Tensor type safety discussion

Specifications

The fundamental specification is that this library is easy to use. No GHC extensions should be necessary for the user to use anything from the DVDA API.

Adding or multiplying a scalar with {scalar/vector/matrix} broadcasts (*) to properly scale the quantity

exprs :: [Expr a]
exprs = [x + y, 2*y]
  where
    x = sym "x"
    y = vec 3 "y"

Adding vector to matrix (or doing other incompatible non-scalar operations) results in failure

exprs :: Expr a
exprs = x + y -- fail
  where
    x = vec 3 "x"
    y = mat (4,2) "y"

Secondary goals

• Use normal math characters (+) (-) (*) (/) as elementwise operations
• Do tensor dimensionality checking at compile time

Type system choices

Option 1: Hijack (+), use -XMultiParamTypeClasses/-XFunctionalDependencies