get function of l. 3 Matching Lenses Matching lenses address the alignment problems that arise in basic lenses by separating the two tasks performed by the put function: matching up pieces of the updated view with the corresponding pieces of the complement, and weaving the view and complement together to produce an updated source.

Eventually each implemented by relying on a “Traversable κ ⇒” context), which satisfy the laws decorate (content x) x = x (5) and decorate y x = decorate y (shape x) (6) Note that (5) is GetPut for get = content and put = decorate. Reasonable definitions will also satisfy the corresponding Partial-PutGet, namely that if decorate y x is defined, then content (decorate y x) = y. Together with the above and the types, Partial-PutPut follows as well. In fact, reasonable definitions of the above three functions let content/decorate be a partial very well-behaved lens, with shape in the role of the chosen complement function res 10 Section 6 also employs this formulation.

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