slovodefinícia
least fixed point
(foldoc)		least fixed point

A function f may have many fixed points (x
such that f x = x). For example, any value is a fixed point
of the identity function, (\ x . x).

If f is recursive, we can represent it as

f = fix F

where F is some higher-order function and

fix F = F (fix F).

The standard denotational semantics of f is then given by
the least fixed point of F. This is the least upper bound
of the infinite sequence (the ascending Kleene chain)
obtained by repeatedly applying F to the totally undefined
value, bottom. I.e.

fix F = LUB bottom, F bottom, F (F bottom), ....

The least fixed point is guaranteed to exist for a
continuous function over a cpo.

(2005-04-12)
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