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The standard well-formed-related predicate can be relatively easily extended to handle untyped PHOAS. The main subtlety is how to handle reduction at the type level. Here's a start of a two-place relation for well-typed in Coq: Require Import Coq.Lists.List. Reserved Infix "@" (left associativity, at level 11). Local Open Scope list_scope. Inductive expr ...

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