[Haskell-beginners] Re: Enforcing Monad Laws

[Heinrich Apfelmus]

Jorden M wrote:
> Heinrich Apfelmus wrote:
>> Jorden M wrote:
>>>
>>> C++ `Concepts', which almost made it into the C++0x standard, are
>>> roughly similar to Haskell type classes. The proposal for concepts in
>>> C++ had a feature called axioms, which allow the programmer to specify
>>> semantics on the functions the concept contains. This allows for
>>> enforcing things such as the Monad Laws, as well as letting the
>>> compiler make certain optimizations it may not have been able to make
>>> without axiomatic guarantees.
>>
>> I have a hard time imagining that axioms are being used to prove properties
>> about programs in a language such as C++... :) Any pointers?
> 
> That is not what they are for. Axiom is probably not a good choice of
> terminology. Axioms let a concept enforce certain statements about
> functions inside the concept. E.g., in a concept that describes
> addition, one could use an axiom statement to enforce commutativity of
> that addition operation. There seems to be no way to do this in
> Haskell, hence my question.

Now that I've had a really short look at Axioms, I think the Haskell 
equivalent would be QuickCheck properties. After all, Axioms are not 
enforced by the compiler, their only effect is documentation. Granted, 
they are part of the source code, but frankly, I don't see how this has 
more effect than stating invariants as QuickCheck properties or writing 
them down in a comment.


Regards,
Heinrich Apfelmus

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