Assuming 1 :: Int, then:
ones = 1 : ones
is equivalent to:
ones = fix (\ones -> 1:ones)
where fix has type ([Int] -> [Int]) -> [Int].
It's also the case that:
inf = 1+inf
is equivalent to:
inf = fix (\inf -> 1+inf)
where fix has type (Int -> Int) -> Int.
Unfortunately (perhaps), the fixed point returned is _|_,
since it is the LEAST solution to the recursive equation.
-Paul
Dan Weston wrote:
But in fact it seems to me that the type variable "a" not only can,
but must unify with "b->c".
Is there any use of fix for which this is not true? If this is true,
is the type "a" instead of "b->c" because it is not possible in
general for the type checker to verify this fact, making it some kind
of underivable true statement?
If it is not true, I would dearly love to see a use of fix with a type
for which functional application is not defined.
For me, it is this aspect (the type of fix) that has made it so much
harder to understand fix than it should have been.
Dan
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