abstract-arrays VS polymorphic-functions

And, there won't be a way to properly understand what exactly PF (or CL) misses without immersing myself into a ML-style something, is there? As in, I get some parts of what you are saying; I myself had to (ab)use deftype and gensym intern for another library for providing (limited) parametric types; but I also fail to see something seriously wrong with it, given that it plays nicely with cl:declare, cl:typep and cl:subtypep for the primitive use case of single value type checking, declaration and with some additional things (compiler)macro based optimization.

If performance is a concern, then you would want to stick to CLHS provided simple-array and create appropriate types using deftype, and then dispatch on the types either by yourself, or by using something like polymorphic-functions and polymorph.maths.

If you want to dispatch on vectors, you can try out polymorphic-functions which was made for the express purpose of dispatching on specialized arrays aka types rather than classes.

Since the past year or two, I have been working on numericals that aims to provide the speed of NumPy with the goodness of Common Lisp. In particular, this includes the use of dynamic variables, restarts, and compiler-notes wherever appropriate. It uses CLTL2 API (and may be slightly more) under the hood to provide AOT dispatch, but nothing stops you from combining it with JAOT dispatch provided by numcl/specialized-function. This also spawned a number of projects most notably polymorphic-functions to dispatch on types instead of classes and extensible-compound-types that allows one to define user defined compound types (beyond just the type-aliases enabled by deftype. Fortunately enough, interoperation between magicl, numcl and numericals/dense-numericals actually looks plausible!

Before reading this, please go and check out https://github.com/digikar99/polymorphic-functions which this project is fully based on. It's great.

What I am calling parametric polymorphism is this test: