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    • Robbert Krebbers's avatar
      The unbounded fractional authoritative camera. · 151dda05
      Robbert Krebbers authored
      The unbounded fractional authoritative camera is a version of the fractional
      authoritative camera that can be used with fractions `> 1`.
      
      Most of the reasoning principles for this version of the fractional
      authoritative cameras are the same as for the original version. There are two
      difference:
      
      - We get the additional rule that can be used to allocate a "surplus", i.e.
        if we have the authoritative element we can always increase its fraction
        and allocate a new fragment.
      
            ✓ (a ⋅ b) → ●U{p} a ~~> ●U{p + q} (a ⋅ b) ⋅ ◯U{q} b
      
      - At the cost of that, we no longer have the `◯U{1} a` is an exclusive
        fragmental element (cf. `frac_auth_frag_validN_op_1_l`).
      151dda05
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    • Jacques-Henri Jourdan's avatar
      A specific constructor for injecting values in expressions · 9646293e
      Jacques-Henri Jourdan authored
      We add a specific constructor to the type of expressions for injecting
      values in expressions.
      
      The advantage are :
      - Values can be assumed to be always closed when performing
        substitutions (even though they could contain free variables, but it
        turns out it does not cause any problem in the proofs in
        practice). This means that we no longer need the `Closed` typeclass
        and everything that comes with it (all the reflection-based machinery
        contained in tactics.v is no longer necessary). I have not measured
        anything, but I guess this would have a significant performance
        impact.
      
      - There is only one constructor for values. As a result, the AsVal and
        IntoVal typeclasses are no longer necessary: an expression which is
        a value will always unify with `Val _`, and therefore lemmas can be
        stated using this constructor.
      
      Of course, this means that there are two ways of writing such a thing
      as "The pair of integers 1 and 2": Either by using the value
      constructor applied to the pair represented as a value, or by using
      the expression pair constructor. So we add reduction rules that
      transform reduced pair, injection and closure expressions into values.
      At first, this seems weird, because of the redundancy. But in fact,
      this has some meaning, since the machine migth actually be doing
      something to e.g., allocate the pair or the closure.
      
      These additional steps of computation show up in the proofs, and some
      additional wp_* tactics need to be called.
      9646293e
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