完成查询优化：谓词下推、投影下推和常量折叠，配置好了benchmark

README.md

@@ -40,3 +40,34 @@
 > Rust和Haskell部分的通信通过管道实现，后期跨平台到Linux后使用Unix Domain Socket
 
 > 如果找到了较好的Rust+Haskell集成方法也会及时替换
+
+# 代码规模
+
+| 语言 / 类别     | 文件数 |     行数 | 说明                                                            |
+| --------------- | -----: | -------: | --------------------------------------------------------------- |
+| Haskell（引擎） |     11 |      902 | `chusql-engine/src/` 10 个模块 + `app/Main.hs`                  |
+| Haskell（测试） |      1 |     1058 | `test/Spec.hs`，124 条用例                                      |
+| Haskell（基准） |      1 |      118 | `benchmark/chusql-engine/src/Main.hs`                           |
+| Rust            |      0 |        0 | `chusql-storage/` 尚未开工                                      |
+| 前端            |      0 |        0 | `chusql-web/` 尚未开工                                          |
+| Markdown 文档   |      6 |     1456 | `README.md` + `docs/` 3 篇 + `benchmark/` 2 篇                  |
+| 构建 / 配置     |      9 |      231 | cabal、`stack.yaml(.lock)`、`tasks.json`、`.gitignore`、LICENSE |
+| 项目计划        |      1 |      368 | `chusql-engine/projectplan.txt`                                 |
+| **合计**        | **29** | **4133** | 另有 3 个 `.gitkeep` 占位文件未计入                             |
+
+> 最近更新：2026-09-19
+
+# 性能基准
+
+**测试环境**：Windows / GHC 9.10.3 / `-O2`
+**数据规模**：`users`、`orders` 各 500 行，两表配对共 25 万对
+**计时方式**：CPU 时间，自适应批量（累计超过 0.3 秒后折算成单次耗时）
+
+| 查询                                       | 结果行数 |   未优化 |      优化后 |      加速 |
+| ------------------------------------------ | -------: | -------: | ----------: | --------: |
+| `JOIN` + `WHERE u.age > 90`                |       45 | 125.0 ms |  **7.1 ms** | **17.7x** |
+| `JOIN`（无 WHERE，只有投影）               |      500 | 132.8 ms |    105.5 ms |      1.3x |
+| `JOIN` + `WHERE` + `ORDER BY` + `LIMIT 10` |       10 | 171.9 ms | **10.3 ms** | **16.8x** |
+| 单表 `WHERE age > 90`（对照组）            |       45 | 0.111 ms |    0.153 ms |      0.7x |
+
+> 最近更新：2026-09-19

benchmark/README.md

@@ -0,0 +1,93 @@
+# ChuSQL 基准测试
+
+这个目录放**性能基准测试**，和 `chusql-engine`、`chusql-storage` 的功能代码分开，
+因为它回答的问题不一样：功能代码回答"对不对"，基准测试回答"快不快、快多少"。
+
+```
+benchmark/
+├── README.md                  本文件：怎么跑、测什么、结果怎么解读
+├── chusql-engine/             Haskell 查询层：优化器开/关的对比
+│   ├── stack.yaml             把 chusql-engine 作为本地包引入
+│   ├── chusql-bench.cabal
+│   └── src/Main.hs
+└── chusql-storage/            Rust 存储层：预留（见该目录下的 README）
+```
+
+---
+
+## 怎么跑
+
+```bash
+cd benchmark/chusql-engine
+stack run                      # 默认 users=500 行、orders=500 行
+stack run -- 1000 1000 0.5     # 也可以自己指定：users 行数、orders 行数、每批目标秒数
+```
+
+第一次跑要编译，之后很快。整个默认跑完约 5 秒。
+
+---
+
+## 测什么
+
+四个用例，**每个都跑两遍**：一遍走"翻译出来的原始工序单"，一遍走"优化后的工序单"。
+两次的结果行数会被打印出来互相对照，**不一致会当场标出来**。
+
+| 用例 | 想看什么 |
+| ---- | -------- |
+| `JOIN` + `WHERE u.age > 90` | 谓词下推的主场：条件能筛掉约 90% 的行 |
+| `JOIN`（无 WHERE） | 只剩投影下推在起作用，收益应该温和 |
+| `JOIN` + `WHERE` + `ORDER BY` + `LIMIT` | 规则叠加时的综合效果 |
+| 单表 `WHERE age > 90` | 对照组：没有下推空间，优化器只剩固定开销 |
+
+---
+
+## 计时怎么做（两个坑都踩过了）
+
+**坑一：Haskell 是惰性的，不强制求值就等于没测。**
+如果只写 `let r = evalRelOp db plan`，`r` 根本没被算出来，测到的是"定义一个变量"的时间。
+所以每次必须把结果**算到底**（本项目里是逐行把列数累加起来当校验和）。
+
+**坑二：Windows 上 CPU 时钟的精度只有约 15.6 毫秒。**
+优化后的查询只要几毫秒，直接测会得到 `0.0 ms` 这种没意义的数字。
+
+所以计时用的是**自适应批量**：把同一个用例连续跑 `k` 次测一整批，`k` 不断翻倍，
+直到一批累计耗时超过目标值（默认 0.3 秒），再折算成单次耗时。
+这样时钟精度的误差会被 `k` 摊薄，几毫秒的用例也能测准。
+程序会打印实际用了多大的批次（例如"优化后 64 次/批"）。
+
+跑正式计时之前还会**预热两遍**，避免把首次构造表数据的开销算进去。
+
+---
+
+## 实测结果
+
+**环境**：Windows，GHC 9.10.3，`-O2`
+**数据**：`users` 500 行（`id / name / age`，`age` 只有 0-99 共 100 种取值），
+`orders` 500 行（`id / user_id / product`），两表配对共 25 万对。
+
+| 查询 | 结果行数 | 未优化 | 优化后 | 加速 |
+| ---- | -------- | ------ | ------ | ---- |
+| `JOIN` + `WHERE u.age > 90` | 45 | 125.0 ms | **7.1 ms** | **17.7x** |
+| `JOIN`（无 WHERE） | 500 | 132.8 ms | 105.5 ms | 1.3x |
+| `JOIN` + `WHERE` + `ORDER BY` + `LIMIT 10` | 10 | 171.9 ms | **10.3 ms** | **16.8x** |
+| 单表 `WHERE age > 90` | 45 | 0.111 ms | 0.153 ms | 0.7x |
+
+### 怎么解读
+
+- **前两行的差距来自谓词下推。** 条件筛掉了约 90% 的用户，配对次数从 25 万降到约 2.25 万，
+  时间直接掉一个数量级。筛得越狠，省得越多。
+- **第二行只有投影下推。** 配对次数一点没变（没有条件可下推），只是每一行变窄了，
+  所以只有 1.3 倍 —— 收益温和但确实是正的。
+- **第四行反而略慢。** 单表查询本来就没有下推空间（条件早已贴着扫描），
+  而优化器自己要走一遍规则，有几十微秒的固定开销（0.153 − 0.111 ≈ 0.04 ms）。
+  **优化不是零成本的**：查询越大、配对越多，这笔账才越划算。
+
+---
+
+## 加新用例
+
+在 `src/Main.hs` 的 `queries` 列表里加一条 SQL 字符串就行，其余全自动
+（会自动翻译、优化、跑两遍、比结果、算加速比）。
+
+想测别的规模，直接命令行传参；想在文档里引用数字，记得把**数据规模一起写上** ——
+脱离规模谈"快了几倍"是没有意义的。

