In my book it is written: $$[[\text{while b do S}]] = \text{FIX F}$$, where $Fg = cond (\beta[[b]], g\circ [[S]], id). $What is cond ?$[[\text{if b then S1 else S2}]] = cond (\beta[[b]], [[S1]], [[S2]])$.  I don't understand why we should use $FIX$. What it is FIX ?For me it is sufficient:$S[[\text{while b do S}]] = cond(\beta[[b]], [[\text{while b do S}]]\circ [[S]], id)$$DEFINITIONS $$S_{ds}[[\text{while b do S}]] = FIX F$$where $Fg= \text{cond}(\beta[[b]], g\circ S_{ds}[[S]], id)$$$FIX: ((State\rightarrow State)\rightarrow (State \rightarrow State)) \rightarrow (State \rightarrow State)$$In brackets functions are partial.
denotional semantic for while - fixed points
semantics;denotational semantics