Re: [Haskell-cafe] Monads, do and strictness

observably different from `undefined`

If we understand `undefined` as meaning a computation that never ends, then you cannot ever observe whether one `undefined` is or is not equivalent to another. In strict languages, this is especially obvious. In any case, I don't accept a concept of `monads` that changes so drastically based upon the host language. The laws for monads only apply to actual values and combinators of the monad algebra - and, since `undefined` is not a value, it need not apply. Similarly, algebraic laws for integer arithmetic don't need to account for `undefined`. And our geometry abstractions and theorems don't need to account for `undefined`. Attempting to shoehorn `undefined` into your reasoning about domain algebras and models and monads is simply a mistake. Regards, Dave On Sun, Jan 22, 2012 at 6:49 AM, Sebastian Fischer wrote:

On Sat, Jan 21, 2012 at 8:09 PM, David Barbour wrote:

...

In any case, I think the monad identity concept messed up. The property: return x >>= f = f x

Logically only has meaning when `=` applies to values in the domain. `undefined` is not a value in the domain.

We can define monads - which meet monad laws - even in strict languages.

In strict languages both `return undefined >>= f` and `f undefined` are observably equivalent to `undefined` so the law holds.

In a lazy language both sides might be observably different from `undefined` but need to be consistently so. The point of equational laws is that one can replace one side with the other without observing a difference. Your implementation of `StrictT` violates this principle.

Sebastian