| My point with math is that Haskell libraries and code use mathematical abstractions (like various sorts of algebraic structures) far more than lisp; I was not taking about what people do with Haskell but rather how they do it. The type system does quite a bit more than just describe cardinality. The single most important feature is typeclasses; you simply can't replicate some of what typeclasses can easily do without a similar type system. Apart from that, you also want the type system to let you control "effects"--not just state and IO but also things like error management and non-determinism. You also want a good way to reuse the type system to enforce your own domain-specific invariants; this is what GADTs are for. The only serious effort I know for adding a type system to lisp is typed Racket, and I don't think it does anywhere near as much as Haskell. It certainly does not have typeclasses, and I think it ends up having union types everywhere which are more awkward and bug-prone than the usual sum types languages have. (This is a necessary compromise to integrate well worth normal Racket, but it's still a compromise.) Beyond that, most people don't use typed Racket at all, so I suppose the main way lisp can come close to Haskell's type system is in having one at all. As far as homo-iconic syntax goes, I sometimes miss it, but not too often. Having a flexible syntax that can look like math is far more important usually, and Haskell gets most of the way there without being too complicated. I personally think that seething like Agda's mixfix syntax is the best option overall. |
In the C programming language types are mainly used to describe cardinalities. For example, char is the cardinality of the smallest addressable unit of memory of the machine (often 256). We don't need more then machine cardinalities as entire operating systems have been written in assembly and C. What advantages do type classes and GADTS have that make them worth adopting? Is there any evidence that they make programs more safe and reliable?
> My point with math is that Haskell libraries and code use mathematical abstractions (like various sorts of algebraic structures) far more than lisp; I was not taking about what people do with Haskell but rather how they do it.
I am building a computer algebra system with Lisp in my free time. There are many Lisp computer algebra systems that I have learned a lot from like Maxima, Reduce, and Axiom. One of my favorite computer algebra systems is GAP and it is written in C and not Haskell. I am not convinced that Haskell uses more mathematical abstractions and algebraic structures and I am not familiar with any well maintained computer algebra system written in Haskell.
> Having a flexible syntax that can look like math is far more important usually, and Haskell gets most of the way there without being too complicated.
Math doesn't look like anything. Mathematics is about abstract concepts (especially the natural numbers) not representations. You mean that Haskell is meant to look like math does on paper, but whats so important about using a paper syntax when we have keyboards?