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least fixed point

 
 
least fixed point A function f may have many (x such that f x = x). For example, any value is a fixed point of the identity function, (\ x . x). If f is , we can represent it as f = fix F where F is some and fix F = F (fix F). The standard of f is then given by the least fixed point of F. This is the of the infinite sequence (the ) 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 function over a .
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