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360372x 360372x 949660x 949660x 949660x 949660x 360372x 360372x 1x 180187x 180187x 180187x 1x 1x 1x 1x 1x 1x 1x 1x 1x 3761498x 3761498x 3761498x 3761498x 1x 1x 1x 1x 1x 92x 92x 92x 92x 92x 92x 1x 1x 1x 1x 1x 4x 4x 1x 1x 1x 1x 1x 3x 3x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | /**
* Expression Evaluator for Flowchart Walker
*
* A simple, safe expression language for computing values in flowcharts.
* Does NOT use JavaScript eval - uses a custom parser for security.
*
* Supported:
* - Field access: left.denom, problem.minuend
* - State variables: $lcd, $borrowed (prefix with $)
* - Arithmetic: +, -, *, /, %
* - Comparison: ==, !=, <, >, <=, >=
* - Boolean: &&, ||, !
* - Ternary: condition ? trueValue : falseValue
* - Functions: lcm, gcd, min, max, abs, floor, ceil, mod
* - Literals: numbers, strings, booleans (true/false), null
*/
import type { ProblemValue, MixedNumberValue } from './schema'
// =============================================================================
// Types
// =============================================================================
type TokenType =
| 'NUMBER'
| 'STRING'
| 'IDENTIFIER'
| 'STATE_VAR'
| 'OPERATOR'
| 'LPAREN'
| 'RPAREN'
| 'COMMA'
| 'DOT'
| 'QUESTION'
| 'COLON'
| 'EOF'
interface Token {
type: TokenType
value: string | number
position: number
}
/** Context for expression evaluation */
export interface EvalContext {
/** Problem input values (e.g., left, right, op) */
problem: Record<string, ProblemValue>
/** Computed variables (e.g., lcd, needsBorrow) */
computed: Record<string, ProblemValue>
/** User-entered state during walkthrough */
userState: Record<string, ProblemValue>
/** Special "input" value for checkpoint validation */
input?: ProblemValue
}
// =============================================================================
// Tokenizer
// =============================================================================
const OPERATORS = ['&&', '||', '==', '!=', '<=', '>=', '<', '>', '+', '-', '*', '/', '%', '!']
function tokenize(expr: string): Token[] {
const tokens: Token[] = []
let pos = 0
while (pos < expr.length) {
// Skip whitespace
if (/\s/.test(expr[pos])) {
pos++
continue
}
// State variable ($varName)
if (expr[pos] === '$') {
const start = pos
pos++ // skip $
let name = ''
while (pos < expr.length && /[a-zA-Z0-9_]/.test(expr[pos])) {
name += expr[pos]
pos++
}
tokens.push({ type: 'STATE_VAR', value: name, position: start })
continue
}
// Number
if (/[0-9]/.test(expr[pos]) || (expr[pos] === '-' && /[0-9]/.test(expr[pos + 1]))) {
const start = pos
let numStr = ''
if (expr[pos] === '-') {
// Check if this is a negative number or subtraction
// It's a negative number if: start of expression, after operator, after ( or ,
const lastToken = tokens[tokens.length - 1]
if (
lastToken &&
lastToken.type !== 'OPERATOR' &&
lastToken.type !== 'LPAREN' &&
lastToken.type !== 'COMMA'
) {
// It's subtraction, not negative number
tokens.push({ type: 'OPERATOR', value: '-', position: pos })
pos++
continue
}
numStr += expr[pos]