benchmark/chusql-engine/chusql-bench.cabal

@@ -0,0 +1,14 @@
+cabal-version: 2.4
+
+name:           chusql-bench
+version:        1.0.0
+synopsis:       ChuSQL 查询优化基准测试（对比开/关优化器）
+build-type:     Simple
+
+executable chusql-bench
+    main-is:          Main.hs
+    hs-source-dirs:   src
+    build-depends:    base >= 4.14 && < 5
+                    , chusql-engine
+    default-language: Haskell2010
+    ghc-options:      -O2 -Wall

benchmark/chusql-engine/src/Main.hs

@@ -0,0 +1,118 @@
+module Main where
+
+import ChuSQL.Algebra.Eval (evalRelOp)
+import ChuSQL.Algebra.Optimize (optimize)
+import ChuSQL.Algebra.Planner (translate)
+import ChuSQL.Model
+import ChuSQL.SQLSyntax.Parser (parseQuery)
+import Control.Exception (evaluate)
+import System.CPUTime (getCPUTime)
+import System.Environment (getArgs)
+import Text.Printf (printf)
+
+mkUsers :: Int -> Table
+mkUsers n =
+    Table
+        { tableName = "users"
+        , tableCols = ["id", "name", "age"]
+        , tableRows =
+            [ [("id", VInt i), ("name", VStr ("user" ++ show i)), ("age", VInt (i `mod` 100))]
+            | i <- [1 .. n]
+            ]
+        }
+
+mkOrders :: Int -> Int -> Table
+mkOrders n m =
+    Table
+        { tableName = "orders"
+        , tableCols = ["id", "user_id", "product"]
+        , tableRows =
+            [ [("id", VInt j), ("user_id", VInt (1 + (j - 1) `mod` n)), ("product", VStr ("item" ++ show (j `mod` 50)))]
+            | j <- [1 .. m]
+            ]
+        }
+
+checksum :: Either String [Row] -> Int
+checksum (Left _) = -1
+checksum (Right rows) = go 0 rows
+  where
+    go acc [] = acc
+    go acc (r : rs) = go (acc + length r) rs
+
+rowCount :: Either String [Row] -> Int
+rowCount (Left _) = -1
+rowCount (Right rows) = length rows
+
+runOnce :: Database -> String -> Bool -> IO Int
+runOnce db sql useOpt = do
+    let result = case parseQuery sql >>= translate db of
+            Left e -> Left e
+            Right plan -> evalRelOp db (if useOpt then optimize db plan else plan)
+    forced <- evaluate (checksum result)
+    return forced
+
+resultRows :: Database -> String -> Bool -> IO Int
+resultRows db sql useOpt = do
+    let result = case parseQuery sql >>= translate db of
+            Left e -> Left e
+            Right plan -> evalRelOp db (if useOpt then optimize db plan else plan)
+    _ <- evaluate (checksum result)
+    return (rowCount result)
+
+timed :: IO a -> IO Double
+timed act = do
+    t0 <- getCPUTime
+    _ <- act
+    t1 <- getCPUTime
+    return (fromIntegral (t1 - t0) / 1e12)
+
+benchOp :: Double -> IO Int -> IO (Double, Int)
+benchOp target act = loop 1
+  where
+    loop k = do
+        t <- timed (mapM_ (const act) [1 .. k])
+        if t < target then loop (k * 2) else return (t / fromIntegral k, k)
+
+report :: Database -> Double -> String -> IO ()
+report db target sql = do
+    nUn <- resultRows db sql False
+    nOp <- resultRows db sql True
+    (tUn, kUn) <- benchOp target (runOnce db sql False)
+    (tOp, kOp) <- benchOp target (runOnce db sql True)
+    let speedup = if tOp <= 0 then 0 else tUn / tOp
+        mismatch = if nUn == nOp then "" else "   <<< 结果不一致！"
+    printf "%s\n" sql
+    printf
+        "    结果行数 %-6d | 未优化 %9.3f ms | 优化后 %9.3f ms | 加速 %6.1fx%s\n"
+        nOp
+        (tUn * 1000)
+        (tOp * 1000)
+        speedup
+        mismatch
+    printf "    （实测批次：未优化 %d 次/批，优化后 %d 次/批）\n\n" kUn kOp
+
+queries :: [String]
+queries =
+    [ "SELECT u.name FROM users u JOIN orders o ON u.id = o.user_id WHERE u.age > 90"
+    , "SELECT u.name, o.product FROM users u JOIN orders o ON u.id = o.user_id"
+    , "SELECT u.name FROM users u JOIN orders o ON u.id = o.user_id WHERE u.age > 90 ORDER BY o.product LIMIT 10"
+    , "SELECT name FROM users WHERE age > 90"
+    ]
+
+warmupSql :: String
+warmupSql = "SELECT name FROM users"
+
+main :: IO ()
+main = do
+    args <- getArgs
+    let pick i d = if length args > i then read (args !! i) else d
+        n = pick 0 500
+        m = pick 1 500
+        target = pick 2 (0.3 :: Double)
+        db = [("users", mkUsers n), ("orders", mkOrders n m)]
+    printf "数据规模：users = %d 行，orders = %d 行\n" n m
+    printf "计时方式：CPU 时间；每个用例自动加倍批量次数，直到一批累计耗时超过 %.2f 秒，再折算成单次耗时\n" target
+    printf "（先跑一遍预热，避免把首次构造数据的开销算进去）\n\n"
+    _ <- runOnce db warmupSql False
+    _ <- runOnce db warmupSql True
+    mapM_ (report db target) queries

