lean-ja / lean-ja/lean-by-example

`WellFoundedRelation` 型クラスを紹介する

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型クラス
Dominant language
Lean
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Description

これは decreasing_by を使用したときに参照される

cf. https://lean-lang.org/blog/2024-1-11-recursive-definitions-in-lean/

Often, the expression after termination_by is of type Nat. Then it is called a measure on the function arguments, and gives an upper bound on how often the function will make recursive calls. Generally, that expression can have any type α with a WellFoundedRelation α instance. This type class declares what it means for a value of α to be “smaller” to another (like < on Nat) and provides a proof that that relation is well-founded, meaning that starting from any value you can go to “smaller” values only a finite number of times.

Contributor guide

Open the contributing guide

First steps

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

Research direction

Start with the linked Lean blog post and the WellFoundedRelation reference at Init/WF.html. Explain how WellFoundedRelation relates to termination_by and decreasing_by, using the scope described in the issue. Done means the documentation clearly introduces the type class and its well-founded ordering.

Written by the indexing model from the issue text.

Assessment

Domain
documentation
Issue type
Documentation
Difficulty
2/5
Estimated time
1-3 hours
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
48/100

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