This implements the first half of #3302: It improves the extensible
`apply_rfl` tactic (the one that looks at `refl` attributes, part of
the `rfl` macro) to
* Check itself and ahead of time that the lhs and rhs are defEq, and
give
a nice consistent error message when they don't (instead of just passing
on
the less helpful error message from `apply Foo.refl`), and using the
machinery that `apply` uses to elaborate expressions to highlight diffs
in implicit arguments.
* Also handle `Eq` and `HEq` (built in) and `Iff` (using the attribute)
Care is taken that, as before, the current transparency setting affects
comparing the lhs and rhs, but not the reduction of the relation
So before we had
```lean
opaque P : Nat → Nat → Prop
@[refl] axiom P.refl (n : Nat) : P n n
/--
error: tactic 'apply' failed, failed to unify
P ?n ?n
with
P 42 23
⊢ P 42 23
-/
#guard_msgs in
example : P 42 23 := by apply_rfl
opaque withImplicitNat {n : Nat} : Nat
/--
error: tactic 'apply' failed, failed to unify
P ?n ?n
with
P withImplicitNat withImplicitNat
⊢ P withImplicitNat withImplicitNat
-/
#guard_msgs in
example : P (@withImplicitNat 42) (@withImplicitNat 23) := by apply_rfl
```
and with this PR the messages we get are
```
error: tactic 'apply_rfl' failed, The lhs
42
is not definitionally equal to rhs
23
⊢ P 42 23
```
resp.
```
error: tactic 'apply_rfl' failed, The lhs
@withImplicitNat 42
is not definitionally equal to rhs
@withImplicitNat 23
⊢ P withImplicitNat withImplicitNat
```
A test file checks the various failure modes and error messages.
I believe this `apply_rfl` can serve as the only implementation of
`rfl`, which would then complete #3302, and actually expose these
improved
error messages to the user. But as that seems to require a
non-trivial bootstrapping dance, it’ll be separate.
closes#5333
This PR tries to address issue #5333.
My conjecture is that the binder annotations for `C.toB` and
`Algebra.toSMul` are not ideal. `Algebra.toSMul` is one of declarations
where the new command `set_synth_order` was used. Both classes, `C` and
`Algebra`, are parametric over instances, and in both cases, the issue
arises due to projection instances: `C.toB` and `Algebra.toSMul`. Let's
focus on the binder annotations for `C.toB`. They are as follows:
```
C.toB [inst : A 20000] [self : @C inst] : @B ...
```
As a projection, it seems odd that `inst` is an instance-implicit
argument instead of an implicit one, given that its value is fixed by
`self`. We observe the same issue in `Algebra.toSMul`:
```
Algebra.toSMul {R : Type u} {A : Type v} [inst1 : CommSemiring R] [inst2 : Semiring A]
[self : @Algebra R A inst1 inst2] : SMul R A
```
The PR changes the binder annotations as follows:
```
C.toB {inst : A 20000} [self : @C inst] : @B ...
```
and
```
Algebra.toSMul {R : Type u} {A : Type v} {inst1 : CommSemiring R} {inst2 : Semiring A}
[self : @Algebra R A inst1 inst2] : SMul R A
```
In both cases, the `set_synth_order` is used to force `self` to be
processed first.
In the MWE, there is no instance for `C ...`, and `C.toB` is quickly
discarded. I suspect a similar issue occurs when trying to use
`Algebra.toSMul`, where there is no `@Algebra R A ... ...`, but Lean
spends unnecessary time trying to synthesize `CommSemiring R` and
`Semiring A` instances. I believe the new binder annotations make sense,
as if there is a way to synthesize `Algebra R A ... ...`, it will tell
us how to retrieve the instance-implicit arguments.
TODO:
- Impact on Mathlib.
- Document changes.
---------
Co-authored-by: Kim Morrison <scott.morrison@gmail.com>
Co-authored-by: Johan Commelin <johan@commelin.net>
A round of clean-up for the context of the functional induction
principle cases.
* Already previously, with `match e with | p => …`, functional induction
would ensure that `h : e = p` is in scope, but it wouldn’t work in
dependent cases. Now it introduces heterogeneous equality where needed
(fixes#4146)
* These equalities are now added always (previously we omitted them when
the discriminant was a variable that occurred in the goal, on the
grounds that the goal gets refined through the match, but it’s more
consistent to introduce the equality in any case)
* We no longer use `MVarId.cleanup` to clean up the goal; it was
sometimes too aggressive (fixes#5347)
* Instead, we clean up more carefully and with a custom strategy:
* First, we substitute all variables without a user-accessible name, if
we can.
* Then, we substitute all variable, if we can, outside in.
* As we do that, we look for `HEq`s that we can turn into `Eq`s to
substitute some more
* We substitute unused `let`s.
**Breaking change**: In some cases leads to a different functional
induction principle (different names and order of assumptions, for
example).
From the new doc-string:
```quote
In early versions of Lean, the typeclasses provided by `/` and `%`
were defined in terms of `tdiv` and `tmod`, and these were named simply as `div` and `mod`.
