least fixed point

(mathematics)A function f may have many fixed points (xsuch that f x = x). For example, any value is a fixed pointof 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 bythe least fixed point of F. This is the least upper boundof the infinite sequence (the ascending Kleene chain)obtained by repeatedly applying F to the totally undefinedvalue, bottom. I.e.

fix F = LUB bottom, F bottom, F.

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

单词	least fixed point
释义	least fixed point least fixed point (mathematics)A function f may have many fixed points (xsuch that f x = x). For example, any value is a fixed pointof 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 bythe least fixed point of F. This is the least upper boundof the infinite sequence (the ascending Kleene chain)obtained by repeatedly applying F to the totally undefinedvalue, bottom. I.e. fix F = LUB bottom, F bottom, F. The least fixed point is guaranteed to exist for acontinuous function over a cpo.
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