This PR extends the notion of “fixed parameter” of a recursive function
also to parameters that come after varying function. The main benefit is
that we get nicer induction principles.
Before the definition
```lean
def app (as : List α) (bs : List α) : List α :=
match as with
| [] => bs
| a::as => a :: app as bs
```
produced
```lean
app.induct.{u_1} {α : Type u_1} (motive : List α → List α → Prop) (case1 : ∀ (bs : List α), motive [] bs)
(case2 : ∀ (bs : List α) (a : α) (as : List α), motive as bs → motive (a :: as) bs) (as bs : List α) : motive as bs
```
and now you get
```lean
app.induct.{u_1} {α : Type u_1} (motive : List α → Prop) (case1 : motive [])
(case2 : ∀ (a : α) (as : List α), motive as → motive (a :: as)) (as : List α) : motive as
```
because `bs` is fixed throughout the recursion (and can completely be
dropped from the principle).
This is a breaking change when such an induction principle is used
explicitly. Using `fun_induction` makes proof tactics robust against
this change.
The rules for when a parameter is fixed are now:
1. A parameter is fixed if it is reducibly defq to the the corresponding
argument in each recursive call, so we have to look at each such call.
2. With mutual recursion, it is not clear a-priori which arguments of
another function correspond to the parameter. This requires an analysis
with some graph algorithms to determine.
3. A parameter can only be fixed if all parameters occurring in its type
are fixed as well.
This dependency graph on parameters can be different for the different
functions in a recursive group, even leading to cycles.
4. For structural recursion, we kinda want to know the fixed parameters
before investigating which argument to actually recurs on. But once we
have that we may find that we fixed an index of the recursive
parameter’s type, and these cannot be fixed. So we have to un-fix them
5. … and all other fixed parameters that have dependencies on them.
Lean tries to identify the largest set of parameters that satisfies
these criteria.
Note that in a definition like
```lean
def app : List α → List α → List α
| [], bs => bs
| a::as, bs => a :: app as bs
```
the `bs` is not considered fixes, as it goes through the matcher
machinery.
Fixes#7027Fixes#2113
This PR changes the internal construction of well-founded recursion, to
not change the type of `fix`’s induction hypothesis in non-defeq ways.
Fixes#7322 and hopefully unblocks #7166.
This PR continues alignment of lemmas about `Int.ediv/fdiv/tdiv`,
including adding notes about "missing" lemmas that do not apply in one
case. Also lemmas about `emod/fmod/tmod`. There's still more to do.
This PR introduces the `assert!` variant `debug_assert!` that is
activated when compiled with `buildType` `debug`.
---------
Co-authored-by: Mac Malone <tydeu@hatpress.net>
This PR ensures that names suggested by tactics like `simp?` are not
shadowed by auxiliary declarations in the local context and that names
of `let rec` and `where` declarations are correctly resolved in tactic
blocks.
This PR contains the following potentially breaking changes:
* Moves the `auxDeclToFullName` map from `TermElab.Context` to
`LocalContext`.
* Refactors `Lean.Elab.Term.resolveLocalName : Name → TermElabM …` to
`Lean.resolveLocalName [MonadResolveName m] [MonadEnv m] [MonadLCtx m] :
Name → m …`.
* Refactors the `TermElabM` action `Lean.Elab.Term.withAuxDecl` to a
monad-polymorphic action `Lean.Meta.withAuxDecl`.
* Adds an optional `filter` argument to `Lean.unresolveNameGlobal`.
Closes#6706, closes#7073.
This PR translates `lean::mk_projections` into Lean, adding
`Lean.Meta.mkProjections`. It also puts `hasLooseBVarInExplicitDomain`
back in sync with the kernel version. Deletes
`src/library/constructions/projection.{h,cpp}`.
This PR implements non-choronological backtracking for the cutsat
procedure. The procedure has two main kinds of case-splits:
disequalities and Cooper resolvents. This PR focus on the first kind.
This PR improves the cutsat search procedure. It adds support for find
an approximate rational solution, checks disequalities, and adds stubs
for all missing cases.
This PR takes Array-specific lemmas at the end of `Array/Lemmas.lean`
(i.e. material that does not have exact correspondences with
`List/Lemmas.lean`) and moves them to more appropriate homes. More to
come.
This PR makes the arity reduction pass in the new code generator match
the old one when it comes to the behavior of decls with no used
parameters. This is important, because otherwise we might create a
top-level decl with no params that contains unreachable code, which
would get evaluated unconditionally during initialization. This actually
happens when initializing Init.Core built with the new code generator.
This PR makes the server consistently not report newlines between trace
nodes to the info view, enabling it to render them on dedicates lines
without extraneous spacing between them in all circumstances.
The info view code will separately need to be adjusted to this new
behavior, until then this change will make adjacent trace node leafs
consistently be rendered *on the same line* if there is sufficient
space. The cmdline should be unaffected in any case.
This PR prevents `exact?` and `apply?` from suggesting tactics that
correspond to correct proofs but do not elaborate, and it allows these
tactics to suggest `expose_names` when needed.
These tactics now indicate that a non-compiling term was generated but
do not suggest that that term be inserted. `exact?` also no longer
suggests that the user try `apply?` if no partial suggestions were
found.
This addresses part of #5407 but does not achieve the exact expected
behavior therein (due to #6122).
This PR adds an addition newline before the "Additional diagnostic
information may be available using the `set_option ... true` command."
messages, to provide better visual separation from the main error
message.
This PR does some stage0 cleanup after #7100, and enables a warning when
the old `structure S extends P : Type` syntax is used. It also updates
the library to put resulting types in the new correct place (`structure
S : Type extends P`).
The `structure` elaborator also has some additional docstrings, and
`StructFieldKind.fromParent` is renamed to
`StructFieldKind.fromSubobject`.
Before/after:
```
make -C build/release test ARGS="-j$(nproc) -R interactive" 208.10s user 20.93s system 1982% cpu 11.552 total
make -C build/release test ARGS="-j$(nproc) -R interactive" 87.22s user 22.58s system 1454% cpu 7.548 total
```
This PR fixes an `Elab.async` regression where elaboration tasks are
cancelled on document edit even though their result may be reused in the
new document version, reporting an incomplete result.
While this PR fixes the functional regression, it does so as an
over-approximation by never cancelling such tasks. A follow-up PR will
implement the correct behavior of only cancelling the tasks that are not
reused.
This PR adds all missing tree map lemmas about the interactions of the
functions `empty`, `isEmpty`, `contains`, `size`, `insert(IfNew)` and
`erase`.
---------
Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