benchmark/chusql-engine/stack.yaml

@@ -0,0 +1,5 @@
+resolver: lts-24.59
+
+packages:
+    - .
+    - ../../chusql-engine

benchmark/chusql-engine/stack.yaml.lock

@@ -0,0 +1,12 @@
+# This file was autogenerated by Stack.
+# You should not edit this file by hand.
+# For more information, please see the documentation at:
+#   https://docs.haskellstack.org/en/stable/topics/lock_files
+
+packages: []
+snapshots:
+- completed:
+    sha256: 0f728e30e843d7f00460ad56858b995a3b227fca683659c7df9f2fc3988a3ce1
+    size: 732465
+    url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/lts/24/59.yaml
+  original: lts-24.59

benchmark/chusql-storage/README.md

@@ -0,0 +1,36 @@
+# chusql-storage 基准测试（预留）
+
+这个目录预留给 **Rust 存储层** 的基准测试代码，目前 `chusql-storage/` 还没有开工，
+所以这里先占位。
+
+## 计划放什么
+
+`chusql-storage` 做的是磁盘那一层的事情，性能指标和查询层完全不同 ——
+查询层关心"少算几行"，存储层关心"少读几次盘"。所以基准要分开测：
+
+| 待测模块 | 关心的指标 |
+| -------- | ---------- |
+| 页管理 | 单页读写延迟、顺序读 vs 随机读吞吐 |
+| B+ 树 | 插入/查找/范围扫描的耗时随数据量增长的趋势 |
+| 缓冲池 | 命中率、缺页次数、替换策略（LRU 等）的对比 |
+| WAL | 追加写吞吐、日志落盘延迟、恢复耗时 |
+| 崩溃恢复 | 从日志重放的时间、恢复后数据一致性 |
+
+## 用什么
+
+Rust 侧的基准测试一般用 [criterion](https://github.com/bheisler/criterion.rs)：
+
+```
+benchmark/chusql-storage/
+├── Cargo.toml
+└── benches/
+    ├── page.rs
+    ├── btree.rs
+    ├── buffer_pool.rs
+    └── wal.rs
+```
+
+跑法：`cargo bench`
+
+另外还要和 Haskell 层对齐口径：查询层的基准是"整条查询的耗时"，
+存储层的基准是"单次 IO / 单次查找的耗时"，两边不要混在一起比。

chusql-engine/app/Main.hs

@@ -1,24 +1,39 @@
 module Main where
 
-import ChuSQL.SQLSyntax.Executor
+import ChuSQL.Algebra.Op (RelOp (..))
+import ChuSQL.Algebra.Optimize (optimize)
+import ChuSQL.Algebra.Planner (translate)
 import ChuSQL.Model
 import ChuSQL.SQLSyntax.AST
+import ChuSQL.SQLSyntax.Executor
 import ChuSQL.SQLSyntax.Parser
 
