[Haskell-cafe] Creating a type for a subset of the integers
Jules Bean
jules at jellybean.co.uk
Wed Dec 19 02:00:53 EST 2007
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.
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
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