人工智能数学验证工具LEAN4【入门介绍6】算法世界-机器人的思维跳步,如何自定义高级证明策略,还有逆否命题的使用

视频点赞过10会继续出下一期哦:人工智能数学验证工具LEAN4【入门介绍6】算法世界-机器人的思维跳步,如何自定义高级证明策略,还有逆否命题的使用_哔哩哔哩_bilibili

import Game.Levels.Algorithm.L07succ_ne_succ

import Game.MyNat.DecidableEq

World "Algorithm"

Level 8

Title "decide"

TheoremTab "Peano"

namespace MyNat

/--

Summary

`decide` will attempt to solve a goal if it can find an algorithm which it

can run to solve it.

Example

A term of type `DecidableEq ℕ` is an algorithm to decide whether two naturals

are equal or different. Hence, once this term is made and made into an `instance`,

the `decide` tactic can use it to solve goals of the form `a = b` or `a ≠ b`.

-/

TacticDoc decide

NewTactic decide

Introduction

"

Implementing the algorithm for equality of naturals, and the proof that it is correct,

looks like this:

```

instance instDecidableEq : DecidableEq ℕ

| 0, 0 => isTrue <| by

show 0 = 0

rfl

| succ m, 0 => isFalse <| by

show succ m ≠ 0

exact succ_ne_zero m

| 0, succ n => isFalse <| by

show 0 ≠ succ n

exact zero_ne_succ n

| succ m, succ n =>

match instDecidableEq m n with

| isTrue (h : m = n) => isTrue <| by

show succ m = succ n

rw [h]

rfl

| isFalse (h : m ≠ n) => isFalse <| by

show succ m ≠ succ n

exact succ_ne_succ m n h

```

This Lean code is a formally verified algorithm for deciding equality

between two naturals. I've typed it in already, behind the scenes.

Because the algorithm is formally verified to be correct, we can

use it in Lean proofs. You can run the algorithm with the `decide` tactic.

"

/-- 20+20=40. -/

Statement : (20 : ℕ) + 20 = 40 := by

decide

Conclusion "You can read more about the `decide` tactic by clicking

on it in the top right."

相关推荐
沉迷...几秒前
手动实现legend 与 echarts图交互 通过js事件实现图标某项的高亮 显示与隐藏
前端·javascript·echarts
可观测性用观测云16 分钟前
观测云数据在Grafana展示的最佳实践
前端
Bruce_Liuxiaowei22 分钟前
基于Python+Flask的MCP SDK响应式文档展示系统设计与实现
开发语言·python·flask·mcp
chuxinweihui30 分钟前
数据结构——栈与队列
c语言·开发语言·数据结构·学习·算法·链表
我不是程序猿儿30 分钟前
[C#]反射的实战应用,实际数据模拟
开发语言·c#
uwvwko37 分钟前
ctfhow——web入门214~218(时间盲注开始)
前端·数据库·mysql·ctf
Json____37 分钟前
使用vue2开发一个医疗预约挂号平台-前端静态网站项目练习
前端·vue2·网站模板·静态网站·项目练习·挂号系统
wt_cs41 分钟前
身份证实名认证接口数字时代的信任基石-node.js实名认证集成
开发语言·node.js·php
littleplayer1 小时前
iOS Swift Redux 架构详解
前端·设计模式·架构
工呈士1 小时前
HTML 模板技术与服务端渲染
前端·html