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A comment on Löb and möb: strange loops in Haskell.
Compare Löb’s theorem with the signature of `loeb` with some renaming to make them match up:
> in any formal system F, for any formula P, if it is provable in F that "if P is provable in F then P is true", then P is provable in F
loeb :: Functor f => f (f p -> p) -> f p
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Compare Löb’s theorem with the signature of `loeb` with some renaming to make them match up:
> in any formal system F, for any formula P, if it is provable in F that "if P is provable in F then P is true", then P is provable in F
To see it even better, look at the section that introduces the modal logic operator (the square that operates on formulae).