draft: gsimp tactic

[JovanGerb]

This is a draft PR for exploring a potential gsimp tactic. It would be able to do some things that the current grw tactic cannot do.

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[mathlib-bors]

This pull request is now in draft mode. No active bors state needed cleanup.

While this PR remains draft, bors will ignore commands on this PR. Mark it ready for review before using commands like bors r+ or bors try.

[github-actions]

🚨 PR Title Needs Formatting

Please update the title to match our commit style conventions.

Errors from script:

error: the PR title should be of the form
  abbrev: main title
or
  abbrev(scope): main title

Details on the required title format

The title should fit the following format:

<kind>(<optional-scope>): <subject>

<kind> is:

• feat (feature)
• fix (bug fix)
• doc (documentation)
• style (formatting, missing semicolons, ...)
• refactor
• test (when adding missing tests)
• chore (maintain)
• perf (performance improvement, optimization, ...)
• ci (changes to continuous integration, repo automation, ...)

<optional-scope> is a name of module or a directory which contains changed modules.
This is not necessary to include, but may be useful if the <subject> is insufficient.
The Mathlib directory prefix is always omitted.
For instance, it could be

• Data/Nat/Basic
• Algebra/Group/Defs
• Topology/Constructions

<subject> has the following constraints:

• do not capitalize the first letter
• no dot(.) at the end
• use imperative, present tense: "change" not "changed" nor "changes"

[github-actions]

PR summary 2640ebcdb4

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Tactic.GSimp.GSimpTheorems (new file)	81
Mathlib.Tactic.GSimp.Types (new file)	82
Mathlib.Tactic.GSimp.Rewrite (new file)	83
Mathlib.Tactic.GSimp.Core (new file)	84
Mathlib.Tactic.GSimp.Elab (new file)	85

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Declarations diff

+ Cache
+ Cache.find?
+ Cache.findIdx?
+ Cache.insert
+ CacheEntry
+ CacheEntry.insert
+ CacheIndex
+ Config
+ Context
+ Discharge
+ DischargeWrapper
+ DischargeWrapper.with
+ GSimpM
+ GSimpM.run
+ GSimpTheorem
+ GSimpTheorem.getValue
+ GSimpTheoremKey
+ GSimpTheoremTree
+ GSimpTheorems
+ GSimpTheorems.addGSimpTheorem
+ GSimpTheorems.unerase
+ GSimproc
+ Methods
+ MethodsRef
+ Result
+ Result.getProof
+ Result.mkTrans
+ State
+ Step
+ _root_.Lean.MVarId.replaceTargetImp
+ applyGSimpResult
+ applyGSimpResultToTarget
+ defaultDischarger
+ elabGSimpArg
+ elabGSimpArgs
+ elabGSimpTheorem
+ eraseFwdIfBwd
+ eraseIfExists
+ evalGSimp
+ getCacheIdx
+ getConfig
+ getContext
+ getGCongrTheorems
+ getMethods
+ getRfl
+ getTrans
+ grewrite?
+ gsimpCore
+ gsimpGoal
+ gsimpLocation
+ gsimpTarget
+ gsimpTargetCore
+ imp_rfl
+ imp_trans
+ instance : BEq GSimpTheorem
+ instance : Nonempty MethodsRef
+ isInv
+ mainCore
+ mkDischargeWrapper
+ mkGSimpContext
+ mkGSimpTheoremCore
+ mkGSimpTheoremFromConst
+ mkGSimpTheoremFromExpr
+ mkGSimpTheoremKeys
+ mkMethods
+ mkSymm
+ post
+ ppGSimpTheorem
+ pre
+ resolveGSimpIdTheorem?
+ rewritePost
+ rewritePre
+ synthesizeArgs
+ tacticToDischarge
+ tryTheorem?
+ tryTheoremCore
+ withContra
+ withFreshCache

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for scripts/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).