This PR modifies the `structure` syntax so that parents can be named,
like in
```lean
structure S extends toParent : P
```
**Breaking change:** The syntax is also modified so that the resultant
type comes *before* the `extends` clause, for example `structure S :
Prop extends P`. This is necessary to prevent a parsing ambiguity, but
also this is the natural place for the resultant type. Implements RFC
#7099.
Will need followup PRs for cleanup after a stage0 update.
This PR modifies structure instance notation and `where` notation to use
the same notation for fields. Structure instance notation now admits
binders, type ascriptions, and equations, and `where` notation admits
full structure lvals. Examples of these for structure instance notation:
```lean
structure PosFun where
f : Nat → Nat
pos : ∀ n, 0 < f n
def p : PosFun :=
{ f n := n + 1
pos := by simp }
def p' : PosFun :=
{ f | 0 => 1
| n + 1 => n + 1
pos := by rintro (_|_) <;> simp }
```
Just like for the structure `where` notation, a field `f x y z : ty :=
val` expands to `f := fun x y z => (val : ty)`. The type ascription is
optional.
The PR also is setting things up for future expansion. Pending some
discussion, in the future structure/`where` notation could have have
embedded `where` clauses; rather than `{ a := { x := 1, y := z } }` one
could write `{ a where x := 1; y := z }`.
We swap the arguments for `Membership.mem` so that when proceeded by a
`SetLike` coercion, as is often the case in Mathlib, the resulting
expression is recognized as eta expanded and reduce for many
computations. The most beneficial outcome is that the discrimination
tree keys for instances and simp lemmas concerning subsets become more
robust resulting in more efficient searches.
Closes `RFC` #4932
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
Co-authored-by: Henrik Böving <hargonix@gmail.com>
This is intended to fail at present: it just adds a test case containing
a minimization of a Mathlib slowdown from #3807.
Prior to #3807, the declaration `exists_algHom_adjoin_of_splits'''` at
the end of the file would take around 16,000 heartbeats. Now it takes
around 210,000 heartbeats.
---------
Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
