Merge numeric ranges in presence of NOT types

[phoe]

The below type is T, because -3.5d0 is a member of (NOT INTEGER). This library does not detect this case though. (And neither do CCL or SBCL's type systems!)

(OR (REAL * (-3.5d0))
    (REAL (-3.5d0))
    (NOT INTEGER))

[jimka2001]

Can you please give more details about what needs to be changed in rte? If sbcl subtype gives the wrong answer I'm not sure what the application can do. I'd love to have a better understanding of your idea.

[phoe]

There is a simple algorithm that I have implemented in CCL's type system once.

1. For each numeric range inside a union type that has an open upper bound (e.g. (REAL * (-3.5d0))), check if, within the same union type, there exists a range that has an equal open lower bound (e.g. (REAL (-3.5d0))).
2. If such a range exists, then check if the number equal to that bound (in this case, (REAL -3.5d0 -3.5d0)) is a part of the rest of the union (in this case. (NOT INTEGER)).
3. If that is true, then we may merge the two unions (in our case, (REAL * (-3.5d0)) and (REAL (-3.5d0)) into REAL).

[jimka2001]

Thanks for the comment, but when I say "give more details" I really mean more details about which call involving rte is failing? What you are describing seems like something that should be fixed in sbcl. Perhaps I'm misunderstanding you. Do you expect rte to do the right thing even when the underlying subtypep is buggy? If so, then we can discuss ways of avoiding sbcl:subtypep, there are several approaches.

[phoe]

Oh! Okay. I expected that the following call would do the right thing and return REAL:

CL-USER> (lisp-types:reduce-lisp-type '(OR (REAL * (-3.5d0))
                                        (REAL (-3.5d0))
                                        (NOT INTEGER)))
(OR (NOT INTEGER) (REAL * (-3.5d0)) (REAL (-3.5d0)))

The algorithm I described is fully independent of SBCL's subtypep - in particular, step 2 can utilize typep instead of subtypep, as (typep -3.5d0 '(or (not integer))) is expected to work. '(or (not integer)) is the remainder of the union after removing the two ranges mentioned in step 1.