 users :: Table
 users =
     Table
         { tableName = "users"
-        , tableCols = ["name", "age"]
+        , tableCols = ["id", "name", "age"]
         , tableRows =
-            [ [("name", VStr "Alice"), ("age", VInt 25)]
-            , [("name", VStr "Bob"), ("age", VInt 17)]
-            , [("name", VStr "Carol"), ("age", VInt 30)]
+            [ [("id", VInt 1), ("name", VStr "Alice"), ("age", VInt 25)]
+            , [("id", VInt 2), ("name", VStr "Bob"), ("age", VInt 17)]
+            , [("id", VInt 3), ("name", VStr "Carol"), ("age", VInt 30)]
+            ]
+        }
+
+orders :: Table
+orders =
+    Table
+        { tableName = "orders"
+        , tableCols = ["id", "user_id", "product"]
+        , tableRows =
+            [ [("id", VInt 1), ("user_id", VInt 1), ("product", VStr "Book")]
+            , [("id", VInt 2), ("user_id", VInt 2), ("product", VStr "Pen")]
+            , [("id", VInt 3), ("user_id", VInt 1), ("product", VStr "Cup")]
             ]
         }
 
 db :: Database
-db = [("users", users)]
+db = [("users", users), ("orders", orders)]
 
 -- runQuery 返回 (更新后的数据库, 结果行)；演示只关心结果行
 rowsOf :: Either String (Database, [Row]) -> Either String [Row]
@@ -26,6 +41,7 @@ rowsOf = fmap snd
 
 main :: IO ()
 main = do
+    putStrLn "==================== Parser Test ====================="
     let q1 = makeSelect ["name"] "users" (Just (Gt (Col "age") (LitInt 18)))
     print (rowsOf (runQuery db q1))
 
@@ -50,3 +66,42 @@ main = do
     -- 解析 SQL 文本，再交给执行引擎
     let parsed = parseQuery "SELECT name FROM users WHERE age > 18 AND name = 'Alice'"
     print (rowsOf (parsed >>= runQuery db))
+
+    putStrLn "\n==================== Optimizer ====================="
+    let planSql =
+            "SELECT u.name, o.product FROM users u \
+            \JOIN orders o ON u.id = o.user_id WHERE u.age > 18"
+    case parseQuery planSql of
+        Left err -> putStrLn err
+        Right query -> case translate db query of
+            Left err -> putStrLn err
+            Right plan -> do
+                putStrLn "--- plan before optimization ---"
+                putStrLn (dump 0 plan)
+                putStrLn "--- plan after optimization ---"
+                putStrLn (dump 0 (optimize db plan))
+                putStrLn "--- rows ---"
+                print (rowsOf (runQuery db query))
+
+dump :: Int -> RelOp -> String
+dump ind op = case op of
+    Scan a t ->
+        pad ++ "Scan " ++ show a ++ " " ++ show t
+    Filter e x ->
+        pad ++ "Filter " ++ show e ++ "\n" ++ dump (ind + 1) x
+    Project c x ->
+        pad ++ "Project " ++ show c ++ "\n" ++ dump (ind + 1) x
+    Sort s x ->
+        pad ++ "Sort " ++ show s ++ "\n" ++ dump (ind + 1) x
+    Limit n x ->
+        pad ++ "Limit " ++ show n ++ "\n" ++ dump (ind + 1) x
+    Join l r c ->
+        pad
+            ++ "Join on "
+            ++ show c
+            ++ "\n"
+            ++ dump (ind + 1) l
+            ++ "\n"
+            ++ dump (ind + 1) r
+  where
+    pad = replicate (ind * 2) ' '

chusql-engine/chusql-engine.cabal

@@ -11,6 +11,7 @@ library
     hs-source-dirs:   src
     exposed-modules:  ChuSQL.Algebra.Eval
                       ChuSQL.Algebra.Op
+                      ChuSQL.Algebra.Optimize
                       ChuSQL.Algebra.Planner
                       ChuSQL.Model
                       ChuSQL.SQLSyntax.AST