pos++
}
while (pos < expr.length && /[0-9.]/.test(expr[pos])) {
numStr += expr[pos]
pos++
}
tokens.push({ type: 'NUMBER', value: parseFloat(numStr), position: start })
continue
}
// String literal
if (expr[pos] === '"' || expr[pos] === "'") {
const quote = expr[pos]
const start = pos
pos++ // skip opening quote
let str = ''
while (pos < expr.length && expr[pos] !== quote) {
str += expr[pos]
pos++
}
pos++ // skip closing quote
tokens.push({ type: 'STRING', value: str, position: start })
continue
}
// Multi-character operators (must check before single-char)
let foundOp = false
for (const op of OPERATORS) {
if (expr.slice(pos, pos + op.length) === op) {
tokens.push({ type: 'OPERATOR', value: op, position: pos })
pos += op.length
foundOp = true
break
}
}
if (foundOp) continue
// Single character tokens
if (expr[pos] === '(') {
tokens.push({ type: 'LPAREN', value: '(', position: pos })
pos++
continue
}
if (expr[pos] === ')') {
tokens.push({ type: 'RPAREN', value: ')', position: pos })
pos++
continue
}
if (expr[pos] === ',') {
tokens.push({ type: 'COMMA', value: ',', position: pos })
pos++
continue
}
if (expr[pos] === '.') {
tokens.push({ type: 'DOT', value: '.', position: pos })
pos++
continue
}
if (expr[pos] === '?') {
tokens.push({ type: 'QUESTION', value: '?', position: pos })
pos++
continue
}
if (expr[pos] === ':') {
tokens.push({ type: 'COLON', value: ':', position: pos })
pos++
continue
}
// Identifier (variable name, function name, true/false/null)
if (/[a-zA-Z_]/.test(expr[pos])) {
const start = pos
let name = ''
while (pos < expr.length && /[a-zA-Z0-9_]/.test(expr[pos])) {
name += expr[pos]
pos++
}
tokens.push({ type: 'IDENTIFIER', value: name, position: start })
continue
}
throw new Error(`Unexpected character '${expr[pos]}' at position ${pos}`)
}
tokens.push({ type: 'EOF', value: '', position: pos })
return tokens
}
// =============================================================================
// Parser
// =============================================================================
class Parser {
private tokens: Token[]
private pos = 0
private context: EvalContext
constructor(tokens: Token[], context: EvalContext) {
this.tokens = tokens
this.context = context
}
private current(): Token {
return this.tokens[this.pos]
}
private advance(): Token {
const token = this.current()
this.pos++
return token
}
private expect(type: TokenType): Token {
const token = this.current()
if (token.type !== type) {
throw new Error(`Expected ${type} but got ${token.type} at position ${token.position}`)
}
return this.advance()
}
parse(): ProblemValue {
const result = this.parseExpression()
if (this.current().type !== 'EOF') {
throw new Error(
`Unexpected token ${this.current().type} at position ${this.current().position}`
)
}
return result
}
// Expression = Ternary
private parseExpression(): ProblemValue {
return this.parseTernary()
}
// Ternary = Or ('?' Expression ':' Expression)?
private parseTernary(): ProblemValue {
const condition = this.parseOr()
if (this.current().type === 'QUESTION') {
this.advance() // skip ?
