• Léon Gondelman's avatar
    This commit fixes the case of computation of `vcg_wp` for the sequence. · d304a819
    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'.
    d304a819
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