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+# Math Expression Evaluator — Implementation Plan
+
+## Phase: Implement
+
+Steps are ordered. Each step includes writing the code and its unit tests (TDD).
+
+### Step 1: Project Skeleton
+- `go mod init matheval`
+- Create directory structure: `cmd/matheval/`, `token/`, `lexer/`, `ast/`, `parser/`, `evaluator/`, `repl/`
+- Create placeholder `main.go`
+
+### Step 2: Token Package
+- Define `Type` enum constants
+- Define `Token` struct
+- Add `String()` method on `Type` for debugging
+
+### Step 3: Lexer
+- Implement `Tokenize(input string) ([]Token, error)`
+- Handle: whitespace skipping, number literals (integers and decimals), operators `+-*/`, parentheses `()`, EOF, invalid characters
+- **Tests:** valid expressions, decimal numbers, invalid chars, empty input, whitespace-only
+
+### Step 4: AST Package
+- Define `Node` interface with sealed marker
+- Define `NumberLit` struct
+- Define `BinaryExpr` struct
+
+### Step 5: Parser
+- Implement recursive-descent parser following grammar:
+  - `expr → term (('+' | '-') term)*`
+  - `term → factor (('*' | '/') factor)*`
+  - `factor → NUMBER | '(' expr ')'`
+- Internal parser struct to track position in token slice
+- Return error on: unexpected token, mismatched parens, trailing tokens
+- **Tests:** single number, simple binary, precedence, parentheses, nested parens, error cases
+
+### Step 6: Evaluator
+- Implement `Eval(node ast.Node) (float64, error)`
+- Recursively walk AST
+- Return error on division by zero
+- **Tests:** literals, all 4 operators, nested expressions, division by zero
+
+### Step 7: REPL
+- Implement `Run(r io.Reader, w io.Writer)`
+- Read line, tokenize, parse, evaluate, print result or error
+- Loop until EOF
+- **Tests:** successful expression, error expression, multi-line session
+
+### Step 8: main.go
+- Wire `repl.Run(os.Stdin, os.Stdout)`
+
+### Step 9: Integration Test
+- End-to-end test: feed expression string through all stages, verify result
+- Test edge cases: deeply nested parens, long expressions
+
+### Step 10: Final Commit & README
+- Write README.md with usage instructions
+- Final commit