const trueValue = this.parseExpression()
this.expect('COLON')
const falseValue = this.parseExpression()
return condition ? trueValue : falseValue
}
return condition
}
// Or = And ('||' And)*
private parseOr(): ProblemValue {
let left = this.parseAnd()
while (this.current().type === 'OPERATOR' && this.current().value === '||') {
this.advance()
const right = this.parseAnd()
left = Boolean(left) || Boolean(right)
}
return left
}
// And = Equality ('&&' Equality)*
private parseAnd(): ProblemValue {
let left = this.parseEquality()
while (this.current().type === 'OPERATOR' && this.current().value === '&&') {
this.advance()
const right = this.parseEquality()
left = Boolean(left) && Boolean(right)
}
return left
}
// Equality = Comparison (('==' | '!=') Comparison)*
private parseEquality(): ProblemValue {
let left = this.parseComparison()
while (
this.current().type === 'OPERATOR' &&
(this.current().value === '==' || this.current().value === '!=')
) {
const op = this.advance().value
const right = this.parseComparison()
left = op === '==' ? left === right : left !== right
}
return left
}
// Comparison = Addition (('<' | '>' | '<=' | '>=') Addition)*
private parseComparison(): ProblemValue {
let left = this.parseAddition()
while (
this.current().type === 'OPERATOR' &&
['<', '>', '<=', '>='].includes(this.current().value as string)
) {
const op = this.advance().value as string
const right = this.parseAddition()
const l = Number(left)
const r = Number(right)
switch (op) {
case '<':
left = l < r
break
case '>':
left = l > r
break
case '<=':
left = l <= r
break
case '>=':
left = l >= r
break
}
}
return left
}
// Addition = Multiplication (('+' | '-') Multiplication)*
private parseAddition(): ProblemValue {
let left = this.parseMultiplication()
while (
this.current().type === 'OPERATOR' &&
(this.current().value === '+' || this.current().value === '-')
) {
const op = this.advance().value
const right = this.parseMultiplication()
if (op === '+') {
// Support string concatenation: if either operand is a string, concatenate
if (typeof left === 'string' || typeof right === 'string') {
left = String(left) + String(right)
} else {
left = Number(left) + Number(right)
}
} else {
left = Number(left) - Number(right)
}
}
return left
}
// Multiplication = Unary (('*' | '/' | '%') Unary)*
private parseMultiplication(): ProblemValue {
let left = this.parseUnary()
while (
this.current().type === 'OPERATOR' &&
(this.current().value === '*' || this.current().value === '/' || this.current().value === '%')
) {
const op = this.advance().value
const right = this.parseUnary()
if (op === '*') {
left = Number(left) * Number(right)
} else if (op === '/') {
left = Number(left) / Number(right)
} else {
left = Number(left) % Number(right)
}
}
return left
}
// Unary = '!' Unary | '-' Unary | Primary
private parseUnary(): ProblemValue {
if (this.current().type === 'OPERATOR' && this.current().value === '!') {
this.advance()
return !this.parseUnary()
}
if (this.current().type === 'OPERATOR' && this.current().value === '-') {
this.advance()
return -Number(this.parseUnary())
}
return this.parsePrimary()
}
// Primary = NUMBER | STRING | IDENTIFIER | STATE_VAR | '(' Expression ')' | FunctionCall
private parsePrimary(): ProblemValue {
const token = this.current()
// Number literal
if (token.type === 'NUMBER') {
this.advance()
return token.value as number
}
// String literal
if (token.type === 'STRING') {
this.advance()
return token.value as string
}
// State variable ($varName)
if (token.type === 'STATE_VAR') {
this.advance()
const name = token.value as string
// Check userState first, then computed
if (name in this.context.userState) {
return this.context.userState[name]
}
if (name in this.context.computed) {
return this.context.computed[name]
}
throw new Error(`Unknown state variable: $${name}`)
}
// Parenthesized expression
if (token.type === 'LPAREN') {
this.advance()
const value = this.parseExpression()
this.expect('RPAREN')
return value
}
// Identifier: could be keyword, function call, or variable access
if (token.type === 'IDENTIFIER') {
const name = token.value as string
this.advance()
// Keywords
if (name === 'true') return true
if (name === 'false') return false
if (name === 'null') return null as unknown as ProblemValue
// Special "input" variable for checkpoint validation
if (name === 'input') {
if (this.context.input === undefined) {
throw new Error('input is not available in this context')
}
return this.context.input
}
// Function call
if (this.current().type === 'LPAREN') {
return this.parseFunctionCall(name)
