# Trying to determine Fixed Points

I'm basically trying to solve 4.2

(Taken from Semantics with Applications)

As I see it, the functional F will be defined like so:

(F g)s = s if s x == 0
(F g)s = gs[x -> x -1] if s x!=0



So, the first function is

g1 s = undefined for all s


I don't think this is a fixed point, because when s x = 0 , the function would output undefined when it really should be s

Am I on the right track?

By that logic, g2 and g3 would be fixed points since they terminate at a state where x = 0.

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