token: add Ident, Comma, Equals token types
diff --git a/docs/plan.md b/docs/plan.md
index 112d4bb..dff29d6 100644
--- a/docs/plan.md
+++ b/docs/plan.md
@@ -1,57 +1,73 @@
-# Math Expression Evaluator — Implementation Plan
+# Implementation Plan: Function Definitions
-## Phase: Implement
+## Overview
+Bottom-up implementation through the stack: token → ast → lexer → parser → evaluator → repl → integration tests. Each step maintains backward compatibility and follows TDD.
-Steps are ordered. Each step includes writing the code and its unit tests (TDD).
+## Steps
-### Step 1: Project Skeleton
-- `go mod init matheval`
-- Create directory structure: `cmd/matheval/`, `token/`, `lexer/`, `ast/`, `parser/`, `evaluator/`, `repl/`
-- Create placeholder `main.go`
+### Step 1: Token layer (`token/token.go`)
+- Add `Ident`, `Comma`, `Equals` constants to `Type` enum
+- Update `String()` for new types
+- No tests needed — pure data types
-### Step 2: Token Package
-- Define `Type` enum constants
-- Define `Token` struct
-- Add `String()` method on `Type` for debugging
+### Step 2: AST layer (`ast/ast.go`)
+- Add `Ident` struct: `Name string`; implements `Node`
+- Add `FuncCall` struct: `Name string`, `Args []Node`; implements `Node`
+- Add `Statement` interface with sealed `stmt()` marker
+- Add `ExprStmt` struct: `Expr Node`; implements `Statement`
+- Add `FuncDef` struct: `Name string`, `Params []string`, `Body Node`; implements `Statement`
+- No tests needed — pure data types
-### 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 3: Lexer (`lexer/lexer.go`)
+- Add `isLetter(ch byte) bool` helper
+- Before the single-char switch, add branch: if `isLetter(ch)`, scan identifier (letter then letters/digits), emit `Ident` token
+- Add `','` → `Comma` and `'='` → `Equals` to single-char switch
+- **Tests:** identifiers (`x`, `foo`, `f1`), comma, equals, full definition `f(x) = x + 1`, call `f(1, 2)`, mixed with numbers
-### Step 4: AST Package
-- Define `Node` interface with sealed marker
-- Define `NumberLit` struct
-- Define `BinaryExpr` struct
+### Step 4: Parser (`parser/parser.go`)
+- Extend `factor()`:
+ - `Ident` followed by `LParen` → parse `FuncCall`: consume `(`, parse args as comma-separated exprs, consume `)`
+ - `Ident` not followed by `LParen` → return `&ast.Ident{Name}`
+- Add `parseFuncDef()`: expects `Ident(` params `) = expr`
+- Add `ParseLine(tokens) (Statement, error)`:
+ - Scan for `Equals` token (not inside parens)
+ - If found → `parseFuncDef()` → `*ast.FuncDef`
+ - If not → `expr()` → `*ast.ExprStmt{Expr}`
+- Keep `Parse()` unchanged for backward compat
+- **Tests:** ParseLine for defs and exprs, factor for ident and func call, error cases
-### 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 5: Evaluator (`evaluator/evaluator.go`)
+- Add `Evaluator` struct with `funcs map[string]*ast.FuncDef`
+- `New() *Evaluator`
+- `Define(def *ast.FuncDef) error` — error on redefinition
+- `Eval(node ast.Node, env map[string]float64) (float64, error)`:
+ - `*ast.NumberLit` → return value
+ - `*ast.BinaryExpr` → recurse left/right with same env
+ - `*ast.Ident` → lookup in env, error if not found
+ - `*ast.FuncCall` → lookup func, eval args in caller env, bind params, eval body in new env
+- Keep package-level `Eval(node) (float64, error)` as backward-compat wrapper
+- **Tests:** all existing tests still pass, new tests for Ident, FuncCall, Define, errors
-### 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 6: REPL (`repl/repl.go`)
+- In `Run()`: create `evaluator.New()` before loop
+- Replace `evalLine()` with inline logic using `ParseLine()`
+- `*ast.FuncDef` → `ev.Define(def)`, print `"defined <name>"`
+- `*ast.ExprStmt` → `ev.Eval(stmt.Expr, nil)`, print result
+- **Tests:** define + call across lines, redefine error, undefined func error
-### 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 7: Integration tests (`integration_test.go`)
+- Update `eval()`/`evalErr()` helpers to use `Evaluator` struct
+- Add tests:
+ - Define and call single-param function
+ - Define and call multi-param function
+ - Cross-function calls
+ - Nested function calls in expressions
+ - Error: undefined function
+ - Error: wrong argument count
+ - Error: function redefinition
+ - Error: undefined variable
-### 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
+## Backward Compatibility
+- `Parse()` remains unchanged — returns `ast.Node`
+- Package-level `Eval()` remains — wraps `New().Eval(node, nil)`
+- Existing tests must continue to pass at every step