This PR adds support for numerals, lower & upper bounds to the offset
constraint module in the `grind` tactic. `grind` can now solve examples
such as:
```
example (f : Nat → Nat) :
f 2 = a →
b ≤ 1 → b ≥ 1 →
c = b + 1 →
f c = a := by
grind
```
In the example above, the literal `2` and the lower&upper bounds, `b ≤
1` and `b ≥ 1`, are now processed by offset constraint module.
This PR records the `fib_impl n = fib_spec n` example, and a proof using
current technologies, as a test.
I'd like to think about eliminating `MProd` from the terms produced by
`do` notation; it seems (at least) a simproc would be required.
This PR completes aligning `List`/`Array`/`Vector` lemmas about
`flatten`. `Vector.flatten` was previously missing, and has been added
(for rectangular sizes only). A small number of missing `Option` lemmas
were also need to get the proofs to go through.
This PR implements support for offset equality constraints in the
`grind` tactic and exhaustive equality propagation for them. The `grind`
tactic can now solve problems such as the following:
```lean
example (f : Nat → Nat) (a b c d e : Nat) :
f (a + 3) = b →
f (c + 1) = d →
c ≤ a + 2 →
a + 1 ≤ e →
e < c →
b = d := by
grind
```
This PR puts the `bv_normalize` simp set into simp_nf and splits up the
bv_normalize implementation across multiple files in preparation for
upcoming changes.
This PR improves the failure message produced by the `grind` tactic. We
now include information about asserted facts, propositions that are
known to be true and false, and equivalence classes.
This PR removes functions from compiling decls from Environment, and
moves all users to functions on CoreM. This is required for supporting
the new code generator, since its implementation uses CoreM.
This PR implements a basic async framework as well as asynchronously
running timers using libuv.
---------
Co-authored-by: Sofia Rodrigues <sofia@algebraic.dev>
Co-authored-by: Markus Himmel <markus@himmel-villmar.de>
Co-authored-by: Markus Himmel <markus@lean-fro.org>
This PR fixes the `Repr` instance of the `Timestamp` type and changes
the `PlainTime` type so that it always represents a clock time that may
be a leap second.
- Fix timestamp `Repr`.
- The `PlainTime` type now always represents a clock time that may be a
leap second.
- Changed `readlink -f` to `IO.FS.realPath`
---------
Co-authored-by: Mac Malone <tydeu@hatpress.net>
Co-authored-by: Markus Himmel <markus@himmel-villmar.de>
This PR implements exhaustive offset constraint propagation in the
`grind` tactic. This enhancement minimizes the number of case splits
performed by `grind`. For instance, it can solve the following example
without performing any case splits:
```lean
example (p q r s : Prop) (a b : Nat) : (a + 1 ≤ c ↔ p) → (a + 2 ≤ c ↔ s) → (a ≤ c ↔ q) → (a ≤ c + 4 ↔ r) → a ≤ b → b + 2 ≤ c → p ∧ q ∧ r ∧ s := by
grind (splits := 0)
```
TODO: support for equational offset constraints.
Tests using `logInfo` were taking an additional two seconds on my
machine. This is a performance issue with the old code generator, where
we spend all this time specializing the logging functions for `GoalM`. I
have not checked whether the new code generator is also affected by this
performance issue.
Here is a small example that exposes the issue:
```lean
import Lean
set_option profiler true
open Lean Meta Grind in
def test (e : Expr): GoalM Unit := do
logInfo e
```
cc @zwarich
This PR implements support for offset constraints in the `grind` tactic.
Several features are still missing, such as constraint propagation and
support for offset equalities, but `grind` can already solve examples
like the following:
```lean
example (a b c : Nat) : a ≤ b → b + 2 ≤ c → a + 1 ≤ c := by
grind
example (a b c : Nat) : a ≤ b → b ≤ c → a ≤ c := by
grind
example (a b c : Nat) : a + 1 ≤ b → b + 1 ≤ c → a + 2 ≤ c := by
grind
example (a b c : Nat) : a + 1 ≤ b → b + 1 ≤ c → a + 1 ≤ c := by
grind
example (a b c : Nat) : a + 1 ≤ b → b ≤ c + 2 → a ≤ c + 1 := by
grind
example (a b c : Nat) : a + 2 ≤ b → b ≤ c + 2 → a ≤ c := by
grind
```
---------
Co-authored-by: Kim Morrison <scott.morrison@gmail.com>
This PR allows the dot ident notation to resolve to the current
definition, or to any of the other definitions in the same mutual block.
Existing code that uses dot ident notation may need to have `nonrec`
added if the ident has the same name as the definition.