}
// Variable access (possibly with dot notation)
return this.parseVariableAccess(name)
}
throw new Error(`Unexpected token ${token.type} at position ${token.position}`)
}
private parseFunctionCall(name: string): ProblemValue {
this.expect('LPAREN')
const args: ProblemValue[] = []
if (this.current().type !== 'RPAREN') {
args.push(this.parseExpression())
while (this.current().type === 'COMMA') {
this.advance()
args.push(this.parseExpression())
}
}
this.expect('RPAREN')
return this.callFunction(name, args)
}
private callFunction(name: string, args: ProblemValue[]): ProblemValue {
switch (name) {
case 'lcm': {
if (args.length !== 2) throw new Error('lcm requires 2 arguments')
return lcm(Number(args[0]), Number(args[1]))
}
case 'gcd': {
if (args.length !== 2) throw new Error('gcd requires 2 arguments')
return gcd(Number(args[0]), Number(args[1]))
}
case 'min': {
if (args.length < 2) throw new Error('min requires at least 2 arguments')
return Math.min(...args.map(Number))
}
case 'max': {
if (args.length < 2) throw new Error('max requires at least 2 arguments')
return Math.max(...args.map(Number))
}
case 'abs': {
if (args.length !== 1) throw new Error('abs requires 1 argument')
return Math.abs(Number(args[0]))
}
case 'floor': {
if (args.length !== 1) throw new Error('floor requires 1 argument')
return Math.floor(Number(args[0]))
}
case 'ceil': {
if (args.length !== 1) throw new Error('ceil requires 1 argument')
return Math.ceil(Number(args[0]))
}
case 'mod': {
if (args.length !== 2) throw new Error('mod requires 2 arguments')
return Number(args[0]) % Number(args[1])
}
default:
throw new Error(`Unknown function: ${name}`)
}
}
private parseVariableAccess(name: string): ProblemValue {
// Start with the base variable from problem context
let value: ProblemValue
if (name in this.context.problem) {
value = this.context.problem[name]
} else if (name in this.context.computed) {
value = this.context.computed[name]
} else if (name in this.context.userState) {
value = this.context.userState[name]
} else {
throw new Error(`Unknown variable: ${name}`)
}
// Handle dot notation for nested access (e.g., left.denom)
while (this.current().type === 'DOT') {
this.advance()
const prop = this.expect('IDENTIFIER').value as string
if (value === null || value === undefined) {
throw new Error(`Cannot access property '${prop}' of ${value}`)
}
if (typeof value === 'object' && value !== null && prop in value) {
// Access property from the object - could be a MixedNumberValue or other nested structure
value = (value as unknown as Record<string, ProblemValue>)[prop]
} else {
throw new Error(`Property '${prop}' does not exist on value`)
}
}
return value
}
}
// =============================================================================
// Math Helpers
// =============================================================================
function gcd(a: number, b: number): number {
a = Math.abs(Math.floor(a))
b = Math.abs(Math.floor(b))
while (b !== 0) {
const t = b
b = a % b
a = t
}
return a
}
function lcm(a: number, b: number): number {
return Math.abs(a * b) / gcd(a, b)
}
// =============================================================================
// Public API
// =============================================================================
/**
* Evaluate an expression string in the given context
*/
export function evaluate(expr: string, context: EvalContext): ProblemValue {
const tokens = tokenize(expr)
const parser = new Parser(tokens, context)
return parser.parse()
}
/**
* Create an empty evaluation context
*/
export function createEmptyContext(): EvalContext {
return {
problem: {},
computed: {},
userState: {},
}
}
/**
* Evaluate a boolean expression (returns true/false)
*/
export function evaluateBoolean(expr: string, context: EvalContext): boolean {
return Boolean(evaluate(expr, context))
}
/**
* Evaluate a numeric expression (returns number)
*/
export function evaluateNumber(expr: string, context: EvalContext): number {
return Number(evaluate(expr, context))
}
/**
* Check if two values are approximately equal (for decimal tolerance)
*/
export function approximatelyEqual(a: number, b: number, tolerance: number): boolean {
return Math.abs(a - b) <= tolerance
}
/**
* Get the numeric value from a mixed number
*/
export function mixedNumberToDecimal(mn: MixedNumberValue): number {
return mn.whole + mn.num / mn.denom
}
/**
* Get the fractional value (num/denom) from a mixed number
*/
export function mixedNumberFraction(mn: MixedNumberValue): number {
return mn.num / mn.denom
}
|