However we decided it was better to use `ediv` and `emod`,
as they are consistent with the conventions used in SMTLib, Mathlib,
and often mathematical reasoning is easier with these conventions.
At that time, we did not rename `div` and `mod` to `tdiv` and `tmod` (along with all their lemma).
In September 2024, we decided to do this rename (with deprecations in place),
and later we intend to rename `ediv` and `emod` to `div` and `mod`, as nearly all users will only
ever need to use these functions and their associated lemmas.
```
This is "upstreaming" mathlib's `unfold_let` tactic by incorporating its
functionality into `unfold`. Now `unfold` can, in addition to unfolding
global definitions, unfold local definitions. The PR also updates the
`conv` version of the tactic.
An improvement over `unfold_let` is that it beta reduces unfolded local
functions.
Two features not present in `unfold` are that (1) `unfold_let` with no
arguments does zeta delta reduction of *all* local definitions, and also
(2) `unfold_let` can interleave unfoldings (in contrast, `unfold a b c`
is exactly the same as `unfold a; unfold b; unfold c`).
Closes RFC #4090
Sebastian mentioned that the use of the kernel defeq was to work around
a performance issue that was fixed since. Let's see if we can do
without.
This is also a semantic change: Ground terms (no free vars, no mvars)
are reduced at
“all” transparency even if the the transparency setting is default. This
was the case
even before 03f6b87647 switched to the
kernel defeq
checking for performance. It seems that this is rather surprising
behavior from the user
point of view. The fallout on batteries and mathlib is rather limited,
only a few
`rfl` proofs seem to have (inadvertently or not) have relied on this.
The speedcenter reports no significant regressions on core or mathlib.
This renames `BitVec.getLsb` to `getLsbD` (`D` for "default" value, i.e.
false), and introduces `getLsb?` and `getLsb'` (which we can rename to
`getLsb` after a deprecation cycle).
(Similarly for `getMsb`.)
Also adds a `GetElem` class so we can use `x[i]` and `x[i]?` notation.
Later, we will turn
```
theorem getLsbD_eq_getElem?_getD (x : BitVec w) (i : Nat) (h : i < w) :
x.getLsbD i = x[i]?.getD false
```
on as a `@[simp]` lemma.
This PR doesn't attempt to demonstrate the benefits, but I think both
arguments are going to get easier, and this will bring the BitVec API
closer in line to List/Array, etc.
---------
Co-authored-by: Markus Himmel <markus@lean-fro.org>
in #4154 and #5129 the rules for equational lemmas have changed, and new
options were introduced that can be used to revert to the pre-4.12
behavior. Hopefully nobody really needs these options besides for
backwards compatibility, therefore we put these options in the
`backward` option name space.
So the previous behavior can be achieved by setting
```lean
set_option backward.eqns.nonrecursive false
set_option backward.eqns.deepRecursiveSplit false
```
With this, lean produces the following zoo of rewrite rules:
```
Option.map.eq_1 : Option.map f none = none
Option.map.eq_2 : Option.map f (some x) = some (f x)
Option.map.eq_def : Option.map f p = match o with | none => none | (some x) => some (f x)
Option.map.eq_unfold : Option.map = fun f p => match o with | none => none | (some x) => some (f x)
```
The `f.eq_unfold` variant is especially useful to rewrite with `rw`
under
binders.
This implements and fixes#5110
`simp only` will not apply this simproc anymore. Users must now write
`simp only [reduceCtorEq]`. See RFC #5046 for motivation.
This PR also renames simproc to `reduceCtorEq`.
close#5046
@semorrison A few `simp only ...` tactics will probably break in
Mathlib. Fix: include `reduceCtorEq`.
This is part of #3983.
After #4154 introduced equational lemmas for non-recursive functions and
#5055
unififed the lemmas for structural and wf recursive funcitons, this now
disables the special handling of recursive functions in
`findMatchToSplit?`, so that the equational lemmas should be the same no
matter how the function was defined.
The new option `eqns.deepRecursiveSplit` can be disabled to get the old
behavior.
### Breaking change
This can break existing code, as there now can be extra equational
lemmas:
* Explicit uses of `f.eq_2` might have to be adjusted if the numbering
changed.
* Uses of `rw [f]` or `simp [f]` may no longer apply if they previously
matched (and introduced a `match` statement), when the equational
lemmas got more fine-grained.
In this case either case analysis on the parameters before rewriting
helps, or setting the option `opt.deepRecursiveSplit false` while
defining the function
This is part of #3983.
Fine-grained equational lemmas are useful even for non-recursive
functions, so this adds them.
The new option `eqns.nonrecursive` can be set to `false` to have the old
behavior.
### Breaking channge
This is a breaking change: Previously, `rw [Option.map]` would rewrite
`Option.map f o` to `match o with … `. Now this rewrite will fail
because the equational lemmas require constructors here (like they do
for, say, `List.map`).
Remedies:
* Split on `o` before rewriting.
* Use `rw [Option.map.eq_def]`, which rewrites any (saturated)
application of `Option.map`
* Use `set_option eqns.nonrecursive false` when *defining* the function
in question.
