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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.
Robbert Krebbers authoredThis 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.