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>
Adds a command and tactic to print the `Array <| DiscrTree.Key` for
equalities helping the user to debug perceived `simp` failures.
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
When the `decide` tactic fails, it can try to give hints about the
failure:
- It tells you which `Decidable` instances it unfolded, by making use of
the diagnostics feature.
- If it encounters `Eq.rec`, it gives you a hint that one of these
instances was likely defined using tactics.
- If it encounters `Classical.choice`, it hints that you might have
classical instances in scope.
- During this, it tries to process `Decidable.rec`s and matchers to pin
blame on a particular instance that failed to reduce.
This idea comes from discussion with Heather Macbeth [on
Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Decidable.20with.20structures/near/449409870).
this code
```
inductive N where
| cons : (Nat -> N) -> N
mutual
def f : N -> Nat
| .cons a => g (a 32) + 1
termination_by structural n => n
def g : N -> Nat
| .cons a => f (a 42) + 1
termination_by structural n => n
end
```
would break. When searching for the right `belowDict` we now have to,
evne after instantiating the paramters for a reflexive argument, again
search through a bunch of `PProd`s.
(Instead of searching we could pass down the index, but since we are
searching anyways in this function let's just re-use.)
Fixes: #4726
if will fail otherwise, but with a worse error message, and it's helpful
in later transformation to know that the parameters are the same for the
whole group.
Upstreaming of basic material on `List.Pairwise` and `List.Nodup`. More
complete API to follow later, this is just a first approximation of what
leansat will need.
I'll update `list_simp.lean` (simp normal form testing) and add missing
lemmas in follow-up PRs.
This just upstreams the material, and reorders the lemmas to match the
other sections.
This PR refactors the 'ext' attribute and implements the following
features:
- The 'local' and 'scoped' attribute kinds are now usable.
- The attribute realizes the `ext`/`ext_iff` lemmas when they do not
already exist, rather than always generating them. This is useful in
conjunction with `@[local ext]`.
- Adding `@[ext]` to a user ext lemma now realizes an `ext_iff` lemma as
well; formerly this was only for structures. The name of the generated
`ext_iff` theorem for a user `ext` theorem named `A.B.myext` is
`A.B.myext_iff`. If this process leads to an error, the user can write
`@[ext (iff := false)]` to disable this feature.
Breaking changes:
- Now the "x" and "y" term arguments to the realized `ext` and `ext_iff`
lemmas are implicit.
- Now the realized `ext` and `ext_iff` lemmas are protected.
Bootstrapping notes:
- There are a few `ext_iff` lemmas to address after the next stage0
update.
Closes https://github.com/leanprover/lean4/issues/3643
Suggested by Floris [on
Zulip](https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/.22Missing.20Tactics.22.20list/near/446267660).
right now, in order to find out how many auxilary datatype are in a
mutual group of inductive with nested data type, one has to jump
through hoops like this:
```
private def numNestedInducts (indName : Name) : MetaM Nat := do
let .inductInfo indVal ← getConstInfo indName | panic! "{indName} is an inductive"
let .recInfo recVal ← getConstInfo (mkRecName indName) | panic! "{indName} has a recursor"
return recVal.numMotives - indVal.all.lengt
```
The `InductiveVal` data structure already has `.isNested : Bool`, so it
seems to be a natural extension to beef that up to `.numNested: Nat`.
This touched kernel code.
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>
Generalizes #3556 to not suppressing errors in tactic steps either when
the parse error is in a later step, as otherwise changes to the end of a
proof would affect (correctness or effectiveness of) incrementality of
preceding steps.
Fixes#4623, in combination with #4643
The previous check, looking only at the type of the parameter, was too
permissive and led to ill-typed terms later on.
This fixes#4671.
In some cases the previous code might have worked by accident, in this
sense this is a breaking change. Affected functions can be fixed by
reordering their parameters to that all the function parameters that
occur in the parameter of the inductive type of the parameter that the
function recurses on come first.
### Preliminary PRs:
- [x] #4597
- [x] #4599
- [x] #4600
- [x] #4602
- [x] #4603
- [x] #4604
- [x] #4605
- [x] #4607
- [x] #4627
- [x] #4629
### Quick overview over API/naming changes compared to `Lean.HashMap`
and `Batteries.HashMap`:
#### Lean
* `find?` -> `get?`/`getElem?`
* `find!` -> `get!`/`gtetElem!`
* `findD` -> `getD`
* `findEntry?` -> not implemented for now
* `insert'` -> `containsThenInsert` (order reversed in result)
* `insertIfNew` -> `getThenInsertIfNew?` (order reversed in result)
* `numBuckets` -> `Internal.numBuckets`
* `ofListWith` -> not implemented for now
* `Array.groupByKey` -> not implemented for now
* `merge` -> not implemented for now, but you can use `insertMany`
#### Batteries
* `modify` -> not implemented for now
* `mergeWith` -> not implemented for now
* `mergeWithM` -> not implemented for now
I made a mistake in #4517, fixed here, so about time to add a test.
I wonder if this generic level optimization should be moved into
`mkLevelMax'`, but not today.
fixes#4650
This is an auxiliary procedured used by `rw` and `apply` tactics. It
synthesizes pending type class instances.
The new test contains an example where it failed. The comment at
`synthAppInstances.step` explains why, and the fix.
Now syntax nodes have their formatters run even if the parsers they wrap
are all arity zero. This fixes an issue where if `ppSpace` appears in a
`macro`/`elab` then it does not format with a space due to the fact that
macro argument processing wraps this as `group(ppSpace)`, and `ppSpace`
has arity zero.
