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Can anonymous functions recurse and still guarantee termination?

Weirich derives a fixed-point combinator so a function can recur without a name. Wadler approaches the same operator from the other direction. Adding unrestricted recursion gives up the termination guarantee of the simply typed calculus.

Compare the passages

the function y calculates the fixpoint of an improver function.
Ruby Conf 12 - Y Not- Adventures in Functional Programming by Jim Weirich · ▶ 46:27–47:02
not using What's called the fixo operator that is unlimited General recursion
"Propositions as Types" by Philip Wadler · ▶ 21:59–22:07