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$\newcommand{\Alg}{\mathsf{Alg}\ }$ $\newcommand{\NatF}{\mathsf{NatF}\ }$ $\newcommand{\Nat}{\mathsf{Nat}}$ $\newcommand{\map}{\mathrm{map}\ }$ $\newcommand{\Z}{\mathrm{Z}}$ $\newcommand{\S}{\mathrm{S}}$ I don't think this is an actual counter-example. Parametricity implies: $$∀(α : \Alg \NatF t) (g : r → t)(x : \NatF r). \\ α\ [r]\ g\ x = α\ [t]\ (λx.x)\ (\...


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