The dependent eliminator for an inductive predicate C is called C.drec
TODO: construct dcases_on and drec_on using C.drec
We need this recursor for implementing dependent elimination for
inductive predicates.
We don't need to define acc.drec and eq.drec in the standard library anymore.
Before this commit, an user could define their own prelude and change
the types of quot, quot.mk, quot.lift or quot.ind.
By doing that, they could prove false.
This commit prevents this kind of abuse.
It also modifies the definition of `quot` and avoids the `setoid`
dependency.
The previous `quot` type is now called `quotient`, and it is defined
using the new `quot` type provided by the kernel.
See discussion at #1330
@kha, I added autocompletion for ^. I try to elaborate the expression
before ^. using the local context provided by the parser.
The autocompletion only works if the type for the expression before ^. can be
inferred. This is a big limitation because this information cannot be
obtained in many cases. Here are examples that do not work:
meta def proof_for (e : expr) : smt_tactic expr :=
do cc ← to_cc_state, cc^.proof_for e
--^ does not work here
If we annotate cc with its type, it works:
meta def proof_for (e : expr) : smt_tactic expr :=
do cc : cc_state ← to_cc_state, cc^.proof_for e
--^ works
We don't have typing information on the equation lhs at
autocompletion time. So, the following will not work
private meta def mk_smt_goals_for (cfg : smt_config)
: list expr → list smt_goal → list expr → tactic (list smt_goal × list expr)
| [] sr tr := return (sr^.reverse, tr^.reverse)
--^ does not work since
| (tg::tgs) sr tr := ...
