M "src/list/raxos/Abstract Paxos Diagram.canvas"

src/list/raxos/Abstract Paxos Diagram.canvas

@@ -8,14 +8,9 @@
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 		{"id":"11003bbfc4ff8328","type":"file","file":"consensus-essence/src/list/raxos/def-T-History-PartialOrd.md","x":420,"y":1320,"width":465,"height":238},
-		{"id":"9c32627fede27385","type":"file","file":"consensus-essence/src/list/raxos/example-RW-single-threaded.md","x":1780,"y":1960,"width":400,"height":400,"color":"5"},
-		{"id":"6f61f61fbd369e9a","type":"file","file":"consensus-essence/src/list/raxos/def-Past-Future.md","x":720,"y":2200,"width":400,"height":400},
-		{"id":"ebae8b958fa8ef58","type":"file","file":"consensus-essence/src/list/raxos/example-Past-Future-distributed.md","x":1120,"y":3260,"width":400,"height":400,"color":"5"},
-		{"id":"23b7153aa3b72e6d","type":"file","file":"consensus-essence/src/list/raxos/example-Past-Future-single-threaded.md","x":1280,"y":2720,"width":400,"height":400,"color":"5"},
 		{"id":"23b19f5ffc793d95","type":"file","file":"consensus-essence/src/list/raxos/def-Apply.md","x":1002,"y":3,"width":400,"height":400},
 		{"id":"6d2f40704a61e31b","type":"file","file":"consensus-essence/src/list/raxos/def-Sub-History.md","x":-160,"y":1120,"width":400,"height":400},
 		{"id":"09a5660b835acde1","type":"file","file":"consensus-essence/src/list/raxos/def-Mergeable-History.md","x":-160,"y":1760,"width":400,"height":400},
-		{"id":"24e816cf21a582e0","type":"file","file":"consensus-essence/src/list/raxos/def-RW-Necessity.md","x":1184,"y":2060,"width":400,"height":400},
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@@ -25,21 +20,31 @@
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-		{"id":"64f0cd59fe29aca7","type":"file","file":"consensus-essence/src/list/raxos/def-Write-Quorum-Set.md","x":640,"y":4360,"width":400,"height":400},
 		{"id":"8e2e4bdc350b67dd","type":"file","file":"consensus-essence/src/list/raxos/example-Quorum-Set-xy.md","x":1360,"y":4760,"width":400,"height":400,"color":"5"},
-		{"id":"eefaf5fc7ce43eba","type":"file","file":"consensus-essence/src/list/raxos/def-Observable-History.md","x":200,"y":4460,"width":400,"height":400},
-		{"id":"2aa96775efaf3504","x":0,"y":5100,"width":400,"height":400,"type":"file","file":"consensus-essence/src/list/raxos/def-T-Committed.md"},
-		{"id":"b33b510032aaea23","x":0,"y":5660,"width":400,"height":400,"type":"file","file":"consensus-essence/src/list/raxos/def-Committed.md"},
-		{"id":"4425d02ad7c436fc","x":1207,"y":5220,"width":400,"height":400,"color":"3","type":"file","file":"consensus-essence/src/list/raxos/desc-Availability.md"},
-		{"id":"e17d353216ad61b2","x":-464,"y":6120,"width":400,"height":400,"color":"6","type":"file","file":"consensus-essence/src/list/raxos/protocol-Write-Forbid-Smaller.md"},
-		{"id":"4fe24a286d42d5c1","x":0,"y":6400,"width":400,"height":400,"color":"6","type":"file","file":"consensus-essence/src/list/raxos/protocol-Write-After-Read.md"},
-		{"id":"64f51b278ec2e315","x":-720,"y":7800,"width":400,"height":400,"color":"6","type":"file","file":"consensus-essence/src/list/raxos/protocol-All.md"},
-		{"id":"04445468a553ca25","x":0,"y":7200,"width":400,"height":400,"color":"6","type":"file","file":"consensus-essence/src/list/raxos/protocol-Write-P2.md"},
-		{"id":"99fd7ad8ee77b8b7","x":-80,"y":8320,"width":400,"height":400,"color":"5","type":"file","file":"consensus-essence/src/list/raxos/example-Classic-Paxos.md"},
-		{"id":"d712fa28e2c9ebae","x":534,"y":8457,"width":400,"height":400,"type":"file","file":"consensus-essence/src/list/raxos/example-Raft.md"},
-		{"id":"a74a6a5cfa5647bc","x":-492,"y":9029,"width":400,"height":400,"type":"file","file":"consensus-essence/src/list/raxos/2d-consensus.md"},
-		{"id":"5d01e9e3355926b6","x":-297,"y":9810,"width":400,"height":390,"color":"5","type":"file","file":"consensus-essence/src/list/raxos/example-2d-consensus.md"},
-		{"id":"877084719c0840fa","x":-323,"y":10613,"width":400,"height":400,"type":"file","file":"consensus-essence/src/list/raxos/def-2d-consensus-Apply.md"}
+		{"id":"2aa96775efaf3504","type":"file","file":"consensus-essence/src/list/raxos/def-T-Committed.md","x":0,"y":5100,"width":400,"height":400},
+		{"id":"b33b510032aaea23","type":"file","file":"consensus-essence/src/list/raxos/def-Committed.md","x":0,"y":5660,"width":400,"height":400},
+		{"id":"4425d02ad7c436fc","type":"file","file":"consensus-essence/src/list/raxos/desc-Availability.md","x":1207,"y":5220,"width":400,"height":400,"color":"3"},
