State of DData
alastair at reid-consulting-uk.ltd.uk
Fri Mar 26 15:00:28 EST 2004
> Arguably then, anything which is an instance of Monad should be a monad.
I would certainly argue strongly for that.
If it ain't true, then small, irrelevant changes in a piece of code could
break. For example, is it safe to make this change:
x <- f y
I'd hope it would be. (And the change might be useful if I want to insert
a check or a debugging printf in the code.)
But if Monads don't have to satisfy this axiom, then I can't make a change
like this without having to write additional conditions in the documentation
or know all possible instances of the code.
> And '+' should be addition. etc. etc.
I think it is well accepted that addition in computers is rarely commutative,
associative, etc. across the whole range of values.
> Haskell doesn't require any of these to be true, and similarly it
> doesn't require that every instance of '==' is equality.
Though it is, perhaps, worth noting that all standard instances of Eq use
observational equality which is plain, ordinary equality for normal values
and, if we look at the common extensions, is 'pointer equality' for mutable
objects like IORefs.
(For abstract datatypes like balanced binary trees, the appropriate equality
would probably be to test whether the trees contain the same set of values
even if they are balanced slightly differently.)
Alastair Reid www.haskell-consulting.com
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