Before this commit, `Simproc`s were defined as `Expr -> SimpM (Option Step)`, where `Step` is inductively defined as follows:
```
inductive Step where
| visit : Result → Step
| done : Result → Step
```
Here, `Result` is a structure containing the resulting expression and a proof demonstrating its equality to the input. Notably, the proof is optional; in its absence, `simp` assumes reflexivity.
A simproc can:
- Fail by returning `none`, indicating its inapplicability. In this case, the next suitable simproc is attempted, along with other simp extensions.
- Succeed and invoke further simplifications using the `.visit`
constructor. This action returns control to the beginning of the
simplification loop.
- Succeed and indicate that the result should not undergo further
simplifications. However, I find the current approach unsatisfactory, as it does not align with the methodology employed in `Transform.lean`, where we have the type:
```
inductive TransformStep where
/-- Return expression without visiting any subexpressions. -/
| done (e : Expr)
/--
Visit expression (which should be different from current expression) instead.
The new expression `e` is passed to `pre` again.
-/
| visit (e : Expr)
/--
Continue transformation with the given expression (defaults to current expression).
For `pre`, this means visiting the children of the expression.
For `post`, this is equivalent to returning `done`. -/
| continue (e? : Option Expr := none)
```
This type makes it clearer what is going on. The new `Simp.Step` type is similar but use `Result` instead of `Expr` because we need a proof.
Adds support for `let_fun` to the `intro` and `intros` tactics. Also
adds support to `intro` for anonymous binder names, since the default
variable name for a `letFun` with an eta reduced body is anonymous.
right now, the `induction` tactic accepts a custom eliminator using the
`using <ident>` syntax, but is restricted to identifiers. This
limitation becomes annoying when the elminator has explicit parameters
that are not targets, and the user (naturally) wants to be able to write
```
induction a, b, c using foo (x := …)
```
This generalizes the syntax to expressions and changes the code
accordingly.
This can be used to instantiate a multi-motive induction:
```
example (a : A) : True := by
induction a using A.rec (motive_2 := fun b => True)
case mkA b IH => exact trivial
case A => exact trivial
case mkB b IH => exact trivial
```
For this to work the term elaborator learned the `heedElabAsElim` flag,
`true` by default. But in the default setting, `A.rec (motive_2 := fun b
=> True)`
would fail to elaborate, because there is no expected type. So the
induction
tactic will elaborate in a mode where that attribute is simply ignored.
As a side effect, the “failed to infer implicit target” error message
is improved and prints the name of the implicit target that could not be
instantiated.
This makes changes to the definitions of Associativity, Commutativity,
Idempotence and Identity classes to be more aligned with Mathlib's
versions.
The changes are:
* Move classes are moved from `Lean` to root namespace.
* Drop `Is` prefix from names.
* Rename `IsNeutral` to `LawfulIdentity` and add Left and Right
subclasses.
* Change neutral/identity element to outParam.
* Introduce `HasIdentity` for operations not intended for proofs to
implement
The identity changes are to make this compatible with
[Mathlib](718042db9d/Mathlib/Init/Algebra/Classes.lean)
and to enable nicer fold operations in Std that can use type classes to
infer the identity/initial element on binary operations.
---------
Co-authored-by: Kyle Miller <kmill31415@gmail.com>
Consider
```
import Std.Tactic.ShowTerm
opaque a : Nat
opaque b : Nat
axiom a_eq_b : a = b
opaque P : Nat → Prop
set_option pp.explicit true
-- Using rw
example (h : P b) : P a := by show_term rw [a_eq_b]; assumption
```
Before, a typical proof term for `rewrite` looked like this:
```
-- Using the proof term that rw produces
example (h : P b) : P a :=
@Eq.mpr (P a) (P b)
(@id (@Eq Prop (P a) (P b))
(@Eq.ndrec Nat a (fun _a => @Eq Prop (P a) (P _a))
(@Eq.refl Prop (P a)) b a_eq_b))
h
```
which is rather round-about, applying `ndrec` to `refl`. It would be
more direct to write
```
example (h : P b) : P a :=
@Eq.mpr (P a) (P b)
(@id (@Eq Prop (P a) (P b))
(@congrArg Nat Prop a b (fun _a => (P _a)) a_eq_b))
h
```
which this change does.
This makes proof terms smaller, causing mild general speed up throughout
the code; if the brenchmarks don’t lie the highlights are
* olean size -2.034 %
* lint wall-clock -3.401 %
* buildtactic execution s -10.462 %
H'T to @digama0 for advice and help.
NB: One might even expect the even simpler
```
-- Using the proof term that I would have expected
example (h : P b) : P a :=
@Eq.ndrec Nat b (fun _a => P _a) h a a_eq_b.symm
```
but that would require non-local changes to the source code, so one step
at a time.
Allow `simproc`s to be declared without setting the `[simproc]`
attribute. A `simproc` declaration is function + pattern.
Motivation: allow them to be provided as arguments to `simp` **and** `simp only`.
TODO: track their use in `simp`.
TODO: builtin simprocs
Motivations:
- We can simplify the big mutual recursion and the implementation.
- We can implement the support for `match`-expressions in the `pre` method.
- It is easier to define and simplify `Simprocs`.
Switches from encoding `let_fun` using an annotated `(fun x : t => b) v`
expression to a function application `letFun v (fun x : t => b)`.
---------
Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
Fixes an issue reported on Zulip; see the test case.
* Modifies the `MonadBacktrack` instance for `SimpM` to also backtrack
the `UsedSimps` field.
* When calling the discharger, `saveState`, and then `restoreState` if
something goes wrong.
I'm not certain that it makes sense to restore the `MetaM` state if
discharging fails. I can easily change this to more conservatively just
backtrack the `UsedSimps` after failed discharging.
We noticed at
https://github.com/leanprover/lean4/pull/2923#discussion_r1400468371
that this instance is not used. It's arguably also incorrect (as it
doesn't backtrack the `usedTheorems` field).
Seems better to just remove to avoid confusion.
Evidence that this is dead code:
* After deleting the instance, calling `saveState` in the `SimpM` monad
raises an error `failed to synthesize instance MonadBacktrack PUnit
SimpM`.
* Understanding the `MonadBacktrack` monad leads one to believe that
would have happened, via the fact that the only instances for
`MonadBacktrack` are either concrete instances (e.g. for `MetaM`,
`TacticM`, etc), or a single lifting instance `instance [MonadBacktrack
s m] [Monad m] : MonadBacktrack s (ExceptT ε m)`. (This is good and
correct behaviour: lifting instances for `MonadBacktrack` would be hard
to model.)
* Mathlib builds after the instance is removed.
Potential evidence that I have not sought, because we don't have
sufficient tooling:
* Compiling Lean/Std/Mathlib with a debugger, breaking on entering this
code.
Modifies `cleanup` so that it takes (1) an array of additional fvarids
to preserve and (2) a flag to control whether to include indirect
propositions.
(This is wanted in mathlib for the `extract_goal` tactic.)
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