+		{"id":"4fe24a286d42d5c1","type":"file","file":"consensus-essence/src/list/raxos/protocol-Write-After-Read.md","x":0,"y":6400,"width":400,"height":400,"color":"6"},
+		{"id":"64f51b278ec2e315","type":"file","file":"consensus-essence/src/list/raxos/protocol-All.md","x":-720,"y":7800,"width":400,"height":400,"color":"6"},
+		{"id":"04445468a553ca25","type":"file","file":"consensus-essence/src/list/raxos/protocol-Write-P2.md","x":0,"y":7200,"width":400,"height":400,"color":"6"},
+		{"id":"99fd7ad8ee77b8b7","type":"file","file":"consensus-essence/src/list/raxos/example-Classic-Paxos.md","x":-80,"y":8320,"width":400,"height":400,"color":"5"},
+		{"id":"d712fa28e2c9ebae","type":"file","file":"consensus-essence/src/list/raxos/example-Raft.md","x":534,"y":8457,"width":400,"height":400,"color":"5"},
+		{"id":"a74a6a5cfa5647bc","type":"file","file":"consensus-essence/src/list/raxos/2d-consensus.md","x":-492,"y":9029,"width":400,"height":400},
+		{"id":"5d01e9e3355926b6","type":"file","file":"consensus-essence/src/list/raxos/example-2d-consensus.md","x":-297,"y":9810,"width":400,"height":390,"color":"5"},
+		{"id":"877084719c0840fa","type":"file","file":"consensus-essence/src/list/raxos/def-2d-consensus-Apply.md","x":-323,"y":10613,"width":400,"height":400},
+		{"id":"24e816cf21a582e0","type":"file","file":"consensus-essence/src/list/raxos/def-RW-Necessity.md","x":1184,"y":2120,"width":400,"height":400},
+		{"id":"6f61f61fbd369e9a","type":"file","file":"consensus-essence/src/list/raxos/def-Past-Future.md","x":1720,"y":2120,"width":400,"height":400},
+		{"id":"9c32627fede27385","type":"file","file":"consensus-essence/src/list/raxos/example-RW-single-threaded.md","x":2200,"y":1832,"width":400,"height":400,"color":"5"},
+		{"id":"23b7153aa3b72e6d","type":"file","file":"consensus-essence/src/list/raxos/example-Past-Future-single-threaded.md","x":2200,"y":2760,"width":400,"height":400,"color":"5"},
+		{"id":"ebae8b958fa8ef58","type":"file","file":"consensus-essence/src/list/raxos/example-Past-Future-distributed.md","x":2200,"y":3320,"width":400,"height":400,"color":"5"},
+		{"id":"64f0cd59fe29aca7","type":"file","file":"consensus-essence/src/list/raxos/def-Write-Quorum-Set.md","x":640,"y":4460,"width":400,"height":400},
+		{"id":"eefaf5fc7ce43eba","type":"file","file":"consensus-essence/src/list/raxos/def-Observable-History.md","x":160,"y":4460,"width":400,"height":400},
+		{"id":"f001ccd718f70347","x":640,"y":5160,"width":400,"height":400,"color":"3","type":"file","file":"consensus-essence/src/list/raxos/desc-History Read Set.md"},
+		{"id":"a838cacb9e50352d","x":236,"y":9019,"width":400,"height":400,"color":"5","type":"file","file":"consensus-essence/src/list/raxos/example-crdt.md"},
+		{"id":"c55a71983b5140b2","x":722,"y":9578,"width":400,"height":400,"color":"5","type":"file","file":"consensus-essence/src/list/raxos/example-2d-non-transitive-time.md"},
+		{"id":"6aca35d4bc6e348f","x":236,"y":10120,"width":400,"height":400,"color":"5","type":"file","file":"consensus-essence/src/list/raxos/exmaple-crdt-define.md"},
+		{"id":"e0499dbb83899c24","x":236,"y":10640,"width":400,"height":400,"color":"5","type":"file","file":"consensus-essence/src/list/raxos/example-crdt-implementation.md"},
+		{"id":"e17d353216ad61b2","type":"file","file":"consensus-essence/src/list/raxos/protocol-Write-Forbid-Smaller.md","x":-520,"y":6280,"width":400,"height":400,"color":"6"}
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 	"edges":[
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@@ -87,6 +92,12 @@
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-		{"id":"fe61a48ba3c61f1e","fromNode":"5d01e9e3355926b6","fromSide":"bottom","toNode":"877084719c0840fa","toSide":"top"}
+		{"id":"fe61a48ba3c61f1e","fromNode":"5d01e9e3355926b6","fromSide":"bottom","toNode":"877084719c0840fa","toSide":"top"},
+		{"id":"065998b773a58476","fromNode":"eefaf5fc7ce43eba","fromSide":"bottom","toNode":"f001ccd718f70347","toSide":"top"},
+		{"id":"ea0a374d1e541e54","fromNode":"64f51b278ec2e315","fromSide":"bottom","toNode":"a838cacb9e50352d","toSide":"top"},
+		{"id":"e56beb199a811c22","fromNode":"a838cacb9e50352d","fromSide":"bottom","toNode":"c55a71983b5140b2","toSide":"top"},
+		{"id":"b6b5fdb98e3ed393","fromNode":"a838cacb9e50352d","fromSide":"bottom","toNode":"6aca35d4bc6e348f","toSide":"top"},
+		{"id":"51d037ce1e9e19b8","fromNode":"c55a71983b5140b2","fromSide":"bottom","toNode":"6aca35d4bc6e348f","toSide":"top"},
+		{"id":"37c8ac0a99460eca","fromNode":"6aca35d4bc6e348f","fromSide":"bottom","toNode":"e0499dbb83899c24","toSide":"top"}
 	]
 }

