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`.

Dave

On Sun, Jan 22, 2012 at 6:49 AM, Sebastian Fischer <fischer@nii.ac.jp> wrote:

On Sat, Jan 21, 2012 at 8:09 PM, David Barbour <dmbarbour@gmail.com> 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