A simple recursive-descent parser for logic formulas (the precedences are probably wrong)

parser.js

const nextToken = s => {
	// Remove leading spaces
	s = s.trim()
	if (s.length === 0)          return [{ kind: 'eof'    }, s.slice(0)]
	if (s.startsWith('V'))       return [{ kind: 'or'     }, s.slice(1)]
	if (s.startsWith('^'))       return [{ kind: 'and'    }, s.slice(1)]
	if (s.startsWith('->'))      return [{ kind: 'then'   }, s.slice(2)]
	if (s.startsWith('<->'))     return [{ kind: 'iff'    }, s.slice(3)]
	if (s.startsWith('('))       return [{ kind: 'lparen' }, s.slice(1)]
	if (s.startsWith(')'))       return [{ kind: 'rparen' }, s.slice(1)]
	if (s.startsWith('Posta'))   return [{ kind: 'true'   }, s.slice(5)]
	if (s.startsWith('Chamuyo')) return [{ kind: 'false'  }, s.slice(7)]
	// Identifier
	const ident_pattern = /^[a-z]+/
	const match = ident_pattern.exec(s)
	if (match != null) {
		const ident = match[0]
		return [{ kind: 'ident', ident }, s.slice(ident.length)]
	}
}

function tokenize(s) {
	let tokens = []
	let token
	do {
		[token, s] = nextToken(s)
		tokens.push(token)
	} while (token.kind !== 'eof')
	return tokens
}

function parse(s) {
	let tokens = tokenize(s)

	function peek() {
		return tokens[0]
	}
	function pop() {
		return tokens.shift()
	}

	return parse_iff()

	function parse_iff() {
		let expr = parse_then()
		while (peek().kind === 'iff') {
			pop()
			expr = { kind: 'iff', lhs: expr, rhs: parse_then() }
		}
		return expr
	}

	function parse_then() {
		let expr = parse_or()
		while (peek().kind === 'then') {
			pop()
			expr = { kind: 'then', lhs: expr, rhs: parse_or() }
		}
		return expr
	}

	function parse_or() {
		let expr = parse_and()
		while (peek().kind === 'or') {
			pop()
			expr = { kind: 'or', lhs: expr, rhs: parse_and() }
		}
		return expr
	}

	function parse_and() {
		let expr = parse_paren() || parse_var() || parse_lit()
		if (expr === undefined) throw new Error('Something somewhere failed!')
		while (peek().kind === 'and') {
			pop()
			expr = { kind: 'and', lhs: expr, rhs: parse_paren() || parse_var() || parse_lit() }
		}
		return expr
	}

	function parse_var() {
		let token = peek()
		if (token.kind === 'ident') {
			pop()
			return token.ident
		}
	}

	function parse_lit() {
		let token = peek()
		if (token.kind === 'true') {
			pop()
			return true
		}
		if (token.kind === 'false') {
			pop()
			return false
		}
	}

	function parse_paren() {
		if (peek().kind === 'lparen') {
			pop()
			let result = parse_iff()
			if (result !== undefined && peek().kind === 'rparen') {
				pop()
				return result
			}
		}
	}
}

console.log(JSON.stringify(parse('Posta -> (a -> Chamuyo <-> b ^ c V a^j)'), null, 2))