Let V and W be two real vector spaces and let &sim be a relation on both V and W. A linear function T : V → W is said to be a linear preserver (respectively strong linear preserver) of &sim if Tx &sim Ty whenever x &sim y (respectively Tx &sim Ty if and only if x &sim y). In this paper we characterize all linear functions T : M_{n,m} → M_{n,k} which preserve or strongly preserve multivariate an...

Type classes are an immensely popular andproductive feature of Haskell. They have since been adoptedin, and adapted to, numerous other languages, including the-orem provers. We show that type classes have a natural andefficient representation in .NET that paves the way for theextension of F#, C# and other .NET languages with typeclasses. Our encoding is type preserving a...