[Merged by Bors] - feat: Bird–Wadler duality theorems

[Parcly-Taxel]

Forms of these three theorems already exist in mathlib and the Lean standard library, but they are scattered about. Bring them together in one file, deprecating the ad hoc names for the first and second theorems.

[github-actions]

PR summary 7d9358ee9d

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Data.List.Fold (new file)	54

---

Declarations diff

+ foldl_cons_eq_apply_foldl
+ foldl_cons_nil
+ foldl_eq_foldr_of_commute
+ foldl_flip_eq_foldr
+ foldr_cons_eq_foldr_apply
+ foldr_flip_eq_foldl

You can run this locally as follows

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

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

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

---

No changes to technical debt.

You can run this locally as

./scripts/reporting/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).

[Vierkantor]

I like that this gives us a consistent set of theorems about foldl/foldr. The name for this file is not completely obvious to me: I don't associate foldl_eq_foldr with "Bird-Wadler duality", and the phrase "Bird-Wadler duality" doesn't give me any search results. Maybe Data/List/Fold.lean would be a good name? (This doesn't really apply to the module doc since it has a good explanation of why we use this name.)

[Vierkantor]

Thanks for making the changes!

bors d+

[mathlib-bors]

✌️ Parcly-Taxel can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[Parcly-Taxel]

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Post-CI job
• ci (staging) / Post-Build Step
• ci (staging) / Lint style
• ci (staging) / Build