Hey folks, I’m scratching my head over typeclass laws in Haskell. They often use a single equals sign (=) instead of the double equals (==) we see with Eq. This got me wondering what kind of equality we’re talking about here.
I’ve looked around but can’t find a solid answer. The Haskell report doesn’t mention laws at all. Some people say it’s about extensional equality or substitution, but nobody seems to have a definite source.
Here’s an example to show what I mean:
class MyClass a where
myFunc :: a -> a
-- Law: myFunc (myFunc x) = myFunc x
What exactly does that = mean? Is there an official definition somewhere? And are there any weird cases where = means something totally different?
Also, how do we handle tricky situations? Like, there’s a Monoid instance for IO a, but how do you compare IO values for equality?
I’d really appreciate any insights or pointers to reliable sources on this. Thanks!
As someone who’s spent a fair bit of time wrestling with Haskell, I can shed some light on this. The single equals sign in typeclass laws isn’t about literal equality, but rather about behavioral equivalence. It’s saying that two expressions should be interchangeable without altering the program’s observable behavior.
Take your example: myFunc (myFunc x) = myFunc x. This law is telling us that applying myFunc twice should have the same effect as applying it once. It’s not about the internal representation, but about what we can observe from the outside.
Regarding IO equality, it’s a thorny issue. You can’t directly compare IO actions, so we tend to reason about their effects and how they combine. The Monoid instance for IO focuses on action composition rather than content comparison.
While there’s no official definition in the Haskell Report, this interpretation is widely accepted in the community. If you’re looking to dive deeper, I’d recommend checking out discussions on the Haskell subreddit or Stack Overflow. They often have some insightful debates on these nuanced topics.
hey, the = in typeclass laws is about behavior, not literal equality. it means you can swap stuff without breaking things. like myFunc (myFunc x) = myFunc x says applying myFunc twice does the same as once.
for IO, it’s messy. you cant compare actions directly, so we focus on how they combine. no official definition, but thats how most haskell folks see it. check out haskell wiki for more details!
The single equals sign in Haskell typeclass laws refers to extensional equality, which is about observable behavior rather than implementation details. It’s not the same as the ‘==’ from Eq, but instead implies that two expressions can be substituted for each other without changing program behavior.
This concept is crucial for reasoning about code and ensuring consistent behavior across different implementations. For instance, in your example ‘myFunc (myFunc x) = myFunc x’, it means that applying myFunc twice should have the same observable result as applying it once.
Handling IO equality is indeed tricky. Since IO actions can’t be directly compared, we typically reason about their properties and effects rather than their internal structure. The laws for Monoid instance of IO focus on how actions combine, not on comparing their contents directly.
While there’s no official definition in the Haskell Report, this understanding is widely accepted in the Haskell community and literature. For more in-depth explanations, I’d recommend checking out the Typeclassopedia on the Haskell Wiki or discussions on platforms like Stack Overflow.