src/list/raxos/def-API-read-write.md

@@ -2,8 +2,10 @@
 
 这个由虚拟时间Time, 事件Event 和 History 的系统中, 读操作和写操作都定义为在一个指定时间上发生的行为:
 ```rust
-fn read(t: Time) -> History({T});
-fn write(h: History({T}));
+impl Node {
+	fn read(&self, t: Time) -> History({T});
+	fn write(&mut self, h: History({T}));
+}
 ```
 
 其中, `read` 读系统中t时刻的历史, 即它应该返回所有t时刻之前发生的Event, read返回的History的最大时刻可能小于参数中的t.

src/list/raxos/def-Observable-History.md

@@ -1,18 +1,18 @@
 **def-Observable**
 ## 对系统总是可见的 History
 
-对于某个时刻`pt`,
-对一个 History, 如果这个时刻的 `read_quorum_set` 中任意一个`read_quorum` 都能读到这个 History,
-那么就认为这个 History 是 **在`pt`时刻可见** 的.
+对于某个时刻`T`,
+对一个 History, 如果这个时刻的 `read_quorum_set` 中每个`read_quorum` 都能读到这个 History,
+那么就认为这个 History 是 **在`T`时刻可见** 的.
 
 注意 **可见** 是跟系统的状态和 `read_quorum_set` 的定义相关的,
-例如, 下图中对 `History = {E1, E2}`来说,
+例如, 下图中对 `History = {E1->E2}`来说,
 如果 `read_quorum_set` 是多数派读写的定义, 即 `{{1,2},{1,3},{2,3}}`,
 那么它 **可见** 的:
 
 ![](history-visible-12.excalidraw.png)
 
