On Friday 04 March 2011 22:33:20, Alexander Solla wrote:
Unfortunately, Haskell's tuples aren't quite products.[1]
I'm not seeing this either. (A,B) is certainly the Cartesian product of A and B.
Not quite in Haskell, there (A,B) = A×B \union {_|_} _|_ and (_|_,b) are distinguishable. (A,()) contains - (a,()) for a in A - (a, _|_) for a in A - _|_ the three classes are distinguishable case x of (a,b) -> do putStrLn "Bona fide tuple" case b of () -> putStrLn "With defined second component" will produce different output for them. In Haskell, |(A,B)| = |A|×|B| + 1 (and |()| = 2, () = { (), _|_ }), and |(A,B,C)| = |A|×|B|×|C| + 1 etc. So one would expect |(A)| = |A| + 1 by consistency for 1-tuples.
In what sense are you using "product" here?
Set theoretic or more general, category theoretic, I presume.
Is your complaint a continuation of your previous (implicit) line of thought regarding distinct bottoms?
I don't think distinguishing bottoms is the issue, but distinuishing bottom from partially defined values.