feat(Computability): ackermann function as hyperoperation + estimates

[felixpernegger]

Express the ackermann function via hyperoperations as well as basic properties about hyperoperations

This is more or less coming from https://github.com/kim-em/name-the-biggest-number

---

[github-actions]

PR summary 29617c441e

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Computability.Ackermann	741	702	-39 (-5.26%)
Mathlib.Data.Nat.Hyperoperation	506	504	-2 (-0.40%)

Import changes for all files

Files	Import difference
Mathlib.Computability.Ackermann	-39
Mathlib.Data.Nat.Hyperoperation	-2

---

Declarations diff (regex)

+ ack_eq_hyperoperation
+ hyperoperation_eq_zero_iff
+ hyperoperation_mono_second_third

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean -- stale; merge master and push to refresh)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 0e2f67c).

• +3 new declarations
• −0 removed declarations

+ack_eq_hyperoperation
+hyperoperation_eq_zero_iff
+hyperoperation_mono_second_third

---

No changes to strong technical debt.
No changes to weak technical debt.

Current commit 29617c441e
Reference commit 1e5fa86cf6

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.py 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).

[felixpernegger]

t-computability