[m-dev.] for review: use bitsets in quantification

[Ralph Becket]

>From Peter Schachte on 07/11/2000 06:07:43
> 
> As you point out later, this isn't required for sparse_bitset.  I think
> there are good reasons for making this class as simple as possible.  I
would
> suggest a subclass of enum (maybe called `dense_enum') should have this
> constraint, and then should have the succ and pred methods etc.  This will
> often be useful, but I see no reason to exclude types for which this is
not
> the case from using the sparse_set representation.

I agree that the solution here would be to have a range of specialised
typeclasses.  Several constraints have been discussed on this thread:

* bounded enumerable types isomorphic to (a subset of) int
:- typeclass enum(T) where [
	func to_int(T) = int,
	func from_int(int) = T is semidet
].

* (unbounded) enumerable types isomorphic to (a subset of) integer

* enumerable types isomorphic to all ints/integers
:- typeclass complete_enum(T) <= enum(T) where [
	% all [X:int] some [Y:T] Y = from_int(X)
].

* enumerable types isomorphic to a contiguous subset of int/integer
:- typeclass contiguous_enum(T) <= enum(T) where [
	% all [X:T, Y:T, N:int]
	%	(to_int(X) =< N, N =< to_int(Y)) =>
	%		some [Z:T] Z = from_int(N)
].

* enumerable types isomorphic to an arbitrary subset of int/integer

* enumerable types with a lower bound
:- typeclass lb_enum(T) <= enum(T) where [
	func min = T
].

* enumerable types with an upper bound
:- typeclass ub_enum(T) <= enum(T) where [
	func max = T
].

* enumerable types with both an upper and lower bound
:- typeclass bounded_enum(T) <= (lb_enum(T), ub_enum(T)) where [].

I like Fergus' suggestion of using `enum' for int enumerations and
`enumerable' for integer enumerations.

Ralph

--
Ralph Becket      |      MSR Cambridge      |      rbeck at microsoft.com 

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