On Wed, 19 Dec 2007 02:00:53 -0500, Jules Bean <[EMAIL PROTECTED]>
wrote:
Brad Larsen wrote:
Hi there list,
How would one go about creating a new type for a subset of the
integers, for (contrived) example just the even integers? I was
thinking of making a new type
newtype EvenInt = EvenInt Integer
but the problem with this is that it accepts any integer, even odd
ones. So to prevent this, the module does not export the constructor
for it---rather, the module exports a function `mkEvenInt' that creates
an EvenInt if the given value is acceptable or raises an error
otherwise.
What's the right way to do this? Thanks!
There are two ways:
(1) Have a representation which admits invalid values, and provide
combinators which only perfect validity, and prove that consumers using
your combinators can't produce invalid values.
(2) Have a cleverly designed representation such that every
representation is valid.
An example here, for (2) would be to store n/2; there is a bijection
between 'Integer' and 'EvenInt' given by n/2.
To make sure I understand, an example of (1) would be to export only a
``smart constructor'' that somehow converts invalid values to valid ones
(say, add 1 to arguments that are odd)?
In your example of 2, how would you go about storing n/2? Store just n as
in (newtype EvenInt = EvenInt Integer) and then write all functions that
deal with EvenInts so that they account for the division by two?
In real, more complex problems, (2) often isn't possible and we resort
to (1). E.g. the representation of balanced trees (AVL? RedBlack?)
admits invalid values (both unbalanced trees and out-of-order trees) and
we rely on the reduced set of combinators never to generate one.
Jules
In my particular case, or what I actually want to do, is define a finite
segment of the integers (0-42, say) as a new type and have that checked at
compile time. Any way of doing this w/o defining Peano numbers or a whole
bunch of nullary constructors (i.e. I'm hoping to be able to define a type
whose constructor will accept only Integer arguments between 0 and 42)?
Thanks!
Brad
_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@haskell.org
http://www.haskell.org/mailman/listinfo/haskell-cafe
