rustompmody at gmail.com
Sun Jul 1 04:37:07 CEST 2012
On Jul 1, 3:05 am, Thomas Jollans <t... at jollybox.de> wrote:
> Yes. My sole point, really, is that "normally", one would expect these
> two expressions to be equivalent:
> a < b < c
> (a < b) < c
> This is clearly not true. That's the inconsistency here....
I dont see the inconsistency with the specific example as you've
given. However if we consider the argument in general, there is
something to be said for being (more) careful to distinguish
associative and conjunctive interpretation of operators. IOW for an
arbitrary operator * (not standard multiply):
If * : t x t -> t, the only meaningful semantics of a*b*c is (a*b)*c
If * : t x t -> Bool the only meaningful semantics of a*b*c is a*b +
where the most reasonable instance of '+' is 'and'
What happens when t = Bool?
Both cases match. And there is something to be said for notationally
allowing for both cases
Dijkstra/Scholten and David Gries books on logic in computer science
expand on this.
A short net-reachable paper is http://wwwhome.ewi.utwente.nl/~fokkinga/mmf2001a.pdf
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