### Interaction with simp
The `simp` tactic so far had a special provision for non-recursive
functions so that `simp [f]` will try to use the equational lemmas, but
will also unfold `f` else, so less breakage here (but maybe performance
improvements with functions with many cases when applied to a
constructor, as the simplifier will no longer unfold to a large
`match`-statement and then collapse it right away).
For projection functions and functions marked `[reducible]`, `simp [f]`
won’t use the equational theorems, and will only use its internal
unfolding machinery.
### Implementation notes
It uses the same `mkEqnTypes` function as for recursive functions, so we
are close to a consistency here. There is still the wrinkle that for
recursive functions we don't split matches without an interesting
recursive call inside. Unifying that is future work.
This restores all of the imports of `Lean.Data.HashMap` and
`Lean.Data.HashSet` so that users actually see the deprecation warnings
instead of a "declaration not found" error.
Currently, the messages in the diagnostic summaries are created by
appending interpolated strings. We wrap these in `.trace`'s, and the
results are better formatted when expanding child nodes in the info
view. Particularly, the latter diagnostic summaries remain on their own
lines flush to the left instead of on the same line directly adjacent to
the last child node.
It is confusing that the message suggesting to use the `diagnostics`
option is given even when the option is already set. This PR makes use
of lazy message data to make the message contingent on the option being
false.
It also tones down the promise that there is any diagonostic information
available, since sometimes there is nothing to report.
Suggested by Johan Commelin.
when transforming the `match` statements in `IndPredBelow`, given a
local variable `x : T`, we need to search for `hx : T.below x`.
Previously this was done using the custom `backwardsChaining` method,
although my hypothesis is that we don’t need to chain anything here, and
can use `apply_assumption`.
code to create nested `PProd`s, and project out, and related functions
were scattered in variuos places. This unifies them in
`Lean.Meta.PProdN`.
It also consistently avoids the terminal `True` or `PUnit`, for slightly
easier to read constructions.
This refactoring PR changes the structure of the `FunInd` module, with
the main purpose to make it easier to support mutual structural
recursion.
In particular the recursive calls are now longer recognized by their
terms (simple for well-founded recursion, `.app oldIH [arg, proof]`, but
tedious for structural recursion and even more so for mutual structural
recursion), but the type after replacing `oldIH` with `newIH`, where the
type will be simply and plainly `mkAppN motive args`).
We also no longer try to guess whether we deal with well-founded or
structural recursion but instead rely on the `EqnInfo` environment
extensions. The previous code tried to handle both variants, but they
differ too much, so having separate top-level functions is easier.
This also fuses the `foldCalls` and `collectIHs` traversals and
introduces a suitable monad for collecting the inductive hypotheses.
This adds the types
* `IndGroupInfo`, a variant of `InductiveVal` with information that
applies to a whole group of mutual inductives and
* `IndGroupInst` which extends `IndGroupInfo` with levels and parameters
to indicate a instantiation of the group.
One purpose of this abstraction is to make it clear when a fuction
operates on a group as a whole, rather than a specific inductive within
the group.
This is extracted from #4718 and #4733 to reduce PR size and improve
bisectability.
We now get `.below` and `.brecOn` definitions for nested inductives.
No surprises in the implementation: the kernel already gives us suitable
`.rec_1` etc. recursors, and our construction follows the structure of
this recursor.
---------
Co-authored-by: Tobias Grosser <tobias@grosser.es>
this idiom shows up multiple times, is non-trivial (in the sense that
the `localInsts` has to be updated, and I am about to use it once more.
Hence time to abstract this out.
This adds support for mutual structural recursive functions.
For now this is opt-in: The functions must have a `termination_by
structural …` annotation (new since #4542) for this to work:
```lean
mutual
inductive A
| self : A → A
| other : B → A
| empty
inductive B
| self : B → B
| other : A → B
| empty
end
mutual
def A.size : A → Nat
| .self a => a.size + 1
| .other b => b.size + 1
| .empty => 0
termination_by structural x => x
def B.size : B → Nat
| .self b => b.size + 1
| .other a => a.size + 1
| .empty => 0
termination_by structural x => x
end
```
The recursive functions don’t have to be in a one-to-one relation to a
set of mutually recursive inductive data types. It is possible to ignore
some of the types:
```lean
def A.self_size : A → Nat
| .self a => a.self_size + 1
| .other _ => 0
| .empty => 0
termination_by structural x => x
```
or have more than one function per argument type:
```lean
def isEven : Nat → Prop
| 0 => True
| n+1 => ¬ isOdd n
termination_by structural x => x
def isOdd : Nat → Prop
| 0 => False
| n+1 => ¬ isEven n
termination_by structural x => x
```
This does not include
* Support for nested inductive data types or nested recursion
* Inferring mutual structural recursion in the absence of
`termination_by`.
* Functional induction principles for these.
* Mutually recursive functions that live in different universes. This
may be possible,
maybe after beefing up the `.below` and `.brecOn` functions; we can look
into this some
other time, maybe when there are concrete use cases.
---------
Co-authored-by: Richard Kiss <him@richardkiss.com>
Co-authored-by: Tobias Grosser <tobias@grosser.es>
