By Zhong Shao (eds.)

This ebook constitutes the court cases of the twenty third ecu Symposium on Programming, ESOP 2014, which came about in Grenoble, France, in April 2014, as a part of the ecu Joint meetings on idea and perform of software program, ETAPS 2014. The 27 papers awarded during this quantity have been rigorously reviewed and chosen from 109 submissions. moreover, the booklet includes invited talks. The contributions are geared up in topical sections named: variety platforms; validated compilation; application verification; semantics; concurrency; linear kinds; community and method calculi; and software analysis.

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Extra info for Programming Languages and Systems: 23rd European Symposium on Programming, ESOP 2014, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2014, Grenoble, France, April 5-13, 2014, Proceedings

Example text

D ... Cells : N × Val Val ∗ Cells n [l1 . . lm lm+1 . . l2m . . lp−m+1 . . lp ]c ... d ... = [l1 . . lm ]d ... [lm+1 . . l2m ]d ... . [lp−m+1 . . lp ]d ... , where length(d . . ) = n n i=1 (di ) = m Fig. 5. Metafunctions used in array semantics Iverson included many composition forms and operators. However, λ allows the programmer or library implementor to define them. A simple compose operator for two unary functions can be defined as: (λ [(f 0)(g 0)] [(λ [(x ∞)] (f (g x)))]• ) J’s fork form applies two functions (referred to as “tines”) to the same input and then applies a third function to their results: (λ [(f 0)(g 0)(h 0)] ([(λ [(x ∞)] (f (g x) (h x)))]• ) A simple use of fork is computing the arithmetic mean: (λ [(xs 1)] (([fork]• [/]• [sum]• [length]• ) xs) The fork divides the sum of its input by its length.

A function can also have expected rank of ∞; such functions consume an entire array of arbitrarily high rank, so they are never lifted. For example, length extracts the first element of an array’s shape vector—how long the array is. The programmer may write a function with negative argument rank −n. Lifting then breaks arguments into a rank n frame around cells of unspecified rank (the “−n-cells”), and then the function’s body processes each cell. A function with −1 argument rank which finds its argument’s length effectively extracts the second dimension instead of the first.

Pointwise application: ([f . . ]n ... v . . ) →map ([f ]• α . . ) . . n ... where f . . is a nonempty sequence n . . = Argrank fj , for each j 0 < k = Rank vj − nj , for each j ((α . . ) . . ) = (Cellsn v . . ) 37 Empty frame: ([f . . ]n ... v . . ) →lift0 [ ]n ... m ... where ρ . . = Argrank fj , for each j ρj ∈ N for each j 0 ∈ n . . = Max n . . , Frame ρ v , . . Rank vj − ρj not same for all j m . . chosen nondeterministically Empty function: ([ ]n ... v . . ) →map0 []n ... m ...

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