Union Types for Haskell!?
Fri, 24 Nov 2000 03:22:46 -0800
At 2000-11-24 02:02, Bernd =?iso-8859-2?Q?Holzm=FCller?= wrote:
>When I got to know Haskell, I was expecting a construct for union types
> data B = ...
> data C = ...
> type A = B | C | D -- A accepts values of either B or C or D (cf. the
>"Either a" type in the Prelude)
>but this is not valid Haskell. Is there any reason for this restriction
>in the Haskell type system?
My understanding is that every value in Haskell is a member of exactly
one type. Well, that's not exactly true: it might be better to say that
every Haskell value represents a set of 'items', each of which has
exactly one fully-specified type (i.e. a type with no free
type-variables). For instance, in such definitions as
data Maybe a = Nothing | Just a
the value that the constructor 'Nothing' gives has type 'Maybe a', which
represents a set of 'items' that have such types as 'Maybe Boolean',
'Maybe String' etc.
This rules out union types and OOP-style polymorphism. It also makes it
difficult to make arrays of values of mixed type.
>Does this lead to losing the principal type property?
>And, if so, would you please give me an example where the
>principal type does not exist any more when introducing union types in
>the form above?
Certainly. Consider, in your extended Haskell:
data B = B1 | B2
data C = ...
type A = B | C | D -- A accepts values of either B or C or D
Both A and B are types for B1, but neither is a substitution-instance of
the other. This violates the principal type property whereby for every
term x, either x is not typable or there exists a type T such that every
type assignable to x is a substitution-instance of T.
A better question might be, having extended the type system (and indeed
the notion of 'type') in this way, how do I need to modify the concept of
>Do any papers exist about this topic? Is there any
>Haskell compiler supporting union types?
You might look at O'Haskell, which I understand has some kind of
OOP-style polymorphism. I don't know if it has union types though.
Ashley Yakeley, Seattle WA