import type { PropAtom, PropFormula } from "../../models";
/**
 * Recursively replaces all occurrences of a specified atom in a formula with a substitute formula or atom.
 *
 * This function traverses the formula tree and replaces every instance of the target atom with the
 * provided substitute. If the atom is not present in the formula, the original formula is returned unchanged.
 *
 * @param {Object} params - Function parameters:
 * @param params.formula - The propositional formula in which substitution will occur.
 * @param params.atom - The atomic proposition (variable) to be replaced.
 * @param params.substitute - The formula or atom to replace the target atom with.
 * @returns A new formula with all occurrences of the atom replaced by the substitute.
 * @category Converters
 *
 * @example
 * // Replace q with s in (p => (q => r))
 * const formula: PropFormula = { operator: Operator.Implies, values: [
 *   { operator: Operator.Var, values: [['p']] },
 *   { operator: Operator.Implies, values: [
 *     { operator: Operator.Var, values: [['q']] },
 *     { operator: Operator.Var, values: [['r']] }
 *   ]}
 * ]};
 * const result = replaceAtomInFormula({ formula, atom: ['q'], substitute: { operator: Operator.Var, values: [['s']] } });
 * // Result: p => (s => r)
 */
export declare function replaceAtomInFormula({ formula, atom, substitute, }: {
    formula: PropFormula;
    atom: PropAtom;
    substitute: PropFormula | PropAtom;
}): PropFormula;