[Haskell-cafe] Fwd: enhancing type classes with properties
neil.mitchell.2 at credit-suisse.com
Wed Oct 22 10:07:28 EDT 2008
Take a look at ESC/Haskell and Sound Haskell, which provide mechanisms for doing some of the things you want. I don't think they integrate with type classes in the way you mention, but I think that is just a question of syntax.
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From: haskell-cafe-bounces at haskell.org [mailto:haskell-cafe-bounces at haskell.org] On Behalf Of Alberto G. Corona
Sent: 22 October 2008 1:43 pm
To: haskell-cafe at haskell.org
Subject: [Haskell-cafe] Fwd: enhancing type classes with properties
I´m just thinking aloud, but, because incorporating deeper mathematics concepts has proven to be the best solution for better and more flexible programming languages with fewer errors, I wonder if raising the type classes incorporating axioms can solve additional problems.
At first sight it does:
class Abelian a where
(+) :: a -> a -> a
property ((+))= a+b == b+a
1- safer polimorphism: I can safely reuse the operator + if the type and the property is obeyed. The lack of ability to redefine operators is a problem for DSLs that must use wreid symbols combinations with unknow meanings. To use common operators with fixed properties is very good. the same aplies for method names.
2- the compiler can use the axions as rewrite rules.
3- in debugging mode, it is possible to verify the axiom for each value a generated during execution. Thus, a generator is not needed like in quickcheck. The logic to quickcheck can be incorporated in the debugging executable.
3 guaranties that 1 and 2 are safe.
a type class can express a relation between types, but it is not possible to define relation between relations.
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