This site is a static rendering of the Trac instance that was used by R7RS-WG1 for its work on R7RS-small (PDF), which was ratified in 2013. For more information, see Home. For a version of this page that may be more recent, see ArraySlicesBreuel in WG2's repo for R7RS-large.


2011-10-16 02:24:07

This is not yet a formal proposal.

In pretty much all modern array languages, the array type is a descriptor for the layout of shared storage, and this is reflected throughout the entire design and API of the array facility. Subscripting and slicing operations return new descriptors, not new storage. Sharing rather than copying is a reasonable default because most array code is written functional style anyway, and the copy operations are unnecessary overhead (this is somewhat analogous to why lists in Scheme are usually both shared and mutable). The descriptors are general enough that they allow rectangular subarrays, arbitrary permutations of the axes, and different strides as views of the same data. (Arbitrary element permutations or boolean masks are not selected by the descriptors.) With these kinds of descriptors, you can basically write most array functions on the last or first axis and efficiently apply them to arbitrary axes. A slice is basically a descriptor without underlying storage. Subscripting an array with a slice creates a descriptor that associates the slice with the storage. There is actually an algebra of slices, so subscripting an array with a slice basically composes the two slices to compute a new slice that is then applied to the underlying storage. (I don't think any of the existing array languages express it quite that cleanly, but that's what's going on abstractly... should probably write this up some time.) The underlying storage for arrays is not made available as a separate "simple array" type because there really is no need to; you can do everything you want to do by using a 1D descriptor for that data. In a sense, the fundamental data type in an array language is the slice, and the array is kind of an afterthought, it's what happens when you associate a slice with data via indexing. (SLICE lo hi step) -> a 1D slice (SLICE-AXIS s i) -> return the 1D slice representing axis i of slice s (SLICE-PRODUCT s1 s2 ...) -> a cartesian product of slices (SLICE-ASSOCIATE s v) -> associate a slice with a data vector, yielding an array (SLICE-COMPOSE s1 s2) -> compose two slices (SLICE-OFFSET-LIST s) -> returns the list of offsets implied by the slice (SLICE-TRANSPOSE s permutation) -> permutes the axes of the slice (ARRAY-SLICE a) -> return the slice associated with an array (ARRAY-DATA a) -> return the data vector associated with an array (ARRAY->LIST a) -> returns the elements of the array in the order implied by its slice With these, ARRAY-REF becomes a special case of slicing (of course, it might still be implemented more efficiently, but array subscripting with integers is pretty rarely used anyway): (ARRAY-INDEX a s) = (SLICE-ASSOCIATE (SLICE-COMPOSE (ARRAY-SLICE a) s) (ARRAY-DATA a))) (ARRAY-REF a i1 i2 ...) = (CAR (ARRAY->LIST (ARRAY-INDEX a (SLICE-PRODUCT (SLICE i1 i1 1) (SLICE i2 i2 1) ...))))) (ARRAY-TRANSPOSE a axes) = (SLICE-ASSOCIATE (SLICE-TRANSPOSE (ARRAY-SLICE a) axes) (ARRAY-DATA a))) (ARRAY-REDUCE-LAST a f) -> returns a new array in which f is mapped over slices representing the last axis Functions like ARRAY-FILTER, ARRAY-PERMUTE, ARRAY-TAKE, etc. of course have to return copies, since slices can't express the kind of complicated sharing they would imply. Just to be clear: the above isn't some complicated generalization from other array languages, it's pretty much the standard functionality that is available in many array languages. (There are some details I have glossed over related to array bounds etc.)