1. 31 Mar, 2017 2 commits
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  4. 27 Mar, 2017 1 commit
  5. 24 Mar, 2017 9 commits
    • Robbert Krebbers's avatar
      Merge branch 'gen_big_op' into 'master' · e906ef70
      Robbert Krebbers authored
      Generic big operators that are computational for lists
      Closes #38
      See merge request !54
    • Robbert Krebbers's avatar
    • Robbert Krebbers's avatar
      Make big_opL type class opaque. · 02a0929d
      Robbert Krebbers authored
      This commit fixes the issues that refolding of big operators did not work nicely
      in the proof mode, e.g., given:
          Goal forall M (P : nat → uPred M) l,
            ([∗ list] x ∈ 10 :: l, P x) -∗ True.
          Proof. iIntros (M P l) "[H1 H2]".
      We got:
          "H1" : P 10
          "H2" : (fix
                  big_opL (M0 : ofeT) (o : M0 → M0 → M0) (H : Monoid o) (A : Type)
                          (f : nat → A → M0) (xs : list A) {struct xs} : M0 :=
                    match xs with
                    | [] => monoid_unit
                    | x :: xs0 => o (f 0 x) (big_opL M0 o H A (λ n : nat, f (S n)) xs0)
                    end) (uPredC M) uPred_sep uPred.uPred_sep_monoid nat
                   (λ _ x : nat, P x) l
      The problem here is that proof mode looked for an instance of `IntoAnd` for
      `[∗ list] x ∈ 10 :: l, P x` and then applies the instance for separating conjunction
      without folding back the fixpoint. This problem is not specific to the Iris proof
      mode, but more of a general problem of Coq's `apply`, for example:
          Goal forall x l, Forall (fun _ => True) (map S (x :: l)).
            intros x l. constructor.
           Forall (λ _ : nat, True)
             ((fix map (l0 : list nat) : list nat :=
                match l0 with
                | [] => []
                | a :: t => S a :: map t
                end) l)
      This commit fixes this issue by making the big operators type class opaque and instead
      handle them solely via corresponding type classes instances for the proof mode tactics.
      Furthermore, note that we already had instances for persistence and timelessness. Those
      were really needed; computation did not help to establish persistence when the list in
      question was not a ground term. In fact, the sitation was worse, to establish persistence
      of `[∗ list] x ∈ 10 :: l, P x` it could either use the persistence instance of big ops
      directly, or use the persistency instance for `∗` first. Worst case, this can lead to an
      exponential blow up because of back tracking.
    • Robbert Krebbers's avatar
      Derive monoid_right_id. · b99023e7
      Robbert Krebbers authored
    • Robbert Krebbers's avatar
    • Robbert Krebbers's avatar
      Generic big operators that are no longer tied to CMRAs. · 6fbff46e
      Robbert Krebbers authored
      Instead, I have introduced a type class `Monoid` that is used by the big operators:
          Class Monoid {M : ofeT} (o : M → M → M) := {
            monoid_unit : M;
            monoid_ne : NonExpansive2 o;
            monoid_assoc : Assoc (≡) o;
            monoid_comm : Comm (≡) o;
            monoid_left_id : LeftId (≡) monoid_unit o;
            monoid_right_id : RightId (≡) monoid_unit o;
      Note that the operation is an argument because we want to have multiple monoids over
      the same type (for example, on `uPred`s we have monoids for `∗`, `∧`, and `∨`). However,
      we do bundle the unit because:
      - If we would not, the unit would appear explicitly in an implicit argument of the
        big operators, which confuses rewrite. By bundling the unit in the `Monoid` class
        it is hidden, and hence rewrite won't even see it.
      - The unit is unique.
      We could in principle have big ops over setoids instead of OFEs. However, since we do
      not have a canonical structure for bundled setoids, I did not go that way.
    • Robbert Krebbers's avatar
      Remove Hints and Instances that are no longer needed. · c52ff261
      Robbert Krebbers authored
      Big ops over list with a cons reduce, hence these just follow
      immediately from conversion.
    • Robbert Krebbers's avatar
    • Ralf Jung's avatar
  6. 23 Mar, 2017 1 commit
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