chusql-engine/src/ChuSQL/Algebra/Optimize.hs

@@ -0,0 +1,162 @@
+module ChuSQL.Algebra.Optimize where
+
+import ChuSQL.Algebra.Op (RelOp (..))
+import ChuSQL.Model
+import ChuSQL.SQLSyntax.AST (Expr (..))
+import ChuSQL.SQLSyntax.Expr (evalExpr)
+
+-- * 谓词下推
+
+-- | 收集表达式里用到的列名；谓词下推判断条件归属、常量折叠判断能否求值，都要用它
+colsInExpr :: Expr -> [String]
+colsInExpr (Col c) = [c]
+colsInExpr (Gt a b) = colsInExpr a ++ colsInExpr b
+colsInExpr (Lt a b) = colsInExpr a ++ colsInExpr b
+colsInExpr (Eq a b) = colsInExpr a ++ colsInExpr b
+colsInExpr (And a b) = colsInExpr a ++ colsInExpr b
+colsInExpr (Or a b) = colsInExpr a ++ colsInExpr b
+colsInExpr _ = []
+
+-- | 一个算子会产出哪些列；返回 ["*"] 表示"全部列，不用挑"
+relOpCols :: Database -> RelOp -> [String]
+relOpCols db (Filter _ x) = relOpCols db x
+relOpCols db (Sort _ x) = relOpCols db x
+relOpCols db (Limit _ x) = relOpCols db x
+relOpCols _ (Project ["*"] _) = ["*"]
+relOpCols _ (Project cols _) = cols
+relOpCols db (Join l r _) = relOpCols db l ++ relOpCols db r
+relOpCols db (Scan mAlias tbl) =
+    case lookup tbl db of
+        Nothing -> []
+        Just t -> map (prefix ++) (tableCols t)
+  where
+    prefix = maybe "" (++ ".") mAlias
+
+-- | need 里的列是不是都能在 have 里找到；have 为 ["*"] 时一律为真
+isSubsetOf :: [String] -> [String] -> Bool
+isSubsetOf _ ["*"] = True
+isSubsetOf need have = all (`elem` have) need
+
+-- | 把一个用 AND 串起来的条件拆成清单：a AND b AND c 变成 [a, b, c]
+splitConj :: Expr -> [Expr]
+splitConj (And a b) = splitConj a ++ splitConj b
+splitConj e = [e]
+
+-- | 反过来：把条件清单用 AND 重新串成一个；空清单表示"没有条件"，返回 Nothing
+combineConj :: [Expr] -> Maybe Expr
+combineConj [] = Nothing
+combineConj (e : es) = Just (foldl And e es)
+
+-- | 把条件按"只用到哪一边的列"分成两堆：能下推过去的 / 必须留在原地的
+partitionPred :: [String] -> [Expr] -> ([Expr], [Expr])
+partitionPred have = foldr pick ([], [])
+  where
+    pick e (yes, no)
+        | colsInExpr e `isSubsetOf` have = (e : yes, no)
+        | otherwise = (yes, e : no)
+
+-- | 把一组条件依次套到算子上，一个条件一层 Filter
+applyFilters :: [Expr] -> RelOp -> RelOp
+applyFilters [] op = op
+applyFilters (e : es) op = applyFilters es (Filter e op)
+
+-- | Filter 压在 Join 上时的下推规则：条件按列归属拆到左右两侧，跨两边的才留在 Join 上方
+pushJoin :: Database -> Expr -> RelOp -> RelOp -> Expr -> RelOp
+pushJoin db p l r c =
+    let preds = splitConj p
+        lCols = relOpCols db l
+        rCols = relOpCols db r
+        (lPs, rest1) = partitionPred lCols preds
+        (rPs, bothPs) = partitionPred rCols rest1
+        l' = applyFilters lPs l
+        r' = applyFilters rPs r
+        joined = Join l' r' c
+     in case combineConj bothPs of
+            Nothing -> joined
+            Just p' -> Filter p' joined
+
+-- | Filter 压在 Filter / Sort 上时的下推规则：合并上下两层 Filter，或把 Filter 挪到 Sort 下面
+pushOne :: Database -> RelOp -> RelOp
+pushOne _ (Filter p (Filter q x)) = Filter (And p q) x
+pushOne _ (Filter p (Sort spec x)) = Sort spec (Filter p x)
+pushOne _ op = op
+
+-- * 投影下推
+
+-- | 工具函数
+needsAll :: [String] -> Bool
+needsAll = elem "*"
+
+pushProject :: Database -> [String] -> RelOp -> RelOp
+pushProject db _ (Project cols x) = case pushProject db cols x of
+    Project cols' y | cols' == cols -> Project cols y
+    other -> Project cols other
+pushProject db need (Filter p x) = Filter p (pushProject db (need ++ colsInExpr p) x)
+pushProject db need (Sort spec x) = Sort spec (pushProject db (need ++ map fst spec) x)
+pushProject db need (Limit n x) = Limit n (pushProject db need x)
+pushProject db need (Join l r c)
+    | needsAll need = Join (pushProject db need l) (pushProject db need r) c
+    | otherwise =
+        let tot = need ++ colsInExpr c
+            lCols = relOpCols db l
+            rCols = relOpCols db r
+            lNeed = if needsAll lCols then ["*"] else [x | x <- tot, x `elem` lCols]
+            rNeed = if needsAll rCols then ["*"] else [x | x <- tot, x `elem` rCols]
+         in Join (pushProject db lNeed l) (pushProject db rNeed r) c
+pushProject db need scan@(Scan _ _)
+    | needsAll need = scan
+    | all (`elem` need) (relOpCols db scan) = scan
+    | otherwise = Project need scan
+
+-- * 常量折叠
+
+-- | 折一个表达式：不含列就直接求值替换成字面量，含列或求值失败则原样返回
+foldNode :: Expr -> Expr
+foldNode e
+    | null (colsInExpr e) = case evalExpr e [] of
+        Right (VInt n) -> LitInt n
+        Right (VStr s) -> LitStr s
+        Right (VBool b) -> LitBool b
+        Left _ -> e
+    | otherwise = e
+
+-- | 自底向上折叠整个表达式：先把子表达式折干净，再折自己
+foldConstants :: Expr -> Expr
+foldConstants (Gt a b) = foldNode (Gt (foldConstants a) (foldConstants b))
+foldConstants (Lt a b) = foldNode (Lt (foldConstants a) (foldConstants b))
+foldConstants (Eq a b) = foldNode (Eq (foldConstants a) (foldConstants b))
+foldConstants (And a b) = foldNode (And (foldConstants a) (foldConstants b))
+foldConstants (Or a b) = foldNode (Or (foldConstants a) (foldConstants b))
+foldConstants e = e
+
+-- * 执行优化
+
+-- | 单节点重写：把 Filter 分派给上面几条规则，另外负责恒真条件删除与恒等投影消除
+rewriteNode :: Database -> RelOp -> RelOp
+rewriteNode db (Filter p (Join l r c)) = pushJoin db p l r c
+rewriteNode db (Filter p x) = case foldConstants p of
+    LitBool True -> x
+    p' -> pushOne db (Filter p' x)
+rewriteNode _ (Project ["*"] x) = x
+rewriteNode db op = pushOne db op
+
+-- | 自底向上遍历整棵算子树，每个节点套一次 rewriteNode
+optimizeRelOp :: Database -> RelOp -> RelOp
+optimizeRelOp db = rewriteNode db . descend
+  where
+    descend (Filter p x) = Filter p (optimizeRelOp db x)
+    descend (Project cols x) = Project cols (optimizeRelOp db x)
+    descend (Sort spec x) = Sort spec (optimizeRelOp db x)
+    descend (Limit n x) = Limit n (optimizeRelOp db x)
+    descend (Join l r c) = Join (optimizeRelOp db l) (optimizeRelOp db r) c
+    descend x = x
+
+-- | 谓词下推 + 常量折叠：反复应用规则，直到算子树的形状不再变化（到不动点为止）
+optimizePredicates :: Database -> RelOp -> RelOp
+optimizePredicates db op =
+    let op' = optimizeRelOp db op
+     in if op' == op then op else optimizePredicates db op'
+
+-- | 优化器总入口：先把谓词下推与常量折叠跑到不动点，再做一次投影下推
+optimize :: Database -> RelOp -> RelOp
+optimize db op = pushProject db ["*"] (optimizePredicates db op)

