# Library search #

This file defines tactics `exact?`

and `apply?`

,
(formerly known as `library_search`

)
and a term elaborator `exact?%`

that tries to find a lemma
solving the current goal
(subgoals are solved using `solveByElim`

).

```
example : x < x + 1 := exact?%
example : Nat := by exact?
```

Wrapper for calling `Lean.Meta.SolveByElim.solveByElim with appropriate arguments for library search.

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A "modifier" for a declaration.

`none`

indicates the original declaration,`mp`

indicates that (possibly after binders) the declaration is an`↔`

, and we want to consider the forward direction,`mpr`

similarly, but for the backward direction.

- none: Lean.Meta.LibrarySearch.DeclMod
the original declaration

- mp: Lean.Meta.LibrarySearch.DeclMod
the forward direction of an

`iff`

- mpr: Lean.Meta.LibrarySearch.DeclMod
the backward direction of an

`iff`

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- Lean.Meta.LibrarySearch.instDecidableEqDeclMod x y = if h : x.toCtorIdx = y.toCtorIdx then isTrue ⋯ else isFalse ⋯

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LibrarySearch has an extension mechanism for replacing the function used to find candidate lemmas.

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We drop `.star`

and `Eq * * *`

from the discriminator trees because
they match too much.

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Create function for finding relevant declarations.

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Return an action that returns true when the remaining heartbeats is less than the currently remaining heartbeats * leavePercent / 100.

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Interleave x y interleaves the elements of x and y until one is empty and then returns final elements in other list.

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Called to abort speculative execution in library search.

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- Lean.Meta.LibrarySearch.abortSpeculation = throw (Lean.Exception.internal Lean.Meta.LibrarySearch.abortSpeculationId)

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Returns true if this is an abort speculation exception.

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A library search candidate using symmetry includes the goal to solve, the metavar context for that goal, and the name and orientation of a rule to try using with goal.

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Run `searchFn`

on both the goal and `symm`

applied to the goal.

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Create lemma from name and mod.

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Sequentially invokes a tactic `act`

on each value in candidates on the current state.

The tactic `act`

should return a list of meta-variables that still need to be resolved.
If this list is empty, then no variables remain to be solved, and `tryOnEach`

returns
`none`

with the environment set so each goal is resolved.

If the action throws an internal exception with the `abortSpeculationId`

id then
further computation is stopped and intermediate results returned. If any other
exception is thrown, then it is silently discarded.

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Tries to solve the goal either by:

- calling
`tactic true`

- or applying a library lemma then calling
`tactic false`

on the resulting goals.

Typically here `tactic`

is `solveByElim`

,
with the `Bool`

flag indicating whether it may retry with `exfalso`

.

If it successfully closes the goal, returns `none`

.
Otherwise, it returns `some a`

, where `a : Array (List MVarId × MetavarContext)`

,
with an entry for each library lemma which was successfully applied,
containing a list of the subsidiary goals, and the metavariable context after the application.

(Always succeeds, and the metavariable context stored in the monad is reverted, unless the goal was completely solved.)

(Note that if `solveByElim`

solves some but not all subsidiary goals,
this is not currently tracked.)

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