Jason Dagit wrote:
In Church's λ-calc the types are ignored,


Not so. Church-style lambda calculus is the one where types matter; Curry-style is the one that ignores types and evaluates as if it were the untyped lambda calculus.

Church encodings are based on the untyped LC rather than Church's simply-typed LC however, which is why they don't typecheck with Hindley--Milner.

--
Live well,
~wren
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