Sets the default value to `pp.fieldNotation.generalized` to `true`.
Updates tests, and fixes some minor flaws in the implementation of the
generalized field notation pretty printer.
Now generalized field notation won't be used for any function that has a
`motive` argument. This is intended to prevent recursors from pretty
printing using it as (1) recursors are more like control flow structures
than actual functions and (2) generalized field notation tends to cause
elaboration problems for recursors.
Note: be sure functions that have an `@[app_unexpander]` use
`@[pp_nodot]` if applicable. For example, `List.toArray` needs
`@[pp_nodot]` to ensure the unexpander prints it using `#[...]`
notation.
Encouraged by the performance gains from making `rewrite` produce
smaller proof objects
(#3121) I am here looking for low-hanging fruit in `simp`.
Consider this typical example:
```
set_option pp.explicit true
theorem test
(a : Nat)
(b : Nat)
(c : Nat)
(heq : a = b)
(h : (c.add (c.add ((c.add b).add c))).add c = c)
: (c.add (c.add ((c.add a).add c))).add c = c
```
We get a rather nice proof term when using
```
:= by rw [heq]; assumption
```
namely
```
theorem test : ∀ (a b c : Nat),
@Eq Nat a b →
@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c →
@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c :=
fun a b c heq h =>
@Eq.mpr (@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c)
(@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c)
(@congrArg Nat Prop a b (fun _a => @Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c _a) c))) c) c) heq) h
```
(this is with #3121).
But with `by simp only [heq]; assumption`, it looks rather different:
```
theorem test : ∀ (a b c : Nat),
@Eq Nat a b →
@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c →
@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c :=
fun a b c heq h =>
@Eq.mpr (@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c)
(@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c)
(@id
(@Eq Prop (@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c)
(@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c))
(@congrFun Nat (fun a => Prop) (@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c))
(@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c))
(@congrArg Nat (Nat → Prop) (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c)
(Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) (@Eq Nat)
(@congrFun Nat (fun a => Nat) (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))))
(Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))))
(@congrArg Nat (Nat → Nat) (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c)))
(Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) Nat.add
(@congrArg Nat Nat (Nat.add c (Nat.add (Nat.add c a) c)) (Nat.add c (Nat.add (Nat.add c b) c)) (Nat.add c)
(@congrArg Nat Nat (Nat.add (Nat.add c a) c) (Nat.add (Nat.add c b) c) (Nat.add c)
(@congrFun Nat (fun a => Nat) (Nat.add (Nat.add c a)) (Nat.add (Nat.add c b))
(@congrArg Nat (Nat → Nat) (Nat.add c a) (Nat.add c b) Nat.add
(@congrArg Nat Nat a b (Nat.add c) heq))
c))))
c))
c))
h
```
Since simp uses only single-step `congrArg`/`congrFun` congruence lemmas
here, the proof
term grows very large, likely quadratic in this case.
Can we do better? Every nesting of `congrArg` (and it's little brother
`congrFun`) can be
turned into a single `congrArg` call.
In this PR I make making the smart app builders `Meta.mkCongrArg` and
`Meta.mkCongrFun` a bit
smarter and not only fuse with `Eq.refl`, but also with
`congrArg`/`congrFun`.
Now we get, in this simple example,
```
theorem test : ∀ (a b c : Nat),
@Eq Nat a b →
@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c →
@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c :=
fun a b c heq h =>
@Eq.mpr (@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c)
(@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c)
(@congrArg Nat Prop a b (fun x => @Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c x) c))) c) c) heq) h
```
Let’s see if it works and how much we gain.
See new test for example that takes exponential time without new simp
theorems.
TODO: replace auxiliary theorems with simprocs as soon as we implement them.