-但对 `History = {E1, E2, E3}`来说,
+但对 `History = {E1->E2->E3}`来说,
 - 如果 `read_quorum_set` 仍然是多数派读写的定义, 即 `{{1,2},{1,3},{2,3}}`,
   那么它不是 **可见** 的, 因为通过`{2,3}`读不到`History = {E1,E2,E3}`,
 - 但如果修改 `read_quorum_set` 为 `{{1,2},{1,3}}`, 那么即使系统状态不变,

src/list/raxos/def-RW-Distributed.md

@@ -2,7 +2,25 @@
 # 分布式多副本中的读写
 
 
-写操作要写一个历史,即 `fn write(h: History({T}), nodes: Vec<Node>)`, 对每个节点的写的内容都一样
+分布式中的读和写都是基于我们单机的API读写来完成的 我们首先看分布式的写 分布式中的写真的比较简单 它只需要把一个要写的history 写到每一个节点上就行了 就像我们下面的代码所展示的那样 分布式里面的读相对会稍微复杂一点 你读的话也是从每个副本上读一个history过来 然后再通过这些读到的结果 然后返回给客户调用者一个结果
+
+```rust
+impl {
+	fn write(&self, h: History({T})) {
+		for node in self.get_write_quorum() {
+			node.write(h);
+		}
+	}
+}
+```
+
+
+
+
+
+
+
+写操作要写一个历史,即 `fn write(h: History({T}), nodes: &[Node])`, 对每个节点的写的内容都一样
 