chusql-engine/src/ChuSQL/SQLSyntax/AST.hs

@@ -25,6 +25,7 @@ data Expr
     = Col String
     | LitInt Int
     | LitStr String
+    | LitBool Bool
     | Gt Expr Expr
     | Lt Expr Expr
     | Eq Expr Expr

chusql-engine/src/ChuSQL/SQLSyntax/Executor.hs

@@ -1,6 +1,7 @@
 module ChuSQL.SQLSyntax.Executor where
 
 import ChuSQL.Algebra.Eval (evalRelOp)
+import ChuSQL.Algebra.Optimize (optimize)
 import ChuSQL.Algebra.Planner (translate)
 import ChuSQL.Model
 import ChuSQL.SQLSyntax.AST
@@ -28,7 +29,7 @@ applyUpdates ((col, e) : rest) row = do
 runQuery :: Database -> Query -> Either String (Database, [Row])
 runQuery db q@Select{} = do
     relOp <- translate db q
-    rows <- evalRelOp db relOp
+    rows <- evalRelOp db (optimize db relOp)
     Right (db, rows)
 
 -- 处理插入

chusql-engine/src/ChuSQL/SQLSyntax/Expr.hs

@@ -10,6 +10,7 @@ evalExpr (Col name) row =
     maybe (Left ("unknown column: " ++ name)) Right (lookup name row)
 evalExpr (LitInt n) _ = Right (VInt n)
 evalExpr (LitStr s) _ = Right (VStr s)
+evalExpr (LitBool b) _ = Right (VBool b)
 evalExpr (Gt a b) row = liftBinOp (intOp (>)) a b row
 evalExpr (Lt a b) row = liftBinOp (intOp (<)) a b row
 evalExpr (Eq a b) row = liftBinOp eqOp a b row

chusql-engine/test/Spec.hs

@@ -1,5 +1,9 @@
 module Main where
 
+import ChuSQL.Algebra.Eval (evalRelOp)
+import ChuSQL.Algebra.Op (RelOp (..))
+import ChuSQL.Algebra.Optimize (optimize, pushProject)
+import ChuSQL.Algebra.Planner (translate)
 import ChuSQL.Model
 import ChuSQL.SQLSyntax.AST
 import ChuSQL.SQLSyntax.Executor
@@ -813,6 +817,169 @@ main = hspec $ do
                     , [("u.name", VStr "Bob"), ("o.product", VStr "Pen")]
                     ]
 