Closes#6601
This PR improves the usability of the `[grind =]` attribute by
automatically handling
forbidden pattern symbols. For example, consider the following theorem
tagged with this attribute:
```
getLast?_eq_some_iff {xs : List α} {a : α} : xs.getLast? = some a ↔ ∃ ys, xs = ys ++ [a]
```
Here, the selected pattern is `xs.getLast? = some a`, but `Eq` is a
forbidden pattern symbol.
Instead of producing an error, this function converts the pattern into a
multi-pattern,
allowing the attribute to be used conveniently.
This PR improves the theorems used to justify the steps performed by the
inequality offset module. See new test for examples of how they are
going to be used.
This PR implements `Std.Net.Addr` which contains structures around IP
and socket addresses.
While we could implement our own parser instead of going through the
`addr_in`/`addr_in6` route we will need to implement these conversions
to make proper system calls anyway. Hence this is likely the approach
with the least amount of non trivial code overall. The only thing I am
uncertain about is whether `ofString` should return `Option` or
`Except`, unfortunately `libuv` doesn't hand out error messages on IP
parsing.
This PR adds support for creating local E-matching theorems for
universal propositions known to be true. It allows `grind` to
automatically solve examples such as:
```lean
example (b : List α) (p : α → Prop) (h₁ : ∀ a ∈ b, p a) (h₂ : ∃ a ∈ b, ¬p a) : False := by
grind
```
This PR fixes the location of the error emitted when the `rintro` and
`intro` tactics cannot introduce the requested number of binders.
This patch adds a few `withRef` wrappers to invocations of
`MVarId.intro` to fix error locations. Perhaps `MVarId.intro` should
take a syntax object to set the location itself in the future; however
there are a couple other call sites which would need non-trivial fixup.
Closes #5659.
This PR adds support for case splitting on `match`-expressions in
`grind`.
We still need to add support for resolving the antecedents of
`match`-conditional equations.
This PR modifies the `induction`/`cases` syntax so that the `with`
clause does not need to be followed by any alternatives. This improves
friendliness of these tactics, since this lets them surface the names of
the missing alternatives:
```lean
example (n : Nat) : True := by
induction n with
/- ~~~~
alternative 'zero' has not been provided
alternative 'succ' has not been provided
-/
```
Related to issue #3555
This PR adds additional tests for `grind`, demonstrating that we can
automate some manual proofs from Mathlib's basic category theory
library, with less reliance on Mathlib's `@[reassoc]` trick.
In several places I've added bidirectional patterns for equational
lemmas.
I've updated some other files to use the new `@[grind_eq]` attribute
(but left as is all cases where we are inspecting the info messages from
`grind_pattern`).
---------
Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
This PR introduces the parametric attribute `[grind]` for annotating
theorems and definitions. It also replaces `[grind_eq]` with `[grind
=]`. For definitions, `[grind]` is equivalent to `[grind =]`.
The new attribute supports the following variants:
- **`[grind =]`**: Uses the left-hand side of the theorem's conclusion
as the pattern for E-matching.
- **`[grind =_]`**: Uses the right-hand side of the theorem's conclusion
as the pattern for E-matching.
- **`[grind _=_]`**: Creates two patterns. One for the left-hand side
and one for the right-hand side.
- **`[grind →]`**: Searches for (multi-)patterns in the theorem's
antecedents, stopping once a usable multi-pattern is found.
- **`[grind ←]`**: Searches for (multi-)patterns in the theorem's
conclusion, stopping once a usable multi-pattern is found.
- **`[grind]`**: Searches for (multi-)patterns in both the theorem's
conclusion and antecedents. It starts with the conclusion and stops once
a usable multi-pattern is found.
The `grind_pattern` command remains available for cases where these
attributes do not yield the desired result.
This PR introduces the `[grind_eq]` attribute, designed to annotate
equational theorems and functions for heuristic instantiations in the
`grind` tactic.
When applied to an equational theorem, the `[grind_eq]` attribute
instructs the `grind` tactic to automatically use the annotated theorem
to instantiate patterns during proof search. If applied to a function,
it marks all equational theorems associated with that function.
```lean
@[grind_eq]
theorem foo_idempotent : foo (foo x) = foo x := ...
@[grind_eq] def f (a : Nat) :=
match a with
| 0 => 10
| x+1 => g (f x)
```
In the example above, the `grind` tactic will add instances of the
theorem `foo_idempotent` to the local context whenever it encounters the
pattern `foo (foo x)`. Similarly, functions annotated with `[grind_eq]`
will propagate this annotation to their associated equational theorems.