 直观上, 分布式环境中的读写变成了对多个节点的读写:
 ```rust

src/list/raxos/def-Read-Quorum-Set.md

@@ -1,24 +1,30 @@
 ## Read Quorum Set
 
 对每个系统, 不论是单机的还是分布式的,
-都显式的或隐含的定义了合法的 `read()` 可用的 `node_set` 有哪些, 系统只有用这样的`node_set` 读的时候才能提供 TODO:
+都显式的或隐含的定义了可用于 `read()` 的 `node_set` 有哪些, 系统只有用这样的`node_set` 读的时候才能提供某种保证, 使用其他node set读取到的结果不提供任何保证:
 
 - 例如单机系统, `read()` 可用的 `node_set` 就是唯一这个节点`{{1}}`,
   显然用一个空的 `node_set` 去读是没意义的.
 
 - 一个简单 3 节点系统中, 如果不做任何限制,
   那么`read()`可用的`node_set`是所有非空节点集合: `{{1}, {2}, {3}, {1,2}, {2,3}, {1,3}, {1,2,3}}`
-  但注意这样一个系统中`read()`得到的结果一般是没有任何高可用保证的, 因为它暗示了写操作必须写到每一个 node 上才能被合法的读读到.
+  但注意这样一个系统中`read()`得到的结果一般是没有任何高可用保证的, 因为它暗示了一个写操作必须写到每一个 node 上才能被合法的读读到.
 
-- 一个多数派读写的 3 节点系统中(n=3, w=2, r=2),
+- 一个 [多数派读写][] 的 3 节点系统中(n=3, w=2, r=2),
   `read()`可用的`node_set`是至少包含 2 节点的集合: `{{1,2}, {2,3}, {1,3}, {1,2,3}}`,
 
 如果一个 read 操作使用的 `node_set` 是这个系统定义的用于读的`node_set`,
 那么认为这个 read 操作是合法的, 系统只给合法的读操作提供保证,
 对于不合法的 read 操作,
 系统对读取的结果不能提供任何保证(undefined behavior).
 
-**def-Read-Quorum-Set** **def-Read-Quorum**:
-在某个时刻`pt`, 可合法的用于`read()`的`node_set`的集合, 就是系统这个`pt`时刻的`read_quorum_set`,
+**def-Read-Quorum-Set**
+**def-Read-Quorum**:
+
+在某个时刻`T`, 可合法的用于`read()`的`node_set`的集合, 就是系统在这个`T`时刻的`read_quorum_set(T)`, 注意不同时间T的`read_quorum_set(T)`可能不同, 例如 [Raft][] 的配置变更时.
+
 `read_quorum_set` 中的一个元素是一个节点集合, 称之为一个`read_quorum`.
-`read_quorum` 是一个节点集合`node_set`, `read_quorum_set` 是一个 节点集合的集合.
+
+
+[多数派读写]: http://a
+[Raft]: http://a

src/list/raxos/raxos.md

@@ -34,48 +34,7 @@ TODO: remove concept History quorum
 
 
 
-## History Read Set
-
-对于
-`fn read(pt: PTime, nodes: Vec<Node>) -> History`,
-对读到的 History 的任一子集 H, 我们可以称这个`node_set` 是这个`History`的一个 ReadSet. 表示这个`History` 可以通过这个`node_set`读到.
-
-对系统的某个特定的状态, Histroy 的 ReadSet 定义为可以读到这个 History 的一个节点的集合.
-
-例如, 在下面,
-
-- `read({1})` 返回: `[History{E1, E2, E3}]`,
-- `read({1, 2})` 返回: `[History{E1, E2, E3}, History{E1, E2}]`,
-- `read({3})` 返回空 `ø`.
-
-例如, 在下面这个 3 节点的系统中, `History{E1,E2,E3}`的 ReadSet, 即能读到它的节点的集合, 有 4 个, 是所有包括 node-1 节点的节点集合:
-
-`{1}, {1,2}, {1,2,3}, {1,3}`
-
-例如`read({1})` 会返回`History{E1,E2,E3}`在结果里,
-`read({1,3})` 也会返回`History{E1,E2,E3}`在结果里.
-
-但是`read({3})` 不会返回`History{E1,E2,E3}`, 所以 `{3}` 不是`History{E1,E2,E3}` 的一个 ReadSet
-
-而`History{E1,E2}`的 ReadSet 有 5 个, 除了`{3}` 之外的所有非空节点集合都是它的 ReadSet:
-`{1}, {1,2}, {1,2,3}, {1,3}, {2,3}`,
-
-例如`read({2,3})` 会返回`History{E1,E2}`在结果里.
-
-![](history-read-set.excalidraw.png)
-
-对于返回的结果, 我们也可以将 `Vec<History>`里的元素做一个并集来简化表示,
-例如, 上图中, `read({1, 2})` 可以看做返回了一个 History: `History{E1, E2, E3}`
-
-而在下图中, 我们可以认为`read({1, 2})` 返回了一个树形的 History:
-
-```
- .->E4
-E1->E2->E3
-```
-
-![](history-read-set-union.excalidraw.png)
-
+[[desc-History Read Set]]
 
 [[def-Read-Quorum-Set]]
 
@@ -237,6 +196,8 @@ node-1 本地将已有 History 跟新写入的 History 合并了, 本地存储
 
 ![](linear-rw.excalidraw.png)
 
+protocol-write-prepare
+
 ## Write Prepare
 
 现在 write 保证了不覆盖已有的 History, 且写到了`write_quorum_set`,
@@ -305,30 +266,18 @@ node-1 本地将已有 History 跟新写入的 History 合并了, 本地存储
 我举这个例子是为了说明, Time 的每个维度之间的类型不能假设是一样的,
 即不支持加法, 但可以支持乘法. 这将会引出后面的有趣的结论.
 
+[[example-crdt]]
 
-# 多维偏序时间应用例子
+[[example-2d-non-transitive-time]]
 
-假设有一个 key value 的存储系统，在这个系统里面，每个 key 都代表一个不同的维度。然后我们的时间，就是一个多维的向量时间内的比较，就是多为向量的比较。
 
-我们先从一个简单的场景来看, 假设这个系统里只有2个key:
-x 和 y,
-这个系统的虚拟时间`T`定义为: 一个操作涉及的key的对应的维度上值为i的向量.
-例如, `let x = 2` 的T为`{x:i}`,
-`let y = 3`的T为`{y:i}`;
-`let x = x + y`的T为`{x:i, y:i}`
-T的比较关系定义为公共分量的大小比较:
-例如, `{x:1} < {x:2,y:2} < {y:3}`, 但`{x:1}` `{y:2}` 之间没有大小关系, 因为它们没有公共分量.
-这个虚拟时间定义了哪些Event可以互补影响的执行, 哪些之间必须有确定的顺序, 以及这些顺序是什么(有`i` 定义).
+[[exmaple-crdt-define]]
 
+[[example-crdt-implementation]]
 
-![](crdt.excalidraw.png)
-
-应用我们的Abstract Paxos到这个系统, 它将构建一个冲突自适应的Multi Master一致性协议.
 
 例如
 
-注意, 我们时间是对应到DAG的结构的, `{x:2,y:2} < {y:3}` 中的 `{y:3}` 顶点和 一个独立的 `{y:3}` 顶点代表的不是一个时间.
-
 如果T不是**传递的**, 那么第一阶段必须在一个read-quorum-set上阻止要写入的History上所有的T, 而不是只有最大的一个T.因为不能通过T来防止之前的顶点被写入.
 而在第二阶段, 也必须逐个判断要写入的History的每个T是否小于已经被阻止的T, 而不仅仅是要写入的History的Maximal T.