>> I guess it could be in simple.el.  But what would be a good name?
>> Maybe 'truncate-lines-p'?
>
> lines-truncated-p, I guess.  Or window-lines-truncated-p.  And I think
> it should be in window.el.

To keep the prefix like in all truncate-related names,
truncated-partial-width-window-p could serve as an example:

  (truncated-partial-width-window-p &optional WINDOW)
  (truncated-lines-p &optional window)

Or can truncated-partial-width-window-p be called directly?  By just

  (or truncate-lines (truncated-partial-width-window-p))

Anyway, here is the patch that probably not needed
when truncated-partial-width-window-p can be used instead: