In article <20050105201737.s24g48oo0w8w4occ@webmail.spamcop.net>, ajb@spamcop.net wrote:
Logical if-then-else has this signature:
mif :: LogicT m a -> (a -> LogicT m b) -> LogicT m b -> LogicT m b
Intuitively, this takes three arguments: the "condition", the "then" case and the "else" case. This obeys the "obvious" laws of if-then-else:
mif (return a) t e = t a mif (mzero) t e = e mif (mif c t' e') t e = mif c (\x -> mif (t' x) t e) (mif e' t e)
plus the "soft cut" law:
mif (return a `mplus` m) t e = t a `mplus` (m >>= t)
The soft cut law is the one that stuffs up the more obvious candidates for the passed context, because of this non-identity:
mif (c1 `mplus` c2) t e /= mif c1 t e `mplus` mif c2 t e
Is mif reducible to some "melse" with mif c t e = do ma <- (c >>= return . Just) `melse` (return Nothing) case ma of Just a -> t a Nothing -> e ...? -- Ashley Yakeley, Seattle WA