In Lean3, we supported two kinds of local constant:
context-less (inherited from Lean2) and context-based (type,
binder-info and pretty printing name are stored in the context).
The context-less was used in the kernel and a few modules we kept when
we moved from Lean2 to Lean3. Even if we keep the hybrind
representation, we should not expose the context-less to users.
Without these annotations, Lean will timeout when trying to synthesize
the type class instance `decidable_eq uint32`. The type class resolution
problem will produce the unification problem:
```
decidable (@eq uint32 a b) =?= decidable (@eq usize ?x ?y)
```
which Lean tries to solve by assigning `?x := a`.
During the assignment, the types of `?x` and `a` are unified with "full
force". Thus, we get the constraint
```
usize_sz =?= uint32_sz
```
which will take forever to be solved when peforming the computation in
unary arithmetic.
Remark: this commit also makes sure that `type_context` will not unfold
irreducible definitions when trying to unify/match the types.
The new test `type_class_performance1.lean` exposes the problem fixed
by this commit.
The tactic mk_dec_eq_instance constructs a function using the brec_on
recursor. The compiler generates horrible code for this kind of
definition. It creates a closure for each recursive call.
Moreover, `brec_on` accumulates all intermediate results.
To generate efficient code, we need to generate a collection of
recursive equations, and then invoke the equation compiler.
cc @kha
All theorems are proved without using the tactic framework.
Thus, we can define `fin/uint32/uint64` types and their operations
before we define the tactic framework.
The tactic_state object will contain a name_generator for creating fresh
names. `tactic_state.mk_empty` is bad because it does not have sufficient
information to create this name_generator.
Moreover `tactic_state.mk_empty` was only being used to convert
`tactic A` into a `parser A`.
We implement this primitive now in C++. In C++, we will be able
to use the parser name generator to initialize a fresh `tactic_state`.
The tactic `mk_fresh_name` is used to create internal unique ids.
We should not use them to create (temporary) user facing
names. Reasons:
1- They are "cryptic".
2- They are not very stable. Minor changes in Lean may change the
value returned and may break proofs that rely on these fresh names.