+    describe "ChuSQL.Algebra.Optimize" $ do
+        it "keeps single-table WHERE results identical" $ do
+            sameResultAsUnoptimized "SELECT name FROM users WHERE age > 18"
+
+        it "keeps JOIN with WHERE results identical" $ do
+            sameResultAsUnoptimized "SELECT u.name, o.product FROM users u JOIN orders o ON u.id = o.user_id WHERE u.age > 20"
+
+        it "keeps JOIN with WHERE, ORDER BY and LIMIT results identical" $ do
+            sameResultAsUnoptimized "SELECT u.name, o.product FROM users u JOIN orders o ON u.id = o.user_id WHERE u.age > 15 ORDER BY o.product DESC LIMIT 2"
+
+        it "keeps SELECT * results identical" $ do
+            sameResultAsUnoptimized "SELECT * FROM users"
+
+        it "pushes a single-side predicate into the left side of a JOIN" $ do
+            case parseQuery "SELECT u.name FROM users u JOIN orders o ON u.id = o.user_id WHERE u.age > 20" of
+                Left err -> expectationFailure err
+                Right q ->
+                    case translate testDB q of
+                        Left err -> expectationFailure err
+                        Right relOp ->
+                            filterPushedIntoLeft (optimize testDB relOp) `shouldBe` True
+
+        it "removes a redundant SELECT * projection" $ do
+            case parseQuery "SELECT * FROM users" of
+                Left err -> expectationFailure err
+                Right q ->
+                    case translate testDB q of
+                        Left err -> expectationFailure err
+                        Right relOp ->
+                            optimize testDB relOp `shouldBe` Scan Nothing "users"
+
+        it "does not push a filter through LIMIT" $ do
+            let cond = Gt (Col "age") (LitInt 18)
+                relOp = Filter cond (Limit 2 (Scan Nothing "users"))
+            optimize testDB relOp `shouldBe` relOp
+
+        it "is idempotent after reaching a fixed point" $ do
+            case parseQuery "SELECT u.name, o.product FROM users u JOIN orders o ON u.id = o.user_id WHERE u.age > 20" of
+                Left err -> expectationFailure err
+                Right q ->
+                    case translate testDB q of
+                        Left err -> expectationFailure err
+                        Right relOp ->
+                            optimize testDB (optimize testDB relOp) `shouldBe` optimize testDB relOp
+
+        it "folds a constant-false predicate into LitBool False" $ do
+            fmap firstFilterCond (optimizedPlan "SELECT name FROM users WHERE 1 > 2")
+                `shouldBe` Right (Just (LitBool False))
+
+        it "removes a filter whose predicate folds to true" $ do
+            fmap anyFilter (optimizedPlan "SELECT name FROM users WHERE 1 = 1")
+                `shouldBe` Right False
+
+        it "removes a constant-true filter sitting above a join" $ do
+            fmap anyFilter (optimizedPlan "SELECT u.name FROM users u JOIN orders o ON u.id = o.user_id WHERE 1 = 1")
+                `shouldBe` Right False
+
+        it "leaves a predicate that mentions a column untouched" $ do
+            fmap firstFilterCond (optimizedPlan "SELECT name FROM users WHERE age > 18")
+                `shouldBe` Right (Just (Gt (Col "age") (LitInt 18)))
+
+        it "folds the constant part of a predicate that cannot fold as a whole" $ do
+            fmap firstFilterCond (optimizedPlan "SELECT name FROM users WHERE age > 18 AND 1 = 1")
+                `shouldBe` Right (Just (And (Gt (Col "age") (LitInt 18)) (LitBool True)))
+
+        it "keeps a constant predicate that fails to evaluate" $ do
+            fmap firstFilterCond (optimizedPlan "SELECT name FROM users WHERE 'abc' > 1")
+                `shouldBe` Right (Just (Gt (LitStr "abc") (LitInt 1)))
+
+        it "keeps constant-false results identical" $ do
+            sameResultAsUnoptimized "SELECT name FROM users WHERE 1 > 2"
+
+        it "keeps constant-true results identical" $ do
+            sameResultAsUnoptimized "SELECT name FROM users WHERE 1 = 1"
+
+        it "keeps mixed constant and column predicates identical" $ do
+            sameResultAsUnoptimized "SELECT name FROM users WHERE age > 18 AND 1 = 1"
+
+        it "keeps a failing constant predicate identical" $ do
+            sameResultAsUnoptimized "SELECT name FROM users WHERE 'abc' > 1"
+
+        it "returns no rows for a constant-false predicate" $ do
+            rowsOf (parseQuery "SELECT name FROM users WHERE 1 > 2" >>= runQuery testDB)
+                `shouldBe` Right []
+
+        it "returns every row for a constant-true predicate" $ do
+            rowsOf (parseQuery "SELECT name FROM users WHERE 1 = 1" >>= runQuery testDB)
+                `shouldBe` Right
+                    [ [("name", VStr "Alice")]
+                    , [("name", VStr "Bob")]
+                    , [("name", VStr "Carol")]
+                    ]
+
+        it "keeps the LIMIT node while pushing projection past it" $ do
+            let plan = Project ["name"] (Limit 2 (Scan Nothing "users"))
+            stripProjects (pushProject testDB ["*"] plan) `shouldBe` stripProjects plan
+
+        it "keeps the sort keys while pushing projection past a sort" $ do
+            let plan = Project ["name"] (Sort [("age", Desc)] (Scan Nothing "users"))
+            stripProjects (pushProject testDB ["*"] plan) `shouldBe` stripProjects plan
+
+        it "keeps both sides of a join" $ do
+            let plan =
+                    Project
+                        ["u.name"]
+                        ( Join
+                            (Scan (Just "u") "users")
+                            (Scan (Just "o") "orders")
+                            (Eq (Col "u.id") (Col "o.user_id"))
+                        )
+            stripProjects (pushProject testDB ["*"] plan) `shouldBe` stripProjects plan
+
+        it "keeps nested projections in place" $ do
+            let plan = Project ["name"] (Project ["name", "age"] (Scan Nothing "users"))
+            stripProjects (pushProject testDB ["*"] plan) `shouldBe` stripProjects plan
+
+        it "keeps the whole spine of a full pipeline" $ do
+            let plan =
+                    Project
+                        ["name"]
+                        ( Limit 2
+                            ( Sort
+                                [("age", Desc)]
+                                (Filter (Gt (Col "age") (LitInt 18)) (Scan Nothing "users"))
+                            )
+                        )
+            stripProjects (pushProject testDB ["*"] plan) `shouldBe` stripProjects plan
+
+        it "merges two predicates pushed into the same side into one filter" $ do
+            fmap leftSideFilters (optimizedPlan "SELECT u.name FROM users u JOIN orders o ON u.id = o.user_id WHERE u.age > 20 AND u.name = 'Alice'")
+                `shouldBe` Right (Just 1)
+
+        it "pushes projection into a single-table scan as one layer" $ do
+            optimizedPlan "SELECT name FROM users"
+                `shouldBe` Right (Project ["name"] (Scan Nothing "users"))
+
+        it "does not add a projection when the scan already supplies every column" $ do
+            optimizedPlan "SELECT id, name, age FROM users"
+                `shouldBe` Right (Project ["id", "name", "age"] (Scan Nothing "users"))
+
+        it "prunes the columns nobody needs on each side of a join" $ do
+            fmap joinSideCols (projectedPlan "SELECT u.name FROM users u JOIN orders o ON u.id = o.user_id")
+                `shouldBe` Right (Just ["u.name", "u.id"], Just ["o.user_id"])
+
+        it "does not prune anything when every column is taken" $ do
+            fmap joinSideCols (projectedPlan "SELECT * FROM users u JOIN orders o ON u.id = o.user_id")
+                `shouldBe` Right (Nothing, Nothing)
+
+        it "activates projection pushdown inside optimize" $ do
+            fmap joinSideCols (optimizedPlan "SELECT u.name FROM users u JOIN orders o ON u.id = o.user_id")
+                `shouldBe` Right (Just ["u.name", "u.id"], Just ["o.user_id"])
+
+        it "keeps projection pushdown idempotent" $ do
+            case projectedPlan "SELECT u.name FROM users u JOIN orders o ON u.id = o.user_id" of
+                Left err -> expectationFailure err
+                Right plan -> pushProject testDB ["*"] plan `shouldBe` plan
+
+        it "keeps a join without WHERE results identical" $ do
+            sameResultAsUnoptimized "SELECT u.name, o.product FROM users u JOIN orders o ON u.id = o.user_id"
+
+        it "keeps projection with ORDER BY and LIMIT results identical" $ do
+            sameResultAsUnoptimized "SELECT u.name FROM users u JOIN orders o ON u.id = o.user_id ORDER BY o.product DESC LIMIT 2"
+
 -- ============================================================
 -- Helpers
 -- ============================================================
@@ -822,3 +989,70 @@ isLeft (Right _) = False
 
