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Léon Gondelman authored
Now all the small tests work, and the `swap` example passes as well. The main idea for fixing `vcg_wp` for sequence, is to change the continuation `(Φ : dval → wp_expr)` of `vcg_wp` so that it takes `denv` as additional parameter. Then, in `vcg_wp` all cases, except for the **sequence** and **store** are simply passing the continuation. The `vcg_wp` for the sequence becomes : ```Coq | dCSeq de1 de2 => vcg_wp E m de1 R (λ m' _, UMod (vcg_wp E (denv_unlock m') de2 R Φ)) ``` The case for **store** is more subtle. The critical part is the case where `vcg_sp E m de1 = Some (mIn, mOut, dv1)` and `dv1 = dLitV (dLitLoc (dLoc i))`, where the continuation will make use of the function `denv_replace_full i dv2 m'` whose specification is ```Coq Some m' = (denv_replace_full i dv m) → ∃ x q dv0 m0, (denv_interp E m0 ∗ dloc_interp E (dLoc i) ↦(x , q ) dval_interp E dv0 ⊣⊢ denv_interp E m) ∧ (denv_interp E m0 ∗ dloc_interp E (dLoc i) ↦(LLvl, 1%Qp) dval_interp E dv ⊣⊢ denv_interp E m'). ``` In that case, we do not need to generate `IsLoc dv1 ...`, inlining instead the precise form of `dv1` in the resulting formula, using `denv_replace_full` in the end: ```Coq | dCStore de1 de2 => match vcg_sp E m de1 with | Some (mIn, mOut, dv1) => match dv1 with | dLitV (dLitLoc (dLoc i)) => mapsto_star_list m (mapsto_wand_list mIn (vcg_wp E mIn de2 R (λ m' dv2, mapsto_wand_list mOut (MapstoStarFull (dLoc i) (λ _, (MapstoWand (dLoc i) dv2 LLvl 1%Qp (match (denv_replace_full i dv2 m') with | Some mf => (Φ mf dv2) | None => Base False (*TODO: maybe this is too strong, return just (Φ m' dv2) *) end))))))) ``` Note the comment for the case where `denv_replace_full i dv2 = None`. Note also, that for the other cases, including `match vcg_sp E m de2 = Some (mIn, mOut, dv1)`, the continuation is passed as such, without replacing its content. For the latter case ( `match vcg_sp E m de2 = Some (mIn, mOut, dv1)`) we probably also need to update the continuation as described above. Finally, the correctness statement for the `vcg_wp` becomes : ```Coq Lemma vcg_wp_correct R E m de Φ : wp_interp E (vcg_wp E m de R Φ) ⊢ awp (dcexpr_interp E de) R (λ v, ∃ dv m', ⌜dval_interp E dv = v⌝ ∧ wp_interp E (Φ m' dv)). ``` This statement is proven for all cases. Somehow surprisingly, the specification for `denv_replace_full` was not needed. The reason for that is probably that the correctness statement only affirms the bare existence of 'm'.
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