• 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
    - 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.