This PR enables import auto-completion to complete partial words in
imports.
Other inconsistencies that I've found in import completion already seem
to be fixed by #3014. Since it will be merged soon, there is no need to
invest time to fix these issues on master.
This adds the concept of **functional induction** to lean.
Derived from the definition of a (possibly mutually) recursive function,
a **functional
induction principle** is tailored to proofs about that function. For
example from:
```
def ackermann : Nat → Nat → Nat
| 0, m => m + 1
| n+1, 0 => ackermann n 1
| n+1, m+1 => ackermann n (ackermann (n + 1) m)
derive_functional_induction ackermann
```
we get
```
ackermann.induct (motive : Nat → Nat → Prop) (case1 : ∀ (m : Nat), motive 0 m)
(case2 : ∀ (n : Nat), motive n 1 → motive (Nat.succ n) 0)
(case3 : ∀ (n m : Nat), motive (n + 1) m → motive n (ackermann (n + 1) m) → motive (Nat.succ n) (Nat.succ m))
(x x : Nat) : motive x x
```
At the moment, the user has to ask for the functional induction
principle explicitly using
```
derive_functional_induction ackermann
```
The module docstring of `Lean/Meta/Tactic/FunInd.lean` contains more
details on the
design and implementation of this command.
More convenience around this (e.g. a `functional induction` tactic) will
follow eventually.
This PR includes a bunch of `PSum`/`PSigma` related functions in the
`Lean.Tactic.FunInd`
namespace. I plan to move these to `PackArgs`/`PackMutual` afterwards,
and do some cleaning
up as I do that.
---------
Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk>
Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
This adds a number of lemmas for simplification of `Bool` and `Prop`
terms. It pulls lemmas from Mathlib and adds additional lemmas where
confluence or consistency suggested they are needed.
It has been tested against Mathlib using some automated test
infrastructure.
That testing module is not yet included in this PR, but will be included
as part of this.
Note. There are currently some comments saying the origin of the simp
rule. These will be removed prior to merging, but are added to clarify
where the rule came from during review.
---------
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
Proves
`Nat.mod_mul : x % (a * b) = x % a + a * (x / a % b)` and
`Nat.mod_pow_succ : x % b ^ (k + 1) = x % b ^ k + b ^ k * ((x / b ^ k) %
b)`, helpful for bitblasting.
We use `let_delayed` to elaborate `match_expr` join points, which
elaborate the body of the `let` before its value. Thus, there is a
difference between:
- `let_delayed f (x : Expr) := <val>; <body>`
- `let_delayed f := fun (x : Expr) => <val>; <body>`
In the latter, when `<body>` is elaborated, the elaborator does not know
that `f` takes an argument of type `Expr`, and that `f` is a function.
Before this commit ensures the former representation is used.
In v4.6.0, there was a significant regression in initial server startup
performance because the .ilean files got bigger in #3082 and we load the
information stored in all .ilean files synchronously when the server
starts up.
This PR makes this loading asynchronous. The trade-off is that requests
that are issued right after the initial server start when the references
are not fully loaded yet may yield incomplete results.
Benchmark for this in a separate PR soon after this one.
---------
Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
