NDLI: Type inference for array programming with dimensioned vector spaces

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Type inference for array programming with dimensioned vector spaces

Content Provider	ACM Digital Library
Author	Griffioen, P. R.
Abstract	Linear algebra operations are a typical application for array programming, but arrays are a more general data structure and not just used for numbers. This generality gives a lot of flexibility, but when numerical data structures like vectors and matrices are build from arrays, it is hard to infer properties like the shape statically, requiring costly out of bound checks to be done at runtime. We extend arrays with units of measurement, and Hindley-Milner typing with a matrix type based on the algebraic structure of units of measurement in matrices that allows type inference up to dimensioned vector spaces. The inference is sound and complete and gives the most general type of any linear algebra expression. Experiments show that the explicit support for linear algebra increases type safety, and that it leads to a more functional and index-free style of programming. It refines the types for linear algebra operators significantly, while the use of arrays as general containers has to be replaced by other data structures. As validation the matrix type system is implemented in the functional matrix language Pacioli.
Starting Page	1
Ending Page	12
Page Count	12
File Format	PDF
ISBN	9781450342735
DOI	10.1145/2897336.2897341
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2015-09-14
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Type inference Unit of measurement Linear algebra Matrix language
Content Type	Text
Resource Type	Article

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