[Haskell-cafe] I Need a Better Functional Language!

[Grigory Sarnitskiy]

Hello! I've just realized that Haskell is no good for working with functions!

First, what are 'functions' we are interested at? It can't be the usual set-theoretic definition, since it is not constructive. The constructive definition should imply functions that can be constructed, computed. Thus these are computable functions that should be of our concern. But computable functions in essence are just a synonym for programs.

One could expect from a language that bears 'functional' as its characteristic to be able to do everything imaginable with functions. However, the only thing Haskell can do with functions is to apply them to arguments and to feed them as arguments, run in parallel (run and concatenate programs).

Obviously, that's not all of the imaginable possibilities. One also can rewrite programs. And write programs that rewrite programs. And write programs that rewrite programs that rewrite the first programs and so on. But there is no such possibility in Haskell, except for introducing a DSL.

So now I wonder, what are the languages that are functional in the sense above? With a reasonable syntax and semantics, thus no assembler. I guess Lisp might be of this kind, but I'm not sure. In addition, I'm not a fan of parentheses. What else? Pure? Mathematica? Maxima?

Note, that the reflectivity is important.