The behaviour a caller's own term representation implements so Ichor.Backtrack.Bindings can unify it -- passed explicitly to every Bindings function (resolve/3, unify/4), the same "module passed as a plain argument, never looked up dynamically" convention Ichor.Actions.evaluate/5 already uses for an actions module.

Nothing here prescribes what a term actually is -- a caller is free to use plain Elixir terms directly for anything atomic (:tom, 42, "a string", compared with ==/2), reserving a distinguishing shape only for the two cases that need special handling:

• variable?/1 + var_id/1 -- a logic variable, keyed by whatever var_id/1 returns (this is exactly the key Bindings stores a binding under, so it must be stable and unique per distinct variable -- an Elixir reference/0 minted fresh per variable is a natural choice).
• compound?/1 + deconstruct/1 -- a compound term (foo(X, bar)), unified by recursively unifying its functor and arguments (deconstruct/1 returning {functor, args}); two compound terms only unify when their functor and arity both match.

Anything that's neither a variable nor a compound term is treated as atomic and unified with plain ==/2.

reconstruct/2 is optional -- the inverse of deconstruct/1, needed only by callers that rebuild terms rather than just inspect them (Ichor.Toolkit.TypeScheme's generalize/4/instantiate/3, which substitute type variables inside a type). Unification itself (Ichor.Backtrack.Bindings) never needs it -- it only ever compares and binds, never constructs.