Implementation note: the fix is to make the `visitArgs` formatter
combinator always visit the last child, even if it does not exist (in
which case the visited node will be `Syntax.missing`). To compensate,
parser combinators like many and optional need to be sure to keep track
of whether there any children. Only optional's needed to be modified.
Closes#4561
Summary:
- Adds configuration option `exponentiation.threshold`
- An expression `b^n` where `b` and `n` are literals is not reduced by
`whnf`, `simp`, and `isDefEq` if `n > exponentiation.threshold`.
Motivation: prevents system from becoming irresponsive and/or crashing
without memory.
TODO: improve support in the kernel. It is using a hard-coded limit for
now.
Before, `pp.instantiateMVars` generally had no effect because most call
sites for the pretty printer instantiated metavariables first, but now
this functionality is entrusted upon the `pp.instantiateMVars` option.
This also has an effect in hovers, where metavariables can be unfolded
one assignment at a time. However, the goal state still sees all
metavariables instantiated due to the fact that the algorithm relies on
expression equality post-instantiation (see
`Lean.Widget.goalToInteractive`).
Closes#4406
Closes#2736
See comment at `ExprDefEq.lean` for explanation.
Side effects:
- Improved error messages in two tests.
- Had to improve `getSuccesses` procedure at `App.lean`. It now
discards candidates that contain postponed elaboration problems.
If it is too disruptive for Mathlib, we should try to discard the
ones that have postponed metavariables.
Fixes#4591. The extra code already existed in the only other user of
`unresolveNameGlobal` (in the pretty printer), although I did not make
it use this function because it has some additional behavior around
universes and in pattern position.
This implements the `termination_by structural` syntax proposed in
#3909.
I went with `termination_by structural` over, say,
`termination_by (config := {method := .structural})` mainly because it
was
easier to get going (otherwise I’d have to look into how to define
recursive
parsers, as `Parser.config` depends on `term` and `termination_by` is
part of
term. But also because I find it more ergonomic and aesthetic as a user.
But syntax can still change.
The `termination_by?` syntax will no longer force well-founded
recursion,
and instead the inferred `termination_by structurally` annotation will
be shown
if structural termination is possible.
While I was it, this fixes#4546 the easy way (log errors about but
otherwise
ignore incomplete `termination_by` sets for mutual recursion). Maybe we
get
multiple replacements (#4551), but even then this this good behavior.
Involves a bit of shuffling around `TerimationHints` (now validated for
a
clique already by `PreDefinition.main`) and `TerminationArguments` (now
lifted
out of the `WF` namespace, and a bit simplified).
Fixes#3909
---------
Co-authored-by: Richard Kiss <him@richardkiss.com>
using the order as it comes out of the `HashMap` led to annying test
suite output variations. Moreover, sorting by the canonical order leads
to messages that are probably easier to digest as a user.
This example, reported from LNSym, started failing when we changed the
definition of `Fin.sub` in
https://github.com/leanprover/lean4/pull/4421.
When we use the new definition, `omega` produces a proof term that the
kernel is very slow on.
To work around this for now, I've removed `BitVec.toNat_sub` from the
`bv_toNat` simp set,
and replaced it with `BitVec.toNat_sub'` which uses the old definition
for subtraction.
This is only a workaround, and I would like to understand why the term
chokes the kernel.
```
example
(n : Nat)
(addr2 addr1 : BitVec 64)
(h0 : n ≤ 18446744073709551616)
(h1 : addr2 + 18446744073709551615#64 - addr1 ≤ BitVec.ofNat 64 (n - 1))
(h2 : addr2 - addr1 ≤ addr2 + 18446744073709551615#64 - addr1) :
n = 18446744073709551616 := by
bv_omega
```
The new option `set_option debug.skipKernelTC true` is meant for
temporarily working around kernel performance issues.
It compromises soundness because a buggy tactic may produce an invalid
proof, and the kernel will not catch it if the new option is set to true.
This appears to have been a semantic merge conflict between #3940 and
#4129. The effect on the language server is that if two edits are
sufficiently close in time to create an interrupt, some elaboration
steps like `simp` may accidentally catch the exception when it is
triggered during their execution, which makes incrementality assume that
elaboration of the body was successful, which can lead to incorrect
reuse, presenting the interrupted state to the user with symptoms such
as "uses sorry" without accompanying errors and incorrect lints.
When the type of a definition or example is a proposition,
we should elaborate on them as we elaborate on theorems.
This is particularly important for examples that are often
used in educational material.
Recall that when elaborating theorem headers, we convert unassigned
universe metavariables into universe parameters. The motivation is
that the proof of a theorem should not influence its statement.
However, before this commit, this was not the case for definitions and
examples when their type was a proposition. This discrepancy often
confused users.
Additionally, we considered extending the above behavior whenever
the type of a definition is provided. That is, we would keep the
current behavior only if `: <type>` was omitted in a definition.
However, this proved to be too restrictive.
For example, the following instance in `Core.lean` would fail:
```
instance {α : Sort u} [Setoid α] : HasEquiv α :=
⟨Setoid.r⟩
```
and we would have to write instead:
```
instance {α : Sort u} [Setoid α] : HasEquiv.{u, 0} α :=
⟨Setoid.r⟩
```
There are other failures like this in the core, and we assume many more
in Mathlib.
closes#4398
@semorrison @jcommelin: what do you think?
this is in preparation for #4542, and extracts from `findRecArg` the
functionality for trying one particular argument.
It also refactors the code a bit. In particular
* It reports errors in the order of the parameters, not the order of
in which they are tried (it tries non-indices first).
* For every argument it will say why it wasn't tried, even if the
reason is quite obviously (fixed prefix, or `Prop`-typed etc.)
Therefore there is some error message churn.
