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Linear algebra is a major field of numerical computation and is widelyapplied. Most linear algebra libraries (in most programming languages) do notstatically guarantee consistency of the dimensions of vectors and matrices,causing runtime errors. While advanced type systems--specifically, dependenttypes on natural numbers--can ensure consistency among the sizes of collectionssuch as lists and arrays, such type systems generally require non-trivialchanges to existing languages and application programs, or tricky type-levelprogramming.  We have developed a linear algebra library interface that verifies theconsistency (with respect to dimensions) of matrix operations by means ofgenerative phantom types, implemented via fairly standard ML types and modulesystem. To evaluate its usability, we ported to it a practical machine learninglibrary from a traditional linear algebra library. We found that most of thechanges required for the porting could be made mechanically, and changes thatneeded human thought are minor.

A Simple and Practical Linear Algebra Library Interface with Static Size Checking