 rowsOf :: Either String (Database, [Row]) -> Either String [Row]
 rowsOf = fmap snd
+
+sameResultAsUnoptimized :: String -> Expectation
+sameResultAsUnoptimized sql =
+    case parseQuery sql of
+        Left err -> expectationFailure err
+        Right q ->
+            case translate testDB q of
+                Left err -> expectationFailure err
+                Right relOp ->
+                    evalRelOp testDB (optimize testDB relOp) `shouldBe` evalRelOp testDB relOp
+
+filterPushedIntoLeft :: RelOp -> Bool
+filterPushedIntoLeft (Project _ (Join (Filter _ _) _ _)) = True
+filterPushedIntoLeft _ = False
+
+optimizedPlan :: String -> Either String RelOp
+optimizedPlan sql = do
+    q <- parseQuery sql
+    optimize testDB <$> translate testDB q
+
+firstFilterCond :: RelOp -> Maybe Expr
+firstFilterCond (Filter p _) = Just p
+firstFilterCond (Project _ x) = firstFilterCond x
+firstFilterCond (Sort _ x) = firstFilterCond x
+firstFilterCond (Limit _ x) = firstFilterCond x
+firstFilterCond (Join l r _) = case firstFilterCond l of
+    Just p -> Just p
+    Nothing -> firstFilterCond r
+firstFilterCond (Scan _ _) = Nothing
+
+anyFilter :: RelOp -> Bool
+anyFilter (Filter _ _) = True
+anyFilter (Project _ x) = anyFilter x
+anyFilter (Sort _ x) = anyFilter x
+anyFilter (Limit _ x) = anyFilter x
+anyFilter (Join l r _) = anyFilter l || anyFilter r
+anyFilter (Scan _ _) = False
+
+stripProjects :: RelOp -> RelOp
+stripProjects (Project _ x) = stripProjects x
+stripProjects (Filter p x) = Filter p (stripProjects x)
+stripProjects (Sort spec x) = Sort spec (stripProjects x)
+stripProjects (Limit n x) = Limit n (stripProjects x)
+stripProjects (Join l r c) = Join (stripProjects l) (stripProjects r) c
+stripProjects (Scan a t) = Scan a t
+
+projectedPlan :: String -> Either String RelOp
+projectedPlan sql = do
+    q <- parseQuery sql
+    plan <- translate testDB q
+    Right (pushProject testDB ["*"] plan)
+
+sideCols :: RelOp -> Maybe [String]
+sideCols (Project cols _) = Just cols
+sideCols _ = Nothing
+
+joinSideCols :: RelOp -> (Maybe [String], Maybe [String])
+joinSideCols (Project _ (Join l r _)) = (sideCols l, sideCols r)
+joinSideCols _ = (Nothing, Nothing)
+
+countFilters :: RelOp -> Int
+countFilters (Filter _ x) = 1 + countFilters x
+countFilters _ = 0
+
+leftSideFilters :: RelOp -> Maybe Int
+leftSideFilters (Project _ (Join l _ _)) = Just (countFilters l)
+leftSideFilters _ = Nothing