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Dan Frumin authored
We define a stronger rule `related_bind_up`, in which there is a baked in semantic type `R`. The idea here is that we don't actually require the expressions that we bind to have the same syntactic type. ``` {E;R::Δ;⤉Γ} ⊨ e1 ≤log≤ e2 : τ ∗ (∀ vv, ⟦ τ ⟧ (R::Δ) vv -∗ {E;Δ;Γ} ⊨ K[v1] ≤log≤ K'[v2] : τ') ____________________________________________________________ {E;Δ;Γ} ⊨ K[e1] ≤log≤ K'[e2] : τ' ``` We can then use `bin_log_related_weaken_2` to prove the original binding rule. The advantages of the new rule is that it allows us to prove the following compatibility rule for seq: ``` {E;(R::Δ);⤉Γ} ⊨ e1 ≤log≤ e1' : τ1 -∗ {E;Δ;Γ} ⊨ e2 ≤log≤ e2' : τ2 -∗ {E;Δ;Γ} ⊨ (e1;; e2) ≤log≤ (e1';; e2') : τ2. ``` The idea here is that we can also pick any *semantic* type to related e1 and e1'. For instance, if both e1 and e1' are expressions of type Nat then it is not necessarily the case that we can relate them at that type -- they might reduce to two different numerals -- but it *should* be the case that we can relate their effects, if it makes sense. E.g. ((#l <- #1;; #0) ;; e) ≤ ((#l <- #1;; #1) ;; e)
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