• Robbert Krebbers's avatar
    Define `fill` in terms of a `foldl` over `fill_item`. · 6fc9c27e
    Robbert Krebbers authored
    This has some advantages:
    - Evaluation contexts behave like a proper "Huet's zipper", and thus:
      + We no longer need to reverse the list of evaluation context items in the
        `reshape_expr` tactic.
      + The `fill` function becomes tail-recursive.
    - It gives rise to more definitional equalities in simulation proofs using
      binary logical relations proofs.
      In the case of binary logical relations, we simulate an expressions in some
      ambient context, i.e. `fill K e`. Now, whenever we reshape `e` by turning it
      into `fill K' e'`, we end up with `fill K (fill K' e')`. In order to use the
      rules for the expression that is being simulated, we need to turn
      `fill K (fill K' e')` into `fill K'' e'` for some `K'`. In case of the old
      `foldr`-based approach, we had to rewrite using the lemma `fill_app` to
      achieve that. However, in case of the old `foldl`-based `fill`, we have that
      `fill K (fill K' e')` is definitionally equal to `fill (K' ++ K) e'` provided
      that `K'` consists of a bunch of `cons`es (which is always the case, since we
      obtained `K'` by reshaping `e`).
    Note that this change hardly affected `heap_lang`. Only the proof of
    `atomic_correct` broke. I fixed this by proving a more general lemma
    `ectxi_language_atomic` about `ectxi`-languages, which should have been there
    in the first place.