[mercury-users] Square types

[Michael Day]

> For example, you can come up with a type for perfectly balanced trees:

> A type containing only an odd number of items:

> We can have a type containing only square numbers of items using the
> fact that the nth square is equal to the sum of the first n odd
> numbers:

> I admit that last one took some thought...

Goodness me, that's clever.

One more question. As I can't make an arbitrarily sized tuple an instance
of a type class in Mercury, it is convenient sometimes to define a tuple
type, basically a list but with the length encoded in the type:

:- type empty_tuple ---> empty_tuple.
:- type tuple(S, T) ---> tuple(S, T).

X = tuple(1, tuple("foo", empty_tuple))

equivalent to X = {1, "foo"}, but allowing this:

:- instance something(tuple(S, T)) <= something(T) ...

Anyway, would it be possible to make a tuple whose length is embedded in
its type and can contain only a square number of elements?

(To be honest, I'd like to use them to store square matrices of arbitrary
size and be able to know that two different tuples have the *same* size).

Michael

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