Usual NbE algorithms for untyped lambda calculus, which use (P)HOAS to embed terms to a host language constructs, results in a beta-normal form of a terms.

Is there algorithms to (efficiently) exploit host language constructs to normalize untyped terms to beta-eta normal form?

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    $\begingroup$ Usually, NbE results in $\beta$-normal $\eta$-long normal forms! Can you cite your source for the first claim? $\endgroup$ – cody Oct 2 '20 at 19:46
  • $\begingroup$ @cody I don't know. Does it holds for untyped lambda calculus too? $\endgroup$ – JetNoBrains Oct 2 '20 at 20:07
  • $\begingroup$ @cody I edited the question to mention untyped LC $\endgroup$ – JetNoBrains Oct 2 '20 at 20:17
  • $\begingroup$ All normalization algorithms exploit host language constructs. More specifically, do you mean algorithms which use eta conversion in the host language? $\endgroup$ – András Kovács Oct 12 '20 at 7:58

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